Tristan bought a shirt that usually sells for $75 but is on sale for 20% off. How much did he pay for the shirt?​

The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Answer: The product of two consecutive negative integers is 600. What is the value of the lesser integer?

Step-by-step explanation:

EDGE2021

Rounding this value, we get P(A|B) ≈ 0.29. Thus, the correct answer is 0.29.

To answer this question, we need to find the conditional probability of A given B, which is represented as P(A|B). We are given the probabilities of event A and event B occurring, as well as the probability of both events occurring. We can use this information to calculate P(A|B) using the formula:

\(P(A|B) = P(A ∩ B) / P(B)\)

Here, P(A ∩ B) represents the probability of both events A and B occurring, and P(B) represents the probability of event B occurring. We are given the following information:

- P(A) = 0.4
- P(B) = 0.7
- P(A ∩ B) = 0.2

Now we can plug these values into the formula to calculate P(A|B):

\(P(A|B) = 0.2 / 0.7 = 0.2857\)

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Answer:

Step-by-step explanation:

1). ∵ 1 L = 1000 ml

   ∴ 4 L = 4000 ml

2). ∵ 1 cm = 10 mm

    ∴ 5 cm = 50 mm

3). ∵ 1 mg = 0.1 cg

    ∴ 5 mg = 0.5 cg

4). ∵ 1 ml = 0.001 L

    ∴ 25 ml = 0.025 L

5). ∵ 1 gm = 1000 mg

    ∴ 0.125 gm = 25 mg

6). ∵ 1 ml = 0.001 L

    ∴ 570 ml = 0.57 L

7). ∵ 1 mm = 0.1 cm

    ∴ 135 mm = 13.5 cm

8). ∵ 1 mg = 0.001 g

    ∴ 1820 mg = 1.82 g

9). ∵ 1 g = 100 cg

    ∴ 0.5 g = 50 cg

10). ∵ 1 ml = 0.001 L

     ∴ 0.2385 ml = 0.0002385 L

slope=7

Explanation

the slope of a line ( or segment) is given by

so

Step 1

Let

now,replace in the formula

therefore, the slope is 7

I hope this helps you

Answer:

P = 37.4 m

Step-by-step explanation:

let the third side of the triangle be x

using Pythagoras' identity in the right triangle.

x² + 7² = 16²

x² + 49 = 256 ( subtract 49 from both sides )

x² = 207 ( take square root of both sides )

x = \(\sqrt{207}\) ≈ 14.4 m ( to 1 decimal place )

the perimeter (P) is then the sum of the 3 sides

P = 7 + 16 + 14.4 = 37.4 m

Answer:

It is given that in every 1/2 hours  Brandon bikes .

The distance 8 1/2 miles  is in the form of mixed fraction.

Therefore, the distance 8 1/2 miles can be written in the form of decimal as follows:

8 1/2 miles = 8.5 miles

Brandon bike's 8.5 miles  in every 1/2 hours .

We know that 1 hour   is equivalent to 60 minutes .

So,  0.5 hours can be converted into minutes as follows:

1 hour = 60 minutes

1.5 hours= 30 minutes

Therefore, in every 30 minutes Brandon bikes .

So, in next 30 minutes Brandon also bikes 8.5 miles .

In every 1 hour   Brandon travels  = 8.5+8.5 = 17 miles.

In every 1:30  Brandon travels  17 +8.5 =25.5 miles.

Method 2:

Speed of Brandon’s bike can be calculated as ,

speed = distance/time

Here, d  is the distance and t is the time.

Now, substitute d=8.5  and t= 0.5 in the equation (1)

Therefore, the rate of travelling of Brandon’s bike is .

4(9+7) = 36+28 = 64

open the parentheses, then simplify.

The project has a net present value of $100,000, an internal rate of return of 15%, and a profitability index of 1.1. Therefore, the project should be accepted.

The project has a cost of $500,000 and is expected to generate annual cash flows of $100,000 for five years. The project has no salvage value and is depreciated straight-line to zero over five years. The firm's required rate of return is 10%.

The net present value (NPV) of the project is calculated as follows:

NPV = -500,000 + 100,000/(1 + 0.1)^1 + 100,000/(1 + 0.1)^2 + ... + 100,000/(1 + 0.1)^5

= 100,000

The internal rate of return (IRR) of the project is calculated as follows:

IRR = n[CF1/(1 + r)^1 + CF2/(1 + r)^2 + ... + CFn/(1 + r)^n] / [-Initial Investment]

= 15%

The profitability index (PI) of the project is calculated as follows:

PI = NPV / Initial Investment

= 1.1

The NPV, IRR, and PI of the project are all positive, which indicates that the project is financially feasible. Therefore, the project should be accepted.

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The 95% confidence interval for μ is (80.52, 82.68).

To find the 95% confidence interval for the population mean (μ), we can use the following formula

CI = X ± z* (σ / √n)

where X is the sample mean, σ is the population standard deviation (unknown), n is the sample size, and z* is the critical value from the standard normal distribution corresponding to the desired confidence level (in this case, 95%).

The critical value z* can be found using a standard normal distribution table or calculator, or using a statistical software. For a 95% confidence level, the z* value is 1.96.

Plugging in the values given, we get

CI = 81.6 ± 1.96 × (5.4 / √100)

Simplifying this expression, we get

CI = 81.6 ± 1.08

=  (80.52, 82.68)

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The given question is incomplete, the complete question is:

A random sample of 100 observations from a normally distributed population possesses a mean equal to 81.6 and a standard deviation equal to 5.4 .  Find a 95% confidence interval for μ

Answer:

1/3

Step-by-step explanation:

There are 12 different sums.

4 of the sums are 9, 9, 10, 11.

All other sums are 8 or less.

p(9 or more) = 4/12 = 1/3

Taking into account the definition of a system of linear equations, the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

The maximum capacity for seating in a theater is 500 people. If they sold out on a certain showtime, this is represented by x+y=500.

On the other side, the theater sells two types of tickets, adult tickets for $7.25 each and child tickets for $4 each and the made a total of $3,157. This is represented by 7.25x +4y=3157.

So, the system of equations to be solved is

\(\left \{ {{x+y=500} \atop {7.25x+4y=3157}} \right.\)

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable x from the first equation you get:

x=500 - y

Substituting this expression in the second equation you get:

7.25× (500 -y) +4y=3157

7.25×500 - 7.25y +4y=3157

3625 - 7.25y +4y=3157

- 7.25y +4y=3157 -3625

-3.25y= -468

y= (-468)÷ (-3.25)

y= 144

Substituting this value in the expression x=500 - y you get:

x=500 - 144

x=356

Remembering that "x" is the amount of adult tickets sold and "y" is the amount of child tickets sold, you get that the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.

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There are 7776 different outcomes possible when 5 dice of different colors are rolled.

The ratio of favorable outcomes to the total number of outcomes of an event is said to be the probability of that event.

P(E) = n(E)/n(S)

It is given that, there are 5 dice with different colors.

There are 6 outcomes for each die rolling. That is the number coming up on each die when it is rolled (1, 2, 3, 4, 5, 6).

So, for five dice when rolled, the number of possible outcomes is

n = 6 × 6 × 6 × 6 × 6

⇒ n = 7776

Therefore, 7776 different outcomes are possible.

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The answer is B.

Statistics is a branch of mathematics that deals with collecting data about the world. Hence, option C is the correct answer.

The study of data gathering, analysis, interpretation, presentation, and organization is known as statistics. In other words, gathering and summarizing data is a mathematical discipline. Additionally, statistics might be considered a subfield of applied mathematics. However, uncertainty and variation are two crucial and fundamental concepts in statistics. Only statistical analysis can determine the uncertainty and variation in many sectors. The probability, which is a key concept in statistics, essentially determines these uncertainties.

According to the definition of statistics; the study of data gathering, analysis, interpretation, presentation, and organization is known as statistics.

Hence, statistics is a branch of mathematics that deals with collecting data about the world. Hence, option C is the correct answer.

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Answer:

ok

Step-by-step explanation:

The best estimate of fraction is 131.445.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is \(\frac{1}{2}\)

Given Data

31\(\frac{3}{4}\) × 4\(\frac{1}{7}\)

Solving mixed fractions

\(\frac{127}{4}\) × \(\frac{29}{7}\)

31.75 × 4.14

Multiplying

131.445

The best estimate of fraction is 131.445.

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Answer:

-3.5

Step-by-step explanation:First you need to order the numbers so the numbers ordered would be -20,-16,-10-,10-,7,0,1,2,5,8 the median is finding the middle number in a list so you would cross of the end numbers until you are left -7 and 0 you then find the mid point of these two numbers which is -3.5 so that would be the answer.

Answer:

The median is -3.5

Step-by-step explanation:

hope this helps

-16, -20, -10, 1, -10, 5, 0 ,8 ,2 ,-7

Arrange the number in numerical order.

-20,-16,-10,-10,-7,0,1,2,5,8

There's two number is the middle which is -7 and 0 all you have to do is add them together and divide by 2.

-7+0= -7÷2=-3.5

In spherical coordinates, the equation \(5z^2 = 6x^2 + 6y^2\) can be written as: \(ρ^2sin^2(φ) = 6ρ^2sin^2(θ)cos^2(φ) + 6ρ^2sin^2(θ)sin^2(φ)\)

Spherical coordinates are a system of coordinates used to represent points in three-dimensional space. In this coordinate system, a point is described by three parameters: ρ (rho), θ (theta), and φ (phi).

ρ (rho) represents the radial distance from the origin to the point.

θ (theta) represents the azimuthal angle, which is the angle measured in the xy-plane from the positive x-axis to the line connecting the origin and the point.

φ (phi) represents the polar angle, which is the angle measured from the positive z-axis to the line connecting the origin and the point.

In spherical coordinates, a point in 3D space is represented using three parameters: ρ (rho), θ (theta), and φ (phi).

ρ (rho) represents the radial distance from the origin to the point.

θ (theta) represents the azimuthal angle, which is the angle measured in the xy-plane from the positive x-axis to the line connecting the origin and the point.

φ (phi) represents the polar angle, which is the angle measured from the positive z-axis to the line connecting the origin and the point.

To express the equation\(5z^2 = 6x^2 + 6y^2\)in spherical coordinates, we need to convert the variables x, y, and z to their corresponding spherical coordinate representations.

In spherical coordinates, the conversions are as follows:

x = ρsin(φ)cos(θ)

y = ρsin(φ)sin(θ)

z = ρcos(φ)

Substituting these values into the equation, we have:

5(ρcos(φ))^2 = 6(ρsin(φ)cos(θ))^2 + 6(ρsin(φ)sin(θ))^2

Simplifying the equation further by expanding the terms and using trigonometric identities, we can obtain the equation in spherical coordinates:

\(ρ^2sin^2(φ) = 6ρ^2sin^2(θ)cos^2(φ) + 6ρ^2sin^2(θ)sin^2(φ)\)

This equation relates the variables ρ, θ, and φ in spherical coordinates and represents the same relationship as the original equation in Cartesian coordinates.

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If angle m∠KLJ = 78° then m∠OFG = 78°.

The angle o a straight line

An angle is the parent shaped by using rays, referred to as the edges of the attitude, sharing a not unusual endpoint, referred to as the vertex of the attitude. Angles shaped via two rays lie inside the plane that includes the rays. Angles are also shaped through the intersection of two planes. those are known as dihedral angles.

The angle in a straight line says that the sum of all the angles on a straight line is 180°.

opposite vertical angle is the two opposite angles on a parallel line at the point of intersection.

         angle ∠KLJ = 78°°   (opposite vertical angle).

The angle on a straight line is 180°

         angle∠OFG = 78°.

angle ∠KLJ =∠OFG = 78°. (parallel angles)

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Answer: 3.5 buckets

Step-by-step explanation:

seven divided by 2 is 3.5

Answer:

So the formula will turn out to be 1.50 x 35 + 5, plug that into a calculator and you get 57.5. Therefore, your answer is $57.50.

Answer:

x=6, x=0

Step-by-step explanation:

\((x - 3) ^{2}\)+ \((y - 2) ^{2}\)= 25

\((x - 3) ^{2}\)+ \((6 - 2) ^{2}\)= 25

x=6, x=0

Answer:

Hamid: 4

Ken: 3

Step-by-step explanation:

Start by finding the LCM (least common multiple) of 80 and 60. To do this we can list all the multiples of 80 and 60 until we get a common multiple.

60: 60, 120, 180, 240

80: 80, 160, 240

They both have a common multiple of 240, so after 240 seconds they will meet again at the start line.

Now we need to find how many laps they'll have to run. To do this we can divide 240 by the amount of time it takes for them to run a lap.

240/60=4

240/80=3

Hamid will have ran 4 laps and Ken will have ran 3 laps

The intersection A13−13∩{0∗1∗} is not equal to {0n1n∣n≥0}.

The claim that A13−13∩{0∗1∗}={0n1n∣n≥0} is not correct.

To see why, let us consider a counterexample. Take the string w = "0000#1000". The middle third of w is "0#1", so the string obtained by removing the middle third is "000011000". This string is not in {0n1n∣n≥0}, as there are more 0s than 1s. However, "000011000" is in A13−13, as it can be written as "0000#1000" with the middle third removed.

Therefore, the intersection A13−13∩{0∗1∗} is not equal to {0n1n∣n≥0}.

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(x + a) (x + b) = x² + (a + b) x + ab

75 * 77=

=(70+5)(70+7)

=70²+(5+7)*70+5*7

=4900+12*70+35

=4900+840+35

=5775

Answer: B

Step-by-step explanation: I got it right.

Answer:

GUYS THE PERSON ABOVE ME IS WRONG THE ANSWER IS NOT B IT IS C TRUST ME

In this particular data set, 10 is the only value that occurs more than once, so it is the only mode

The mode is the value that occurs most frequently in a data set. In the given data set {10, 30, 10, 36, 26, 22}, we can see that the value 10 occurs twice, and all other values occur only once. Therefore, the mode of the data set is 10, since it occurs more frequently than any other value in the set.

Note that a data set can have multiple modes if two or more values occur with the same highest frequency. However, in this particular data set, 10 is the only value that occurs more than once, so it is the only mode.

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