The drop that riders experience on Dr. Doom's Free Fall can be modeled by the quadratic function, \(h(t)=-9.8t^{2} -5t+39\) where h is height in meters and t is time in seconds. Show your work for each parts.

Part A: What is the starting height of riders?

Part B: According to the function, when will the height of the riders equal 0?

Part C: Will the height ever actually equal 0? Why or why not?

Answer:

x = -7

Step-by-step explanation:

Solve for x:

4 (1 - x) + 2 x = -3 (x + 1)

4 (1 - x) = 4 - 4 x:

2 x + 4 - 4 x = -3 (x + 1)

2 x - 4 x = -2 x:

-2 x + 4 = -3 (x + 1)

Expand out terms of the right hand side:

4 - 2 x = -3 x - 3

Add 3 x to both sides:

3 x - 2 x + 4 = (3 x - 3 x) - 3

3 x - 3 x = 0:

3 x - 2 x + 4 = -3

3 x - 2 x = x:

x + 4 = -3

Subtract 4 from both sides:

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

4 - 4 = 0:

x = -4 - 3

-4 - 3 = -7:

Answer:  x = -7

Answer:

X=-7

Step-by-step explanation:

Answer:

\(3x+b+p^2\) is already simplified

Step-by-step explanation:

\(3x+b+p^2\) is already simplified

Answer:

The equation is already simplified

Step-by-step explanation:

Nothing fuurther can be done to this equation

Answer:

Step-by-step explanation: 4

Answer:

There are no solutions to the system because the equations represent parallel lines.

Step-by-step explanation:

Answer:

What does 0 = −12 mean regarding the solution to the system? There are no solutions to the system because the equations represent parallel lines.

60% of the fruit punch is orange juice.

In this question, we have been given 3/5 of a fruit punch is orange juice.

We need to find the percentage of the fruit punch is orange juice.

3/5 of a fruit punch is orange juice, means 3 of 5 fruit punch is orange juice.

Using the percentage formula,

3/5 * 100

= 0.6 * 100

= 60%

Therefore, 60% of the fruit punch is orange juice.

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For the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.

As given in the question,

Ratio of orange juice in the given fruit juice = 3/5

From the given ratio it indicates out of 5 fruits 3 are orange

Percentage of fruit punch is orange juice in the given juice is equal to

= ( 3 / 5 ) × 100

= ( 3 × 100 ) / 5

= 300 / 5

= 60%

60% of the fruit punch is orange juice.

Therefore,  for the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.

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Answer:

15

Step-by-step explanation:

The lines that are perpendicular to 3x – y = 10. is option C (x+3y= 27).

Line equation:

3x - y = 10

y = 3x - 10

here slope m = 3.

perpendicular line slope = -1/m = -1/3

so the perpendicular line must have slope m = -1/3

A.  

y = 3x + 5

here slope m = 3

This line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.

B.

y = -13x + 17

here slope m = -13

This line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.

C.

x + 3y = 27

3y = -x + 27

y = -1/3(x) + 27/3

y = -1/3(x) + 9

here slope m = -1/3

This line is perpendicular to the 3x - y = 10 because here slope is equal to -1/3.

D.

y - 2 = 13(3x+36)

y = 39x + 468 - 2

y = 39x + 466.

here slope m = 39.

So this line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.

Therefore the lines that are perpendicular to 3x – y = 10. is option C (x+3y= 27).

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The number of times on the hour in 3 days at least two owls will not hoot obtained using number theory are 69 times.

Number theory is the study of integers and functions of arithmetic.

The number of hours in 3 days = 72 hours

Number theory indicates that the multiples of the periods of hooting are;

The multiples of 8 are; 8, 16, 24, 32, 40, 48, 56, 64, 72

The multiples of 3 are; 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72

The multiples of 12 are; 12, 24, 36, 48, 60, 72

The common multiples of 3 and 8 are 24, 48, 72

The common multiples of 8 and 12 are 24, 48, 72

The number of times in 72 hours when at least 2 owls are hooting are therefore;

The times when only one owl is hooting are

8, 16, 32, 40, 56, 64, = 6 times only the second owl is hooting

3, 6, 9, 12, 15, 18, 21, 27, 30, 33, 36, 39, 42, 45, 51, 54, 57, 60, 63, 66, 69   = 21 times when only the first owl hoots

The times when non of the owls hoot  are;

72 - 24 - 6 = 42 times

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The interval of the graph at which Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

Given data ,

Susan is running a 5k race. The graph of distance vs. time is shown

So , the slope of the first line is m₁

And , the slope of the second line is m₂

where the points are A ( 0 , 0 ) , B ( 10 , 3 ) , C ( 20 , 4 )

Now , slope of AB is

m₁ = ( 3/10 ) = 0.3

And , m₁ = 0.3 kilometers per minute

And , slope of BC is

m₂ = ( 4 - 3 ) / ( 20 - 10 )

m₂ = 1/10

m₂ = 0.1 kilometers per minute

Therefore , the interval is fastest at second line from B ( 10 , 3 ) , C ( 20 , 4 )

Hence , Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

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The ratio of boxes to the circles is 7: 10

Answer:

25 cm

Step-by-step explanation:

the whole parallelograph is 5 times 10 which equals 50. Devide that by 2 and you get 25

Answer:

the answer is 25 cm total

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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The correlation coefficient of the health research institute data measures the relationship between the age and the years of the smokers

The correlation coefficient is 0.53

The correlation coefficient (r) is calculated as:

\(r = \frac{n(\sum xy) - \sum x \sum y}{\sqrt{[n \sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2}}\)

Using the given parameters, we have:

\(r = \frac{20 *8249 - 1257* 116}{\sqrt{[20 * 98823 - 1257^2][20 * 836 - 116^2}}\)

Evaluate the exponents

\(r = \frac{20 *8249 - 1257* 116}{\sqrt{[20 * 98823 - 1580049][20 * 836 - 13456}}\)

Evaluate the products

\(r = \frac{164980 - 145812}{\sqrt{[1976460 - 1580049][16720 - 13456}}\)

Evaluate the differences

\(r = \frac{19168}{\sqrt{[396411*3264}}\)

Evaluate the product

\(r = \frac{19168}{\sqrt{1293885504}}\)

Evaluate the root

\(r = \frac{19168}{35970.6}\)

Evaluate the quotient

\(r = 0.53\)

Hence, the correlation coefficient is 0.53

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Answer:

Multiply each of the 3 prices by the associated probability, and then add up these three products:

($48)(1/2) + ($56)(1/8) + ($72)(3/8) = $24 + $7 + $27 = $58 (answer)

Step-by-step explanation:

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Answer:

The answer is √156

Step-by-step explanation:

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Answer:

Step-by-step explanation:

9/x

Answer:

B) in the modern art section of an art museum

Step-by-step explanation:

Hope it helps! =D

The function that best models this scenario is C of x equals 3.75 times x if x is less than 5 and 3.25x plus 5 if x is greater than 6.

Let the number of hours be illustrated as x. In this situation, local city park rents kayaks for $3.75 per hour. This will be:

= 3.75 × x

= 3.75x

Also, customer rents for four or more hours, the cost is only $3.25 per hour, plus a $5 processing fee. This will be illustrated as:

= 5 + (3.25 × x)

= 5 + 3.25x

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Step-by-step explanation:

to find the area of a parallelogram multiply the base by the height. multiply so 8x4= 32. but thats not it, ill come back when i get it or ask a tutor

Answer:

A=bh

Step-by-step explanation:

Answer:

800,000=8,00,000 in Indian system.

Eight Hundred Thousands(800,000)=Eight Lakh(8,00,000)

in Indian system.

Answer:

$127.17 per week

Step-by-step explanation:

10019.4*0.66/52

= 127.169308

Rounded = $127.17 per week

Answer:

$65.51

Step-by-step explanation:

She only pays 34%=$3406.60 annually

Company pays 66%=$6612.80 annually

Divide both numbers by 52 because they want weekly

*weekly 52, biweekly 26, semimonthly 24, monthly 12*

$3406.60 / 52= $65.51 she pays weekly

$6612.80 / 52= $127.17 the company pays weekly

The rectangle that is shaded has an area of 18 square units.

The framed rectangle is represented by the darkened area, while the frame is shown in white.

The frame's known width is two units, and both the rectangle and the frame have the following dimensions:

width = 7 units

length = 10 units

Now, if we remove the frame, each measure will lose 2*2 units, or 4 units (because for each measure we have the frame in both sides).

As a result, the measurements for the shaded rectangle are as follows:

width = 7 units - 4 units = 3 units

length = 10 units - 4 units = 6 units.

And since the product of a rectangle's width and length determines its area, we may calculate:

A = (3 units)*(6 units) = 18 square units.

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The correct option regarding the solution and graph of the inequality is given as follows:

Option D.

The compound inequality in this problem is defined as follows:

4x < -16 or 3x + 5 ≥ 17.

As we have the or operation, we solve each separate equality, and them combine the solution.

The solution to the first inequality is given as follows:

4x < -16

x < -4.

(values to the left of the open circle at x = -4).

The solution to the second inequality is given as follows:

3x + 5 ≥ 17

3x ≥ 12

x ≥ 4.

(values to the right of the closed circle at x = 4).

Hence option D is the correct option for this problem.

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The ratio of the volume of water in Jug B to the volume of water in Jug C is 35:18.

Let's assume the volume of water in Jug B is x.

According to the given information, Jug A contains 6/7 as much water as Jug B. Therefore, the volume of water in Jug A can be calculated as (6/7) * x.

Similarly, Jug C contains 3/5 as much water as Jug A. Hence, the volume of water in Jug C can be expressed as (3/5) * [(6/7) * x].

To find the ratio of the volume of water in Jug B to the volume of water in Jug C, we divide the volume of water in Jug B by the volume of water in Jug C:

(x) / [(3/5) * (6/7) * x]

Simplifying the expression, we get:

x / (18/35 * x)

The x values cancel out, leaving us with:

1 / (18/35)

To simplify further, we multiply the numerator and denominator by the reciprocal of the denominator:

1 * (35/18)

The final ratio is:

35/18

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Answer:

2

Step-by-step explanation:

Answer:

correct

Step-by-step explanation:

Based on an equation, the amount that Isabel spent on bread was $2.42.

To solve the equation for the amount spent on bread, we determined the total amount Isabel spent by subtracting the change from the total bills she had.

An equation is a mathematical statement of the equality or equivalence of two or more mathematical expressions.

The amount Isabel spent on vegetables = $15.91

The amount she spent on fruits = $11.22

Let the amount she spent on bread = x

The total amount she went with = $30 (3 x $10)

The change she got after giving the cashier $30 = $0.45

The total amount Isabel spent for vegetables, fruits, and bread = $29.55 ($30.00 - $0.45)

x = $2.42 ($29.55 - $15.91 - $11.22)

Check:

Vegetables = $15.91

Fruits = $11.22

Bread = $2.42

Total expenses = $29.55

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Answer:

B

Step-by-step explanation: