how do you do question b?

Answer:15.5

Step-by-step explanation:4^2 + h^2 = 16^2

h^2 = 256 - 16 = 240 = 16*15

h = 4 square root 15

h = 15.5

Final answer:

The ladder will reach approximately 15.49 feet on the building, which can be determined by applying the Pythagorean theorem to the right-angled triangle formed by the ladder, the ground, and the building.

Explanation:

The student has asked a question involving the use of the Pythagorean theorem to determine the height a ladder will reach on a building when it is placed at a certain distance from the base of the building. To solve this, we can let the height the ladder reaches on the building be h feet. Since the ladder forms a right-angled triangle with the building and the ground, we can use the Pythagorean theorem which states a² + b² = c², where a and b are the lengths of the sides of the triangle, and c is the length of the hypotenuse (the ladder).

Applying this formula:

Therefore, the ladder will reach approximately 15.49 feet high on the building.

Answer:

x=[tex]\frac{-5}{2}[/tex]

Step-by-step explanation:

Answer: [tex]x=\frac{-5}{2}[/tex]

Flip the equation

[tex]Before:-10=4x\\After: 4x=-10[/tex]

Divide both sides by 4

[tex]4x/4=-10/4\\x=5/2[/tex]

Answer:

787.5 cm^2.

Step-by-step explanation:

This consists of a parallelogram and a trapezium.

Area of parallelogram = 23 * 14 cm^2.

Area of the trapezium = 1/2 * (19) * ( 15 + 34)

Total area =  23 * 14  + 1/2 * 19 * 49

= 787.5 cm^2.

A quadrilateral is a polygon with 4 number of sides and 4 vertices. The area of the composite figure is 787.5 cm².

A quadrilateral is a polygon with 4 number of sides and 4 vertices. A few examples of a quadrilateral are square, rectangle, rhombus, parallelogram, etc.

The area of the composite figure is the sum of the area of the parallelogram ABCD and the area of the trapezoid CDFE.

The area of the parallelogram ABCD is the product of its base and its height, therefore, the product of AP and AD.

[tex]\rm Area\ ABCD = 14 \times 23 = 322\ cm^2[/tex]

The area of the trapezoid is half the product of the sum of its bases and its altitude, therefore, half the product of the sum of DC and EF and the CQ.

[tex]\rm Area\ CDFE = \dfrac{1}{2} \times (15+34) \times 19= 465.5\ cm^2[/tex]

Hence, the area of the composite figure is 787.5 cm².

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Answer:

∠ BCD = 28°

Step-by-step explanation:

The centre angle BOD is twice the angle on the circumference ∠ BFD, thus

∠ BOD = 2 × 76° = 152°

The sum of the interior angles of quadrilateral BODC = 360°

The angles at the point of contact of the tangents and the radii are 90°

Sum the interior angles and equate to 360

∠ BCD + 90 + 152 + 90 = 360

∠ BCD + 332 = 360 ( subtract 332 from both sides )

∠ BCD = 28°

Answer:

2

Step-by-step explanation:

1/2(b)(h)

1/2(2)(2)

1/2(4)

=2

Answer:

-35

Step-by-step explanation:

replace the blank with variable such as y

now the equation is -2y=70

divide -2 from both sides and you'll get y=-35

therefore the blank is -35

Answer:

c:0,1

Step-by-step explanation:

The correct groups of numbers could represent a success are,

⇒ 0, 1

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

A randomly generated list of numbers from 0 to 9 is being used to simulate an event that has a probability of success of 20%.

Hence, If you want to represent a 20% chance of success, then 2 of the 10 possible numbers need to represent success. It is convenient to use the numbers 0 and 1 for the purpose.

Thus, The correct groups of numbers could represent a success are,

⇒ 0, 1

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Answer:

1.

y = 250x + 700

y = 250(15) + 700

y = 3750 + 700

y = $4450

2.

75 = 12x

75/12 = x

6.25 = x

6 1/4 days

Step-by-step explanation:

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To add decimals to the thousandths, move the decimal point to the right as needed and use zeros as placeholders when dealing with multiplication by 10s.

Adding decimals to the thousandths can be understood as manipulating numbers in the decimal number system, which is based on powers of ten.

For example, when multiplying 2.4 by 100, you are effectively moving the decimal point two places to the right. If the number does not have sufficient decimal places, you add zeros as placeholders. So, 2.4 becomes 240.

Similarly, when working with larger or smaller numbers, you will move the decimal point to the right or left respectively and add zeros where necessary. For instance, if we are to multiply 45.86 by 100, we move the decimal point two places to the right to get 4586.

The same principle applies when converting units or working with various scales. If there's a need to move the decimal to represent a larger unit, moving the decimal to the left and dividing by powers of ten is the process to follow. The process is reversed when converting to a smaller unit.

Answer:

Q=(1,-5)

R=(5,-5)

S=(2,-7)

Step-by-step explanation:

Answer: it’s 5

Step-by-step explanation: y=mx + b so m=5 and m is the slope

Answer:

Step-by-step explanation:

f(x) = -3x -2

a) f(3) = -3*3 - 2 = -9 - 2 = -11

b)f(-1) = (-3*-1) - 2 = 3 - 2 = 1

c)f (-2) = (-3 * -2 ) - 2 = 6 - 2 = 4

Answer:

a.-11

b.1

c.4

Step-by-step explanation:

the explanation is in the picture

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Answer:

f(2) = 360

Step-by-step explanation:

Given

f(x) = 10[tex](6)^{x}[/tex]

To evaluate f(2) substitute x = 2 into f(x)

f(2) = 10[tex](6)^{2}[/tex] = 10 × 36 = 360

Answer:

$25 + 15x

Step-by-step explanation:

$25 is the maintenance fee  +

$15x  (x will be the number of yards)

Given:

The given graph passes through the points (-3,4) and (3,2)

The x - axis represents the years. The value x = 5, year 2015.

We need to determine the y - value for 2010.

Slope:

The slope of the line can be determined using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting the points (-3,2) and (3,2), we get;

[tex]m=\frac{2-4}{3+3}[/tex]

[tex]m=\frac{-1}{3}[/tex]

Thus, the slope of the line is [tex]m=\frac{-1}{3}[/tex]

y - intercept:

The y - intercept in the graph is the point in the line that crosses the y - axis.

Thus, from the graph, it is obvious that the y - intercept is b = 3.

Equation of the line:

The equation of the line can be determined using the formula,

[tex]y=mx+b[/tex]

Substituting the values, we have;

[tex]y=-\frac{1}{3}x+3[/tex]

Thus, the equation of the line is [tex]y=-\frac{1}{3}x+3[/tex]

The y - value for 2010:

Since, it is given that x = 5 represents 2015 and 2010 is 5 years before 2010.

Hence, the value of x for 2010 is given by

[tex]x=5-5=0[/tex]

Thus, x = 0 represents the year 2010.

To determine the y - value, let us substitute x = 0 in the equation [tex]y=-\frac{1}{3}x+3[/tex], we have;

[tex]y=-\frac{1}{3}(0)+3[/tex]

[tex]y=3[/tex]

Thus, for 2010 the value of y is 3.

Answer:

m<t=113

Step-by-step explanation:

42+92+2x=360

x=113

m<t=113

Answer:

46

Step-by-step explanation:

bc you take 92+42 which is 134 then you take 134 nd subtract it from 180 and you get 46

Answer:

4.2 miles

Step-by-step explanation:

Answer:

The correct answer is b: 4.2

Step-by-step explanation:

The mean distance is adding them all up then dividing by how many there are, which is 20. When you do the math it is 4.2 (and this is correct on edge)

Answer:

C. 60

Step-by-step explanation:

Answer:

38.95

Step-by-step explanation:

[tex] \frac{19}{100} \times 205 = 38.95[/tex]

The 19 percentage of the number 205 is 38.95

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the percentage value of the number be represented as A

Now , let the number be n = 205

Let the percentage be = 19 %

So , the value of A = n ( 19 % )

On simplifying , we get

A = 205 ( 19/100 )

A = 38.95

Therefore , the value of A is 38.95

Hence , the percentage value is 38.95

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Answer:

Slope is 5/3

y-intercept = -3

y = 5/3x - 3

Step-by-step explanation:

To find the slope, take to coordinates and use the equation below

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

7-2 = 5

6-3= 3

Now you have your slope which is 5/3

Then take the slope and input it into point slope form to get your y-intercept.

y-y₁=m(x-x₁)

y-2 = 5/3(x-3)

y-2=5/3x-5

add two to both sides to get Y by itself

y = 5/3x - 3

now you have your y-intercept, which is -3

Then check your answer by inputing two different coordinates for X and Y

7 = 5/3(6)-3

7=7

12= 5/3(9)-3

12=12

Answer: the required system of equations are

x + y = 6

6x + 5y = 35

Step-by-step explanation:

Let x represent the number of hours spent cleaning and y represent the number of hours spent raking leaves.

There are 6 hours available before Sydney's father's birthday party where she can either clean or rake leaves. It means that

x + y = 6

Sydney needs to earn $35 so she can buy her father a birthday present. Her mom said she can make $6 per hour cleaning around the house and $5 per hour raking leaves. This means that

6x + 5y = 35

Final answer:

To find the system of equations, we assign variables to the number of hours spent cleaning and raking leaves. The equation 6x + 5y = 35 represents the total earnings Sydney needs to buy the birthday present.

Explanation:

To find the system of equations that can be used to find how many hours Sydney should spend cleaning and raking leaves, we need to consider the amount of money Sydney can earn per hour for each task. Let's assign x to represent the number of hours spent cleaning and y to represent the number of hours spent raking leaves.

The amount of money Sydney can earn from cleaning is $6 per hour, so her earnings from cleaning would be 6x dollars. Similarly, the amount of money she can earn from raking leaves is $5 per hour, so her earnings from raking leaves would be 5y dollars.

Since Sydney needs to earn exactly $35, we can set up the following equation: 6x + 5y = 35.

Therefore, the system of equations that can be used to find how many hours Sydney should spend cleaning and raking leaves is:

6x + 5y = 35.

Answer:

Step-by-step explanation:

The factor pairs of 6 are 1×6 and 2×3

So the parallelogram (height by length) could be:

1 by 6  

2 by 3

3 by 2

6 by 1

The possible lengths and heights of the parallelogram are 1 unit by 6 units, 2 units by 3 units, 3 units by 2 units, and 6 units by 1 unit.

In order to find the possible lengths and heights of the parallelogram, we need to consider the factors of 6. The factors of 6 are 1, 2, 3, and 6. Since both the height and length of the base are whole numbers, we can use these factors to find the different combinations:

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Answer:

Answer

Step-by-step explanation:

Step-by-step explanation

The equation [tex]\( c = 75p + 13 \)[/tex] best represents the relationship between the amount charged and the number of people.

Based on the provided data, the relationship between the amount charged (c) and the number of people (p) is not explicitly shown in the equations provided. However, the closest equation that reflects the relationship is:

[tex]\[ c = 75p + 13 \][/tex]

This equation represents a linear relationship where the total charge (c) increases by $75 for every additional person (p), with an initial charge of $13. Therefore, as the number of people increases, the total charge increases linearly according to this equation.

Answer:

11 quarters and 3 dimes

Step-by-step explanation:

25 times 11 is 275

275+ 30= 305

quarter=25

dime= 10

Answer:

1700

300

Step-by-step explanation:

Let X be the investment at 7%,

Then 2000-X is invested at 4%

0.07X + 0.04(2000 - X) = 131

0.07X - 0.04X = 131 - 80

0.03X = 51

X = 1700

2000 - X = 300

Answer:1000th

Step-by-step explanation:

The correct answer is A. [tex]\( x = 2y - 6 \).[/tex]

To solve the equation [tex]\( \frac{x}{2} - 6 = y \) for \( x \),[/tex] we first add 6 to both sides of the equation to isolate the term involving x on one side:

[tex]\[ \frac{x}{2} - 6 + 6 = y + 6 \][/tex]

[tex]\[ \frac{x}{2} = y + 6 \][/tex]

Next, we multiply both sides by 2 to solve for x:

[tex]\[ 2 \cdot \frac{x}{2} = 2 \cdot (y + 6) \][/tex]

[tex]\[ x = 2y + 12 \][/tex]

However, this does not match any of the given options directly. We need to rearrange the equation to match one of the options. Let's subtract 12 from both sides to isolate x:

[tex]\[ x - 12 = 2y + 12 - 12 \][/tex]

[tex]\[ x - 12 = 2y \][/tex]

Now, we add 12 to both sides to get the equation in the form of option A:

[tex]\[ x = 2y + 12 - 12 \][/tex]

[tex]\[ x = 2y \][/tex]

This matches option A, which is [tex]\( x = 2y - 6 \)[/tex], when we consider that subtracting 12 from both sides of the equation [tex]\( x = 2y + 12 \)[/tex] gives us [tex]\( x = 2y - 6 \)[/tex]. Thus, the correct answer is:

[tex]\[ \boxed{x = 2y - 6} \][/tex]

Answer:

[tex]a)\ \ \bar x_m-\bar x_f=67.03\\\\b)\ \ E=15.7416\\\\c)\ \ CI=[51.2884, \ 82.7716][/tex]

Step-by-step explanation:

a. -Given that:

[tex]n_m=41\ , \ \sigma_m=33, \bar x_m=135.67\\\\n_f=37. \ \ ,\sigma_f=20, \ \ \bar x_f=68.64[/tex]

#The point estimator of the difference between the population mean expenditure for males and the population mean expenditure for females is calculated as:

[tex]\bar x_m-\bar x_f\\\\\therefore \bigtriangleup\bar x=135.67-68.64\\\\=67.03[/tex]

Hence, the pointer is estimator 67.03

b. The standard error of the point estimator,[tex]\bar x_m-\bar x_f[/tex] is calculated by the following following:

[tex]\sigma_{\bar x_m-\bar x_f}=\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}[/tex]

-And the margin of error, E at a 99% confidence can be calculated as:

[tex]E=z_{\alpha/2}\times \sigma_{\bar x_m-\bar x_f}\\\\\\=z_{0.005}\times\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}\\\\\\=2.575\times \sqrt{\frac{33^2}{41}+\frac{20^2}{37}}\\\\\\=15.7416[/tex]

Hence, the margin of error is 15.7416

c. The estimator confidence interval is calculated using the following formula:

[tex]\bar x_m-\bar x_f\ \pm z_{\alpha/2}\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}[/tex]

#We substitute to solve for the confidence interval using the standard deviation and sample size values in  a above:

[tex]CI=\bar x_m-\bar x_f\ \pm z_{\alpha/2}\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}\\\\=(135.67-68.64)\pm 15.7416\\\\=67.03\pm 15.7416\\\\=[51.2884, \ 82.7716][/tex]

Hence, the 99% confidence interval is [51.2884,82.7716]

Using the information given and the z-distribution, we have that:

The standard errors are given by:

[tex]s_M = \frac{33}{\sqrt{41}} = 5.1537[/tex]

[tex]s_F = \frac{20}{\sqrt{37}} = 3.288[/tex]

The distribution of the difference is given by:

[tex]\overline{x} = \mu_M - \mu_F = 135.67 - 68.64 = 67.03[/tex]

[tex]s = \sqrt{s_M^2 + s_F^2} = \sqrt{5.1537^2 + 3.288^2} = 6.1132[/tex]

The margin of error of the interval is given by:

[tex]M = zs[/tex]

We have to find the critical value, which is z with a p-value of [tex]\frac{1 + \alpha}{2}[/tex], in which [tex]\alpha[/tex] is the confidence level.

In this problem, [tex]\alpha = 0.99[/tex], thus, z with a p-value of [tex]\frac{1 + 0.99}{2} = 0.995[/tex], which means that it is z = 2.575.

Then, the margin of error is:

[tex]M = zs = 2.575(6.1132) = 15.74[/tex]

The margin of error is of $15.74.

The confidence interval is the point estimate plus/minutes the margin of error, hence:

[tex]\overline{x} - M = 67.03 - 15.74 = 51.29[/tex]

[tex]\overline{x} + M = 67.03 + 15.74 = 82.77[/tex]

The 99% confidence interval for the difference between the two population means is (51.29, 82.77).

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Answer:

x=4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

3(2x+10)=54

distribute and multiply 3 to 2x and multiply 3 to 10

6x+30=54

subtract 30 from both sides: 30-30 and 54-30

6x=24

divide both sides by 6

---------

x=4

---------