(a) 5:8 < 7:10
To compare the ratios, we can find their equivalent fractions. For 5:8, the equivalent fraction is (5/8), and for 7:10, it is (7/10).
Comparing the fractions, (5/8) is less than (7/10) because the denominator of (8) is larger than the denominator of (10), and the numerators (5 and 7) are the same.
To compare ratios, we can convert them into equivalent fractions. In the first case, 5:8 and 7:10 can be written as fractions (5/8) and (7/10), respectively. To determine which fraction is larger, we compare their numerators and denominators. In this case, both fractions have the same numerator (5 and 7). However, the denominator of (5/8) is 8, which is larger than the denominator of (7/10), which is 10. Since the numerators are equal and the denominator of (5/8) is larger, we can conclude that 5:8 is less than 7:10.
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Omar has four times as many apples as bananas. He has 30 pieces of fruit in all. If a represents the number of apples and b represents the number of bananas, how many of each fruit does Omar have? Use the table to answer the question. Types of Fruit a b a b = 30 Check a = 4 b 16 14 30 20 10 30 22 8 30 24 6 30 16 apples and 14 bananas 20 apples and 10 bananas 22 apples and 8 bananas 24 apples and 6 bananas.
The solution to the problem is that Omar has 16 apples and 14 bananas. the first row satisfy the condition that Omar has four times as many apples as bananas.
To solve this problem, we are given that Omar has four times as many apples as bananas and a total of 30 pieces of fruit.
Let's represent the number of apples as 'a' and the number of bananas as 'b'.
We know that a + b = 30, as the total number of fruits is 30.
From the given information, we are also told that Omar has four times as many apples as bananas, which can be expressed as a = 4b.
To find the values of 'a' and 'b', we can use the table provided:
Types of Fruit | a | b | a + b |
-------------------------------
16 apples and 14 bananas
20 apples and 10 bananas
22 apples and 8 bananas
24 apples and 6 bananas
We can observe that in the first row, a = 16 and b = 14. Let's check if these values satisfy the given conditions.
If we add the number of apples and bananas, we get 16 + 14 = 30, which matches the total number of fruits given.
We can also verify that a = 4b: 16 = 4 * 14.
Therefore, the solution to the problem is that Omar has 16 apples and 14 bananas.
It's worth noting that the other rows in the table represent different combinations of apples and bananas that sum up to 30, but only the values in the first row satisfy the condition that Omar has four times as many apples as bananas.
In conclusion, Omar has 16 apples and 14 bananas, as per the given information and by checking the values in the table.
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step by step explanation for expressions d and e Thank you loads!!!
Answer:
Step-by-step explanation:
D)
[tex]\frac{4\sqrt{b} }{\sqrt{3}-b }[/tex] > in order to get rid of root on bottom like this, you
need to multiply top and bottom by conjugate
√3 +b
[tex]=\frac{4\sqrt{b} }{\sqrt{3}-b }\frac{\sqrt{3}+b}{\sqrt{3}+b}[/tex] > Distribute on top and FOIL bottom
[tex]=\frac{4\sqrt{3b}+4b\sqrt{b} }{3 -b^{2} }[/tex] >This is simplified, you cannot combine anything else
E)
[tex]\frac{3\sqrt{a^{2} } } {\sqrt{3} } / 2a^{\frac{3}{2} }[/tex] >√a² = a
[tex]=\frac{3a } {\sqrt{3} } / 2a^{\frac{3}{2} }[/tex] >Division of fraction keep change flip
[tex]=\frac{3a } {\sqrt{3} } * \frac{1}{2a^{\frac{3}{2}} }[/tex] >Because 2a is not in parenthesis 3/2 exp.
is only for a
[tex]=\frac{3a } {\sqrt{3} } * \frac{1}{2\sqrt{a^{3} } }[/tex] > You can make 1 set of a² so 1 comes out but 1 stays
[tex]=\frac{3a } {\sqrt{3} } * \frac{1}{2a\sqrt{a } }[/tex] >put like items under root
[tex]=\frac{3a } {2a\sqrt{3a} }[/tex] >multiply top and bottom by root
[tex]=\frac{3a } {2a\sqrt{3a} }*\frac{\sqrt{3a}}{\sqrt{3a}}[/tex] >multiply
[tex]=\frac{3a\sqrt{3a} } {2a(3a)} }[/tex] >3a cancels
[tex]=\frac{\sqrt{3a} } {2a} }[/tex] >This is simplified
Someone help me do this
Answer:
I believe it's A
Step-by-step explanation:
What happens to the value of f(x) = log4x as x approaches [infinity]?.
As x approaches infinity, the value of the function f(x) = log4x approaches infinity as well. The logarithm function with a base greater than 1 increases without bound as its input increases, so the value of log4x becomes arbitrarily large as x becomes larger.
The logarithm function log4x represents the exponent to which the base 4 must be raised to obtain x. As x approaches infinity, the function evaluates the behavior of the logarithm for extremely large values.
In this case, as x becomes larger and larger, log4x increases without bound. This means that there is no finite limit or specific value that f(x) approaches as x approaches infinity. Instead, f(x) grows infinitely, indicating that the function's value becomes arbitrarily large as x becomes larger. Therefore, the value of f(x) = log4x approaches infinity as x approaches infinity.
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30% of the members of a tennis club are pensioners. 36 members are pensioners
a) how many members there in total ?
b) how many members are not pensioners
Answer
there's 120 members in total
84 not pensioners
Explaination
36÷30% = 120
70% are not pensioners
so 70% × 120 = 84
or you could minus the pensioners from the total 120-36=84
Las aspas de un ventilador de techo están girando alrededor de un eje fijo estas parten del reposo con aceleración angular constante en un tiempo están girando 10 revoluciones por segundo y dan 60 vueltas después Irán a 15 revoluciones por segundo
The question provides that the blades of a ceiling fan rotate around a fixed axis and begin to rotate with a constant angular acceleration such that they are rotating at 10 revolutions per second after a certain period of time.
After 60 turns, the fan will be rotating at 15 revolutions per second.
Solution:The given data is:Initial angular speed, ω₁ = 0 (since they start from rest)
Final angular speed, ω₂ = 15 revolutions/sec
Angular acceleration, α = constant
Number of revolutions for the first part, n₁ = 60
Number of revolutions for the second part, n₂ = (total revolutions) - (n₁) = (60 + 10) - 60 = 10 revolutions
Using the formula for the angular velocity, ω = ω₀ + αt
and the formula for the number of revolutions, n = ωt / 2π
We can find out the time required to reach a final speed of 15 rev/s as follows:15 = 0 + αt ⇒ t = 15 / α
The total time required to reach a speed of 15 rev/s would be the sum of the time required to reach a speed of 10 rev/s and the time required to reach 15 rev/s.t = t₁ + t₂ ⇒ t₂ = t - t₁
We can find the value of t₁ from the formula for the number of revolutions during the first part of the motion as follows:n₁ = ω₁t₁ / 2π0 = αt₁² / 2 + ω₁t₁ / 2π ⇒ t₁ = 0
Using the formula for the number of revolutions, we can find the value of t₂ as follows:n₂ = (ω₁t₂ + 1/2 αt₂²) / 2π ⇒ t₂ = 20/α
The value of α can be found by equating the two formulas for t₂ obtained above:
20/α = 15 / α + t₁⇒ α = 100 / 3 rad/s²
We can now substitute this value in the formulas for t and t₂ to find the times required to reach speeds of 10 and 15 rev/s respectively.t₁ = 0 s, t₂ = 60 / 3 = 20 s
Answer: The time required for the blades of the ceiling fan to rotate with a constant angular acceleration before rotating at 10 revolutions per second is 0 seconds and the time required to reach a speed of 15 revolutions per second is 20 seconds.
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Examine the reasons why so many artists were seeking a different world
During the late 19th and early 20th centuries, many artists were seeking a different world due to several reasons.
1. Social and Political Changes During the late 19th and early 20th centuries, social and political changes were occurring at a rapid pace. The industrial revolution led to the growth of cities, which, in turn, caused a breakdown in traditional society. As a result, many artists were seeking a different world that was more in line with their ideals.2. Technological Advancements Inventions such as the telegraph and the telephone enabled artists to communicate with one another and share their ideas. Artists were inspired by new technologies and used them to create new forms of art.3. World War I World War I was a traumatic event that had a significant impact on the artistic community. Many artists were disillusioned by the horrors of war and sought to create a new world that was free from conflict and violence.4. Industrialization and Urbanization .The growth of industry and the shift from rural to urban life had a profound effect on the artistic communit.5. Romanticism .Romanticism was a cultural movement that emphasized emotion, imagination, and individualism. Many artists were inspired by the romantic ideal and sought to create works that expressed their innermost feelings and thoughts. The movement emphasized the importance of nature, beauty, and the sublime, which were seen as antidotes to the dehumanizing effects of industrialization and urbanization.
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An acute triangle A B C has three heights AD, BE and CF respectively. Prove that the perimeter of triangle DEF is not over half of the perimeter of triangle ABC.
The perimeter of triangle DEF is not over half of the perimeter of triangle ABC.This is proven below.
How to illustrate tej proofGiven: Triangle ABC is acute with heights AD, BE, and CF.
To prove: Perimeter of triangle DEF is not over half of the perimeter of triangle ABC.
1. Let the side lengths of triangle ABC be a, b, and c.
2. Then the lengths of the heights are h1 = a/2, h2 = b/2, and h3 = c/2.
3. The perimeter of triangle ABC is a + b + c.
4. The perimeter of triangle DEF is h1 + h2 + h3 = a/2 + b/2 + c/2.
5. 1/2 < 1, so a/2 + b/2 + c/2 < a + b + c.
6. Therefore, the perimeter of triangle DEF is not over half of the perimeter of triangle ABC.
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Explain the process of solving a system of equations using substitution
One variable, from either of the equations, the subject of that equation and substitute it in the other equation.
We have,
To describe the process of solving a system of equations using substitution.
Now,
For any given system of linear equations, we use a method called substitution method for solving the equations.
We can make one variable, from either of the equations, the subject of equation and substitute it in the other equation.
This way, we get to find the value of the remaining variable and next we substitute this value in one of the equations to get the value of the variable left.
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what is the answer to this problem 2 ft 5 in + 9 in =
The problem requires adding two measurements in different units, 2 ft 5 in and 9 in. We need to determine the sum of these measurements.
To add the given measurements, we should first convert them to a consistent unit. In this case, we will convert everything to inches since the second measurement is already in inches.
1 foot is equal to 12 inches, so 2 ft is equal to 2 * 12 = 24 inches. Therefore, 2 ft 5 in can be written as 24 in + 5 in. Adding 24 in and 5 in, we get 29 in. Thus, the sum of 2 ft 5 in and 9 in is 29 inches. In conclusion, when we add 2 ft 5 in and 9 in, the result is 29 inches.
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A force of 80. Newtons pushes a 50. -kilogram object across a level floor for 8. 0 meters. The work done is
The work done is 400.0 Joules A force of 80 Newtons pushes a 50-kilogram object across a level floor for 8.0 meters.
To find the work done, we can use the formula:work = force x distance x cos(theta)where force is 80 N, distance is 8.0 m, and theta is the angle between the force and the displacement. Since the force is applied in the direction of motion, theta is 0° and cos(0°) is 1.
we can simplify the formula as:work = force x distance x cos(theta)work = 80 N x 8.0 m x cos(0°)work = 640.0 JHowever, we need to check the units of our answer to make sure they are in Joules (J). The units of force are Newtons (N), the units of distance are meters (m), and the units of cos(theta) are dimensionless. Therefore, our answer is in Joules (J).So, the work done is 640.0 Joules.
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Which could be used to solve this equation? 3 and one-fifth n = 9 Subtract 3 and one-fifth from both sides of the equation. 3 and one-fifth minus 3 and one-fifth n = 9 3 and one-fifth Add 3 and one-fifth to both sides of the equation. 9 3 and one-fifth = 12 and one-fifth.
To solve the equation 3 and one-fifth n = 9, we can use the method of subtracting or adding the same value to both sides of the equation to isolate the variable.
In this case, we can subtract 3 and one-fifth from both sides or add 3 and one-fifth to both sides of the equation.
To solve the equation 3 and one-fifth n = 9, we can subtract 3 and one-fifth from both sides of the equation, which gives us:
3 and one-fifth n - 3 and one-fifth = 9 - 3 and one-fifth.
Simplifying the left side of the equation, we get:
n = 9 - 3 and one-fifth.
Alternatively, we can add 3 and one-fifth to both sides of the equation, which gives us:
3 and one-fifth n + 3 and one-fifth = 9 + 3 and one-fifth.
Simplifying the left side of the equation, we get:
n = 9 + 3 and one-fifth.
In either case, we have isolated the variable n and obtained the solution by either subtracting or adding the same value to both sides of the equation.
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Kyle Lowry shoots a basketball towards the net, hoping to make a 3 pointer. The ball reaches its highest point of 12 m above the ground 0.5 s after it is released from his hands. The ball lands on the ground after 1.3 seconds. Determine an equation in vertex form that models the height of the basketball above the ground versus time. Include a sketch with your solution.
We are to determine an equation in vertex form that models the height of the basketball above the ground versus time. We can determine this using the formula:h(t) = -16t² + vt + h₀
We are given that the basketball reaches its highest point of 12 m above the ground 0.5 s after it is released from his hands. Thus, the initial height is:h₀ = 12 mWe are also given that the ball lands on the ground after 1.3 seconds. Thus, the time it took for the ball to reach the ground is:t = 1.3 sLet's find the initial vertical velocity using the information that the basketball reaches its highest point 0.5 seconds after it is released.
The vertical velocity of the basketball at its highest point is zero since it stops before coming down.So we know:
v + (-9.8)(0.5) = 0v = 4.9 m/s
Substituting the given information into the equation above, we obtain:
h(t) = -16t² + vt + h₀h(t) = -16t² + (4.9)t + 12
The vertex form of this equation can be determined by completing the square. To complete the square, we can add and subtract the square of half of the coefficient of t from the equation above
:h(t) = -16(t² - 0.30625t) + 12
To complete the square, we add and subtract
(0.30625/2)² = 0.02368164062:h(t) = -16(t² - 0.30625t + 0.02368164062 - 0.02368164062) + 12h(t) = -16(t - 0.153125)² + 12
The vertex of this equation is the point (0.153125, 12) and is the highest point of the basketball. The coefficient of t² is negative, which means that the graph of this equation is a downward-facing equation .
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Simplify this numerical expression using the order of operations. 5. 75 - 1 2 (20 ÷ 2. 5) ÷ 2 6 Order of Operations: 1. Evaluate within parentheses. 2. Evaluate exponents. 3. Multiply and divide from left to right. 4. Add and subtract from left to right. What is the value of the expression?.
The value of the given expression is approximately 71.31.
[tex]$$75 - 12(20 ÷ 2.5) ÷ 26$$[/tex]
The Order of Operations states that the sequence of steps in which we carry out the operations of a given problem.
So, we follow the Order of Operations to solve this expression.
Firstly, we will evaluate the parentheses:
[tex]$$20 ÷ 2.5 = 8$$[/tex]
Now, the given expression becomes:
[tex]$$75 - 12 × 8 ÷ 26$$[/tex]
Then, we will evaluate multiplication and division in order from left to right.
12 × 8 = 96
So, the given expression becomes:
[tex]$$75 - 96 ÷ 26$$[/tex]
Evaluating division, we get:
[tex]$$75 - 3.6923$$[/tex]
Now, we will add and subtract from left to right.
[tex]75 − 3.6923 ≈ 71.31[/tex]
Therefore, the value of the given expression is approximately 71.31.
So, the required is approximately 71.31.
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The line of best fit can be represented by the equation y=−6x+97, where x represents the number of absences and y represents the final grade.
The line of best fit is a straight line that best fits the scattered data points on a scatterplot. It is represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.
In this particular case, the equation of the line of best fit is y = -6x + 97, where x represents the number of absences and y represents the final grade.
This means that for every additional absence a student has, their final grade is expected to decrease by 6 points. The y-intercept of 97 means that if a student had zero absences, their predicted final grade would be 97.
It is important to note that the line of best fit is a prediction, and not a definitive statement about the relationship between the variables. While it can provide some insight into the relationship between the number of absences and final grade, there may be other factors that are not taken into account by the model.
Additionally, the equation of the line of best fit is only valid within the range of the data used to create the model. Extrapolating beyond this range may not produce accurate predictions.
Overall, the line of best fit is a useful tool for analyzing relationships between variables, but it should be used with caution and in conjunction with other analyses to get a complete understanding of the relationship between variables.
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B.
zoom in
Find the value of the variables for
which ABCD must be a parallelogram.
~ 3x
X
3
3y
3y
D
21
Required
X =
?/1
I
22
Required
y =
?/1
.
D
Given a quadrilateral ABCD, with the sides AB and DC parallel and equal in length. Let us denote angle BAD as ∠α and angle ADC as ∠β. Now, we have to find the values of the variables x and y such that ABCD is a parallelogram.
Parallelogram has a pair of parallel sides. So, we have AB ∥ CD. It is given that ∠α = ∠β and AB = CD. So, by angle-angle-side rule, the two triangles ABD and DCA are congruent.
In triangle ABD, we have:∠DAB = 180° - ∠α = 180° - ∠β (as ∠α = ∠β)⇒ ∠DAB + ∠CDA = 180° (linear pair of angles)⇒ ∠CDA = ∠β.In triangle DCA, we have:∠CDA = ∠β (as obtained above)⇒ ∠CAD = ∠α (as ∠α = ∠β)⇒ ∠BDC = 180° - ∠α = 180° - ∠β (linear pair of angles)⇒ ∠BDC = ∠DAB.In quadrilateral ABCD, the adjacent angles are supplementary. So, we have:∠BDC + ∠BCD = 180° (adjacent angles are supplementary)⇒ ∠DAB + ∠BCD = 180° (as ∠BDC = ∠DAB)⇒ ∠BCD = 180° - ∠DAB.In triangle ACD, we have:∠C = ∠C (common)⇒ ∠CAD + ∠BCD = 180° (angles of a triangle add up to 180°)⇒ ∠α + (180° - ∠DAB) = 180°⇒ ∠α + ∠β = 180°.
Now, we can solve for x and y.In triangle ABD, we have:AB = BD⇒ 3x = 21 - x⇒ 4x = 21⇒ x = 21/4.In triangle DCA, we have:CD = DA⇒ 3y = 22 - y⇒ 4y = 22⇒ y = 11/2. Therefore, the value of x is 21/4 and the value of y is 11/2.
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The area of a rectangle is 384 square inches and length is 8 inches greater than width. What are the dimensions
The dimensions of the rectangle are 16 inches in width and 24 inches in length.
Let's assume the width of the rectangle is x inches. According to the problem, the length is 8 inches greater than the width, so the length can be represented as (x + 8) inches.
The formula for the area of a rectangle is length multiplied by width. In this case, the area is given as 384 square inches. So, we can set up the equation:
Length * Width = Area
(x + 8) * x = 384
Expanding the equation:
x^2 + 8x = 384
Rearranging the equation to solve for x:
x^2 + 8x - 384 = 0
We can solve this quadratic equation by factoring or using the quadratic formula. Factoring it, we find:
(x - 16)(x + 24) = 0
So, x = 16 or x = -24.
Since dimensions cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 16 inches.
Substituting this value back into the equation for the length:
Length = x + 8 = 16 + 8 = 24 inches
Hence, the dimensions of the rectangle are 16 inches in width and 24 inches in length, which gives an area of 384 square inches.
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7th grade math
Paula measured the auditorium and made a scale drawing. The stage, which is 56 feet long in real life, is 84 inches long in the drawing. What scale did Paula use?
3 inches : ____ feet
Paula made a scale drawing of the auditorium, which is a replica of the actual auditorium, but smaller in size. The scale drawing shows measurements of the actual auditorium at a reduced size.
Paula needs to determine the scale used to draw the auditorium. The scale is the ratio of the lengths of the corresponding sides of the actual auditorium and the scale drawing. We can use the following formula to find out the scale of the drawing:
Scale = (Length of the corresponding side of the actual object) / (Length of the corresponding side of the scale drawing)First, we have to convert 56 feet to inches:1 foot = 12 inches56 feet = 56 x 12 = 672 inchesNow, we can find the scale of the drawing as follows:
Now, we can use the scale to determine the length of other parts of the auditorium. For example, if a door in the auditorium is 32 inches long on the drawing, its actual length would be 32 x 8 = 256 inches or 21.3 feet. Therefore, the missing value in the ratio 3 inches : ____ feet is 2.333 feet. (This is obtained by dividing 84 inches by 36 inches, which is equivalent to 3 feet. Then multiplying the result by 3 inches, which gives 7/12 or 0.5833 feet or 7 inches. This can be written as 2.333 feet.)
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coordinate plane with triangles QRS and UTS with Q at negative 6 comma 2, R at negative 2 comma 6, S at negative 2 comma 2, T at negative 2 comma 0, and U at negative 4 comma 2
Which set of transformations would prove ΔQRS ~ ΔUTS?
Reflect ΔUTS over y = 2, and dilate ΔU′T′S′ by a scale factor of 2 from point S.
Reflect ΔUTS over y = 2, and translate ΔU′T′S′ by the rule (x − 2, y + 0).
Translate ΔUTS by the rule (x + 0, y + 6), and reflect ΔU′T′S′ over y = 6.
Translate ΔUTS by the rule (x − 2, y + 0), and reflect ΔU′T′S′ over y = 2.
The set of transformations that would prove ΔQRS ~ ΔUTS is to translate ΔUTS by the rule (x - 2, y + 0) and reflect ΔU'T'S' over y = 2.
To prove that ΔQRS ~ ΔUTS, we need to show that the two triangles are related through a combination of transformations.
The first transformation is a translation of ΔUTS by the rule (x - 2, y + 0). This means that every point in ΔUTS will be moved 2 units to the left and 0 units vertically. The translated triangle is denoted as ΔU'T'S'.
The second transformation is a reflection of ΔU'T'S' over the line y = 2. This reflection flips the triangle across the line, maintaining the same shape but reversing the orientation.
These two transformations combined, translation and reflection, establish a correspondence between the corresponding vertices of the two triangles. ΔU'T'S' is the transformed version of ΔUTS.
Since the two triangles undergo the same transformations, they have a proportional relationship and are therefore similar, which can be denoted as ΔQRS ~ ΔU'T'S'.
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Which equation represents this problem? Twelve dollars is divided equally among 4 people
The equation that represents the problem of dividing twelve dollars equally among four people is as follows:12 / 4 = 3The given problem of dividing twelve dollars equally among four people can be represented by the equation 12/4 = 3.
Here, 12 represents the total amount of money that is being divided and 4 represents the number of people among whom the money is being divided .In this problem, we divide the total amount of money by the number of people to find out how much money each person will get. As there are four people to divide the money among, we divide the total amount of $12 by 4 to get $3 as the share of each person. Therefore, the equation that represents this problem is 12/4 = 3.
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Martin's car travels 360 miles on 12 gallons of gas. How far will the car travel on 3 gallons of gas?
distance travel by the car with 3 gallons of gas, we have to use a proportion.
To determine how far Martin's car will travel on 3 gallons of gas, we can set up a proportion based on the given information.
We know that Martin's car travels 360 miles on 12 gallons of gas. Therefore, the mileage per gallon can be calculated as:
Mileage per gallon = Total miles / Total gallons
Mileage per gallon = 360 miles / 12 gallons
Mileage per gallon = 30 miles/gallon
Now, we can use this mileage per gallon to calculate the distance the car will travel on 3 gallons of gas:
Distance = Mileage per gallon × Number of gallons
Distance = 30 miles/gallon × 3 gallons
Distance = 90 miles
Therefore, Martin's car will travel 90 miles on 3 gallons of gas.
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Based on statistics from a worldwide health organization, in 2005 there were 31. 6 million people worldwide living with a certain disease, and 2. 4 million deaths from the disease. By , 2015 the number of people living with the disease had fallen to 27. 3 million, and 1. 2 million deaths were reported. Find the percent change for each statistic, and write any conclusions you can draw
There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.
There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.
To calculate the percent change, we'll use the following formula:
Percent Change = ((New Value - Old Value) / Old Value) * 100
Let's calculate the percent change for each statistic:
1. Number of people living with the disease:
Percent Change = ((27.3 million - 31.6 million) / 31.6 million) * 100
≈ (-4.3 million / 31.6 million) * 100
≈ -0.136 * 100
≈ -13.6%
Conclusion: There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.
2. Number of deaths from the disease:
Percent Change = ((1.2 million - 2.4 million) / 2.4 million) * 100
≈ (-1.2 million / 2.4 million) * 100
≈ -0.5 * 100
≈ -50%
Conclusion: There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.
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A rectangular box has width (x), length (5x - 1), and height (2x + 3). The area is 29,946 in. Find X
I need help please
To find the value of x in the given problem, we can start by calculating the area of the rectangular box. The area of a rectangular box is given by the formula A = 2lw + 2lh + 2wh, where l represents the length, w represents the width, and h represents the height. In this case, the area is given as 29,946 in².
The first step is to substitute the given values into the formula:
29,946 = 2(x)(5x - 1) + 2(x)(2x + 3) + 2(5x - 1)(2x + 3).
Next, we simplify the equation and distribute the terms:
29,946 = 2(5x² - x) + 2(2x² + 3x) + 2(10x² + 15x - 2x - 3).
After combining like terms, we have:
29,946 = 10x² - 2x + 4x² + 6x + 20x² + 30x - 4x - 6.
Combining similar terms further, we get:
29,946 = 34x² + 40x - 6.
Now, we can rearrange the equation and set it equal to zero:
34x² + 40x - 29,946 = 0.
To solve this quadratic equation, we can either factor it or use the quadratic formula. However, since the equation is not easily factorable, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a).
By substituting the values a = 34, b = 40, and c = -29,946 into the quadratic formula, we can find the two possible values of x. However, since we are looking for a real-world length, we can discard any negative or non-real solutions.
After solving the equation, we find that x is approximately equal to 24.4 or x ≈ -29.36. Since negative values are not meaningful in the context of length, we can conclude that the value of x for which the rectangular box has the given area of 29,946 in² is approximately 24.4 inches.
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(2a) A cuboid has its length, width and height as 12cm, 6cm and 5cm respectively. Calculate its;(1) Surface area (2) length of diagonal (3) volume of the cuboid.
(2b) Given that the sides of a kite is 8cm and 6cm respectively. If its vertical diagonal is 5cm, calculate its area
The surface area of the cuboid is 324 cm2, the volume of the cuboid is 360 cm3. And the Area of kite = (5 × 6.403)/2 = 16.008 cm²2a)
Solution: Length of cuboid = l = 12cmWidth of cuboid = b = 6cmHeight of cuboid = h = 5cmSurface area of cuboid = 2 (lb + bh + lh)
By substituting the given values of l, b and h, we get:
Surface area of cuboid = 2 (12 × 6 + 6 × 5 + 12 × 5) = 2 (72 + 30 + 60) = 2 × 162 = 324 cm2∴ The surface area of the cuboid is 324 cm2.Length of diagonal of cuboid, d =√l2 + b2 + h2By substituting the given values of l, b and h, we get:d =√12² + 6² + 5²=√144 + 36 + 25=√205=14.317 cm (approx)∴
The length of diagonal of the cuboid is 14.317 cm.
Volume of cuboid = lbh
By substituting the given values of l, b and h, we get:
Volume of cuboid = 12 × 6 × 5 = 360 cm3∴
The volume of the cuboid is 360 cm3.
(2b) Calculation of the area of a kite when its sides are 8cm and 6cm, and its vertical diagonal is 5cm.Given, sides of the kite are 8cm and 6cm respectively. Vertical diagonal of kite = 5cmArea of kite = (Product of diagonals)/2By using Pythagoras theorem on a kite, we have:
Horizontal diagonal of kite, d =√(52 + 42)=√41 = 6.403 cm
Area of kite = (Product of diagonals)/2
By substituting the given values of vertical diagonal and horizontal diagonal, we get:
Area of kite = (5 × 6.403)/2 = 16.008 cm²2a)
Surface area of cuboid = 2 (lb + bh + lh)
Length of diagonal of cuboid, d =√l2 + b2 + h2Volume of cuboid = lbh2b) Area of kite = (Product of diagonals)/2.
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What values of p will the equation x^2=p have 0 real number solution why
The equation x^2 = p has 0 real number solution when p is less than or equal to 0. This is because the square of any real number is always non-negative. Therefore, if p is less than or equal to 0, then there is no real number x such that x^2 = p.
For example, if p = -1, then the equation x^2 = -1 has no real number solutions. This is because the square of any real number is always non-negative. Therefore, there is no real number x such that x^2 = -1.
However, if p is greater than 0, then there are two real number solutions to the equation x^2 = p. These solutions are x = sqrt(p) and x = -sqrt(p).
For example, if p = 4, then the equation x^2 = 4 has two real number solutions. These solutions are x = 2 and x = -2.
In conclusion, the equation x^2 = p has 0 real number solution when p is less than or equal to 0. This is because the square of any real number is always non-negative.
Ryan works at a concession stand. Over the past 7 nights he sold 16,23,32,24,19,27 and 18 bags of caramel corn what is the mean absolute deviation (MAD)of this data set,rounded to the nearest tenth?
The mean absolute deviation (MAD) of the data set, rounded to the nearest tenth, is 5.4 bags of caramel corn.
To calculate the mean absolute deviation, we first find the mean of the data set by adding up all the values and dividing by the total number of nights: (16 + 23 + 32 + 24 + 19 + 27 + 18) / 7 = 19.7 bags.
Next, we find the absolute deviation for each night by subtracting the mean from each data point and taking the absolute value of the difference: |16 - 19.7| = 3.7, |23 - 19.7| = 3.3, |32 - 19.7| = 12.3, |24 - 19.7| = 4.3, |19 - 19.7| = 0.7, |27 - 19.7| = 7.3, |18 - 19.7| = 1.7.
We then calculate the average of these absolute deviations by adding them up and dividing by the total number of nights: (3.7 + 3.3 + 12.3 + 4.3 + 0.7 + 7.3 + 1.7) / 7 = 5.4 bags.
Therefore, the mean absolute deviation of this data set is 5.4 bags of caramel corn. This value represents the average distance between each data point and the mean, providing an indication of the variability or dispersion in the number of bags sold each night at the concession stand.
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Maggie is working at a store that pays by the hour and by commission (pay for how much you sell). Maggie wants to go this weekend to the lake with her friends but she needs to make at least $225 today. She gets paid $15 per hour plus $25 for every sale she makes. What are all the possible values of the number of sales that Maggie can make to go to the lake if she is scheduled to work from 8am until 4pm?
Maggie can make anywhere from 5 to 4 sales to earn at least $225 and go to the lake with her friends.
Maggie gets paid $15 per hour plus $25 for every sale she makes. The number of sales she makes can be represented by x.
In order to calculate Maggie's earnings in terms of commission, we can use the equation 25x.
To calculate Maggie's earnings in terms of hourly pay, we can use the equation 15(8), since she works from 8am until 4pm, which is 8 hours. This simplifies to 120.The total amount Maggie earns can be represented by the equation:
Total earnings = 25x + 120
To find the minimum number of sales Maggie needs to make to earn at least $225, lets set up the inequality:
25x + 120 ≥ 225
Subtracting 120 from both sides, we get:
25x ≥ 105
Dividing both sides by 25, we get:
x ≥ 4.2
Maggie cannot make a fraction of a sale, so we can round up to find the minimum number of sales she needs to make, which is 5 sales.
To find the maximum number of sales Maggie can make, lets consider the fact that she is scheduled to work from 8am until 4pm, which is 8 hours. If she makes 0 sales, she will earn $120 (her hourly pay for 8 hours of work).
To find the maximum number of sales, we can set up the equation:25x + 120 ≤ 225
Subtracting 120 from both sides, we get:
25x ≤ 105
Dividing both sides by 25, we get:
x ≤ 4.2
Maggie cannot make a negative number of sales, so we can round down to find the maximum number of sales she can make, which is 4 sales.
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The possible values of the number of sales that Maggie can make to go to the lake are 5 and 4.
Given:
Maggie gets paid $15 per hour plus $25 for every sale she makes.
She needs to make at least $225 today.
She is scheduled to work from 8 am until 4 pm.
To find:
All the possible values of the number of sales that Maggie can make to go to the lake.
Solution:
Let's consider x to be the number of sales that Maggie makes.
To determine the minimum amount she needs to earn:
Her hourly wage for 8 hours of work = $15 × 8 = $120
Total earnings that she needs = $225 - $120 = $105
If y is the number of sales she needs to make to earn $105, then:
$25y = $105
Dividing both sides by $25, we get:
y = 4.2
This means she needs to make at least 5 sales.
Let's calculate the maximum number of sales that she can make. If she has to earn $240 for 8 hours of work:
Total earnings required = $240 - $120 = $120
$25y = $120
Dividing both sides by $25, we get:
y = 4.8
This means the maximum number of sales she can make is 4.
As such, the possible values of the number of sales that Maggie can make to go to the lake are 5 and 4.
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Differentiate from the first principle I obtain the gradient of the tangent to the curve
Y=2x2-5x+3 at the point where x=2
In calculus, there are different ways to differentiate the tangent to a curve. The first principle is one of the ways to differentiate the tangent to a curve.
Differentiation is the foundation of calculus, and it's used to find rates of change, maxima and minima, and the behavior of functions in general.The first principle of differentiation.
The first principle is the fundamental approach to finding derivatives, which involves finding the limit of the difference quotient, or f(x + h) – f(x) / h as h approaches zero. This difference quotient represents the slope of the line tangent to the curve at the point (x, f(x)).
The first principle formula for differentiation is given by:lim h → 0 [f(x + h) – f(x) / h]To differentiate the tangent to the curve y = 2x² – 5x + 3 at the point where x = 2 using the first principle, we need to find the slope of the line tangent to the curve at x = 2. We start by finding the equation of the tangent line and then calculate its slope using the first principle.To find the equation of the tangent line, we differentiate the given function, y = 2x² – 5x + 3:dy/dx = 4x – 5At x = 2, dy/dx = 4(2) – 5 = 3.
Thus, the slope of the tangent line at x = 2 is 3.
Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line:
y – f(2) = m(x – 2)y – (2(2)² – 5(2) + 3) = 3(x – 2)y – 4 = 3x – 6y = 3x – 2
This is the equation of the tangent line to the curve
y = 2x² – 5x + 3
at the point where x = 2. The slope of the tangent line is 3.
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The Indian currency has notes of ₹5
, ₹10
, ₹20
, ₹50
, and ₹100
. Vicky has ₹300
and Ricky has ₹260
. Both of them have notes of the same denominations.
What denominations of notes can they have? Write in increasing order.
PLEASE PLEASE TRY TO GIVE ME THE ANSWER AS QUICK AS POSSIBLE PLEASE FRIENDS PLEASE!
The possible denominations of notes that Vicky and Ricky can have, in increasing order, are:
Vicky: ₹50, ₹100
Ricky: ₹10, ₹20, ₹50, ₹100
To determine the possible denominations of notes that Vicky and Ricky can have, we need to find combinations of notes that add up to their respective amounts.
Let's consider Vicky first. With ₹300, the possible combinations of notes are:
3 number of notes of ₹100 (₹100 + ₹100 + ₹100)
1 note of ₹100 and 2 notes of ₹100 (₹100 + ₹100 + ₹100)
two notes of ₹100 and 5 notes of ₹50 (₹100 + ₹100 + ₹50 + ₹50 + ₹50 + ₹50 + ₹50)
Now let's consider Ricky. With ₹260, the possible combinations of notes are:
2 notes of ₹100 and 3 notes of ₹20 taking their sum (₹100 + ₹100 + ₹20 + ₹20 + ₹20)
1 note of ₹100, 3 notes of ₹50, and 1 note of ₹10 (₹100 + ₹50 + ₹50 + ₹50 + ₹10)
2 notes of ₹100, 2 notes of ₹20, and 1 note of ₹10 (₹100 + ₹100 + ₹20 + ₹20 + ₹10)
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Amir is sorting his stamp collection. he made a chart of the fraction of stamps from each country in his collection. 7/12 of Amir's stamps are either from either Morocco or Spain.
Amir is sorting his stamp collection. He made a chart of the fraction of stamps from each country in his collection. 7/12 of Amir's stamps are either from either Morocco or Spain. The long answer to this question is given below:Answer:7/12 of Amir's stamps are either from Morocco or Spain.
5/12 of his stamps are from Spain and the remaining 2/12 of his stamps are from Morocco. The denominator of the given fraction is 12. Therefore, the numerator of the fraction represents the number of stamps from either Morocco or Spain. Let's consider the given fraction; 7/12The numerator of this fraction represents the number of stamps from either Morocco or Spain. Let S be the number of stamps from Spain.
Let M be the number of stamps from Morocco. Using the given information, we have: S + M = 7/12..... (1)Also, S/12 represents the fraction of stamps from Spain and 2/12 represents the fraction of stamps from Morocco. We can represent the number of stamps from Spain and Morocco in the following manner: S = 5/12 and M = 2/12Let's substitute these values in equation (1).We get:5/12 + 2/12 = 7/12Hence, 7/12 of Amir's stamps are either from either Morocco or Spain. Out of the 7/12 of the stamps, 5/12 are from Spain, and the remaining 2/12 are from Morocco.
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