Please help! will mark brainliest!

Answer: f(−3) = -5/2

f(−1) = -5/2

f(3) = 3/4

Step-by-step explanation: For x ≤ -1, we have:

f(x) = 7/2 + 2x

For x = -3, we have:

f(-3) = 7/2 + 2(-3)

f(-3) = 7/2 - 6

f(-3) = -5/2

For x = -1, we have:

f(-1) = -5 + 3(-1)/2

f(-1) = -5/2

For -1 < x < 3, we have:

f(x) = -5 + 3x/2

For x = 3, we have:

f(3) = 1/4 (3)

f(3) = 3/4

To find the height of the tissue box, we use the formula for the volume of a rectangular prism, substituting the given values. We get a height of approximately 11.0 inches, rounded to the nearest tenth.

To find the height of the tissue box, we need to use the formula for the volume of a rectangular prism, which is:

volume = length x width x height

We are given the volume of the tissue box as 1,001 cubic inches, and its width and length as 7 inches and 13 inches, respectively.  We can enter these values as substitutes in the formula to obtain:

1,001 = 13 x 7 x height

The right side of the equation is simplified, and the outcome is:

1,001 = 91 x height

Dividing both sides by 91 gives:

height = 1,001 / 91

We can evaluate this expression with a calculator to obtain:

height ≈ 11.0

Therefore, the height of the tissue box is approximately 11.0 inches, rounded to the nearest tenth.

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Answer:

40

Step-by-step explanation:

Perimeter of rectangle = 2(l + w)

L= 12

W = 8

Let's solve

2(12 + 8) = 40

So, the perimeter of the rectangle is 40

Sara should have $4,578 removed from her projected income of $124,075 for the year 2022.

Determine Sara's taxable income by subtracting the standard deduction for head of household from her projected income. According to the tax table, the standard deduction for head of household for 2022 is $18,650. Therefore, Sara's taxable income is:

$124,075 - $18,650 = $105,425

Find the tax bracket that Sara's taxable income falls into. According to the tax table, for head of household, the tax brackets for 2022 are:

10% on taxable income from $0 to $14,100

12% on taxable income over $14,100 to $54,200

22% on taxable income over $54,200 to $86,350

24% on taxable income over $86,350 to $164,900

32% on taxable income over $164,900 to $209,400

35% on taxable income over $209,400 to $523,600

37% on taxable income over $523,600

Since Sara's taxable income is $105,425, she falls into the 24% tax bracket.

Calculate the amount of taxes that Sara owes based on her tax bracket. To do this, we need to find the amount of taxable income that falls within the 24% tax bracket, and multiply it by the tax rate. According to the tax table, the amount of taxable income within the 24% tax bracket for head of household is:

$105,425 - $86,350 = $19,075

Therefore, Sara's tax liability is:

$19,075 x 0.24 = $4,578

So, Sara should have $4,578 removed from her projected income to cover her taxes for the year.

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The requried completely factored form of the given polynomial is (q+w)(c+y).

We can group the first two terms and the last two terms together, then factor out the common factors:
= cq+cw+qy+wy
= c(q+w) + y(q+w)
= (q+w)(c+y)

Therefore, the completely factored form of the given polynomial is (q+w)(c+y).

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It would take the assistant 17 hours, 30 minutes to do it alone

Algebraic expressions are defined as expressions that are composed of terms, variables, constants, factors and coefficients.

They are also made up of arithmetic operations, such as;

From the information given, we have that;

Josephine makes the correction in 7 hours

They both do it for 5 hours

Let the assistant be x, we then have;

7x/7 + x = 5

cross multiply the values

7x = 37 + 5x

collect the like terms

2x = 35

x = 35/2

x = 17. 5 hours

x =17 hours, 30 minutes

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Answer:

Step-by-step explanation:

The b is area of the base which is l x w

so if you substituted in you get V= l x w x h

So they are the same

The firm maximizes its profit where MR equals MC and here at quantity 9, MR equals MC.

A. 9 unit.

The firm maximizes its profit where MR equals MC and here at quantity 9, MR equals MC.

B. 7.25

In perfect competition, the price is equal to MR. Because firms are price takers. So the price will be 30.

Profit per unit =Price - ATC

=30-22.75

=7.25

C. 65.25

Profit =(Price - ATC) *quantity

=(30-22.75)*9

=65.25

A market having perfect competition involves buyers and sellers exerting no significant impact on product pricing. Such markets are composed of numerous parties possessing alike items, with easy ingress and egress from the same domain.

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The model predicts that there will be 89.3 million vinyl album sales in the country in the year 2030 by using quadratic equation.

Define quadratic equation?

A quadratic equation is  a polynomial equation of the second degree, meaning it contains at least one squared term (x²). The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The values of a, b, and c determine the shape of the parabola, which is the graph of a quadratic equation.

To predict the number of vinyl album sales in the year 2030, we need to substitute x = 20 into the polynomial:

[tex]0.2x^2 + 0.3x + 3.3[/tex]

[tex]= 0.2(20)^2 + 0.3(20) + 3.3[/tex]

[tex]= 80 + 6 + 3.3[/tex]

[tex]= 89.3[/tex]

Therefore, the model predicts that there will be 89.3 million vinyl album sales in the country in the year 2030.

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Answer & Step-by-step explanation:

The Radius should be about 2.228 and the Diameter is 4.456. The area of the circle is 15.59

"The solutions to the equation are complex conjugates of each other" as Lindsey is solving the quadratic equation [tex]x^2[/tex]−2x+6=0.

To solve the quadratic equation [tex]x^2 - 2x + 6 = 0[/tex], Lindsey can use the quadratic formula:

x = (-b ± √([tex]b^2[/tex] - 4ac)) / 2a

In this case, a = 1, b = -2, and c = 6. Substituting these values into the formula, we get:

x = (-(-2) ± √([tex](-2)^2[/tex] - 4(1)(6))) / 2(1)

x = (2 ± √(-20)) / 2

Since the discriminant ([tex]b^2[/tex] - 4ac) is negative, the square root of -20 is an imaginary number.

Therefore, the two solutions to the equation are complex conjugates of each other:

x = (1 + √5i) and x = (1 - √5i)

Thus, the correct statement is: "The solutions to the equation are complex conjugates of each other."

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Answer:

Step-by-step explanation:

Triangle area formula: 1/2bh

Then use the Pythagorean theorem to find out what AB is.

AB= sqrt 76

8.72

8.72*18*1/2

78.5 approx

Neither (2, 1, 1) nor (-1, 0, -1) is a solution to the respective systems of equations.

We have,

To determine if an ordered triple (x, y, z) is a solution of a system of equations, we need to substitute the values of x, y, and z into each equation and check if the resulting equations are true.

Let's take the first system of equations:

x + 2y - z = 1

2x + 7y + 4z = 11

x + 3y + z = 4

Let's check if the ordered triple (2, 1, 1) is a solution of this system:

2 + 2(1) - 1 = 3, which is not equal to 1, so (2, 1, 1) is not a solution of equation 1.

2(2) + 7(1) + 4(1) = 17, which is not equal to 11, so (2, 1, 1) is not a solution of equation 2.

2 + 3(1) + 1 = 6, which is not equal to 4, so (2, 1, 1) is not a solution of equation 3.

Since (2, 1, 1) is not a solution of any of the equations in the system, it is not a solution of the system.

Now, let's take the second system of equations:

x + 2y - 3z = -1

x - 3y + z = 1

2x - y - 2z = 2

Let's check if the ordered triple (-1, 0, -1) is a solution of this system:

(-1) + 2(0) - 3(-1) = 2, which is not equal to -1, so (-1, 0, -1) is not a solution of equation 1.

(-1) - 3(0) + (-1) = -2, which is not equal to 1, so (-1, 0, -1) is not a solution of equation 2.

2(-1) - 0 - 2(-1) = 0, which is not equal to 2, so (-1, 0, -1) is not a solution of equation 3.

Since (-1, 0, -1) is not a solution of any of the equations in the system, it is not a solution of the system.

Therefore,

Neither (2, 1, 1) nor (-1, 0, -1) is a solution of the respective systems of equations.

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Answer:

the resale value after 4 years would be 11,812.5

Step-by-step explanation:

I'm sorry if this is wrong this is based on what I know :)

Answer:

The answer to your question is $8,384.77

Step-by-step explanation:

Average annual value lost: $12,913.57

First year depreciation: $6,625.00

Total depreciation: $18,115.23

Total depreciation percentage: 68.36%

Value of vehicle at end of ownership period: $8,384.77

I hope this helps and have a wonderful day!

We can plot 7/10 as 0.7 and 1(1/5) as 1.2 on the number line.

We have,

To plot 7/10, we need to divide the number line into 10 equal parts and then count 7 parts starting from 0.

We can label this point as 7/10.

To plot 1(1/5), we first note that 1 is to the left of the 1/5 mark on the number line.

We can divide the section between 0 and 1/5 into 5 equal parts and count 1 part starting from 0.

Then, we can move to the left of 1 and count 1 more part starting from the 1/5 mark.

We can label this point as 1(1/5).

Alternatively,

We can convert 1 1/5 to an improper fraction first:

1 (1/5) = (5 x 1 + 1) / 5 = 6/5

Then, we can plot 6/5 by dividing the number line into 5 equal parts and counting 6 parts starting from 0.

We can label this point as 6/5 or 1(1/5).

Thus,

We can plot 7/10 as 0.7 and 1(1/5) as 1.2 on the number line.

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a. The probability that a person has the virus given that they have tested positive is approximately 4.3%.

b. The probability that a person does not have the virus given that they test negative is approximately 99.0%.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

a) We need to find the probability that a person has the virus given that they have tested positive, i.e., P(A|B). We can use Bayes' theorem to calculate this probability:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B|A) is the probability of testing positive given that the person has the virus, P(A) is the prior probability of a person having the virus, and P(B) is the probability of testing positive.

From the problem statement, we know that:

To calculate P(B), we can use the law of total probability:

P(B) = P(B|A) * P(A) + P(B|A') * P(A')

= 0.9 * 0.005 + 0.1 * (1 - 0.005)

= 0.1045

Therefore, we can compute P(A|B) as:

P(A|B) = P(B|A) * P(A) / P(B)

= 0.9 * 0.005 / 0.1045

≈ 4.3%

So, the probability that a person has the virus given that they have tested positive is approximately 4.3%.

b) We need to find the probability that a person does not have the virus given that they test negative, i.e., P(A'|B'). We can again use Bayes' theorem:

P(A'|B') = P(B'|A') * P(A') / P(B')

where P(B'|A') is the probability of testing negative given that the person does not have the virus, P(A') is the prior probability of a person not having the virus, and P(B') is the probability of testing negative.

From the problem statement, we know that:

To calculate P(B'), we can again use the law of total probability:

P(B') = P(B'|A) * P(A) + P(B'|A') * P(A')

= 0.1 * 0.005 + 0.9 * 0.995

≈ 0.895

Therefore, we can compute P(A'|B') as:

P(A'|B') = P(B'|A') * P(A') / P(B')

= 0.9 * 0.995 / 0.895

≈ 99.0%

So, the probability that a person does not have the virus given that they test negative is approximately 99.0%.

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The value of the missing side is 14.22.

We have,

From the figure,

Sin 52 = x/18

Sin 52 = 0.79

So,

0.79 = x/18

x = 0.79 x 18

x = 14.22

Thus,

The value of the missing side is 14.22.

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Based on their unit rates (hourly rates), William earns $3.20 less per hour than Carson.

The unit rates can be determined as the quotients of the total earnings divided by the number of hours worked by each worker.

Total earnings in 21 hours = $451.50

The total number of hours worked = 21 hours

Hourly rate = $21.50 ($451.50 ÷ 21)

Hours (x)  Earnings (y)   Hourly Rate

   8             $146.40        $18.30 ($146.40 ÷ 8)

 32             $585.60      $18.30 ($585.60 ÷ 32)

 36             $658.80      $18.30 ($658.80 ÷ 36)

40             $732.00       $18.30 ($732.00 ÷ 40)

William's hourly rate = $18.30

Difference between Carson's and William's hourly rate = $3.20 ($21.50 - $18.30)

Thus, judging from their hourly rates, we can conclude that Carson earns more per hour than William.

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William's Earnings

Hours (x)  Earnings (y)

   8             $146.40

 32             $585.60

 36             $658.80

40             $732.00

The equation that expresses y in terms of x is y = x - 2.

To find an equation that expresses y in terms of x, we need to determine the relationship between the two variables. One way to do this is by finding the slope of the line that passes through the given points.

Using the two points (40, 38) and (70, 68), we can find the slope as:

slope = (change in y) / (change in x)

slope = (68 - 38) / (70 - 40)

slope = 30 / 30

slope = 1

This means that for every increase of 1 in x, y also increases by 1.

We can now use the point-slope form of a linear equation to find the equation of the line passing through these points:

y - 38 = 1(x - 40)

Simplifying:

y = x - 2

Therefore, the equation that expresses y in terms of x is y = x - 2.

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Answer:

3√2

Step-by-step explanation:

We can find the value of x using the following equation:

x² = 2×9

x² = 2×9

x² = 18

x = 3√2

Answer:

-------------------------

Convert the equation in below steps to solve for x:

Divide both sides by a:

Log both sides with base b:

Here is the answer:

Answer:

x

Step-by-step explanation:

[tex] \frac{1}{5} (25x - 10x) - 2x \\ = \frac{1}{5} (15x) - 2x \\ = 3x - 2x \\ = x[/tex]

The solution is:

a) 22-t mph; is the rate of the boat when it travels upstream.

b) 22+t mph. is the rate of the boat when it travels downstream.

Here, we have,

a) When the boat travels​ upstream, the current hinders the boat (the speed of the boat decreases). Thus, the speed of the boat upstream becomes

22-t mph.

b) When the boat travels​ downstream, the current helps the boat (the speed of the boat increases). Thus, the speed of the boat downstream becomes

22+t mph.

Hence, The solution is:

a) 22-t mph; is the rate of the boat when it travels upstream.

b) 22+t mph. is the rate of the boat when it travels downstream.

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The total number of possible outcomes for Event A and Event B is 66.

The total number of outcomes for both events occurring simultaneously is just the product of the number of outcomes for each event if event A has 11 potential outcomes and event B has 6 possible outcomes and both events are independent.

Therefore, we can multiply the number of possibilities for event A (11) by the number of outcomes for event B (6) to determine the total number of potential outcomes for both events A and B:

11 x 6 = 66

Therefore, if events A and B occur simultaneously, there are 66 alternative outcomes.

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Answer:

2((7)(9) + (7)(10) + (9)(10)) = 2(63 + 70 + 90)

= 2(223) = 446 square feet

Answer:

the first one and the second one.

The height of the rectangular pyramid is calculated as:

h = 17 units.

The formula for calculating the volume of a rectangular pyramid is expressed as:

Volume (V) = 1/3 * lwh, where:

Given the following:

l = 9 units

w = 14 units

Volume of rectangular pyramid (V) = 714 cubic units.

Plug in the values:

714 = 1/3 * 9 * 14 * h

714 = 42h

714/42 = h

h = 17 units.

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The ship moved almost 72.5 degrees north of west to arrive at its destination.

1.: According to a trigonometrical rule, the square of a side in a plane triangle is equal to the sum of the squares of the other sides minus twice that amount plus the cosine of the angle between the other two sides.

BC² is equal to AB² + AC² - 2AB AC cosx

BC² = 17657 - 22068 cosx BC² = 942 + 1192 - 2 94 119 cosx

BC ≈ 105.2

cos(x) = (2 BC AB) / (BC² + AB² - AC²)

cos(x) = (105.2² + 94² - 119²) / (2 × 105.2 × 94)

cos(x)=0.301 = 72.5 degrees

As a result, the ship moved almost 72.5 degrees north of west to arrive at its destination.

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Answer:

first car =48

Second Car=52

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 kilogram has 1,000,000 milligrams so we do 1,000,000x28= 28,000,000 milligrams

Answer: 28 million milligrams