y varies directly with x Part 2

22. If y = 5 when x = -3, find x when y = -1
23. If y = -7 when x = -3, find y when x = 9
24. If y = 25 when x = 15, find y when x = 6

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

Answer: $400 million

Step-by-step explanation: $500-100= $400 million :)

Answer:

Step-by-step explanation:

3:7 = ___: 49

3 : 7 = x : 49

x = 3 × 49 ÷ 7

x = 147 ÷ 7

x = 21

3 : 7 = 21 : 49  (your answer)

Answer:

-5p+99

Step-by-step explanation:

Original Equation;

3(p - 29) - 4(2p - 39 -5)

★First Step: Multiply the number 3 by p and -29 which is in the first term so it's going to be;

3 multiplied by p and 3 multiplied by -29

3p - 87

★Second step: Add the -39 and -5 which is going to give you -44 because - + - is = -

-44

★Third step: Multiply -4 by 2p and -44 so it's going to be;

-4×2p=-8p and -4×-44=176 we have positive 176 because - × - = +

★Fourth Step: Remove brackets

So it's going to be;

3p - 87 -8p +176

★Then you combine like terms

3p - 8p - 87 +176

-5p + 99

3(p-29)-4(2p-39-5)

3p-87-4(2p-44)

3p-87-8p+176

3p-8p-87+176

-5p+99

Answer:

(A)

Step-by-step explanation:

The survey follows of women's height a normal distribution.

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

The new height requirements would be 57.7 to 68.6 inches

The given parameters are:

\mathbf{\mu = 63.5}μ=63.5 --- mean

\mathbf{\sigma = 2.5}σ=2.5 --- standard deviation

(a) Percentage of women between 58 and 80 inches

This means that: x = 58 and x = 80

When x = 58, the z-score is:

\mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

This gives

\mathbf{z_1= \frac{58 - 63.5}{2.5}}z

1

=

2.5

58−63.5

\mathbf{z_1= \frac{-5.5}{2.5}}z

1

=

2.5

−5.5

\mathbf{z_1= -2.2}z

1

=−2.2

When x = 80, the z-score is:

\mathbf{z_2= \frac{80 - 63.5}{2.5}}z

2

=

2.5

80−63.5

\mathbf{z_2= \frac{16.5}{2.5}}z

2

=

2.5

16.5

\mathbf{z_2= 6.6}z

2

=6.6

So, the percentage of women is:

\mathbf{p = P(z < z_2) - P(z < z_1)}p=P(z<z

2

)−P(z<z

1

)

Substitute known values

\mathbf{p = P(z < 6.6) - P(z < -2.2)}p=P(z<6.6)−P(z<−2.2)

Using the p-value table, we have:

\mathbf{p = 0.9999982 - 0.0139034}p=0.9999982−0.0139034

\mathbf{p = 0.9860948}p=0.9860948

Express as percentage

\mathbf{p = 0.9860948 \times 100\%}p=0.9860948×100%

\mathbf{p = 98.60948\%}p=98.60948%

Approximate

\mathbf{p = 98.61\%}p=98.61%

This means that:

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

So, many women (outside this range) would be denied the opportunity, because they are either too short or too tall.

(b) Change of requirement

Shortest = 1%

Tallest = 2%

If the tallest is 2%, then the upper end of the shortest range is 98% (i.e. 100% - 2%).

So, we have:

Shortest = 1% to 98%

This means that:

The p values are: 1% to 98%

Using the z-score table

When p = 1%, z = -2.32635

When p = 98%, z = 2.05375

Next, we calculate the x values from \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

Substitute \mathbf{z = -2.32635}z=−2.32635

\mathbf{-2.32635 = \frac{x - 63.5}{2.5}}−2.32635=

2.5

x−63.5

Multiply through by 2.5

\mathbf{-2.32635 \times 2.5= x - 63.5}−2.32635×2.5=x−63.5

Make x the subject

\mathbf{x = -2.32635 \times 2.5 + 63.5}x=−2.32635×2.5+63.5

\mathbf{x = 57.684125}x=57.684125

Approximate

\mathbf{x = 57.7}x=57.7

Similarly, substitute \mathbf{z = 2.05375}z=2.05375 in \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

\mathbf{2.05375= \frac{x - 63.5}{2.5}}2.05375=

2.5

x−63.5

Multiply through by 2.5

\mathbf{2.05375\times 2.5= x - 63.5}2.05375×2.5=x−63.5

Make x the subject

\mathbf{x= 2.05375\times 2.5 + 63.5}x=2.05375×2.5+63.5

\mathbf{x= 68.634375}x=68.634375

Approximate

\mathbf{x= 68.6}x=68.6

Hence, the new height requirements would be 57.7 to 68.6 inches

Answer:

160 hours

Step-by-step explanation:

y=3+.18(hours)

31.80=3+.18(hours)

28.8=.18(hours)

160=hours

Answer:

15 weeks

$270

Step-by-step explanation:

Let y = total money saved

x = weeks

I am saving $14 every week, so I multiply x by 14

y = 14x

And I already have $60 to begin with

y = 14x + 60

My sister is saving $10 every week, so I multiply x by 10

y = 10x

And she already has $120 to begin with

y = 10x + 120

Now we just need to find a point where they are the same

14x + 60 = 10x + 120

Move like terms to one side, so subtract 10x from both sides

14x + 60 = 10x + 120

-10x         -10x

4x + 60 = 120

Subtract 60 from both sides

4x + 60 = 120

    - 60    - 60

4x = 60

Divide both sides by 4

4x/4 = 60/4

x = 15

Now plug in the new x into one of the original equations to find the money amount. We'll use sister's.

y = 10(15) + 120

y = 150 + 120

y = 270

She needs to pay N $8378.31 in two and a half years from now to meet her obligation.

What are the basic arithmetic operations?

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

Let's first calculate the total interest on the loan for three and a half years:

Interest = Principal × Rate × Time

Interest = 20000 × 0.05 × 3.5

Interest = 3500

So, the total amount she needs to pay back on maturity is:

20000 + 3500 = N$23500

Now, let's subtract the amount she plans to pay in the next 10 months and 16 months:

N$23500 - N$2000 - N$5000 = N$16500

So, she needs to pay N$16500 in two and a half years from now to meet her obligation.

Alternatively, we can also calculate the present value of the remaining payments using the formula for present value of an annuity:

PV = \(PMT \times (1 - (1 + r)^{(-n)}) / r\)

where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.

Using this formula, we get:

PV = \(2000 \times (1 - (1 + 0.05/12)^{(-10})) / (0.05/12) + 5000 \times x (1 - (1 + 0.05/12)^{(-16)}) / (0.05/12)\)

PV = N$13658.80

So, the amount she needs to pay in two and a half years from now to meet her obligation is the present value of the remaining payments:

PV = \(PMT \times (1 + r)^{(-n)}\)

N$13658.80 = \(PMT \times (1 + 0.05/12)^{(-30)}\)

PMT = N$8378.31

Hence, she needs to pay N$8378.31 in two and a half years from now to meet her obligation.

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The three true statements are as follows:

In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.

A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.

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Answer : 8$

you have 1$ left

Answer:

x = -232

Step-by-step explanation:

Ronu's present age is "x “years and her sister Shaani's present age is twice  of Ronu's age.

(a) Ronu's present age = x years

(b) Ronu's age after 2 years = (x+2) years

(c) Shaani's present age = 2x years

(d) Shaani's age after 2 years = (2x+2) years

Let x should be added to 100 to get -132.

x+100 = -132

x = -100-132

x = -232

Hence, -232 must be added to 100 to get -132.

Answer:

The correct answer is k = 5.

Step-by-step explanation:

The Chi-square goodness of fit test would be used to determine whether the frequency of insect heads in batches follows a distribution called a Poisson distribution.

The hypothesis for the test can be defined as follows:

H₀: The frequency of insect heads in batches does not follows a Poisson distribution.

Hₐ: The frequency of insect heads in batches follows a Poisson distribution.

Assume that the significance level of the test is, α = 0.05.

The Chi-square test statistic is given by:

\(\chi^{2}=\sum\limits^{k}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}\)

It is provided that the 500 batches included at least 5 batches having 0, 1, 2, 3, or 4 insect heads. No batches had more than four heads.

So, the number of classes or categories are, k = 5.

Thus, the correct answer is k = 5.

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer: 9

Step-by-step explanation: Convert 3/4 into 9/12. Then you see there are 9 markers.

Answer: 6/7

Step-by-step explanation:

Answer:

I think its 61.3

Step-by-step explanation:

dont be mad if its wrong. also 10 has one zero so you move the decimal place once to the right

Answer:

1 real root   2 imaginary roots

Step-by-step explanation:

f(x) = x^3 + 5x^2 + x + 5

Set equal to zero to find the zeros

0  = x^3 + 5x^2 + x + 5

Factor by grouping

0 = x^2( x+5)  + 1( x+5)

0 = (x+5) ( x^2+1)

Using the zero product property

x+5 =0    x^2+1 =0

x=-5    x^2 = -1

x=-5    x = ±i

1 real root   2 imaginary roots

Answer:

1 real root   2 imaginary roots

Step-by-step explanation:

f(x) = x^3 + 5x^2 + x + 5

Set equal to zero to find the zeros

0  = x^3 + 5x^2 + x + 5

Factor by grouping

0 = x^2( x+5)  + 1( x+5)

0 = (x+5) ( x^2+1)

Using the zero product property

x+5 =0    x^2+1 =0

x=-5    x^2 = -1

x=-5    x = ±i

1 real root   2 imaginary roots

Answer:

Concept:

When encountering questions that ask for simplifying expressions through operation, following the PEMDAS method would be easier:

Therefore, the whole process of simplifying the given expression should follow the PEMDAS method. For extra, whenever there are two occurences of the same operation, then prioritize the leftmost and go right.

Hope this helps!! :)

Please let me know if you have any questions or need further explanation

Step-by-step explanation:

→ 4 + 5(3x - 2) - 3x

→ 4 + 15x - 10 - 3x

→ 12x - 6

therefore, option A is correct.

hope this answer helps you dear!

The required simplified solution of the given expression is 12x -6. Option A is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
= 4 + 5(3x -2) - 3x
Following the distributive property,
= 4 + 15x - 10 - 3x
Following the associative property,
= 4 - 10 + 15x - 3x
= -6 + 12x
= 12x - 6

Thus, the required simplified solution of the given expression is 12x -6. Option A is correct.

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Answer:

1) 9x

2) 3b

3) 3m

4) 5a

5) 7x

6) 3a + 5b

7) 9x - 4

8) 2b + m

9) 13a + b + 6c

10) 9b + 1

11) 7p

12) 2a + b -10

Step-by-step explanation:

For each variable, the possible values are:

a) T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

b) X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}

c) U = {0, 1, 2, 3, 4, 5, 6}

d) Z = {0, 1, 2}

Item a:

In total, there are 10 pumps, hence the possible values are all integers from 0 to 10, that is:

T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Item b:

In the first, there are 6 pumps, and in the second 4, hence, the difference ranges from -4 to 6, that is:

X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}

Item c:

The maximum number in a station is 6 pumps, hence this variable ranges from 0 to 6.

U = {0, 1, 2, 3, 4, 5, 6}

Item d:

Either none of the stations has exactly two pumps in use, or one has or both, hence the variable ranges from 0 to 2.

Z = {0, 1, 2}

The question is incomplete. The complete question is:

"The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables. (Enter your answers in set notation.)

a. T = the total number of pumps in use

b. X = the difference between the numbers in use at stations 1 and 2.

c. U = the maximum number of pumps in use at either station

d. Z = the number of stations having exactly two pumps in use"

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Carey's graph will be a straight line with a slope of -1 and a y-intercept of 3.

Carey correctly graphs a linear function with a slope of -1 and a y-intercept of 3. A linear function is represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope is -1, which means that for every unit increase in the x-coordinate, the y-coordinate decreases by 1 unit. The y-intercept is 3, indicating that the graph intersects the y-axis at the point (0, 3).

To plot the graph, Carey starts by marking the point (0, 3) on the graph. Then, for every unit increase in the x-coordinate, Carey moves one unit downward. Similarly, for every unit decrease in the x-coordinate, Carey moves one unit upward. These steps ensure the correct slope of -1.

After connecting the points, Carey will obtain a line that starts at the y-intercept (0, 3) and slants downward, with a slope of -1. The resulting graph will be a straight line extending to both sides of the coordinate plane.

In conclusion, it is represented by the equation y = -x + 3.

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Answer:

-16 because the difference in between 10 and -4 is -16

Answer:

−2

Step-by-step explanation:

Using the slope-intercept form, the slope is −2 .

So, we know that he ran 65 miles, and he ran one short mile of 8.2 miles. We also know that the rest of the miles are among five long runs.

1. Subtract the known data.

65 - 8.2 = 56.8

2. Divide 56.8 by 5 to determine the distance of each long run.

56.8 / 5 = 11.36

This summarizes that each long run was 11.36 miles long.

Answer:

0 liters

Step-by-step explanation:

The first step in solving this problem is to find the volume of water that was originally in the tank when it was filled up to of its height. Since the tank is rectangular, we can use the formula for the volume of a rectangular prism:

Volume of tank = length x width x height = 100 cm x 80 cm x 30 cm = 240,000 cm³

Since the tank was filled up to of its height, the volume of water in the tank at this point is:

Volume of water in tank = 100 cm x 80 cm x 30 cm x 0.5 = 1,200,000 cm³

To find the amount of water that was poured into the tank to fill it up to 3 of its height, we need to subtract the volume of water that was originally in the tank from the total volume of water when it is 3 filled, which is 384 liters or 384,000 cm³ (since 1 liter = 1000 cm³):

Volume of water poured into tank = Volume of water when 3 filled - Volume of water in tank at of its height

= 384,000 cm³ - 1,200,000 cm³

= -816,000 cm³

Wait a minute, this result is negative, which means there was no water poured into the tank to reach the 3 filled level. In fact, it suggests that there was an excess of water that had to be removed from the tank to reach the desired level. This could be because the dimensions of the tank were not exact or because the tank was not level when filled to the first level.

Therefore, the answer to the problem is 0 liters or 0 cm³.

Note: It is important to always check the result of a calculation to ensure it makes sense in the context of the problem. In this case, the negative volume of water poured into the tank indicates that there may be an error in the problem statement or in the measurements provided.

Answer:

40 Squared units

Step-by-step explanation:

\(A=2*2*4+2*2*6=40\)

Answer: The answer is...

y = -2/3 x + 1

Step-by-step explanation:

The others would have crossed paths with y = -2/3 x + 10

Calista's grade on her last assignment is 98.

To determine Calista's grade on her last assignment, we can calculate the average grade using the given information.

The sum of Calista's grades on the first five assignments is: 62 + 88 + 92 + 74 + 78 = 394.

Since the average grade is given as 82, we can find the total sum of all six assignments by multiplying the average grade by the number of assignments, which is 6: 82 * 6 = 492.

To find Calista's grade on her last assignment, we subtract the sum of her grades on the first five assignments from the total sum: 492 - 394 = 98.

To determine Calista's grade on her last assignment, we can calculate the average grade using the given information.

The sum of Calista's grades on the first five assignments is: 62 + 88 + 92 + 74 + 78 = 394.

Since the average grade is given as 82, we can find the total sum of all six assignments by multiplying the average grade by the number of assignments, which is 6: 82 * 6 = 492.

To find Calista's grade on her last assignment, we subtract the sum of her grades on the first five assignments from the total sum: 492 - 394 = 98.

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