What is the volume of this prism?

In the event  of alteration in the rate at which the water level of the funnel is changing when the water is 15 inches high is 0.42 cubic inches per second.
The volume of a cone is given by the formula V = (1/3)πr²h here r is the radius of the base and h is the height of the cone.

Now we have differentiate this formula concerning t to get
dV/dt = (1/3)πr²dh/dt + (2/3)πrh²dr/dt.

It is given to us  that water is coming out a giant cone shaped funnel at a rate of 15 cubic inches per second, then we  can say that
dV/dt = -15 cubic inches per second

Therefore the funnel has a maximum radius of 40 inches and a height of 75 inches. We need to evaluate  dh/dt
If h = 15 inches.

In order to find dh/dt,
we need to evaluate  dr/dt and place it in  equation for dV/dt.

Therefore, to find dr/dh = r/h.
Given
when h = 75 inches,
r = 40 inches.
Therefore, dr/dh
= 40/75.

Staging this into the equation for dV/dt,

-15 = (1/3)π(40²)(dh/dt) + (2/3)π(40)(15)²(40/75)

Here simplification takes place


dh/dt = -0.4π/3
≈ -0.42 cubic inches per second
In the event  of alteration in the rate at which the water level of the funnel is changing when the water is 15 inches high is 0.42 cubic inches per second.


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Answer:

17.7

Step-by-step explanation:

using the pythagorean theorem, plug in and solve.

hi

with Pythagoras we have :

13²+12² = 313

so answer is [tex]\sqrt{313}[/tex] ≈ 17.7  rounded.

The standard deviation of the height distribution is approximately 6 inches (since 6 is half of 12), which corresponds to option (C).

The distribution of the heights of students in a large class is roughly Normal, with an average height of 68 inches, and approximately 95% of the heights are between 62 and 74 inches.

The height distribution is approximately Normal, we can use the empirical rule, which states that approximately 95% of the data falls within 2 standard deviations of the mean, to estimate the standard deviation.

The range of heights within which approximately 95% of the students fall is from 62 to 74 inches.

This range is 12 inches wide, and it corresponds to 2 standard deviations from the mean.

Thus, we have:

2 standard deviations = range of 95% of the data = 74 - 62 = 12 inches

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by solving the following equation we can conclude that the value of 4¤(5¤6) is 72.

Mathematical operations including multiplication, division, addition, and subtraction are possible. The construction of an expression looks like this: Expression, number, and mathematical operator Numbers, variables, and functions are the elements of a mathematical expression (such as addition, subtraction, multiplication, and division, etc.). Expressions and phrases can be contrasted. Expressions are any equations that comprise numbers, variables, and an arithmetic operation. They are occasionally referred to as algebraic expressions. For instance, the value of m in the computation of 4m + 5 is the same as the word m in the provided equation, which has been separated from the figures 4m and 5 by the mathematical symbol +.

given,

To find the value of 4¤(5¤6), we need to evaluate the expression from the inside out, following the order of operations.

We must first determine the worth of 5¤6. Using the given operation, we have:

5¤6 = 5*6 - 6 = 24

Now we can substitute this value into 4¤(5¤6) and evaluate:

4¤(5¤6) = 4¤24 = 4*24 - 24 = 96 - 24 = 72

Therefore, the value of 4¤(5¤6) is 72.

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The axis of symmetry for y = (x - 1)² - 4 is x = 1.

Given the equation in the question;

y = (x - 1)² - 4

The axis of symmetry for a parabola in standard form is expressed as:

y = a(x - h)² + k is the vertical line passing through the vertex (h, k).

Comparing y = (x - 1)² - 4 to the standard form

We can see that h = 1 and k = -4.

Therefore, the vertex is (1, -4).

Since the axis of symmetry is the vertical line passing through the vertex, the equation of the axis of symmetry is

x = 1.

Therefore, the axis of symmetry is x = 1.

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The x-intercept is (-4, 0). The y-intercept can also be located by setting x = 0: f(0) = (0 + 4)/(0 - 3) = -4/3. So the y-intercept is (0, -4/3).

By rearranging the equation to take on its general form, f(x) = mx + c, where m is the slope, one can determine the slope of a linear function. By rearranging the equation to take on its general form, the vertex of a quadratic function can be determined.

The formula for f(x) is

f(x) = (x + 4)/(x - 3)

This function is rational, which means it is the ratio of two polynomials. X + 4 makes up the numerator, and X – 3 makes up the denominator.

Several things about this function are worth mentioning:

Due to the illogical nature of division by zero, the denominator cannot be equal to zero. As a result, at x = 3, there is a vertical asymptote and the function is undefined.

The function cannot be further simplified because the numerator and denominator have no shared factors.

The function approaches the horizontal asymptote y = 1 when x approaches positive or negative infinity because the maximum power of x in the numerator and denominator is the same (both are 1).

To graph this function, we can start by plotting the vertical asymptote at x = 3, and the horizontal asymptote at y = 1. The x-intercept can alternatively be determined by setting the numerator to zero:

x + 4 = 0

x = -4

So the x-intercept is (-4, 0).

f(0) = (0 + 4)/(0 - 3) = -4/3

So the y-intercept is (0, -4/3).

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The sides of the triangle are;

c = 5√2

b = 3√3

A right triangle is a triangle that has a right angle that measures 90 degrees. The hypotenuse, which is the side that faces the right angle, is the longest side. The right triangle's other two sides are referred to as its legs.

1) Cos 45 = 5/c

√2/2 = 5/c

c√2 = 10

c = 10/√2

c = 5√2

2) Tan 30 = b/3

√3/3 = b/3

3√3= 3b

b = 3√3/3

b = 3√3

We have used to concept of the special angles to solve the problem above.

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Answer:

Step-by-step explanation:

Split it into 3 shapes.

2 triangles and 1 square.

The squares answer is 53.25 And for the triangles you would get 26 and there are 2 triangles so 52.

52+53.25=105.25.

To find the area of a specific parallelogram, we need to know the length of its base and the height.

To find the area of a parallelogram, we multiply the base of the parallelogram by its height, where the height is the perpendicular distance between the base and its opposite side. So, the formula for the area of a parallelogram is:

Area = base x height

where the base and height are both expressed in the same units.

We know that the area of the parallelogram can be given as bh or absinα

Thus we have for each of the parallelograms shown;

1) 6 * 4 = 24 ft^2

2) 9 * 5 = 45 yd^2

3) 8 * 10 sin 45 = 56.6 cm^2

4) 5 * 11 sin 60 = 47.6 m^2

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The building is approximately 74.8 feet tall, and your head is approximately 117.7 feet away from the base of the building.

We can use trigonometry to solve this problem. Let's call the height of the building "h" and the distance from your head to the base of the building "d".

Using the tangent function;

tan(55°) = h/d

We know that h + 60 = d, so we can substitute h with d - 60:

tan(55°) = (d - 60)/d

Simplifying this equation, we get;

d = (h + 60)/tan(55°)

Substituting this value of d in first equation, we have;

tan(55°) = h/[(h + 60)/tan(55°)]

Simplifying this equation, we get;

h = 60 tan(55°)

Using a calculator, we find that h ≈ 74.8 feet.

Therefore, the building is approximately 74.8 feet tall.

To find the distance from your head to the base of the building, we can use the Pythagorean theorem;

d² = h² + 60²

Substituting h with 60 tan(55°), we get;

d² = (60 tan(55°)² + 60²

Using a calculator, we find that d ≈ 117.7 feet.

Therefore, your head is approximately 117.7 feet away from the base of the building.

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Answer: To find the decimal expansion of 5/7, we can perform long division as follows:

0.7│5.0

    4 2

 ────

  8 │ 30

    28

  ───

20 │ 200

    196

  ────

      4

Hence, 5/7 = 0.714285... where the digits 714285 repeat indefinitely. To find the maximum number of digits in the repeating block of digits, we can observe that the repeating block will be at most 6 digits long because 7 has a factor of 2 and 5, and therefore 7 divides 10^6 - 1 = 999999.

In fact, we can see that the repeating block in this case has 6 digits, since the digits 714285 repeat indefinitely, and there are 6 digits in this repeating block. Therefore, the maximum number of digits in the repeating block of digits in the decimal expansion of 5/7 is 6.

Step-by-step explanation:

The function f(x) = 3x⁵ - 5x³ + 15 has relative maxima at x = -1 and relative minima at x = 1, so the answer is (d) -1 and 1 only.

To find the relative maximum of the function f(x) = 3x⁵ - 5x³ + 15, we need to find the critical points and then determine whether they correspond to a maximum or minimum.

To find the critical points, we need to find where the derivative of the function is equal to zero

f'(x) = 15x⁴ - 15x²

f'(x) = 15x²(x² - 1)

Setting f'(x) equal to zero, we get

x²(x² - 1) = 0

This equation is true when x = 0, x = 1, and x = -1.

Now we need to determine whether these points correspond to a relative maximum or minimum. To do this, we can use the second derivative test.

f''(x) = 60x³ - 30x

Plugging in x = -1, we get

f''(-1) = -30 < 0

This means that x = -1 corresponds to a relative maximum.

Plugging in x = 0, we get

f''(0) = 0

This test is inconclusive, so we need to use another method to determine the nature of the critical point at x = 0.

Plugging in x = 1, we get

f''(1) = 30 > 0

This means that x = 1 corresponds to a relative minimum.

Therefore, the correct option is (d) -1 and 1 only

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The probability that a randomly selected adult has an IQ score between 89 and 121 is 0.5328

To find the probability that a randomly selected adult has an IQ score between 89 and 121, we need to calculate the area under the normal curve between these two scores.

First, we need to standardize the scores by converting them into z-scores using the formula

z = (x - μ) / σ

where x is the IQ score, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

For x = 89

z = (89 - 105) / 20 = -0.8

For x = 121

z = (121 - 105) / 20 = 0.8

Now, we need to find the area under the normal curve between z = -0.8 and z = 0.8. We can do this by using a standard normal distribution table or a calculator.

The area under the curve between z = -0.8 and z = 0.8 is 0.5328.

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The given question is incomplete, the complete question is:

Assume that adults have iq scores that are normally distributed with a mean of 105 and a standard deviation of 20. Find the probability that a randomly selected adult has an iq between 89 and 121.

The given statement "You can measure the amount of overlap of 2 data sets by comparing the distance between the medians of the IQR" is False. Because the distance between the medians can give some indication of how much overlap there is between two data sets, it is not the only factor to consider other factors are means or standard deviation.

The median is a measure of central tendency that divides the data into two halves. The interquartile range (IQR) is a measure of spread that gives the range of the middle 50% of the data.

Therefore, the distance between the medians of the IQR can give an idea of how much overlap there is between two data sets, but it is not the only measure to consider.

Other measures of overlap include comparing the means or standard deviations of the data sets, or using statistical tests such as a t-test or ANOVA to compare the groups. So, the given statement is False.

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--The given question is incomplete, the complete question is given

" You can measure the amount of overlap of 2 data sets by only comparing the distance between the medians of the IQR. True or False."--

Thus, the value of x for the given set of similar triangles is found as: x = 42.

Triangles that are similar to one another in terms of shape but not always in terms of size.

Identical triangles always have congruent corresponding angles and proportional corresponding sides. Two angles must share the same measure in order to be congruent.

The triangles both have proportional equivalent sides. Hence, each pair of corresponding sides' ratios is the same. The scale factor is the name of this ratio.

In smaller triangle. applying angle sum property :

Let the unknown angle be y

y + 126 + 16 = 180

y = 180 - 142

y = 38

For the given similar triangles:

The corresponding angles are also equal.

So,

on the straight line:

16 + 3x + 38 = 180 (linear pair)

3x = 180 - 54

x = 126/3

x = 42

Thus, the value of x for the given set of similar triangles is found as: x = 42.

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To find the area under the standard normal curve, we need to use a standard normal distribution table or a calculator with a normal probability distribution function.

(a) To find the area between z = -1.20 and z = 1.20, we can use the symmetry property of the normal distribution curve and find the area to the right of z = -1.20 and double it:

P(-1.20 < z < 1.20) = 2 * P(z < 1.20) - 1 = 2 * 0.8849 - 1 = 0.7698

Therefore, the area under the standard normal curve between z = -1.20 and z = 1.20 is approximately 0.7698.

(b) area between z = 1.23 and z = 1.87

P(1.23 < z < 1.87) = P(z < 1.87) - P(z < 1.23) = 0.9693 - 0.8907 = 0.0786

Therefore, the area under the standard normal curve between z = 1.23 and z = 1.87 is approximately 0.0786.

(c) area between z = -2.35 and z = -0.5

P(-2.35 < z < -0.5) = P(z < -0.5) - P(z < -2.35) = 0.3085 - 0.0094 = 0.2991

Therefore, the area under the standard normal curve between z = -2.35 and z = -0.5 is approximately 0.2991.

(d) To find the area to the right of z = 2.16

P(z > 2.16) = 1 - P(z < 2.16) = 1 - 0.9842 = 0.0158

Therefore, the area under the standard normal curve to the right of z = 2.16 is approximately 0.0158.

(e) To find the area between z = -0.8 and z = 1.53

P(-0.8 < z < 1.53) = P(z < 1.53) - P(z < -0.8) = 0.9370 - 0.2119 = 0.7251

Therefore, the area under the standard normal curve between z = -0.8 and z = 1.53 is approximately 0.7251.

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There are two buildings that you want to have in the amusement park.

a) The expression that represents the area of the gift shop, in terms of x, is

Area = length x width

Area = (20x + 24) (36x - 20)

Area = 720[tex]x^{2}[/tex] + 208x - 480

Therefore, the area of the gift shop is 720[tex]x^{2}[/tex]  + 208x - 480 square feet.

b) The expression that represents the perimeter of the gift shop, in terms of x, is

Perimeter = 2(length + width)

Perimeter = 2(20x + 24 + 36x - 20)

Perimeter = 2(56x + 4)

Perimeter = 112x + 8

Therefore, the perimeter of the gift shop is 112x + 8 feet.

c) If the perimeter is going to be 176 feet, we can set the expression for the perimeter equal to 176 and solve for x

112x + 8 = 176

Subtracting 8 from both sides

112x = 168

Dividing both sides by 112

x = 1.5

Now that we know x, we can substitute it into the expressions for the length and width of the gift shop

Length = 20x + 24 = 20(1.5) + 24 = 54 feet

Width = 36x - 20 = 36(1.5) - 20 = 34 feet

Therefore, the dimensions of the gift shop are 54 feet by 34 feet.

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No, tripling the length of time for the investment does not double the interest earned with compound interest.

When interest is compounded, the interest earned depends not only on the length of time, but also on the interest rate and the number of compounding periods.

For example, if an investment of $100 earns 5% annual interest compounded annually for 1 year, the interest earned would be:

Interest = $100 x 0.05 = $5

If the same investment is compounded for 2 years instead of 1, the interest earned would be:

Interest = $100 x (1 + 0.05)^2 - $100 = $10.25

As we can see, doubling the length of time for the investment does not double the interest earned with compound interest.

The interest earned depends on the interest rate and the number of compounding periods as well.

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Answer: To find the proportion of students who performed worse than Aaron, we need to find the area to the left of his score of 989 on the normal distribution curve.

First, we need to standardize Aaron's score using the formula:

z = (x - mu) / sigma

where x is the score, mu is the mean, and sigma is the standard deviation.

Plugging in the values, we get:

z = (989 - 1100) / 200 = -0.55

Next, we look up the area to the left of z = -0.55 on the standard normal distribution table, or use a calculator to find:

P(Z < -0.55) = 0.2912

Therefore, the proportion of students who performed worse than Aaron is approximately 0.2912, or 29.12% (rounded to 2 decimal places).

Step-by-step explanation:

The equivalent expression is 8

Note that algebraic expressions are described as expressions that are composed of variables, constants, terms, coefficients, and factors.

These algebraic expressions are also composed of mathematical operations. These operations are;

Also, equivalent expressions are expressions that have the same solution but may differ in their arrangement.

From the information given, we have that;

(-6y + 8) + 6y

expand the bracket, we have;

-6y + 8 + 6y

collect the like terms

-6y + 6y + 8

8

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The complete question:

Combine the like terms to create an equivalent expression: (-6y + 8) + 6y

To construct a 98% confidence interval,  the critical value is 2.624.

We have,

98% Confidence Interval

Sample size, n= 15

At 98%,

Degree = n-1

             = 15-1= 14

So, For a 98% confidence level with 14 degrees of freedom, the critical value is 2.624.

Therefore, to construct a 98% confidence interval, the critical value is 2.624.

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The scatter plot reveals a positive connection since the y-values grow as the x-values grow.

An example of a graph that employs Cartesian coordinates to show values for two categories for a collection of data is a scatter plot, sometimes referred to as a scatter diagram. Each pixel in the data's representations is a point with a horizontal position (indicating the value of one variable) and a vertical displacement (representing the value of the other variable). In order to observe correlations among variables and spot patterns in the data, scatter plots is utilised. They are frequently employed in data processing, statistics, and academic studies.

given

The scatter plot reveals a positive connection since the y-values grow as the x-values grow.

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Answer:

Let's start by using a proportion to find the total number of questions on the test. We know that Charles answered 23 questions correctly and received a grade of 92%, which means he missed 8% of the questions.

Let x be the total number of questions on the test. Then 8% of the questions that Charles missed can be expressed as 0.08x.

The number of questions that Charles answered correctly plus the number of questions he missed must add up to the total number of questions on the test:

23 + 0.08x = x

Simplifying and solving for x, we get:

0.92x = 23

x = 23 / 0.92

x ≈ 25

Therefore, the total number of questions on the test was approximately 25.

Answer:

42.39

Step-by-step explanation:

The formula for the volume of a cylinder:

V= πr^2h

Substitute values into the formula that was given:

π = 3.14

r = 3/2

h = 6

3.14(1.5^2)6=

3.14(13.5)=

42.39

I hoped this solved your problem <3

(I took the FLVS test too and got it right)