If f(x) = 3x - 1 and g(x) = x^2-4x, find f(g(x)).
A) 3x-1
____
x^2- 4x

B) 3x^2-12x-1
C) 3x^3-13x^2+4x
D) 9x^2-18x+5

Answer:

According to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.

What is the right angle triangle property?

In a right-angle triangle ratio of the opposite side to the adjacent side is equal to the tangent angle between the adjacent side and the hypotenuse side.

Here, (b) is the opposite side, (a) is the adjacent side, and is the angle made between the adjacent side and the hypotenuse side.

The sides of the triangle are 8, 15, and 17 units long and the measure of the angles of the right angle triangle is 62, 90, and 28 degrees.

Re-draw, the  Here in the given triangle, the base is the side which is 15 units long. Re-draw the triangle as shown below.

In the attached triangle below, the opposite side of the triangle is 15 units and the adjacent side of the triangle is 8 units long.

The angle between the opposite side and the adjacent side is 62 degrees. Thus using the right angle triangle property as,

Thus, according to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.

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The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median.

A whisker plot, also known as a box and whisker plot, is a graphical representation of a set of numerical data through their quartiles. The plot consists of a box with whiskers extending from the top and bottom, showing the spread and distribution of the data. The five-number summary, which includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value, is used to create the whisker plot.

Here,

To create a box and whisker plot, we need to find the five-number summary of the data set, which includes:

Minimum value: the smallest value in the data set.

First quartile (Q1): the median of the lower half of the data set.

Median: the middle value in the data set.

Third quartile (Q3): the median of the upper half of the data set.

Maximum value: the largest value in the data set.

First, we need to put the data in order:

10, 12, 14, 15, 16, 18, 22, 24, 25, 28

The minimum value is 10 and the maximum value is 28.

The median is the middle value, which is 18.

To find the first quartile, we need to find the median of the lower half of the data set, which is:

10, 12, 14, 15, 16

The median of this lower half is 14.

To find the third quartile, we need to find the median of the upper half of the data set, which is:

22, 24, 25, 28

The median of this upper half is 24.

So, the five-number summary for this data set is:

Minimum value = 10

First quartile (Q1) = 14

Median = 18

Third quartile (Q3) = 24

Maximum value = 28

Now we can use this information to create the box and whisker plot:

      |          |      

 ----+----+----+----+----

    10   14   18   24   28

The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median. The whiskers extend from the box to the minimum and maximum values in the data set.

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Answer:

y=1+3x

Step-by-step explanation:

y= 1 + 3x

Hope I helped

Answer:

y= 3x + 1

Answer Explanation:

Recall:

If z varies directly with x, that will be z = kx

If z varies inversely with y, that will be z = k/y

Combining the two equations, we get:

We will be using the first set of values to solve for the constant of variation k.

At x = 2, y = 5 and z = 10,

We get,

Now apply the constant k with the second values to solve for z.

At x = 3 and y = 15,

We get,

Therefore, z = 5

Answer: y = (x - 1)² - 3

Step-by-step explanation:

y = (1-1)²-3
y=0-3
y=-3

Answer:

About 75 (75.0002)

Step-by-step explanation:

25÷3.14=7.9618

7.9618×3=23.8854

23.8854×3.14=74.0002

Hope this helps:)

Answer:

the product of (4x) (-3x^8)=-12x^9

Answer:

-12x^9

Step-by-step explanation:

multipy :)

The water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

We have

Number of students= 1200

Water consumption per student= 750 ml

So, Total water consumption

= Number of students × Water consumption per student

= 1200 × 750 ml

= 900000 ml

= 900 Liter

Now, the time cooler tank has to be filled to quench the thirst

= 900 / 50

= 18 times

Thus, the water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

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Answer:

1/2 of

4/3 x

3 x

1 unit of

Step-by-step explanation:

have a nice day!

Answer:

1/2 of

4/3 x

3 x

1 unit of

half of, twice, greater than

Step-by-step explanation:

Hope this helps!

If not, I am sorry.

Answer:

18 1/16

Step-by-step explanation:

4 1/4 = 4.25

4.25 * 4.25 = 18.0625

18.0625 = 18 1/16

Answer:

c

Step-by-step explanation:

Writing numbers correctly in accounting records is essential for accuracy, compliance and the prevention of human error.

It is important to write numbers correctly in accounting records in order to ensure accuracy when recording, tracking and analysing financial data. When numbers are written incorrectly, the accuracy of the data can be compromised, leading to incorrect calculations and financial analyses. Writing numbers correctly also helps to eliminate human error, which is important when dealing with finances. In addition, writing numbers correctly helps to ensure regulatory compliance, as incorrect numbers can lead to reporting errors that can result in penalties or other legal repercussions.Good accounting practices require that numbers be written in the correct numerical format. This means that numbers should be written in the standard format, using symbols such as commas and decimal points to indicate thousands and tenths. For example, if a total amount is $1,450.50, the correct way to write it would be 1,450.50. Writing it as 1450.50 or 1.450,50 would be incorrect. In conclusion, writing numbers correctly in accounting records is essential for accuracy, compliance and the prevention of human error. It is important to use the correct numerical format and symbols to ensure that numbers are written correctly in accounting records.

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Why is it important to correctly write the numbers in accounting records?

Answer:

To determine the amount of engine oil needed, we need to find 5% of 3.8 gallons:

0.05 x 3.8 = 0.19

So, 0.19 gallons of engine oil should be added to the jerry can.

Answer:

4×4×4 =

16×4=

64 in^3(cu.in)

The domain of the given relation is: {x| x = –7, –6, 2, 3, 11}.

A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

Additionally, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

In this context, we can reasonably infer and logically deduce that the domain of the given relation include the following: {x| x = –7, –6, 2, 3, 11}.

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Answer:

Since the slope is undefined, this is a vertical line. Vertical lines have no y-intercept. No y-intercept.

Step-by-step explanation:

hope this helped:)

Answer:

To write the equation of a line in slope-intercept form, we need to first find the slope of the line. The slope is a measure of the steepness of the line, and is calculated as the rise over the run between two points on the line. In this case, we can use the points (-6,-3) and (6,-7) to calculate the slope.

To find the slope, we first need to find the difference between the y-coordinates of the two points, which is -3 - (-7) = 4. We then need to find the difference between the x-coordinates of the two points, which is 6 - (-6) = 12. The slope is then calculated as the rise over the run, which is 4/12 = 1/3.

Once we have the slope, we can use the point-slope formula to write the equation of the line in slope-intercept form. The point-slope formula is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, we can use the point (-6,-3) and the slope 1/3 to write the equation of the line.

The equation of the line in slope-intercept form is then y - (-3) = 1/3(x - (-6)), which simplifies to y + 3 = 1/3x + 2. This is the equation of the line that passes through the points (-6,-3) and (6,-7) in slope-intercept form.

Therefore, the correct answer is y + 3 = 1/3x + 2.

Step-by-step explanation:

Step-by-step explanation:

Let the husband's income be x

Wife's income be x + 9000

X + X + 9000 = 81000

2X + 9000 – 9000 = 81000 – 9000

2X= 72000

X = 36000

Husband, 36000,

Wife, 9000+36000, 45000

The addition property used by Bill in finding the actual December temperature is the commutative property of addition.

According to the question,

We have the following information:

Bill claims that he found the actual December temperature by adding either -5 + 3 or 3 +-5.

We know that are five properties of addition: closure property, commutative property, associative property, additive identity property of addition and additive inverse property.

The commutative property of addition means that if two numbers are added and their order is inversed then  the result of addition will always be the same.

For example, we get -2 by adding -5+3 and 3+(-5). The change in order of digits does not affect the final result.

Hence, the addition property used by Bill in finding the actual December temperature is the commutative property of addition.

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Given:

Price of car = $32,000

Sales tax = 8%

To find:

The price of car including sales tax.

Solution:

We have,

Price of car = $32,000

Salas tax = 8%

Amount of sales tax = 8% of price of car

\(\text{ Sales Tax}=\dfrac{8}{100}\times 32000\)

\(\text{Sales Tax}=2560\)

Now,

Total price of car including tax = Price of car + Sales tax

\(\text{Total price of car including tax}=32000+2560\)

\(\text{Total price of car including tax}=34560\)

Therefore, the price of car including tax is $34560.

Saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.

As given in the question,

Interest rate = 5%

Types of account = Saving account

Pays the interest in two forms :

Compounded semiannually and Compounded daily

Saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.

Reason :

Frequency of interest given on compounded daily is much higher and increase the amount much faster as compare to compounded semiannually.

When interest compounded daily generate 365 compounding periods a year, where as compounded semiannually generates two times in a year.

Therefore, saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.

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Answer:

Step-by-step explanation:

All the angles that have a cosine of 9/15 are,

⇒ ∠P and ∠X

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Triangle PQR is similar to triangle XYZ.

Hence, We get;

In triangle PQR,

cos P = 9/15

And, In triangle XYZ,

cos X = XZ / ZY

cos X = 9 / 15

Thus, All the angles that have a cosine of 9/15 are,

⇒ ∠P and ∠X

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Answer:

V= πr2h = π·182·3≈ 3053ft³

V = 3053ft³

Answer:

32.

Step-by-step explanation:

The first 32 have buttons but NO zips.

Then 35 have NEITHER buttons OR zips.

Then 32 have ZIPs, but no buttons.

The question only asks for zips. The other bag is unaccounted for.

The required sample sizes are given as follows:

a) Previous estimate of 0.52: n = 1839.

b) No previous estimate: n = 1842.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of 0.995, so the critical value is z = 2.575.

The margin of error is given as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

For an estimate of 0.52, the parameters are given as follows:

\(M = 0.03, \pi = 0.52\)

Hence the sample size is obtained as follows:

\(0.03 = 2.575\sqrt{\frac{0.52(0.48)}{n}}\)

\(0.03\sqrt{n} = 2.575\sqrt{0.52 \times 0.48}\)

\(\sqrt{n} = \frac{2.575\sqrt{0.52 \times 0.48}}{0.03}\)

\((\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.52 \times 0.48}}{0.03}\right)^2\)

n = 1839.

Without a previous estimate, the sample size is given as follows:

\(0.03 = 2.575\sqrt{\frac{0.5(0.4)}{n}}\)

\(0.03\sqrt{n} = 2.575\sqrt{0.5 \times 0.5}\)

\(\sqrt{n} = \frac{2.575\sqrt{0.5 \times 0.5}}{0.03}\)

\((\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.52 \times 0.5}}{0.03}\right)^2\)

n = 1842.

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The equations x² + 4x + 3 = 0 and x² -6x + 13 = 0 are equivalent to (x + 2)² = 1 and (x - 3)² = -4

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

The standard equation of a quadratic function is:

y = ax² + bx + c

1) Given that:

x² + 4x + 3 = 0

subtract 3 from both sides:

x² + 4x = -3

add to both sides the square of half the coefficient of x:

x² + 4x + 4 = -3 + 4

(x + 2)² = 1

2) Given that:

x² - 6x + 13 = 0

subtract 13 from both sides:

x² - 6x = -13

add to both sides the square of half the coefficient of x:

x² - 6x + 9 = -13 + 9

(x - 3)² = -4

The equations are (x + 2)² = 1 and (x - 3)² = -4

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Answer:

A= 78.4602

Step-by-step explanation:

To find the area of a circle, we would need the radius. We can find that from the circumference.

C=2πr

31.4=2πr

31.4/2π= r

r= 157/10π or 4.99747

Now we can use the radius to find the area of a circle.

A=πr^2

A=π(157/10π)^2

A= 78.4602

Answer:

A = 1/2 l*w

So the answer is 4.

Answer:

area=1/2(bh)

area=1/2(2 times 4)

area=1/2(8)

area=4

:)