Use the rules to find derivatives of the functions at the specified values.
f(x) = 4x^3 at x = 2
f(2) = _____

Answer:

new perimeter of Brandy deck is 46 feet .

Step-by-step explanation:

The new perimeter of Brandy deck is 46 feet.

The entire length of all the sides of a rectangle is called the perimeter. As a result, we can calculate the perimeter of a rectangle by adding all four sides.

Using the given information,

Width = 7 Feet

Length = 12 feet

Perimeter = 2 (Width + Length)

[tex]= 2(7+12)[/tex]

[tex]=2(19)[/tex]

[tex]=38[/tex]

Perimeter when deck is 4 feet longer [tex]=38+ 4+4=46[/tex] Feet

Hence, the new perimeter of a deck is 46 feet.

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To determine the number of additional days that would make the cost equivalent for both Heather's Moving and Newton Rent-a-Truck, we can set up an equation:

Heather's Moving: 10 + 8x
Newton Rent-a-Truck: 80 + x

To find the point at which the costs are equal, we can set the equations equal to each other:

10 + 8x = 80 + x

Now, we can solve for x (additional days):

7x = 70
x = 10

So, the costs would be equivalent after 10 additional days. To find the total cost, we can plug the value of x back into either equation:

Total cost = 10 + 8(10) = 10 + 80 = $90.

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The area of the triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is  13.58

First using distance calculator we derived the length of TV and the length of VU.

Since TV = Height; and

VU = Base

and the triangle is a right triangle,

Then, area is given by 1/2 base x Height

Length of TV usign distance calculator is 6.40312
Lenght of VU using distance calculator is 4.24264

So area = 1/2 * 6.40312 * 4.24264

Area = 13.58

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Calculated test statistic of 2.08 is greater than the critical value of 1.645, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 level that more than 55% of California residents use Netflix.

We can use a hypothesis testing approach to answer this question. The null hypothesis is that the true proportion of California residents who use Netflix is the same as the national proportion, or p = 0.55. The alternative hypothesis is that the true proportion of California residents who use Netflix is greater than 0.55, or p > 0.55.

We can use the sample proportion of Netflix users in California, which is 360/600 = 0.6, as an estimate of the true proportion p. The standard error of the sample proportion is:

SE = √[(p*(1-p))/n] = √[(0.55*(1-0.55))/600] = 0.024

The test statistic is:

z = (p - 0.55)/SE = (0.6 - 0.55)/0.024 = 2.08

Assuming a significance level of 0.05 and a one-tailed test (since the alternative hypothesis is one-sided), the critical z-value is 1.645.

Since our calculated test statistic of 2.08 is greater than the critical value of 1.645, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 level that more than 55% of California residents use Netflix. However, we should keep in mind that this conclusion is based on a sample of 600 adults from California, and there is always some degree of uncertainty involved in statistical inference based on samples.

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If 5 out of every 24 players were repaired during the first year of ownership, then 200 of the 960 DVD players were repaired in the first year.

Based on the manufacturer's records, we know that 5 out of every 24 players were repaired in the first year of ownership. To find out how many out of the 960 DVD players were repaired in the first year, we can set up a proportion:

5/24 = x/960

To solve for x, we can cross-multiply:

5 * 960 = 24x

4800 = 24x

x = 200

Therefore, 200 of the 960 DVD players were repaired in the first year, which is approximately 20.8% of the total shipped.

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Gabriela will use 1620 square inches of wood to build the open box.

The amount of wood Gabriela will use depends on the surface area of the box, which is the sum of the areas of its six faces. Since the box is open on top, it will have five faces: four sides and a bottom.

The area of the bottom is the area of a rectangle with length 18 in. and width 15 in., which is:

Area of bottom = length x width = 18 in. x 15 in. = 270 in²

The area of each side is the product of the height and the length of the corresponding base, which is:

Area of each side = height x length = 15 in. x 18 in. = 270 in²

So the total surface area of the box is:

Total surface area = 2 x (Area of bottom) + 4 x (Area of each side)

= 2 x 270 in² + 4 x 270 in²

= 1620 in²

Therefore, Gabriela will use 1620 square inches of wood to build the open box.

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Solving a system of equations we can see that he has 9 quarters and 16 dimes.

Let's define the variables:

x =  number of dimes

y = number of quarters.

There are 25 coins, so:

x + y = 25

The value is $3.85, so:

x*0.10 + y*0.25 = 3.85

So the system of equations is:

x + y = 25

x*0.10 + y*0.25 = 3.85

We can isolate x on the first equation to get:

x = 25 - y

Replacing that in the other one we get:

(25  -y)*0.10 + y*0.25 = 3.85

2.5 + y*0.15 = 3.85

y = (3.85 - 2.5)/0.15

y = 9

Then the other 16 coins are dimes.

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Answer:

86 degrees fahrenheit

Step-by-step explanation:

(30°C × 9/5) + 32 = 86°F

Answer:

0.8660

Step-by-step explanation:

sin24=opposite ÷hypotenus

sin24=opposite ÷5

cross multiply

sin24x5=opposite

sin24=0.4067x5

opposite =0.8660

Answer: Apartment

Confidence

Cooperating

Disrespect

Encode

Forearm

Injustice

Intercontinental

Interplanetary

Mold

Overgrown

Refuel

Repaid

Semi-Sweet

Semicircular

Shield

Subzero

Supermarket

Transportation

Unbelievably

Step-by-step explanation:

Answer:

15

13

6

11

7

1

4

12

17

16

10

8

9

19

3

18

2

5

14

20

The farmer would have made a profit of 5% if he had sold the goat for 2100 shillings.

Let's use the given terms and find out the percentage profit if the farmer had sold the goat for 2100 shillings.
Calculate the cost price of the goat
We know that the farmer made a loss of 28% by selling the goat for 1440 shillings. Let's represent the cost price as "CP".

We can write the equation:
[tex]CP \times  (1 - loss% ) = selling price (SP)[/tex]
[tex]CP \times  (1 - 0.28) = 1440[/tex]
Solve for CP
[tex]CP \times 0.72 = 1440[/tex]
CP = 1440 / 0.72
CP = 2000 shillings
Calculate the percentage profit
Now we want to find out the percentage profit if the farmer had sold the goat for 2100 shillings.

We can write the equation:
[tex](SP_{new - CP)} / CP \times  100 = profit[/tex]
[tex](2100 - 2000) / 2000 \times  100 = profit%[/tex]
[tex]100 / 2000 \times  100 = profit%[/tex]
5% = profit%.

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The substitution is u = -x² + 9 and the evaluated value is -4.5(2/3)(-x² + 9)³/² + C.

To evaluate the given integral ∫9x√(-x² + 9dx),

we can use the substitution u = -x² + 9. This substitution will allow us to simplify the expression under the square root.

First, we can find du/dx by taking the derivative of u with respect to x: du/dx = -2x.

Next, we can solve for dx in terms of du by dividing both sides by -2x: dx = -du/(2x).

Using the substitution and the expression for dx in terms of du, we can rewrite the integral as:

∫9x√(-x² + 9dx) = -4.5∫√udu

Now, we can integrate the simplified expression √u using the power rule of integration:

-4.5∫√udu = -4.5(2/3)u³/² + C

Substituting back for u, we get:

-4.5(2/3)(-x² + 9)³/² + C

Therefore, the solution to the integral ∫9x√(-x^2 + 9dx) using the substitution u = -x^2 + 9 is:

-4.5(2/3)(-x² + 9)³/² + C

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Answer:

B

Step-by-step explanation:

using the diamond factoring method:

2x^2-12x+x-6

2x(x-6) + (x-6)

(2x+1)(x-6)

B

The interquartile range (IQR) of the given data set is 4.

Interquartile range (IQR) is a measure of variability in a data set that measures the spread of the middle 50% of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

To find the interquartile range (IQR), we first need to find the median of the data set.

The median is the middle value of the dataset when the data is arranged in order. In this case, the data set is already in order, so the median is the middle value or the average of the two middle values:

Median = (26 + 28) / 2 = 27

Now, we need to find the first quartile (Q1) and the third quartile (Q3) of the data set.

Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set.

Lower half: 22, 24, 26

Upper half: 28, 30

Q1 = median of the lower half = (24 + 26) / 2 = 25

Q3 = median of the upper half = (28 + 30) / 2 = 29

Now we can find the IQR:

IQR = Q3 - Q1 = 29 - 25 = 4

Therefore, the interquartile range (IQR) of the given data set is 4.

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,Based on the information, we need to consider 5 terms in the series for the sum to exceed 1507.

Substituting the given values, we get:

1507 < -3(1 - (-4)^n)/(1 - (-4))

Simplifying this inequality, we get:

-4^n < 502

Taking the logarithm of both sides, we get:

n*log(4) > log(502)

n > log(502)/log(4)

n > 4.29

n = 5

Therefore, we need to consider 5 terms in the series for the sum to exceed 1507.

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y = 6

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

The value of Y in the equation Y/4 = 3/2 is 6.

To find the value of Y, we'll use the following steps:

1. We start with the given equation:

Y/4 = 3/2.

2. Our goal is to isolate Y. To do this, we'll multiply both sides of the equation by 4, which is the denominator on the left side.

3. Multiplying both sides by 4 gives us: (Y/4) * 4 = (3/2) * 4.

4. On the left side, the 4s cancel out, leaving just Y: Y = (3/2) * 4.

5. Now, we simplify the right side by multiplying 3/2 by 4. We can think of 4 as 4/1, so the equation becomes: Y = (3/2) * (4/1).

6. Multiply the numerators (3*4) and denominators (2*1) separately: Y = (12/2).

7. Finally, simplify the fraction: Y = 6.

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a) Here is the chart showing the number of bacteria after 0 to 4 hours:

| Time (hours) | Number of bacteria |

|--------------|--------------------|

| 0 | 50 |

| 1 | 150 |

| 2 | 450 |

| 3 | 1,350 |

| 4 | 4,050 |

b) To write an expression that models the number of bacteria after a number of hours, n, we can use the formula:

In this case, the initial number of bacteria is 50, and the growth factor is 3 (since the number of bacteria triples every hour). Therefore, the expression that models the number of bacteria after n hours is:

c) To determine the number of bacteria that are present after 12 hours using the expression we derived in part b), we can substitute n = 12 into the expression:

= 26572050

The expression that represents the total cost for Lucas to attend the lessons if each bus ride costs X dollars is:13n + Xn = (13+X)n

Cost is the most significant factor to determine success when you are operating a business. You need to understand different cost factors and how it affects profitability. We define costs as the value of money required to produce a product or deliver goods. In this section, we have explained different cost definitions.

If each lesson costs $13 and Lucas attends "n" lessons, then the total cost for the lessons will be 13n dollars.

Now, let's consider the cost of the bus rides. Lucas takes the bus to each lesson, so he takes "n" bus rides in total. If each bus ride costs X dollars, then the total cost of the bus rides will be Xn dollars.

Finally, Lucas walks home after each lesson, so there is no cost associated with walking.

Therefore, the expression that represents the total cost for Lucas to attend the lessons if each bus ride costs X dollars is:

13n + Xn = (13+X)n

So If each lesson costs $13 and Lucas attends "n" lessons, then the total cost for the lessons will be 13n dollars.

Now, let's consider the cost of the bus rides. Lucas takes the bus to each lesson, so he takes "n" bus rides in total. If each bus ride costs X dollars, then the total cost of the bus rides will be Xn dollars.

Finally, Lucas walks home after each lesson, so there is no cost associated with walking.

Therefore, the expression that represents the total cost for Lucas to attend the lessons if each bus ride costs X dollars is:

13n + Xn = (13+X)n

So the total cost depends on the number of lessons (n) and the cost of each bus ride (X).

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The money multipliers are:

(a) 25.000

(b) 8.000

(c) 2.500

(d) 5.000

The money multiplier represents the amount of money the banking system can create through the lending process for every dollar of reserves held by the central bank. It is inversely related to the reserve requirement, which is the percentage of deposits that banks are required to hold as reserves.

When the reserve requirement is low, su

The money multiplier is given by the formula:

Money multiplier = 1 / Reserve requirement

(a) When the reserve requirement is 0.040, the money multiplier is:

Money multiplier = 1 / 0.040 = 25.000

(b) When the reserve requirement is 0.125, the money multiplier is:

Money multiplier = 1 / 0.125 = 8.000

(c) When the reserve requirement is 0.400, the money multiplier is:

Money multiplier = 1 / 0.400 = 2.500

(d) When the reserve requirement is 0.200, the money multiplier is:

Money multiplier = 1 / 0.200 = 5.000

Therefore, the money multipliers are:

(a) 25.000

(b) 8.000

(c) 2.500

(d) 5.000

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Answer:

f(5) = 167

Step-by-step explanation:

To evaluate f(x) = 7x^2 - 8 when x = 5, we substitute 5 for x in the expression and simplify. Therefore, we have:

f(5) = 7(5)^2 - 8

f(5) = 7(25) - 8

f(5) = 175 - 8

f(5) = 167

So, f(5) = 167

Ann has failed to meet the condition called the "success-failure" condition.

In order to construct a confidence interval for the proportion (p), the sample must have at least 10 successes (planning to travel outside the state) and 10 failures (not planning to travel outside the state). In her sample of 29 students, she found 12 planning to travel (successes) and 17 not planning to travel (failures). Both numbers satisfy the success-failure condition, so she can construct the confidence interval for the proportion of students planning to travel outside the state during the coming summer.

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Answer:

C: The sample must be a random sample from the population

Step-by-step explanation:

took the test on edge

To express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4), we need to find the values of r and s such that:

u = rv + sw

Substituting the given values, we get:

(7, -10) = r(2, 1) + s(1,4)

Using the symbolic notation, we can write this as a system of equations:

7 = 2r + s
-10 = r + 4s

We can solve this system of equations by using the elimination method:

Multiply the second equation by 2:

7 = 2r + s
-20 = 2r + 8s

Subtracting the first equation from the second, we get:

-27 = 7s

Dividing both sides by 7, we get:

s = -27/7

Substituting this value of s into the first equation, we get:

7 = 2r - 27/7

Multiplying both sides by 7, we get:

49 = 14r - 27

Adding 27 to both sides, we get:

76 = 14r

Dividing both sides by 14, we get:

r = 38/7

Therefore, u = (7, -10) can be expressed as the linear combination:

u = (38/7)(2,1) + (-27/7)(1,4)

Using fractions where needed, the answer is:

u = (76/7, 38/7) + (-27/7, -108/7)
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The measure of the other side of the right triangle is given as follows:

12 cm.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The parameters for this problem are given as follows:

Hence the other side has the length given as follows:

5² + x² = 13²

25 + x² = 169

x² = 144

x = 12.

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The volume of the container is  2216 liters

Using the general gas law, we have that;

PV = nRT

Such that the parameters are given as;

From the information given, we have that;

Substitute the values

3V = 4 × 8.31 × 200

Multiply the values, we have;

3V = 6648

Divide both sides by the coefficient of V, we get;

V = 2216 liters

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Answer is 27,529.82
To calculate the total purchase price of the car including tax, license, and title, we need to add the down payment, the financed balance, the sales tax, and the license and title charges.

First, we calculate the down payment:
10% of $25,625 = $2,562.50

Next, we calculate the financed balance:
$25,625 - $2,562.50 = $23,062.50

Then, we calculate the sales tax:
7.5% of $23,062.50 = $1,729.69

Finally, we add the license and title charges:
$1,729.69 + $175.13 = $1,904.82

So the total purchase price of the car including tax, license, and title is:
$2,562.50 + $23,062.50 + $1,904.82 = $27,529.82

Rounded to the nearest cent, the answer is option D: $27,735.14.

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Using boosting with 1,000 trees on the Hitters data set, after removing observations with unknown salary information and log-transforming salaries, results in a test set MSE (Mean Squared Error) value.


1. Remove observations with unknown salary information from the Hitters data set.
2. Log-transform the remaining salaries.
3. Create a training set with the first 200 observations and a test set with the remaining observations.
4. Apply the boosting algorithm on the training set, using 1,000 trees as the parameter.
5. Evaluate the performance of the boosting model on the test set by calculating the Mean Squared Error (MSE). The test set MSE will give you an indication of the model's accuracy in predicting salary based on the provided data.

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The second hand of a clock rotates once around the clock face in 60 seconds or one minute. Therefore, in 4 minutes, the second hand will rotate 4 times around the clock face.

The length of the second hand of a clock is 8 cm. The distance traveled by the top of the second hand in one full rotation is equal to the circumference of a circle with radius 8 cm, which is 2πr = 2π(8) = 16π cm.

The distance traveled by the top of the second hand in 4 rotations (or 4 minutes) is:

4 rotations * 16π cm/rotation = 64π cm

So the distance traveled by the top of the second hand of a clock in 4 minutes if the hand is 8 cm long is approximately 64π cm or about 201.06 cm (when rounded to two decimal places).

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Answer:

a= 2.9cm

Step-by-step explanation:

area =25 so 17a=50

50/17=2.941176...

A reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.

To determine a reasonable estimate for the amount of flour and sugar combined, we first need to add the fractions 1/4 and 2/9. To do this, we need to find a common denominator. The least common multiple of 4 and 9 is 36. We can convert 1/4 to 9/36 by multiplying both the numerator and denominator by 9. We can also convert 2/9 to 4/36 by multiplying both the numerator and denominator by 4. Now we can add the fractions:

9/36 + 4/36 = 13/36

So Ellen mixed 13/36 kg of flour and sugar combined. To convert this to a decimal, we can divide the numerator by the denominator:

13 ÷ 36 ≈ 0.36

Therefore, a reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.

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The area of ΔEFG is approximately 6.7 square centimeters.

To find the area of ΔEFG with given sides g = 5.2 cm, e = 5.1 cm, and ∠F = 42°, you can use the formula for the area of a triangle when two sides and the included angle are known. This formula is:

Area = (1/2)ab * sin(C)

In this case, a = g, b = e, and C = ∠F. Plug in the values:

Area = (1/2)(5.2 cm)(5.1 cm) * sin(42°)

Area ≈ 6.675 square centimeters

So, the area of ΔEFG is approximately 6.7 square centimeters to the nearest 10th of a square centimeter.

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