– 42 – 54 + 96 =

what is the answer

Answer:

The volume is

[tex]339.4 {yd}^{3} [/tex]

Step-by-step explanation:

The solution is in the image

Answer:

The first one, you cannot factor because the two values do not share any common factors. Hence, the answer would just be:

a. 51x-25

The other one, we can factorise to:

b. 3x(4-x)

Step-by-step explanation:

For the second option:

Common factor between 12x and 3x^2 is 3x.

Take this out to the front, we are left with:

3x(4-x)

A website I recommend you use (math calculator with some instructions) is Symbolab.

https://www.symbolab.com/solver/factor-calculator/factor%2012x-3x%5E%7B2%7D?or=input

Using the z-distribution, the p-value would be given as follows:

b) 0.0086.

At the null hypothesis we test if the means are equal, hence:

[tex]H_0: \mu_D - \mu_C = 0[/tex]

At the alternative hypothesis, it is tested if they are different, hence:

[tex]H_1: \mu_D - \mu_C \neq 0[/tex]

For each sample, they are given as follows:

Hence, for the distribution of differences, they are given by:

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

[tex]z = \frac{-2 - 0}{0.76}[/tex]

z = -2.63.

Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.

Hence option B is correct.

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Answer:

45° rotation clockwise

Step-by-step explanation:

When you plot these on the graph, the non prime ones are on quadrant 2 and when you plot the prime ones, it is on quadrant 1. This means that it is 45° to the right(clockwise)

⬇️red is prime blue is regular ⬇️

Answer: [tex]\frac{3x+1}{x^{2}-6}[/tex]

Step-by-step explanation:

(f/g) represents the division of function f by function g.

The number of people who can go to the game only on Sunday by applying the concept of set theory is equal to 5.

Total number of people for a trip to a baseball game = 15

Number of people planning to go on Saturday = 10

Number of people planning to go Sunday = 12

Let x be the number of people who can go on both Saturday and Sunday.

Then, the number of people who can go only on Saturday is 10 - x.

And the number of people who can go only on Sunday is 12 - x.

Total of 15 people are going to the baseball game.

Using set theory we have,

Number of people going on Saturday only + number of people going on Sunday only + number of people going on both = 15

Substitute the value we have,

⇒(10 - x) + (12 - x) + x = 15

Simplifying the above equation, we get,

⇒22 - x = 15

⇒ x = 7

The number of people who can only go to the game on Sunday is

= 12 - x

= 12 - 7

= 5

Therefore, using set theory number of people can only go to the game on Sunday is equal to 5 .

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The equation that shows the proportional relationship between his defense and offense cards is y = 2x

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the defense cards and x represent the offense cards.

For every 2 offense cards, he owns 4 defense cards. Hence:

4 = 2m

m = 2

y = 2x

The equation that shows the proportional relationship between his defense and offense cards is y = 2x

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The definition of the piece-wise function is:

A piece-wise function is a function that has different definitions, depending on the input.

In this problem, for inputs between -2 and 2, the function is a line that goes through (-2,-4) and (2,6). The slope is:

m = (6 - (-4))/(2 - (-2)) = 2.5.

The y-intercept is of b = 1, hence the rule is:

[tex]f(x) = 2.5x + 1, -2 \leq x \leq 2[/tex]

For x greater than 2 and less than 6, the function is constant at -3, hence the rule is:

[tex]f(x) = -3, 2 < x < 6[/tex].

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answer:

x = - 9/2

y = -10

Step-by-step explanation:

make both equations look like y =

2x-3y=21 -> -3y= -2x+21 -> y = (-2x+21)/-3 -> y = 2/3x - 7

-6x + 2y = 7 -> 2y = 6x + 7 -> y = 3x + 7/2

now make the equations equal to each other (since they both equal y)

get x

2/3x - 7 = 3x + 7/2

-7 -7/2 = 3x - 2/3x

-14/2 -7/2 = 9/3x - 2/3x

-21/2 = 7/3x

(3/7) -21/2 = x

x = (3/7) -21/2

x = - 63/14

x = - 9/2

put it back in an equation to get y

y = 3x + 7/2

y = 3(-9/2) + 7/2

y = -27/2 + 7/2

y = -20/2

y = - 10

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[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4}{10}\times x\right)-(2 \times x)+\frac{8}{5}=\frac{4}{5} \end{gathered}$}[/tex]

Reduce the fraction 4/10, to its minimum expression, extracting and canceling 2.

Combine [tex]\bf{\frac{2}{5}x }[/tex] and -2x to get [tex]\bf{-\frac{8}{5}x}[/tex].

Subtract 8/5 from both sides.

Since 4/5 and 5/8 have the same denominator, join their numerators to subtract them.

Subtract 8 from 4 to get -4.

Multiply both sides by [tex]\bf{-\frac{5}{8}}[/tex], the reciprocal of [tex]\bf{-\frac{5}{8}}[/tex].

Multiply -4/5 by -5/8 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

Reduce the fraction 20/40 to its lowest expression by extracting and canceling 20.

Answer: 178 ft^3

Step-by-step explanation:

A cylinder has the formula V=pi radius ^2 height

A cone has the formula V= 1/3 pi radius ^2 height

So 1/3 of the volume of the cylinder is the volume of a cone

1/3 of 534 = 178 ft^3

Answer:

y-intercept: (0,3)

Step-by-step explanation:

To find the y-intercept, we set x to equal 0, giving the equation:

-3(0)+2y = 6

0+2y = 6

y = 3

The equation of the parabola is [tex]y=\frac{1}{24} x^2+3[/tex]

None of the given options is correct

Given:

Focus: (0, 3)

Directrix: y = -3

Note that:

f - k = k - (-3)

f - 3 = 3 + 3

f = 6 + 3

f = 9

The equation of the parabola is of the form:

[tex]y=\frac{1}{4(f-k)} (x-h)^2+k[/tex]

Substitute f = 9, k = 3, h = 0 into the equation

[tex]y=\frac{1}{24} (x-0)^2+3\\\\y=\frac{1}{24}x^2+3[/tex]

The equation of the parabola is [tex]y=\frac{1}{24} x^2+3[/tex]

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Angles on straight line = 180

180 - 115 = 65

So, angle above 4 in the top corner is 65.

Co-interior angles add up to 180.

(180-65=115)

Thus, the value of 4 is 115 degrees.

Hope this helps!

The quantity of rainfall that fell in the second half of the month is; ¹/₆ of an inch.

We are given;

Rainfall during first half of the month = 1/2 inch

Total rainfall for the month = 2/3 inch

Now, to find the rainfall for the second half of the month, we just subtract the one for the first half from the one for the month to get;

Rainfall in second half of the month = ²/₃ - ¹/₂ = ¹/₆ inches

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Angle L: 70°

The trigonometric ratio used to solve for NM is the tangent ratio.

NM = 57.7 [nearest tenth]

Using the triangle sum theorem, find angle L.

Angle L = 180 - 90 - 20 = 70°

Using the tangent ratio, we can use  ∠M and LN to solve for NM

Tan 20 = 21/NM [tan ∅ = opposite/adjacent]

NM = 21/tan 20

NM = 57.7 [nearest tenth]

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Answer:

70, tangent, 57.7

Step-by-step explanation:

The time he spent running is 13.80 seconds.

The equation that can be used to represent the time he gets to the tree is:

Time he gets to the tree = (time of each spin x total spins) + time he spent running

21 = (6 x 1.2) + r

21 = 7.20 + r

r = 21 - 7.20

r = 13.80 seconds

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By reduction to the absurd, the two lines do not intercept each other because of the following absurd: 5 = - 4.

From statement we have two lines in space, whose vector forms are described below:

(x, y, z) = (1, - 9, 1) + t · (4, 1, 2)     (1)

(x, y, z) = (1, 0, - 9) + s · (5, - 1, 5)     (2)

The point of intersection satisfies the following condition:

(1, - 9, 1) + t · (4, 1, 2) = (1, 0, - 9) + s · (5, - 1, 5)

(1, - 9, 1) - (1, 0, - 9) = s · (5, - 1, 5) + t · (- 4, - 1, - 2)

s · (5, - 1, 5) + t · (- 4, - 1, - 2) = (0, - 9, - 8)

There is a point of intersection if the resulting system of linear equations has at least a solution:

5 · s - 4 · t = 0      (2)

- s - t = - 9      (3)

5 · s - 2 · t = - 8     (4)

By (2):

s = 4 · t/5

(2) in (3):

- 4 · t/5 - t = - 9

- 9 · t/5 = - 9

t/5 = 1

t = 5

(2) in (4):

5 · (4 · t/5) - 2 · t = - 8

4 · t - 2 · t = - 8

2 · t = - 8

t = - 4

By reduction to the absurd, the two lines do not intercept each other because of the following absurd: 5 = - 4.

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's get started ~

[tex]\qquad \sf  \dashrightarrow \: volume = length \sdot width \sdot height[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = (24) \sdot(15) \sdot(2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = 720 \: \: ft {}^{3} [/tex]

now, we know :

[tex]\qquad \sf  \dashrightarrow \: 1 \: \: yard {}^{3} = 27 \: \: ft {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 1 \: \: ft {}^{3} = \cfrac{1}{27} \: \: yard {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 720 \: \: ft {}^{3} = \cfrac{1}{27} \times 720 \: \: yard {}^{3} [/tex]

[tex]\qquad \sf  \approx\: 26.67 \: \: yard {}^{3} [/tex]

now, total cost of ingredients used is :

[tex]\qquad \sf  \dashrightarrow \: 26.67 \times 12.75[/tex]

[tex]\qquad \sf  \dashrightarrow \: 340.04[/tex]

so, total cost is $ 340.04

Answer:

undefined

Step-by-step explanation:

because

the figure does not appear

Answer:

40. 398nine

41: 432six

42: 14714eight

Step-by-step explanation:

765-367=398

The 'nine' is probably confusing you

3x144=432

The 'six' is there to confuse you.

2x7357=14714

The 'eight' is again here to confuse you.

Ignore the 'six' and 'eight' and 'nine' they are making it harder for no reason

Due to length restrictions, we kindly invite to read the explanation of this question for further details about the table and graph of the function.

In this problem we must plot the graph of a function on a Cartesian plane. The procedure is summarized below:

After following the procedure, we have the following result:

Input, x             x + 4                Output, y             (x, y)

   - 2               - 2 + 4                     2                    (- 2, 2)

     0                 0 + 4                     4                     (0, 4)

     2                 2 + 4                     6                     (2, 6)

     4                 4 + 4                     8                      (4, 8)

     6                 6 + 4                    10                      (6, 10)

     8                 8 + 4                    12                      (8, 12)

Lastly, we plot the graph of the linear function.

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Answer:

$1800

Step-by-step explanation:

Volume of the foundation: 30*12*6 = 2160 cubic feet

we need to convert this into yards because a truckload is 8 cubic yards, 2160/3 = 720 cubic yd

One truckload is 8 cubic yards

# of truckloads needed: 720/8 = 90 truckloads

Cost: $20*90 = $1800

Step-by-step explanation:

(f+g)(x)=4x-1+2x²+3===> 2x²+4x+2

The couple are owning income tax of $22,996.

What is tax?

Tax is the obligatory payment payable to the government on earnings.

In this case, the amount of tax to be paid is the sum of $9,235 plus 22% of the excess of the combined taxable income of the couple over $80,250.

Excess over $80,250=$142,800-$80,250

Excess over $80,250=$62,550

Initial tax amount=$9,235

extra tax amount=$62,550*22%

extra tax= 13,761

total tax amount=initial tax amount+ extra tax

total tax amount=$9,235+$13,761

total tax amount=$22,996

In essence, the couple would pay an initial tax of $9,235 plus an extra tax of $13,761 which gives a total tax liability of $22,996

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Answer: B

Step-by-step explanation: Trust me bro

The first ten terms of the sequence are 1, 2, 8, 33, 148, 765, 4626, 32431, 259512, 2335689.

The n-th term of the sequence is aₙ ₊ ₁ = (aₙ + 1) · n.

A sequence is a set of elements generated by at least one condition, usually an equation. In this case, the sequence is generated by a recurrence formula:

a₁ = 1, aₙ ₊ ₁ = (aₙ + 1) · n        (1)

The first ten terms of the sequence are:

n = 1

a₂ = (a₁ + 1) · 1

a₂ = 2

n = 2

a₃ = (a₂ + 2) · 2

a₃ = 4 · 2

a₃ = 8

n = 3

a₄ = (a₃ + 3) · 3

a₄ = 11 · 3

a₄ = 33

n = 4

a₅ = (a₄ + 4) · 4

a₅ = 37 · 4

a₅ = 148

n = 5

a₆ = (a₅ + 5) · 5

a₆ = 153 · 5

a₆ = 765

n = 6

a₇ = (a₆ + 6) · 6

a₇ = (765 + 6) · 6

a₇ = 4626

n = 7

a₈ = (a₇ + 7) · 7

a₈ = 4633 · 7

a₈ = 32431

n = 8

a₉ = (a₈ + 8) · 8

a₉ = 32439 · 8

a₉ = 259512

n = 9

a₁₀ = (a₁₀ + 9) · 9

a₁₀ = 259521 · 9

a₁₀ = 2335689

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Answer:

0.375 second and 3.5 second

Step-by-step explanation:

The position can be modeled by a quadratic function [tex]\displaystyle{h=-16t^2+62t+6}[/tex]. We are tasked to find the time when a ball reaches a height of 27 feet. Therefore, let h = 27:

[tex]\displaystyle{27=-16t^2+62t+6}[/tex]

Solve for t:

[tex]\displaystyle{27-6=-16t^2+62t}\\\\\displaystyle{21=-16t^2+62t}\\\\\displaystyle{16t^2-62t+21=0}[/tex]

Since the equation is quite complicated and more time-consuming to solve, i'll skip the factoring or quadratic part:

[tex]\displaystyle{t=0.375, 3.5}[/tex]

After done solving the equation, you'll get t = 0.375 and 3.5 seconds. These solutions are valid since both are positive values and time can only be positive.

Hence, it'll take 0.375 and 3.5 seconds for a ball to reach 27 feet.

Based on the calculations, all of the numbers belong to this arithmetic sequence.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

[tex]a_n = a_1 +(n-1)d[/tex]

Where:

Next, we would determine the common difference as follows:

d = a₂ - a₁

d = 105 - 99 = 6.

d = a₃ - a₂

d = 111 - 105 = 6.

d = a₄ - a₃

d = 117 - 111 = 6.

Based on the calculations, all of the numbers belong to this arithmetic sequence.

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Complete Question:

What is the number that does not belong to this sequence 99, 105, 111, 117, 123, 129, 135, 141, 147, 153