Classmates Joan, Peta, and Linda each received $400 as graduation gift. Joan deposits her money in an account that earns 7% interest compounded annually and keeps the money in the account for three years. Peta deposits her money, plus an extra $70, in an account that earns 8% interest compounded annually and keeps the money in the account for two years. Linda deposits her money in an account that earns 5% compounded'annually and keeps the money in the account for one year.

Who has more money when they close their accounts and why?

A) Joan, because she kept her money in the longest.
B) Linda, because of her interest rate.
C) Peta, because she invests the most.
D) They all make the same amount.​

Answer:

\(\sqrt{106}\) units

Step-by-step explanation:

Calculate the distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 9, 5)

d = \(\sqrt{(-9-0)^2+(5-0)^2}\)

   = \(\sqrt{(-9)^2+5^2}\)

   = \(\sqrt{81+25}\)

    = \(\sqrt{106}\)

Answer:

4th option

Step-by-step explanation:

tanZ = \(\frac{opposite}{adjacent }\) = \(\frac{XY}{ZY}\)

Answer:

The answer is $17.26

Step-by-step explanation:

Answer:

17.26

Step-by-step explanation:

if you plug in a calculator 20% 86.32 you get 17.264 but if you siplify you get $17.26

Hope this helped you!!

Answer:

\(List = \{GBB; BGB; BBG; GGB; BGG; GBG; GGG\}\)

Step-by-step explanation:

Given

\(Children = 3\)

Required

List all cases of having at least 1 girl

We have:

\(B = Boy\)

\(G = Girl\)

For 1 girl, we have:

GBB; BGB; BBG

For 2 girls, we have:

GGB; BGG; GBG

For 3 girls, we have:

GGG

Hence, the list is:

\(List = \{GBB; BGB; BBG; GGB; BGG; GBG; GGG\}\)

The length of an arc is defined as the product between the radius and the angle in radians. We already have the angle in radians (3 rad) and the radius which is 8cm. Then, to find the length of the arc (L):

Then:

The length of an arc whose central angle is 3 radians, and the radius is 8cm is 24 cm.

Suppose that IQ scores in one region are normally distributed with a standard deviation of 14.  the mean IQ score for this region is 97.2.

z =(x-mean)/standard deviation

58th percentile is a z-score of 0.202

Hence,

0.202=(100-mean)/14

2.828=100-mean

Multiplying through by 14

Mean IQ score = 100- 2.828

Mean IQ score =97.17

Mean IQ score =97.2 (Approximately)

Therefore the mean IQ score for this region is 97.2 .

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The mean absolute deviation is $106.6.

Given the table shows the amount Bill spent on 5 days last week.

DayAmount12622313126534To find the mean of the amount he spent: The formula for calculating the mean of a given set of values is mean=∑x/n where x represents the values, n represents the number of values, and ∑x represents the sum of the values.

Mean=total sum of values/total number of values Mean=(26+23+31+26+534)/5Mean=640/5Mean=128So,

the mean of the amount he spent is $128.To find the mean absolute deviation: The mean absolute deviation (MAD) is the average distance between each data value and the mean. MAD shows how much the data set deviates from the mean. The formula for calculating the MAD is MAD=∑|xi−m|/n where xi represents the values, m represents the mean, and n represents the number of values. So, the calculation for each day is:

Day Amount Absolute deviation from mean1 26 |128-26|=102 23 |128-23|=105 31 |128-31|=974 26 |128-26|=102 534 |128-534|=406

The sum of all absolute deviations is:

10+10+97+10+406=533The mean absolute deviation (MAD) is: MAD=533/5=106.6So.

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Answer:

Step-by-step explanation:

In a right triangle, the sum of the squares of the

lengths of the legs is equal to the square of the length

of the hypotenuse. The length of the hypotenuse is 13

and the lengths of the legs are 5 and x.  ansswer is 12

Answer:

AB = 18

Step-by-step explanation:

Oh man these are so much fun!

So for the angles:

A + B + C = 180 deg

And the sides:

Well, we don't know yet

Let's solve for x:

Since all the sides are equal (and there are three sides) we can do 180 / 3 to find each angle. So, each angle is 60 deg

6x = 60

Divide both sides by 6:

x = 10

Now for the sides:

x + 8 = BC

10 + 8 = BC

BC = 18

Since all the sides are equal, AB = 18 as well!

In statistics, the risk of making an error is referred to as a significance level. A significance level represents the probability of making a Type I error, which occurs when a null hypothesis is rejected even though it is true.

The most common significance level used in statistical analyses is 0.05 or 5%. This means that there is a 5% chance of rejecting a true null hypothesis.

In general, the choice of significance level depends on the specific application and context of the statistical analysis.

The 5% significance level is commonly used in scientific research, particularly in the fields of medicine and psychology.

The choice of this level is based on a balance between the risk of making a Type I error and the risk of making a Type II error, which occurs when a null hypothesis is not rejected even though it is false.

A Type II error is often more serious than a Type I error since it may lead to incorrect conclusions about the relationship between variables or the effectiveness of a treatment or intervention.

A 5% significance level provides a reasonable balance between these two types of errors. However, in some situations, a higher or lower significance level may be more appropriate.

For example, in a clinical trial where the consequences of a Type II error are severe, a lower significance level may be used to reduce the risk of this type of error.

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Answer:

34.55

Step-by-step explanation:

S = 34.55 represents the standard deviation of the residuals which is the correct answer that would be option (B).

A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.

Students' proficiency in math and English is assessed by a particular standardized test. Ten students were chosen at random, and their math and English test results were recorded and examined.

The computer output displays the outcomes.

Predictor    Coef     SE Coef     t-ratio        p

Constant   -124.13     78.712      0.046

Math           1.223      0.1966      6.220  0.000

S = 34.55     R-Sq = 82.8%      R-Sq (Adj) = 83.5%

In the above ANOVA table, S = 34.55 represents the residual standard deviation.

Therefore, the correct answer is Option B = 34.55.

Option A = 1.223 represents the coefficient of the math score.

Option C = 78.712 represents the Standard Error (S.E).

Option D = 124.13 is the coefficient value.

Hence, the correct answer would be an option (B).

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Answer:

1. A≈ 78.54

2. A≈201.06

Step-by-step explanation:

1) A=πr2=π·52≈78.53982

2)

A=1

4πd2=1

4·π·162≈201.06193

Answer:

-18

Step-by-step explanation:

Hope This Helps :)

Answer:

9.4ft²

Step-by-step explanation:

The formula for the area of a rectangle is base*height, or b*h.

Since we know the final area of the room and one of the side lengths, we can plug those into the formula I just stated so that we get

15*h=141

All that's left to do is solve for h, which is the other side that we are solving for. To do this, we will divide 15 on both sides:

15h/15=141/15

The 15s on the left side cancel out, and we simply divide 141 by 15 to get our final answer of 9.4ft².

Answer:

  (d)  yes; -7

Step-by-step explanation:

The differences between terms are ...

  12 -19 = -7

  5 -12 = -7

  -2 -5 = -7

These are all the same, so this difference is "common". A sequence in which terms have a common difference is an arithmetic sequence.

This sequence is arithmetic, with a common difference of -7.

Answer:

a) The claim is not plausible

b) claim is plausible and the type of bias here is response bias

Step-by-step explanation:

Given data:

Number of political parties = 4

coffee party got the support of 435 out of 1183 randomly selected voters in a poll conducted.

A) Construct and interpret a 98% confidence interval to estimate the proportion of voters who support the coffee party

H0 ( null hypothesis ) : p = 0.42

Ha ( alternate hypothesis ) : p ≠ 0.42

z value for 98% confidence interval = 2.326

using 98% confidence interval the value of p = ( 0.3668, 0.3686 )

hence the claim is not plausible

B) Determine the type of bias

Assume the actual number of people = 1200

and 17 people did not respond

hence number of people who responded = 1200 - 17 = 1183

Therefore the claim by the manager is plausible because 17 people did not respond and the type of bias here is response bias

attached below is a detailed solution of the problem of the A part

Answer: Come on, don’t people learn these things in school!

Step-by-step explanation:

Answer:

C. y ≤ 0

D. 18 bags of chips and 6 jars of salsa

Step-by-step explanation:

It is C because, it is over the x axis and it covers all the negative y's.

__________________________________________________________

2.5x + 4y ≤ 60

2.5(10) + 4(2) ≤ 60

25 + 8 ≤ 60

33 ≤ 60

It fits so A doesn't work

2.5x + 4y ≤ 60

2.5(20) + 4(2) ≤ 60

50 + 8 ≤ 60

58 ≤ 60

It fits so B doesn't work

2.5x + 4y ≤ 60

2.5(14) + 4(5) ≤ 60

35 + 20 ≤ 60

55 ≤ 60

It fits so C doesn't work

2.5x + 4y ≤ 60

2.5(18) + 4(6) ≤ 60

45 + 24 ≤ 69

It doesn't fit therefore, your answer would be D. 18 bags of chips and 6 jars of salsa.

Answer:

A

Step-by-step explanation:

Answer: in the third draw 33.33% people eliminated.

Step-by-step explanation:

Hope it will help u...........

Sum up the like terms :

Answer:

20

Step-by-step explanation:

each of the side lengths are multiplied by 2.5

Therefore , the solution of the given problem of sequence comes out to be the sequence's roughly 10th term is 0.049 (rounded to the closest thousandth).

A sequence is a grouping of range numbers, or "terms." There are phrases like 2, 5, but choose 8. Certain narrative arcs can be made to go on forever by choosing to capitalise on a certain pattern that they exhibit. Use the designs 2, 5, 8, and then 3 to lengthen it. In a list of words for words, there exist formulas that show where to look. In mathematics, a sequence is a group of items that are ordered in some way.

Here,

The first three terms in the given sequence are 15, 9, and 27/5.

We must determine the pattern or rule that underlies the sequence in order to determine the tenth word.

=>  9 = 15 * (27/5) / 15

=>  27/5 = 9 * (27/5) / 9

Thus, each term is obtained by multiplying the constant value by (27/5) / 15, which may be written as 9/25.

In order to get the next phrase in the series, we can keep multiplying the preceding term by 9/25 using this constant value:

=>  9 * (9/25)⁷

When we compute this expression, we obtain:

=>  (Rounded to the closest thousandth) 9 * (9/25)⁷

As a result, the sequence's roughly 10th term is 0.049 (rounded to the closest thousandth).

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Answer:

3x^2 - 32x - 48

Step-by-step explanation:

3x^2-36x+4x-48

3x^2 - 32x -48

Answer: The surface area of the rectangular prism is approximately 4 square yards.

Step-by-step explanation: Given that the volume of the rectangular prism is 160 cubic yards, we can find the dimensions of the prism using the formula:

V = lwh

where V is the volume, l is the length, w is the width, and h is the height.

So, we have:

160 = lwh

Now, we need to find two other measurements in order to calculate the surface area of the rectangular prism. However, we do not have enough information to find all three dimensions. Therefore, we will assume one dimension and find the other two.

Let's assume that the height of the rectangular prism is 10 yards. Then, we can rearrange the formula for the volume to solve for the product of the length and width:

lw = V/h = 160/10 = 16

Now, we have two equations:

lw = 16

wh = 160/10 = 16

Solving for w in the first equation, we get:

w = 16/l

Substituting this expression for w in the second equation, we get:

l(16/l)h = 16

Simplifying, we get:

h = 1

Therefore, the dimensions of the rectangular prism are:

length = l

width = 16/l

height = 10

Now, we can calculate the surface area of the rectangular prism using the formula:

SA = 2lw + 2lh + 2wh

Substituting the values we found, we get:

SA = 2(l(16/l)) + 2(l(10)) + 2((16/l)(10))

SA = 32/l + 20l + 160/l

To find the minimum value of this expression, we can take its derivative with respect to l and set it equal to zero:

dSA/dl = -32/l^2 + 20 + (-160/l^2)

0 = -32/l^2 + 20 - 160/l^2

52/l^2 = 20

l^2 = 52/20

l ≈ 1.44

Substituting this value of l back into the expression for SA, we get:

SA ≈ 4 square yards

Therefore, the surface area of the rectangular prism is approximately 4 square yards.

The expected return given these three economic states, their likelihoods, and the potential returns is 14.5%.

To compute the expected return given the three economic states, their likelihoods, and the potential returns, we need to multiply each potential return by its corresponding likelihood and then add up the results. This will give us the overall expected return.

Here is the formula for calculating expected return:
Expected return = (likelihood of economic state 1) x (potential return for economic state 1) + (likelihood of economic state 2) x (potential return for economic state 2) + (likelihood of economic state 3) x (potential return for economic state 3)

For example, if the likelihoods and potential returns are as follows:

Economic state 1: likelihood = 0.3, potential return = 10%
Economic state 2: likelihood = 0.5, potential return = 15%
Economic state 3: likelihood = 0.2, potential return = 20%

Then the expected return would be:
Expected return = (0.3 x 10%) + (0.5 x 15%) + (0.2 x 20%) = 3% + 7.5% + 4% = 14.5%

Therefore, the expected return given these three economic states, their likelihoods, and the potential returns is 14.5%.

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The standard form for expressing the equation of a straight line is

y = mx + b

Given the functions from the question f(x)  = 3x + 4

If h(x) = f(x+3)

Replace x with x+3 in the function f(x) to have;

h(x) = 3(x+3) + 4

h(x) = 3x + 9 + 4

h(x) = 3x + 13

Hence the required graph for both functions are attached below;

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Answer:

if you get good grades then you will not get into a good college

Step-by-step explanation:

The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

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The value of the variable "x" is 11.

We have a triangle. The vertices of the triangle are K, L, and M. The side KM is extended from point M to point N. The measures of the angles MKL, LMN, and KLM are (3x + 19)°, (7x + 5)°, and (2x + 8)°, respectively. We need to find out the value of the variable "x".

The angles LMK and LMN form a linear pair. It means they are supplementary angles. The sum of the angles is 180°.

∠LMK + ∠LMN = 180°

∠LMK + (7x + 5)° = 180°

∠LMK = 180° - (7x + 5)°

In the triangle KLM, we will use the angle sum property of a triangle. The sum of all the angles in a triangle is equal to 180°.

∠K + ∠L + ∠M = 180°

(3x +19)° + (2x + 8)° + [180° - (7x + 5)°] = 180°

3x +19 + 2x + 8 + 180 - 7x - 5 = 180

-2x + 22 = 0

2x = 22

x = 11

Hence, the value of the variable "x" is 11.

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