Clara goes miniature golfing. She pays $7.50 for an admission ticket and $6.25 for each round she golfs. The total amount Clara pays for admission and the number of rounds she golfs is $26.25.

Given,

The Tasty Bottling Company distributes cola in cans labeled 12 oz. The Bureau of Weights and Measures randomly selected 36 cans, measured their contents, and obtained a sample mean of I I .82 oz. and a sample standard deviation of 0.38 oz.

Now,

Claim translates that :

The mean is less than 12 oz.

µ<12

Therefore,

\(H_{0}\) : µ≥12

\(H_{1}\) : µ<12

The critical Z value is -2.33 .

Test statistic:

Z = 11.82-12/0.38/√36

Z = -2.84

As we see the test statistic is in critical region, we reject \(H_{0}\) .

Hence we can claim that the company is cheating with its consumers.

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The effective annual interest rate of the investment is approximately 5.4%.

To find the effective annual interest rate, we need to consider the compounding frequency and the total accumulated amount after the specified time period. In this case, the investment is compounded monthly, and it accumulates to $773.45 after 2 years.

Convert the nominal interest rate to the monthly rate:

Since the interest is compounded monthly, we need to convert the nominal yearly interest rate to the monthly rate. Assuming a nominal interest rate of \(\(r\)\), the monthly rate can be calculated as \(\(i = \frac{r}{12}\)\).

Calculate the effective annual interest rate:

To find the effective annual interest rate, we can use the formula:

\(\((1 + i)^{12} = (1 + \text{effective annual interest rate})\)\).

Rearranging the formula and solving for the effective annual interest rate, we have:

\(\(\text{effective annual interest rate} = (1 + i)^{12} - 1\)\).

Substitute the values and calculate:

In this case, the accumulated amount is $773.45 after 2 years. By substituting the values into the formula, we have:

\(\(773.45 = 700(1 + \frac{r}{12})^{24}\)\).

Solving for \(\(r\)\), we find:

\(\(\frac{r}{12} \approx 0.0045\)\).

Converting the monthly rate to the effective annual interest rate, we get:

\(\((1 + \frac{r}{12})^{12} - 1 \approx 0.054\),\) which is equivalent to 5.4%.

Therefore, the effective annual interest rate of the investment is approximately 5.4%.

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Answer:

y + 9 = -2(x - 10)

The correct answer is d.

By the end of the 24th day of autumn, there is exactly 1,594,323 number leaf total on the ground.

So, let uscalculate the total number of leaves as follows:

A number of leaves on day 1.

A number of leaves on day 2.

A number of leaves of day 3.

A number of leaves on day 4.

A number of leaves on day 5.

A number of leaves on day 6.

A number of leaves of day 7.

A number of leaves on day 8.

A number of leaves on day 9.

A number of leaves on day 10.

A number of leaves on day 11.

A number of leaves on day 12.

A number of leaves on day 13.

Therefore, by the end of the 24th day of autumn, there is exactly 1,594,323 number leaf total on the ground.

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A residual is the difference between "the measured and predicted values of the quantity of interest".

In regression analysis, a residual would be the difference between an observable and anticipated value.

The formula is;

Residual = Observed value – Predicted value

Some key features regarding the residuals are-

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Answer:

top left choice

Step-by-step explanation:

A car going at a higher speed than a second car will travel more distance in the same amount of time.

Look at the graph. For example, imagine that each grid line on the x-axis is 1 hour. Look at the 5th grid line to the right of the origin. That would mean 5 hours into the trips.

Now imagine that each grid line on the y-axis is 10 miles.

For the low speed car, at 5 hours, it traveled 40 miles.

For the high speed car, it traveled 70 miles in the same 5 hours.

That makes the x-axis the independent variable representing time, and the y-axis the dependent variable representing position.

Answer: top left choice

The outcomes that satisfy event A are A = {3, 6}. These are the numbers on which the die can land to fulfill the condition of being a multiple of 3.

The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.

In the given sample space S = {1, 2, 3, 4, 5, 6}, we have all the possible outcomes when rolling a six-sided die.

The event A is defined as "The die lands on a multiple of 3." Multiples of 3 in the given sample space are 3 and 6 since these numbers can be divided evenly by 3 without any remainder.

Therefore, A = 3, 6 is the set of outcomes that satisfy event A. These are the possible outcomes for the die to land on in order to satisfy the requirement of being a multiple of 3.

The complete question is:

Consider rolling a six-sided die, numbered 1-6. Whatever number lands face up is your score. Fill in the missing value to describe the sample space of a single roll of the dice: S = {1, 2 , 3, 4, 5, 6} And suppose you were interested in the event A = The die lands on a multiple of 3. Fill in the blanks to show all the outcomes which satisfy A:

A = {_ , _ }

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Answer:

The area inside the running track is 248.5 m².

Step-by-step explanation:

The area inside the running track is given by the sum of the area of a rectangle and the area of a semicircle:

\( A_{t} = A_{r} + 2A_{c} \)                

\( A_{t} = x*(2r) + 2*(\frac{\pi r^{2}}{2}) \)      

Where:

x: is one side of the rectangle = 30 m            

r: is the radius = half of the other side of the rectangle = 7/2 m = 3.5 m

Hence, the total area is:

\( A_{t} = 30*7 + \pi (3.5)^{2} = 248.5 m^{2} \)                            

Therefore, the area inside the running track is 248.5 m².

I hope it helps you!                                                    

Is it 4965 sph (slices per hour)

The lateral area of a cylinder is the sum of the areas of its lateral faces. To calculate the lateral area of a cylinder, you need to know its height and radius. The formula for the lateral area of a cylinder is L = 2πrh, where L is the lateral area, r is the radius, and h is the height.

Using the formula, we can find the lateral area of the cylinder given in the problem statement. The first step is to determine the radius and height of the cylinder. Unfortunately, this information is not provided. Instead, we are given the lateral area itself, which is not enough to determine the radius and height. Therefore, we cannot directly calculate the lateral area of the cylinder.

However, we can use the given answer choices to determine the correct lateral area of the cylinder. Since the answer choices are all in terms of π, we know that the lateral area must also be in terms of π. Therefore, we can eliminate answer choices 90π in² and 25π in² since they are not in terms of π.

Next, we can use the formula for the lateral area of a cylinder, L = 2πrh, to determine which of the remaining answer choices is correct. We know that the lateral area must be greater than 2πr² (the area of the top and bottom faces of the cylinder), so we can eliminate answer choice 2π in².

This leaves us with only one answer choice: 29π in². Therefore, the lateral area of the cylinder is 29π in².

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Answer:

11.725

Step-by-step explanation:

Add all the numbers together and divide it by how many numbers are in the set

Answer:

Slope=75 y-intercept=500 Equation: y=75x+500

Step-by-step explanation:

We use the equation for slope to find this (1100-800)/(8-4)=300/4=150

To find y-intercept we can do the equation 800-4(75)=500

The final equation is written in slope-intercept form, which is y=mx+b with m=slope and b=y-intercept so we should have y=75x+500

Answer: C, 2 2/8

Step-by-step explanation: To turn a mixed number into an improper fraction, multiply the whole number by the denominator. Then, add the numerator. So in this example it would be:

4 3/8 = 35/8

2 1/8 = 17/8

Now, since the denominators are equivalent, all we need to do is subtract the numerators.

35/8 - 17/8 = 18/8

The answer needs to be changed back to a mixed number. For this problem, there is an easy way to do this.

18/8 = 8/8 + 8/8 +2/8, which as a mixed number would be 2 2/8.

So the correct choice would be (C).

The train will take 3hour 7.5min to travel a distance of 250 km

Given that,

Distance of 250 km with a speed of 80 kmh

To find: Time taken by train to travel a distance of 250 km with a speed of 80 kmh

Distance = 250km

Speed of the train =80km/h

Speed is calculated as distance times speed. You need to be aware of the units for distance and time in order to calculate the units for speed. The units in this example will be metres per second (m/s), since the distance is measured in metres (m) and the time is measured in seconds (s).

Time = Distance /speed

=250km /80km/h

=25/8 h

= 3⅛h

= 3hour ⅛*60

= 3hour 7.5min.

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Answer:

3 hours 7.5 mim

Step-by-step explanation:

The train will take 3hour 7.5min to travel a distance of 250 km

Given that,

Distance of 250 km with a speed of 80 kmh

To find: Time taken by train to travel a distance of 250 km with a speed of 80 kmh

Distance = 250km

Speed of the train =80km/h

Speed is calculated as distance times speed. You need to be aware of the units for distance and time in order to calculate the units for speed. The units in this example will be metres per second (m/s), since the distance is measured in metres (m) and the time is measured in seconds (s).

Time = Distance /speed

=250km /80km/h

=25/8 h

= 3⅛h

= 3hour ⅛*60

= 3hour 7.5min.

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Distance can be defined as the amount of ground covered (traveled) by a physical object over a specific period of time and speed, regardless of its direction, starting point or ending point.

Mathematically, the distance (traveled) by a physical object can be calculated by using this formula:

Distance = speed × time

Making time the subject of formula, we have:

Time = distance/speed

Next, we would calculate the amount of time it will take for the two couriers to meet:

t = d/(Vm + Vn)

t = 8/(1 + 3)

t = 8/4

Time, t = 2 hours.

For the meeting time, we have:

Meeting time = 8:00 AM + 2 hours

Meeting time = 10:00 AM.

For the distance from M, we have:

Distance = 1 × 4

Distance = 4 km.

For the distance from N, we have:

Distance = 3 × 4

Distance = 12 km.

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Complete Question:

Two couriers leave two cities M and N(N is west of M) distant from each other 8kms and both go east. The one from M leaves at 6:00am and goes 1k/h and the one from N leaves at 8:00am and walks 3k/h. At what time did they meet and at what distance from M and N?

Using the rules of exponents, the expression (5 x^−5 y^3)^−2 is equivalent to x^10 / (25 y^6) or "x raised to the tenth power over quantity 25 times y raised to the sixth power end quantity".

Given: (5 x^−5 y^3)^−2

1. Distribute the power of two using the Power of a Power Rule. "When a power is raised to another power, multiply the exponents."

5^−2 x^(−5)(−2) y^(3)(−2) =  5^−2 x^10 y^-6

2. Use Negative Rule of Exponent. "A number with a negative exponent should be put to the denominator, and vice versa."

5^−2 x^10 y^-6 = (x^10) / (5^2 y^6)

3. Simplify the constant term.

(x^10) / (5^2 y^6) = x^10 / 25 y^6

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Answer:

Step-by-step explanation:

A

(y-3)/(0-3) = (x-4)(6-4)

(y-3)/-3 = (x-4)/2

(-y+3)/3 = (x-4)/2

6 *(-y+3)/3 = 6 * (x-4)/2

-2y + 6 = 3x - 12

-3x -2y + 6 + 12 = 0

-3x - 2y + 18 = 0

3x + 2y - 18 = 0

Verify point A

3(4) + 2(3) - 18 = 0

12 + 6 - 18 = 0

0 = 0 (ok)

B

(y-3)/(0-3) = (x-4)/(-1-4)

(y-3)/-3 = (x-4)/-5

-15 * (y-3)/-3 = -15 * (x-4)/-5

5y-15 = 3x - 12

3x - 5y - 12 + 15 = 0

3x - 5y + 3 = 0

Verify point A

3(4) - 5(3) + 3 = 0

12 - 15 + 3 = 0

0 = 0 (ok)

Answer:

D . No because it fails the vertical line test .

Step-by-step explanation:

Answer: Width = 4.7 meters, Length = 6.7 meters

Step-by-step explanation:

Let the width be \(w\). It follows that the length is \(w+2\).

\(w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7\)

Value of mean is, 40.2

Value of median is, 45

Value of mode is, 28

Value of range is, 25

Given that;

Data set is,

⇒ 28, 45, 53, 28, 47

Now, We can arrange into ascending order as;

⇒ 28, 28, 45, 47, 53

Hence, Value of mean is,

⇒ (28 + 28 + 45 + 47 + 53) / 5

⇒ 40.2

And, The value of median is,

⇒ (5 + 1) / 2

⇒ 6/2

⇒ 3rd term

⇒ 45

The value of mode =28

And, The value of range is,

⇒ 53 - 28

⇒ 25

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The solution of a quadratic equation once it has been graphed is indicated by the x-intercept(s) of the parabola. Option C is correct.

The solution of a quadratic equation once it has been graphed is indicated by the x-intercept(s) of the parabola. Therefore, the correct option is c. x-intercept(s). The x-intercept(s) are the points where the parabola intersects the x-axis and represents the values of x that make the quadratic equation true. If the equation has two real solutions, they will be the x-coordinates of the two x-intercepts.

Options a, b, and d are related to the properties of the parabola itself and are useful for understanding its shape and behavior, but they do not directly provide information about the solutions of the quadratic equation. The vertex, option a, is the highest or lowest point on the parabola, the y-intercept(s), option b, is the point(s) where the parabola intersects the y-axis, and the axis of symmetry, option d, is a vertical line that divides the parabola into two symmetrical halves.

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Answer:

-5

Step-by-step explanation:

Answer:

1. )0.35

2. )1.15

3.)0.5 (5 repeating's)

4.)2.72

Step-by-step explanation:

7 divide  20=0.35

-23 divide 20=1.15

-60 divide 22 = 2.727272 but it is 2.72

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The given expression is ~

So, the Correct options are ~

and

Answer:

A and C

Step-by-step explanation:

Answer: 3 years

Step-by-step explanation:

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