An arrow is launched upward with a velocity of 256
feet per second from the top of a 80
-foot stage. What is the maximum height attained by the arrow?

The doubling time of a bank account balance is the amount of time it takes for the balance to double. In this case, the doubling time is 10 years, which means that the balance will double every 10 years.

Let's say the initial balance in the bank account is B. After 10 years, the balance will have doubled to 2B. After another 10 years (i.e., 20 years from the initial balance), the balance will have doubled again to 4B. Finally, after another 10 years (i.e., 30 years from the initial balance), the balance will have doubled one more time to 8B.

Therefore, after 30 years, the balance in the bank account will have grown by a factor of 8B/B, which simplifies to just 8. This means that the balance in the bank account will be 8 times the initial balance after 30 years.

To summarize, the balance in the bank account will double every 10 years due to the given doubling time. After 30 years, it will have doubled three times, resulting in a growth factor of 2 x 2 x 2 = 8, which means the balance will be 8 times the initial balance.

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The probability that a card greater than 4 or less than 5 is 1 or 100%

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability of picking a card greater than 4 i.e 5 or 6 = 2/3

The probability of picking a card less than 5 i.e

4 = 1/3

Therefore the probability of picking of a card greater than 4 or less than 5 = 2/3 + 1/3 = 3/3

= 1

the total probably is given by 1.

therefore in percentage , it will be 1/1 × 100 = 100%

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For the given quadratic equation, the value of constant abc is 45/8.

We need to rewrite the given quadratic equation in the form of a(x+b)²+c, where a, b, and c are constants, and then find the product abc. To do this, we'll complete the square.

Given quadratic equation: 2x² -10x+8

Follow these steps to determine the product:

1: Divide the entire equation by the leading coefficient 2:

x² -5x+4

2: Add and subtract the square of half the linear coefficient inside the parentheses. Half of 5 is 5/2, and (5/2)² is 25/4:

x² - 5x + 25/4 - 25/4 + 4

3: Combine the terms and rewrite the equation in the form a(x+b)²+c:

(1)(x - 5/2)² - 9/4

4: Now, we can see that a = 1, b = -5/2, and c = -9/4. So the product abc is:

abc = (1)(-5/2)(-9/4) = (45/8)

Therefore, the value of abc is 45/8.

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Answer:

Area of annulus is 40.85cm² to 2d.p

Step-by-step explanation:

Area of shaded part=Area of bigger circle -Area of smaler circle

Area of annulus= πR²- πr²= π(R²-r²)

A=3.142(7²-6²)

A=3.142(49-36)

A=3.142×13

A=40.846cm²

A=40.85cm² to 2d.p

The range of h(x)=-4x^2-6x-4 is  (∞, -13).

Using the vertex notion, find the range of the function h(x)=-4x2-6x-4.

The function's vertex is at x = -b/2a,

where a and b are the coefficients of x2 and x, respectively.

Because a = -4 and b = -6 in this situation, the vertex is at x = -(-6)/(2*(-4)) = 3/4.

To find the vertex's y-coordinate, enter x = 3/4 into the function:

h(3/4) = -4(3/4)^2 - 6(3/4) - 4 = -13

As a result, the function's vertex is at (3/4, -13).

Hence, the function's range is (∞, -13).

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What is proration?

It's when you only pay for part of something you used.

Like if you only use half of a month of a service, you only pay for half of the monthly cost.y cost.

When is proration used?

When you sign up for a service that you don't use for a full month.

When you change your service in the middle of a billing cycle.

Why is proration used?

To make sure people only pay for what they use.

To be fair and not overcharge people for services they didn't fully use.

chatgpt

Answer:

B

Step-by-step explanation:

If you take any set of the values and divide the cost (y) by the gummy worms (x) you get 8.4

We can conjecture that the value of the instantaneous velocity at t=3 is  81.6.

To find the average velocity over an interval, we use the formula:

average velocity = (change in distance)/(change in time)

Using the position function s(t) = -16t^2 + 100t, we can find the change in distance over an interval [a, b] by subtracting the value of s(a) from the value of s(b):

change in distance = s(b) - s(a)

change in distance = [-16(b^2) + 100b] - [-16(a^2) + 100a]

change in distance= -16(b^2 - a^2) + 100(b - a)

Similarly, we can find the change in time over the same interval by subtracting a from b:

change in time = b - a

Using these formulas, we can complete the table as follows:

Time Interval | Average Velocity

[2,3] | 84

[2.9,3] | 82

[2.99,3] | 81.6

[2.999, 3] | 81.6

[2.9999,3] | 81.6

Based on these results, we can make a conjecture about the value of the instantaneous velocity at t = 3.

From the table, the average velocity over smaller and smaller intervals around t=3 is approaching a value of 81.6.

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The surface area is about 157.08 square feet. use formula for the surface area of a right cylinder  to get answer .

what is surface area ?

Surface area is the measure of the total area that the surface of a three-dimensional object occupies. In other words, it is the sum of the areas of all the faces or surfaces of the object. Surface area is usually measured in square units

In the given question,

The formula for the surface area of a right cylinder is:

S = 2πr² + 2πrh

where r is the radius of the cylinder, h is its height, and π is a mathematical constant approximately equal to 3.14159.

Substituting the given values, we get:

S = 2π(2.5)² + 2π(2.5)(7.5)

S ≈ 2π(6.25) + 2π(18.75)

S ≈ 39.27 + 117.81

S ≈ 157.08

Rounding this to the nearest hundredth, we get:

The surface area is about 157.08 square feet.

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The exponential function that represents the net value of the antique desk is: f(x) = -37 × [tex]0.7027^{x}[/tex]

The exponential function is a mathematical function denoted as "exp(x)" or "[tex]e^x[/tex]", where "e" is Euler's number (a mathematical constant approximately equal to 2.71828) and "x" is the input variable. The exponential function is a special type of mathematical function that grows or decays rapidly as the input value changes.

"Net value" typically refers to the residual value or worth of something after all relevant expenses, debts, or liabilities have been subtracted from its total value or assets.

The table provides values of f(x) for x = 0, 1, 2, 3, 4, and 5. The corresponding values of f(x) are -37, -26, -13, 0, 15, and 32, respectively.

Using the given data, we can create the following exponential function in the form f(x) = a × [tex]b^{x}[/tex], where a and b are constants to be determined:

f(0) = a ×[tex]b^{0}[/tex] = -37

f(1) = a × b¹= -26

f(2) = a × b² = -13

f(3) = a × b³ = 0

f(4) = a × b⁴ = 15

f(5) = a × b⁵ = 32

To find the values of a and b, we can use a system of equations. We can divide the equations f(1) = a × b¹ = -26 by f(0) = a ×b⁰ = -37 to eliminate a:

(-26) / (-37) = b¹ / b⁰

0.7027 ≈ b

Substituting the value of b back into any of the equations, we can solve for a. Using f(0) = a ×b⁰ = -37:

-37 = a × 1

a = -37

So, the exponential function that represents the net value of the antique desk is:

f(x) = -37 × [tex]0.7027^{x}[/tex]

The values are rounded to the nearest whole dollar.

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Answer:

During the first three years Trevor owned the desk, the resale value was less than the cost. Then it exceeded the cost after year 3.

Step-by-step explanation:

See attachment

Answer:

China's fiscal stimulus increases global aggregate demand because it increases China's GDP and imports, which increases other countries' exports to China. This fiscal stimulus might have lost some of its force because it decreases China's government budget surplus and raises the world real interest rate.

Step-by-step explanation:

hope this helps

The domain and range of this sine function y = sinx include the following:

C. Domain: All real numbers

D. Range: -1 ≤ y ≤ 1

In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Furthermore, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left-hand side of the graph to the right-hand side.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞}, x|x ∈ R, or all real numbers.

Range = {-1, 1}, y ≥ or -1 ≤ y ≤ 1.

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Answer: it is reflected by y-axis

Step-by-step explanation: as we know when point (x,y) reflected  by y axis the value of y remains the same and the sign of x will be changed since the image is rotated horizontaly

Answer:

y-axis

Step-by-step explanation:

When a point is reflected over the y-axis, the x-coordinate of the point becomes the additive inverse of the original number.

Here, (8, -15) became (-8, -15). The only change in value of the coordinates is the value of the x-coordinate, 8, which became its additive inverse, -8.

Answer: y-axis

Answer: it is reflected by y-axis

Step-by-step explanation: as we know when point (x,y) reflected  by y axis the value of y remains the same and the sign of x will be changed since the image is rotated horizontaly

Answer:

y-axis

Step-by-step explanation:

When a point is reflected over the y-axis, the x-coordinate of the point becomes the additive inverse of the original number.

Here, (8, -15) became (-8, -15). The only change in value of the coordinates is the value of the x-coordinate, 8, which became its additive inverse, -8.

Answer: y-axis

Answer:

For y = tan(x), there is no horizontal or vertical shift (h = 0, k = 0). The amplitude is not applicable in this case. The frequency is b = 1 and the period is P = π.

For y = cot(x), there is no horizontal or vertical shift (h = 0, k = 0). The amplitude is not applicable in this case. The frequency is b = 1 and the period is P = π.

Answer:

Step-by-step explanation:

a) This is a minimization problem. The objective is to minimize the daily cost of feed for the horses while meeting their minimum nutritional requirements.

b) Let X1, X2, and X3 represent the number of pounds of oat product, enriched grain, and mineral product, respectively, that the stable owner should feed to the horses daily.

The objective function is:

Minimize 0.8X1 + 0.9X2 + 1.1X3

The constraints are:

Ingredient A: 0.15X1 + 0.20X2 + 0.25X3 >= 2.5

Ingredient B: 0.10X1 + 0.15X2 + 0.05X3 >= 2.0

Ingredient C: 0.05X1 + 0.05X2 + 0.10X3 >= 1.0

Ingredient D: 0.02X1 + 0.04X2 + 0.03X3 >= 0.3

Ingredient E: 0.08X1 + 0.07X2 + 0.06X3 >= 1.4

Non-negativity: X1 >= 0, X2 >= 0, X3 >= 0

c) To set up this problem in Excel, we can create a spreadsheet with the following columns: "Feed Mix," "Ingredient A," "Ingredient B," "Ingredient C," "Ingredient D," "Ingredient E," "Cost per Pound," and "Amount to Feed."

We can then enter the data from the table provided in the problem, and add formulas to calculate the total amount of each ingredient in each feed mix and the total cost of each feed mix based on the amount fed.

Next, we can use Solver to find the optimal mix of feed for the horses. We will set the objective to minimize the total cost of feed, subject to the constraints listed above. Solver should be able to find the optimal values of X1, X2, and X3 that meet the nutritional requirements and minimize the cost of feed.

84cm³

V= 12 x 7 = 84

volume is always cubed btw

Answer:

1) 26

2) 118

3) 144

4) 58

5) 38

6) 96

7) 84

8) 156

9) 240

Step-by-step explanation:

Draw a Venn diagram to confirm my answers.

35% of the 240 students were interested in athletics, so .35 × 240 = 84 students were interested in athletics. Since 26 students were interested in both athletics and academic clubs, 84 - 26 = 58 students were interested in athletics only.

3/5 of the 240 students were interested in academic clubs, so 3/5 × 240 = 144 students were interested in academic clubs. Since 26 students were interested in both athletics and academic clubs,

144 - 26 = 118 students were interested in academic clubs only. From this information, you should be able to complete the two-way table.

Answer:

Step-by-step explanation:

11.7

Answer:

1 2/7

Step-by-step explanation:

State that 1 = 7/7

2 2/7 - 7/7

Convert 2 2/7 into improper fraction

= 16/7

=16/7 - 7/7

16 - 7 = 9

= 9/7

Simplify back to mixed fraction

= 1 2/7

The exact values of x and y in the triangles are calculated and listed below

Figure 7

Here, we have

y = √(6² + 1²) --- pythagorean theorem

This gives

y = √37

And, we have

x = √(10² - 6²) --- pythagorean theorem

x = 8

Figure 8

Here, we have

x = 1/2 * 10 --- midsegment of equilateral triangle

This gives

x = 5

And, we have

y = √(10² - 5²) --- pythagorean theorem

y = 5√5

Figure 10

Here, we have

2x = √(6² + 8²) --- pythagorean theorem

2x = 10

x = 5

So, we have

x = y = 5

Figure 11

Here, we have

y = 5

And we have

x = √(13² - 5²) --- pythagorean theorem

x = 12

Figure 13

By similar triangles, we have

x/5 = (x + y)/10

This gives

x = y

So, we have

x = y = 3

Figure 14

By similar triangles, we have

x = 6/3 * 4

x = 8

And then, we have

y = √(6² + 8²) --- pythagorean theorem

y = 10

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The decision rule is Reject the null hypothesis if the calculated z-value is greater than 2.33.

To determine the decision rule, we need to perform a hypothesis test to see if the sample mean of 4.6 pounds/square inch is significantly different from the population mean of 4.4 pounds/square inch.

Null hypothesis: The population mean pressure is equal to 4.4 pounds/square inch.

Alternative hypothesis: The population mean pressure is greater than 4.4 pounds/square inch.

We will use a one-tailed z-test with a level of significance of 0.01. Since the standard deviation is known, we can use the z-test formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we get:

z = (4.6 - 4.4) / (0.8 / √110) = 2.75

The critical value for a one-tailed test with a level of significance of 0.01 is 2.33 (obtained from a standard normal distribution table). Since our calculated z-value of 2.75 is greater than the critical value of 2.33, we reject the null hypothesis.

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Answer:

23

Step-by-step explanation:

replace x with 2 8×2+7=23

Answer:23

Step-by-step explanation: its actually really simple, all you have to do is replace x for 2, giving you the equation: f(2) = 8x2 + 7 then all you have to do is solve, 8x2 is 16 and 16+7 is 23, and thats how you get the answer.

The margin of error is given as 4.22 mph

Margin of Error = t * (sample standard deviation / √(sample size))

degrees of freedom (df), which is calculated as:

df = n - 1 = 13 - 1 = 12

95% confidence level with 12 degrees of freedom = 2.179.

Margin of Error = t * (s / √n)

Margin of Error = 2.179 * (7 / √13)

Margin of Error ≈ 2.179 * (7 / 3.606)

Margin of Error ≈ 2.179 * 1.939

Margin of Error ≈ 4.22 mph

The margin of error is given as 4.22 mph

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Answer:

(x+10)/(x+8).

Step-by-step explanation:

(x+5)/(x+8) = (x+5)/(x+8) + (x+5)/(x+1)

= (x+5) + (x+5)/(x+1)

= (x+10)

In the cylinder , height of the water tank is 5.5 feet.

What is volume?

The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.

Given that,

A cubic foot contains roughly 7.48 liquid gallons.

We have to find what is roughly the height of a cylindrical water tank with a capacity of 1,500 liquid gallons and a radius of 3.4 feet.

We know that,

7.48 liquid gallons are contained in one cubic foot.

The cylindrical water tank's radius is 3.4 feet.

1,500 liquid gallons are the maximum capacity.

The cylindrical water tank's volume is calculated to hold 1500 liquid gallons ,

= [tex]\frac{1500}{7.48}[/tex]

= 200.53 ft³

Volume of the cylinder= πr²h

=> 200.53= 3.14 ×3.4×3.4×h

=> 200.53 = 3.14 × 11.56 × h

=> 200.53 = 36.29 × h

=> h= 5.5

=> h= 5.5 feet (Approximately)

Therefore, height of the water tank is 5.5 feet.

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The transformation rule used for the diagram is: Shift by 3 units upwards and a shift by 5 units to the left.

There are different methods of transformation such as:

Reflection

Dilation

Rotation

Translation

Now, from the given graph, we see that both objects remain the same size and the object on the right was first if all shifted by 3 units upwards.

Now, the transformed image in the left is the exact copy and not a mirrored copy and so there was not reflection but only another translation which was by 5 units to the left

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2 students to get a grade C and 0 students to get a grade A.

In mathematics , in addition to the mode and median, the mean is one of the measures of central tendency. the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.

The relation between a value and a set of values of  mean is described by the statistical measurement is known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point of  score is the same as the mean score.

We require the distribution of scores in order to estimate the number of students who should earn a given grade. We may determine the z-score for each grade using the mean and standard deviation, presuming that the scores have a normal distribution.

(a) We must locate the z-score equivalent to a C grade in order to establish the number of pupils who should receive a C. Assuming that a C equals a score between 70 and 79, the following formula can be used to determine the z-scores for these values:

(70 - 60) / 5 = 2 is the z-score for 70.

79's z-score is (79 - 60) / 5 = 3.8

We can calculate the percentage of the distribution that falls between these two z-scores using a z-table or a calculator:

P(2 ≤ z ≤ 3.8)

This implies that roughly 4.55% of the students to get a C grade. We can multiply this percentage by the total number of students  Than we get

0.0455 x 35 ≈ 2

therefore,approximately 2 students to get a grade C.

b)  the z-score  to calculate the number of pupils who should receive an grade A. Considering that a grade A of 90 or above 90,Now we can calculate the z-score for 90

than we get .

the z-score for 90 = (90 - 60) / 5 = 6 .

We calculate the percentage of the distribution that lies to the right of this z-score using a z-table or a calculator:

P(z ≥ 6) ≈ 0

therefore,0 students to get a grade A.

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The probability of picking a card with an 'E' is 2/6 and not picking an E is 4/6

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

REFLEX

In the above, we have

Letters = 6

E = 2

So, we have

P(E) = 2/6

This also means that

P(Not E)  = 1 - 2/6

P(Not E)  = 4/6

Hence, the letters are

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