Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed.
C=0.90, x=13.7, s =3.0, n= 10

According to the given percentage,

The original price of the jacket was $64.

Jeremy surveyed 100 students for his math project.

If the jacket was on sale for 25% off, that means the price Linda paid was equal to 75% of the original price. We can set up an equation to represent this:

0.75x = 48

where x is the original price of the jacket. To solve for x, we divide both sides by 0.75:

x = 48 / 0.75

x = 64

If 18% of the students surveyed selected hamburgers, that means the remaining 82% did not select hamburgers. We can represent this with an equation:

0.18x + 0.82x = x

where x is the total number of students surveyed. The left-hand side of the equation represents the number of students who selected hamburgers (0.18x) plus the number who did not (0.82x), which must equal the total number surveyed (x).

Simplifying the equation, we get:

x = 100x / 100

Dividing both sides by 100, we get:

x = 1 / 0.01

x = 100

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Based on available research and studies, the answer is B: A higher percentage of millennials have at least $100,000 saved for retirement when comparing to Gen X.

According to a report from Fidelity Investments, 30% of millennials have saved at least $100,000 for retirement. In contrast, a 2019 study from the Transamerica Center for Retirement Studies found that 31% of Gen Xers have no retirement savings at all.

This suggests that the fraction of millennials with at least $100,000 saved for retirement is higher than the portion of Gen X people who have no retirement savings.

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Answer:

A

Step-by-step explanation:

-4x²+7x+8=0

4x²-7x-8=0

a = 4, b = -7, c = - 8

x= (−b ± √b²−4ac) ÷ 2a

x= [ −(−7) ± √(−7)²−4(4)(−8) ] ÷ 2(4)

x = 7±√177

Hence,

x = 7+√177 and x = 7-√177

It has two solutions

The probability of Event A is 1/360 and the probability of Event B is 1/15.

For Event A, we can calculate the probability by considering the order in which the acts are scheduled.

There are 6 acts, so there are 6 possible choices for the first act. After the first act is scheduled, there are 5 remaining acts, so there are 5 possible choices for the second act.

Similarly, there are 4 possible choices for the third act, and 3 possible choices for the fourth act.

Finally, there are 2 possible choices for the fifth act, and only 1 choice remains for the last act.

Therefore, the total number of possible ways to schedule all 6 acts is:

6 x 5 x 4 x 3 x 2 x 1 = 720

Since we are only interested in one specific order of the first four acts, we need to count the number of ways to schedule the remaining two acts after the first four have been scheduled in the desired order.

There are 2 remaining acts, so there are 2 possible choices for the fifth act.

Only one act remains for the last slot.

Therefore, the total number of ways to schedule all 6 acts such that the acrobat is first, the singer is second, the violinist is third, and the whistler is fourth is:

1 x 1 x 1 x 1 x 2 x 1 = 2

Thus, the probability of Event A is:

P(A) = 2/720 = 1/360

For Event B, we want to count the number of ways to schedule the first four acts as the whistler, the acrobat, the guitarist, and the dancer, in any order.

There are 4 acts, so there are 4 possible choices for the first act. After the first act is scheduled, there are 3 remaining acts, so there are 3 possible choices for the second act.

Similarly, there are 2 possible choices for the third act, and only one choice remains for the fourth act.

Therefore, the total number of possible ways to schedule the first four acts is:

4 x 3 x 2 x 1 = 24

Since we do not care about the order in which the last two acts are scheduled, we can simply choose any two acts from the remaining 2. There are 2 ways to do this.

Therefore, the total number of ways to schedule all 6 acts such that the first four acts are the whistler, the acrobat, the guitarist, and the dancer, in any order is:

24 x 2 = 48

Thus, the probability of Event B is:

P(B) = 48/720 = 1/15

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The exact area of a regular hexagon with a side length of 50ft is 6495.15ft²

The given length of the side of the hexagon is 50ft. Since a regular hexagon consists of 6 equilateral triangles therefore the area of the hexagon is equal to [tex]A=6*A_{triangle}[/tex].

Area of an equilateral triangle = √3/4{a}²

=1082.53ft²

Therefore, the area of the hexagon=6*1082.53ft²=6495.15ft²

Hence, the area of the hexagon is 6495.15ft².

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Answer: $7,000.

Step-by-step explanation:

4% = 0.04. Multiply that by the sales price to calculate commission.

$175,000 x 0.04 = $7,000.

The ratios of the identities are;

sin R = 9/15

cos R = 12/15

tan R = 9/15

It is important that we note the different trigonometric identities and their corresponding ratios.

From the information given, we get;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have the parameters given as;

Hypotenuse side = 15

Opposite side = 9

Adjacent side = 12

Now, substitute the values, we have;

sin R = 9/15

cos R = 12/15

tan R = 9/15

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The reflection preserves the side lengths and angles of triangle. The dilation preserves angles but not side lengths.

The triangle underwent the following operations:

As a result, while the dilation would only maintain the angles, the reflection would preserve both side lengths and angles.

Thus, Angles are preserved, but side lengths are not.

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The solution is:

⇒ 6b = 95.94   (equation to determine cost of one box)

cost of one box 'b' = $`15.99

⇒ 12t = 95.94   (equation to determine cost of per tile)

cost of one tile t = $0.7995.

Given :

Jorge bought a crate of floor tiles for $95.94.

The crate had 6 boxes of floor tiles.

Each box contained 20 floor tiles .

To Find :

Write and solve equation to determine the cost per box'b'.

Write and solve a second equation to determine the cost per tile't'

Solution :

Cost of one box = b

There are 6 boxes

So, cost of 6 boxes = $  6b

Since Jorge bought 1 crate( = 6 boxes) of cost $95.94

⇒     (equation to determine cost of one box)

⇒6b = 95.94

⇒b =15.99

Thus cost of one box = $`15.99

Since 1 box 20 floor tiles

So, 6 boxes (=1 crate) contain tiles = 6*20 = 120 tiles

We are given that cost of 1 crate( = 6 boxes = 120 tiles) is $95.94

Cost of one tile = t

Cost of 120 tiles = $120t

⇒ (equation to determine cost of per tile)

⇒12t = 95.94

⇒t = 0.7995.

Thus cost of one tile t = $0.7995.

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Answer:

600.1 m³

Step-by-step explanation:

V = (1/3)πr²h

V = (1/3)(3.14159)(6.1 m)²(15.4 m)

V = 600.1 m³

Answer:

d: (0, pi)

r: [-1/2, 1/2]

Step-by-step explanation:

Compound interest, also known as interest on principal and interest, is the practice of adding interest towards the principal amount of a loan or deposit.

The yearly interest rate is raised to the amount of compounded periods minus one, and the starting principal amount is multiplied by both of these factors. The resulting value is subsequently deducted from the loan's entire original amount.

P = $5,000 for the principle (initial investment)

Annual interest rate equals 0.03 (as a decimal)

t = the number of years (10).

Euler's number is e = 2.718281.

A = the sum at time t, or A = P·(e(rt))

[tex]\sf A = 5000(2.718281^{(0.03\times10)})[/tex]

[tex]\sf A = \$6,749.29[/tex]

After 10 years, you'll have $6,749.29 in your account.

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The numbers are 5, 5, 10, 10, 15

To find the value of x, we need to use the fact that the mean of the five numbers is 9. The mean is equal to the sum of all the numbers divided by the total number of numbers. In this case, we have:

(mean) = (sum of all numbers) / (total number of numbers)

We know the mean is 9, and there are 5 numbers, so we can write:

9 = (x + x + 2x + 2x + 3x) / 5

Simplifying the right-hand side, we get:

9 = 9x / 5

Multiplying both sides by 5, we get:

45 = 9x

Dividing both sides by 9, we get:

5 = x

So we now know that the first two numbers are both equal to 5. Using the ratio, we can find the values of the next two numbers:

2x = 2(5) = 10

So the third and fourth numbers are both equal to 10.

Finally, we can use the ratio to find the value of the fifth number:

3x = 3(5) = 15

So the five numbers are:

5, 5, 10, 10, 15

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Answer:

1617.5mm^3

Step-by-step explanation:

The square base with a side length of 10 mm and an overall height of 17.25 mm.

Based on your question, it seems that you have a figure with a square base and a height.

The extent or potential of a rectangular pyramid can be calculated the usage of the formula:

V = (1/3)abH

Where "a" and "b" are the size and width of the rectangular base, and "H" is the top of the pyramid.

Similarly, the floor vicinity of a rectangular pyramid can be calculated the use of the formula:

A = ab + (1/2)P(lateral)

where "P(lateral)" is the perimeter of the lateral face, which can be calculated as the sum of the slant heights of the 4 triangular faces.

The slant top can be calculated the use of the Pythagorean theorem, the place the base of the triangle is one facet of the rectangular base, the top is the top of the pyramid, and the hypotenuse is the slant height.

To provide a relevant answer,

I need to know the type of figure you are referring to (e.g., pyramid, prism). Once you provide that information.

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Answer:

Step-by-step explanation:

It's given that, The base of a triangle is 1 cm more than the height

Let's assume height of the triangle be x and base of the triangle be 1 + x

Also the area of the triangle is 10 cm².

We know that area of triangle is calculated by,

Putting the values we get ,

[tex] \frac{1}{2} (1 + x) x = 10 \\ \\ (1 + x)x = 10 \times 2 \\ \\ {x}^{2} + x = 20 \\ \\ {x}^{2} + x - 20 = 0[/tex]

Further solving by factorisation,

[tex]x^2 + x-20 = 0 \\ \\ x^2 +5x-4x - 20 = 0 \\ \\ x(x+5)-4(x+5)= 0 \\ \\ (x-4) (x+5) = 0 \\ \\ (x-4) = 0 \: or \: (x+5)=0 \\ \\ { \underline{x= 4 \: or \: x = 5 }}[/tex]

Since value can't be negative.

So, x = 4.

Hence, height of triangle x = 4 cm

base of triangle = x + 1

= 4 + 1

= 5 cm

Therefore the Base of traingle will be 5 cm and Height of the triangle will be 4 cm.

The function rule for g(x) is h(x) = (x - 0)² - 7.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the vertex (0, -7) and other points (-3, 2), we can determine the value of a as follows:

f(x) = a(x - h)² + k

2 = a(-3 - 0)² - 7

2 + 7 = 9a

9 = 9a

a = 1

Therefore, the required quadratic function in vertex form is given by:

h(x) = a(x - h)² + k

h(x) = (x - 0)² - 7

h(x) = x² - 7

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The only function among the given options that has a rate of change that stays the same is Option A: y = -4x + 10.

In this context, a rate of change refers to how much the output of a function changes in response to a change in its input. The rate of change of a function is also known as the slope of its graph, which measures the steepness of the line connecting two points on the graph.

Now, let's look at the given functions and determine which one has a rate of change that stays the same.

The function y = -4x + 10 is a linear function, which means that its graph is a straight line.

The slope of a linear function is constant, which means that the rate of change of the function stays the same.

In this case, the slope is -4, which means that the output of the function decreases by 4 units for every 1 unit increase in its input.

Hence the correct option is (a).

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Answer:

A) Angles 3 and 4 are complementary angles.

Answer:

A

Step-by-step explanation:

All quadrilaterals have a total of 360° for the interior angles

X = 360 - (125+95+105) = 360 - 325 = 35°

The graph that shows the solution set for the system y ≥ -2, x < 2 is illustrated below.

First, we graph y ≥ -2. This inequality represents all the points above or on the line y = -2. To graph this, we draw a horizontal line at y = -2 and shade in all the points above this line.

Next, we graph x < 2. This inequality represents all the points to the left of the line x = 2. To graph this, we draw a vertical line at x = 2 and shade in all the points to the left of this line.

The solution set of the system is the region that satisfies both inequalities simultaneously. Since the region that satisfies both inequalities is the shaded region above the line y = -2 and to the left of the line x = 2, we select the graph that shows this shaded region.

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The two students that mix the same ratio of juice to water is given as follows:

A. Luca.

D. Micah.

The ratio between two amounts a and b is given as follows:

a to b.

Which is also the division of the two amounts.

Hence the ratio of juice to water for each person is given as follows:

Hence Luca and Micah used the same ratio, meaning that options A and D are correct.

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Answer:

A. ASA

B. LA

E. AAS

Step-by-step explanation:

A. ASA

∠D≅∠J, DE≅JK and ∠E≅∠K => ASA

B. LA

DE ≅ JK, ∠E≅∠K and ∠F≅∠L => the LA theorem.

E. AAS

∠E≅∠K, ∠F≅∠L, and DE≅JK.  => AAS.

The congruence theorems applicable in this case are SAS and AA.

To determine the congruence theorems or postulates that can be used to prove ADEF = AJKL based on the given information, we need to analyze the diagram.

From the diagram, we can see that sides AD and AK are congruent. This indicates that we can potentially use the SAS (Side-Angle-Side) congruence theorem to prove the triangles congruent.

Additionally, angles A and A are congruent, so we can also use the AA (Angle-Angle) congruence test. Therefore, the congruence theorems applicable in this case are SAS and AA.

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1402800 is the number of people who would test positive for the virus

To find the probability for the number who tested positive we divide the positive cases between the total of the covid tests and then mutiply by 100.

P = (8,533/68,811) × 100

P = 12.400, the nearest hundredth of a percent is 12.

11690000 people who live in ohio and the testing results is that 12% of this people would test positive for the virus.

so we need to find percentage 12 for 11690000.

(11690000×12) / 100

Hence, 1402800 is the number of people who would test positive for the virus

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The state of Ohio conducted COVID 19 tests on 68,811 people, and 8,533 tested positive. (6 points)A. What is p for the number who tested positive (round to the nearest hundredth of a percent)?B. Based upon the testing results above, of the 11.69 million people who live in Ohio, what is the bestestimate for the number of people who would test positive for the virus?

Answer:

C// 1.5

Step-by-step explanation:

Yes, the random, 10%, and large counts conditions are all met.

Here, the expected count of players who win a large prize is

np = 100 x 0.10

np = 10

and, the expected count of players who do not win a large prize is

n(1-p) = 100 x 0.90 = 90.

The second prerequisite is also satisfied because both of these anticipated counts are higher than or equal to 10.

The independence criteria is also satisfied if each player's outcome is independent of the results of the other players.

Therefore, Yes, the random, 10%, and large counts conditions are all met.

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For the person to reach a retirement savings goal (future value) of $100,000 at age 55, they need to invest an additional $81 monthly.

Determining the additional monthly investment:

The additional monthly investment is computed as the difference between the expected monthly deposits and the intended monthly deposits.

The expected monthly deposits (periodic payments) are determined using an online finance calculator.

Current age = 21 years old

Retirement age = 55 years old

Investment period = 34 years (55 - 21)

N (of periods) = 408 months (34 years x 12)

I/Y (Interest per year) = 2.5%

Present Value = $0

FV (Future Value) = $100,000

Periodic Payments (PMT) = $155.75

Sum of all periodic payments = $63,546

Total Interest = $36,454

Intended monthly deposits = $75

Additional monthly deposits required = $80.75 ($155.75 - $75) = $81

Thus, the investor needs to invest an additional $81 to the $75 monthly deposits to reach a future value of $100,000 in 34 years, compounded at 2.5% monthly.

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The complete question =

A person is 21 years old and plans on retiring at age 55. This person is going to invest $75 each month into an IRA that is expected to earn 2.5% interest, compounded monthly. How much more money, rounded to the nearest dollar, is needed per month to reach a retirement savings goal of $100,000?

The blanks are filled using the concept of translation transformation  as follows

Parabola            Equation

Red                       y = x²

Blue                     y = x² + 3

Green                  y = (x - 3)²

Orange                y = x² - 3

Purple                  y = (x + 3)²

Applying translation the graphs are interpreted as follows

y = x²: the parent function

y = x² + 3: shift 3 units up

y = (x - 3)²: shift to the right 3 units

y = x² - 3: shift 3 units down

y = (x + 3)²: a shift 3 units to the left

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