Singular Savings Bank received an initial deposit of $3000. It kept a percentage of this money in reserve based on the reserve rate and loaned out the rest. The amount it loaned out was eventually all deposited back into the bank. If this cycle continued indefinitely and eventually the $3000 turned into $50,000, what was the reserve rate? And what are the steps to solve?

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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The median of the distances is M = 6.5 kilometers

Given data ,

To find the median of a set of numbers, we arrange the numbers in ascending order and then locate the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

Arranging the given set of numbers in ascending order: {4, 5, 8, 11}

Since the set has an even number of values, the median is the average of the two middle numbers. In this case, the two middle numbers are 5 and 8. To find the average, we add these two numbers and divide by 2:

(5 + 8) / 2 = 13 / 2 = 6.5

Hence , the median of the given set {4, 5, 8, 11} is 6.5

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The required explanation for hypothesis test is described.

When the null hypothesis is true in this setting, it means that the true proportion of students at Mr. Tabor's school who completed their math homework last night is equal to 0.75, or 75%. This is the value that Mr. Tabor initially believed, but the sample data suggests that only 68% of the students completed their homework.

A PP-value is the probability of observing a sample proportion as extreme or more extreme than the sample proportion, given that the null hypothesis is true. In this case, the PP-value of 0.1265 is not small enough to reject the null hypothesis. A commonly used significance level is 0.05, which means that if the PP-value is less than 0.05, the null hypothesis would be rejected.

So, given the PP-value of 0.1265, which is greater than 0.05, we cannot reject the null hypothesis and must conclude that there is not enough evidence to suggest that the true proportion of students who completed their homework is less than 0.75. This means that, based on the sample data, the null hypothesis that the true proportion is equal to 0.75 is not ruled out, and there is not enough evidence to support the alternative hypothesis that the true proportion is less than 0.75.

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Answer:

m = 3

Step-by-step explanation:

Use the slope formula to find the slope  m .

By completing the square, the vertex form of quadratic equation is (x - 1)² - 3.

In this question we find a quadratic equation in standard form, which must be modified into vertex form by completing the square, which consists in modifying part of the equation into a perfect square trinomial. The vertex form of the quadratic equation is:

y = C · (x - h)² + k

First, write the polynomial in standard form:

x² - 2 · x - 2

Second, use algebra properties to expand the expression:

(x² - 2 · x - 2) + 0

(x² - 2 · x - 2) + 3 - 3

(x² - 2 · x + 1) - 3

Third, use the definition of perfect square trinomial:

(x - 1)² - 3

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the correct answer is A) y = -2/5x + 1

Step-by-step explanation:

2x + 5y - 5 = 0

2/5x + y - 1 = 0

y = - 2/5x + 1

1. Mean = 33.61

2. Standard Deviation = 11.3284

3. Variance = 128.33

The given data are: \(22.8, 49.8, 17.5, 44.1, 33.2, 20.6, 43.2, 37.7\)

To get mean, we will sum up all the numbers and divide by the total count. The mean is:

= (22.8 + 49.8 + 17.5 + 44.1 + 33.2 + 20.6 + 43.2 + 37.7) / 8

= 268.9 / 8

= 33.62

Standard Deviation: \(\sqrt((22.8 - 33.61)^2 + (49.8 - 33.61)^2 + (17.5 - 33.61)^2 + (44.1 - 33.61)^2 + (33.2 - 33.61)^2 + (20.6 - 33.61)^2 + (43.2 - 33.61)^2 + (37.7 - 33.61)^2) / 8\)

= \(\sqrt{128.3336}\)

= 11.3284420818

= 11.3284

Variance = (Standard Deviation)^2

Variance = \(11.3284 ^2\)

Variance = 128.33264656

Variance = 128.33.

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Answer:

nothing

Step-by-step explanation:

If you are translating entire triangle, then translating doesn't influence the area. It's just going to change where the triangle is located not its size

Answer:

Abdiel's total would be $23.22, which is the answer choice C.

Step-by-step explanation:

The total cost of Abdiel's order would be calculated as follows:

Calculate the tip before the discount: $21.50 x 20% = $4.30

Add the tip to the subtotal: $21.50 + $4.30 = $25.80

Calculate the discount: $25.80 x 10% = $2.58

Subtract the discount from the total cost: $25.80 - $2.58 = $23.22

So, Abdiel's total would be $23.22, which is the answer choice C.

Answer:

\(P(x\geq 3)=0.3233\)

Step-by-step explanation:

If the number of defects in poured metal follows a Poisson distribution, the probability that x defects occurs is:

\(P(x)=\frac{e^{-m}*(m)^{x}}{x!}\)

Where x is bigger or equal to zero and m is the average. So replacing m by 2, we get that the probability is equal to:

\(P(x)=\frac{e^{-2}*(2)^{x}}{x!}\)

Finally, the probability that there will be at least three defects in a randomly selected cubic millimeter of this metal is equal to:

\(P(x\geq 3)=1-p(x\leq 2)\\\)

Where \(P(x\leq 2)=P(0)+P(1)+P(2)\)

So, P(0), P(1) and P(2) are equal to:

\(P(0)=\frac{e^{-2}*(2)^{0}}{0!}=0.1353\\P(1)=\frac{e^{-2}*(2)^{1}}{1!}=0.2707\\P(2)=\frac{e^{-2}*(2)^{2}}{2!}=0.2707\)

Finally, \(P(x\leq2)\) and \(P(x\geq3)\) are equal to:

\(P(x\leq 2)=0.1353+0.2707+0.2707=0.6767\\P(x\geq 3)=1-0.6767=0.3233\)

Answer:

$26.87

Step-by-step explanation:

if the shirt was 35% off, then you paid 65% of the cost

that value can be found by:

39 x .65 = 25.35 (this is the amount paid for the shirt)

sales tax of 6% on 25.35 is:

.06 x 25.35 which equals 1.52

25.35 + 1.52 = 26.87

Answer:

parallel slope = \(\frac{13}{8}\) , perpendicular = \(\frac{-8}{13}\)

Step-by-step explanation:

to find slope, formula: \(\frac{y2-y1}{x2-x1}\)

                                   : \(\frac{6--7}{6--2}\)

                                   : \(\frac{13}{8}\)

if parallel, same slope, so slope = 13/8

if perpendicular, slope = -1/n = -1/13/8 =  -8/13 is the perpendicular slope.

The plot of the residuals to the area indicates that the graph that corresponds to the residuals is the second option.

Please find attached the graph of the residual plot for the data created with MS Excel

A residual plot is a tool used for assessment of statistical models, to determine how fit the model is to the data. A residual plot is a plot of the residuals to the input or x-values of the data.

The trend line for the data in the question obtained using MS Excel indicates that we get; y = 0.1128·x + 3.6158

The residuals, which is the difference between the actual values and the calculated value obtained using MS Excel are;

Area (in²)    \({}\)              Residuals

x-value

5 \({}\)                             -1.0178

10 \({}\)                           -0.2718

24 \({}\)                           0.605

46 \({}\)                           0.7874

53 \({}\)                           0.7018

78 \({}\)                           0.0758

84 \({}\)                           -0.129

100 \({}\)                         -0.7538

The above values for the areas and the residuals indicates that the residual plot is n shaped, with the first two values being below the x-axis, which corresponds to the second option

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Answer:

2355

Step-by-step explanation:

Answer:

Kyle typed 574 words in 14 minutes. How many...........?????????

il.l just divide 574 divided by 14= 41

Step-by-step explanation:

:)

Answer:

41 like I said in the comments.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

35=5×7

5=5

70=2×5×7

G.C.F. is 5

The difference between a root and a factor is roots are zero of the function.

What's the difference between a root and a factor?

You can switch back and forth between a polynomial's factors and roots, according to the factor theorem. In other words, if you are familiar with one, you are familiar with the other. A polynomial of a degree of more than two may occasionally be asked of you by your teacher or your textbook. Finding its causes can help you discover its roots.

You can substitute a number for x and obtain a true assertion by using the root a.

(a – a)(a – b) = 0

The initial factor in this scenario is 0.

In order to produce a true assertion, you can alternatively replace x with the root b's number.

(b – a)(b – b) = 0

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Answer:

Step-by-step explanation:

It really is just a matter of substituting the given values into the given equations.

f(x)=-3x

f(2)=-3(2)

f(2)=-6

h(a)=4a

h(4)=4(4)

h(4)=16

g(x)=x^2-1

g(8)=8^2-1

g(8)=64-1

g(8)=63

The perimeter and the area of the rectangle are 26 units and 42 square units, respectively.

A rectangle is a quadrilateral with all four interior angles 90°.

Given that, the vertices of the rectangle are (-3.5,3), (3.5,3), (3.5,-3), and (-3.5,-3).

The length of the  rectangle is:

l = 3.5 - (-3.5)

l = 3.5 + 3.5

l = 7

The width of the rectangle is:

w = 3-(-3)

w = 3 + 3

w = 6

The perimeter of the rectangle is given by:

P = 2 (l +w)

P = 2(7 + 6)

P = 26

The area of the rectangle is:
A = l × w

A = 7 × 6

A = 42

Hence, the perimeter and the area of the rectangle are 26 units and 42 square units, respectively.

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Answer:

3.34.

Step-by-step explanation:

4.2 * 0.2 + 2.5

= 0.84 + 2.5

= 3.34.

Answer:

3.34

Step-by-step explanation:

the product is 4.2×0.2=0.84

add is 2.5 + 0.84=3.34

Answer:

10°C

Step-by-step explanation:

F = 50

C = 5/9 * (F - 32) = 5/9 * (50 - 32) = 5/9 * 18 = 5 * 2 = 10

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

it is 8

Step-by-step explanation:

1+1+1+1+1+1+1+1

2+2+2+2

4+4

8

Answer:

8

Step-by-step explanation:

Answer: y = -1x + 3

Step-by-step explanation:

it's going through the y intercept ( 3 )

and down ( negative by 1 )

you can also write the answer as y = -x + 3

either one, its the same.

Answer:

Step-by-step explanation:

152 cubic ft

Answer:

Volume of solid figure=Volume of

upper cuboid+volume of lower cuboid

=l*b*h+l*b*h=10*4*3+4*4*2=152 cubic ft

152 cubic ft

Answer:

Volume of solid figure=Volume of

upper cuboid+volume of lower cuboid

=l*b*h+l*b*h=10*4*3+4*4*2=152 cubic ft

Answer:

Reasons 1. Given

2. Angle Addition Postulate

Statements

+

1. AD|| BC

2. mZ3+m25 mZDAB

3. m24+mZDAB = 180*

4. m24+mZ3+ m25 180°

5. 21 $ 24, 22 & 25

6. mZ1 m24, m22 m25

7. mZ1+m/2+mZ3 180°

3. Linear Pair Postulate

4. Substitution Property of Equality

15.

2

6. Definition of Congruent Angles

7

?

The

2 matches "Given", 3 matches "Supplements to - angles", 4 matches "Reflexive",  5 matches "ASA" and  6 matches with "CPCTE

A triangle is a three-sided polygon that consists of three edges and three vertices.

We start at what it gives us, so 2 matches "Given".

So, 3 matches "Supplements to - angles".

From what we see that 1 matches "Exterior sides in oppposite rays".

We can see that 4 matches "Reflexive".

From this we got that 5 matches "ASA", because the triangles are congruent by angle-side-angle.

Because they are congruent, we match 6 with "CPCTE" (Corresponding Parts of Congruent Triangles are Equal).

Hence, 2 matches "Given", 3 matches "Supplements to - angles", 4 matches "Reflexive",  5 matches "ASA" and  6 matches with "CPCTE"

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Answer:

Setting can reveal the theme of the text because if the setting is a funeral, the theme may be about death or appreciation of life.

Answer:

a. We are 90% sure that the mean GPA for all students at her school is between 3.14 and 3.52.

b. The length would increase.

c. The interval would be narrower.

d. The biggest potential source of bias is making the students state their grades aloud, which makes it possible that students with low grades could lie their grades, making it seem higher, and the interval biased.

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

Margin of error of a confidence interval:

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which z is related to the confidence level(higher the confidence level, higher z) \(\sigma\) is the standard deviation of the population and n is the size of the sample.

This shows that if we increase the confidence level, the margin of error gets larger and the interval gets wider, while if we increase the sample size the margin of error gets smaller and the interval gets narrower.

a. Interpret the confidence level.

We are 90% sure that the mean GPA for all students at her school is between 3.14 and 3.52.

b. Explain what would happen to the length of the interval if the confidence level were increased to 99%.

We would increase the confidence level, and the interval would get wider, that is, the length would increase.

c. How would a 90% confidence interval based on a sample of size 200 compare to the original 90% interval?

Larger sample size means that the interval would be narrower.

d. Describe one potential source of bias in Ellery's study that is not accounted for by the margin of error.

The biggest potential source of bias is making the students state their grades aloud, which makes it possible that students with low grades could lie their grades, making it seem higher, and the interval biased.

Based on the information given in the sample, it should be noted that this implies that we are 90% sure that the mean GPA for all students at the school is between 3.14 and 3.52.

Lastly, a potential source of bias in Ellery's study that is not accounted for by the margin of error is making the students state their grades aloud. This will make some of them with lower grades lie.

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