A trebuchet launches a projectile on a parabolic arc from a height of 47 feet at a velocity of 40 ft/s.

Using the function h(t) = -16t^2 + vt + h0, determine when the projectile will first reach a height of 60 feet and how many seconds later it will again be at 60 feet.

A. 1/48. B. 1/24. C. 2/15. The rental truck agency has 6 moving vans, and 2 of them have brake problems.

A. To find the probability that the last van with brake problems is the fourth van tested, we need to find the number of possible sequences of van tests that meet this condition and divide by the total number of possible sequences of van tests.  The total number of possible sequences of van tests is 6!/(6-4)! = 720. So the probability that the last van with brake problems is the fourth van tested is 15/720 = 1/48.

B. To find the probability that no more than four vans need to be tested before both brake problems are detected, we need to find the number of possible sequences of van tests that meet this condition and divide by the total number of possible sequences of van tests. So the number of possible sequences is 15 + 15 = 30. The total number of possible sequences of van tests is 6!/(6-4)! = 720. So the probability that no more than four vans need to be tested before both brake problems are detected is 30/720 = 1/24.

C. To find the probability that the remaining van is found on the third or fourth test, given that one van with bad brakes is detected in the first two tests, The number of possible sequences where the remaining van is found on the third or fourth test is C(4,1) = 4. The total number of possible sequences of van tests that include detecting one brake problem in the first two tests is C(6,1) * C(5,1) = 30. So the probability that the remaining van is found on the third or fourth test is 4/30 = 2/15.

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Based on the given data, there are a total of 13 packets and 5 of them are spicy. Therefore, the probability that the next packet Cooper pulls out of the box will be spicy is 5/13 or approximately 0.385 (rounded to three decimal places).

To calculate the probability of the next packet being spicy, we need to know how many packets of each flavor are in the box. Assuming that Cooper doesn't put back the packets he has pulled out, we can count the number of spicy packets and divide it by the total number of packets he pulled out.

In this case, out of the 13 packets he pulled out, 5 were spicy. Therefore, the probability of the next packet being spicy is 5/13, or approximately 0.38, or 38%. However, if the box is refilled with packets of different flavors, this probability may not hold.

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Answer: 4/13

Step-by-step explanation: i did this IXL and this was the correct answer

The ratio of the number of students who have chocolate to the total number of students  is \(\frac{5}{22}\)

In the above question it is given that,

There are students some of them have gotten the vanilla ice-cream and some have chocolate ice-cream

The total number of students are = 22

The number of students who had vanilla ice-cream are = 17

The number of students who had chocolate ice-cream are = 22 - 17 = 5

We need to find the ratio of the number of students who have chocolate to the total number of students

Therefore, the ratio of the number of students who have chocolate to the total number of students = \(\frac{5}{22}\)

Hence, the ratio of the number of students who have chocolate to the total number of students  is \(\frac{5}{22}\)

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So, four days of the week have an even number of letters. { Monday (6 letters), Tuesday (7 letters), Friday (6 letters), Sunday (6 letters)

An even number is one that can be divided by two and leaves a residue of zero. Even numbers include 2, 4, 6, 8, 10, and so on. Even numbers are ones that can be split into two equal parts, but odd numbers cannot be divided into two equal parts.  Odd numbers are those that cannot be equally divided by two.

It cannot be equally split into two different integers. An odd number will leave a leftover when divided by two. 1, 3, 5, 7, and other odd numbers are instances. The idea of odd numbers is identical to that of even numbers.

The days of the week with an even number of letters are:

Monday (6 letters)

Tuesday (7 letters)

Friday (6 letters)

Sunday (6 letters)

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Answer:

y=−7x2+98x−337 is the answer

The segments AB and CD are classified as follows:

Neither parallel nor perpendicular.

To classify the segments as parallel, perpendicular or neither, we must observe the slope of the segment, as follows:

Given two points, the slope is calculated as the change in y divided by the change in x.

Then the slope of segment AB is given as follows:

m = (-2 - (-8))/(4 - (-2))

m = 1.

The slope of segment CD is given as follows:

m = (5 - 6)/(8 - 4)

m = -1/4.

The slopes are different and the product is of -1/4 different of -1, hence the segments are neither parallel nor perpendicular.

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Answer:

Here ya go!

Step-by-step explanation:

(look at picture below

A prism is a three-dimensional shape with the same cross-section all the way through.

A prism is a solid shape that is bound on all its sides by plane faces.

A prism is a type of three-dimensional (3D) shape with flat sides. It has two ends that are the same shape and size (and look like a 2D shape).It has the same cross-section all along the shape from end to end; that means if you cut through it you would see the same 2D shape as on either end.

Hence, a prism is a three-dimensional shape with the same cross-section all the way through.

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Answer:

5

Step-by-step explanation:

multiply 1/10 by 50

1/10×50= 5

Answer:

5

Step-by-step explanation:

1/10 x 50 = 5

PLEASE GIVE ME BRAINLIEST!

i hope this helps. thank you and have a good day :)

Answer:

a principle in fluid mechanics that states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.

Step-by-step explanation:

pressure applied to a fluid is transmitted equally throughout the fluid in all directions. This is named after the French mathematician and physicist Blaise Pascal, who first formulated it in the mid-17th century.

Answer:

76.275

Step-by-step explanation:

First - the entire circles area is 78.54. \(\pi r^{2}\) with r being 5

6 triangles of that size could fit in that circle.

A=3\(\sqrt{3}\)/(2) * a2

The area of that would equal 64.95

78.54-64.95 = 13.59

then divide that number by 6

which is 2.265.

Take that number from the original 78.54

78.54-2.265 = 76.275

Answer:

d Because I just took the test and got it right

Answer:

c

Step-by-step explanation:

if y= -9, the y intercept will be at -9.

The value of Absolute maximum are (a) 8, (b) -30.36, (c) -10 and the Absolute minimum are (a) -10, (b) -362.39, (c) -362.39.

We are given a function:f(x) = x³ - 12x² - 27x + 8We need to find the absolute maximum and absolute minimum values of the function f(x) over each of the indicated intervals. The intervals are:

a) Interval = [-2, 0]

b) Interval = [1, 10]

c) Interval = [-2, 10]

Let's begin:

(a) Interval = [-2, 0]

To find the absolute max/min, we need to find the critical points in the interval and then plug them in the function to see which one produces the highest or lowest value.

To find the critical points, we need to differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 0].

Checking for x = 4 + √37:f(-2) = -10f(0) = 8

Checking for x = 4 - √37:f(-2) = -10f(0) = 8

Therefore, the absolute max is 8 and the absolute min is -10.(b) Interval = [1, 10]

We will follow the same method as above to find the absolute max/min.

We differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)

x = (24 ± √(888)) / 6

x = (24 ± 6√37) / 6

x = 4 ± √37

We need to check which critical point lies in the interval [1, 10].

Checking for x = 4 + √37:f(1) = -30.36f(10) = -362.39

Checking for x = 4 - √37:f(1) = -30.36f(10) = -362.39

Therefore, the absolute max is -30.36 and the absolute min is -362.39.

(c) Interval = [-2, 10]

We will follow the same method as above to find the absolute max/min. We differentiate the function:

f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:

f'(x) = 0

Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 10].

Checking for x = 4 + √37:f(-2) = -10f(10) = -362.39

Checking for x = 4 - √37:f(-2) = -10f(10) = -362.39

Therefore, the absolute max is -10 and the absolute min is -362.39.

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Answer:

x = 3

Step-by-step explanation:

8.4 ÷ 6 = 1.4

4.2 ÷ 1.4 = 3

The graph that represents the linear equation is attached below.

A linear graph can be modelled by an equation in slope-intercept form, as: y = mx + b. Here, we have:

Given the linear equation, y = 5x + 10, it means the slope of the graph that represents this equation would be 5, while the line that intersects the y-axis would be at 10.

In the graph attached below, the slope is 5, and the y-intercept is 10.

Therefore, the graph that represents the linear equation is attached below.

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Answer:

B

A=2

B=6

Step-by-step explanation:

The expression that shows how much farther Adam can see to the horizon should be considered as the d = 400 - 256 and d = 256 - 400.

Since

Pam's eye–level height is 256 feet above sea level and Adam's eye–level height is 400 feet above sea level.

So here the expression be like The expression that shows how much farther Adam can see to the horizon should be considered as the d = 400 - 256 and d = 256 - 400.

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The special-edition magazine by The Times Herald has fixed publishing expenses of $1400 and printing costs of 40 cents per magazine. The selling price of each magazine is $1. By analyzing the cost and revenue components, we can determine the breakeven point and profitability of the magazine.

To calculate the breakeven point, we need to determine the number of magazines that need to be sold in order to cover the total expenses. The total expenses consist of the fixed costs and the variable costs per magazine. In this case, the variable cost per magazine is the printing cost of 40 cents.

Let's denote the number of magazines to be sold as "x." The total cost can be calculated as $1400 (fixed costs) plus 40 cents multiplied by "x" (printing costs per magazine). The total revenue can be calculated as $1 multiplied by "x" (selling price per magazine).

To determine the breakeven point, we set the total cost equal to the total revenue and solve for "x." This will give us the number of magazines that need to be sold to break even. Any sales beyond this point will result in profitability.

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Answer:

the 2nd option

Step-by-step explanation:

the second option is in standard form (y = ax^2 + bx + c), c gives us the y intercept

Answer:

suitable is (4, 8)

Step-by-step explanation:

slope of MN (y2-y1)/(x2-x1) = (2-3)/(-3-2)= -1/-5 = 1/5

line MN and line K is perpendicular

(1/5)*(m2) = -1  

slope of k which is m2 is -5

slope of K (y2-y1)/(x2-x1)= 5

slope of MN (-3-y1)/(3-x1)=5

suitable is (4, 8)

Answer:

2,2 is correct

Step-by-step explanation:

The goalpost is 15.13 meters tall which is labeled as X in the figure which has been attached below.

She walks 13.45 meters away from the goalpost, then places a mirror flat on the ground with an X in the center. She next walks 1.2 meters to the opposite side of the mirror, where she can easily see the top of the goalpost depicted in the X. Her partner determines that the distance between her eyes and the ground is 1.35 meters.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

As per the given information, the figure has been attached below.

Set up the proportional and solve for x

1.2 : 13.45 = 1.35 : x

⇒ 1.2 / 13.45 = 1.35 / x

Cross multiplication, and we get

⇒ 1.2x  = 1.35 × 13.45

Divided by 1.2 into both sides of the above equation,

⇒ x = (1.35 × 13.45) / 1.2

⇒ x = 15.13

Therefore, the goalpost is 15.13 meters tall.

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Answer:

£1 = €1.21875

Step-by-step explanation:

We have the following exchange rates

$1 = £0.64

and

$1 = €0.78

Equating the two values on the right side since they both convert to $1 gives us

£0.64 = €0.78

Divide both sides by 0.64 to see how much a pound is worth when converted to euros

0.64/0.64 = 0.78/0.64

£1 = €1.21875

Therefore, Clausen has 32 cards.The correct answer is Clausen has 32 cards.

Juan and Clausen are playing a card game called "Magic." The number of cards they have is in a ratio of Juan: Clausen = 7:4. Juan has 56 cards. To find the number of cards Clausen has, we can use the concept of ratios and proportions.Since the ratio of Juan's cards to Clausen's cards is 7:4, we can say that Juan has 7x cards, where x is a constant.

Similarly, Clausen has 4x cards.Now, we know that Juan has 56 cards. We can use this information to find the value of x.7x = 56

Dividing both sides by 7, we get:

x = 8

Now that we know the value of x, we can find the number of cards Clausen has.4x = 4(8) = 32

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The domain of a function is the set of numbers that can go into a given function.

The set of input values (x) for which a function generates an output value is known as the domain of the function (y).

we can write \(y = f(x).\)

domain is the full set of x-values that can be plugged into a function to produce a y-value.

The most effective approach to finding a domain will depend on the type of function.

The domain is expressed using an open bracket or parenthesis, the domain's two endpoints separated by a comma, and then a closed bracket or parenthesis.

To find domain of function we should know the property of that function like what the function can take inside it.

Like if we consider square root function \(\sqrt{x}\) so inside root negative numbers are not allowed so value of x should be positive means x>=0

So domain of square root function [0, ∞).

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A consumer loan of $40,000 with a 15.8% interest rate will require monthly payments over a period of 2 years. The total amount to be paid, including both principal and interest, will be approximately $45,380.

To calculate the monthly payments, we need to determine the total amount to be paid over the loan period, including the principal amount and the interest. The formula used for calculating equal monthly installments is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Principal amount

r = Monthly interest rate

n = Number of monthly payments

In this case, the principal amount (P) is $40,000, the interest rate (r) is 15.8% per year, and the loan duration (n) is 2 years (24 months).

First, we convert the annual interest rate to a monthly rate by dividing it by 12: 15.8% / 12 = 0.0132.

Next, we substitute the values into the formula:

M = 40,000 * (0.0132 * (1 + 0.0132)^24) / ((1 + 0.0132)^24 - 1)

Calculating this formula gives us the monthly payment (M) of approximately $1,907.42.

To find the total amount to be paid, we multiply the monthly payment by the number of payments: $1,907.42 * 24 = $45,778.08. However, this includes both the principal and the interest. Subtracting the principal amount ($40,000) gives us the total interest paid: $45,778.08 - $40,000 = $5,778.08.

Therefore, the total amount to be paid, including both principal and interest, will be approximately $45,778.08.

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Answer:

149

Step-by-step explanation:

63+86 = 149

180-149=31 for the third angle inside the triangle

then 180-31 =149

x is 149

The curve is y = In(sec(x)) and we have to find its length. We are given the range as 0 ≤ x ≤ π/4. So, the formula for the length of the curve is given as:

To solve for the length of the curve of y = In(sec(x)), we use the formula,

`L = ∫[a,b] √[1+(f′(x))^2] dx`.Where, `a = 0` and `b = π/4`. And `f′(x)` is the derivative of `In(sec(x))`.

We know that:`f′(x) = d/dx[In(sec(x))]`

Using the formula of logarithm differentiation, we can write the above equation as:

`f′(x) = d/dx[In(1/cos(x))]`

So,`f′(x) = -d/dx[In(cos(x))]`

Therefore,`f′(x) = -sin(x)/cos(x)`

Substituting the values, we get:

`L = ∫[a,b] √[1+(f′(x))^2] dx`

`L = ∫[0,π/4] √[1+(-sin(x)/cos(x))^2] dx`

`L = ∫[0,π/4] √[(cos^2(x)+sin^2(x))/(cos^2(x))] dx`

`L = ∫[0,π/4] sec(x) dx`

Now, `L = ln(sec(x) + tan(x)) + C` where `C` is a constant.

We calculate the constant by substituting the values of `a = 0` and `b = π/4`:

`L = ln(sec(π/4) + tan(π/4)) - ln(sec(0) + tan(0))`

`L = ln(√2 + 1) - ln(1 + 0)`

`L = ln(√2 + 1)`

Thus, the exact length of the curve is `ln(√2 + 1)` units.

Thus, the exact length of the curve of y = In(sec(x)), 0≤x≤π/4 is `ln(√2 + 1)` units.

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Answer:

Step-by-step explanation:

The GCF of 8 and 9 is 1

Divide both terms by the GCF, 1:

8 ÷ 1 = 8

9 ÷ 1 = 9

The ratio 8 : 9 cannot be reduced further by dividing both terms by the GCF = 1 :

This ratio is already in lowest terms.

Therefore:

8 : 9 = 8 : 9

Answer:

0.125

Step-by-step explanation:

1/8=0.125