A ball is thrown from a height of 32 meters with an initial downward velocity of 2 m/s. The ball's height h (in meters) after t seconds is given by the following.h = 32 -21-57How long after the ball is thrown does it hit the ground?Round your answer(s) to the nearest hundredth.(If there is more than one answer, use the "or" button.)

The mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

Given data values are 55, 56, 70, 61, 53, 57, 50, 73, 52, 69, and 2. We need to calculate the mean, median, and mode of this sample.So, let's first arrange the data values in ascending order:2, 50, 52, 53, 55, 56, 57, 61, 69, 70, 73

Mean:The mean is the sum of all the data values divided by the total number of data values. So, we can use the following formula to calculate the mean:

Mean = (sum of all the data values) / (total number of data values)Sum of all the data values = 55 + 56 + 70 + 61 + 53 + 57 + 50 + 73 + 52 + 69 + 2 = 598Total number of data values = 11

Therefore,Mean = (sum of all the data values) / (total number of data values) = 598 / 11 = 54.36 (rounded to two decimal places)Therefore, the mean of the given data values is 54.36.

Median:The median is the middle value of a sorted data set. Since the data set has 11 data values, the median is the average of the 6th and 7th values (counting from smallest to largest).

Therefore, the median is :Median = (55 + 56) / 2 = 55.5Therefore, the median of the given data values is 55.5.

Mode:The mode is the data value that appears most frequently in the data set. In this case, there is no data value that appears more than once. So, there is no mode.

Therefore, the mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

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10.95

Simplified: √120 = 2√30

No, the triangle with vertices (-1, -1), (2, 3), (-4, 3) is not equilateral.

An equilateral triangle is a triangle that has all three sides of equal length, also known as a "regular" triangle.

Now, as per the given question.

The vertices are given as (-1, -1), (2, 3), (-4, 3).

Find the distance between the two corresponding vertices.

First, find distances between (-1, -1), (2, 3) lets say 'c'.

c² = (-1-3)² + (-1-2)²

c² = 4² + 3²

c² = 16 + 9

c² = 25

c = 5

Now, find the distance between (2, 3), (-4, 3), let say it 'd'.

d² = (-4-2)² + (3-3)²

d² = 36

d = 6

Now, find the distance between (-1, -1), (-4, 3) say it 'p'

p² = (-1-(-4 ))² +(-1-3)²

p² = 3² +4²

p² = 25

p = 5

As, all three distances are not same. Thus, the given vertices does not form equilateral triangle.

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The correct question is-

An equilateral triangle has sides of equal length. Determine whether the triangle with vertices (-1, -1), (2, 3), (-4, 3) is equilateral.

Answer: 18 1/2, 6.2, 1.75, -1/4 and -4

Given the following set

-4, 6.2, 18 1/2, - 1/4 and 1.75

Arranging from greatest to least

18 1/2, 6.2, 1.75, -1/4 and -4

the cost when the two companies charge the same is $3006.

To solve the problem presented in the student's question, we need to determine the amount of sugar for which the two companies charge the same. Let x represent the amount of sugar in tons.
The first company charges $2406 to rent trucks plus an additional fee of $50.25 for each ton of sugar. Therefore, the total cost for the first company is:
2406 + 50.25x
The second company does not charge to rent trucks but charges $250.75 for each ton of sugar. Therefore, the total cost for the second company is:
250.75x
We can set these two equations equal to each other to find the amount of sugar for which the two companies charge the same:
2406 + 50.25x = 250.75x
To solve for x, we can simplify the equation:
2406 = 200.5x
x = 12
Therefore, the two companies charge the same amount for 12 tons of sugar. To find the cost when the two companies charge the same, we can substitute x = 12 into either equation:
2406 + 50.25(12) = 3006
250.75(12) = 3009
Therefore, the cost when the two companies charge the same is $3006.

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There are 120 different orders in which the 5 cars can be parked.

The car salesman can park the first car in any of the 5 visible spaces. Once the first car is parked, he has only 4 visible spaces left to park the second car.

For the third car, he has 3 visible spaces left, for the fourth car he has 2 visible spaces left, and for the fifth car, he has only 1 visible space left. Therefore, the total number of different orders in which he can park 5 different cars is:
5 x 4 x 3 x 2 x 1 = 120

So, the car salesman can park 5 different cars in 120 different orders.

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Answer:

Domain: -5. -4, -2, 0, 1

Range: 4, -1, 1, 3

If the matching sides and angles of two triangles are proportional, then the triangles are said to be similar.

Triangles that share the same form but differ in size are said to be similar.

Hence from the above properties we can find if any two triangles are similar.

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Given data:

The given fraction is 1242/99.

The given fraction is,

Thus, the result of the fraction is 13.

Answer:

10% probability that the number is greater than 2, then P

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

Event A: Number greater than 2.

Event B: Letter P.

These events are independent, so:

\(P(A \cap B) = P(A) \times P(B)\)

P(A)

There are 5 numbers.

3, 4 or 5, that is, 3 numbers greater than 2.

3/5 = 0.6. So P(A) = 0.6.

P(B)

6 letters, one of which is P. So

P(B) = 1/6 = 0.1667.

What is the probability the number is greater than 2, then P?

\(P(A \cap B) = P(A) \times P(B) = 0.6 \times 0.1667 = 0.1\)

10% probability that the number is greater than 2, then P

The distance between the two points is 19.2 units.

Let the point (7, 8) be A and point (-5, -7) be B.

By joining these two points and drawing a right-angled triangle ABC with AB as the hypotenuse, we get point C at (7, -7)

The altitude of triangle ABC, AC = A - C

AC = 15 units

The base of the triangle ABC, BC = C - B

BC = 12 units

According to Pythagoras Theorem,

√(AC² + BC²) = AB

AB = √(12² + 15²)

AB = 19.2 units

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Answer:

slope = 5/8

Step-by-step explanation:

y2 - y1 / x2 - x1

-7 - (-2) / -3 - 5

-5 / -8

= 5/8

========================================

Work Shown:

Solve the equation for y

-13y - 5 = 8

-13y = 8+5

-13y = 13

y = 13/(-13)

y = -1

Then use this y value to compute 4y+7

4y+7 = 4(-1)+7 = -4+7 = 3

The surface area of the cylinder is approximately 401.92 square centimeters. To find the surface area of the cylinder, we need to add the area of the top and bottom circles to the area of the lateral surface.

The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

where r is the radius of the base, h is the height of the cylinder, and π ≈ 3.14.

Given that the radius is 8 cm and the height is also 8 cm, we can plug in the values in the formula:

SA = 2π(8²) + 2π(8)(8)

SA = 401.92

Rounding to the nearest hundredth, we get:

SA ≈ 401.92 square centimeters

Therefore, the surface area of the cylinder is approximately 401.92 square centimeters.

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Answer:

10(x - 12)

Step-by-step explanation:

10(x - 12)

10x - 120 Distributive Property

Answer to the question is D.  \sqrt6/2

The quotient of the given expression is √6/2. Therefore, option D is the correct answer.

The given expression is √12/2√2.

We need to find the equivalent quotient to the given expression.

In Mathematics, surds are the values in the square roots that cannot be further simplified into whole numbers or integers. Surds are irrational numbers.

Now, √12/2√2

We can write √12 as √4×3

Then, we get 2√3/2√2

Further, rationalise the denominator

A fraction whose denominator is a surd can be simplified by making the denominator rational. This process is called rationalising the denominator.

That is √3×√2/√2×√2=√6/2

Therefore, option D is the correct answer.

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Answer:

400 = (x - 10)²

x² -20x -300 = 0

x = 30 and x = -10

Length side of the garden = 20 feet

Step-by-step explanation:

Given:

Area of square garden = 400 square feet

Length side of the garden = (x - 10) feet

Find:

Length side of the garden

Computation:

Area of square = side²

Area of square garden = Length side of the garden²

400 = (x - 10)²

400 = x² -20x + 100

x² -20x -300 = 0

x² -30x  + 10x -300 = 0

x(x - 30) + 10(x - 30) = 0

(x - 30)(x + 10) = 0

So,

x = 30 and x = -10

Use x = 30 positive number

Length side of the garden = (x - 10) feet

Length side of the garden = (30 - 10) feet

Length side of the garden = 20 feet

If m and n are odd numbers, then we will have:

In the diagram we can see a 3 by 5 checkboard, it has:

3*5 = 15 boxes.

And there we can count that we have 8 black ones and 7 white ones.

As long as both numbers are odd, the product will be odd, so we always will have one more black box than whites boxes, and that is because we will start having more black boxes (and end) like in the given diagram.

Then we will have that m*n is odd.

Then the number of white boxes is (m*n - 1)/2

And the number of black boxes is 1 more than that, it can be written as:

(m*n - 1)/2 + 1 = (m*n + 1)/2

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Answer:

your answer would be 2 hours cause you know its not gonna be neither of the 3 hour cause it says it lasted 3 hours and that was over time and the other 2 was wrong so the answer is 2 hours

Answer:

it would be cheaper to buy a pack of 45.

Step-by-step explanation:

Shayley would spend $30 on 20 single bottles because 1.50 times 20 = 30

The expression S÷7 when s = 4 is simplified to 4/7

A fraction can be described as the part of a whole variable, number or element

There are several types of fractions which includes;

From the information given, we have that;

S÷7 is the given expression as a quotient.

For s = 4, we have to substitute the value of s as 4 in the expression, we have;

4/7

Hence, it is an example of a proper fraction where the denominator is greater than the numerator.

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All of the aforementioned are factors that influence whether an infant will show stranger wariness except: A. the infant's ability to regulate emotion.

In Psychology, stranger wariness is sometimes referred to as stranger anxiety or stranger fear and it can be defined as any form of distress and apprehension that is typically experienced by infants (young children or babies) when they are around or within the proximity of individuals who are strange (unfamiliar) to them.

This ultimately implies that, stranger wariness simply refers to a form of distress and apprehension which an infant (young child or baby) experiences when exposed to strangers.

In this context, we can reasonably infer and logically deduce that the ability of an infant (young child or baby) to regulate emotion is not a factor that would influence whether an infant shows stranger wariness.

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Complete Question:

All of these are factors that influence whether an infant will show stranger wariness EXCEPT ______.

A. the infant's ability to regulate emotion

B. the overall temperament of the infant

C. the past experience of the infant

D. the situation in which the infant meets the stranger

10x - 6y = 34 ----------------(1)

y= -5x + 21 ------------------------(2)

substitute y= -5x + 21 in equation (1)

10x - 6(-5x + 21) = 34

open the parenthesis

10x + 30x - 126 = 34

40x - 126 = 34

add 126 to both-side of the equation

40x - 126 + 126 = 34 + 126

40x = 160

Divide both-side of the equation by 40

x= 4

substitute x=4 into equation (2)

y = -5(4) + 21

y = -20 + 21

y = 1

The solution is

(4, 1)

This \(\rm P(Z\geq 1.7)\)  is equivalent to  \(\rm 1-P(Z\leq 1.7)\)

It is given that the  \(\rm P(Z\geq 1.7)\)

It is required to find which statement is equivalent to \(\rm P(Z\geq 1.7)\)

The statements are:

\(a) \ \rm P(Z\geq -1.7)\\b) \ \rm 1-P(Z\geq -1.7)\\c) \ \rm P(Z\leq 1.7)\\d) \ \rm 1-P(Z\leq 1.7)\)

It is defined as the continuous distribution probability curve which is most likely symmetric around the mean. At Z=0, the probability is 50-50% on the Z curve. It is also called a bell-shaped curve.

We have the \(\rm P(Z\geq 1.7)\)

We know that:

\(\rm P(Z\leq a)=P(Z\geq -a)\\\rm P(Z\geq a)=P(Z\leq -a)\)

If we compare statement (a) and statement (c), we will see these options are not equivalent to  \(\rm P(Z\geq 1.7)\)

For statement (b) if we plot the graph for the given statement we will get the negative area of the bell curve hence it is also incorrect.

For statement (d) if we plot the graph for the given statement we will get the positive area which is equivalent to the \(\rm P(Z\geq 1.7)\)

Thus, the \(\rm P(Z\geq 1.7)\)  is equivalent to  \(\rm 1-P(Z\leq 1.7)\)

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Answer:

Step-by-step explanation:

Solve the inequalities and match with the graphs

Answer:

7x < 42

x + 1 < 8

3x > 15

2x > 12

Step-by-step explanation:

> means "more than" (shading to the right)

< means "less than" (shading to the left)

Solve the given inequalities

    7x < 42  

⇒ 7x ÷ 7 < 42 ÷ 7

⇒  x < 6

An open circle on 6, shading to the left

   3x > 15  

⇒ 3x ÷ 3 > 15 ÷ 3

⇒ x > 5

An open circle on 5, shading to the right

   x + 1 < 8  

⇒ x + 1 - 1 < 8 - 1

⇒ x < 7

An open circle on 7, shading to the left

   2x > 12  

⇒ 2x ÷ 2 > 12 ÷ 2

⇒ x > 6

An open circle on 6, shading to the right

Answer:

Penelope worked 5 hours.

Sarah worked 10 hours.

Step-by-step explanation:

Let's start by setting up some equations to represent the given information:

Let x be the number of hours Penelope worked.

Then Sarah worked 2x hours.

The total number of shirts they ironed is given by:

30(2x) + 35x = 475

Simplifying and solving for x:

60x + 35x = 475

95x = 475

x = 5

So Penelope worked 5 hours.

And Sarah worked 2x = 2(5) = 10 hours.

p = 5

So Penelope worked 5 hours.

And since Sarah worked twice as many hours, she worked:

2p = 2(5) = 10

So Sarah worked 10 hours.