Use the rules of exponents to simplify the expression (x2)(x9) .

The range of mileages that Company A would charge less than Company B would be m > 80.

The function for Company A is $ 121 to show that the company price does not change.

The function of Company B would be 65 + 0. 70 m to show that $ 0.70 is charged per mile.

The mileage where Company B charges more is:

121 < 65 + 0. 70 m

56 < 0. 70 m

m > 56 / 0. 70

m > 80

In conclusion, when the miles are over 80 miles, then Company B is more expensive.

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A graph of the linear equation is shown below.

The slope of this linear equation is equal to 3.

The y-intercept of this linear equation is equal to 2.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

Based on the information provided above, a linear equation that models the line is represented by this mathematical equation;

y = mx + c

y = 3x + 2

By comparison, we have the following:

mx = 3x

Slope, m = 3.

Initial value or y-intercept, c = 2.

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A graph of the equation of the cosine function is shown below.

The amplitude of the cosine function is equal to 1/2.

The period of the cosine function is equal to 8π.

In Mathematics and Geometry, the standard equation of a cosine function is represented or modeled by the following mathematical equation (formula):

y = Acos(Bx - C) + D

Where:

Based on the information about this cosine function, it is denoted by;

f(x) = 1/2cos(1/4x) - 1

By comparison, we have the following:

Amplitude, A = 1/2.

B = 1/4

1/4 = 2π/P

Period, P = 2π × 4 = 8π

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Step-by-step explanation:

the formula

4/3πr3

so

36π cm3 is the answer

Answer: 113.1 cm³

Step-by-step explanation:

[tex]V=\frac{4}{3}\pi r^{3}[/tex]          r=3

= [tex]\frac{4}{3} \pi 3^{3}[/tex]

[tex]=36\pi[/tex]

=113.1 cm³

Revenue is decreasing at a rate of $5,576.58 per month.

What is revenue?

Revenue is the multiplication of the quantity of items sold and the cost at that they are sold.

The mathematical form of revenue is R(p) = z(p) × p where z(p) is the number of items sold at price p

Here given that the equation z = 30000/√(4p+1).

Now, we can use the chain rule to find the rate of change of revenue with respect to time t, given that the price is increasing at a rate of $3 per month. The chain rule tells us that: dR/dt = (dR/dp) × (dp/dt)

We want to find dR/dt when p = $210. We know that dp/dt = $3 per month, so we just need to find dR/dp at p = $210. We can do this by differentiating the expression for R(p) with respect to p:

dR/dp = dz/dp × p + z(p) where dz/dp is the derivative of z with respect to p. We can find this using the quotient rule:

[tex] \frac{dz}{dp} = \frac{-15000}{(4p+1)^{(3/2)}}[/tex]

Putting it all together, we have:

[tex] \frac{dR}{dp} = \frac{-15000p}{(4p+1)^{(3/2) }}+ \frac{30000}{√(4p+1)}[/tex]

When p = $210, we have:

dR/dp = -1858.86

And when dp/dt = $3, we have:

dp/dt = 3

So, by the chain rule:

dR/dt = (dR/dp) × (dp/dt) = (-1858.86) × 3 = -5576.58

Therefore, the rate of change of revenue when the company is selling widgets at 210 each and increasing the price by 3 per month is approximately -5,576.58 per month. This means that revenue is decreasing at a rate of 5,576.58 per month under these conditions.

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Answer:

hope this helps in some form of a way....im not that good with math:(

Step-by-step explanation:

Answer:

To find the experimental probability of rolling a 3, we need to write a ratio of the number of times 3 occurs to the total number of trials. Therefore, the best explanation of how to find the experimental probability of rolling a 3 is:

Step-by-step explanation:

"To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary."

In this case, we can see from the table that the number 3 occurs 5 times out of a total of 35 trials. Therefore, the experimental probability of rolling a 3 is:

experimental probability of rolling a 3 = number of times 3 occurs / total number of trials

experimental probability of rolling a 3 = 5 / 35

experimental probability of rolling a 3 = 1/7

Therefore, the experimental probability of rolling a 3 is 1/7, or approximately 0.143 or 14.3%.

the number of students who like at least one subject cannot be determined from the given information. The number of students who like at most one subject and did not like Mathematics and Science is s, and the number of students who like only one subject is m + s - 100.

How to solve the question?

Based on the given information, we can construct a Venn diagram with three sets: M (Mathematics), S (Social), and N (None or neither Mathematics nor Social). Let the number of students who like Mathematics, Social, and neither be denoted by m, s, and n, respectively.

We know that there are 330 students in total, and 50 of them like both Mathematics and Social. Thus, we can start filling in the diagram as follows:

Next, we know that m + 50 students like Mathematics, and s + 50 students like Social. However, we have to subtract the 50 students who like both from both groups to avoid double-counting. Therefore:

m + 50 - 50 = m

s + 50 - 50 = s

We also know that there are no students who like neither Mathematics nor Social, so n = 0.

Now, we can use the principle of inclusion-exclusion to find the number of students who like at least one subject. This is simply the union of the three sets M, S, and N:

| M ∪ S ∪ N | = | M | + | S | + | N | - | M ∩ S | - | M ∩ N | - | S ∩ N | + | M ∩ S ∩ N |

| M ∪ S ∪ N | = m + s + 0 - 50 - 0 - 0 + 50

| M ∪ S ∪ N | = m + s

Therefore, the number of students who like at least one subject is m + s, which we can't determine from the given information.

To find the number of students who like at most one subject and did not like Mathematics and Science, we need to focus on the sets S and N. Since we know that n = 0, we can simplify the diagram:

We are looking for the number of students who like at most one subject and did not like Mathematics and Science, which is simply the set S (since no one likes neither Mathematics nor Social). Therefore, the number of students who like at most one subject and did not like Mathematics and Science is s.

Finally, to find the number of students who like only one subject, we need to subtract the number of students who like both subjects from the total number of students who like at least one subject:

| M ∪ S | = | M | + | S | - | M ∩ S |

| M ∪ S | = m + s - 50

The number of students who like only one subject is therefore:

| M ∪ S | - | M ∩ S | = (m + s - 50) - 50 = m + s - 100

In summary, the number of students who like at least one subject cannot be determined from the given information. The number of students who like at most one subject and did not like Mathematics and Science is s, and the number of students who like only one subject is m + s - 100.

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The variable x represents the angle at which the baseball is hit in degrees.

The variable y represents the baseball's distance traveled in feet.

The y-intercept of the function B(x) reflects the distance traveled by the baseball when it is struck at a 0 degree angle, i.e. directly horizontally.

The distance traveled in this situation is given by:

B(0) = -0.2(0)² + 14(0) - 21 = -21

As a result, the y-intercept is -21 feet, indicating that if the baseball is hit horizontally, it will travel 21 feet backwards. However, because a baseball cannot be hit horizontally, the y-intercept is not a useful value.

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The slope of the Least-Square Regression Line is 1.585 from the regression output given, hence, for each additional increase in hand span, the number of pretzels increases by 1.585

Given that,

A graph titled Grabbing Pretzels has hand span (centimeters) on the x-axis, and number of pretzels on the y-axis. A line goes through points (19, 16) and (22, 20).

Predictor Coef SE Coef t-ratio p

Constant -14.71 4.317 1.689 0.046

Hand spun 1.585 0.310 5.114 0.000

S = 3.05 R-Sq = 52.1% R-Sq(Adj) = 51.7%

The slope of a linear regression line gives the rate of increase in y-value per change in x

The Handspun Coefficient on the table is the slope of the regression line

Therefore, for every 1 centimeter increase in handspun, number of pretzels increases by 1.585

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complete question:

The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. An analysis was completed and the computer output is shown.

A graph titled Grabbing Pretzels has handspan (centimeters) on the x-axis, and number of pretzels on the y-axis. A line goes through points (19, 16) and (22, 20).

Predictor Coef SE Coef t-ratio p

Constant -14.71 4.317 1.689 0.046

Handspan 1.585 0.310 5.114 0.000

S = 3.05 R-Sq = 52.1% R-Sq(Adj) = 51.7%

Using the computer output, the slope of the least-squares regression line means for each additional

The possible polynomial function with the given properties is:

f(x) = -1/5(x2 - 10x + 16)

Now, Based on the given properties, a possible polynomial function would be:

⇒ f (x) = a(x + 2)(x - 4)

To satisfy the second-degree requirement, we need to have an x² term in the function.

By factoring the function above as shown, we can see that it has two roots: x = -2 and x = 4.

Therefore, we can say that this function has zeros at x = -2 and x = 4.

To determine the value of the coefficient "a", we can use the information that the function goes to -∞ as x → -∞.

This means that the leading coefficient of the function must be negative.

Since, we have a(x + 2)(x - 4), and the x² term has a coefficient of a, we can see that a must be negative.

To further simplify the function and reduce all fractions to lowest terms, we can distribute the negative sign and multiply out the factors:

f(x) = a(x + 2)(x - 4)

     = a(x² - 2x - 8x + 16)

     = a(x² - 10x + 16)

Therefore, The possible polynomial function with the given properties is:

f(x) = -1/5(x2 - 10x + 16)

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Answer:

73.4%

Step-by-step explanation:

The standardized value, or z-score, for a height of 22.7 inches can be calculated as:

z = (22.7 - 23.2) / 0.8 = -0.625

Using a standard normal distribution table, we can find that the area to the right of z = -0.625 is 0.734, or 73.4%.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{ 4540+1328.54 }{\$ 5868.54}\\ P=\textit{original amount deposited}\dotfill &\$4540\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]5868.54 = 4540\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 10} \implies \cfrac{5868.54}{4540}=\left( 1+\cfrac{r}{100} \right)^{10} \\\\\\ \cfrac{5868.54}{4540}=\left( \cfrac{100+r}{100} \right)^{10}\implies \sqrt[10]{\cfrac{5868.54}{4540}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[10]{\cfrac{5868.54}{4540}}=100+r\implies 100\sqrt[10]{\cfrac{5868.54}{4540}}-100=r\implies \stackrel{ \% }{2.6}\approx r[/tex]

The half-life of the substance is approximately 3.18 time units (where the unit depends on what t is measured in).

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two sides separated by an equal sign, and it expresses a relationship between the values of the expressions on either side of the equal sign. Equations can be used to describe various mathematical relationships, such as the properties of shapes, the behavior of physical systems, or the patterns of numbers.

The given equation is:

[tex]Q = 72(0.5)t/32.5[/tex]

where Q is the quantity of the substance remaining after time t.

To find the half-life of the substance, we need to find the value of t for which Q is half of its initial quantity.

Initially, let's assume that the quantity of the substance is Q₀. Then we have:

Q₀ = 72

Now, we need to find the value of t for which Q = Q₀/2.

Substituting Q = Q₀/2 in the given equation, we get:

Q₀/2 = 72(0.5)t/32.5

Simplifying this equation, we get:

[tex]2^(t/h) = 32.5/72[/tex]

where h is the half-life of the substance.

Taking the logarithm of both sides, we get:

t/h = log₂(32.5/72)

Solving for h, we get:

h = t/log₂(32.5/72)

We don't have a specific value of t given in the question, but we can calculate the half-life using any value of t. For example, if we take t = 1, then we get:

h = 1/log₂(32.5/72) ≈ 3.18

Therefore, the half-life of the substance is approximately 3.18 time units (where the unit depends on what t is measured in).

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The half-life of the substance is approximately 3.18 time units (where the unit depends on what t is measured in).

What is equation?

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two sides separated by an equal sign, and it expresses a relationship between the values of the expressions on either side of the equal sign.

The given equation is:

Q = 72(0.5)t/32.5

where Q is the quantity of the substance remaining after time t.

To find the half-life of the substance, we need to find the value of t for which Q is half of its initial quantity.

Initially, let's assume that the quantity of the substance is Q₀. Then we have:

Q₀ = 72

Now, we need to find the value of t for which Q = Q₀/2.

Substituting Q = Q₀/2 in the given equation, we get:

Q₀/2 = 72(0.5)t/32.5

Simplifying this equation, we get:

[tex]2^{(t/h)}=32.5/72[/tex]

where h is the half-life of the substance.

Taking the logarithm of both sides, we get:

t/h = log₂(32.5/72)

Solving for h, we get:

h = t/log₂(32.5/72)

We don't have a specific value of t given in the question, but we can calculate the half-life using any value of t. For example, if we take t = 1, then we get:

h = 1/log₂(32.5/72) ≈ 3.18

Therefore, the half-life of the substance is approximately 3.18 time units (where the unit depends on what t is measured in).

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Answer:

a^2 + b^2 = c^2

8^2 + 15^2 = c^2

64 + 225 = c^2

289 = c^2

17 = c

The hypotenuse is 17.

Brainliest? ;)

The domain and the range of the equation y = 7ˣ - 4 are (a) Domain: All real numbers Range: y>-4

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

y = 7ˣ - 4

The above equation is an exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

In this case, it is -4

So, the range is y > -4

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Answer:

(4, 6)

Step-by-step explanation:

The first quadrant is in the top right, second is in bottom right, third in bottom left, and fourth in top left.

The x-axis is told by the first number listed in the point (#, #), and the y-axis is listed in the second number.

(4, -6) is in the second quadrant and is listed on the graph.

(4, 6) is in the first quadrant and is listed on the graph.

(6, 4) is in the first quadrant and is not listed on the graph.

(-4, 6) is in the fourth quadrant and is not listed on the graph.

(the point in the third quadrant is at the point (-4, -6), which is not listed)

Brainliest? ;)

Answer:  141 °

Step-by-step explanation:

we know sum of angles of a triangle is always 180°.(Angle sum property)

then,

∠E+∠F+∠G=180°

8x+5+2x-1+x-11=180°

11x-7=180C

x=187/11

x=17°

m∠E=8x+15=8*17+5=141°

The shaded area for the given figure is equal to 10.32 square units.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of rectangle = 4 × 12

Area of rectangle = 48 square units.

For the total area of circle, we have:

Area of circle, A = πr²

Total area of circle, T = 3 × 3.14 × (4/2)²

Total area of circle, T = 37.68 square units.

Shaded area = 48 square units - 37.68 square units.

Shaded area = 10.32 square units

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

You want the largest angle and the area of a triangle with side lengths 7.5 cm, 14.6 cm, and 21.4 cm.

The law of cosines tells you ...

  b² = a² + c² -2ac·cos(B)

Solving for angle B, we have ...

  B = arccos((a² +c² -b²)/(2ac))

  B = arccos((7.5² +14.6² -21.4²)/(2·7.5·14.6)) ≈ 149° . . . angle ABC

The area of the triangle can be found using the formula ...

  Area = 1/2(ac·sin(B))

  Area = 1/2·7.5·14.6·sin(149°) ≈ 28 cm² . . . area

__

Additional comment

Angle ABC is opposite side AC, which is the longest side. Hence, angle ABC is the largest angle.

We used the original (full precision) angle value to calculate the area. The rounded angle value would be inappropriate for that purpose. (Second attachment.) Note the calculator mode is set to DEGrees.

Answer: To find the selling price of the house, we can use the formula for the present value of an annuity:

PV = A * ((1 - (1 + r)^-n) / r)

Where:

PV = Present Value

A = Annuity payment per period

r = Interest rate per period

n = Total number of periods

In this case, the annuity payment is $525 per month, the interest rate is 7.8% per year compounded monthly (which is equivalent to a monthly interest rate of 7.8% / 12 = 0.65%), and the total number of periods is 30 years * 12 months/year = 360 months.

Using these values, we can calculate the present value of the annuity:

PV = 525 * ((1 - (1 + 0.0065)^-360) / 0.0065)

PV = 525 * 162.577

PV = $85,192.25

So the selling price of the house was $85,192.25 + $25,000 down payment = $110,192.25.

To calculate the total interest paid over 30 years, we can subtract the total payments from the selling price:

Total payments = $525/month * 360 months = $189,000

Total interest paid = $189,000 - $110,192.25 = $78,807.75

Therefore, the friends will pay $78,807.75 in interest over 30 years.

Step-by-step explanation:

The experimental probability for each type of car that José sees at the car show is determined using the formula:

Experimental probability is one that is primarily based on a series of tests.

A random experiment is carried out and repeatedly repeated, with each repetition acting as a trial, to assess their likelihood.

Because the goal of the experiment is to ascertain the likelihood that an event will occur, or whether it will occur at all.

Examples include tossing a coin, rolling dice, or spinning a spinner. In mathematics, the probability of an event is always equal to its frequency divided by the total number of trials.

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Step-by-step explanation:

First, we need to determine the total revenue from docking 100 boats:

$850 per boat x 100 boats = $85,000

Next, we need to determine the total cost of operating the boathouse:

$2200 (fixed cost) + $550 for each of the 100 boats = $77,200

Finally, we can calculate the monthly profit:

Revenue - Cost = $85,000 - $77,200 = $7,800

Therefore, the answer is option C: $27,800.

The required formula for distance is distance = 500t,  where t is the time in minutes and distance is the distance traveled in the corresponding time.

If Thabang's speed is 500 units per minute, then the formula for distance traveled in a certain amount of time t in minutes would be:

distance = speed x time

In this case, Tha bang's speed is 500 units per minute, so the formula becomes:

distance = 500t

Where t is the time in minutes and distance is the distance traveled in the corresponding time.

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Answer:

Yes

Step-by-step explanation:

This is a statistical question because you have to collect statistical data to answer the question

Answer:

124

Step-by-step explanation:

add 4 and 5 which gives you 9

the solve 280 x 4/9

and you get 124

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The new goal time for the promotion should be 3 minutes and 42 seconds in order to ensure that only about 5% of the orders will be free.

We can use the inverse of the cumulative distribution function of a normal distribution with a mean of the goal time and a standard deviation of 2 minutes and 15 seconds to find the new goal time.

Specifically, we want to find the time t such that the area under the normal distribution curve to the left of t is 0.95 (since we want 95% of orders to be within the goal time frame).

Using a standard normal distribution table or calculator, we find that the z-score corresponding to an area of 0.95 to the left is approximately 1.645.

We know that the standard normal distribution has a mean of 0 and a standard deviation of 1, so we can set up the following equation:

1.645 = (t - goal time) / (2 minutes + 15 seconds expressed in decimal minutes)

Solving for t, we get:

t = goal time + 1.645 * (2.25 minutes)

Since we want the answer in minutes and seconds, we can convert the decimal minutes back to minutes and seconds:

2.25 minutes = 2 minutes + 0.25 minutes

= 2 minutes + 0.25 * 60 seconds

= 2 minutes + 15 seconds

Substituting this back into the equation for t, we get:

t = goal time + 1.645 * (2 minutes + 15 seconds)

= goal time + 3.70725

To solve for the new goal time, we need to round to the nearest second:

t ≈ goal time + 3.707 ≈ goal time + 3.71

Since we want about 5% of orders to be free, the goal time should be set at 3 minutes and 42 seconds.

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