The Bermuda Triangle is a part of the Atlantic Ocean reputed to cause mysterious navigational problems for ships and airplanes. The sides of
the Bermuda Triangle run from Miami, Florida, southeast to San Juan, Puerto Rico; then north to Bermuda, Bermuda; and then southwest back
to Miami. The region is roughly equilateral with each side about 1000 miles long. A coordinate grid is placed on a map so that Miami is at
(0,0) and San Juan is at (10,0). What are the coordinates of Bermuda?

The height of the pistol after 10 seconds is 783 feet.

We can use the method of finite differences to find the degree of the polynomial function that models the data. The first differences are:

3, 18, 37, 56, 72

The second differences are:

15, 19, 19, 16

Since the second differences are constant, we know that the function that models the data is a quadratic function of the form:

h(t) = at² + bt + c

where a, b, and c are constants to be determined.

To find a, we can use the fact that the coefficient of t² in the quadratic function is equal to half of the second difference. Thus, we have:

a = 1/2(15) = 7.5

To find b, we can use the fact that the coefficient of t in the quadratic function is equal to the first difference minus twice the coefficient of t². Thus, we have:

b = 18 - 2(7.5) = 3

To find c, we can use the fact that the constant term in the quadratic function is equal to the value of h(0). Thus, we have:

c = h(0) = 3

Therefore, the equation that models the data is:

h(t) = 7.5t² + 3t + 3

To find the height of the pistol after 10 seconds, we can substitute t = 10 into the equation:

h(10) = 7.5(10)² + 3(10) + 3

h(10) = 750 + 30 + 3

h(10) = 783

Thus, the height of the pistol after 10 seconds is 783 feet.

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If after the plumber has worked alone for 3 hours, his apprentice joins him and working together they complete the job 4 hours later, it would take the plumber 9 hours to do the entire job by himself.

Let's start by assigning some b to represent the rate at which each person works. Let's say that the plumber's rate is P (in units of job per hour) and the apprentice's rate is A (also in units of job per hour). Since the plumber works twice as fast as the apprentice, we can write:

P = 2A

Next, let's think about how much work can be done in a certain amount of time. If the plumber works alone for 3 hours, he completes 3P units of work. When the apprentice joins him, they work together for another 4 hours to complete the entire job, which is a total of 7 hours of work. So, the amount of work done in those 4 hours is:

4(P + A)

We also know that the total amount of work is 1 (since it's one complete job). Putting this all together, we can write an equation:

3P + 4(P + A) = 1

We can simplify this to:

7P + 4A = 1

But we also know that P = 2A, so we can substitute that in:

7(2A) + 4A = 1

Simplifying this, we get:

18A = 1

So, A = 1/18. This means that the apprentice can complete 1/18 of the job in one hour. Since the plumber works twice as fast, he can complete 2/18 of the job (or 1/9) in one hour.

To find out how long it would take the plumber to do the entire job by himself, we can use the formula:

Time = Work / Rate

The entire job is 1, and the plumber's rate is 1/9. So:

Time = 1 / (1/9) = 9 hours

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Answer:

The figure is omitted--please sketch it to confirm my answer.

Set your calculator to degree mode.

Let h be the height of the flagpole.

[tex] \tan(18) = \frac{h}{80} [/tex]

[tex]h = 80 \tan(18) = 25.994[/tex]

The height of the flagpole is approximately 26.0 meters. #3 is correct.

Answer:

The answer is 20

Step-by-step explanation:

when x=7

(4x+9)-4(x-1)+x

(4(7)+9)-4(7-1)+7

28+9 -4(6)+7

37+7-24

44-24

=20

An equation in slope-intercept form for the perpendicular bisector of the segment with endpoints H (-3, 2) and K (7, -5) is y = -0.7x - 0.1.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-5 - 2)/(7 + 3)

Slope (m) = -7/10

Slope (m) = -0.7.

At data point (-3, 2) and a slope of -7/10, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = -7/10(x + 3)

y - 2 = -7x/10 - 21/10

y = -7x/10 - 21/10 + 2

y = -0.7x - 0.1

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Given the above prompt on hypothesis testing, we can state that specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.

To determine if there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage, we can conduct a two-sample t-test assuming unequal variances. The null hypothesis is that there is no difference in the average city mileage between the two types of transmissions, and the alternative hypothesis is that there is a difference.

The t-test statistic is calculated as follows:

t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2))

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the values from the given statistics, we get:

t = (16.12 - 19.85) / sqrt((3.85^2/26) + (4.51^2/26))

t = -3.31

Using a significance level of 0.05 and 50 degrees of freedom (approximated by n1+n2-2), the critical t-value is ±2.01.

Since the calculated t-value (-3.31) is less than the critical t-value, we can reject the null hypothesis and conclude that there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage.

Specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached image.

The probability of having 8 occurrences in 10 minutes is approximately 0.0241, which means the answer is (b).

The number of occurrences of an event in 10 minutes as a Poisson distribution with mean lambda = 5.3.

The probability of having 8 occurrences in 10 minutes is:

[tex]P(X = 8) = (e^(-5.3) * 5.3^8) / 8![/tex]

where X is the random variable representing the number of occurrences of the event in 10 minutes.

Using a calculator, we can evaluate this expression:

[tex]P(X = 8) = (e^(-5.3) * 5.3^8) / 8! ≈ 0.0241[/tex]

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the slope of the line perpendicular to 4x - 2y = 20 is -1/2, which can also be expressed as 1/(-2). This means that the line perpendicular to the given line has a slope that is the negative reciprocal of the slope of the given line.

How to solve the question?

To find the slope of a line perpendicular to the given line, we first need to find the slope of the given line. We can do this by putting the equation of the line in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Starting with the equation of the line, 4x - 2y = 20, we can isolate y on one side by subtracting 4x from both sides and then dividing by -2. This gives us:

-2y = -4x + 20

y = 2x - 10

Comparing this equation with the slope-intercept form, we can see that the slope of the line is 2.

To find the slope of a line perpendicular to this line, we need to use the fact that the product of the slopes of two perpendicular lines is -1. That is, if the slope of the given line is m, then the slope of a line perpendicular to it is -1/m.

So, the slope of the line perpendicular to 4x - 2y = 20 is:

-1/2

To fully simplify this answer, we can write it as a fraction with a positive numerator by multiplying both the numerator and denominator by -1:

1/(-2)

Therefore, the slope of the line perpendicular to 4x - 2y = 20 is -1/2, which can also be expressed as 1/(-2). This means that the line perpendicular to the given line has a slope that is the negative reciprocal of the slope of the given line.

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Answer:

Step-by-step explanation:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:

(

3

,

0

)

Focus:

(

3

,

1

4

)

Axis of Symmetry:

x

=

3

Directrix:

y

=

−

1

4

x

y

1

4

2

1

3

0

4

1

5

4

Tap to view steps...

The overall shapes of the distributions are symmetric  and right skewed

In statistics, a distribution is considered symmetric if the right and left halves of the distribution are mirror images of each other.

In this case, the overall shape of the distribution is symmetric

From the dot plot, we have the following readings

0,3,4,5,5,6,6,7,7,8,8

Using a graphing tool, we have

Mean absolute deviation = 1.79

A right-skewed distribution is a type of probability distribution where the majority of the data values are clustered on the left side of the distribution, while a few large values extend out to the right side.

In this case, the overall shape of the distribution is right skewed

From the histogram, the true statement about the distribution is that the distribution has an outlier

The datapoints for the last question are not given

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(a). The rocket will reach height of 500 feet at  5.12 seconds and 17.38 seconds. (b). The maximum height rocket is 2012.5 feet. (c). The rocket will hit ground at approximately 31.88 seconds.

a) We can substitute h(t) = 500 in given equation and solve for "t".

[tex]-16t^2 + 400t + 50 = 500[/tex]

[tex]-16t^2 + 400t - 450 = 0[/tex]

Dividing both sides by -2, we get:

[tex]8t^2 - 200t + 225 = 0[/tex]

This quadratic equation can be solved using quadratic formula:

[tex]t = [200 ± sqrt((200)^2 - 4(8)(225))] / (2(8)) \\t = [200 ± sqrt(40000 - 7200)] / 16 \\t = [200 ± sqrt(32800)] / 16 \\[/tex]

t ≈ 5.12 seconds or t ≈ 17.38 seconds

b) The t-coordinate of the vertex can be found using the formula t = -b / 2a:

[tex]t = -400 / (2(-16)) = 12.5 seconds[/tex]

[tex]h(12.5) = -16(12.5)^2 + 400(12.5) + 50[/tex]  ≈ 2012.5 feet

c) We need to find the value of "t" when h(t) = 0.

[tex]-16t^2 + 400t + 50 = 0[/tex]

[tex]-8t^2 + 200t + 25 = 0[/tex]

[tex]8t^2 - 200t - 25 = 0[/tex]

Using the quadratic formula, we get:

[tex]t = [200 ± sqrt((200)^2 - 4(8)(-25))] / (2(8))\\t = [200 ± sqrt(40400)] / 16[/tex]

t ≈ 0.62 seconds or t ≈ 31.88 seconds

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--The complete Question is, A rocket is launched in the air. Its height in feet, "h", is given by the equation h(t) = -16t^2 + 400t + 50, where "t" represents time in seconds after the rocket is launched.

a) At what time(s) will the rocket reach a height of 500 feet?

b) What is the maximum height the rocket will reach?

c) How long will it take for the rocket to hit the ground? --

Let x be the length of the pen and y be the width of the pen.

The total cost of the pen is given by:

Cost = 3x + 5y = 300

3x + 5y = 300

3x = 300 - 5y

x = (300 - 5y)/3

The area of the pen is given by:

Area = xy = (300 - 5y)/3 * y

The area of the paper remains  is 238.14 cm².

Area is the region bounded by a plane shape.

To calculate the area of the paper that remains, we use the formula below.

Formula:

Where:

From the diagram in the question,

Given:

Substitute these values into equation 1

Hence, the area  is 238.14 cm².

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The expression that represents the volume of the cylinder is:

V = π[tex]r^{2}[/tex]h

What is cylinder?

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases. The cylinder can be thought of as a tube or a can. The lateral surface of the cylinder is formed by "unrolling" a rectangular shape along the circumference of the base.

There appears to be a typographical error in the given formula for the volume of a cylinder. The correct formula is:

V = π[tex]r^{2}[/tex]h

where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder.

Using this formula, the expression that represents the volume of the cylinder is:

V = π[tex]r^{2}[/tex]h

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The sample variances is calculated by option b, which is the sum of all squared differences between actual values and the overall mean divided by the total number of observations less one.

The sample variance is calculated by the sum of all squared differences between actual values and the overall mean divided by the total number of observations less than one.

The sample variance is a measure of the spread of a sample data set. It measures how far each value in the set is from the mean of the set. The formula for the sample variance involves taking the sum of the squared differences between each data point and the mean, and then dividing that sum by the total number of observations minus one. Dividing by the number of observations minus one instead of just the number of observations is known as Bessel's correction and is used to correct for bias in the sample variance calculation. The resulting value represents the average squared deviation from the mean, and is often used as an estimate of the population variance. Therefore, the sample variance is calculated by the sum of all squared differences between actual values and the overall mean divided by the total number of observations less than one.

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Answer:

B. 1152π cm^3

Step-by-step explanation:

I'm 99.9% sure that this is correct!

I'm really really sorry if it's not! please tell me if I'm wrong!

The distance from point A to point B is approximately 926.4 feet.

An angle is a measure of the amount of rotation between two lines, rays, or line segments that share a common endpoint, called the vertex. It is typically measured in degrees or radians.

Let's call the distance between point A and the lighthouse "x" and the distance between point B and the lighthouse "y". We want to find the value of "y".

From point A, the crew measures the angle of elevation to the lighthouse to be 6. This means that the angle formed between the horizontal line passing through point A and the line connecting point A to the top of the lighthouse is 6. We can draw a right triangle ABC where point A is the bottom left corner, point B is the bottom right corner, and point C is the top of the lighthouse. The line segment AC represents the height of the lighthouse (111 feet) and the line segment AB represents the distance between point A and the lighthouse (x).

Using trigonometry, we know that:

tan(6) = AC/AB

tan(6) = 111/x

x = 111/tan(6)

Now, from point B, the crew measures the angle of elevation to the lighthouse to be 13. This means that the angle formed between the horizontal line passing through point B and the line connecting point B to the top of the lighthouse is 13. We can draw a right triangle BCD where point B is the bottom left corner, point C is the top of the lighthouse (the same point as in the previous triangle), and point D is the bottom right corner. The line segment CD represents the height of the lighthouse (111 feet) and the line segment BD represents the distance between point B and the lighthouse (y).

Using trigonometry, we know that:

tan(13) = CD/BD

tan(13) = 111/y

y = 111/tan(13)

Therefore, the distance between point A and point B is:

y - x = 111/tan(13) - 111/tan(6)

Using a calculator, we get:

y - x ≈ 926.4 feet

Rounding to the nearest tenth of a foot, the distance from point A to point B is approximately 926.4 feet.

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Therefore, the answer is: 360 and 360; the proportion is true.

54 and 540; the proportion is true.

360 and 360; the proportion is true.

To find the cross-products of the proportion 6/40 = 9/60, we multiply the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.

So we have:

6 × 60 = 360

9 × 40 = 360

The cross-products are 360 and 360.

To check if the proportion is true, we compare the cross-products. If they are equal, then the proportion is true; otherwise, it is false.

Since the cross-products are equal, the proportion is true.

Therefore, the answer is:

360 and 360; the proportion is true.

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The percent increase in the number of channels Jose has to watch is 150%.

To find the percent increase in the number of channels Jose has to watch, we need to find the difference between the new number of channels and the old number of channels, divide that by the old number of channels, and then multiply by 100 to get the percentage increase.

The difference between the new and old number of channels is 300 - 120 = 180.

Dividing that by the old number of channels and multiplying by 100 gives us:

(180/120) x 100% = 150%

Therefore, the percent increase in the number of channels Jose has to watch is 150%. This means that Jose now has 150% more channels to watch than he did before he switched to satellite TV.

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The value of k is given as follows:

k = 5.

The function in the context of this problem is defined as follows:

f(x) = x³ + kx - 6.

We have that x - 1 is a factor of the function, meaning that, by the Factor Theorem:

f(1) = 0, x - 1 = 0 -> x = 1.

Hence, applying the numeric value, the value of k is obtained as follows:

1 + k - 6 = 0

k - 5 = 0

k = 5.

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Answer:

[tex]d) \ y=4x+1[/tex]

Step-by-step explanation:

I suppose the table looks like this:

[tex]\begin{array}{|r|r|} x & y \\ \cline{0-1}-1 & -3 \\0 & 1 \\ 1 & 5\end{array}[/tex]

Thus, we can select two points and apply the formula for the equation of a line given two points to derive an equation that represents the table.

[tex]y-y_1=(\frac{y_2-y_1}{x_2-x_1} )(x-x_1)[/tex]

I select this points:

[tex](x_1,y_1)= (0,1)\\(x_2,y_2)= (1,5)[/tex]

Now, we substitute this values in the previous equation:

[tex]y-(1)=(\frac{5-1}{1-0} )(x-0)\\\\y-1=4 x\\y=4x+1[/tex]

Therefore, the correct answer it's option D

The amount of ribbon you need to create the border is 4 1/4 feet if x = 17/24

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

The length of the paper is 2 times as long as the width

This means that

Length = 2x

Width = x

The perimeter is

Perimeter = 2 * (2x + x)

Perimeter = 6x

Assuming that x = 17/24

So, we have

Perimeter = 6 * 17/24

Evaluate

Perimeter = 17/4

Simplify

Perimeter = 4 1/4

Hence, the amount needed is 4 1/4 feet

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True. An integer overflow attack occurs when an attacker manipulates a variable in a way that causes it to exceed its maximum value or minimum value, leading to unexpected and potentially harmful behavior.

This can happen if a programmer fails to properly check and validate the input values that are being used in their code, allowing an attacker to inject a value that triggers an overflow.

As a result, the variable may be assigned a value that is outside the intended range, leading to unpredictable behavior and potentially causing the program to crash or execute unintended code. It is important for programmers to take steps to prevent integer overflow attacks, such as validating input values and using data types with sufficient capacity to hold the expected range of values.

This occurs when an arithmetic operation results in a value that is too large to be stored in the allocated memory, causing the value to wrap around and become smaller, or even negative. This can lead to unintended consequences in a program's behavior, which an attacker can exploit to gain unauthorized access or cause other security issues.

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The point where marginal cost equals $15 is at the production of the 7th pizza. Therefore, the firm should produce 7 pizzas.

The firm's shut-down price is the price at which the firm is indifferent between producing and shutting down.

Using the table provided, we can calculate the missing values:

Variable Cost:

For 0 pizzas, the variable cost is $0.

For 1 pizza, the variable cost is $10.

For 2 pizzas, the variable cost is $12.

For 3 pizzas, the variable cost is $2.

For 4 pizzas, the variable cost is $1.

For 5 pizzas, the variable cost is $2.

For 6 pizzas, the variable cost is $3.

For 7 pizzas, the variable cost is $13.

For 8 pizzas, the variable cost is $16.

For 9 pizzas, the variable cost is $3.

For 10 pizzas, the variable cost is $6.

For 11 pizzas, the variable cost is $4.

Total Cost: To calculate the total cost, we simply add the variable cost and the fixed cost for each level of output. The fixed cost is not given in the table, so we cannot calculate the total cost.

Average Variable Cost:

To calculate the average variable cost, we divide the variable cost by the level of output. For example, the average variable cost for 1 pizza is $10/1 = $10.

Average Fixed Cost:To calculate the average fixed cost, we divide the fixed cost by the level of output.

Average Total Cost: To calculate the average total cost, we add the average variable cost and the average fixed cost. The firm should produce pizzas up to the point where marginal cost equals marginal revenue.

This is the point where the firm maximizes its profit. From the table, we can see that the marginal cost is increasing as output increases, while the marginal revenue remains constant at $15.

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Answer: 100001

Step-by-step explanation: The trick for binary is that it only uses 1 & 0 for its number system. It goes by a system where you take 1 and multiply by 2, then you multiply 2 by 2, and so forth. So 33 has one 32, and one 1.

2 x 10-7  is the probability of drawing a T, replacing it, then drawing a C.

What is Probability?

Probability is simply the chance that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Analyzing events according to their probabilities is called statistics. 

There are 11 letters in MATHEMATICS which consist of 2 each of M, A and T and 1 each of H, E, I, C and S.  

P(M on 1st choice) = 2/11   since there are 2 M's out of 11 letters

P(A on 2nd choice) = 2/10   since there are 2 A's out of 10 remaining letters

P(T on 3rd choice) = 2/9     since there are 2 T's out of 9 remaining letters

At this point there are 8 letters remaining which are all distinct so they must be chosen in the correct order

P(H on 4th choice) = 1/8

P(E on 5th choice) = 1/7

P(M on 6th choice) = 1/6

P(A on 7th choice) = 1/5

P(T on 8th choice) = 1/4

P(I on 9th choice) = 1/3

P(C on 10th choice) = 1/2

P(S on 11th choice) = 1/1  

The probability of spelling the word correctly is the product of all the probabilities

P = 2*2*2 / 11! = 8 / 39916800 = 1 / 4989600 ~ 2 x 10-7

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To find the argument of the complex number z = 1/16 - (sqrt(3)/16)i, we need to find the angle that the complex number forms with the positive real axis in the complex plane.

We can start by finding the magnitude of z, which is the distance between the origin and the point representing z in the complex plane:

|z| = sqrt( (1/16)^2 + (sqrt(3)/16)^2 )

= sqrt(1/256 + 3/256)

= sqrt(4/256)

= 1/4

Next, we can find the argument of z using the formula:

arg(z) = tan^(-1)(Im(z)/Re(z))

where Im(z) is the imaginary part of z, and Re(z) is the real part of z.

In this case, we have:

Re(z) = 1/16

Im(z) = -(sqrt(3)/16)

Therefore, we get:

arg(z) = tan^(-1)(Im(z)/Re(z))

= tan^(-1)(-(sqrt(3)/16)/(1/16))

= tan^(-1)(-sqrt(3))

= -60° (in degrees)

So, the argument of z is -60 degrees (or -π/3 radians).

Answer:

A

Step-by-step explanation:

The probability of a score for a recent basketball game, shenille attempted only three-point shots and two-point shots is 18 points in the game. The answer is Option B.

Let x be the number of three-point shots and y be the number of two-point shots attempted by Shenille.

Then, we have:

x + y = 30 (total number of shots attempted)

Let's solve for one of the variables. For example, we can solve for x by subtracting y from both sides of the equation:

x = 30 - y

Now, we can express Shenille's points in terms of x and y:

Points = 3x + 2y

Substituting x = 30 - y, we get:

Points = 3(30 - y) + 2y

Points = 90 - y

Shenille's success rate for three-point shots is 20%, so the number of successful three-point shots she made is 0.2x. Similarly, the number of successful two-point shots she made is 0.3y.

Total points scored = (0.2x)(3) + (0.3y)(2)

Substituting x = 30 - y, we get:

Total points scored = (0.2(30 - y))(3) + (0.3y)(2

Total points scored = 18 + 0.4y

Now we need to maximize the total points scored by Shenille. Since she attempted 30 shots in total, we have:

y = 30 - x

Substituting this into the equation for total points, we get:

Total points scored = 18 + 0.4(30 - x)

Total points scored = 30 - 0.4x

This is a linear function, which is maximized at its endpoint. The maximum value of this function occurs at x = 0, which means Shenille attempted all two-point shots. In this case, y = 30, and the total points scored would be:

Total points scored = 0 + 0.3(30)(2)

Total points scored = 18

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The question is -

In a recent basketball game, Shenille attempted only three-point shots and two-point shots. She was successful on 20% of her three-point shots and 30% of her two-point shots. Shenille attempted 30 shots. How many points did she score?

(A) 12

(B) 18

(C) 24

(D) 30

(E) 36

The exact volume of each cone-shaped basket is (240/π) cubic inches.

The formula for the volume of a cone is,

V = (1/3)πr^2h

Where,

V is the volume of the cone

π is the mathematical constant pi (approximately 3.14159)

r is the radius of the base of the cone

h is the height of the cone

In this case, the height of the cone-shaped basket is 20 inches and the radius is 6 inches. So, substituting these values into the formula,

V = (1/3)π(6^2)(20)

V = (1/3)π(36)(20)

V = (1/3)π(720)

V = (240/π) cubic inches

Hence, volume is (240/π) cubic inches.

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Answer:

Gemma can type 3150 words in 3/4hr

Step-by-step explanation:

350 word------>five minutes

x words------->3/4hr

convert 3/4hr-minutes

3/4×60=45minutes

x word =350×45/5

x word=3,150 words