The sum of two numbers is 45 the difference is 15 what are the numbers

The concept of ratio is used here to determine the number of boys in the school. Here the in a school of 425 pupils, the total number of boys in the school is 200.

Here there are 425 pupils, If the ratio of boys to girls is 8 to 9, then 8 out of 17 are boys and 9 out of every 17 are girls. Set up a proportion for the boys, where b = the total number of boys.

8 / 17 = b / 425

17 b = 8 × 425

b = 8 × 425 / 17

b = 200

So the number of boys are 200 and the number of girls are 425 - 200 = 225.

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The principal amount is Rs. 468.75 and the rate of interest is 16% per annum.

According to the given information, the simple interest on the principal amount for 3 years is Rs. 225, so we have:

Simple Interest (S.I.) = P * r * t = 225

Substituting t = 3 years, we get:

P * r * 3 = 225

P * r = 75 --- (1)

Also, the compound interest on the same principal amount and at the same rate for 2 years is Rs. 153, so we have:

Compound Interest (C.I.) = [tex]P * (1 + r)^t - P = 153[/tex]

Substituting t = 2 years, we get:

[tex]P * (1 + r)^2 - P = 153P * [(1 + r)^2 - 1] = 153P * [(1 + r + r^2) - 1] = 153P * (r + r^2) = 153 / 2[/tex]--- (2)

Dividing equation (2) by equation (1), we get:

(r + r^2) / r = (153 / 2) / 75

Simplifying and solving for r, we get:

r^2 + r - 0.68 = 0

Using the quadratic formula, we get:

r = (-1 ± √(1 + 4 * 0.68)) / 2

r = (-1 ± 1.32) / 2

Since r cannot be negative, we take the positive value:

r = (0.32) / 2 = 0.16

Substituting r = 0.16 in equation (1), we get:

P * 0.16 = 75

P = 75 / 0.16 = Rs. 468.75

Therefore, the principal amount is Rs. 468.75 and the rate of interest is 16% per annum.

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The correct alternative hypothesis in this case would be Ha: u not equal to 8, option a. This is because the null hypothesis in this scenario would be that the mean of the bottles of cream being filled is equal to 8 ounces.

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Answer: c

Step-by-step explanation: i took the test and got it right sorry if it is wrong hope it helps

Answer:

Plot the points on the graphing calculator, and then generate an exponential regression equation. That equation is

[tex]y = 11.77( {1.84}^{x} )[/tex]

This equation is not one of the choices, so the closest equation is

[tex]y = 11.55( {1.85}^{x} )[/tex]

The median is 1

The first step is to write out the set of numbers

-31, 19, -19, -20, -26, 19, 23, 22

The next step is to arrange the number in an orderly manner

19, 19, -19, -20, 22, 23, -26, -31

The two middle numbers are -20 and 22

The median can be calculated as follows

= -20 + 22/2

= 2/2

= 1

Hence the median is 1

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Answer:

48, 192, 768, 3072, 12288

Step-by-step explanation:

This is a geometric sequence where each successive number is obtained by multiplying the current number by 4

So the common ratio is

To find the numbers after 12 multiply each number by 4 so we get the next 5 terms as

48, 192, 768, 3072, 12288

The first 8 terms are therefore
3/16, 3/4, 3, 12, 48, 192, 768, 3072, 12288

**Note**
Since the image is cropped, I cannot see how many terms were asked for so I just found the next 5 terms

The expected number of choices needed to select the first CS PhD student is 4.

To solve this problem, we can use the concept of geometric distribution. The geometric distribution represents the number of independent and identical trials that are needed to obtain the first success, where the probability of success is p.

In this case, the probability of selecting a CS PhD student on any given trial is 50/200 = 0.25. Therefore, the number of trials needed to obtain the first CS PhD student follows a geometric distribution with p = 0.25.

The expected value of a geometric distribution with parameter p is given by E(X) = 1/p. Therefore, the expected number of choices needed to select the first CS PhD student is

E(X) = 1/p = 1/0.25 = 4

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The relationship between the two linear functions is given as follows:

A. Parallel.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

Given two points, the slope of the linear function is calculated as the change in y divided by the change in x.

Hence the slopes of each line are given as follows:

As the two lines have the same slope, they are parallel lines.

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Answer:

he desired equation is y = (3/5)x + 4

Step-by-step explanation:

Solving the given 5x + 3y = -21 for 3y yields  3y = -5x - 21.  Dividing all three terms by 3, we get:

y = (-5/3)x - 7, indicating that the given line has slope -5/3.

The slope of a line perpendicular to this y = (-5/3)x - 7 is 3/5, the negative reciprocal of -5/3.

Start with y = mx + b.  Substitute 1 for y, -5 for x and 3/5 for m.  Then:

1 = (3/5)(-5) + b, or

1 = -3 + b.  Then b must be 4, and so the desired equation is y = (3/5)x + 4.

Step-by-step explanation:

area of triangle A

= 1/2×9×3

=13.5 units^2

area of triangle B

= 1/2×3×7

= 10.5 units^2

area of whole figure

= 13.5+10.5

= 24 units^2

Answer: The range is 7

Step-by-step explanation: To find the range you should find the lowest and the highest numbers in the number set. In this case they are 9 and 2, and subtract the smallest from the largest.

The answer will therefore be 7.

The required volume and surface area of the cone is  [tex]V = \pi \int[f(x)]^2 dx[/tex] and [tex]A = 2\pi \int [f(x)] \sqrt{(1+[f'(x)]^2)} dx[/tex] respectively.

If a cone is rotated around its axis, the resulting solid is a three-dimensional object called a "rotational solid" or "solid of revolution." The surface area and volume of the solid can be calculated using specific formulas.

The surface area of a solid of revolution can be found using the formula:

[tex]A = 2\pi \int [f(x)] \sqrt{(1+[f'(x)]^2)} dx[/tex]

where f(x) is the equation of the curve being rotated and f'(x) is its derivative.

The volume of a solid of revolution can be found using the formula:

[tex]V = \pi \int[f(x)]^2 dx[/tex]

where f(x) is the equation of the curve being rotated.

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The remote interior angles of <5 are given as follows:

A. <2.

C. <1.

The remote interior angles of an exterior angle in a triangle are the angles that do not share a vertex with the given exterior angle.

The internal angles of the triangle in this problem are given as follows:

<1, <2 and <3.

Angle 3 shares a common vertex with the angle 5, hence it is not a remote interior angle.

The other interior angles, <1 and <2, do not share any vertex with <5, hence they are the remote interior angles.

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The total number of possible combination using 3 sweatshirt and 2 running pants are equal to 6.

Total number of sweatshirts = 3

White, a Red, and a Gray sweatshirt.

Total number of running paints = 2

Black and gray running pants.

Tree diagram to represents all the possible combinations of training outfits are ,

Attached diagram.

White sweatshirt → Black running pants or gray running pants

Red sweatshirt → Black running pants or gray running pants

Gray sweatshirt → Black running pants or gray running pants

With each sweatshirt two possible outfits are possible.

These choices are represented by branches in the tree diagram.

The possible combinations of jacket and running pants are shown at the end of each branch.

Total possible combination of all the outfits are

= 2 + 2 + 2

= 6

or

³P₂ = 3! / (3 - 2)!

     = 6

Therefore, possible number of combination for the given outfits are 6.

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The above question is incomplete, the complete question is:

A cross country athlete has a white, a red, and a gray sweatshirt. She has black and gray running pants. Use a tree diagram to show the possible combinations of training outfits.

The probability that both the balls drawn are white is 2/7 when two balls are drawn successively without replacement from a box which contains 4 white balls and 3 red balls.

Two balls are drawn successively without replacement from a box which contains 4 white balls and 3 red balls.

Therefore, Total number of balls in the box = 4+ 3 = 7 balls

Thus, the probability that the first ball drawn is a white is = (Total number of white balls) /  ( Total number of balls)

=4/7

The next ball is drawn without replacement thus the number of balls in the box is 6.

And if 1 ball is picked in drawn n first tie, then remaining number of white balls is 3.

Thus, the probability that the second ball drawn is a white is = (Remaining number of total white balls) /  ( Remaining number of total balls)

= 3/6 = 1/2

Therefore, the probability that both the balls drawn are white is

= (4/7)*(1/2)

= 2/7

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X is the total number of cakes she made. From the question, we know there are two kinds of cakes; those she sold and those she didn't. So;

X= number of sold cakes + number of cakes not sold

Here, the number of sold cakes is 15, and the number of cakes left is 4. So,

X= number of sold cakes + number of cakes not sold= 15+4=20

So, the total number of cakes is 20

The following are true statements regarding stocks:

A. Holding stock entitles you to ownership in a corporation.

B. Firms sell stocks to raise capital for their operations.

D. Factors like the news and unfounded rumors might have an impact on stock prices.

A share of ownership in a corporation is represented by the stock. So, having stock means you have ownership of the company.

In order to raise capital for their businesses, companies issue stocks. Companies can raise funds without taking on debt by selling stocks.

A gain in stock prices over the long run is not always assured. The truth is that a number of factors, including news, rumors, the status of the economy, and qualities unique to a certain organization,

There is no guarantee that the value of equity would increase over time, as was stated in paragraph C.

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The margin of error for a survey which has a sample size of 260, would be ± 6. 2 %.

Margin of error indicates the extent to which sample data is likely to differ from population characteristics. It's presented as a proportion and demonstrates the range of values within which the accurate population value may fall with confidence. This statistical term also highlights random sampling errors that can occur in survey outcomes.

The margin of error for a sample of size 260 would therefore be :

= ± 1 / n

= ± 1 / √ 260

= ± 0. 062

= ± 6. 2 %

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Answer:

We can use the formula for the lateral surface area of a cone to find the slant height:

Lateral surface area = πrℓ, where r is the radius and ℓ is the slant height.

Since the paper cup is hollow, the lateral surface area is equal to the outer surface area of the cup, which is given as 17.9 square inches. The radius of the cup is half the diameter, which we do not know, so let's call it d:

r = d/2

We also know that the lateral surface area is given by:

17.9 = πrℓ

Substituting r = d/2, we get:

17.9 = π(d/2)ℓ

Simplifying, we get:

ℓ = (2*17.9)/(πd)

Using an approximation of π = 3.14, we can calculate:

ℓ ≈ (2*17.9)/(3.14d) = 11.40/d

Since we do not have any information about the diameter of the paper cup, we cannot calculate the exact slant height.

The linear approximation of f(x)= sqrt(4-x) at a=0 can be used to approximate sqrt(3.9) and sqrt(3.99) as 0.0500 and 0.0050, respectively.

The linear approximation of the function f(x)= sqrt(4-x) at a=0 is given by:

L(x) = f(a) + f'(a)(x-a)
    = sqrt(4-0) + (-1/2)(x-0)
    = 2 - 0.5x

To approximate the numbers sqrt(3.9) and sqrt(3.99) using L(x), we need to plug in the values of x and round the answer to four decimal places.

For sqrt(3.9), we have:

L(3.9) = 2 - 0.5(3.9)
      = 0.05

Rounding to four decimal places, we get:

L(3.9) ≈ 0.0500

For sqrt(3.99), we have:

L(3.99) = 2 - 0.5(3.99)
       = 0.005

Rounding to four decimal places, we get:

L(3.99) ≈ 0.0050

Therefore, the linear approximation of f(x)= sqrt(4-x) at a=0 can be used to approximate sqrt(3.9) and sqrt(3.99) as 0.0500 and 0.0050, respectively.

To find the linear approximation L(x) of the function f(x) = sqrt(4-x) at a=0, we need to calculate the value of the function and its derivative at a=0:

f(a) = f(0) = sqrt(4-0) = sqrt(4) = 2

Now, we find the derivative of f(x) with respect to x:
f'(x) = d/dx(sqrt(4-x)) = -1/(2*sqrt(4-x))

Next, evaluate f'(x) at a=0:
f'(0) = -1/(2*sqrt(4-0)) = -1/(2*2) = -1/4

The linear approximation L(x) is given by:
L(x) = f(a) + f'(a)(x-a)
L(x) = 2 - (1/4)(x-0) = 2 - (1/4)x

Now, we use L(x) to approximate sqrt(3.9) and sqrt(3.99):
L(0.1) = 2 - (1/4)(0.1) = 1.9750
L(0.01) = 2 - (1/4)(0.01) = 1.9975

So, the linear approximations of sqrt(3.9) and sqrt(3.99) are 1.9750 and 1.9975, respectively.

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D

The 95% confidence interval for the mean of a population is computed to be 6 to 14. This means that we are 95% confident that the true population mean falls within this interval.

Based on this information, we can make the following claims:

A. The population mean is more than 7: This claim cannot be supported or refuted by the given confidence interval, since it is possible that the population mean is less than 7 and still falls within the interval.

B. The population mean is less than 15: This claim cannot be refuted by the given confidence interval, since it is possible that the population mean is less than 15 and still falls within the interval.

C. The population mean is exactly 9: This claim cannot be supported or refuted by the given confidence interval, since it is possible that the population mean is not equal to 9 and still falls within the interval.

D. The population mean is between 8 and 10: This claim can be supported by the given confidence interval, since the interval (6, 14) contains the values 8 and 10.

E. The population mean is more than 17: This claim can be refuted by the given confidence interval, since the upper bound of the interval is 14, which is less than 17.

Therefore, the claim that the confidence interval tends to support is D. The population mean is between 8 and 10.

The total cost of fencing the garden with the dimensions 20m,12m and 12m is equal to Rs. 6,600.

Side length of the garden to be fenced is equal to,

20m,12m and 12m

Cost of fencing at rupees per meter = Rs.150.

Calculate the total length of the fence.

⇒Total length of the fence = 20m + 12m + 12m

⇒ Total length of the fence = 44m

Now calculate the cost of fencing using the formula,

⇒ Cost of fencing = Total length of the fence x Cost per meter

⇒ Cost of fencing = 44m x Rs. 150/m

⇒ Cost of fencing = Rs. 6,600

Therefore, the cost of fencing the garden will be Rs.6,600 at a rate of Rs. 150 per meter.

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The given question is incomplete, I answer the question in general according to my knowledge:

Elina wants to fence the garden in front of a house on the side with the length 20m,12m and 12m. Find the cost of fencing at rupees 150 per meter.

Answer:

6C + $50 is the correct answer

Answer:

-----------------

Given inequality:

To select a correct solution we need to consider:

As we see, option C is reflecting the correct graph for the given inequality.

When comparing the data, a measure of center which should be used to determine which location typically has the cooler temperature is: B. Mean, because Sunny Town is skewed.

In Mathematics, skewness can be defined as a measure of the asymmetry of a box plot (box-and-whisker plot) or histogram and as such, a box plot (box-and-whisker plot) or histogram has a normal distribution when it is symmetrical.

By critically observing the histogram which represent Sunny Town, we can logically deduce that it is skewed.

In conclusion, we can reasonably infer and logically deduce that the data distribution is skewed to the left because the mean is less than the median and this area would have a cooler temperature.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: 379.94 yd²

Step-by-step explanation:

A = [tex]\pi r^{2}[/tex]    r=11    radius is half the diameter

 =(3.14)(11²)

 =379.94 yd²

Reducing the number of people in the sample from 2,500 to 1,500 will likely decrease the accuracy and precision of the estimate of the proportion of people who purchase the product online.

With a smaller sample size, there is a greater chance of sampling error and the results may not be representative of the entire population. The director should be aware that the smaller sample size may limit the reliability of the findings and consider adjusting the analysis accordingly.

The effect of reducing the number of people in the sample from 2,500 to 1,500 for the marketing department's study can be described as follows:

1. Decreased precision: By using a smaller random sample, the precision of the estimated proportion of people who purchase the product online will be reduced. This means that the range of possible values for the true proportion will be wider, leading to less certainty in the results.

2. Increased margin of error: With a smaller sample size, the margin of error will increase. This means that the range within which the true proportion lies will be larger, making it more difficult for the marketing department to make accurate predictions about online purchasing behavior.

3. Potential for increased bias: If the random sample of 1,500 people does not adequately represent the population of interest, the results may be more susceptible to bias. This could lead to inaccurate conclusions about the proportion of people who purchase the product online.

In summary, by reducing the sample size from 2,500 to 1,500 due to budget concerns, the marketing department will face a decrease in precision, an increase in the margin of error, and a potential for increased bias in their estimation of the proportion of people who purchase the product online.

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According to the above, the plants of group B have an average of 6 leaves more than those of group A.

To calculate the differences in leaves in the plants of both groups we must carry out the following procedure:

We must identify the number of leaves that the plants in each group have in total.

Group A

B Group

In this case, we must identify the average of each group and find the difference:

According to the above, the plants of group B have an average of 6 leaves more than those of group A.

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Result:

The p (the total number of players at the baseball game) = 16 players:

The equation to determine p: 3/4 = 12/p

The total number of players at the baseball game = p.

Given that, 3/4 of the players chose a bottle of water = 12p.

To write an equation to determine p, we can set up the following proportion:

3/4 = 12/p

This equation above represents the ratio of players who chose a bottle of water (3/4) to the total number of players, which is =  12 players.

To solve for p, we cross-multiply and then solve for P:

3p= 4 * 12

3p = 48

p = 48 / 3

p = 16

Therefore,  = 16 (represents the total number of players at the baseball game).

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