An auditorium has 79 rows of seats. The first row contains 60 seats. As you move to the rear of the auditorium, each row has 3 more seats than the previous row. How many seats are in row 24? How many seats are in the auditorium? Question 10 Find the infinite sum, if it exists for this series: (-2) + (0.5) + (-0.125) +

Answer:

line b

Step-by-step explanation:

go up 4 and over 3 on line b

2 is a function h that multiplies a number x by 3.

The problem can be solved by following the given steps:

Step 1: Multiply a number x by 3.

Step 2: Subtract the cube of x from the result of step 1.

Step 3: Divide the result of step 2 by your age.

We can express this problem as an equation using function notation.

Let h(x) be the function that multiplies a number x by 3, then subtracts the cube of x, and divides the result by your age.

Then, we have:

\(h(x) =\frac{ (3x-x^3)}{a}\)

Where a represents your age.

We can substitute any value of x and a into this equation to find the result.

For example, if x = 2 and a = 20, then

\(h(2) = \frac{(3(2) - (2^3))}{20h(2)}\)

\(h(2) = \frac{(6 - 8)}{20h(2)}\)

\(h(2) = \frac{-2}{20h(2)}\)

\(h(2) = -0.1\)

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Answer:

Step-by-step explanation:

17

The probability that 45 or more people in this sample have consumed alcoholic beverages is 0.0516, or about 5.16 percent.

The probability that 45 or more people in a sample have consumed alcoholic beverages can be determined using normal distribution, as the sample size is sufficiently large. The distribution is also normal because of the large sample size. Using the normal distribution table or a calculator, the probability can be determined. The formula is:

P(X > 44.5) = 1 - P(X ≤ 44.5) = 1 - 0.9484 = 0.0516, approximately.

(Note: We use 44.5 because it is the midpoint of the interval 44.5 to 45.5, which is the one that includes 45.)

Therefore, the probability that 45 or more people in this sample have consumed alcoholic beverages is 0.0516, or about 5.16 percent.

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Answer:

it is angles x and p because of you rotate triangle wzx around you can see that angle x corresponds with angle p

Answer:

C ) 1/3

Step-by-step explanation:

In the given equation, y = 1/3x, where it represents a proportional relationship:

1/3 represents the constant of proportionality which shows that as x increases, y also increases at the same rate. The constant of proportionality in this given instance is also the rate of change, or the slope.

The constant of proportionality under the direct proportion condition is the slope of the line when plotted for two proportional constants x and y on a graph.

Therefore, the correct answer is C) 1/3.

When the ice cream is allowed to melt, the cone's 6 cm height will be able to hold the entire container.

A sphere has a spherical, symmetrical shape. On the basis of its radius, it has a surface area and a volume. The set of all points in three-dimensional Euclidean space that are separated by a certain amount of space, or "radius," is known as a sphere (the "center"). The diameter of a sphere is equal to twice its radius, and pairs of locations on its opposing sides are referred to as antipodes.

given

The formula for the volume of a sphere would be used to calculate the volume of the ice cream scoop.

A sphere's volume is equal to 4/3 x pi x r^3.

= 4/3 x 22/7 x 1.5^3 = 14.14 cm³

The following equation can be used to calculate the cone's height:

The scoop's volume is equal to (1/3 xπ x r2).

14.14 / (1/3 x 1.5² x 22/7) = 6 cm

When the ice cream is allowed to melt, the cone's 6 cm height will be able to hold the entire container.

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The probability that Aaron selects a terrier, given Rebecka selects a poodle, is 1/3.

To find the probability that Aaron selects a terrier, given Rebecka selects a poodle, we need to use conditional probability.

First, we need to find the probability that Rebecka selects a poodle. Since there are four poodles out of seven puppies total, the probability that Rebecka selects a poodle is 4/7.

Next, we need to find the probability that Aaron selects a terrier, given that Rebecka has already selected a poodle. Now there are only three poodles and two terriers left in the store, so the probability that Aaron selects a terrier is 2/6 (or simplified, 1/3).

Putting it all together, we can use the formula for conditional probability:

P(Aaron selects a terrier | Rebecka selects a poodle) = P(Aaron selects a terrier and Rebecka selects a poodle) / P(Rebecka selects a poodle)

Since we know that Rebecka selects a poodle, the numerator is just the probability that Aaron selects a terrier given that there are three puppies left in the store. So:

P(Aaron selects a terrier and Rebecka selects a poodle) = (1/3) * (4/7) = 4/21

And we already calculated that P(Rebecka selects a poodle) = 4/7. So:

P(Aaron selects a terrier | Rebecka selects a poodle) = (4/21) / (4/7) = 1/3

Therefore, the probability that Aaron selects a terrier, given Rebecka selects a poodle, is 1/3.

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Answer:

Correlation doesn't prove causation because just because two things correlate does not necessarily mean that one causes the other.It's easy to think that just because two things seem related, that one must be the cause of the other. But that can be a foolish and sometimes dangerous assumption

the merchant uses 48 pounds of the $3 tea and 32 pounds of the $2.75 tea in the blend.

To determine the amount of each type of tea used in the blend, we can set up a system of equations based on the given information. Let's assume x pounds of the $3 tea are used and y pounds of the $2.75 tea are used.

The first equation represents the total weight of the mixture: x + y = 80 (equation 1).

The second equation represents the average price per pound of the mixture: (3x + 2.75y) / 80 = 2.90 (equation 2).

To solve this system of equations, we can use the method of substitution or elimination.

Using substitution, we can solve equation 1 for x: x = 80 - y. Substituting this into equation 2, we have (3(80 - y) + 2.75y) / 80 = 2.90.

Simplifying the equation, we get (240 - 3y + 2.75y) / 80 = 2.90.

Combining like terms, we have (240 - 0.25y) / 80 = 2.90.

Cross-multiplying, we get 240 - 0.25y = 2.90 * 80.

Simplifying further, we have 240 - 0.25y = 232.

Subtracting 240 from both sides, we get -0.25y = -8.

Dividing both sides by -0.25, we find y = 32.

Substituting this value of y into equation 1, we have x + 32 = 80.

Solving for x, we get x = 80 - 32 = 48.

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For a 4.5m high column poured at a temperature of 35°C, with a desired stud spacing of 0.5m, the stud spacing would be approximately 9 studs per meter.

To calculate the stud spacing for the vertical formwork of a 4.5m high column poured at a temperature of 35°C, you need to consider the expansion and contraction of the formwork due to temperature changes.

First, determine the coefficient of thermal expansion for the material being used. Let's assume it is 0.000012/°C for this example.

Next, calculate the temperature difference between the pouring temperature (35°C) and the reference temperature (usually 20°C). In this case, the temperature difference is 35°C - 20°C = 15°C.

Now, calculate the change in height due to thermal expansion using the formula: Change in height = original height * coefficient of thermal expansion * temperature difference. Plugging in the values, we get:
Change in height = 4.5m * 0.000012/°C * 15°C = 0.00081m.

To ensure proper spacing, subtract the change in height from the original height:
Effective height = 4.5m - 0.00081m = 4.49919m.

Finally, divide the effective height by the desired stud spacing. For example, if you want a stud spacing of 0.5m, the calculation would be:
Stud spacing = 4.49919m / 0.5m = 8.99838

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correct value of x will 9 if Maggie corrected her mistake.

When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it. The typical form of a linear equation with one variable is Ax + B = 0. The variables x and A in this situation are variables, whereas B is a constant.

Applying the parallel line theorem

alternate angles are always equal -

therefore ,

 4x + 2 = 7x - 25

27 = 3x

x = 9

so , the correct value of x will be 9 if maggie corrected her mistake

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Answer:

answer is h=

\( \frac{7}{2} \)

Answer:

\(\frac{343}{8}\)

Step-by-step explanation:

Firstly, we need to calculate the value of h:

Step 1 - Divide the first equation by 2 to find the value of 1h:

\(\frac{2h}{2} = \frac{7}{2}\)

h = \(\frac{7}{2}\)

Now, to calculate 5 - h3 (assuming the answer is 0 and h3 is actually h³) :

5 - h³

5 - \(\frac{7}{2}\)³

We can find \((\frac{7}{2})^{3}\) by:

Step 1 - Calculate the denominator and numerator:

7³ = 343

2³ = 8

Step 2 - Put the values back into fraction form:

\(\frac{343}{8}\)

Or in decimal form:

42.875.

Hope this helps!

The surface area of the rectangular prism is 213 square meters.

To calculate the surface area of a rectangular prism, we need to find the areas of all its faces and then sum them up.

A rectangular prism has six faces: top, bottom, front, back, left, and right.

The top and bottom faces are identical and have the same dimensions as the base of the prism. So, the area of each of these faces is 6 m * 3.5 m = 21 m².

The front and back faces have dimensions of 6 m (width) and 9 m (height). So, the area of each of these faces is 6 m * 9 m = 54 m².

The left and right faces have dimensions of 3.5 m (width) and 9 m (height). So, the area of each of these faces is 3.5 m * 9 m = 31.5 m².

To find the total surface area, we sum up the areas of all the faces:

Total Surface Area = 2 * (Area of top face) + 2 * (Area of front face) + 2 * (Area of left face)

Total Surface Area = 2 * 21 m² + 2 * 54 m² + 2 * 31.5 m²

Total Surface Area = 42 m² + 108 m² + 63 m²

Total Surface Area = 213 m²

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The man has approximately 1.5820708e+30 unique paths to choose from to make the trip from (0,0) to (50,51).

To calculate the number of unique paths the man can take to travel from point (0,0) to point (50,51), we can use the concept of combinatorics.

The man needs to take a total of 50 steps horizontally (to reach the x-coordinate 50) and 51 steps vertically (to reach the y-coordinate 51). He can only move either to the right (horizontally) or upwards (vertically) at each step.

To reach the destination, the man needs to make a total of 50 + 51 = 101 steps.

Now, we need to determine in how many ways the man can arrange these 101 steps.

The number of unique paths can be calculated using the binomial coefficient formula, which is given by:

C(n, k) = n! / (k!(n-k)!),

where n represents the total number of steps and k represents the number of steps in one direction (either horizontally or vertically).

In this case, n = 101 (total steps) and k = 50 (number of steps in one direction).

Using the formula, we can calculate the number of unique paths as:

C(101, 50) = 101! / (50!(101-50)!) = (101! / 50!51!) = 101C50.

Calculating this combination:

C(101, 50) = 101C50 = 101! / (50!51!) ≈ 1.5820708e+30.

Therefore, the man has approximately 1.5820708e+30 unique paths to choose from to make the trip from (0,0) to (50,51).

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Answer:

Step-by-step explanation:

y - 9 = 3(x - 0)

y - 9 = 3x - 0

y = 3x + 9

Answer:

y = -2x + 10

Step-by-step explanation:

8x + 4y = 40

4y = -8x + 40

y = -2x + 10

Answer:

The value of x if the scale factor of figure A to figure B is 4:5 is; x = 12

We are given the scale factor of figure A to figure B as 4:5.

By use of similar triangles theorem, we can deduce that the ratio of corresponding sides of figure A to corresponding sides of figure B must be equal to 4:5.

Now, looking at both triangles, we can say that;

x:15 = 4:5

Thus,we can write in fraction as;

x/15 = 4/5

x = 15 × 4/5

x = 12

In conclusion, the value of x from the given proportion between both triangles is 12.

Answer:

L=15-8t

Step-by-step explanation:

Given data

initial length= 15in

time of burning = 8 hours

final length = 5in

let the length of the candle be L

and the number of hours burnt be t

given that the initial length was 15in

the expression to represent the L in  terms of t is given as

L=15-8t

Answer:

L= -1.25t+15

Step-by-step explanation:

The test statistic is, -2.06.

What is test statistic?

A programme and any related documentation are examined during static testing, a type of software testing that does not call for the programme to be run. Software testing also includes dynamic testing, which involves interacting with the application as it is being used.

Given: Americans work less than 40 hours a week on average in 1977?

In 1977, the GSS included questions about the number of hours that the respondent worked per week.

The average number of hours worked per week was 34. 61 hours with a standard deviation of 14. 77 hours.

A sample of 32 respondents was questioned.

So, the test statistics is,

Z = (x bar - μ)/(σ /√n)

 = (34.61 - 40)/(14.77/sqrt(32))

Z = -2.06

Hence, the test statistics is -2.06.

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Answer:

12x - 12

Step-by-step explanation:

4(3x)= 12x

-2 x 6 = -12

And since you are taking away 12 it works.

( Have a nice day hope this helps)

The area of the shaded sector of the circle is 3π ft².

A sector of a circle is simply a region bounded by two radii of the circle and an arc of the circle.

The area of a sector can be found using the formula:

A = (θ/360) × πr²

Where A is the area of the sector, θ is the central angle in degrees, r is the radius of the circle, and π is pi.

From the image:

Central angle θ =  360° - 90° = 270°

Radius r = 2ft

Plug the given values into the above formula and solve for area.

A = (θ/360) × πr²

A = (270/360) × π × (2ft)²

A = (270/360) × π × 4ft²

A = 3/4 × π × 4ft²

A = 3π ft²

Therefore, the area is 3π ft².

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Answer:

i cant see the question :(

Step-by-step explanation:

Step-by-step explanation:

I am not sure I can read the original expression right, the picture is too blurry for the small digits.

is it 3^(5/5) ?

or rather 3^(5/6) ?

in any case, you should know that a number written like this always has the structure

a^(b/c)

so,

a = 3

b = 5 (or whatever is the numerator or top of the fraction)

c = 5 (or whatever is the denominator or bottom of the fraction).

the denominator of a fraction in an exponent gives us the grade of root to be taken.

the numerator gives us the power of the base number.

and if the exponent is negative it would mean that the whole thing is a 1/... fraction.

like 3^-2 means 1/3².

Answer:

x = 5 and y = 22

Step-by-step explanation:

See attached image.

The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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Value of p is approximately 0.987.

To find the p-value for the given claim that the mean body temperature at 12 AM is μ > 98.6°F with a sample size of n=8 and a test statistic of t=-2.687, follow these steps:

1. Identify the degrees of freedom: Since the sample size is n=8, the degrees of freedom (df) are calculated as n-1, which is 8-1=7.

2. Determine the tail of the test: The claim states that the mean body temperature is greater than 98.6°F (μ > 98.6), which indicates a right-tailed test.

3. Find the p-value using the t-distribution table or a calculator: With a test statistic of t=-2.687 and df=7, you can look up the corresponding p-value using a t-distribution table or an online calculator. Since it's a right-tailed test, the p-value will be the area to the right of the test statistic in the t-distribution.

After completing these steps, the p-value is found to be approximately 0.987.

Therefore, your answer is: The p-value for the claim that the mean body temperature at 12 AM is μ > 98.6°F, given a sample size of n=8 and a test statistic of t=-2.687, is approximately 0.987.

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