If a ball is thrown upward at 96 feet per second from a height of 12 feet, the height of the ball can be modeled by S=12+96t- 16t² feet,
where t is the number of seconds after the ball is thrown. How long after the ball is thrown is the height 152 feet?
It takes seconds for the ball to reach the height 152 feet.

a. The missing value in the table 0.03

b. The mean is 4.18

c. The variance is 3.23 and standard deviation is 1.80

d.  The larger the standard deviation, the greater the spread of the probability distribution.

A random variable is a variable that can take on different values depending on the outcome of a random event. In this case, the random variable X represents the number of calls per hour to a call center in the last month.

a. The missing value in the table is the number of calls per hour for the probability 0.03. From the table, we see that the number of calls per hour is 7.

b. The mean, also known as the expected value, is a measure of the center of the probability distribution. It is calculated by taking the sum of the product of each possible value of X and its corresponding probability. In mathematical terms, the mean of X is given by:

E(X) = 1 * P(1) + 2 * P(2) + 4 * P(4) + 5 * P(5) + 6 * P(6) + 7 * P(7)

E(X) = 0.01 + 0.2 + 1.04 + 1.65 + 1.08 + 0.21 = 4.18

So, the mean number of calls per hour to the call center in the last month is 4.18.

c. The variance of X is a measure of the spread of the probability distribution. It is calculated by taking the sum of the squared differences between each possible value of X and the mean, multiplied by the corresponding probability. In mathematical terms, the variance of X is given by:

Var(X) = (1 - 4.18)² * P(1) + (2 - 4.18)² * P(2) + (4 - 4.18)² * P(4) + (5 - 4.18)² * P(5) + (6 - 4.18)² * P(6) + (7 - 4.18)² * P(7)

Var(X) = 3.23

The standard deviation is the square root of the variance, and it is also a measure of the spread of the probability distribution. In mathematical terms, the standard deviation of X is given by:

=> SD(X) = √(Var(X)) = √(3.23) = 1.80

d. Interpretation:

The mean of 4.18 calls per hour represents the average number of calls to the call center in the last month.

The standard deviation of 1.80 indicates that the number of calls per hour deviates from the mean by approximately 1.80 calls on average.

This means that about 68% of the time, the number of calls per hour will be between 2.38 (4.18 - 1.80) and 6.08 (4.18 + 1.80).

Complete Question:

The random variable X represents the number of calls per hour to a call center in the last month. The probability distribution for X is below.

x 1 2 4 5 6 7

P(x) 0.01 0.10 0.26 0.33 0.18 0.06 0.03

a. What is the missing value in the table?

b. Find the mean.

c. Find the variance and standard deviation.

d. Interpret your results.

To know more about standard deviation here.

https://brainly.com/question/16555520

#SPJ4

Answer:

plane

Step-by-step explanation:

Answer:

D. Plane

Step-by-step explanation:

A plane extends in two dimensions. This figure is a plane. It is not a point, a segment or a ray.

There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

For more questions on bags

https://brainly.com/question/31835238

#SPJ8

Answer:

\(d=2Q-c\)

Step-by-step explanation:

\(Q=\frac{c+d}{2}\)

⇒ Switch sides:-

\(\frac{c+d}{2}=Q\)

⇒ Multiply both sides by 2:-

\(\frac{2\left(c+d\right)}{2}=2Q\)

\(c+d=2\)

⇒ Subtract c from both sides:-

\(c+d-c=2Q-c\)

\(d=2Q-c\)

OAmalOHopeO

The mean absolute deviation of 4 in data set is -7

First, we need to determine the value of the mean

We have from the information given that;

6, 22, 14, 9, 11, 4​

Mean = sum of the given set of data/number of the data given

Substitute the values, we have that;

Mean = 6 + 22 + 14 + 9 + 11 + 4/6

add the values, we get

Mean = 66/6

Divide the values

Mean = 11

Mean absolute deviation = data value - mean

Mean absolute deviation = (4 -11) = -7

Learn about mean absolute deviation at: https://brainly.com/question/3998118

#SPJ1

Answer:

1)  The functions are not inverses.

\(\textsf{2)} \quad g^{-1}(n)=&\dfrac{3}{8}n-\dfrac{7}{8}\)

\(\textsf{3)} \quad g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\)

Step-by-step explanation:

The inverse composition rule states that if two functions are inverses of each other, then their compositions result in the identity function.

Given functions:

\(g(x) = 4 + \dfrac{7}{2}x \qquad \qquad f(x) = 5 - \dfrac{4}{5}x\)

Find g(f(x)) and f(g(x)):

\(\begin{aligned} g(f(x))&=4+\dfrac{7}{2}f(x)\\\\&=4+\dfrac{7}{2}\left(5 - \dfrac{4}{5}x\right)\\\\&=4+\dfrac{35}{2}-\dfrac{14}{5}x\\\\&=\dfrac{43}{2}-\dfrac{14}{5}x\\\\\end{aligned}\)                 \(\begin{aligned} f(g(x))&=5 - \dfrac{4}{5}g(x)\\\\&=5 - \dfrac{4}{5}\left(4 + \dfrac{7}{2}x \right)\\\\&=5-\dfrac{16}{5}-\dfrac{14}{5}x\\\\&=\dfrac{9}{5}-\dfrac{14}{5}x\end{aligned}\)

As g(f(x)) or f(g(x)) is not equal to x, then f and g cannot be inverses.

\(\hrulefill\)

To find the inverse of a function, swap the dependent and independent variables, and solve for the new dependent variable.

Calculate the inverse of g(n):

\(\begin{aligned}y &= \dfrac{8}{3}n + \dfrac{7}{3}\\\\n &= \dfrac{8}{3}y + \dfrac{7}{3}\\\\3n &= 8y + 7\\\\3n-7 &= 8y\\\\y&=\dfrac{3}{8}n-\dfrac{7}{8}\\\\g^{-1}(n)&=\dfrac{3}{8}n-\dfrac{7}{8}\end{aligned}\)

Calculate the inverse of g(x):

\(\begin{aligned}y &= 1-2x^3\\\\x &= 1-2y^3\\\\x -1&=-2y^3\\\\2y^3&=1-x\\\\y^3&=\dfrac{1}{2}-\dfrac{1}{2}x\\\\y&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\\end{aligned}\)

Answer:

1.

If the composition of two functions is the identity function, then the two functions are inverses. In other words, if f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

For\(\bold{g(x) = 4 + \frac{7}{2}x\: and \:f(x) = 5 -\frac{4}{5}x}\), we have:

\(f(g(x)) = 5 - \frac{4}{5}(4 + \frac{7}{2}x)\\ =5 - \frac{4}{5}(\frac{8+7x}{2})\\=5 - \frac{2}{5}(8+7x)\\=\frac{25-16-14x}{5}\\=\frac{9-14x}{5}\)

\(g(f(x)) = 4 + (\frac{7}{5})(5 - \frac{4}{5}x) \\=4 + (\frac{7}{5})(\frac{25-4x}{5})\\=4+ \frac{175-28x}{25}\\=\frac{100+175-28x}{25}\\=\frac{175-28x}{25}\)

As you can see, f(g(x)) does not equal x, and g(f(x)) does not equal x. Therefore, g(x) and f(x) are not inverses.

Sure, here are the inverses of the functions you provided:

2. g(n) = (8/3)n + 7/3

we can swap the roles of x and y and solve for y to find the inverse of g(n). In other words, we can write the equation as y = (8/3)n + 7/3 and solve for n.

y = (8/3)n + 7/3

n =3/8*( y-7/3)

Therefore, the inverse of g(n) is:

\(g^{-1}(n) = \frac{3}{8}(n - \frac{7}{3})=\frac{3}{8}*\frac{3n-7}{3}=\boxed{\frac{3n-7}{8}}\)

3. g(x) = 1 - 2x^3

We can use the method of substitution to find the inverse of g(x). We can substitute y for g(x) and solve for x.

\(y = 1 - 2x^3\\2x^3 = 1 - y\\x = \sqrt[3]{\frac{1 - y}{2}}\)

Therefore, the inverse of g(x) is:

\(g^{-1}(x) =\boxed{ \sqrt[3]{\frac{1 - x}{2}}}\)

Equation A: y = (-1/2)x - 2.

Equation B:  y = x - 6.

To find the equations of the lines, we can use the slope-intercept form, which is given by y = mx + b, where m represents the slope and b represents the y-intercept.

Equation A:

Given two points (-10, 3) and (0, -2), we can calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1).

m = (-2 - 3) / (0 - (-10)) = (-2 - 3) / (0 + 10) = -5 / 10 = -1/2.

Now, we have the slope (m) as -1/2. To find the y-intercept (b), we can choose any of the given points and substitute the values into the equation y = mx + b.

Using the point (-10, 3):

3 = (-1/2)(-10) + b

3 = 5 + b

b = 3 - 5

b = -2.

Therefore, the equation of line A is y = (-1/2)x - 2.

Equation B:

Given two points (6, 0) and (0, -6), we can calculate the slope (m):

m = (-6 - 0) / (0 - 6) = -6 / -6 = 1.

Now, we have the slope (m) as 1. Using the point (6, 0) to find the y-intercept (b):

0 = 1(6) + b

0 = 6 + b

b = -6.

Thus, the equation of line B is y = x - 6.

To learn more about the slope;

brainly.com/question/3605446

#SPJ1

Answer:

a) about 190 acres

b) around 240 acres

c) exponential decay because the amount of land available is decreasing at an increasingly rapid rate over time.

The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

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

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

Read more about range at

brainly.com/question/27910766

#SPJ1

The equation of the line in slope-intercept form is y = 3x + 4.

We can use the combination formula to determine how many different packages can be created from a set of 24 crayons with 36 different colours.

The formula for the mixture is provided by:

n C r equals n!/r! (n-r)!

where r is the number of items we want to choose, n is the total number of items, and! stands for the factorial of a number, which is the sum of all positive integers up to that number.

In this instance, we are trying to determine how many various methods there are to choose 24 crayons from a set of 36 colours, regardless of the sequence in which they are chosen. Consequently, we can apply the following combination formula:

36 C 24 = 36! / (24! * 12!)

For such more questions on slope-intercept

https://brainly.com/question/1884491

#SPJ8

Solution:

Given:

The margin of error is equal to half the width of the entire confidence interval.

Hence, the width of the confidence interval is;

Hence, the margin of error is half the width of the confidence interval.

Therefore, OPTION B is the correct answer.

Let's assume the number of cookies Lily bought is represented by "C," and the number of brownies is represented by "B."

According to the problem, the cost of one cookie is $2, and the cost of one brownie is $3. Lily spent a total of $144.

We can set up two equations based on the given information:

C + B = 60 (equation 1, representing the total number of sweets)

2C + 3B = 144 (equation 2, representing the total cost in dollars)

To solve this system of equations, we can use substitution or elimination method. Here, we'll use the substitution method.

From equation 1, we can rewrite it as C = 60 - B.

Now substitute this value of C in equation 2:

2(60 - B) + 3B = 144

Simplify the equation:

120 - 2B + 3B = 144

Combine like terms:

120 + B = 144

Subtract 120 from both sides:

B = 144 - 120

B = 24

Now substitute the value of B back into equation 1 to find C:

C + 24 = 60

C = 60 - 24

C = 36

Therefore, Lily bought 36 cookies and 24 brownies.

Answer: 160 L

Step-by-step explanation:

There is 24 weeks in 6 months. 6x4= 24

24 weeks divided by 3 (the amount of weeks Danny’s family consumes 20L of milk). You end up with 8 weeks.

Then multiple 8 weeks time the 20 L.

According to the equation the given all necessary math work are:

\(A: (x -f)^2 +(y -g)^2 = h^2\)

B:  domain: [-5, 11]; range: [-9, 7]

C:  yes, inside

The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.

Part A:

Use οf the Pythagοrean theοrem gets yοu tο the equatiοn fοr a circle in essentially οne step:

sum οf squares οf sides = square οf hypοtenuse

\((x -f)^2 +(y -g)^2 = h^2\) . . . . . . circle cantered οn (f, g) with radius h

Part B:

The circle will be defined fοr values οf x in the dοmain f ± h, and fοr values οf y in the range g ± h.

dοmain: 3 ± 8 = [-5, 11]

range: -1 ±8 = [-9, 7]

Part C:

The distance frοm pοint (10, -4) tο (f, g) is ...

\(h^2 = (10 -3)^2 +(-4 -(-1))^2\)

\(h^2 = 7^2 +(-3)^2 = 49 +9 = 58\)

h = √58 < 8 . . . . the distance tο the pοint is less than h=8.

The pοint is inside the circle.

Learn more about Pythagoras theorem, by the following link

https://brainly.com/question/231802

#SPJ1

Answer:

a

Step-by-step explanation:

The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

learn more about similar triangles from

https://brainly.com/question/14285697

#SPJ1

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

For more questions on probability

https://brainly.com/question/251701

#SPJ8

Answer:

360

Step-by-step explanation:

You simply need to multiply 60 by 6 which is 60*6=360

Please give brainliest if I helped! :)

Answer:

Subtract 5x

Step-by-step explanation:

Cause then you would only get one x in the equation instead of 6x and 5x. Hope this helps!

Answer:

this is what i used as my answer on the advice i would give tucker for what to do as his first step.

Step-by-step explanation:

i would tell tucker to add 5 negative x-tiles because then he would be isolating the x variable and that would help him with not getting confused when gets to the part where he has to isolate the variable if he was to add 1 negative unit tile to both sides as his first step.

Either first step will isolate the variable.

Answer:0.03125

Step-by-step explanation:

GOO*OOGLE

Step-by-step explanation:

(1/2)^5   = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 =   1/32

Based on the given clues, the mystery number is 12.

Let's analyze the clues given to find the mystery number:

It is a 2-digit number: This means the number is greater than or equal to 10 and less than 100.

It is a factor of 48: The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

It is a multiple of 6: The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, and so on.

The sum of the digits is 3: From the clues, we know that the mystery number is a 2-digit number, so let's consider the possible numbers where the sum of the digits is 3:

12 (1 + 2 = 3)

21 (2 + 1 = 3)

Now let's check which of these numbers satisfy the first three clues:

12: This number is a factor of 48 (48 ÷ 12 = 4) and it is a multiple of 6 (12 ÷ 6 = 2). The sum of the digits is 3. Therefore, 12 satisfies all the clues.

21: This number is not a factor of 48 (48 ÷ 21 ≈ 2.29), so it doesn't satisfy the second clue.

Based on the given clues, the mystery number is 12.

for such more question on mystery number

https://brainly.com/question/20737927

#SPJ8

Answer:14

Step-by-step explanation: minus *minus = + so its +27

and then you just do the maths 27-13=14

Complete Question:

Lucas is planting grass on the shaded portions of the yard. What will be the total area of covered by grass? Fill in the missing.

Part A= 12 x ? = ? ft²

Part B= 0.5 x ? x 9 = ?ft²

Part C= 0.5 x 7 x ? = ?ft²

Total Area= ?ft²

Answer:

\(A = 108ft^2\)

\(B = 27ft^2\)

\(C = 24.5ft^2\)

\(Area = 159.50ft^2\)

Step-by-step explanation:

Given

See attachment

From the attachment;

Part A is a rectangle with dimension 9ft by 12ft

So,

\(A = 12ft * 9ft\)

\(A = 108ft^2\)

Part B is a triangle with dimension: height = 6 and base = 9

The height is calculated as:

\(Height = 12ft - 6ft = 6ft\)

And the base is:

\(Base = 18ft - 9ft = 9ft\)

So, the area is:

\(B = 0.5 * 6ft * 9ft\)

\(B = 27ft^2\)

Part C is a triangle with dimension: height = 7 and base = 7

So, the area is:

\(C = 0.5 * 7 * 7ft^2\)

\(C = 24.5ft^2\)

Total Area is:

\(Area = A + B + C\)

\(Area = 108ft^2 + 27ft^2 + 24.5ft^2\)

\(Area = 159.50ft^2\)

Answer:

*20 Songs and 2 Movies

*8 Songs and 6 movies

Step-by-step explanation:

Answer:

Ross's profit it 1,781.37

Step-by-step explanation:

$35 per person and 54 people= 35x54=1890

Profit= the amount of money he makes after his expenses.

1890-108.63=1781.37

Answer:

price and quantity demanded

Step-by-step explanation:

Answer:

In which direction must the graph of f(x) = |x| be shifted to produce the graph of g(x) = |x − 3|?

A. left

B. down

C. up

✓D. right

Right is the right answer.

Answer:

Down

Step-by-step explanation:

I took the test and got it right

Answer:

Its B 0.454554555

Step-by-step explanation:

it has a pattern which is repeating. So its known as rational number..