kate started solving the problem by finding 200% of of $25,000 how might she have finished solving the problem??​

a. A function that represents the balance (in dollars) or the future value of the savings account after t years is C. s(t) = 6,000(1 + 0.045/12)^12t.

b) The balance (future value) of the account after 6 years, to the nearest cent, is $7,855.82.

The future value can be computed using the FV formula or function below:

s(t) = 6,000(1 + 0.045/12)^12t

s(t) = 6,000(1 + 0.045/12)^12(6)

= $7,855.8186

= $7,855.82

This future value can also be computed using an online finance calculator as follows:

N (# of periods) = 72 months (6 years x 12)

I/Y (Interest per year) = 4.5%

PV (Present Value) = $6,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $7,855.82

Total Interest = $1,855.82

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If a researcher has access to a list of all pilots who are members of the Air Line Pilots Association and she wishes to conduct a study, she can use this list as the frame for selecting a random sample of pilots. By doing so, she can ensure that the sample is representative of the larger population of pilots who are members of the association.  

Suppose a researcher wants to conduct a study on pilots who are members of the Air Line Pilots Association. The researcher has access to a list of all these pilots, which serves as the frame for the study. In order to randomly select a sample of pilots, the researcher can follow these steps:

1. Assign a unique number to each pilot on the list.
2. Determine the sample size required for the study based on the research objectives.
3. Use a random number generator or a random sampling technique (e.g., simple random sampling) to select the desired number of pilots from the list.
4. Once the sample has been chosen, the researcher can proceed with the study by contacting the selected pilot members and collecting the necessary data.

This method ensures that the sample is representative of the entire population of pilots in the Air Line Pilots Association and helps maintain the validity of the research findings.  This is important because it allows her to draw conclusions about the population based on the sample data. The sample should be selected in a random and unbiased manner to ensure that it is a true representation of the population. The researcher can then use the data collected from the sample to make inferences about the population of pilots who are members of the Air Line Pilots Association.

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The future value of the IRA is given as $5149.78. Option C

Raymond and his wife plan to deposit $100 per month,  

semi-annual period, deposit = $100 × 6

= $600

[tex]FV = P * [(1 + r)^n - 1] / r[/tex] = 8.58297

We have to define the terms in the formula

FV is the future value of the IRA,

P is the payment per period ($600),

r is the interest rate per period (2% or 0.02 as a decimal),

n is the number of periods (8).

FV = $600 * 8.58297

FV = $5,149.78

The futire value is given as FV = $5,149.78

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The amount of servings are in 16.8 grams of the snack is: 5 servings

Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve basic arithmetic operations and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.

We are told that:

Serving Size for a snack = 3¹/₅ grams = 16/5 grams

In 16.8 grams, we can write as 168/10 or 84/5

Thus:

The amount of servings are in 16.8 grams of the snack is:

84/5 ÷ 16/5

= 84/5 * 5/16

= 84/16

= 21/4

= 5.25

Approximately 5 servings

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If we wanted to calculate the p-value, we would find the probability of getting a z-score of 2.16 or higher (in the right tail) using the standard normal distribution, which is approximately 0.015. The p-value is less than the significance level of 0.03, so we would still reject the null hypothesis.

Let p be the proportion of left-handers in the college population, and p0 be the proportion of left-handers in the general American population. We are given that p0 = 0.11.

Our null hypothesis is that the proportion of left-handers in the college population is the same as in the general American population:

H0: p = 0.11

Our alternative hypothesis is that the proportion of left-handers in the college population is higher than in the general American population:

Ha: p > 0.11

We will use a significance level of 0.03.

The test statistic for the one-sample proportion test is:

z = (p - p0) / √(p0*(1-p0)/n)

where n is the sample size.

Using the values given in the problem, we have:

p = 63/440 = 0.143

n = 440

p0 = 0.11

Substituting these values into the formula, we get:

z = (0.143 - 0.11) / √(0.11*(1-0.11)/440)

= 2.16

Looking at the z-table, we see that the probability of getting a z-score of 2.16 or higher (in the right tail) is about 0.015. Since this is smaller than our significance level of 0.03, we reject the null hypothesis.

Therefore, we have evidence to suggest that the proportion of left-handers in the college population is higher than in the general American population.

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The situation that can be represented by the expression x-2 where x represents the original price (in dollars) is B) $2 less than the original price

The value of x-2 symbolizes a price, subtracted with two dollars. However, if "$2 less than three-quarters of the original price" is to be written and represented through an expression, it becomes (3/4)x - 2 instead of x-2.

.

Thus, showing that this situation cannot be indicated by x-2. On the other hand, " $2 less than the original price" can be rightfully denoted using the expression x-2. It fulfills the task effectively and accurately represents the given scenario.

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Answer:

$96.25

Step-by-step explanation:

$77 x 25% = $19.25

$77 + $19.25 = $96.25

There are 210 different selections of 4 books that can be made from 10 different books with no restriction. There are 28 different selections of 4 books that can be made from 10 different books if two particular books are always selected. There are 70 different selections of 4 books that can be made from 10 different books if two particular books are never selected.

(i) If there is no restriction, then we can choose any combination of 4 books from the 10 different books. This is a combination problem, and the formula for combinations is:

n C r = n! / r!(n-r)!

where n is the total number of items to choose from, and r is the number of items we want to choose.

So, in this case, we have n = 10 and r = 4. Plugging these values into the formula, we get:

10 C 4 = 10! / 4!(10-4)! = 210


(ii) If two particular books are always selected, then we only need to choose the remaining 2 books from the remaining 8 books. We can do this using the same combination formula, but with different values of n and r:

n = 8 (since we only have 8 books to choose from)
r = 2 (since we want to choose 2 books)

Plugging these values into the formula, we get:

8 C 2 = 8! / 2!(8-2)! = 28


(iii) If two particular books are never selected, then we need to choose 4 books from the remaining 8 books. Again, we can use the same combination formula:

n = 8
r = 4

Plugging these values into the formula, we get:

8 C 4 = 8! / 4!(8-4)! = 70

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Step-by-step explanation:

to find to multiply it 3 times

V=length x width x height

V=25in x 25in x 25in

V=15,625 cubic inches

Answer:

[tex]V = 15,625 in^3[/tex]

Step-by-step explanation:

The formula for the area of a square is if x is the length of a side

V = x^3

V =25^3

V = 25 · 25 · 25

V = 625 ·25

V = 15,625 in^3

Tukey's procedure to investigate significant differences between brands is x3. and x5.

x4. and x5.

To use Tukey's procedure to investigate significant differences between brands, we need to calculate the value of W and compare it with the critical value from the Studentized Range Distribution.

The formula for W is:

W = q(α, 5, 15) * √(MSE/4)

where q(α, 5, 15) is the critical value from the Studentized Range Distribution with α = 0.05, k = 5 (number of brands), and df = 15 (total degrees of freedom). Using a table or calculator, we find:

q(0.05, 5, 15) = 3.07

Plugging in the given values, we get:

W = 3.07 * √(450.8/4) ≈ 17.99

Since the computed value of F was found to be significant at level α = 0.05, we can conclude that there are significant differences between at least some of the brands. To determine which brands differ significantly from one another, we can use the formula:

|xi. - xj.| ≥ W / √(2MSE/4)

where xi. and xj. are the sample averages for any two brands i and j. If this inequality is satisfied, then we can say that the two brands differ significantly from one another.

Calculating the absolute differences between all pairs of sample averages and comparing them with the right-hand side of the inequality above, we get:

|462.0 - 502.8| = 40.8 ≥ 8.99 → Significant

|462.0 - 427.5| = 34.5 < 8.99 → Not significant

|462.0 - 469.3| = 7.3 < 8.99 → Not significant

|462.0 - 532.1| = 70.1 ≥ 8.99 → Significant

|502.8 - 427.5| = 75.3 ≥ 8.99 → Significant

|502.8 - 469.3| = 33.5 < 8.99 → Not significant

|502.8 - 532.1| = 29.3 < 8.99 → Not significant

|427.5 - 469.3| = 41.8 ≥ 8.99 → Significant

|427.5 - 532.1| = 104.6 ≥ 8.99 → Significant

|469.3 - 532.1| = 62.8 ≥ 8.99 → Significant

Using the critical value W, we can conclude that brands 1, 2, 4, and 5 differ significantly from one another. Therefore, the correct answer is:

x1. and x2.

x1. and x5.

x2. and x3.

x3. and x4.

x3. and x5.

x4. and x5.

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The solution to the linear equation graph problems are:

a) 20 months

b) 7 pounds

c) 27 pounds

d) Rate of change of weight per month

e) Weight of the infant at birth

The general form of the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

a) The corresponding age at which the infant weighed 11 pounds from the graph is: 20 months

b) The infants weight at birth is the age at 0 years which in this case is 7 pounds

c) Paul's function is given as:

y = ⁵/₄x + 7

Thus, at 16 months, the weight is:

y = ⁵/₄(16) + 7

y = 27 pounds

d) What the number 5/4 represents in the model is the rate of change of weight per month.

e) The number 7 in part c denotes the weight at birth.

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The length of a 135° arc with a radius of 10 feet is 23.56 feet.

To find the length of the arc, we need to first find the circumference of the circle.

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference and r is the radius.

Substituting radius = 10 feet:

C = 2π(10) = 20π feet

To find the length of a 135° arc, we need to find what fraction of the circle's circumference is represented by 135°.

Since a full circle is 360°, the fraction of the circle represented by 135° is:

135/360 = 3/8

So the length of the arc is:

(3/8) × 20π = 23.5 feet

Therefore, the length of a 135° arc with a radius of 10 feet is 23.56 feet.

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In this hypothetical two-way layout, we are studying the effects of two drugs A and B on remaining life. The drugs are each taken in quantities of 0g, 1g or 2g, resulting in a total of 9 possible treatment combinations.

Our outcome of interest is years of remaining life. To analyze this data, we would likely use a two-way ANOVA to assess the main effects of each drug and the interaction effect between the two drugs. This analysis would allow us to determine if there is a significant difference in remaining life between the different drug doses and if the effect of one drug is influenced by the dose of the other drug.

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The range of the graphed function is  y  ≤ 1, or written in interval form, it is:

(-∞, 1]

The range is the set of the possible outputs of the function, so we need to look at the vertical axis (also called the y-axis).

Here we can see that we have the maximum at y = 1, and then the function goes down. (We can assume it will go to negative infinity, this is beacuse we can see arrow points at the ends, which means that the function keeps going downwards)

Then the range is:

y  ≤ 1

Or (-∞, 1] in interval form.

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The negation of "p and q" is "not p or not q", which means that "p and q" is false if either "p" or "q" is false.

To negate a conjunction, which is a statement of the form "p and q", we need to negate each of the component statements and change "and" to "or". The negation of "p and q" is "not p or not q", which means that "p and q" is false if either "p" or "q" is false.

For example, if we have the statement "John will go to the beach and he will go to the park", we can negate it by saying "It is not the case that John will go to the beach and he will go to the park", which can be written symbolically as "not (John will go to the beach and he will go to the park)". Using the rule for negating a conjunction, we can rewrite this statement as "John will not go to the beach or he will not go to the park".

Note that this is different from the negation of a disjunction, which is a statement of the form "p or q". The negation of "p or q" is "not p and not q", which means that "p or q" is false if both "p" and "q" are false.

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The ratio of ages of a man who has three children whose ages are 9 years, 12 years, and 24 years is 1:4/3:8/3.

To find the ratio of the ages of the man's three children, we need to divide their ages by their greatest common factor (GCF). The GCF of 9, 12, and 24 is 3. So, we divide each age by 3:

9 ÷ 3 = 3

12 ÷ 3 = 4

24 ÷ 3 = 8

Therefore, the ratio of their ages is 3:4:8. This means that for every 3 years the youngest child ages, the middle child ages 4 years, and the oldest child ages 8 years. We can simplify the ratio by dividing all three numbers by their GCF of 3, which gives us the simplified ratio of 1:4/3:8/3.

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Our calculated t-value of -0.20 falls within this range, we cannot reject the null hypothesis that the true mean package weight is 10 oz. The t-statistic for a two-sided test would be -0.20.

To calculate the t-statistic, we use the formula:

t = (x - μ) / (s / √n)

Where:
x = mean of the sample = (10.2 + 10.5 + 9.3 + 9.8 + 10.0) / 5 = 10.16 oz
μ = hypothesized population mean = 10 oz
s = sample standard deviation = 0.45 oz
n = sample size = 5

Plugging in the values, we get:

t = (10.16 - 10) / (0.45 / √5) ≈ -0.20

Since this is a two-sided test, we look for the t-value that corresponds to a two-tailed 95% confidence interval with 4 degrees of freedom (n-1 = 4). Using a t-table or calculator, we find that the critical t-value is ±2.776.

Since our calculated t-value of -0.20 falls within this range, we cannot reject the null hypothesis that the true mean package weight is 10 oz.
To calculate the t-statistic for a two-sided test, we need to compare the sample mean with the population mean, and divide the difference by the standard error. First, let's calculate the sample mean and standard error:

Sample mean = (10.2 + 10.5 + 9.3 + 9.8 + 10.0) / 5 = 49.8 / 5 = 9.96 oz.

Standard error = standard deviation / √(sample size) = 0.45 / sqrt(5) ≈ 0.20

Now, let's find the t-statistic:

t-statistic = (sample mean - population mean) / standard error = (9.96 - 10) / 0.20 = -0.04 / 0.20 = -0.20

The t-statistic for a two-sided test would be -0.20. So, the correct answer is:

O -0.20

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Answer:

[tex] \frac{1}{5} [/tex]

Step-by-step explanation:

[tex] \frac{2}{5} = y \: \\ x \ = 2 \\ \frac{ \frac{2}{5} }{2} = \frac{2}{2} \: \\ \frac{1}{5} = y \: when \: \: 1= x[/tex]

Answer:

right angle

Step-by-step explanation:

the sign you find in the angle ABC means that it is a right angle, therefore 90°

1) the resulting points or figure from the given cordinates is a compound   shape comprising of two rectangles. The distance between the coordintes or points are arrived at using a calculation. See graph and sample calculations below.

2) the are of the compound shape is 104 units.

1) First, using a graphing calculation, we arrived at the ponts on the coordinates.  See the attached image for all the labelled coordinagtes.

2) Then we joined all coordinteas or points.

3) then using the distance formula, we arrived at the distance between each coordinate. See sample of the first calculation that was done:

To compte the distance between: A (−6, 6) and B( 6,6) we use the following formula:

d = √ ((x2 - x1) ²   + (y2 - y 1)²)
Thus,  we have


d=√(6−(−6))²+(6−6)²)

d = √[(12²) + (0²)

d = √144

d = 12

We repeated this for all the sides or coordinate pairs.


4) having arrrived at all the sides, we simplified the compound shape by puting dividing it into tow rectangles.

As you know the formula for the Area of a Rectangle is:

lxw

Sor for the Bigger rectangle Rb we have

L = 12
W = 7
Thus,

Ab = 12 x 7 = 84

For the Smaller rectangle Rs, we have:

As = 4 x 5
As = 20

Since the compound shape = Rb + Rs
Asb = 84 + 20

Area of the resulting  Figure thus, is 104 units.

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Answer:

1. If X^2 = 144, then X = 12 or X = -12

2. If X = 12 or X = -12, then X^2 = 144

Step-by-step explanation:

he biconditional statement can be written as:

X^2 = 144 if and only if X = 12 or X = -12

This statement can be broken down into two conditional statements:

1. If X^2 = 144, then X = 12 or X = -12

2. If X = 12 or X = -12, then X^2 = 144

There is a very low probability of fewer than 100 insects surviving in the rose garden.

Given that the insecticide is advertised as being 99% effective, it means that 1% of the insects are not affected by the insecticide. Therefore, the probability of an insect surviving the insecticide is 0.01.

Let's assume that the number of surviving insects, X, follows a binomial distribution with parameters n = 2000 and p = 0.01. We want to find the probability that fewer than 100 insects survive, i.e., P(X < 100).

Since the number of trials is large (n = 2000) and the probability of success is small (p = 0.01), we can approximate the binomial distribution with a Poisson distribution with parameter λ = np = 2000*0.01 = 20.

Using the Poisson distribution, we can calculate the probability of fewer than 100 insects surviving as:

P(X < 100) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 99)
          = e^(-20) * (20^0/0!) + e^(-20) * (20^1/1!) + e^(-20) * (20^2/2!) + ... + e^(-20) * (20^99/99!)

We can use a calculator or a software program to calculate this sum, which gives us an approximation of 0.0000386 or 0.00386%.

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The original price of the hammock, when rounded to the nearest penny, can be found to be $ 102.67.

To determine the initial amount of the hammock, we must consider its price prior to the 25% sale that Ronald bought it for $77. Let us denote the original price as P. If we deduct 25% from the original price, then the new cost is equivalent to 75% of its total value (100% - 25% = 75%).

Thus, we can represent this calculation as:

Sales price = 0. 75 x P

77 = 0. 75P

P = 77 / 0. 75

P = $ 102. 67

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It should be noted that a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.

Positive numbers are plotted to the right of the origin while negative numbers are plotted to the left of the origin. Arrows are put on the ends of the horizontal line to show that the line continues to infinity.

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There is a 9.85% probability of obtaining a sample with a mean time to relief of 3.3 minutes or less.

To calculate the probability of obtaining a sample with a mean time to relief of 3.3 minutes or less, we need to use the standard error formula:

Standard error = population standard deviation / square root of sample size

In this case, the standard error would be:

Standard error = 1.1 / square root of 50
Standard error = 0.155

Next, we need to calculate the z-score using the following formula:

z-score = (sample mean - population mean) / standard error

Since the population mean is not given, we can use the sample mean as an estimate of the population mean. Therefore, the z-score would be:

z-score = (3.3 - 3.5) / 0.155
z-score = -1.29

Using a z-table or calculator, we can find the probability of obtaining a z-score of -1.29 or less. The probability is approximately 0.0985, or 9.85%.

Therefore, the probability of obtaining a sample with a mean time to relief of 3.3 minutes or less is 9.85%. This means that there is a relatively low probability of obtaining such a sample if the manufacturer's claim is not true. However, since the manufacturer presented statistical evidence to the FDA, it is likely that the claim is supported by the data.
The manufacturer of the heartburn relief medication claims that its product brings relief in less than 3.5 minutes, on average. They provided statistical evidence with a sample of 50 heartburn sufferers, where the mean time to relief was 3.3 minutes and the population standard deviation was 1.1 minutes. To calculate the probability of obtaining a sample with a mean time to relief of 3.3 minutes or less, we can use the z-score formula:

z = (sample mean - population mean) / (population standard deviation / √sample size)

z = (3.3 - 3.5) / (1.1 / √50)
z = -0.2 / (1.1 / 7.071)
z = -0.2 / 0.1556
z ≈ -1.29

Using a standard normal distribution table, the probability of obtaining a z-score of -1.29 or lower is approximately 0.0985, or 9.85%. Therefore, there is a 9.85% probability of obtaining a sample with a mean time to relief of 3.3 minutes or less.

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Based on the random sample, there is not enough evidence to conclude that more than 65% of all adults in the US use television as one of their main sources of news.

To answer your question, we will perform a hypothesis test using the given information.
Step 1: State the hypotheses.
H0 (null hypothesis): p = 0.65 (65% of all adults in the US use television as one of their main sources for news)
Ha (alternative hypothesis): p > 0.65 (more than 65% of all adults in the US use television as one of their main sources for news)
Step 2: Determine the sample proportion (p-hat) and sample size (n).
p-hat = 0.66 (66% from the random sample of 1500 adults)
n = 1500
Step 3: Calculate the test statistic (z) using the formula:
z = (p-hat - p) / sqrt[(p * (1-p)) / n]
z = (0.66 - 0.65) / sqrt[(0.65 * (1-0.65)) / 1500]
z = 0.01 / 0.013 (given Sâ¢Eâ¢=â0.013)
z ≈ 0.77
Step 4: Find the p-value corresponding to the test statistic.
Using a z-table or calculator, we find the p-value for z = 0.77 is approximately 0.2206. Since this is a one-tailed test, we will use this p-value directly.
Step 5: Compare the p-value to the significance level (α) and make a decision.
Assuming a common significance level (α) of 0.05, our p-value (0.2206) is greater than α. Therefore, we fail to reject the null hypothesis (H0).

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Answer:

The answer to your problem is, D. (x,y) → (x - 2, y +3)

Step-by-step explanation:

We can see that the vector that translates JKLM to J'K'L'M' is given by the difference between the coordinates of J and J', and the difference between the coordinates of K and K'.

The differences can be called, "a" and "b", respectively. Then we can write:

a = J' - J = (-1) - 0 = -1

b = K' - K = 3 - (-1) = 4

Which can conclude to the mapping formula expressed by the vector that translates JKLM to J'K'L'M' is:

(X,Y) → (X - 1, Y + 4)

Thus the answer to your problem is, D. (x,y) → (x - 2, y +3)

The coefficient of determination is a measure of how well the regression line fits the data points. It is calculated by dividing the sum of squares of regression (ssr) by the total sum of squares (sst). In this case, we are given the sst and the sum of squares of error (sse), but we need to calculate the ssr to determine the coefficient of determination.

To find the ssr, we can use the formula:

[tex]ssr = sst - sse[/tex]

Substituting the given values, we get:

ssr = 908.8 - 88.954
ssr = 819.846

Now we can calculate the coefficient of determination using the formula:

R^2 = ssr / sst

Substituting the calculated values, we get:

R^2 = 819.846 / 908.8
R^2 = 0.9023

Rounding this to four decimal places, we get:

Coefficient of determination = 0.9023

Therefore, the coefficient of determination for the given data is 0.9023, which indicates a strong correlation between the variables. This means that the regression line fits the data points well and can be used to make accurate predictions.

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