Phylea can repackage the candy into smaller bags, each containing 6 fireballs and 6 Jolly Ranchers.
To repackage the candy into smaller bags with an equal number of fireballs and Jolly Ranchers, we need to find the greatest common divisor (GCD) of 30 and 24. The GCD represents the largest number that divides both 30 and 24 evenly.
The prime factorization of 30 is 2 * 3 * 5, and the prime factorization of 24 is 2 * 2 * 2 * 3. To find the GCD, we take the common factors with the lowest exponent: 2 * 3 = 6.
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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 total home attendance for a professional football team in 2010 was about 5.44 × 10^5, and in 2008 was about 4.32 × 10^5. About how many times as large was the attendance in 2010 as the attendance in 2008?
When compared to the number of persons who were there in 2008, the number of people who were present in 2010 was roughly 1.26 times higher.
In 2008, the professional football team's home games averaged an attendance of around 4.32 times 10-5 people. The number of people who attended from their homes reached around 5.44 times 10-5 in the year 2010. We can determine how many times larger the attendance was in 2010 in comparison to 2008 by dividing the number of people who attended in 2010 by the number of people who attended in 2008.
The approximate value that is arrived at after taking 5.44 x 10-5 and dividing it by 4.32 x 10-5 is 1.26. As a direct consequence of this, the total number of individuals who participated in the event in 2010 was roughly 1.26 times more than the total number of people who participated in the event in 2008.
Between the years 2008 and 2010, there was an increase in attendance that was approximately equivalent to a 26 percent increase. Attendance at the professional football team's games has increased, which is a direct reflection of the growing interest in, and support for, the team over the course of the past two years.
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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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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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which statement cannot be justified given only that triangle PBJ = traingle TIM
When it comes to geometry, it's vital to understand that a statement that cannot be justified using a given premise doesn't necessarily mean that the statement is false.
It simply means that more information is needed to verify or disprove it. Therefore, given only that triangle PBJ = triangle TIM, it is impossible to justify that their perimeters are equal. This statement cannot be justified using the given information alone.
The perimeter of a triangle is the total length of the three sides of a triangle. Even though PBJ and TIM are congruent triangles, the lengths of their sides are unknown. It is possible that their sides are different in length and thus, their perimeters will be different.
Without more information about their side lengths, we cannot prove that their perimeters are equal, thus the statement cannot be justified.
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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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3
Type the correct answer in the box. Use numerals instead of words.
This system of equations has been placed in a matrix:
y= 700x + 200
y= 5,000 - 75x
Complete the matrix by filling
The coefficients of the variables and the constants. [tex]\[\begin{bmatrix}\phantom{-}700 & -1 & \phantom{-}200 \\\phantom{-}75 & -1 & -5000\end{bmatrix}\][/tex].
To complete the matrix, we need to fill in the coefficients and constants from the given system of equations:
The given system of equations:
[tex]\[y &= 700x + 200 \\y &= 5000 - 75x\][/tex]
To complete the matrix, we'll organize the coefficients of the variables and the constants.
[tex]\[\begin{bmatrix}\phantom{-}700 & -1 & \phantom{-}200 \\\phantom{-}75 & -1 & -5000\end{bmatrix}\][/tex]
In the matrix, the coefficients of the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex] are arranged in the first two columns, and the constants are in the third column.
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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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Can anyone help me with this? I need this done by today. Please and thank you.
Geometry.
Similarity statements
In geometry, similarity statements are used to indicate that two or more figures are similar. Similarity means that the figures have the same shape but may differ in size. A similarity statement consists of two parts: the corresponding sides and the corresponding angles.
The corresponding sides of similar figures are proportional, which means that the ratio of the lengths of corresponding sides is the same. For example, if we have two similar triangles, we can write their similarity statement as "Triangle ABC ~ Triangle DEF," indicating that the corresponding sides AB/DE, BC/EF, and AC/DF are all in the same ratio.
Similarly, the corresponding angles of similar figures are congruent, meaning that they have the same measure. In the case of our example triangles, the corresponding angles ∠A ≅ ∠D, ∠B ≅ ∠E, and ∠C ≅ ∠F.
By using similarity statements, we can solve various geometric problems. We can use the known ratios of corresponding sides to find missing side lengths, determine scale factors between similar figures, or establish relationships between different parts of the figures.
In conclusion, similarity statements are essential in geometry to express the similarity between figures. They provide a concise way to indicate that corresponding sides are proportional and corresponding angles are congruent. By applying the properties of similarity, we can solve problems involving similar figures and analyze their geometric properties. If you have specific questions or examples you'd like assistance with, please provide them, and I'll be glad to assist you further.
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Penicillin stars being metabolized by your body as soon as you take it (true ofall medicications). Penicillin is eliminated expenentially. Suppose you receive a 300-mg dose of penicillin to combat strep throat. About 180-mg will remain
active in your blood after 1 day.
Penicillin is an antibiotic drug that is used to treat bacterial infections. The process of eliminating penicillin from the body is an important factor to consider when determining the correct dose of this drug.
This means that the amount of penicillin in the body decreases at a constant rate over time. Suppose a person receives a 300-mg dose of penicillin to combat strep throat. After one day, approximately 180-mg of the drug will remain active in their bloodstream. This is due to the fact that the elimination half-life of penicillin is approximately 1 hour. Therefore, after 1 hour, 150-mg of the drug will remain in the bloodstream. After 2 hours, this amount will decrease to 75-mg, and so on.
The expenential elimination of penicillin from the body is important to consider when determining the frequency and dose of this drug.
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This hyperbola is centered at the origin find its equation. Foci: (0,-9) and (0,9) Vertices: (0,-7) and (0,7)
The equation of the hyperbola centered at the origin, with the given foci (0, -9) and (0, 9), and vertices (0, -7) and (0, 7), is x^2/32 - y^2/49 = 1.
The equation of the hyperbola centered at the origin with the given foci and vertices can be found as follows:
The foci of the hyperbola are located at (0, -9) and (0, 9). The distance between the center of the hyperbola (0, 0) and each focus is 9 units, which gives us the value of c.
The vertices of the hyperbola are given as (0, -7) and (0, 7). The distance between the center and each vertex is 7 units, denoted by a.
In a hyperbola, the distance between the center and each focus is related to the distance between the center and each vertex by the equation c^2 = a^2 + b^2.
Since the center is at the origin, the equation simplifies to c^2 = a^2 + b^2.
Substituting the known values, we have 9^2 = 7^2 + b^2.
Simplifying the equation, we get 81 = 49 + b^2.
By subtracting 49 from both sides, we find b^2 = 32.
Thus, the equation of the hyperbola centered at the origin is x^2/32 - y^2/49 = 1.
In this equation, the squared term with the positive coefficient is associated with the x-axis, while the squared term with the negative coefficient is associated with the y-axis. The center of the hyperbola is at the origin, and its foci and vertices are as given.
Therefore, the equation of the hyperbola centered at the origin, with the given foci (0, -9) and (0, 9), and vertices (0, -7) and (0, 7), is x^2/32 - y^2/49 = 1.
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Braedyn notices that there are Twenty-One short shelves and 9 tall shelves how can the expression 21 a + 9 B help him find the total number of items on the shelves?
Total number of items = 21a + 9b. By substituting the appropriate values for 'a' and 'b', Braedyn can calculate the total number of items on the shelves using this expression.
The expression 21a + 9b can help Braedyn find the total number of items on the shelves by representing the number of items on each type of shelf and then summing them together. Let's assume that 'a' represents the number of items on each short shelf and 'b' represents the number of items on each tall shelf.
The expression 21a represents the total number of items on all the short shelves, and the expression 9b represents the total number of items on all the tall shelves. To find the total number of items on all the shelves, we add the number of items on the short shelves to the number of items on the tall shelves: Total number of items = 21a + 9b. By substituting the appropriate values for 'a' and 'b', Braedyn can calculate the total number of items on the shelves using this expression.
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Plot points at (2, 0), (4, 0) and (3, 0). What is true about all points whit a y- coordinate of 0?
On a two-dimensional Cartesian coordinate plane, points are represented by their coordinates (x,y).
The horizontal axis is called the x-axis and the vertical axis is called the y-axis. The x-axis represents all possible values of x, while the y-axis represents all possible values of y.
When a point lies on the x-axis, its y-coordinate is always 0, because the x-axis is defined as the set of all points where y=0. Therefore, any point with a y-coordinate of 0 will lie on the x-axis.
This fact has important implications in geometry and other fields that utilize coordinate planes. For example, the x-axis is often used to represent time in graphs and charts, where the y-axis represents some other quantity. Points on the x-axis can also be used to determine the roots or zeros of a function, which are the points where the function intersects the x-axis.
Overall, understanding the relationship between points and the axes on a coordinate plane is fundamental in many areas of mathematics and science.
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An expression to determine the growth rate of a cell is written as 3(1. 25)t/5. What would be an approximate form of this expression for all values of t?
The approximate form of the expression for all values of t is simply
3(1.05)ˣ (for x = t)How to find the expressionTo find an approximate form of the expression [tex]3(1.25)^{t/5}[/tex] for all values of t, we can simplify it by evaluating the exponent.
First, let's simplify
= [tex]3(1.25)^{t/5}[/tex]
= [tex]3 \sqrt[5]{1.25} ^{t}[/tex]
= 3 * (1.05)ˣ (Assuming x = t)
Now, let's rewrite the expression:
3(1.05)ˣ
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Directions: Write your answer in the box. Do not use spaces.
Look at the system of equations.
+
y=-x+2
7x+4y=-1
What is the value of y for the solution to this system of equations?
V =
The given system of equations is: y = -x + 27x + 4y = -1. To find the value of y, substitute the value of x from the first equation in the second equation. So, 7x + 4y = -1 can be written as 7(-y + 2) + 4y = -1 ⇒ -7y + 14 + 4y = -1 ⇒ -3y = -15 ⇒ y = 5. Therefore, the value of y for the solution to this system of equations is 5.
In order to solve the given system of equations, we need to first find the values of x and y that satisfy both equations. The system of equations is: y = -x + 27x + 4y = -1. We can use any method, either substitution or elimination, to find the values of x and y. However, in this case, the substitution method would be more convenient because one of the variables has a coefficient of 1. So, we can solve one of the equations for x or y and then substitute that value into the other equation. Let's solve the first equation for x:y = -x + 2 x = -y + 2. Now, substitute this value of x in the second equation and solve for y: 7x + 4y = -1 7(-y + 2) + 4y = -1 -7y + 14 + 4y = -1 -3y = -15 y = 5. Therefore, the value of y for the solution to this system of equations is 5.
The solution to the given system of equations is y = 5.
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In the past month, Dan rented 1 video game 5 and DVDs. The rental price for the video game was $2.70 . The rental price for each DVD was $4.60 . What is the total amount that Dan spent on video game and DVD rentals in the past month?
Dan spent $25.70 in the past month on video game and DVD rentals.
In the past month, Dan rented 1 video game and 5 DVDs. The rental price for the video game was $2.70, and the rental price for each DVD was $4.60.
Let's calculate the total amount that Dan spent on video game and DVD rentals in the past month.
The cost of renting a video game was $2.70, and Dan rented only one video game.
Total cost of renting one video game is = $2.70
The cost of renting one DVD is $4.60, and Dan rented five DVDs.
Total cost of renting five DVDs is = $4.60 × 5= $23
Therefore, Dan spent $2.70 + $23 = $25.70 in the past month on video game and DVD rentals.
In summary, Dan spent $25.70 in the past month on video game and DVD rentals.
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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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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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15×5-3 +4÷7×3 when Charlie gets 20 apples divide the apples by the answer to the first problem
When Charlie gets 20 apples and divides them by the answer to the first problem, he will get 35/143 of an apple. Firstly, let's solve the expression 15×5-3 +4÷7×3. Using the order of operations, we do the multiplication and division first. 15×5 = 75 and 4÷7×3 = 12/7.
Firstly, let's solve the expression 15×5-3 +4÷7×3. Using the order of operations, we do the multiplication and division first. 15×5 = 75 and 4÷7×3 = 12/7
So, 15×5-3 +4÷7×3 = 75 - 3 + 12/7
Next, we simplify the fraction by finding a common denominator. The common denominator for 7 and 1 is 7, so we multiply the numerator and denominator of 12/7 by 1 to get: 12/7 × 1/1 = 12/7
Now, 75 - 3 + 12/7 = 572/7. Therefore, the answer to the first problem is 572/7. Now, Charlie has 20 apples. If he divides these apples by the answer to the first problem, he will get: 20 ÷ 572/7
We can solve this by multiplying the dividend by the reciprocal of the divisor. In other words, we multiply 20 by 7/572.20 ÷ 572/7 = 20 × 7/572 = 140/572
We can simplify this fraction by finding a common factor of the numerator and denominator. Both 140 and 572 are divisible by 4.140/572 = 35/143
So, when Charlie gets 20 apples and divides them by the answer to the first problem, he will get 35/143 of an apple.
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A student drops a ball from a school roof 45 ft aboveground. How long is the ball in the air?The gravity equation (earth) is -16t^2+subzero (initial height), but I don't know how to complete it ):Thanks if you help!
the ball will be in the air for approximately 1.34 seconds before it reaches the ground.
To determine the time the ball is in the air, we can use the given gravity equation -16t^2 + subzero (initial height), where t represents time and subzero represents the initial height of the ball. In this case, the initial height is 45 ft above the ground.Setting up the equation, we have:
-16t^2 + 45 = 0
To solve for t, we need to isolate t on one side of the equation. Rearranging the equation, we get:
16t^2 = 45
Dividing both sides by 16, we have:
t^2 = 45/16
Taking the square root of both sides, we find:
t = √(45/16)
Evaluating the square root, we get:
t ≈ 1.34 seconds
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Suppose you want to start an ice cream business. You buy a freezer for $200 to costs you $0. 45 to make each single-scoop ice cream cone. If each cone sells for 1. 25, how many cones will you need to sell in order to break-even?
To calculate the number of cones that need to be sold in order to break even, we need to use the formula, Break-even point = Fixed costs / (Selling price per unit - Variable cost per unit).
Here, the fixed cost is the cost of the freezer which is $200. The variable cost per unit is the cost of making each single-scoop ice cream cone which is $0.45. The selling price per unit is $1.25.Substituting the values in the formula, we get, Break-even point = $200 / ($1.25 - $0.45) = $200 / $0.8 = 250 cones Therefore, 250 cones need to be sold in order to break even.
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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.
Jerome has three pairs of jeans two pairs of joggers one pair of black pants and one pair of khaki pants it’s your room so likes his pants at random what is the probability he will select jeans or joggers P(jeans or joggers)=
The probability of Jerome selecting jeans or joggers from his collection of pants is 5/7, indicating a high likelihood of choosing either jeans or joggers.
Jerome has a total of 3 pairs of jeans and 2 pairs of joggers. Since the question asks for the probability of selecting jeans or joggers, we need to consider the favorable outcomes, which are the jeans and joggers, and the total number of possible outcomes, which is the total number of pants.
The total number of pants Jerome has is 3 (jeans) + 2 (joggers) + 1 (black pants) + 1 (khaki pants) = 7. Out of these 7 pants, the favorable outcomes are the jeans and joggers, which total 3 (jeans) + 2 (joggers) = 5.
Therefore, the probability of Jerome selecting jeans or joggers can be calculated as the favorable outcomes divided by the total number of outcomes: P(jeans or joggers) = 5/7.
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13.) Jack was making a model volcano for his science project. He had 5
6/10 cups of baking soda in a box. He POURED 3 1/2 cups into the volcano.
How many cups of baking soda are LEFT in the box? *
There are 21/10 fractions of cups of baking soda left in the box. The correct answer is 21/10.
Initially, Jack had 5 6/10 cups of baking soda in the box. He poured 3 1/2 cups into the volcano. To find out how much baking soda is left in the box, we need to subtract the amount poured from the initial amount.
First, let's convert the mixed numbers to improper fractions. The initial amount of baking soda is 5 6/10 cups, which is equivalent to 56/10 cups. The amount poured into the volcano is 3 1/2 cups, equivalent to 7/2 cups.
To subtract fractions, we need a common denominator. In this case, the common denominator is 10. Now, we subtract the fractions: (56/10) - (7/2) = (56/10) - (35/10) = 21/10.
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Thor travels 24 miles per hour. How long does it take him to travel 2 miles? Your answer should be in hours, rounded to the nearest tenth.
Answer:
To calculate the time it takes for Thor to travel 2 miles at a speed of 24 miles per hour, we can use the formula:
Time = Distance / Speed
Given:
Distance = 2 miles
Speed = 24 miles per hour
Plugging these values into the formula, we have:
Time = 2 miles / 24 miles per hour
Calculating this, we get:
Time = 0.08333 hours
Rounding to the nearest tenth, the time it takes for Thor to travel 2 miles is approximately 0.1 hours.
Therefore, it takes Thor approximately 0.1 hours (or 6 minutes) to travel 2 miles at a speed of 24 miles per hour.
The long jump pit was recently rebuilt to make it level with the runway. Volunteers provided pieces of wood. Determine the amount of wood needed to build the frame of the rectangle if the length is 9.54 M and the width is 2.75 M
To build the frame of the rectangle long jump pit with a length of 9.54 meters and a width of 2.75 meters, a total of 24.58 meters of wood is needed.
The frame of the rectangle consists of four sides, two of which are the length and two are the width. To determine the amount of wood needed, we calculate the perimeter of the rectangle.
The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width.
Substituting the given values, we have P = 2(9.54) + 2(2.75) = 19.08 + 5.50 = 24.58 meters.
Therefore, to build the frame of the rectangle long jump pit, a total of 24.58 meters of wood is needed.
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Given A is the center of circle at (3, -2) , radius is 7 in and m angle E A F equal 135 degree
What is the equation of given circle?
The center of the circle is given as (3, -2) and the radius is given as 7 in. To find the equation of the circle, we can use the standard form equation for a circle, which is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
Substituting the given values, we get the equation as:(x - 3)² + (y + 2)² = 7²This is the equation of the given circle. Now, we need to find the measures of angles EAF and EBF. To do this, we can use the fact that the angle subtended by an arc at the center of the circle is twice the angle subtended by it at any point on the circumference.
Hence, we can say that:∠EAF = 1/2(arc EF)∠EBF = 1/2(arc EF)Since arc EF is the arc subtended by the angle EAFEBF, which is equal to the difference of the angles subtended by the same arc at the center of the circle, we can say that:arc EF = 360° - ∠EAFEBF = 360° - ∠EAF - 135°Now, we can substitute the value of arc EF and the measures of ∠EAF and ∠EBF in the above equations to get the values of both angles.
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Jessica is trying to pack up her apartment and has a wall map that is 11 feet long when she rolls it up. Will it fit diagonally into her storage bin that is 8 feet long, by 6 feet wide, and 2 feet tall.
Given that Jessica has a wall map of length 11 feet and a storage bin with length 8 feet, width 6 feet, and height 2 feet. We have to determine if the wall map can fit diagonally into the storage bin. Diagonal of the storage bin = √(l²+w²+h²)
where l, w, and h are the length, width, and height of the bin respectively. The data collected through a census is used for a variety of purposes, including public policy-making, resource allocation, and research. To ensure that a census provides accurate and reliable data, it is necessary to sample the entire population. This means that every individual in the population must be included in the census sample.
In other words, a census is a complete enumeration of all the people living in a given area. Diagonal of the storage bin = √(8²+6²+2²) = √(64+36+4) = √104 feet Now, the length of the wall map is 11 feet, which is greater than the diagonal of the storage bin. The data collected through a census is used for a variety of purposes, including public policy-making, resource allocation, and research. To ensure that a census provides accurate and reliable data, it is necessary to sample the entire population. So, the wall map won't fit diagonally into the storage bin. Hence, the wall map won't fit diagonally into her storage bin.
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Which equation represents a line that is perpendicular to the line represented by 2 x minus y equals 7 ?
The equation represents a line that is perpendicular to the line represented by 2x − y = 7 is y = −(1/2)x + b
The equation represents a line that is perpendicular to the line represented by 2x − y = 7 is y = 2x + b.
Explanation: The given equation of line is 2x − y = 7.
We can rearrange the given equation of line in slope-intercept form, y = mx + b ,
where m is the slope of the line and b is the y-intercept of the line.
Rewrite the given equation of line, 2x − y = 7, in slope-intercept form:
First, add y to both sides of the equation to isolate the variable y:
2x − y + y = 7 + y
Simplify to get: 2x = y + 7
Then, subtract 7 from both sides to isolate y.
So, 2x − 7 = y or y = 2x − 7
We now have the slope-intercept form, where m = 2 is the slope and b = −7 is the y-intercept of the line.
Thus, the slope of the line 2x − y = 7 is m = 2.
Now, to find the equation of line that is perpendicular to 2x − y = 7, we need to flip the sign of the slope and switch the places of m and n (as the product of slopes of two perpendicular lines is −1).
Therefore, the slope of the line that is perpendicular to the line 2x − y = 7 is m = −1/2 (flip the sign of the slope) and
the equation of the line can be written as: y = −(1/2)x + b.
So, the answer is: The equation represents a line that is perpendicular to the line represented by 2x − y = 7 is y = −(1/2)x + b.
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Find the length of the arc, s, on a circle of radius r intercepted by a central angle 0 Express arc length in terms of Then round your answer to two decimal places
Radius, r= 5 feet, Central angle, o = 230°
S
feet
(Simplify your answer. Type an exact answer in terms of Use integers or fractions for any numbers in the expression)
S = feet
(Round to two decimal places as needed.)
The length of the arc intercepted by a central angle of 230° on a circle with a radius of 5 feet is approximately 4.02 feet.
To find the length of the arc, denoted as s, on a circle with radius r intercepted by a central angle θ, we can use the formula:
s = (θ/360°) * 2πr
Given:
Radius, r = 5 feet
Central angle, θ = 230°
Substituting the values into the formula, we have:
s = (230°/360°) * 2π * 5
Simplifying the expression:
s = (23/36) * 2π * 5
s = (23/36) * 10π
s = (23/18)π
To round the answer to two decimal places, we can approximate the value of π as 3.14:
s ≈ (23/18) * 3.14
s ≈ 4.02 feet
Therefore, the length of the arc intercepted by a central angle of 230° on a circle with a radius of 5 feet is approximately 4.02 feet.
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