Question 16 (1 point) An object is thrown from the top of a building. The following data measure the height of the object from the ground for a five second period. Calculate the correlation coefficient using technology (you can copy and paste the data into Excel). Round answer to 4 decimal places. Make sure you put the 0 in front of the decimal. Seconds Height 0.5 112.5 1 110.875 1.5 106.8 2 100.275 2.5 91.3 3 79.875 3.5 70.083 4 59.83 4.5 30.65 5 0 Answer:___ Question 16 options:

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Answer:

Step-by-step explanation:

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.                                        

Answer:

No, a 25-year-old job applicant cannot be two standard deviations below the mean

Step-by-step explanation:

There are two frequencies 25 and 65

Mean of the two frequencies = 25+65/2 = 45

Standard deviation =

\(\frac{65-25}{\sqrt{12} } \\= 11.55\)

Mean - 2 x standard deviation \(= 45 - 2 * 11.55 = 21.9\)

\(21.9 < 25\)

Thus, a 25-year-old job applicant cannot be two standard deviations below the mean

Answer: T'=(-1,-1), U'=(-3,-1), V'=(-1,-4)

Step-by-step explanation:

Answer:

36 - x²

Step-by-step explanation:

(x-6)(-x-6) = (-1)(x-6)(x+6) = (-1)(x² - 36) = 36 - x²

this is based on the "well known" (a+b)(a-b) = a²-b²

Since y is between x and z, so

XZ is the total length of XY and YZ

Since XZ = 3 inches

YZ = 1 5/8 = 1.625 inches

Substitute them in the equation above

Subtract 1.625 from both sides to find XY

XY = 1.375 = 1 3/8

Answer:

Step-by-step explanation:

50% of 366 is 183, therefore your answer is 366.

Given:

Initial balance = $234.45

Paycheck (Cr) = $917.00

Paycheck (Cr) = $917.00

Groceries, Dr. = $102.78

Credit card bill, Dr. = $322.20

Utility bill, Dr. = $129.29

Rent, Dr. = $510.00

Let's find the final balance in her checking account on May 30.

To find Yolanda's final balance, let's subtract the total withdrawal from the total deposit.

Thus, we have:

Total deposit and credit = initial balance + paycheck = $234.45 + $917.00 + $917.00 = $2068.45

Total withdrawal = groceries + credit card bill + utility bill + rent

Total withdrawal = $102.78 + $322.00 + $129.29 + $510.00 = $1064.07

To find the final balance, we have:

Final balance = Total deposit and credit - Total withdrawal

Final balance = $2068.45 - $1064.07 = $1004.38

Therefore, Yolanda's final balance is = $1004.38

ANSWER:

$1004.38

Answer:

12.6

Step-by-step explanation:

15/2 = 2.4

15-2.4= 12.6

Answer:

12.6

Step-by-step explanation:

YOu just subtract 15 and 12/5

Answer:

7 ten dollar bills and 5 twenty dollar bills

Step-by-step explanation

He recieved 5 bills of $20 and 7 bills of $10.

We have the following statement Angelo cashed a check for $170, the bank teller gave him 12 bills, some $20 bills and the rest $10 bills

We can write -

20x + 10y = 170

x + y = 12

So, we can write -

y = 12 - x

We can write -

20x + 10(12 - x) = 170

20x + 120 - 10x = 170

10x = 50

x = 5

then -

y = 7

Therefore, he recieved 5 bills of $20 and 7 bills of $10.

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The side AC corresponds to the side AC in the other triangle and the length of BC is 15 units

For two triangles to be similar, the corresponding sides of the triangles must be in proportion

Having said  that

The side AC corresponds to the side AC in the other triangle

The length BC is calculated as

BC/9 = 25/15

Express as products

So, we have

BC = 9 * 25/15

Evaluate the products

BC = 15

Hence, the length of BC is 15 units

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Answer:

(x - 5)^2 = 15 and (x + 13)^2 = 3

Step-by-step explanation:

Sure, I can help you with that.

Let's start with the first equation:

0 = x^2 - 10x + 10

To rewrite this equation in the form (x - p)^2 = q, we need to complete the square.

First, let's factor out the coefficient of x^2:

0 = 1(x^2 - 10x + 10)

Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (10/2)^2 = 25:

0 = 1(x^2 - 10x + 25 - 25 + 10)

Now we can rearrange the terms inside the parentheses and simplify:

0 = 1((x - 5)^2 - 15)

Finally, we can rewrite the equation in the desired form by adding 15 to both sides:

15 = (x - 5)^2

So the first equation in the form (x - p)^2 = q is:

(x - 5)^2 = 15

Now let's move on to the second equation:

x^2 + 26x + 167.5 = 0

Again, we need to complete the square to rewrite this equation in the form (x - p)^2 = q.

First, let's factor out the coefficient of x^2:

x^2 + 26x + 167.5 = 1(x^2 + 26x + 167.5)

Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (26/2)^2 = 169:

x^2 + 26x + 167.5 = 1(x^2 + 26x + 169 - 169 + 167.5)

Now we can rearrange the terms inside the parentheses and simplify:

x^2 + 26x + 167.5 = 1((x + 13)^2 - 1.5)

Finally, we can rewrite the equation in the desired form by adding 1.5 to both sides:

1.5 = (x + 13)^2 - 1.5

So the second equation in the form (x - p)^2 = q is:

(x + 13)^2 = 3

The experimental probability of an event can be found through:

in this case, the possible cases are the number of spins that are made until the moment which is 30.

the specific cases refer to the probability we want to find, which in this case refers to landing in yellow next time, for that matter we know that until the spinner has landed in yellow 8 times.

then,

simplify the fraction

Answer:

The experimental probability that the next time the spinner will land on yellow is 4/15.

Answer:

The population in 11 years will be of 53,199.

Step-by-step explanation:

Equation for a population that doubles every n years.

The population of an specie, after t years, considering that is doubles after n years, is given by an equation in the following format:

\(P(t) = P(0)(2)^{\frac{t}{n}}\)

In which P(0) is the initial population.

The population doubles every 15 years, and the current population is 32,000

This means that \(n = 15, P(0) = 32000\). So

\(P(t) = P(0)(2)^{\frac{t}{n}}\)

\(P(t) = 32000(2)^{\frac{t}{15}}\)

What will be the population in 11 years?

This is P(11). So

\(P(t) = 32000(2)^{\frac{t}{15}}\)

\(P(11) = 32000(2)^{\frac{11}{15}}\)

\(P(11) = 53199\)

The population in 11 years will be of 53,199.

Complete question is;

The diameter of bushings turned out by a manufacturing process is a normally distributed random variable with a mean of 4.035 mm and a standard deviation of 0.005 mm. A sample of 25 bushings is taken once an hour.

a. Within what range should 95 percent of the bushing diameters fall?

b. Within what range should 95 percent of the sample means fall?

c. What conclusion would you reach if you saw a sample mean of 4.020?

Answer:

A) (4.0252, 4.0448).

B) (4.0331, 4.0369).

C) If i saw a sample mean of 4.020, i would conclude that the sample came from a population that did not have a population mean equal to 4.035

Step-by-step explanation:

A) We know that an approximate 95% confidence interval for the item in question has a range of diameter given by the equation;

Range = x¯ ± 1.96σ

Now, since we have a mean of 4.035 mm and a standard deviation of 0.005 mm, we can solve;

Range of bushing diameter = 4.035 ± (1.96 × 0.005) = 4.035 ± (0.0098)

= 4.0252 or 4.0448 and it can be written as;(4.0252, 4.0448).

B) We also know that In the large-sample case, a 95% confidence interval estimate for the population mean is given by the formula;

CI = x¯ ± (1.96s/√n))

Thus, if we solve, we get;

CI = 4.035 ± (1.96 × 0.005 )/√25

CI = 4.035 ± 0.0019

or (4.0331, 4.0369).

c. If i saw a sample mean of 4.020, i would conclude that the sample came from a population that did not have a population mean equal to 4.035 because it doesn't fall into the range of confidence intervals we got earlier.

Answer:

6050.5

Step-by-step explanation:

The key to this is "rounded to the nearest one"

If the question was to say "round to the nearest 10" you would do 10÷2 = 5

Always divide by 2

1 ÷2 = 0.5

6051 - 0.5 = 6050.5

If it was upper bond it would be:

6051 + 0 5 = 6051.5

the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The given function is:

f(x) = -(x + 3) - 1

To find the interval over which the function is decreasing, we need to find the values of x where the function's derivative is negative.

The derivative of the function is:

f'(x) = -1

The derivative is a constant, which means the function has a constant slope of -1. Since the slope is negative, the function is decreasing over its entire domain.

Therefore, the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).

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Answer:

18 1/2

Step-by-step explanation:

add 13 1/3 and 4 3/4

The volume of a cylinder is given by:

Where:

V = Volume = 141 cm³

h = Height

r = radius = 3cm

π = 3.14

Therefore:

Solve for h:

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

Isoceles and obtuse

Step-by-step explanation:

The exact expression for g(x) is 2.25cos((2π/4.5)×(x-3.5)) - 4.

A function can be represented using a formula or an equation, and it can be graphed on a coordinate plane. The input values are typically represented on the x-axis and the output values on the y-axis.

From the given information, we know that the function g(x) has a maximum point at (3.5, -4) and a minimum point at (-1, -5).

The general form of a cosine function is f(x) = A×cos(Bx + C) + D, where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.

Since the function has a maximum point at (3.5, -4), we know that the graph has been shifted to the left by 3.5 units. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) + D.

Similarly, since the function has a minimum point at (-1, -5), we know that the graph has been shifted upwards by 1 unit. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) - 4.

To determine A and B, we can use the fact that the period of the function is 4.5 units (the distance between the maximum and minimum points). Therefore, we have B = 2*pi/4.5.

To determine A, we can use the fact that the amplitude is half the distance between the maximum and minimum points, which is 0.5*(5-(-4)) = 4.5. Therefore, we have A = 4.5/2 = 2.25.

Substituting these values into the equation for g(x), we have:

g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4

Therefore, the exact expression for g(x) is:

g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4.

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Answer:

Answer: 630

Step-by-step explanation: 18 feet tall is the gateway arch . The angle of elevation from a park bench 778 feet from the base of the Gateway Arch in St

Answer:

Step-by-step explanation:

The vertex is at (-3, -1)  and the leading coefficient is negative ( because  the curve is inverted)

y = -a(x + 3)^2 - 1

One point on the curve is (-2, -3) so

-3 = -a(-2+3)^2 - 1

-3 = -a - 1

-a = -2

So we have

y = -2(x + 3)^2 -  1

y = -2(x^2 + 6x + 9) - 1

y = -2x^2 - 12x - 19.

Answer:

The graph opens down, Maximum ⇒ B

Step-by-step explanation:

The vertex form of the quadratic equation is y = a(x - h)² + b, where

Let us use these facts to solve the question

∵ The equation of the graph is y = -3(x + 4)² - 1

→ Compare it with the form above

∴ a = -3 and (h, k) = (-4, -1)

∵ a is negative

→ That means a < 0

∴ The graph is opened downward

∴ The graph opens down

∵ The graph is opened downward

→ That means the vertex point will be a maximum point

∴ The graph has a maximum vertex

∴ The graph opens down and has a maximum vertex

The attached graph for more understanding

Answer:

0.325

Step-by-step explanation:

Let A represent the event: winning a prestigious scholarship
Let B represent the event: plays a varsity sport

Given

Therefore the probability that someone wins the scholarship given that they play a varsity sport is 0.325