A random sample of 100 customers at a local ice cream shop were asked what their favorite topping was. The following data was collected from the customers.


Topping Sprinkles Nuts Hot Fudge Chocolate Chips
Number of Customers 12 17 44 27


Which of the following graphs correctly displays the data?
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27, and the fourth bar labeled chocolate chips going to a value of 44
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27 ,and the fourth bar labeled chocolate chips going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44

8.3E-7 represents  0.00000083 in a calculator

The scientific notation of 8. 3E-7 indicates a minute decimal value. More precisely, it can be understood as the product of 8. 3 and 10 raised to the negative seventh power.

To express 8. 3E-7 in decimal form, calculate 8. 3 multiplied by 10 raised to the exponent -7.

The value of 8. 3 multiplied by 10 to the power of negative 7 is equal to 0. 00000083

In other words, the value of 8. 3E-7 can be expressed numerically as 0. 00000083 Put simply, it denotes a value that is equivalent to 0. 000083% or 83 millionths of 1.

In scientific and mathematical contexts, a minuscule quantity or an exquisitely accurate measurement is commonly denoted by an exceedingly diminutive number.

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Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

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The statement "If the segments of the triangle are proportional then we can prove lines parallel" is false.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

We may infer that the respective sides of a triangle are proportionate if the segments of the triangle are. This does not, however, establish that any lines are parallel. We often require more information, such as the angles between the lines or their locations with respect to one another, to demonstrate that two lines are parallel.

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The profit at the optimal solution is $1000.

First, let's plot the feasible region defined by the constraints. We can start by drawing the boundary lines for each constraint and shading the region that satisfies all the constraints.

Constraint A: 1x ≤ 100

This constraint represents a line with a slope of 1 and intercepts the x-axis at 100.

Constraint B: 1y ≤ 80

This constraint represents a line with a slope of 1 and intercepts the y-axis at 80.

Constraint C: 2x + 4y ≤ 400

This constraint represents a line with a slope of -1/2 and intercepts the x-axis at 200 and the y-axis at 100.

In this case, we have three vertices:

Vertex 1: (0, 0)

Vertex 2: (100, 0)

Vertex 3: (200, 0)

Next, we need to evaluate the objective function 5x + 10y at each vertex to determine the profit associated with each solution.

For Vertex 1: (0, 0)

Profit = 5(0) + 10(0) = 0

For Vertex 2: (100, 0)

Profit = 5(100) + 10(0) = 500

For Vertex 3: (200, 0)

Profit = 5(200) + 10(0) = 1000

Comparing the profits obtained at each vertex, we can see that the optimal solution with the highest profit occurs at Vertex 3, which corresponds to the point (200, 0). At this solution, the profit is $1000.

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Complete Question:

Solve the following linear program:

Max 5x + 10y

1x <= 100 A

1y<= 80 B

2x + 4y <= 400 C

What is the profit at the optimal solution?

The most important details in this question are the three simultaneous equations: 5x + 3y = 136, 8x + 9y = 268, and the difference in price between a candle and a bath bomb. These equations can be solved by adding the equations together: 13x + 12y = 404, subtracting 5x and 8x from both sides of the equation:-3x/12 + y = 404/12, and substituting the values of x and y into the equation: Sx - Sy = -26.472.

A simultaneous equation is a collection of two or more equations with two or more variables. Because they share variables, these equations must be solved together. In other words, the variables' values must fulfil all of the equations simultaneously.

(a) 5x + 3y = 136

Substitute the values given in the equation:

5(25) + 3(15) = 136

125 + 45 = 136

Simplify:

170 = 136

This equation is not true.

(b) 8x + 9y = 268

Substitute the values given in the equation:

8(16) + 9(18) = 268

128 + 162 = 268

Simplify:

290 = 268

This equation is not true.

(c) Solve these simultaneous equations.

5x + 3y = 136

8x + 9y = 268

Add the equations together:

13x + 12y = 404

Subtract 5x and 8x from both sides of the equation:

-3x + 12y = 404

Divide both sides of the equation by 12:

-3x/12 + y = 404/12

Simplify:

-1/4x + y = 33.67

Substitute this equation into the original equation:

5x + 3y = 136

5x + 3(33.67) = 136

Simplify:

5x + 100.01 = 136

Subtract 100.01 from both sides of the equation:

5x = 35.99

Divide both sides of the equation by 5:

x = 7.198

Substitute this value into one of the original equations:

5(7.198) + 3y = 136

Simplify:

35.99 + 3y = 136

Subtract 35.99 from both sides of the equation:

3y = 100.01

Divide both sides of the equation by 3:

y = 33.67

(d) Calculate the difference in price between a candle and a bath bomb.

Substitute the values of x and y into the equation:

Sx - Sy = 7.198 - 33.67

Simplify:

Sx - Sy = -26.472

Therefore, the difference in price between a candle and a bath bomb is Sx - Sy = -26.472.

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Answer:

Step-by-step explanation:

17f+1i

6f+5f+4f=15f

11i+4i+10i=25i     ---------> 2f+1i

1feet=12inch

Answer:

7-(a-2)

Step-by-step explanation:

The expression for the nth term an, for the infinite series s=∑n=1[infinity]an is ∑n=4¹⁶an = 468

We know that the sum of the first n terms of the series is given by sn. Therefore, we can find an expression for the nth term an by taking the difference between successive values of sn:

sn - sn-1 = an

(4-4n²) - (4-4(n-1)²) = an

Simplifying this expression, we get:

an = 8n - 4

Now we can use this expression to find the values of ∑n=1¹⁰an and ∑n=4¹⁶an:

∑n=1¹⁰an = a1 + a2 + ... + a10

= (81 - 4) + (82 - 4) + ... + (8*10 - 4)

= 76

Therefore, ∑n=1¹⁰an = 76.

Similarly,

∑n=4¹⁶an = a4 + a5 + ... + a16

= (84 - 4) + (85 - 4) + ... + (8*16 - 4)

= 468

Therefore, ∑n=4¹⁶an = 468.

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The correct option is (c) i.e. The segments are parallel.

What are parallel lines?

Parallel lines are two lines in a two-dimensional space that never intersect, no matter how far they are extended in either direction. They always maintain the same distance between them and have the same slope. The symbol for parallel lines is "||".

In geometry, parallel lines are important because they create angles that are congruent or equal to each other when intersected by a third line, known as a transversal. This concept is used in many practical applications, such as in construction, engineering, and navigation.

The segments are parallel.

If the slopes of two lines are equal, it means that the lines are either parallel or they are the same line. In this case, since the two segments have zero slope, it means that they are horizontal lines. Horizontal lines are always parallel to each other, so we can conclude that the two segments are parallel.

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Answer:

\({x}^{2} - 10x + 25\)

Step-by-step explanation:

For this problem, we can break the equation into (x - 5) use FOIL. First, Outer, Inner, Last.

(x - 5) (x - 5)

First, multiply the two Xs together.

X * X =

\( {x}^{2} \)

Now, the outer numbers and values.

X * -5 =

\( - 5x\)

Then, it's the inner numbers and values.

-5 * x =

\( - 5x\)

Finally, multiply the last numbers.

-5 * -5 =

\( 25\)

Now that we have multiplied all of the values, we can put the answers from FOIL together.

\( {x}^{2} - 5x - 5x + 25\)

Now, add any like terms.

\( - 5x - 5x = - 10x\)

The answer is

\( {x}^{2} - 10x + 25\)

Answer:

80%

Step-by-step explanation:

50 x 50 would be 100 and 50kg=100% and 10 x 2 = 20 so you used 20% therefore you have 80% left.

Answer:

80% of sugar left.

Step-by-step explanation:

If we start of with 50 kg of sugar and we take away 10 kg of sugar, we are left with \(50-10=40\) kg of sugar.

To find the percentage of sugar left, we divide the decreased number by the original number.

\(\frac{40}{50} = \frac{4}{5} = 0.8\)

If we have a decimal and want to convert it to a percentage, we multiply it by 100.

\(0.8\cdot100=80\)

So, 80% of the sugar is left.

Hope this helped!

Answer:

36

Step-by-step explanation:

the volume of the prism is, the area of the base x height

.

b x 16 = 576

b = 36

so the answer is 36

Answer:

C) 36

Step-by-step explanation:

Answer:

3(6)

??

Step-by-step explanation:

Answer:

1/5x^12 * y^8.

Step-by-step explanation:

((5x^8*y^7/25)x^4)(y)

=1/5x^12 * y^8.

Answer:

yes this is

Step-by-step explanation:

Answer: range:  {0in, 16in}

               domain {0min, 12.8 min}

Step-by-step explanation:

When we have a function:

f(x) = y.

The range is the set of possible values of y and the domain is the set of all the possible values of x.

In this case, our function is:

H(x) = 16 - 1.25*x

which is a linear equation, and we know that the linear equations are defined (for range and domain) in the set of all the real numbers, but this is a physical situation, so we must see at the real problem.

The bucket can not have more water than the initial amount, 16 inches, so this is the maximum in the range.

The minimum height of water that we can find in the bucket is 0 inches (so the bucket is empty) then this is the minimum of the range.

Then we can write the range as:

R: 0in ≤ y ≤ 16in. = {0in, 16in}

Now we can find the extremes of the domain by using the extremes of the range:

y = 16 = 16 - 1.25*x

       0 = -1.25*x

then we have x = 0min, this will be the minimum of the domain.

Now using the minimum of the range y = 0 we have:

y  = 0 = 16 - 1.25*x

      1.25*x = 16

            x  = 16/1.25 = 12.8 mins

This is the maximum time in the domain (because after this time, there is no water in the bucket)

Then the domain is:

D: 0min ≤ x ≤ 12.8 min

The recursive formula for the height of the ball after nth bounce is: an = 3/4 * an-1. This formula allows us to calculate the height of the ball after a specific bounce by using the height after the previous bounce.

a0: The initial height of the ball is 128 meters.
a1: After the first bounce, the ball rises to three quarters of its previous height. So, a1 = 3/4 * 128 = 96 meters.
a2: After the second bounce, the ball rises to three quarters of its previous height. So, a2 = 3/4 * 96 = 72 meters.
a3: After the third bounce, the ball rises to three quarters of its previous height. So, a3 = 3/4 * 72 = 54 meters.

b) To find the height of the ball after the 10th bounce, we need to determine a10. We can use the recursive formula to find a10. The recursive formula states that an = 3/4 * an-1. Starting from a0, we can find a10 by repeatedly applying the recursive formula: a1 = 3/4 * a0, a2 = 3/4 * a1, a3 = 3/4 * a2, and so on. Continuing this pattern, we find a10 = 3/4 * a9 = 3/4 * (3/4 * a8) = (3/4)^10 * a0 = (3/4)^10 * 128. So, the height of the ball after the 10th bounce is (3/4)^10 * 128 meters.

c) The general formula for the height of the ball after the nth bounce can be written as: an = (3/4)^n * a0. This formula allows us to directly calculate the height of the ball after any bounce without having to go through each intermediate bounce.

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The ratio of the perimeter of the smaller rectangle to the bigger rectangle is: 26 : 43

Perimeter of a rectangle = 2(length + width).

Perimeter of the smaller rectangle:

Perimeter of the bigger rectangle:

The ratio of the smaller to the bigger = 52 : 86

Simplified further

Ratio = 26 : 43

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To identify the restaurant with the distribution closest to normal for sodium, we can calculate the goodness-of-fit measures, such as the Anderson-Darling test or the Shapiro-Wilk test, for each restaurant's sodium distribution and select the one with the highest p-value indicating the closest agreement to normality.

To answer the probability questions and identify the restaurant with the distribution closest to normal for sodium, we need access to the dataset and perform statistical calculations using R programming language. Unfortunately, as a text-based AI, I don't have direct access to external datasets or the capability to execute code. However, I can provide you with an outline of the steps you can follow to conduct the analysis:

1. Load the dataset: Import the dataset containing information about the restaurants, including the variable of interest (sodium levels).

2. Probability questions: Formulate two probability questions related to the dataset. For example:

  a) What is the probability that a randomly selected restaurant has sodium levels above a certain threshold?

  b) What is the probability that a randomly selected restaurant has sodium levels within a specific range?

3. Theoretical normal distribution: Assuming that the sodium variable follows a normal distribution, calculate the probabilities using the theoretical normal distribution. You will need to estimate the mean and standard deviation from the dataset.

4. Empirical distribution: Calculate the probabilities using the empirical distribution. This involves computing the sample mean and sample standard deviation from the dataset and using these estimates to calculate the probabilities.

5. Compare the results: Compare the probabilities obtained from the theoretical normal distribution and the empirical distribution. Assess the agreement between the two methods by examining the differences in probabilities.

6. Identify closest to normal distribution: Analyze the sodium variable for each restaurant and assess which restaurant's distribution exhibits the closest resemblance to a normal distribution. This can be done by visually inspecting histograms or using statistical tests such as the Shapiro-Wilk test.

By following these steps and implementing the necessary code in R, you will be able to answer the probability questions and determine which restaurant's sodium distribution is closest to normal.

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Answer:

its a commutative property becaus its just changing the order

The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct

Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.

The formula for calculating YTM is as follows:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

Where:

C = Interest payment

F = Face value

P = Market price

n = Number of coupon payments

Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.

First, let's calculate the semi-annual coupon payment:

Semi-annual coupon rate = 5.2% / 2 = 2.6%

Face value = $1000

Market price = $884

Number of years remaining until maturity = 10 years

Number of semi-annual coupon payments = 2 x 10 = 20

Semi-annual coupon payment = Semi-annual coupon rate x Face value

Semi-annual coupon payment = 2.6% x $1000 = $26

Now, we can calculate the yield to maturity using the formula:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100

YTM = 6.23%

Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.

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By using division, if 89 members of the Taft school band spend a total of $4628 for tickets to Hammond's amusement park, The the cost of each amusement park ticket is $52

The total number of members of the Taft school = 89 members

The total cost for the ticket to Hammond's amusement park = $4628

The cost of each amusement park ticket = The total cost for the ticket to Hammond's amusement park ÷ The total number of members of the Taft school

Substitute the values in the equation

The cost of each amusement park ticket = 4628/89

= $52

Hence, by using division, if 89 members of the Taft school band spend a total of $4628 for tickets to Hammond's amusement park, The the cost of each amusement park ticket is $52

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Answer:

DE=18

Step-by-step explanation:

The reason is because that parallelogram ABCD has most of the sides equal to each other.

The length of DB = 36 and half of 36/2 gets us DE.

DE=36/2=18

DE=18 also equals to BE=18

Diagonals of a parallelogram bisect each other

So

Putting DE=BE

Answer:

This is an English server

Step-by-step explanation:

Welcome to Brainly! I'm happy to help!

We see that there are 1,610 meters in a mile. However, we are looking for millimeters, not meters. But, knowing the meters will help us out.

A millimeter is a very small measurement. There are 1,000 millimeters in 1 meter. A meter is much larger. So, if we want to convert 1,610 meters to millimeters, there are going to be way more millimeters because they are so minute.

This means that we will have to multiply. We know that there are 1,000 millimeters in 1 meter, so if we multiply our meters by 1,000 (which is basically just adding 3 zeros), we will get the number of millimeters in one mile!

1,610×1,000=1,610,000 (one million six hundred and ten thousand!)

Don't forget that we are looking for 3 miles though, so we can take the number of millimeters in one mile and multiply by three.

1,610,000×3=4,830,000 (four million eight hundred and thirty thousand!)

So, Tobias ran 4,830,000 millimeters!

Have a wonderful day and keep on learning! :D

Answer:

Julia had 120 peas to start .

Answer:

  120 peas

Step-by-step explanation:

Before Julia gave Vlada 15 peas, the ratio of their numbers was 3:2. Afterward, Julia still had 10 more peas. You want to know the number Julia started with.

Let j represent the initial number of peas Julia had. Then Vlada had 2/3j peas. After the transfer, the difference was ...

  (j -15) -(2/3j +15) = 10

  1/3j -30 = 10

  1/3j = 40

  j = 120

Julia had 120 peas at first.

__

Additional comment

The transfer of peas decreases the difference by 30, so if it remains 10 it must have originally been 40. The difference in initial ratio units is 3-2 = 1, so Julia's initial 3 ratio units represent 3·40 = 120 peas.

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The correct answer is,

D. The second card is the better choice because the daily periodic interest on the first card is 0.041%, compared to 0.038% on the second card.

Since, We know that;

Our daily periodic rate is = APR / 365%

For the first card it can be represented as, ( daily periodic rate equaling )

= 14.99/365

= 0.041%.

And, For the second it can be represented as, ( daily periodic rate equaling ) 0.038%.

We know because it can be given.

Compare them; 0.041% > 0.038% ( by 0.003% )

Hence, Its Making Option D correct.

Thus the answer to your problem is,

D. The second card is the better choice because the daily periodic interest on the first card is 0.041%, compared to 0.038% on the second card.

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Answer:

6

Step-by-step explanation:

add the two exponents

Answer:

Step-by-step explanation:

Add all the powers of the term.

4 + 2 = 6

Degree = 6

Information is needed to evaluate the project's financial viability, considering factors such as the initial investment, expected cash flows, cost of capital, and project duration.

To calculate the year 1 operating cash flows (OCF), we need to subtract the year 1 costs from the year 1 revenues:

OCF = Year 1 Revenues - Year 1 Costs

OCF = $192,000 - $125,000

OCF = $67,000

To find the depreciation expense in year 3, we need to determine the depreciation method. The provided information is incomplete regarding the depreciation method, so we cannot calculate the depreciation expense in year 3 without knowing the specific method.

The change in Net Working Capital (NWC) in year 2 can be determined by multiplying the Net Working Capital percentage (given as a percentage of t+1 revenues) by the year 1 revenues and subtracting the result from the year 2 revenues:

Change in NWC = (Year 2 Revenues - Net Working Capital percentage * Year 1 Revenues) - Year 1 Revenues

Without the specific Net Working Capital percentage or Year 2 Revenues values, we cannot calculate the exact change in NWC in year 2.

The net cash flow from salvage (ATSV) is calculated by multiplying the Salvage Value percentage by the Initial Cost:

ATSV = Salvage Value percentage * Initial Cost

ATSV = 28% * $390,000

ATSV = $109,200

To calculate the project's NPV, we need the cash flows for each year, the cost of capital, and the project duration. Unfortunately, the information provided does not include the cash flows for each year, so we cannot calculate the project's NPV.

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The complete question is:

Below are your numerical inputs for the problem: 4 & Initial Cost (\$) & 390000 5 & Year 1 Revenues (\$) & 192000 6 & Year 1 Costs (\$) & 125000  7 & Inflation & 2.75% 8 & Project Duration (years) & 6 9 & Depreciation Method & 10 & Tax Rate & 11 & Net Working Capital (\% oft+1 Revenues) & MACRS 12 & Salvage Value (\$) & 28.00% 13 & Cost of Capital & 15.00% & 245000 How much are the year 1 operating cash flows (OCF)? How much is the depreciation expense in year 3 ? What is the change in Net Working Capital (NWC) in year 2? What is the net cash flow from salvage (aka, the after-tax salvage value, or ATSV)? What is the project's NPV? Would you recommend purchasing the ranch? Briefly explain.

The probability of the shop purchasing is 5/9.

Let X be the number of non-defective engines purchased by the auto shop out of the 4 engines bought. We want to find P(X >= 3), the probability of getting at least 3 non-defective engines.

Using the hypergeometric distribution formula, we have:

P(X >= 3) = P(X = 3) + P(X = 4)

where

P(X = k) = (C(7, k) * C(2, 4-k)) / C(9, 4)

So, we have:

P(X = 3) = (C(7, 3) * C(2, 1)) / C(9, 4) = (35 * 2) / 126 = 5/18

P(X = 4) = (C(7, 4) * C(2, 0)) / C(9, 4) = (35 * 1) / 126 = 5/18

Therefore,

P(X >= 3) = 5/18 + 5/18 = 10/18 = 5/9

So the probability of the shop purchasing at least 3 non-defective engines is 5/9.

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