graph the curve. x = 3et cos(t), y = 3et sin(t), 0 ≤ t ≤ π

Answer: $28 per week

Step-by-step explanation:

1 month = 4 weeks

18 times 4 = 72 weeks

So you know you want to save 2000 to buy a car 72 weeks from now.

So take 2000 divided by 72 = $27.77 per week

So you need to save about $28 per week.

Answer:b

Step-by-step explanation:

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis.

What is test statistic?

A statistic (a number obtained from the sample) used in statistical hypothesis testing is known as a test statistic. Usually, a hypothesis test is described in words.

A test statistic is a figure obtained from a statistical analysis. It explains how distant your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

The alternative and null hypotheses are listed below.

Lack of hypothesis H0: μ = 13

Ha: 13 Alternative Hypothesis

Statistical test, z = (xbar - mu)/(sigma/sqrt(n))

z = (11 - 13)/(8/sqrt(50))

z = -1.77

Region of Rejection

For α= 0.05, this is a left-tailed test.

Z has a critical value of -1.645.

Therefore, if z -1.645, reject H0 and accept the null hypothesis.

P-value Approach

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis

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The given geometric series [tex]$\quad 8+7+\frac{49}{8}+\frac{343}{64}+\cdots$[/tex] is convergent in nature.

[tex]$\quad 8+7+\frac{49}{8}+\frac{343}{64}+\cdots$[/tex]

Since it is geometric series. (As it is given in the question)

A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series typically go to ∞, go to −∞, or don't approach one specific number.

Here the value of a=8, while the value of the common ratio [tex](r)=\frac{a_2}{a_1}=\frac{7}{8}=\frac{7}{8}[/tex]

since [tex]$|r|=\frac{7}{8} < 1$[/tex]

So the given series is convergent.

The sum of geometric series with infinite terms is equal to [tex]$\frac{a}{1-r}$$$[/tex]

Sum[tex]=\frac{8}{1-\frac{7}{8}}=\frac{8}{\frac{1}{8}}=64[/tex]

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Answer:

Step-by-step explanation:

105 cm

The probability that exactly two people out of a group of five have responded to a telephone poll is approximately 26%.

The probability that exactly two people out of a group of five have responded to a telephone poll can be calculated using the binomial distribution. The probability of a single person responding to a call in a poll is 15%, and the probability of a single person not responding to a call in a poll is 85%.

The probability of two people out of a group of five responding to a call in a poll can be calculated using the formula for the binomial probability mass function:

[tex]P(X=2) = (5 choose 2) * (0.15)^2 * (0.85)^3[/tex]

where (5 choose 2) is the binomial coefficient, which represents the number of ways to choose 2 people out of a group of 5.

Plugging in the values, we get:

[tex]P(X=2) = (10) * (0.15)^2 * (0.85)^3 = 0.2574[/tex]

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Answer: 0 = 2

Step-by-step explanation:

First you need to multiply the numbers:

2x + 2(-x) = 2

2x - 2x = 2

Combine the like terms:

2x-2x = 2

So, 0 = 2

Answer:

(0,10)

Step-by-step explanation:

You could put any ordered pair, as long as the y value is 10.

The equation of this function is

y = 10  It is a horizontal line going through.  The y intercept is (0,10)                      

The price of the microwave before sales is 350 dollars.

Javier bought a microwave for $105. The cost was 30% off the original price.  Therefore, the price of the microwave before sales can be calculated as follows:

let

x = price before sales(original price)

Therefore,

105 = 30% of x

105 = 30 / 100 × x

105 = 30x / 100

cross multiply

10500 = 30x

divide both sides by 30

10500 / 30 = 30x / 30

x = 350 dollars

Therefore, the original price is 350 dollars.

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When they buy 125 identical stuffed animals for $312.50 and sell them for $7 a piece, the percent markup is 64.2%.

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The sign "%" represents it. To compute a percentage, divide the value by the entire amount and multiply the result by 100. (value/total value)100% is the formula for calculating percentage.

Here,

Total cost=$312.50

Total sell price=7*125

=$875

Markup Price=(875-312.5)/875*100

=0.642*100

=64.2%

The percent markup is 64.2% when they purchase 125 identical stuffed animal for total cost of 312. 50 and sell them for $7 each.

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Answer:8 cm 6 cm 8 cm 6 cm The perimeter of the shape is 8 + 6 + 8 + 6 = 28cm.

Step-by-step explanation:

Answer:

Step-by-step explanation:c because I’m in college and Ik trust me

The expression when expressed in its exponent is a²+c²

In mathematics, we should understand that exponent tell the power to which a number is raise.

 It shows the number of times a number multiplies itself to get the certain member.

The given expression is a*a*c*.

Using the law of multiplication that says when two or more numbers in the same base are multiplied, we add their powers.

Here a appeared twice a*a=a²

And c appeared twice that is c*c=c²

Combining the two exponents together we have that

a²+c²

In conclusion, the exponent of a*a*a*a is a²+c²

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To find the loan amount after five years, we need to calculate the compound interest on the loan. The compound interest is calculated by multiplying the principal (the initial amount borrowed) by the compound interest rate, raised to the power of the number of compounding periods. In this case, the compound interest rate is 5.75%/12 = 0.475% per month, and there are 12*5 = 60 compounding periods (12 months per year for 5 years).

The compound interest is therefore calculated as follows:

Compound interest = $1,500 * (1 + 0.475%)^60 - $1,500

= $1,725 - $1,500

= $225

So the loan amount after five years is $1,725. Therefore, the correct answer is [D] $1,725.

The simplest expression is x³ - x² - 17x + 20.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(x - 4) (x² + 3x - 5)

x³ + 3x² - 5x - 4x² - 12x + 20

x³ - x² - 17x + 20

Thus,

The final expression is

x³ - x² - 17x + 20

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Step-by-step explanation:

45° is an alternate angle with 5y+10. All alternate angles are equal. opposite sides of a parallelogram are equal, we equate to find x.

source: A tutor on another math app. (Brainly doesn't recognize the name)

The lines q and t are, perpendicular to each other.

If two lines are perpendicular to each other, then their slopes are negative reciprocal of each other. That means, if one line's slope is 'a', then its perpendicular line's slope would be -1/a

Noted that Parallel lines have the same slope, the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

Given that Lines q, r, s, and t are distinct lines in the same plane.

IF the lines are;

q is perpendicular to r,

r is perpendicular to s

s is perpendicular to t

Then we can conclude that q is perpendicular to t

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Area of a square:

We have s = 6⁴, then the area is:

Or, apply the power of the power rule (xᵃ)ᵇ=xᵃᵇ to get:

Answer:

[tex] \sf \: t = 19[/tex]

Step-by-step explanation:

Given equation,

→ t - 6 = 13

Now the value of t will be,

→ t - 6 = 13

→ t = 13 + 6

→ [ t = 19 ]

Hence, the value of t is 19.

Arithmetic operations can be used to solve this question by using the topic of order of operations. We need to use × and - operators to get the correct answer.

Many straightforward inequalities can be resolved by adding, taking away, multiplying, or dividing both sides until the variable is all that remains. However, these factors will shift the direction of inequality: Using a negative number to multiply or divide both sides. switching the left and right sides. When resolving an inequality, you can do one of the following:

• Add the same amount to each side;

• Subtract the same amount from each side;

• Multiply or divide each side by the same positive amount. You must flip the inequality sign if you multiply or divide each side by a negative number.

5 x (23-18) x (8-4)=100

So we can subtract 23 from 18 where we will get 5 and by subtracting 4 from 8 you will get 4. By multiplying the numbers using × operator you will get the final answer.

Arithmetic operations can be used to solve this question by using the topic of order of operations. We need to use × and - operators to get the correct answer.

Arithmetic operations can be used to solve this question by using the topic of order of operations. We need to use × and - operators to get the correct answer.

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Answer:

B

Step-by-step explanation:

The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. It is calculated using a formula that takes into account the values of the two variables and their relationship to each other. This formula is not affected by changes in the units of measurement of either variable. Therefore, changing the units of time from minutes to seconds in this scenario would not affect the value of the correlation coefficient, so it would remain the same.

Option A, "The correlation and time measurement would change proportionally to one another," is incorrect because the correlation coefficient is not affected by changes in the units of measurement of either variable.

Option C, "The correlation would increase because changing the units for time would result in an increase in time values," is also incorrect because the correlation coefficient is not affected by changes in the actual values of the variables, only by the strength and direction of the relationship between them.

Option D, "It is impossible to determine the amount of change experienced by the correlation," is incorrect because, as explained above, the correlation coefficient is not affected by changes in the units of measurement of either variable.

Option E, "The correlation would decrease because only the units for one of the variables changed," is also incorrect because, as explained above, the correlation coefficient is not affected by changes in the units of measurement of either variable.

Answer: x = 9

Step-by-step explanation:

Let's start with what we know. We know that the sum of all angles is 180 so:

13x + 2 + 3x - 4+ 5x - 7 = 180

21x - 9 = 180

21x = 189

Divide by 21 on both sides:

x = 9

Answer:

The ball travels (exactly) 75 feet.

Step-by-step explanation:

Assuming the balls comes to rest:

S = a1 / (1 - r)

Now a1 is the first bounce, 20 ft (10 feet up, 10 feet down.

r is 2/3

S = 20 (1 / (1 - 2/3)

S = 20 / (1/3)

S = 60

Yet that is only the bounce. The drop of 15 feet must be added.

The linear equation for their total combined age in 5 years is 2x + 17 = 31.

Let the age of Alex be x years old.

Let the age of June be 'y'.

June is exactly 7 years older than Alex.

y = x+7

In next 5 years, combined  total age will be of 31 years.

(x+5) + (y+5) = 31

Now, the linear equation that models total combined age in 5 years

Replace y with (x+7)

x + 5 + (x+7) + 5 = 31

2x + 17 = 31

Thus, linear equation for their total combined age in 5 years is 2x + 17 = 31.

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Answer:

2

Step-by-step explanation:

2x - y = -1

-y = -2x - 1

y = 2x + 1

parallel line = same slope

The right response is C. Only X-values inside the original data's range give meaning to the prediction values.

A statistical model that depicts the relationship between two variables is a regression line. It is utilized to forecast the value of a dependent variable depending on the value of an independent variable (independent variable).

The degree to which the regression line matches the data determines how accurate these forecasts are. For values of the independent variable that are similar to the values used to fit the model, the regression line will typically offer the most precise predictions. Prediction values therefore typically only have significance for X-values that fall within or very near the range of the original data set.

The predictions might not be correct if you use the regression line to construct them for independent variable values that are far outside the original data range. This is because, outside of the range of the data that was used to construct the model, the model may not effectively represent the connection between the two variables.

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The new dilation vertices of the rectangle are J'(-15, 5), K'(-10, 10) L'(0, 0) and M'(-5, -5).

What is the Dilation of the rectangle?

Dilation occurs when a polygon grows or shrinks while maintaining its overall shape. It's similar to zooming in or out on a camera. The polygon in the figure above is a rectangle JKLM. As you move the slider on the right, the transformed rectangle J'K'L'M' grows and shrinks but retains its shape.

We have,

Rectangle JKLM with vertices:

J(-6,2), K(-4,4), L(0,0) M(-2,-2): K= 5/2

New dilation vertices of the rectangle are:

J'(-15, 5), K'(-10, 10) L'(0, 0) and M'(-5, -5)

Hence, the new dilation vertices of the rectangle are J'(-15, 5), K'(-10, 10) L'(0, 0), and M'(-5, -5).

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By using congruency, it can be calculated that

x = 6, y = 5

What are congruent triangles?

Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are same. There are different axioms of congruency. They are-

AAS axiom, SAS axiom, ASA axiom, SSS axiom, RHS axiom

It is given that [tex]\Delta[/tex] ABC [tex]\cong[/tex] [tex]\Delta[/tex] BAD

So [tex]\angle[/tex]CAB = [tex]\angle[/tex]ABD [Corrosponding parts of congruent triangles are congruent]

4y = 20

y = [tex]\frac{20}{4}\\[/tex]

y = 5

Also,

AC = BD [Corrosponding parts of congruent triangles are congruent]

5x - 3 = 3x + 9

5x - 3x = 9 + 3

2x = 12

x = [tex]\frac{12}{2}[/tex]

x = 6

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The given Commutative Property is 8y - 0.2y + 0.5y + 2.2 + 1.3 - 0.4 by solving this property we get the answer as (8.3y + 3.1).

The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.

According to the associative property of addition, the sum of three or more numbers remains the same regardless of how the numbers are grouped. According to the question,

Steps involved are:-

So,

8y - 0.2y + 0.5y + 2.2 + 1.3 - 0.4

= (8 - 0.2 + 0.5) y + (2.2 + 1.3 - 0.4)

= (8 + 0.5 - 0.2) y + (2.2 + 1.3 - 0.4)    

= (8.5 - 0.2) y + (3.5 - 0.4)    

= (8.3) y + 3.1    

= (8.3y + 3.1)

Thus , by following all the steps and properties we get the obtained result.

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Answer:

∠M ≅ ∠G

Step-by-step explanation:

Given:

This means that triangle MTD is congruent to triangle GLS.

Two triangles are said to be congruent if:

Therefore:

Similarly:

Therefore, the true statement is ∠M ≅ ∠G.