A driving range charges $4 to rent a golf club plus $2.75 for every bucket of golf balls you hit. Write an equation that shows the total cost c of hitting b buckets of golf balls.​

Answer:

Y= 2X

Step-by-step explanation:

The Y intercept is 0, therefore it would not have a "b" if it were in the form y=mx+b.

The line is going right, so it's positive. From 0, the line goes over 2, up 2, so the slope is 2.

30.

\(g(x)=2x^2+18x-14\\\\a)\\g(9)=2\cdot9^2+18\cdot9-14=162+162-14=310\\\\b)\\ g(3x)=2(3x)^2+18(3x)-14=18x^2+54x-14\\\\c)\\ g(1+5m)=2(1+5m)^2+18(1+5m)-14=\\\\=2(1+10m+25m^2)+18+90m-14=2+20m+50m^2+4+90m=\\\\=50m^2+110m+6\)

31.

\(h(y)=-3y^3-6y+9\\\\a)\\h(4)=-3(4)^3-6(4)+9=-3\cdot64-24+9=-192-15=-207\\\\ b)\\h(-2y)=-3(-2y)^3-6(-2y)+9=24y^3+12y+9\\\\c)\\h(5b+3)=-3(5b+3)^3-6(5b+3)+9=\\\\=-3[(5b)^3+3\cdot(5b)^2\cdot3+3\cdot5b\cdot3^2+3^3)-30b-18+9=\\\\=-375b^3-675b^2-405b-81-30b-9=-375b^3-675b^2-435b-90\)

32.

\(f(t)=\dfrac{4t+11}{3t^2+5t+1}\\\\a)\\f(-6)=\dfrac{4(-6)+11}{3(-6)^2+5(-6)+1}=\dfrac{-24+11}{3(36)-30+1}=\dfrac{-13}{108-29}=-\dfrac{13}{79}\\\\b)\\f(4t)=\dfrac{4(4t)+11}{3(4t)^2+5(4t)+1}=\dfrac{16t+11}{48t^2+20t+1}\\\\c)\\f(3-2a)=\dfrac{4(3-2a)+11}{3(3-2a)^2+5(3-2a)+1}=\dfrac{12-8a+11}{3(9-12a+4a^2)+15-10a+1}=\\\\=\dfrac{-8a+23}{27-36a+12a^2+16-10a}=\dfrac{-8a+23}{12a^2-46a+43}\)

33.

\(g(x)=\dfrac{3x^3}{x^2+x-4}\\\\a)\\g(-2)=\dfrac{3(-2)^3}{(-2)^2+(-2)-4}=\dfrac{3(-8)}{4-2-4}=\dfrac{-24}{-2}=12\\\\b)\\g(5x)=\dfrac{3(5x)^3}{(5x)^2+(5x)-4}=\dfrac{3(125x^3)}{25x^2+5x-4}=\dfrac{375x^3}{25x^2+5x-4}\\\\c)\\g(8-4b)=\dfrac{3(8-4b)^3}{(8-4b)^2+(8-4b)-4}=\dfrac{3[8^3-3\cdot8^2\cdot4b+3\cdot8\cdot(4b)^2-(4b)^3]}{64-64b+16b^2+8-4b-4}=\\\\=\dfrac{3(512-768b+384b^2-64b^3)}{16b^2-68b+68}=\dfrac{3\cdot4(128-192b+96b^2-16b^3)}{4(4b^2-17b+17)}=\\\\=\dfrac{384-576b+288b^2-48b^3}{4b^2-17b+17}\)

The inverse of the function is y = ( 1/5 )x - 6.

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Consider the function,

y = 5x + 30

To find the inverse of the function we interchange x and y then find the equation for y.

Therefore, after interchanging x and y:

x = 5y + 30

Subtracting 30 from each side of the equation.

x - 30 = 5y + 30 - 30

x - 30 = 5y

Now, dividing the whole equation by 5

( x - 30 ) / 5 = 5y / 5

y = ( 1/5 )x - 30/ 5

y = ( 1/5 )x - 6

Therefore, the inverse of the function y = 5x + 30 is y = ( 1/5 )x - 6.

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The expression that represents the cost of m tickets is simply 2m.

To write an algebraic expression, follow these steps:

If the cost of a single raffle ticket is $2, then the cost of m tickets would be:

2m

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The area of the walkway is 24π square meters.

To find the area of the walkway, we need to subtract the area of the inner circle from the area of the outer circle.

The inner circle has a radius of 5 meters, so its area can be calculated using the formula for the area of a circle: A_inner = π * \((r_inner)^{2}\).

A_inner = π * \(5^{2}\) = 25π square meters.

The outer circle has a radius equal to the sum of the inner radius and the width of the walkway. In this case, the outer radius is 5 + 2 = 7 meters.

The area of the outer circle can be calculated in the same way: A_outer = π * \((r_outer)^{2}\).

A_outer = π * \(7^{2}\) = 49π square meters.

Now, we can find the area of the walkway by subtracting the area of the inner circle from the area of the outer circle: A_walkway = A_outer - A_inner.

A_walkway = 49π - 25π = 24π square meters.

The area of the walkway is 24π square meters, where π (pi) is a mathematical constant approximately equal to 3.14159.

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To express 2log 4 + 3log 2 as a single logarithm, you can use the property of logarithms that states that loga(mn) = logam + logan. This property can be used to rewrite the given expression as follows:

2log 4 + 3log 2 = log 4^2 + log 2^3

= log 16 + log 8

= log 16 * 8

= log 128

here  2log 4 + 3log 2 equals to log 128

Therefore, 2log 4 + 3log 2 = log 128, which is answer choice (D) log 128.

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Answer:

Step-by-step explanation:

Using Trigonometry: SOH CAH TOA,

Cross multiplying:

x = tan (47°) × 35

  =  37.5329

  = 37.53 to two decimal places

To determine which statements are true about the circle whose equation is x^2 + y^2 - 2x - 8 = 0:

First, we can rewrite the equation in standard form by completing the square:

x^2 - 2x + y^2 = 8

(x - 1)^2 + y^2 = 9

From this form, we can see that the center of the circle is at (1, 0), which is on the x-axis. Therefore, statement 2 is true.

The radius of the circle is the square root of the constant term in the standard form equation, which is 3. Therefore, statement 1 is false and statement 5 is true.

Finally, the equation of the circle is in standard form, and we can see that the squared term for y is positive, which means that the center of the circle cannot lie on the y-axis. Therefore, statement 3 is false.

In summary, the three true statements are:

- The center of the circle lies on the x-axis.

- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

- The standard form of the equation is (x – 1)² + y² = 3.

Answer:

a.) Marginal Product (MP) = 120

b.) Average Product = 126

c.) At x = 12, the output is maximum.

d.) After 5 levels of inputs diminishing returns set in.

Step-by-step explanation:

Given that,

Q = 72x + 15x² - x³

a.)

Marginal Product is equal to

\(\frac{dQ}{dx} = 72 + 30x - 3x^{2}\)

At x = 8

MP = 72 + 30(8) - 3(8)²

     = 72 + 240 - 192

     = 120

∴ we get

Marginal Product (MP) = 120

b.)

Average Product is equals to

= \(\frac{Q}{x}\)

= 72 + 15x - x²

At x = 6

Average Product = 72 + 15(6) - 6²

                             = 72 + 90 - 36

                             = 126

∴ we get

Average Product = 126

c.)

For Maximizing Q,

Put \(\frac{dQ}{dx} = 0\)

⇒72 + 30x - 3x² = 0

⇒24 + 10x - x² = 0

⇒x² - 10x - 24 = 0

⇒x² - 12x + 2x - 24 = 0

⇒x(x - 12) + 2(x - 12) = 0

⇒(x + 2)(x - 12) = 0

⇒x = -2, 12

As items can not be negative

∴ we get

At x = 12, the output is maximum.

d.)

Now,

For Diminishing Return

\(\frac{d(MP)}{dx} = \frac{d^{2}Q}{dx^{2} } < 0\)

⇒30 - 6x < 0

⇒-6x < -30

⇒6x > 30

⇒x > 5

∴ we get

For x > 5, the diminishing returns set in

i.e.

After 5 levels of inputs diminishing returns set in.

Answer:

-2

Step-by-step explanation:

m = 10 / -5 = 2 / -1 = -2

Answer:

(2,1)

Step-by-step explanation:

Answer:

Given vertices:

Plot the points.

We see the diagonals are:

The midpoint of any diagonal is the intersection of the diagonals.

Use midpoint formula to find the coordinates:

The point is (2, 1)

The correct statement regarding the limit of f(x) as x -> 1 is given as follows:

lim x -> 1 f(x) = -∞.

Here,

To obtain lateral limits, we need to take the limit of a function as it approaches a point from the left-hand side and the right-hand side separately.

If the two limits are equal, then this is the limit of the function, while if the lateral limits are different, then the limit of the function does not exist for the value of x.

From quadrant 2, the function approaches x = 1 on quadrant 4, hence the limit to the left is given as follows:

lim x -> 1^- f(x) = -∞.

A graph approaches x = 1 in quadrant 1, and curves down and approaches the x-axis in quadrant 1, hence the limit to the right is given as follows:

lim x -> 1^+ f(x) = -∞.

As the lateral limits are equal, the limit of the function is given as follows:

lim x -> 1 f(x) = -∞.

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complete question:

Review the graph of function f(x). On a coordinate plane, a graph approaches x = negative 3 in quadrant 2, has inflection point (negative 1, 0) and approaches x = 1 in quadrant 4. A graph approaches x = 1 in quadrant 1, and curves down and approaches the x-axis in quadrant 1. Which statement describes Limit of f (x) as x approaches 1?

Missing Information

The problem describes the graph of the function.

The approximate P-value for this test is D. 0.01267.

From the information, Mrs. Peterson claims to produce random numbers from 1 to 5 (inclusive) on her calculator, but you've been keeping track. In the past 80 selections, the number "five" has come up only 8 times.

The p(cap) will be:

= 8 / 80

= 0.1

The z score will be:

= (0.1 - 0.2) / (✓0.2(0.8)/80

= -0.1 / ✓0.0019

= -2.236

= -2.24

By using the distribution table after getting the z score, the p value is 0.01267.

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The spread of the data in the histogram is uneven or skewed to the right.

A histogram is a graphical representation of data used to display the distribution of values in a dataset, showing data in bins or intervals along the horizontal axis.

The data distribution in the histogram is uneven or tilted to the right. This suggests that there are fewer students who have gone water skiing less frequently (1 to 5 trips) and more students who have gone water skiing more frequently (11 to 15 trips). The frequency is greatest between 11 and 15 visits, which is reflected by the largest bar in the histogram.

In given problem, the skewed distribution of the given data shows that there are more no. of the students doing water-skiing regularly than those who are doing it less frequently.

This might imply that there is a group of students who are more experienced or enthusiastic about water skiing, and they have gone on more excursions than other students who have gone on less trips. It also implies that the majority of students fall within the 11 to 15 trip period, which might imply a common pattern or trend in the data.

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The best description of the spread of the data is that it is skewed or unevenly distributed.

A histogram is a graphical representation of data used to display the distribution of values in a dataset, showing data in bins or intervals along the horizontal axis.

Based on the given histogram, the data is not evenly distributed across the five intervals. The majority of students have been water-skiing between 11 and 15 times, with a frequency of 5. There are fewer students who have been water-skiing between 16 and 20 times, with a frequency of 4, and even fewer students who have been water-skiing between 21 and 25 times, with a frequency of 3.

The spread of the data refers to how far apart the values in the dataset are from each other. In this case, the data is not evenly spread across the different intervals. The values in the dataset are more concentrated in the interval of 11 to 15, and less concentrated in the intervals of 1 to 5 and 21 to 25. This indicates that the majority of students have been water-skiing a similar number of times, while fewer students have been water-skiing either a lot or a little.

Therefore, the best description of the spread of the data is that it is skewed or unevenly distributed.

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The complete question is:

A group of students was asked about the number of times they had been water-skiing. The data is shown in the histogram.

A histogram titled Water Skiing Trips. The x-axis is labeled Number of Times Water Skiing and has intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 6. There is a shaded bar for 1 to 5 that stops at 1, for 6 to 10 that stops at 2, for 11 to 15 that stops at 5, for 16 to 20 that stops at 4, and for 21 to 25 that stops at 3.

Which of the following best describes the spread of the data? Explain its meaning in this situation?

Answer:

$1,608

Step-by-step explanation:

I think you have to do $70 x 24

Answer:

$1680

Step-by-step explanation:

For 1 ticket price=$70

For 24 ticket price=$70 x 24

=$1680

The correct answers are: c) vomiting and d) weight loss. Gastroesophageal reflux can cause frequent vomiting, which can lead to weight loss in infants.

A nurse caring for an infant with gastroesophageal reflux may observe the following findings associated with this condition:
b) wheezing
c) vomiting
d) weight loss

Infants and children diagnosed with gastroesophageal reflux should not sit or lie down immediately after a meal; patients will be advised to lie face down for at least the first hour after a meal; Sleeping in this position has been shown to reduce the frequency of gastroesophageal reflux. Expressed milk can be thickened as described, in addition to increasing the frequency of feedings; in addition, early teaching (at three (3) months) to eat rice can be attempted; small meals are also recommended; oily and spicy. foods that promote postprandial reflux by increasing gastric emptying and slowing digestion; Chocolate, mint, tomato, citrus fruits, and caffeine should be avoided, which lowers LES pressure.

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9514 1404 393

Answer:

  4p

Step-by-step explanation:

Since there are 4 cards in each pack, the number of cards is 4 times the number of packs:

  4p . . . . number of cards Adriana bought

A family-wise inflation of error rate is the increase in the probability that one or more results of a numerous, independently (separately) conducted statistical analyses to become statistically significant, but these results can actually be attributed to random variation or measurement error.

In Statistics, a family-wise inflation of error rate is also referred to as family-wise error rate (FWER) and it can be defined as the probability of making at least one false conclusion or type I errors in numerous, separate statistical analyses or hypothesis tests.

Hence, a family-wise inflation of error rate increases the probability that one or more of the results among groups within an independent data set to be statistically significant, especially due to random variation or measurement error.

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Using it's concept, it is found that there is a 8% probability of the card being a king, given that it is a black card.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In a standard deck, there are 26 black cards, of which 2 are kings, hence the probability is given by:

p = 2/26 = 0.0769 = 7.69%.

Rounded to the nearest whole number, 8% probability of the card being a king, given that it is a black card.

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Step-by-step explanation:

\(2\pi \times r = 2\pi \times 18 = 113.09 = 113 \: {feet}^{2} \)

Answer:

\( 2 \times x \times \frac{1}{x} = 2 \\ {x}^{2} + {y }^{2} + 2xy = {(x + y)}^{2} \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = {(x + \frac{1}{x} })^{2} = {3}^{2} = 9\)

The result of subtracting 7x - 9 from 2x² - 11 is 2x² - 7x - 2.

To subtract the expression 7x - 9 from 2x² - 11, we need to distribute the negative sign to every term within the expression 7x - 9, and then combine like terms.

First, let's distribute the negative sign:

2x² - 11 - (7x - 9)

Now, distribute the negative sign to each term within the parentheses:

2x² - 11 - 7x + 9

Next, let's combine like terms:

2x² - 7x - 2

Therefore, the result of subtracting 7x - 9 from 2x² - 11 is 2x² - 7x - 2.

In this expression, the highest power of x is 2, which means it is a quadratic expression. The coefficient of x² is 2, and the coefficient of x is -7. The constant term is -2.

This quadratic expression can be further simplified or factored if needed, but the subtraction process is complete with the result 2x² - 7x - 2.

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Answer:

7

Step-by-step explanation:

since 3x-6 and x+8 are congruent x had to make both the equations equal eachother. 7 is the only number that does that

Answer:

because they all have 3 corners

The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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Answer:

Step-by-step explanation:

this is a positive slope, since it goes up from left...

vertical distance           rise         3

_______________ = _____ = ____  

horizontal distance       run         5

Answer:

20,000

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Y intercept is -4, slope goes up 4 and over 5. Hope this helps.

Answer: \(y=4/5x-2\); Option 2

Step-by-step explanation: Look at graphical points that can help you find the solution. In this case you can locate the y-intercept which is at negative two. Eliminate Option 1. Then look for the slope. Since it goes up 4 and down 5, it is 4/5. The only right answer is option 2.

Answer:

A. 36

Step-by-step explanation:

Answer: The answer is 4...

Explanation: this is a simple equation if you're trying to find X and f(x) = 12  but A(x) equals 3x your basically doing 3 times what equals 12 which in this case that would be 4 (well in any case it would be 4) I know this is confusing so hear me out (sorry)

f(x) = 12

A(x) = 3x  

3 x 4 = 12

x = 4

Like I said sorry if this makes you confused but the answer is 4 :)

brainliest? (even though I'm two weeks late)

Answer:

\(e\approx2.71828\)

Step-by-step explanation:

I assume you mean \(\lim_{x \to 0} (1+x)^{\frac{1}{x}}\), which is just the definition of the constant \(e\), also known as Euler's Number.