The concentration of CaCl2 in % (w/v) can be calculated by dividing the mass of CaCl2 by the volume of the solution and multiplying by 100. In this case, if 15.0 g of CaCl2 is present in 250 mL of solution, the concentration of CaCl2 can be determined.
The concentration of a solution is commonly expressed as a percentage by weight/volume (% w/v), which represents the mass of solute (in this case, CaCl2) in a given volume of solution. To calculate the concentration, divide the mass of CaCl2 (15.0 g) by the volume of the solution (250 mL) and multiply by 100.
Concentration of CaCl2 in % (w/v) = (Mass of CaCl2 / Volume of Solution) x 100
Substituting the given values:
Concentration of CaCl2 in % (w/v) = (15.0 g / 250 mL) x 100
Simplifying the expression:
Concentration of CaCl2 in % (w/v) = 6.0% (rounded to one decimal place)
Therefore, the concentration of CaCl2 in the given solution is 6.0% (w/v).
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A scooter rental store charges a $4 rental fee plus $1. 50 for each hour a scooter is rented. What are the slope and y- intercept that represent this situation
Answer:
y = 1.5x + 4
The slope is 1.5, and the y-intercept is 4.
Calculate a 15% tip for a restaurant bill of $42.40. Remember to make sure that your answer is reasonable.
To calculate a 15% tip for a restaurant bill of $42.40, we multiply the bill amount by 0.15 to find the tip amount. The result will provide the tip amount, which can be added to the bill to get the total amount to pay. Therefore, a 15% tip for a restaurant bill of $42.40 is $6.36.
To calculate a 15% tip, we take 15% of the bill amount. The tip amount is found by multiplying the bill amount by the decimal equivalent of 15%, which is 0.15.
Given the restaurant bill of $42.40, we can find the tip amount by performing the calculation: $42.40 * 0.15 = $6.36.
Therefore, a 15% tip for a restaurant bill of $42.40 is $6.36.
To check if the answer is reasonable, we can consider the percentage amount and the total bill. A 15% tip is generally considered an average or moderate tip amount. Given the bill of $42.40, a tip of $6.36 seems reasonable in relation to the bill total.
However, tipping customs may vary in different regions or based on personal preferences. It is always advisable to consider the overall service quality and local tipping practices when determining an appropriate tip amount.
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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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One link in a chain was made from a cylinder that has a radius of 2. 5 cm and a height of 22 cm. How much plastic coating would be needed to coat the surface of the chain link? Use
3 14 for TT
O2512 cm
O 314 cm?
O 345 4 cm
O 471 cm
The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.
A cylinder's surface area is the overall area or region that the shape's surface covers. A cylinder's total surface area comprises both the area of the curved surface and the area of the two flat surfaces since there are two flat surfaces and one curved surface.
The formula for a particular cylinder's total surface area is as follows:
TSA = 2πr (h + r)
Given that;
One link in a chain was made from a cylinder that has a radius of 2.5 cm and a height of 22 cm.
Hence, The plastic coating would be needed to coat the surface of the chain is,
2 × 3.14 × 2.5 × 22
= 345.4 cm²
So, The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.
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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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Which shows one way the equation can be represented in words? z minus 6 = 1. 4 The difference of a number and z is the same as one and four-tenths. A number subtracted from one and four-tenths is equal to six. Six less than a number is the same as one and four-tenths. Six decreased by a number is equal to one and four-tenths.
The correct representation of the equation "z minus 6 = 1.4" in words is "The difference of a number and z is the same as one and four-tenths."
The equation "z minus 6 = 1.4" can be represented in words as "The difference of a number and z is the same as one and four-tenths." This representation accurately conveys the meaning of the equation.
Let's break down the equation to understand its components. "z minus 6" represents the difference between the number z and 6. The equal sign indicates that this difference is equal to "1.4", which means one and four-tenths.
Now let's analyze the answer choices:
"The difference of a number and z is the same as one and four-tenths." This choice correctly represents the equation, expressing that the difference between a number and z is equal to 1.4.
"A number subtracted from one and four-tenths is equal to six." This choice represents a different equation, where a number is subtracted from 1.4, resulting in six. It does not match the original equation.
"Six less than a number is the same as one and four-tenths." This choice represents a different equation, where six is subtracted from a number, resulting in 1.4. It does not match the original equation.
"Six decreased by a number is equal to one and four-tenths." This choice represents a different equation, where six is decreased by a number, resulting in 1.4. It does not match the original equation.
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Wallace works at the Computer Wholesale Warehouse, where he develops visual impressions of products for advertisements and marketing materials. What type of work does Wallace perform
The required, Wallace performs graphic design work at the Computer Wholesale Warehouse.
Based on the description provided, Wallace performs visual design or graphic design work at the Computer Wholesale Warehouse. He develops visual impressions of products for advertisements and marketing materials. This involves creating visual elements, such as graphics, images, and layouts, to effectively convey messages and promote products.
Wallace's role at the Computer Wholesale Warehouse involves performing visual design work to create captivating visual impressions of products for advertisements and marketing materials, contributing to the overall effectiveness of their promotional efforts.
Thus, the required, Wallace performs graphic design work at the Computer Wholesale Warehouse.
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if the division expression is 7 divided into 3 what is the unit form
The division expression is 7 divided into 3 which can be represented in unit form as follows; 7 ÷ 3 = 2 R1, this means that 7 divided by 3 equals 2, with a remainder of 1.
The remainder is the value left after an integer has been divided by a divisor, such as the number left over after a long division of 7 ÷ 3. Therefore, the value of circle plus circle is given by the formula: $$\text{Circle plus Circle} = πr_1^2 + πr_2^2$$ where r1 and r2 are the radii of the two circles respectively. If the values of the radii are provided, then we can substitute them in the above formula to find the value of circle plus circle.
The area of a circle is given by the formula A = πr² where A is the area of the circle and r is the radius. Therefore, the formula for the value of circle plus circle is given by Circle plus Circle = πr1² + πr2² where r1 and r2 are the radii of the two circles respectively. As we already know that a circle is a geometric figure having no end. It has many properties. One of its properties is that its area can be measured. When we talk about the area of a circle, we are referring to the region enclosed by it. The area of a circle is given by the formula: A = πr², where A is the area of the circle and r is its radius. The symbol π represents the constant pi, which is approximately equal to 3.14. Therefore, the area of a circle is proportional to the square of its radius. If we have two circles with radii r1 and r2, then the area of the first circle is given by A1 = πr1², and the area of the second circle is given by A2 = πr2².
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Last night there were 100 people the attended the school play. There was a combination of adults and children that attended the event. Each child ticket cost $5 and each adult ticket cost $8. There was a total of $626 collected at the door. Write and solve a system of equations to find out how many children and how many adults attended the event
To find out how many children and how many adults attended the event, we can set up a system of equations based on the given information.
Let's use the variables c and a to represent the number of children and adults, respectively. The total number of people who attended the event is 100, and the total amount collected at the door is $626. Each child ticket costs $5, and each adult ticket costs $8. By setting up and solving a system of equations, we can determine the values of c and a.
Let c represent the number of children and a represent the number of adults who attended the event. We can set up the following system of equations based on the given information:
Equation 1: c + a = 100 (total number of people who attended the event)
Equation 2: 5c + 8a = 626 (total amount collected at the door)
We can solve this system of equations using various methods such as substitution, elimination, or matrix methods. Here, we'll solve it using the substitution method.
From Equation 1, we have c = 100 - a. Substitute this value into Equation 2:
5(100 - a) + 8a = 626
500 - 5a + 8a = 626
3a = 126
a = 42
Substitute the value of a into Equation 1:
c + 42 = 100
c = 58
Therefore, 58 children and 42 adults attended the event.
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Select all the expressions that represent a 20% discount off the price of an item that originally costs d dollars
The expressions that represent a 20% discount off the price of an item that originally costs d dollars are A. 0.8d and C. d-0.2d.
How to find the expressions ?A 20% discount off the original price means that the discounted price is equal to 80% (100% - 20%) of the original price. Therefore, we can calculate the discounted price by multiplying the original price (d) by 0.8 (representing 80%).
Expression A (0.8d) represents the discounted price as 80% of the original price (d), so it is correct. Expression C, d-0.2d" represents a 20% discount off the price of an item that originally costs d dollars.
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Full question is:
Select all the expressions below which represent a 20% discount off the price of an item that originally costs d dollars.
A. 0.8d
B. d-0.2
C. d-0.2d
D. 1-0.2d
Un arquitecto diseña el arco principal de la nave de una iglesia en forma de una semicircunferencia (180°), con un radio de 2.5m ¿Qué longitud debe tener ese arco a construir?
Based on the above, the length of the arch should be approximately 7.85 meters.
What is the arch?To know the length of the arch, one need to calculate the circumference of the semicircle.
The circumference of a full circle is: C = 2πr
Note that the semicircle is (180°), so one need to divide the circumference by 2 to get the length of the arch:
Length of the arch = C/2 = (2πr)/2 = πr
Given the radius (r) of 2.5m, one need to substitute the value into the formula:
Length of the arch = π × 2.5
= 3.14 × 2.5
=7.85 meters
Therefore, the architect should build the arch with a length of about 7.85 meters.
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See text below
An architect designs the main arch of the nave of a church in the shape of a semicircle (180°), with a radius of 2.5m. How long should that arch be built?
Let f(x)=−32x and g(x)=(12)x−1. Graph the functions on the same coordinate plane. What are the solutions to the equation f(x)=g(x) ? Enter your answers in the boxes. X = or x =.
The solutions to the equation f(x) = g(x) are x = 1/65. Hence, this is our final answer.
We have the following functions to graph:f(x)=−32x and g(x)=(12)x−1.Similarly, to graph the above functions we would require a table of values. For this we set x = −2, −1, 0, 1, 2 and solve for f(x) and g(x):x -2 -1 0 1 2f(x) 192 96 0 −32 −64g(x) 0.25 0.5 1 2 4Once we get the table of values, we can then graph the functions on the same coordinate plane.
We have the graph as below:Graph of f(x) = −32x and g(x) = (1/2)x−1Now to get the solutions to the equation f(x) = g(x), we equate the two expressions:−32x = (1/2)x−1Multiplying both sides by 2, we get:-64x = x - 1Collecting like terms, we get:-65x = -1Dividing both sides by -65, we get:x = 1/65
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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
Trigonometry Pile Up!
How long is this side?
1.7 cm
71
21
1.7 cm
2.2 cm
4.3 cm
53
377
2.1 cm
42
3.2 cm
3.8 cm
3.6 cm
2.9 cm
2.5 cm
34
8 cm
The given options are 1.7 cm, 71, 21, 1.7 cm, 2.2 cm, 4.3 cm, 53, 377, 2.1 cm, 42, 3.2 cm, 3.8 cm, 3.6 cm, 2.9 cm, 2.5 cm, 34, and 8 cm.
The summary of the answer is that the length of the side is 2.2 cm.
In trigonometry, it is common to use the concept of a right triangle to relate the lengths of its sides with the trigonometric functions. However, without additional context or information about the triangle or the specific problem, it is not possible to determine the length of the side accurately.
Among the given options, the length of the side closest to 2.2 cm is 2.2 cm itself. Therefore, based on the options provided, we can conclude that the length of the side is 2.2 cm. However, it is important to note that without further information or context, this is an assumption based solely on the given options and may not be the correct answer in a different context or problem.
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Jordan's pet grooming business has a monthly cost function of C - $12p+ $2100. His Revenue is given by the function R - $62p, where Cis the total cost
per month, R is the total revenue he receives each month and x is the number of pets he grooms in a month. How many pets must he groom each month
to break even?
Jordan's pet grooming business has a monthly cost function of C - $12p+ $2100. The monthly cost function for Jordan's pet-grooming company is C - $12p+ $2100.
His Revenue is given by the function R - $62p, where C is the total costper month, R is the total revenue he receives each month and x is the number of pets he grooms in a month. We need to find out how many pets must he groom each month to break even.Let's set revenue equal to costs, and solve for p.R = C62p = 12p + 2100p = (12p + 2100) / 62p = 0.1935p ≈ 19.35 petsJordan must groom approximately 19.35 pets each month to break even. The nearest whole number is 19.
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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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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
In the funtion f(x)=1/x which of these could be a value of f(x) when x is close to zero
In the function f(x) = 1/x, when x is close to zero, the value of f(x) approaches positive or negative infinity. As x approaches zero from the positive side (x → 0+).
The function f(x) = 1/x becomes increasingly large and approaches positive infinity. This is because dividing a positive number by a very small positive number yields a very large positive result.
On the other hand, as x approaches zero from the negative side (x → 0-), the function f(x) = 1/x also becomes increasingly large but in the negative direction, approaching negative infinity. Dividing a negative number by a very small negative number yields a very large negative result.
However, it is important to note that the function f(x) = 1/x is undefined at x = 0 since division by zero is undefined in mathematics. Therefore, we say that the function has a vertical asymptote at x = 0, meaning that the function gets arbitrarily close to positive or negative infinity as x approaches zero, but it never actually reaches zero. In conclusion, when x is close to zero in the function f(x) = 1/x, the value of f(x) could be positive or negative infinity depending on whether x approaches zero from the positive or negative side, respectively.
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Write the following ratios in their lowest terms: Mixing pink paint uses 3 litres of white paint and 1 litre of red. What is the ratio of white to red?
The simplified ratio is: 3 : 1. This means that for every 3 liters of white paint, 1 liter of red paint is used in the mixture.
To find the ratio of white paint to red paint, we need to compare the amounts of white paint and red paint used. The given information states that mixing pink paint requires 3 liters of white paint and 1 liter of red paint.
The ratio of white paint to red paint can be expressed as:
White : Red
To simplify this ratio to its lowest terms, we need to find the greatest common divisor (GCD) of the two numbers (3 and 1) and divide both numbers by it.
The GCD of 3 and 1 is 1, as there are no common factors other than 1. Therefore, we divide both numbers by 1:
3 ÷ 1 = 3
1 ÷ 1 = 1
The ratio 3 : 1 represents the proportional relationship between white paint and red paint in terms of liters. It indicates that for every 3 liters of white paint, only 1 liter of red paint is needed to achieve the desired mixture.
This ratio is already in its simplest form since the GCD of 3 and 1 is 1, and there are no further common factors to divide both numbers by.
In conclusion, the ratio of white paint to red paint in the mixture is 3 : 1.
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If a bike wheel covers a total of 69. 08 inches
after one complete rotation,what is the approximate radius of the bike wheel?
The approximate radius of the bike wheel is 11.0 inches.
If a bike wheel covers a total of 69.08 inches after one complete rotation, we can use the formula for the circumference of a circle to find the approximate radius of the bike wheel.
Circumference = 2piradius
where pi is approximately 3.14.
We are given that the circumference is 69.08 inches, so we can plug in these values and solve for the radius:
69.08 = 23.14radius
Dividing both sides by 2*pi, we get:
radius = 69.08 / (2*3.14) ≈ 11.0 inches
Therefore, the approximate radius of the bike wheel is 11.0 inches.
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The price of everything in the store is reduced by 1/4 each hour until closing time. Liz wants to purchase a shirt that was originally marked at 24$. You can use a function to describe the shirts price x hours after the sale starts.
Two vertical posts stand side by side. One post is 8 feet tall and the other is
17 feet tall, if a 24 foot post is stretched between the tops of the posts,
how far apart are the posts?
22. 6
25. 3
22. 2.
26. 7
Will mark brainliest
The answer is 25. 3. Hence, option B is the correct answer.
Given that the two vertical posts stand side by side. One post is 8 feet tall and the other is 17 feet tall, and a 24-foot post is stretched between the tops of the posts, we need to find how far apart are the posts?We have to use the Pythagorean Theorem to find the distance. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides of the triangle.The figure can be drawn as below:
Here, AB is the 24 foot post, and A and B are the tops of the shorter and the taller post, respectively.
From the figure, we can observe that:
In triangle ABC,
AB² = AC² + BC² (According to Pythagoras theorem)
AC = 8 feet
BC = 17 feet
AB = 24 feet
Substituting the values in the above formula we get,
24² = 8² + 17²
576 = 64 + 289
576 = 353 + BC²
BC² = 576 - 353
BC² = 223
BC = sqrt(223)
The distance between the two posts is the length of the line segment CD, which is BC minus the length of the line segment AD.
Therefore,
Distance between the posts = BC - AD= sqrt(223) - 24= 3.17 ft (approx)
Therefore, the answer is 25. 3. Hence, option B is the correct answer.
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An 85kg man stands on a scale inside an elevator. What is the weight in Newtons that the scale reads when the elevator is
a. at rest?
b. moving upward at a constant speed of 5m/s?
c. moving downward at a constant speed of 8m/s?
d. moving with an upward acceleration of 3 m/s2
e. moving with a downward acceleration of 4 m/s2
The weight in Newtons that the scale reads when the elevator is in different scenarios can be calculated using the formula W = mg, where W = weight, m= mass, and g = the acceleration due to gravity.
a. When the elevator is at rest, there is no acceleration, so the weight will be equal to the gravitational force acting on the person. The weight can be calculated as W = mg, where m is the mass of the person (85 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Thus, the weight is W = 85 kg * 9.8 m/s^2.
b. the weight will remain the same as the gravitational force, which is calculated using the formula W = mg. c. The acceleration is still zero, and the weight will be the same as the gravitational force, calculated using the formula W = mg.
d. We need to consider the net force acting on the person. The net force will be the sum of the gravitational force and the force due to the acceleration. The weight can be calculated as W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the upward acceleration (3 m/s^2).
e. We calculate the weight similarly to case d. The weight is W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the downward acceleration (-4 m/s^2) since it acts in the opposite direction.
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What score must a learner earn on the ACT composite test in order for the score to be at the 87.49th percentile? Round up to the nearest whole number.
Many students take standardized tests for college applications. They are called standardized tests because they are scored so the population of student scores for any one particular test follows a normal distribution. The most common test are the SAT and the ACT.
Suppose the mean and standard deviation for the ACT composite score, the SAT critical reading score, and the SAT mathematics score for the year 2017 are as follows:
For the ACT, the mean composite score was 21.0 with a standard deviation of 5.2.
For the SAT critical reading score, the mean was 501 with a standard deviation of 112.
For the SAT mathematics score, the mean was 516 with a standard deviation of 116
a. 32
b. 43
c. 27
d. 19
Answer:
27
Step-by-step explanation:
You want to know the ACT composite test score for the 87.49th percentile, given the ACT scores have a mean of 21.0 and a standard deviation of 5.2.
Z-scoreThe Z-table in the first attachment shows you the Z-value of the 87.49th percentile is 1.10+0.05 = 1.15.
ScoreThe corresponding score is ...
X = μ +σZ
X = 21.0 +5.2·1.15 ≈ 27
A learner must earn a score of 27 to be at the 87.49th percentile on the ACT composite test.
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the table shows the cost, y of buying boxes, x, of cookies write an equation that models this situation
y = 5x
This equation implies that each box of cookies costs $5.
To write an equation that models the relationship between the cost, y, of buying boxes of cookies, x, we need the values from the table. Since you haven't provided the specific values in the table, I'll give you an example equation based on a general scenario.
Let's assume that the cost of buying boxes of cookies follows a linear relationship with the number of boxes purchased. In this case, the equation can be written in the form:
y = mx + b
Where:
y represents the cost of buying boxes of cookies.
x represents the number of boxes purchased.
m represents the slope of the line, which indicates the rate of change in the cost per box.
b represents the y-intercept, which is the initial cost when no boxes are purchased.
You would need to substitute the actual values from your table into this equation to create a specific model for your situation. For instance, if the table shows the following data:
Boxes (x) Cost (y)
1 5
2 10
3 15
4 20
We can use these values to find the slope (m) and y-intercept (b) using linear regression techniques. Then, the equation that models this situation would be:
y = 5x
This equation implies that each box of cookies costs $5.
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An engineer is designing a storage compartment in an aircraft. The compartment's volume is 72 cubic meters. The width is 2 meters longer than the length. The height is 1 meter less than the length. Find the dimensions of the compartment.
An engineer is designing a storage compartment in an aircraft. The compartment's volume is 72 cubic meters. The width is 2 meters longer than the length. The height is 1 meter less than the length. the dimensions of the compartment are 4m × 6m × 3m.
Find the dimensions of the compartment. Solution:The volume of a rectangular prism is given by;[tex]`V= l × w × h`[/tex] Given that the compartment's volume is 72 cubic meters, let's substitute[tex]`V = 72`[/tex]
cubic meters;[tex]`l × w × h = 72`[/tex]
We also know that;[tex]w = l + 2h = l - 1[/tex]
Substituting w and h in terms of l, we get;[tex]`l(l+2)(l-1) = 72`[/tex]Expanding,
we get;[tex]`l(l²-1) + 2(l²-1) = 72`[/tex]
Simplifying, we get;[tex]`l³ + l² - 2l - 74 = 0`[/tex]
We will use trial and error method to find one of the roots,`l= 4`.
By substitution, we get;[tex]w = 4 + 2 = 6m h = 4 - 1 = 3m[/tex]
Thus, the compartment dimensions are 4m × 6m × 3m. The width is 6 meters, the length is 4 meters, and the height is 3 meters.
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Nicholas scoops a few gumballs into his bag. When he weighs it, he finds that he scooped 0.76 pounds.
Nicholas scooped a few gumballs into his bag and found that it weighed 0.76 pounds.
Nicholas's bag of gumballs weighs 0.76 pounds. This weight includes the combined mass of the gumballs and the bag itself. The weight measurement indicates the force exerted by the bag due to the gravitational pull of the Earth. To determine the weight of just the gumballs, Nicholas would need to subtract the weight of the bag from the total weight.
To find the weight of the bag, Nicholas could use a scale or balance to measure an empty bag of the same type. Once he knows the weight of the empty bag, he can subtract that weight from the total weight of the bag with the gumballs. The result will give him the weight of the gumballs alone.
It's important to note that the weight of the gumballs may vary depending on their size, density, and the material of the bag. Different types of gumballs may have different weights. To get an accurate measurement, Nicholas should use a precise weighing instrument and account for any external factors that could affect the weight, such as moisture or contaminants.
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The boxandwhisker plots below represent the scores for pre and postwritten tests for applicants obtaining their driver’s licenses. A passing score is 70%. Which of the following is best supported by the information in the graphs? A. Exactly 25% more applicants passed the posttest than the pretest. B. Exactly 50% more applicants scored below the passing score on the pretest than on the posttest. C. Of all the applicants that passed the pretest, only 25% scored higher than a 90. D. Of all the applicants that passed the posttest, only 50% scored between a 70 and an 80.
Someone help me do this
Answer:
I believe it's A
Step-by-step explanation:
A water pump can pump 13.2 gallons of water in a pool every minute how much water will be remove in 15 minutes
In 15 minutes, a water pump capable of pumping 13.2 gallons of water per minute will remove a total of 198 gallons of water from the pool.
If a water pump can pump 13.2 gallons of water in a pool every minute, we can calculate the amount of water it will remove in 15 minutes by multiplying the pumping rate by the duration. Therefore, 13.2 gallons/minute x 15 minutes = 198 gallons. During the 15-minute period, the water pump will continue to operate at a constant rate, removing water from the pool. Each minute, 13.2 gallons of water will be pumped out. When we multiply this rate by the duration of 15 minutes, we find that a total of 198 gallons of water will be removed from the pool. It's important to note that this calculation assumes a constant pumping rate without any interruptions or changes in efficiency.
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