a. According to an online calculator, there are 1728 cubic inches in a cubic foot.i. Explain how to check the calculator's answer. Is it correct?

The range of the function is {1,-1,10} for function f(x)=2x³−3x .

A relation is a function if it has only One y-value for each x-value.

In a function what can go into a function is called the Domain. What may possibly come out of a function is called the Codomain. What actually comes out of a function is called the Range.

The given function is f(x)=2x³−3x

The domain is {-1,1,2}

Now f(-1)=2(-1)³-3(-1)

=-2+3=1

f(1)=2(1)³-3(1)=2-3=-1

f(2)=2(2)³-3(2)=16-6=10

Hence, the range of the function is {1,-1,10} for  f(x)=2x³−3x .

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Answer:

You need to add the graphs

Step-by-step explanation:

Answer:

(3,1)

Step-by-step explanation:

This system of equation has one solution, which is (3,1)

Hope this helps!

Answer:

f^-1(x) =  (2x + 4) / 3

Step-by-step explanation:

- switch 'y' with 'x'

x = 3/2y - 2

- solve for 'y'

x + 2 = 3/2y

- multiply each side by 2

y = (2x + 4) / 3

Since a kite is a quadrilateral, it has the value of 360 total degrees.

Answer:

Monthly Loan Payment

Loan Amount (P) = $6,000

Monthly Interest Rate (n) = 0.75% per month [9.00% / 12 Months]

Number of months (n) = 36 Months [3 Years x 12 months]

Monthly Loan Payment = [P x {r (1+r)n} ] / [( 1+r)n – 1]

= [$6,000 x {0.0075 x (1 + 0.0075)36}] / [(1 + 0.0075)36 – 1]

= [$6,000 x {0.0075 x 1.308645}] / [1.308645 – 1]

= [$6,000 x 0.009815] / 0.308645

= $58.89 / 0.308645

= $190.80

Monthly Loan Amortization Schedule

“Therefore, the total interest paid during the first year will be $465.99”

HOPE this example helps

Answer:it says there is no answer did u type the wrong problem?

Step-by-step explanation:

Answer:

31.4

Step-by-step explanation:

diameter (d) = 10

circumference = (3.14)d

                        = (3.14)10 = 31.4

circumference = 31.4

Answer:

It would be A

Step-by-step explanation:

Answer:

144? or 126 sorry

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 and 2/3 minus 4/5

Answer:

-20 3/4, - 15 1/2, - 14 3/4, - 1/4

Step-by-step explanation:

Given the depths :

-14 3/4, - 15 1/2, - 1/4, - 20 3/4

Ordering from least to greatest :

Since the numbers are negative; arranging the numbers as it would appear on a number line ; Large whole number negative values are always the least.

-20 3/4, - 15 1/2, - 14 3/4, - 1/4

Answer:In the number, 687,760, there are two 7s; one is at a place value of hundred and the other is at thousand.

Hence, the higher place value 7 is 10 times greater than lower place value 7. Every consecutive place value is 10 times greater than the right one.

Step-by-step explanation:

Answer:

third option

Step-by-step explanation:

under a counterclockwise rotation of 90° about the origin

a point (x, y ) → (y, - x )

Then

A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )

B (2, - 2 ) → (- 2, - 2 )

C (1, - 4 ) → (- 4, - 1 )

The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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

The figure,

Where, we have

A = (-1, -2)

B = (2, -2)

C = (1, -4)

The rule of 90 degrees counterclockwise is

(x, y) = (-y, x)

Using the above as a guide, we have the following:

A = (2, -1)

B = (2, 2)

C = (4, 1)

Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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Answer:

Step-by-step explanation:

To classify the quadrilateral formed by the given points, we need to find the length of each side and the measure of each angle.

Using the distance formula, we can find the length of each side:

AB = sqrt((4 - (-3))^2 + (2 - 1)^2) = sqrt(49 + 1) = sqrt(50)

BC = sqrt((9 - 4)^2 + (-3 - 2)^2) = sqrt(25 + 25) = 5sqrt(2)

CD = sqrt((2 - 9)^2 + (-4 - (-3))^2) = sqrt(49 + 1) = sqrt(50)

DA = sqrt((-3 - 2)^2 + (1 - (-4))^2) = sqrt(25 + 25) = 5

Using the slope formula, we can find the measure of each angle:

Angle ABC: m1 = (2 - 1)/(4 - (-3)) = 1/7

m2 = (-3 - 2)/(9 - 4) = -1/5

tan(ABC) = |(m2 - m1)/(1 + m1m2)| = 3/4

ABC = arctan(3/4) ≈ 36.87°

Angle BCD: m1 = (-3 - 2)/(9 - 4) = -1/5

m2 = (-4 - (-3))/(2 - 9) = 1/7

tan(BCD) = |(m2 - m1)/(1 + m1m2)| = 3/4

BCD = arctan(3/4) ≈ 36.87°

Angle CDA: m1 = (-4 - 1)/(2 - (-3)) = -1

m2 = (1 - (-3))/(-3 - 9) = 1/2

tan(CDA) = |(m2 - m1)/(1 + m1m2)| = 7/5

CDA = arctan(7/5) ≈ 54.46°

Angle DAB: m1 = (1 - (-4))/(4 - (-3)) = 5/7

m2 = (-4 - (-3))/(-3 - 2) = 1/5

tan(DAB) = |(m2 - m1)/(1 + m1m2)| = 3/4

DAB = arctan(3/4) ≈ 36.87°

Therefore, the quadrilateral formed by the given points is a kite, because adjacent sides are congruent and one diagonal bisects the other diagonal at a right angle.

Answer:

$8.25

Step-by-step explanation:

1.25+(2.25x2)+1.00+(1.25x2)=8.25

Step-by-step explanation: La Noche Triste (Spanish for "The Sad Night") was a famous battle between the Spanish conquistadors and the Aztecs, a native people of Mexico. ... Between 400 and 800 Spanish soldiers were killed or captured. Between 2,000 and 4,000 native Mexican allies of the Spanish were killed or captured.

Location: Tenochtitlan

End date: July 1, 1520

Date: June 30

Answer:  was a famous battle between the Spanish conquistadors and the Aztecs, a native people of Mexico. Between 400 and 800 Spanish soldiers were killed or captured. Between 2,000 and 4,000 native Mexican allies of the Spanish were killed or captured.

Step-by-step explanation:

Answer:

D)  4.45 m by 6.82 m

Step-by-step explanation:

The given dimensions of the floor plan are 4.9 cm by 7.5 cm.

Given scale factor = 0.011

⇒ 0.011 m = (0.011 × 100) cm = 1.1 cm

Therefore, every 1.1 cm on the plan equals 1 m in the actual room.

To find the dimensions of the actual room in meters, divide the floor plan dimensions by 1.1:

⇒ 4.9 ÷ 1.1 = 4.45 m (2 d.p.)

⇒ 7.5 ÷ 1.1 = 6.82 m (2 d.p.)

Answer:

E

Step-by-step explanation:

2018 :   75 000 pines

2019 :     2000 pines / km^2  *  30 km^2 = 60 000 pines

(75 000 - 60 000) / 75 000 = .2        or 20 %  

Answer:

(A)6 kilometers

Step-by-step explanation:

First, we determine the value of a using Pythagoras Theorem.

\(Hypotenuse^2=Opposite^2+Adjacent^2\\17^2=a^2+15^2\\a^2=17^2-15^2\\a^2=289-225\\a^2=64\\a^2=8^2\\a=8$ km\)

Therefore:

Distance along the long route = 8 + 15 =23 km

Distance along the shortcut =17 km

Difference =23-17 =6km

Therefore, Mr. Jones bikes 6km less when he takes the shortcut instead of the long route.

Answer:

a

Step-by-step explanation:

on edge

Answer:

a) Mean blood pressure for people in China, which has mean 128 and standard deviation 23.

b) 0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c) 0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.

d) 0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e) Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f) 90% of all people in China have a blood pressure of less than 157.44 mmHg.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg

This means that \(\mu = 128, \sigma = 23\)

a.) State the random variable.

Mean blood pressure for people in China, which has mean 128 and standard deviation 23.

b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.

This is 1 subtracted by the p-value of Z when X = 135, so:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{135 - 128}{23}\)

\(Z = 0.3\)

\(Z = 0.3\) has a p-value of 0.6179.

1 - 0.6179 = 0.3821

0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.

This is the p-value of Z when X = 141, so:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{141 - 128}{23}\)

\(Z = 0.565\)

\(Z = 0.565\) has a p-value of 0.7140.

0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.

d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

This is the p-value of Z when X = 125 subtracted by the p-value of Z when X = 120, so:

X = 125

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{125 - 128}{23}\)

\(Z = -0.13\)

\(Z = -0.13\) has a p-value of 0.4483.

X = 120

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{120 - 128}{23}\)

\(Z = -0.35\)

\(Z = -0.35\) has a p-value of 0.3632.

0.4483 - 0.3632 = 0.0851

0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?

From item b, when X = 135, Z = 0.3.

Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f.) What blood pressure do 90% of all people in China have less than?

The 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.28 = \frac{X - 128}{23}\)

\(X - 128 = 1.28*23\)

\(X = 157.44\)

90% of all people in China have a blood pressure of less than 157.44 mmHg.

       The equation representing the relationship between Electricity and  Gas used, and your Bill is:

      T  =  0.25 * k + 0.97 * t

        Make a plan:

We need to find the equation that represents the relationship between the total monthly bill (T), The Kilowatt Hours of Electricity used (k), and the Terms of Gas used (t).

T  =  0.25  *  k  +  0.97  *  t

1 - Write the Equation for the cost of Electricity:

        0.25 * k

2 - Write the Equation for the Cost of Gas:

       0.97 * t

3 - Combine the Equations to Represent the total Monthly Bill (T):

       T  =  0.25 * k + 0.97 * t

Hence,  The equation representing the relationship between Electricity and  Gas used, and your Bill is:

       T  =  0.25 * k + 0.97 * t

I hope that helps!

The purchasing power in five years will be $15,476.

To predict the purchasing power in five years, we can substitute the value of X as 5 into the equation y = 20000(0.95)^X.

Plugging in X = 5, we have:

\(y = 20000(0.95)^5\)

Calculating the expression, we find:

\(y ≈ 20000(0.774)\)

Simplifying further, we get:

\(y ≈ 15480\)

Rounding the result to the nearest dollar, the predicted purchasing power in five years would be approximately $15,480.

Therefore, the closest option to the predicted purchasing power in five years is $15,476.

So the correct answer is:

$15,476.

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Rounding to the nearest dollar, the predicted purchasing power in five years is approximately $15,480.

To predict the purchasing power in five years using the given equation, we substitute the value of x (representing the number of years) as 5 and calculate the result.

The equation provided is: y = 20000(0.95)^x

Substituting x = 5 into the equation, we have:

y = 20000(0.95)⁵

Now, let's calculate the result:

y ≈ 20000(0.95)⁵

≈ 20000(0.774)

y ≈ 20000(0.774)

≈ 15,480

This means that, according to the given equation, the purchasing power of $20,000, with an inflation rate of five percent, would be predicted to be approximately $15,480 after five years.

By changing the value of x (representing the number of years) to 5, we can use the preceding equation to forecast the buying power in five years.

The example equation is: y = 20000(0.95)^x

When x = 5 is substituted into the equation, we get y = 20000(0.95).⁵

Let's now compute the outcome:

y ≈ 20000(0.95)⁵ ≈ 20000(0.774)

y ≈ 20000(0.774) ≈ 15,480

This indicates that based on the equation, after five years, the purchasing power of $20,000 would be estimated to be around $15,480 with a five percent inflation rate.

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9514 1404 393

Answer:

  20

Step-by-step explanation:

This triangle is your basic 3-4-5 triangle multiplied by 5 to become a 15-20-25 triangle. The missing leg is 20.

_____

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Notice that:

Therefore:

Now, recall that:

Therefore:

Answer: 50000 divided by 12 is equal to:

Answer: 4.16666666667

Step-by-step explanation: