8. The top of a building is 20 feet tall. If a fireman has a ladder that is 24 feet long, how far out
does the ladder need to be placed from the bottom of the wall to reach the top of the
building?

By making and solving the equations we know that the number of children and adults that swam at the pool is 350 and 335 respectively.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others. Let's learn more about math equations in this tutorial.

For instance, a formula might be 3x - 5 = 16.

After solving this equation, we learn that the value of the variable x is 7.

So, make equations as follows:

c + a = 685 (1)

c = 685 - a

Now, substitute c = 685 - a in the 2nd equation as follows:

1.75c + 2a = 1.282.50 (2)

1.75(685 - a) + 2a = 1,282.50

1,198.75 - 1.75a + 2a = 1,282.50

0.25a = 83.75

a = 83.75/0.25

a = 335

Then, the children:

c = 685 - a

c = 685 - 335

c = 350

Therefore, by making and solving the equations we know that the number of children and adults that swam at the pool is 350 and 335 respectively.

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Answer:

I don't know yet bye

Step-by-step explanation:

The exponential regression equation that models the data is y = 101 × (0.899)ˣ and when the air pressure is 29 kPa, the altitude is 6.09 km.

To find an exponential regression equation that models the given data, we can use the general form:

y = abˣ

where y is the air pressure and x is the altitude.

Using the provided data, we can substitute the values of x and y into the equation to obtain a system of equations:

When x = 0, y = 101:

101 = ab⁰

101 = a

When x = 1, y = 90:

90 = ab¹

90 = ab

90=101b

Divide both sides by 101:

b=90/101

b= 0.899

Therefore, the exponential regression equation that models the data is:

y = 101 × (0.899)ˣ

To determine the altitude when the air pressure is 29 kPa, we can substitute y = 29 into the equation and solve for x:

29 = 101 × (0.899)ˣ

Dividing both sides by 101:

0.287 = (0.899)ˣ

log(0.287) = log((0.899)ˣ)

log(0.287) = x × log(0.899)

x = log(0.287) / log(0.899)

x = 6.093.

Hence, when the air pressure is 29 kPa, the altitude is 6.09 km.

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The table below gives air pressures in kPa at selected altitudes above sea level measured in

kilometers.

x      Altitude                    0             1              2              3             4             5

y      Air pressure         101         90            79         70           62         54

Write an exponential regression equation that models these data rounding all values to the nearest

thousandth.

Use this equation to algebraically determine the altitude, to the nearest hundredth of a kilometer,

when the air pressure is 29 kPa.

18x+30

Step-by-step explanation:

O think That's the answer...

The first and second lengths are not possible lengths of triangle.

The third and fourth lengths are possible lengths of triangle.

For the first case; 3 ft, 5 ft, 9 ft: Not possible. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. However, in this case, 3 ft + 5 ft = 8 ft, which is less than 9 ft.

For the second case. 11 cm, 6 cm, 17 cm: Not possible. Using the same reasoning as above, we see that 6 cm + 11 cm = 17 cm, which means that the three sides cannot form a triangle.

For the third case. 4 in., 4 in., 6 in.: Possible. The sum of any two sides is greater than the third side, since 4 in. + 4 in. = 8 in., which is greater than 6 in. Therefore, these lengths can form a triangle.

For the fourth case. 16 yd, 10 yd, 12 yd: Possible. Again, we see that the sum of any two sides is greater than the third side, since 10 yd + 12 yd = 22 yd, which is greater than 16 yd. Therefore, these lengths can form a triangle.

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Answer:

Step-by-step explanation:

Part A: The population for this sample survey is all people who live in Virginia, and the sample is the random group of 48,548 people who were interviewed for the survey.

Part B: One method that could have been used to obtain the random sample is simple random sampling. This involves selecting individuals from the population at random, so that each person in the population has an equal chance of being selected. This can be done using a random number generator or by selecting names from a list of the population.

Part C: It's difficult to say whether the estimates are close to the truth about the entire population without more information about the survey methodology and potential sources of bias. However, assuming that the survey was conducted using sound sampling techniques and that the sample is representative of the population, it's possible that the estimates are reasonably accurate. Nevertheless, it's important to keep in mind that survey estimates always have some degree of sampling error, so the true population values could be slightly different from the survey results. Additionally, the survey may not capture people who don't have access to healthcare or who choose not to seek medical care, so the estimates may not be fully representative of the entire population.

Answer: Part A: The population for this sample survey is all people who live in Virginia, while the sample is the 48,548 people who were interviewed in the Virginia Health Survey.

Part B: One method that could have been used to obtain the random sample is simple random sampling. This involves randomly selecting individuals from the population using a random number generator or other randomization method to ensure that each member of the population has an equal chance of being selected. Another method could be stratified random sampling, which involves dividing the population into strata based on relevant characteristics (such as age or income), and then randomly selecting individuals from each stratum in proportion to their representation in the population.

Part C: It is difficult to determine whether these estimates are close to the truth about the entire population without additional information. However, if the sample was selected using appropriate sampling methods (such as simple random sampling or stratified random sampling) and had a large enough sample size, then the estimates are likely to be relatively accurate. The margin of error, which depends on the sample size and variability in the population, can also be calculated to provide an estimate of the range in which the true population value is likely to fall. Overall, the accuracy of the estimates will depend on the quality of the sampling method used, the size of the sample, and the representativeness of the sample in relation to the population.

The linear equation that has no solutions with y = (5/4)x - 7 is

2y = (5/2)x - 14

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

y = (5/4)x - 7

We can create a linear equation that has no solutions with y = (5/4)x - 7.

Step 1:

y = (5/4)x - 7

Multiply 2 on both sides.

2y = (5/2)x - 14

Thus,

2y = (5/2)x - 14 is the linear equation that has no solutions with the given equation.

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Answer:

3.00000000000

Step-by-step explanation:

2.77247497343 is closer to 3.00000000000 than 2.00000000000

Answer:

Step-by-step explanation:

La ecuación y = -7x - 5 es una ecuación lineal en la forma y = mx + b, donde "m" es la pendiente y "b" es el punto de intersección en el eje y. Por lo tanto, podemos identificar la pendiente y el punto de intersección de la línea directamente de la ecuación.

Pendiente:

La pendiente "m" de la línea se encuentra en el coeficiente que acompaña a "x" en la ecuación de la línea. En este caso, la pendiente es "-7", por lo que la pendiente de la línea es -7.

Punto de intersección:

El punto de intersección "b" se encuentra en el término independiente de la ecuación de la línea, que es el número que no tiene una "x" al lado. En este caso, el punto de intersección es "-5", por lo que la línea cruza el eje y en el punto (0,-5).

Por lo tanto, la pendiente de la línea es -7 y el punto de intersección es (0,-5).

Answer: Y-intercept: -5, Slope of the line: -7 or -7/1

Step-by-step explanation:

The equation for the slope is y=mx+b.

m= slope of the line

b= y-intercept

So when you take the equation y=-7x-5, you take out those plugged in values.

So the slope of the line is -7 (or -7/1) and the y-intercept is -5.

The key features of this rational function include the following:

Domain: (-∞, -1) ∪ (-1, ∞)

Range: (-∞, -2) ∪ (-2, ∞)

Y-intercept: 1.

X-intercept: 1/2.

Vertical asymptote: x = -1.

Horizontal asymptote​: y = -2.

In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).

In order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines.

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Answer:

Below

Step-by-step explanation:

The quations are both equal to 'y'  so the equations are equal

5x-10 = -3x+ 14

8x = 24

x = 3     <====== use this value of 'x' in one of the equations to calculate y

y = 5x-10

y = 5(3)-10 = 5  

Answer:

Photo below.

Step-by-step explanation:

Red Line = y=3x−3/4

Blue Line =  y=−x/3−3/2

Hope it helped!

Answer: (2,1.6)

y=1.6

Step-by-step explanation:

you have the x coordinate, so that means x=2.

Plug in values for x:

5(2) + 5y = 18

10 + 5y = 18

Solve for y.

Answer:

The missing coordinate is 1.6.

Step-by-step explanation:

A coordinate is two points, x value and y value, on a graph. Ex: 1, 4. 1 is on the x axis, and 4 is on the y axis. In some Math problems, the point in the x value will be replaced with x.

5x + 5y = 18

5(2) + 5y = 18

10 + 5y = 18

10 - 10 + 5y = 18 - 10

5y = 8

5y/5 = 8/5

y = 1.6

To check this, we need to input 2 and 1.6 into the original problem.

5(2) + 5(1.6) = 18

10 + 5(1.6) = 18

10 + 8 = 18

18 = 18

This is true, so we know 1.6 is correct.

To construct a 2x2 matrix B such that AB is the zero matrix, we need to find two different nonzero columns for B that will result in the product of AB being the zero matrix. One way to do this is to choose the columns of B such that they are the negatives of the rows of A. This will result in the product of AB being the zero matrix.

Let A = [[a,b],[c,d]]

We can choose the columns of B to be [[-a,-c],[-b,-d]]. This will result in the product of AB being the zero matrix.

So, B = [[-a,-b],[-c,-d]]

AB = [[a,b],[c,d]] * [[-a,-b],[-c,-d]] = [[0,0],[0,0]]

Therefore, the 2x2 matrix B that will result in the product of AB being the zero matrix is B = [[-a,-b],[-c,-d]].

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Answer: Using the formula F=9/5C+32, we can convert 59°C to degrees Fahrenheit:

F = 9/5 * 59°C + 32

F = 118.2°F + 32

F ≈ 150.8°F

Therefore, 59°C is approximately equal to 150.8°F.

Step-by-step explanation:

The standard deviation of the movie times is given as follows:

27.7 minutes.

Considering that an hour has 60 minutes, the time in minutes of each movie is given as follows:

107 minutes, 92 minutes, 134 minutes, 116 minutes, 152 minutes, 182 minutes.

The mean of a data-set is given by the sum of all observations divided by the number of observations, hence:

Mean = (107 + 92 + 134 + 116 + 152 + 182)/6

Mean = 130.5 minutes.

The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, hence:

s = sqrt([(107-130.5)² + (92-130.5)² + (134-130.5)² + (116-130.5)² + (152-130.5)² + (182-130.5)²]/7)

s = 27.7 minutes.

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18x+30 is the solution of the expression which we get by adding all the expressions.

An expression is combination of variables, numbers and operators.

The given expressions from 1 to 9 are -4(x-5), 6(x+1), 4x-20,3x+12, -1(x-9), -x-12, 8-x, -2x, 7(2x+1)

Add all the nine expressions.

-4(x-5)+6(x+1)+4x-20+3x+12-1(x-9)-x-12+8-x -2x+ 7(2x+1)

-4x+20+6x+6+4x-20+3x+12-x+9-x-12+8-x-2x+14x+7

Combine the like terms

18x+30

Hence, 18x+30 is the solution of the expression which we get by adding all the expressions.

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you would save $6,000 in annual fuel expenses.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given,  you drive 40,000 miles per year and gas averages $4 per gallon

Since,

Fuel expenses = (Miles driven / Miles per gallon) x Price per gallon

For the SUV, with an average of 16 miles per gallon, the fuel expenses would be:

Fuel expenses for SUV = (40,000 / 16) x 4 = $10,000

For the hybrid car, with an average of 40 miles per gallon, the fuel expenses would be:

Fuel expenses for hybrid car = (40,000 / 40) x 4 = $4,000

To find the difference in fuel expenses between the two vehicles, we subtract the fuel expenses for the hybrid car from the fuel expenses for the SUV:

$10,000 - $4,000 = $6,000

Therefore, by owning a hybrid car averaging 40 miles per gallon instead of an SUV averaging 16 miles per gallon, you would save $6,000 in annual fuel expenses.

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A) the z-critical value associated with a 99% confidence interval is 2.58. B) the z-critical value associated with a 95% confidence interval is 1.96. C) the z-critical value associated with a 90% confidence interval is 1.64. D)  the z-critical value associated with an 80% confidence interval is 1.28.

The z-critical value (or the critical z-value) is the number of standard deviations from the mean that corresponds to a given level of significance in a two-tailed z-test. It is used in statistical hypothesis testing to determine whether to reject or fail to reject the null hypothesis.

A) For a 99% confidence interval, the area in each tail is (1-0.99)/2 = 0.005. Using the provided tool and selecting "two tails", we can find the z-critical value associated with this probability:

z-critical value = 2.58

Therefore, the z-critical value associated with a 99% confidence interval is 2.58.

B) For a 95% confidence interval, the area in each tail is (1-0.95)/2 = 0.025. Using the provided tool and selecting "two tails", we can find the z-critical value associated with this probability:

z-critical value = 1.96

Therefore, the z-critical value associated with a 95% confidence interval is 1.96.

C) For a 90% confidence interval, the area in each tail is (1-0.90)/2 = 0.05. Using the provided tool and selecting "two tails", we can find the z-critical value associated with this probability:

z-critical value = 1.64

Therefore, the z-critical value associated with a 90% confidence interval is 1.64.

D) For an 80% confidence interval, the area in each tail is (1-0.80)/2 = 0.10. Using the provided tool and selecting "two tails", we can find the z-critical value associated with this probability:

z-critical value = 1.28

Therefore, the z-critical value associated with an 80% confidence interval is 1.28.

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Answer:

X=4.5, or X=4 1/2

Step-by-step explanation:

Answer:

4095 yd³

The volume of any figure is the total space enclosed inside of any figure. For example, the total space inside the cube is the volume of the cube. The formula to find the volume of a cube is (side)³ or (side)(side)(side) Please also note that volume is usually labelled in cubic units.

Here, we are given a figure that is 3-dimensional. Therefore, the volume of this 3-dimensional figure must be in cubic units. We can also see that the figure has been split into two 3-dimensional figures. Thus, the sum of those divided 3-dimensional figures will result in the volume of the figure.

Step-1) Find the volume of both 3-dimensional figures:

Volume of cuboid = Length × Width × Height

Volume of trapezoidal prism = Area of base × Length

Step-2) Add the volumes of both prisms.

Volume of figure = Volume of cuboid + Volume of trapezoidal prism

Volume of figure = 1890 yd³ + 2205 yd³ = 4095 yd³

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Answer:

14

Step-by-step explanation:

So, 49 divided by 7 is 7 so there are 7 groups of 7 strawberries. With each of those 7 groups there are 2 blueberries. So, you are then going to multiply 7 by 2 and that gives you 14 blueberries.

So Katya's rectangular table is 1.6 meters long and 3/4 meters wide, with an area of 1 1/5 square meters.

Area is a measure of the size of a two-dimensional surface, such as the surface of a shape or object. It is usually measured in square units, such as square meters, square centimeters, square feet, or square inches. The area of a shape tells us how much surface area it covers, and is often used in a variety of fields, such as architecture, engineering, and physics. For example, the area of a room can help determine how much flooring is needed to cover it, the area of a building facade can help determine how much material is needed to cover it, and the area of a wing can help determine its lift and drag characteristics in aerodynamics.

Here,

Let's start by using the formula for the area of a rectangle:

A = lw

where A is the area, l is the length, and w is the width.

We are given that the width of the table is 3/4 meters, so we can substitute this value into the formula and simplify:

A = l(3/4)

l = (4/3)A

Next, we are told that the table has an area of 1 1/5 m^2. We can convert this mixed number to an improper fraction by multiplying the whole number by the denominator and then adding the numerator:

1 1/5 = (5*1 + 1)/5 = 6/5

So the area of the table is 6/5 m^2. Substituting this value for A in the formula above, we get:

l = (4/3)(6/5)

l = 8/5 m

Therefore, the length of the table is 8/5 meters, or 1.6 meters when converted to a decimal.

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The most accurate calculation for the product of 2, 9, and 11, is 1, or 0 + 1.

Best estimate refers to the figure arrived at by an assessor using deterministic techniques that most accurately captures the anticipated result without optimism or conservatism.

To estimate a number is to round it up to the nearest full number.

We now have February 9 and November 11.

Hence, as 2/9 is closer to 0 than 0.5, we will estimate it to be 0.

Similarly, we will estimate 10/11 as 1 since it is closer to 1 than 0.5.

Hence, 0 + 1 = 1 is the result of adding up their estimates.

In conclusion, 0 + 1 = 1 is the best estimate for the product of the numbers 2/9 and 10/11.

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Answer:

112cm³

Step-by-step explanation:

Let us ignore the bottom part of the figure and first find only the volume of the cuboid at the top

from the figure we know that

length of the cuboid is 10 cm

Width is 2 cm

height is 5 cm

now the formula for Volume of cuboid is Length×Width×Height

so,

Volume of the Upper Cuboid = 10×2×5= 100cm³ ---(1)

Now we will ignore the cuboid on top and find the volume of the one at the bottom

From the figure, we know that its dimensions are

length = 2cm

height = 3cm

width = 2cm

Volume of the lower cuboid = 2×2×3 = 12cm³ ---(2)

Adding (1) and (2)

100cm³ + 12 cm³ = 112cm³

Therefore the volume of the given figure is 112cm³

The volume of the box is 112 cm³.

We have,

The figure can be considered as two boxes.

Now,

One box:

Volume.

= Length x Width x height
= 10 x 2 x 5

= 100 cm³

Another box:

Volume.

= Length x Width x height
= 2 x 2 x 3

= 12 cm³

Now,

The volume of the box.

= 100 + 12

= 112 cm³

Thus,

The volume of the box is 112 cm³.

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Answer:

3

Step-by-step explanation:

Amplitude is the absolute value of the number in front

3cos(2x) + 5

The volume of the stump in cubic inches is approximately 2,214.53 cubic inches

First, we need to convert the height of the stump from feet to inches, since the radius is given in inches:

1.3 ft = 15.6 in

Next, we can use the formula for the volume of a cylinder:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

We are given the radius as 6 in and the height as 15.6 in, so we can plug in these values and simplify:

V = π(6 in)^2(15.6 in)

V = π(36 in^2)(15.6 in)

V = 2,214.53 cubic inches (rounded to two decimal places)

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y = -3/2 x + 24. is the equation of the line in slope intercept form.

The formula for calculating the equation of a line in point slope form is expressed as:

y - y0 = m(x - x0)

where:

m is the slope

(x0, y0) is the point on the line

Using the coordinate points (2, 9) and (4, 6). The slope is calculated as:

Slope = 6-9/4-2
Slope = -3/2

The required equation will therefore be expressed as:

y - 9 = -3/2(x - 2)

2y - 18 = -3x + 6

2y = -3x + 24

y = -3/2 x + 24

Hence the slope-intercept form of the equation is y = -3/2 x + 24.

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Answer:

Step-by-step explanation:

We can use proportionality to find out how much Gino will get paid if he has to plow for 40 hours. Since we know that he gets paid $640 for 20 hours of work, we can set up a proportion to find out how much he will get paid for 40 hours of work.

The proportion can be written as:

Payment for 20 hours / 20 hours = Payment for 40 hours / 40 hours

We can simplify this proportion to:

Payment for 20 hours / 20 = Payment for 40 hours / 40

Substituting the given values, we get:

640 / 20 = Payment for 40 hours / 40

Simplifying this equation, we get:

32 = Payment for 40 hours / 40

Multiplying both sides by 40, we get:

Payment for 40 hours = 32 * 40

Payment for 40 hours = 1280

Therefore, Gino will get paid $1,280 if he has to plow for 40 hours. Hence, the correct answer is (D) $1,280.

Answer:

1.280$

because 20hrs=640 so If it's 40hrs it will add additional 640

The following terms are;

Chord = EJ

Tangent line; GD

Secant line ; KH

For a circle, take two points on its circumference. That divides the circumference of the assumed circle in two parts. Those both parts are called arcs of the circle. The bigger part will be called the major arc, and the smaller one will be called the minor arc.

WE are given that c is the center, FE is a diameter, GD intersects the

circle at E, and KH intersects the circle at E and 1.

Here we have to find the following;

If the assumed circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting the line segment AB.

Chord = EJ

Tangent line; GD

Secant line ; KH

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