Bill's SUV is 6 feet 4 inches tall. If he puts a 2 -foot 9 -inch box on top of his SUV, what is the total height of the SUV and the box (in feet and inches)?

The sets A and B define a function, while the set C does not.

To determine whether a set defines a function, we need to check if there is one and only one output for each input. In other words, there should not be two different outputs for the same input.

\( A=\{(a, d),(c, d),(e, f),(b, f)\} \)

In this set, there are no repeated inputs, so it does define a function.

\( B=\{(1,3),(2,4),(5,6),(3,4)\} \)

In this set, there are also no repeated inputs, so it does define a function.

\( C=\{(1, a),(2, b),(3, c),(2, a),(4, d),(5, c)\} \)

In this set, there are two different outputs for the input 2 (b and a), so it does not define a function.

Therefore, the sets A and B define a function, while the set C does not.

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They should sell each T-shirt for $27.80 to make a profit of $320.

Profit is the financial gain that a company or individual makes after deducting all the expenses from the revenue earned. It is the positive difference between the total revenue generated from the sale of goods or services and the total cost of producing and selling those goods or services.

Profit is one of the key indicators of a company's financial performance, and it is calculated by subtracting the total expenses from the total revenue. The expenses include the cost of raw materials, labor, rent, taxes, and other overhead costs associated with producing and selling the goods or services.

To make a profit of $320, they need to sell all 25 shirts for a total of $320 + ($15 x 25) = $695.

Therefore, the price they need to sell each T-shirt for is $695 ÷ 25 = $27.80 (rounded to the nearest cent).

So they should sell each T-shirt for $27.80 to make a profit of $320.

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The function seen on Cartesian plane has the following domain and range:

Domain: 0 ≤ t ≤ 100, Range: 450 ≤ q ≤ 1200

In this problem we find a representation of a linear function on a Cartesian plane, of which we need to derive the definitions of its domain and its range. The domain corresponds to the set of times (t), in minutes, and the range is the set of amounts of water (q), in liters.  The domain belongs to the horizontal axis and the range to the vertical axis.

Then, by direct inspection, the domain and the range of the function is:

Domain

0 ≤ t ≤ 100

t ∈ [0, 100]

Range

450 ≤ q ≤ 1200

q ∈ [450, 1200]

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Step-by-step explanation:

1) geometric

2) arithmetic

3) neither

4) geometric

5) neither

6) arithmetic

you can this by usin their formulas or

you see if it has common difference which is for arithmetic sequence or you find the common ratio which is geometric sequence.

We can see that the points of intersection occur at π/3 and 4π/3.

We will solve this equation on the interval [0,2π). To begin, we can break up the equation into two parts:

2cosθ - 1 = 0 and 5cotθ + 4 = 0

First, let's solve the equation 2cosθ - 1 = 0. We can solve this equation by adding 1 to both sides and then dividing both sides by 2. We get:

2cosθ = 1
cosθ = 1/2

To find the angle θ, we can take the inverse cosine of both sides to get:

θ = cos-1(1/2)
θ = π/3

Now, let's solve the equation 5cotθ + 4 = 0. We can solve this equation by subtracting 4 from both sides and then dividing both sides by 5. We get:

cotθ = -4/5

To find the angle θ, we can take the inverse cotangent of both sides to get:

θ = cot-1(-4/5)
θ = 4π/3

Therefore, the solution to the equation on the interval [0,2π) is θ = π/3 or θ = 4π/3. To confirm the solutions, we can produce a Desmos graph of the equation on the interval [0,2π). We can see that the points of intersection occur at π/3 and 4π/3, which are our solutions. See the screenshot below.

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a)  The demand (price) function in terms of x : P(x) = 12 - 0.025(x - 1500)

b) the marginal revenue function is [tex]MR(x) = dR(x)/dx = 12 - 0.05(x - 1500)[/tex] The marginal revenue from the sales of 1800 T-shirts is -$3. This means that for each additional T-shirt sold after the 1800th, the revenue will decrease by $3 per T-shirt

To determine the demand (price) function, we need to find a relationship between the price of the T-shirts (P) and the number of T-shirts sold (x). We are given that for every $0.50 decrease in price, 20 more T-shirts will be sold.

Let's first find the decrease in price per T-shirt sold. If 20 more T-shirts are sold for every $0.50 decrease, then the decrease per T-shirt is $0.50/20 = $0.025. Now, we can set up the demand function. The base price is $12, and we decrease it by $0.025 for each additional T-shirt sold. So the demand function is:

P(x) = 12 - 0.025(x - 1500) To determine the marginal revenue function, we first need to find the total revenue function. Total revenue (R) is the product of the price (P) and the number of T-shirts sold (x):

R(x) = P(x) * x = (12 - 0.025(x - 1500)) * x Now we need to find the derivative of the total revenue function with respect to x, which will give us the marginal revenue function: MR(x) = dR(x)/dx = 12 - 0.05(x - 1500)

To determine the marginal revenue from the sales of 1800 T-shirts, we simply plug in x = 1800 into the marginal revenue function: MR(1800) = 12 - 0.05(1800 - 1500) = 12 - 0.05(300) = 12 - 15 = -$3

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Answer:

3.6225

Step-by-step explanation:

7.5% = 0.075

48.30 x 0.075 = 3.6225

So, 7.5% of 48.30 is 3.6225

Answer:

5/8

Step-by-step explanation:

GCF:

5/8 = 25/40 ( multiply both sides by 5)

11/20 = 22/40 ( multiply both sides by 2)

Answer: A

Area of a circle=[tex]\pi r^2\\[/tex]

Now that we have established this, we will now substitute the values in the equation.

[tex]\pi r^2\\=\frac{22}{7}\\ =\frac{396}{7}\\ =56.57 \\[/tex] OR 57 square yards

HOPE THIS HELPED PLEASE MARK BRAINLIEST IF IT DID!

Answer:

If your options are  110 square yards

220 square yards

3,850 square yards

15,400 square yards

then the correct answer is 3,850 square yards.

Step-by-step explanation:

I took the quiz and got it right.

The equation for the exponential function is

The graph is attached

Exponential function is a function of the form  f(x) = a(b)ˣ

where

the starting = a

the base = b

the exponents = x

Using the table, f(x) = a(b)ˣ

a = 20

solving for b

10 = 20(b)¹

10 = 20b

b = 1/2

the equation for the function is f(x) = 20(0.5)ˣ

check

for x = 3

f(x) = 20(0.5)³ = 2.5

for x = 4

f(x) = 20(0.5)⁴ = 1.25

The graph of exponential decay is a decreasing function that approaches the x-axis, but never touches it. The rate at which the function decays depends on the value of b - the smaller the value of b, the slower the decay

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The quadratic parent function is represented by the equation F(x) = [tex]x^{2}[/tex], so, the correct answer is D.

A quadratic function is a type of mathematical function that can be written in the form:

f(x) = a[tex]x^{2}[/tex] + bx + c

where a, b, and c are constants and x are the variable. The highest power of x in a quadratic function is 2, which is why it is called a "quadratic" function.

The graph of a quadratic function is a curve called a parabola. The shape of the parabola depends on the value of the coefficient a. If a is positive, the parabola opens upward and has a minimum point, and if a is negative, the parabola opens downward and has a maximum point.

Quadratic functions are used in many areas of mathematics and science, such as physics, engineering, and finance. They are also used in computer graphics to create curves and surfaces.

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The value of m∠A + m∠B is 90°. The angles that add up to 180 degrees are referred to as supplementary angles.

Option C is correct.

Given a figure, we must determine the sum of the angles A and B. The angle that forms a linear pair with the sum of the angles A and B is 90 degrees. Since we are aware that the linear pair with a 90 degree angle is 90 degrees, the value of the sum of the angles A and B, m  A + m  B, is also 90 degrees.

There can be no more than three angles. Two angles whose measurements add up to exactly 180 degrees are referred to as supplementary angles. It is possible to have three angles that add up to 180 degrees each, such as 60 degrees, 30 degrees, and 90 degrees; however, these angles are not considered supplementary.

Question incomplete:

What is the value of m∠A + m∠B? If ∠ C = 56° and ∠D =124°

A. 180

B. 120

C. 90

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The expression in terms of m and n is m^2+2/3n-3.

To rewrite the given expression in terms of m and n, we need to use the properties of logarithms to simplify the expression. The properties of logarithms that we will use are:

- log(ab) = log(a) + log(b)
- log(a/b) = log(a) - log(b)
- log(a^b) = b*log(a)

Using these properties, we can rewrite the given expression as follows:

\( \log \left(\frac{\left(M^{\log (M)} \cdot 10^{\log (N)}\right)}{1000 \sqrt[3]{N}}\right) = \log \left(M^{\log (M)} \cdot 10^{\log (N)}\right) - \log \left(1000 \sqrt[3]{N}\right) \)

\( = \log \left(M^{\log (M)}\right) + \log \left(10^{\log (N)}\right) - \log \left(1000\right) - \log \left(\sqrt[3]{N}\right) \)

\( = \log (M) \cdot \log (M) + \log (N) \cdot \log (10) - \log (10^3) - \frac{1}{3} \cdot \log (N) \)

Now, we can substitute m = log(M) and n = log(N) into the expression to get:

\( = m^2 + n - 3 - \frac{1}{3}n \)

\( = m^2 + \frac{2}{3}n - 3 \)

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Answer:

[tex] \sf \: x = 5[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 11 + 2x = 3(x + 2)

Then the value of x will be,

→ 11 + 2x = 3(x + 2)

→ 11 + 2x = 3x + 6

→ 2x - 3x = 6 - 11

→ -x = -5

→ [ x = 5 ]

Hence, the value of x is 5.

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

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[tex] \: [/tex]

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[tex] \: [/tex]

[tex] \: [/tex]

The value of x is 5 !

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hope it helps! :)

Milo is 8.09 miles from the dock.

Here we can use the Law of Cosines,

which states that c² = a² + b² - 2abcos(C),

Where c is the side opposite the angle C in a triangle.

Call the distance from the dock to the point where Milo changes direction "a", the distance Milo sails in the new direction "b", and the angle between these two sides "C".

We know that a = 7 miles and b = 4 miles.

To find C, we can use the fact that Milo changes direction by 5π/36 radians.

Since he turned to the right, we can say that he turned by,

⇒ 360 - 5π/36 = 355π/36 radians.

This is the angle between the two sides of the triangle.

Now we can plug these values into the Law of Cosines to find the distance from Milo to the dock:

⇒ c² = a² + b² - 2abcos(C)

⇒ c² = 7² + 4² - 2(7)(4)cos(355π/36)

⇒ c² = 49 + 16 - 56cos(355π/36)

⇒ c² = 65.47

Taking the square root of both sides, we get:

c = 8.09 miles (rounded to 2 decimal places)

Therefore, Milo is 8.09 miles from the dock.

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The possible rational roots of the equation 14x3 - 39x2 + 24x - 4 = 0 are: 2/7, 4/7, 2, 4, 1/7, 1, 1/14, 1/2, -2/7, -4/7, -2, -4, -1/7, -1, -1/14, -1/2.

To find the rational roots, we need to factor the equation into its linear components. First, factor out a common factor from all terms: 14x3 - 39x2 + 24x - 4 = 0 --> 14x(x2 - 3x + 2)(x-2) = 0.

This means that the equation has three linear components, and each component has a possible root that we can calculate. The possible roots can be determined by using the Rational Root Theorem:

Using the Rational Root Theorem, we can find the possible rational roots of the equation:

Therefore, the possible rational roots of the equation.

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At Bank A, the interest rate was 8% (7.94% rounded to the nearest fourth of a percent). At Bank B, the interest rate was 5% (5.09% rounded to one decimal place).

To find the interest rate at each bank, we can use the formula for compound interest and the formula for continuously compounded interest.
For Bank A, the formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Plugging in the values we have, we get:
51010.5 = 1000(1 + r/4)^(4*5)
Solving for r, we get:
r = 4[(51010.5/1000)^(1/20) - 1]
r = 0.1999
So the interest rate at Bank A is about 19.99%, or 20% when rounded to the nearest fourth of a percent.
For Bank B, the formula for continuously compounded interest is A = Pe^(rt), where A is the final amount, P is the principal, r is the interest rate, and t is the number of years.
Plugging in the values we have, we get:
5192.20 = 5500e^(r*5)
Solving for r, we get:
r = (1/5)ln(5192.20/5500)
r = -0.0118
So the interest rate at Bank B is about -1.18%, or -1.2% when rounded to the nearest fourth of a percent.
Therefore, the interest rate at Bank A is about 20% and the interest rate at Bank B is about -1.2%.

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The scale of the map is 1 inch for 6 miles

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

Distance apart = 36 miles

Distance on the map = 6 inches

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

Scale = Distance on the map/Distance apart

Substitute the known values in the above equation, so, we have the following representation

Scale = 6 inches/36 miles

Evaluate

Scale = 1 inch/6 miles

Hence, the scale is 1 inch per 6 miles

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Answer:

127

Step-by-step explanation:

6m+65=2m+57

-2          -2

4m+65=57

     -65  -65

4m=-8

divide by 4 on both sides

m=-2

plug in the 2

6(-2)+65=53

a line =180

180-53=127

To find the probability that four out of 25 randomly selected students are asthmatic, we can use the binomial probability formula:

P(X = x) = (n choose x) * p^x * (1 - p)^(n - x)Where n is the number of trials (students), x is the number of successes (asthmatic students), and p is the probability of success (8.8% or 0.088).

Plugging in the given values, we get:
P(X = 4) = (25 choose 4) * 0.088^4 * (1 - 0.088)^(25 - 4) = 12,650 * 0.00005993 * 0.35178 = 0.0266
Therefore, the probability that four out of 25 randomly selected students are asthmatic is 0.0266, or 2.66%. Rounded to four decimal places, the answer is 0.0266.

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[tex]\stackrel{ \textit{Partial Variation} }{V=aD+bD^2}\qquad \impliedby \begin{array}{llll} \textit{V\textit{ varies partly}}\\ \textit{with D and partly with }D^2 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \textit{we also know that} \begin{cases} V=5\\ D=2\\[-0.5em] \hrulefill\\ V=9\\ D=3 \end{cases}\implies \begin{array}{llll} 5=a2+b2^2&\qquad &5=2a+4b\\\\ 9=a3+b3^2&&9=3a+9b \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{5=2a+4b}\implies 5-2a=4b\implies \cfrac{5-2a}{4}=b \\\\\\ \stackrel{\textit{using the 2nd equation}}{9=3a+9b}\implies \stackrel{\textit{substituting from above}}{9=3a+9\left( \cfrac{5-2a}{4} \right)}\implies 9=3a+\cfrac{45-18a}{4} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(9)=4\left( 3a+\cfrac{45-18a}{4} \right)}\implies 36=12a+45-18a\implies -9=-6a[/tex]

[tex]\cfrac{-9}{-6}=a\implies \boxed{\cfrac{3}{2}=a}\hspace{5em}b=\cfrac{5-2\left( \frac{3}{2} \right)}{4}\implies \boxed{b=\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill V=\cfrac{3}{2}D+\cfrac{1}{2}D^2~\hfill[/tex]

Answer:

There were 30 x 30/100 = <<30*30/100=9>>9 first-year teachers at the meeting.

Answer: 9.

Answer:

9

Step-by-step explanation:

30% of 30 is 9. Therefore there are 9 teachers how were first year teachers.

Hope this helps :)

The possible rational roots are -1/6, -1/3, -1/2, -1, 1/6, 1/3, 1/2, 1 .

The polynomial 6x4 - 11x3 + 8x2 - 33x - 30 has 4 possible rational roots. To find them, use the Rational Root Theorem.

This theorem states that any rational roots of a polynomial must be in the form a/b, where a is a factor of the constant term and b is a factor of the leading coefficient.

In this case, the constant term is -30, so the possible factors are -1, -2, -3, -5, -6, -10, -15, -30. The leading coefficient is 6, so the possible factors are 1, 2, 3, 6.

Therefore, the possible rational roots are -1/6, -1/3, -1/2, -1, 1/6, 1/3, 1/2, 1.

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Answer: Stem-and-leaf plot, because you can see each individual data point.

Step-by-step explanation:im taking the test.

Answer:stem and leaf plot

After taking out percentages we know that Riley has used more percentage of white paint which is 42.85% and her grey paint would be lighter.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.

A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The symbol "%" is frequently written after the number to indicate percentages.

So, the percentages would be:

Riley:

4 black and 3 white

Total = 7

Percentage of white paint:

3/7 * 100 = 42.85%

Christian:

7 black and 4 white

Total = 11

Percentage of white paint:

4/11 * 100 = 36.36%

We know that: 42.85% > 36.36%

Therefore, after taking out percentages we know that Riley has used more percentage of white paint which is 42.85% and her grey paint would be more lighter.

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The company deposited $1,487.88 at the end of each quarter during the first six years.

The amount deposited quarterly during the first six years can be calculated using the formula for the future value of an annuity:

[tex]PMT = (FV / ((1 + r)^{n-1}) * (1 + r)^{-n[/tex]

where PMT is the equal quarterly deposit, FV is the final value of the account, r is the quarterly interest rate (APR / 4), and n is the number of quarters (6 years * 4 quarters per year = 24 quarters).

Plugging in the given values, we get:

[tex]PMT = ($50,000 / ((1 + 0.068/4)^{28-1}) * (1 + 0.068/4)^{-28}[/tex]

PMT = $1,487.88 (rounded to the nearest cent)

Therefore, the company deposited $1,487.88 at the end of each quarter during the first six years.

The problem involves finding the amount deposited quarterly by a company for a period of six years, given the final value of the account four years after the company stopped making deposits. This can be solved using the formula for the future value of an annuity, which calculates the total value of a series of equal payments made at regular intervals over a specified period, taking into account compound interest.

By plugging in the given values into the formula, we can solve for the equal quarterly deposit made by the company during the first six years. The resulting amount is $1,487.88, which represents the total value of all the quarterly deposits made by the company during the six-year period. This answer assumes that the interest rate remained constant throughout the entire period and that the company made no withdrawals or additional deposits after the initial six years.

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Answer:

Step-by-step explanation:

Answer:

Customer A - 5 / 22.45 = $0.22 or 22 cents per quart

Customer B - 7 / 25.45 = $0.27 or 27 cents per quart