A pole 8 feet tall is used to support a guy wire for a tower, which runs from the tower
to a metal stake in the ground. After placing the pole, Mav measures the distance
from the pole to the stake and from the pole to the tower, as shown in the diagram
below. Find the length of the guy wire, to the nearest foot.
8 ft
H24 ft +
(Diagram is not to scale.)

The better deal is 12 donuts for $10 because the unit rate is $0.83.

Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In order to determine the unit price, we would determine the unit price for number of donuts by using the following mathematical expression;

Unit price = Cost of donuts/Number of donuts

Substituting the given parameters into the unit price formula, we have the following;

Unit price = $10/12

Unit price = $0.83.

For the second deal, we have:

Unit price = $6/6.99

Unit price = $0.86.

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Answer: 164

Step-by-step explanation: (16 X 8) + (6 X 5)+ (^^triang)+ 164

Patrick bought 4 times the number of beans in each bag.

What is expressions ?

An expression is a combination of one or more numbers, variables, and operations. It can contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can be evaluated to obtain a numerical result or simplified by combining like terms or using mathematical rules.

To find an expression that shows how many beans Patrick bought, you can multiply the number of bags by the number of beans in each bag.

So, if Patrick bought 4 bags of beans, and there are b beans in each bag, then the expression would be:

4b

This means that Patrick bought 4 times the number of beans in each bag.

Therefore, Patrick bought 4 times the number of beans in each bag.

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S = 30 - 0.15(30) or S = 0.85 can be used to calculate the sale price S of an oil change (30).

By resolving this equation, we find that the value of the variable x is 7. An equation is a mathematical formula that states that two quantities or values are equal, as in the example 6 x 4 = 12 x 2.

S will serve as a stand-in for the sale price of the oil change.

Mr. Allen has a 15% off voucher, and the oil change normally costs $30. The reduction can be shown as 15% of the standard price, or:

0.15 * $30 = $4.50

We can deduct the discount from the list price to determine the oil change's selling price:

S = $30 - $4.50

S = $25.50

As a result, S = 30 - 0.15 can be used to calculate the sale price S of an oil change (30)

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Answer:

The answer is  s=0.85*30=22.50(final sale price)  which will be 15 % of the 30 dollars

Step-by-step explanation:

Answer:

20/125 is the answer

Step-by-step explanation:

The surface area of the shape when a cube is taken out of it would be = 164.

The surface area is defined as the area that is being occupied by outer surface of a shape of object.

The surface area of a given shape = 314

An area of a cube shape is taken out of it with sides = 5×5

The area of a cube = 6(a²)

where a = 5

area of the cube = 6(5²)

= 6×25 = 150

Therefore, the surface area of the shape after area of cube such as = 150 has been removed from it ;

= 314-150

= 164.

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By answering the above question, we may infer that The equation's answer is B) 60 ft.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

What is the distance between the bases on a softball field

A) 50 ft

B) 60 ft

C) 70 ft

D) 80 ft

The answer is B) 60 ft.

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The value of area of triangle ABC is found as 11.42 sq. unit.

Area of a triangle = ½ × base × height.

From the given data:

Using trigonometric function.

tan 25 = 7 / AC

AC  = 7*tan 25

AC = 3.26

Area of  triangle ABC = ½ × 7× 3.26

Area of  triangle ABC = 11.42

Thus, the value of  area of triangle ABC is found as 11.42 sq. unit.

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Answer:

It seems like there is a mistake in the variable provided. The variable mentioned is "Gender" but the data provided is about "Age" and "f" (frequency). Assuming that "f" is the frequency of participants at each age, here are the answers to your questions:

For the variable "f", the most appropriate measure of central tendency would be the mode, which represents the most frequently occurring value. For the variable "Age", the most appropriate measure of central tendency would be the median, as it is less affected by outliers than the mean.

Mode = 8; Median = 11; Mean = 10.11 (rounded to two decimal places)

Range = 15 - 7 = 8; Variance = 8.99 (rounded to two decimal places); Standard deviation = 2.99 (rounded to two decimal places)

To calculate the age range that reflects 68% of the sample, we need to find the mean age and the standard deviation. The mean age is 10.11, and the standard deviation is 2.99. 68% of the data falls within one standard deviation of the mean. Using the empirical rule, we can say that the ages of participants that reflect 68% of the sample are between (10.11 - 2.99) and (10.11 + 2.99), which is between 7.12 and 13.10.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the variable Gender is not given in the data, we cannot compute any measure of central tendency for it. For the variable Age, the most appropriate measure of central tendency would be the mode, since all the observations have the same value for this variable.

To calculate the mode, median and mean for Age, we can first arrange the data in ascending order of age:

7, 2

8, 2

9, 0

10, 1

11, 1

12, 1

13, 1

14, 1

15, 1

The mode is the most frequently occurring value, which is 1 for all ages. The median is the middle value when the data is arranged in ascending order. Since there are 9 observations, the median is the average of the 5th and 6th values, which are 12 and 13. So, the median is (12+13)/2 = 12.5. The mean is the sum of all the values divided by the number of observations, which is:

(72 + 82 + 90 + 101 + 111 + 121 + 131 + 141 + 15*1) / 9 = 11.44 (rounded to two decimal places)

Therefore, the mode is 1, the median is 12.5 and the mean is 11.44.

To calculate the range, variance and standard deviation for Age, we can use the following formulas (assuming the data is a population):

Range = maximum value - minimum value = 15 - 7 = 8

Mean = 11.44 (computed in step 2)

Variance = Σ(x - μ)^2 / N, where μ is the mean, x is each value, and N is the number of observations. Plugging in the values, we get:

Variance = [(7-11.44)^2 + (8-11.44)^2 + (9-11.44)^2 + (10-11.44)^2 + (11-11.44)^2 + (12-11.44)^2 + (13-11.44)^2 + (14-11.44)^2 + (15-11.44)^2] / 9 = 5.72 (rounded to two decimal places)

Standard deviation = square root of variance = √5.72 = 2.39 (rounded to two decimal places)

Therefore, the range is 8, the variance is 5.72, and the standard deviation is 2.39.

Since the data is approximately normally distributed, we can use the empirical rule to estimate the ages that reflect 68% of the sample. According to the empirical rule, 68% of the data falls within one standard deviation of the mean. So, we can compute the lower and upper limits of this range by subtracting and adding one standard deviation from the mean, respectively:

Lower limit = mean - standard deviation = 11.44 - 2.39 = 9.05 (rounded to two decimal places)

Upper limit = mean + standard deviation = 11.44 + 2.39 = 13.83 (rounded to two decimal places)

Therefore, the ages of participants that reflect 68% of the sample are between 9.05 and 13.83 years old.

Answer:

64%

Step-by-step explanation:

Convert a fraction to a decimal and move the decimal point to make a percent

The response to the given question would be that As a result, there is a probability 1.3% chance (or about 0.013) that a random sample of 50 seniors will have a mean score of no higher than 415.

Calculating the chance that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all possible outcomes when a certain event occurs.

The sample mean's sampling distribution may be approximated using the central limit theorem as having a mean of 425 and a standard deviation of[tex]80\sqrt(50) = 11.31.[/tex]

z is equal to (x - mu) / (sigma / sqrt(n))

where n is the sample size, x is the sample mean, mu is the population mean, sigma is the population standard deviation.

When we enter the values, we obtain:

[tex]z = (415 - 425) / (80\sqrt(50)) = -2.23[/tex]

As a result, there is a 1.3% chance (or about 0.013) that a random sample of 50 seniors will have a mean score of no higher than 415.

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The probability that the next person will purchase no costume is 0.13.

It is a branch of mathematics that deals with the occurrence of a random event.

The total number of visitors to the website in a single day is:

38 + 239 + 12 = 289

Of these visitors, we know that 38 purchased no costume.

Therefore, the probability that the next person to visit the website will also purchase no costume is:

38/289 = 0.13

Hence, the probability that the next person will purchase no costume is approximately 0.13, or 13% to the nearest hundredth.

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Answer:

21 miles per gallon

Step-by-step explanation:

find the gradient of the line:

change in y = 105 - 21 = 84

change in x = 5 - 1 = 4

gradient is change in y/ change in x

= 84/4 = 21

hi

im pretty sure the answer is

a. numerators

hope this helps

good luck;)

Answer:

A

Step-by-step explanation:

You have to add the numerator and keep the denominators the same! :)

Answer: 6 cups of flour = 4 cups of sugar

              9 cups of flour = 6 cups of sugar

             12 cups of flour = 9 cups of sugar

Step-by-step explanation:

Well, if Kurt uses 3 cups of flour for every 2 cups of sugar, than for every 6 cups of flour, he would need 4 cups of sugar. With 9 cups of flour, he would need 6 cups of sugar. For 12 cups of flour, he would need 9 cups of sugar.

The length of segment in the given circle x is 5 cm.

A circle is formed by all points in a plane that are at a particular distance from the centre. The radius of a circle is the separation between any point on the circle and its center.

The product of the measures of the secant segment and its external secant segment equals the square of the measure of the tangent segment if a tangent segment from a location outside the circle, secant segments are drawn.

In the circle shown, if

AB=6cm

AC=4cm and

CD=x?

AC×AD=[tex]AB^{2}[/tex]

4(4+x)=[tex]6^{2}[/tex]

4+x=36/4

x=5

Hence, The length of segment in the given circle x is 5cm.

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The diagram shows the quantity x is 13.

A tape diagram, also known as a bar model or a strip diagram, is a visual representation of a problem or situation that helps students to organize and solve mathematical problems. It involves drawing a rectangular strip or bar to represent a quantity or a value, and then dividing or labeling the strip to represent different parts of the problem.

The full completed question is related to an equation as shown in the below diagram (Check it).

Given equation is x+4 = 17

If we select part 'a' the diagram is shown in the below diagram, see it.

For part 'b' the quantity x can be represent by:

x+4 = 17

x = 17 - 4

x = 13

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Answer: Marginal cost is the added cost to produce an additional good or the increase in production costs generated by the production of additional product units

Step-by-step explanation:  It is calculated by taking the total change in the cost of producing more goods and dividing that by the change in the number of goods produced.

Answer:

So it's basically the cost added by producing one extra unit of a product or service. I hoped this helped and if you need a better explanation let me know!

Answer:

(4,1)

Step-by-step explanation:

(4,1) is the answer

The function which has the same zeros as h(x) = (x² - 4)(x² - 9) is f(x) = (x - 2)(x + 2)(x - 3)(x + 3).

To determine which function has the same zeros as h(x) = (x² - 4)(x² - 9), we need to first find the zeros of h(x).

The zeros of h(x) are the values of x that make h(x) equal to zero.

h(x) = (x² - 4)(x² - 9)

h(x) = 0 if and only if (x² - 4) = 0 or (x² - 9) = 0

Solving for x, we get -

x² - 4 = 0 -> x = ±2

x² - 9 = 0 -> x = ±3

So, the zeros of h(x) are x = ±2 and x = ±3.

Now, we need to find the function that has the same zeros.

A function that has the same zeros will have the same factors of (x - 2), (x + 2), (x - 3), and (x + 3).

One such function is -

f(x) = (x - 2)(x + 2)(x - 3)(x + 3)

Therefore, this function has the same zeros as h(x) = (x² - 4)(x² - 9).

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Answer:

Step-by-step explanation:

The supply of the supply of eggs is changing at 10.7¢ per carton per week

The equation of the function is given as

625p^2 - x^2 = 100

When the supply is 37000, we have

x = 37

So, the equation becomes

625p^2 - 37^2 = 100

Evaluate

625p^2 - 1369 = 100

This gives

625p^2 = 1469

Divide by 625

p^2 = 2.3504

Take the square roots of both sides

x = 1.53

The supply rate is then calculated as

Rate = 7¢ * 1.53

Evaluate

Rate = 10.7¢

Hence, the supply is changing at 10.7¢ per carton per week

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Answer:

I think is D'C becausse everything goes back words

Answer:

What is the unit price of each battery in each package?

To find the unit price of each battery in each package, we need to divide the total cost of each package by the number of batteries in each package.

For the package of 8 count AA batteries:

Total cost: $6.16

Number of batteries: 8

Unit price = Total cost / Number of batteries = $6.16 / 8 = $0.77 per battery

For the package of 20 count AA batteries:

Total cost: $15.20

Number of batteries: 20

Unit price = Total cost / Number of batteries = $15.20 / 20 = $0.76 per battery

Therefore, the unit price of each battery in the package of 8 count AA batteries is $0.77, and the unit price of each battery in the package of 20 count AA batteries is $0.76.

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Step-by-step explanation:

To find the unit price of each battery in each package, we need to divide the total cost of each package by the number of batteries in each package.

For the package of 8 count AA batteries:

Total cost: $6.16

Number of batteries: 8

Unit price = Total cost / Number of batteries = $6.16 / 8 = $0.77 per battery

For the package of 20 count AA batteries:

Total cost: $15.20

Number of batteries: 20

Unit price = Total cost / Number of batteries = $15.20 / 20 = $0.76 per battery

Therefore, the unit price of each battery in the package of 8 count AA batteries is $0.77, and the unit price of each battery in the package of 20 count AA batteries is $0.76.

Using arithmetic operation, the statement that is true is -

A: The 20-count pack of AA batteries has a lower unit price of $0.78 per battery.

D: The 8-count pack of AA batteries has a lower unit price of S0.77 per battery

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

To find the unit price per battery, we divide the cost of each package by the number of batteries in the package.

For the 8-count pack -

Use the arithmetic operation of division.

Unit price per battery = $6.16 / 8 batteries = $0.77 per battery

For the 20-count pack -

Use the arithmetic operation of division.

Unit price per battery = $15.60 / 20 batteries = $0.78 per battery

Therefore, the statements A and D are correct.

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The value of x that makes the equation true is 2.25.

A mathematical model is an abstract, mathematically based description of a physical system. Mathematical modelling is the process of creating a mathematical model. Both applied mathematics and the natural sciences employ mathematical models. The area of operations research is largely concerned with using mathematical models to resolve issues in commercial or military operations.

Using the figure we see that, for the left model we have:

3 (-x) = -3x.

Also, we have 10(1) = 10

Thus the left model has the equation:

-3x + 10

For the right model we have:

5x - 8

Equate the two models:

-3x + 10 = 5x - 8

18 = 8x

x = 2.25

Hence, the value of x that makes the equation true is 2.25.

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The solution is : the predicted blood pressure for a person aged 64 will be : 156.

A quadratic equation is a second-order polynomial equation in a single variable x ; ax^2+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution.

here, we have,

Given the data:

Age (X) :

38

41

45

48

51

53

57

61

65

Pressure(Y) :

116

120

123

131

142

145

148

150

152

From the data, we could obtain a regression equation to mod the data Given using a linear regression calculator :

The regression equation obtained is :

y = 1.48769X + 60.46103

Using the model, the predicted blood pressure for a person aged 64 will be :

y = 1.48769(64) + 60.46103

y = 95.21216 + 60.46103

y = 155.67319

y = 156 (nearest whole number)

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The best predicted value of y for the given x=41 is 121.45.

The correlation coefficient describes how one variable moves in relation to another. A positive correlation indicates that the two move in the same direction, with a value of 1 denoting a perfect positive correlation. A value of -1 shows a perfect negative, or inverse, correlation, while zero means no linear correlation exists.

Given that,

X= 38 41 45 48 51 53 57 61 65

Y= 116 120 123 131 142 145 148 150 152

∑x= 459

∑y= 1227

∑x²= 24059

∑y²= 168843

∑xy= 63544

Sxx= ∑x²-∑x²/n

= 24059-459²/9

= 650

Sxy = ∑xy-(∑x·∑y)/n

= 63544-(459×1227)/9

= 63544-62577

= 967

Now, slope =967/650= 1.488

Mean of x=459/9 =51

Mean of y=1227/9 = 136.33

Now, intercept is b=136.33-(1.488×51)

= 60.442

Here, the equation of a line is y=1.488x+60.442

When x=41, we get

y=1.488×41+60.442

y= 121.45

Therefore, the best predicted value of y is 121.45.

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Answer:

Ignore my handwriting loll

Step-by-step explanation:

Hope this helps! :)

Answer:

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

Step-by-step explanation:

o find the equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) using implicit differentiation, we can follow these steps:

Differentiate both sides of the equation with respect to x:

cos(x+y) * (1 + dy/dx) = 4 - 4dy/dx

Simplify by grouping the terms with dy/dx on one side and the rest on the other side:

cos(x+y) * (1 + dy/dx) + 4dy/dx = 4

Substitute x = π and y = π, since we want to find the equation of the tangent line at the point (π,π):

cos(2π) * (1 + dy/dx) + 4dy/dx = 4

Simplify:

-5dy/dx = 4 - cos(2π)

dy/dx = -4/5

Use the point-slope form of the equation of a line to write the equation of the tangent line:

y - π = (-4/5)(x - π)

Simplify:

y = (-4/5)x + (8/5) + π

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

Answer:

[tex] \frac{25}{2} [/tex]

Step-by-step explanation:

Given 15 ÷6/5

[tex]15 \div \frac{6}{5} \\ = > 15 \times \frac{5}{6} \\ = > 5 \times \frac{5}{2} \\ = > \frac{25}{2} \\ therefore \: the \: answer \: is \: \frac{25}{2} \\ this \: is \: because \: it \: cannot \: be \: broken \: down \: into \: lowest \: term \: again[/tex]

Answer:

3y²+6y-2y²+3y

collect like terms

3y²-2y²+6y+3y

5y²+9y