a car's velocity is modeled by
\( v(t) = 0.5t {}^{2} - 10.5t + 45 \: for\leqslant t \leqslant 10.5\)
Where velocity is in feet per second and time is in seconds. When does the car come to a complete stop?​

The formula for calculating the volume of a cone is expressed as

Volume = 1/3πr^h

where

r is the radius of the cone

h is the height of the cone

From the information given,

diameter = 6

r = diameter/2 = 6/2 = 3

h = 8

π = 3.14

Thus,

Volume = 1/3 x 3.14 x 3^2 x 8

Volume = 75.36 ft^3

Answer: f(x)= -76

Step-by-step explanation:

Plug the given value in where you see x

f(x) = 4(-16) - 12

f(x) = -64 - 12

f(x)= -76

Answer:

-76

Step-by-step explanation:

f(-16)=4(-16)-12

f(-16)=-64-12

f(-16)=-76

PART (A):

As the total amount increases double each month. It is a geometric sequence equation. Fill the table.

Geometric Sequence: y = a(r)ˣ⁻¹

Here given:
First term (a) = 40
Common Difference (d) = 2

Equation: y = 40(2)ˣ⁻¹

After 1 year: y = 40(2)¹²⁻¹ = $81920

\(\rule{300}{1}\)

PART (B):

As the amount increases by $50 each month. It is a arithmetic or linear sequence.

Linear Equation: y = mx + b

Here given:
slope (m) = 50
starting (b) = 30

Equation: y = 50x + 30

After 1 year: y =  50(12) + 30 = 630

#a

Use geometric progression formula

Here

First term =2(20)=40

Equation

\(\\ \rm\Rrightarrow y=40(2)^{n-1}\)

After a year

\(\\ \rm\Rrightarrow y=40(2)^{11}\)

\(\\ \rm\Rrightarrow y=40(2048)\)

\(\\ \rm\Rrightarrow y=\$81920\)

#b

It's arithmetic as common difference is 50

\(\\ \rm\Rrightarrow a_n=a+(n-1)d\)

Equation

\(\\ \rm\Rrightarrow a_n=80+(n-1)50\)

After a year

\(\\ \rm\Rrightarrow a_{12}=80+11(50)\)

\(\\ \rm\Rrightarrow 80+550\)

\(\\ \rm\Rrightarrow \$630\)

The cartons of food and clothing that should be sent to maximize the number of people assisted are 300 and 400 respectively.

In order to determine the required number of cartons of food and clothing, we would have to first of all write a system of equations that models the situation.

Additionally, we would assign variables to the carton of food box and number of accessories sold, and then translate the word problem into algebraic equation as follows:

Therefore, translating the word problem into algebraic equation, we have the following:

20x + 30y ≤ 18000      ......equation 1.

40x + 10y ≤ 16000      ......equation 2.

Dividing both equations 1 and 2 by 10, we have:

2x + 3y ≤ 1800

4x + y ≤ 1600

Next, we would solve the system of equations simultaneously as follows:

2x + 3(1600 - 4x) ≤ 1800

2x + 4800 - 12x ≤ 1800

-10x ≤ -3000

x ≤ 3000/10

x ≤ 300

For the value of y, we have:

y ≤ 1600 - 4(300)

y ≤ 1600 - 1200

y ≤ 400

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Complete Question:

An agency wants to ship food and clothing to hurricane victims in Louisiana. Commercial carriers have volunteered to transport the​ packages, provided they fit in the available cargo space. Each ​20ft³ box of food weighs 40 lb and each ​30 ft³ box of clothing weighs 10 lb. The total weight cannot exceed​ 16,000 lb, and the total volume must be at most​ 18,000 ft³. Each carton of food will feed 8 ​people, while each carton of clothing will help 8 people.

How many cartons of food and clothing should be sent to maximize the number of people assisted?

Answer:

2

Step-by-step explanation:

( 3x + 6 ) ( 4x - 8 ) = 0

( 3x + 6 ) = 0 / ( 4x - 8 )

3x + 6 = 0

3x = 6

x = 6 / 3

x = 2

Without any values of the functions f, g, h, and k, it is not possible to find the equation of each function. The equation of a function can be determined by analyzing the values of the function. Based on the given values, a possible equation can be found and then verified by plotting the points on a graph and seeing if they align with the equation.

It's important to note that the equation can be a linear or exponential equation but it's impossible to determine it without any values.

Answer:

Below

Step-by-step explanation:

Find unit rate (since it starts at 0,0)

at 45 seconds  it is 900 bottles

             900 bottles / 45 seconds = 20 bottle / sec

20 bottles / sec * 80 sec = 1600 bottles

Answer: 39 ft2

Step-by-step explanation:

The area of the trapezoid is 39 square feet.

To find the area of a trapezoid, you can use the formula:

Area = (1/2) × (base1 + base2) × height

Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:

Area = (1/2) × (16 + 10) × 3

Area = (1/2) × 26 × 3

Area = (1/2) × 78

Area = 39 ft^2

Therefore, the area of the trapezoid is 39 square feet.

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Answer:

2.

3.225, 3.219, 3.215, 2.9, 2.108

3.

3³, 8, sqrt 64, 22/5, 2 3/5, -0.53, -4/7, -2 2/3

Step-by-step explanation:

hope that it helps^^

Answer:

The 99% confidence interval for the proportion of donors who donated is (0.0547, 0.0585).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

For this problem, we have that:

\(n = 100000, \pi = \frac{5066}{100000} = 0.0566\)

99% confidence level

So \(\alpha = 0.01\), z is the value of Z that has a pvalue of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0566 - 2.575\sqrt{\frac{0.0566*0.9434}{100000}} = 0.0547\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0566 + 2.575\sqrt{\frac{0.0566*0.9434}{100000}} = 0.0585\)

The 99% confidence interval for the proportion of donors who donated is (0.0547, 0.0585).

Answer: how are you doing this tho

Step-by-step explanation:

The 1/3 of 5/8 as a fraction is 5/24 after applying the arithmetic operation the answer is 5/24.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

1/3 of 5/8 as a fraction

Let x be the fraction:

x = 1/3 of 5/8

Or

x = (1/3)(5/8)

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

After multiplication:

x = 5/24

Thus, the 1/3 of 5/8 as a fraction is 5/24 after applying the arithmetic operation the answer is 5/24.

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Answer:

  -1/2

Step-by-step explanation:

You want to know the exact value of sin(-5π/6).

The reference angle is the smallest angle its terminal side makes with the x-axis. The angle -5π/6 is a 3rd-quadrant angle, whose reference angle is ...

  -5π/6 +π = π/6

You know that the signs of the sine and cosine trig functions are negative in the 3rd quadrant. Since you have memorized the short table of trig functions (first attachment), you know the value you're looking for is ...

  sin(-5π/6) = -sin(π/6) = -1/2

__

Additional comment

The second attachment shows the functions that are positive in the different quadrants. The ones not listed are negative.

The third attachment shows the coordinates on the unit circle as (cos, sin). The angle 7π/6 is the same as the angle -5π/6.

The fourth attachment shows you can put your calculator in radian mode and have it tell you the answer.

Answer:

"Vx: if x is a valid argument with true premises then x has a true conclusion"

In a symbol form

Vx ( P(x) ⇒ 2(x) )

Step-by-step explanation:

The Following statement in the form  âˆ€x ______, if _______ then _______ is a valid argument and this because any valid argument with "true premises" has a "true conclusion" as well

we will rewrite this statement in a universal condition statement form

assume x is a valid argument with true premises

then the following holds true

p(x) : x is a valid argument with true premises

q(x) : x has true conclusion

applying universal conditional statement

"Vx, if x is a valid argument with true premises then x has a true conclusion"

In a symbol form

Vx ( P(x) ⇒ 2(x) )

Answer:

The 95% confidence interval for the mean time for all players, in minutes, is: (7.95, 11.01).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 10 - 1 = 9

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.95}{2} = 0.975\). So we have T = 2.2622.

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 2.2622\frac{2.14}{\sqrt{10}} = 1.53\)

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 9.48 - 1.53 = 7.95 minutes.

The upper end of the interval is the sample mean added to M. So it is 9.48 + 1.53 = 11.01 minutes.

The 95% confidence interval for the mean time for all players, in minutes, is: (7.95, 11.01).

Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.

Given that, a truck needs 7 gallons of fuel to travel 56 miles.

The truck travel 48 miles with 6 gallons of fuel.

Here, the proportion is

7:56::6:48

We know that, the proportion is product of extremes = product of means

7×48 = 56×6

336 = 336

Therefore, the correct answer is option B.

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The area of the 72-degree sector of a circle with a radius of 10 is approximately 62.8318 square units.

To find the area of a sector, you can use the formula:

Area of sector = (θ/360) * π * \(r^2\)

where θ is the central angle of the sector, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

In this case, the central angle is 72 degrees and the radius is 10. Plugging these values into the formula, we get:

Area of sector = (72/360) * π * \(10^2\)

= (1/5) * π * 100

= (1/5) * 3.14159 * 100

= 0.2 * 3.14159 * 100

= 0.628318 * 100

= 62.8318

Therefore, the area of the 72-degree sector of a circle with a radius of 10 is approximately 62.8318 square units.

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Answer:

one

Step-by-step explanation:

one is the only number that evenly adds up to six and multplys to 77

Step-by-step explanation:

4^2/3

but I got 4^-3/3

hope help ful

Answer:

3 cups

Step-by-step explanation:

The same amount of each is needed if I read that correctly.

Answer:

C) 3 5/12

Step-by-step explanation:

Answer:

Brand A  Costs 37.38 per ounce and Brand B cost 31.19 per ounce hope this helped ^-^

Answer:

y=-5/2+x

Step-by-step explanation:

An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

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Answer:

KL = 7, so B is the correct answer.

The equation for the cost of n t-shirts is c = 15 + 9(n + 1), the term 9(n + 1) represents the cost of additional shirts beyond the first shirt, and the coefficient 9 represents the amount by the cost decreases for each additional shirt.

The cost of n t-shirts is given by the equation:

c = 15 + 9(n + 1)

c is the cost in dollars and n is the number of t-shirts.

The cost for 2 t-shirts, we substitute n = 1 into the equation:

c = 15 + 9(1 + 1) = 33

So it will cost \($33\) for 2 t-shirts.

The cost for 5 t-shirts, we substitute n = 4 into the equation:

c = 15 + 9(4 + 1) = 51

So it will cost \($51\) for 5 t-shirts.

The cost of additional shirts after the first one is \($9\) per shirt.

The equation for the cost of n t-shirts is c = 15 + 9(n + 1), the term 9(n + 1) represents the cost of additional shirts beyond the first shirt, and the coefficient 9 represents the amount by which the cost decreases for each additional shirt.

The following formula calculates the price of n t-shirts: c = 15 + 9(n + 1).

n is the quantity of t-shirts, and c represents the price in dollars.

We change n = 1 to represent the price of 2 t-shirts:

c = 15 + 9(1 + 1) = 33

the price will be.

t-shirts for two.

We enter n = 4 to get the price for 5 t-shirts: c = 15 + 9(4 + 1) = 51

the price will be.

Five t-shirts worth.

After the first shirt, additional shirts cost each shirt.

The cost of n t-shirts is given by the equation c = 15 + 9(n + 1), where the phrase 9(n + 1) denotes the price of subsequent shirts after the first shirt and the coefficient 9 denotes the amount by which the cost increases.

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Answer:

Step-by-step explanation:

f(x) = cx + d

For the first equation

f(50) = 27,000

Substitute the value of x that's 50 into the expression

That's

50c + d = 27,000

For the second equation

f(100) = 38,000

Substitute the value of x that's 100 into the expression

We have

100c + d = 38,000

Subtract the first equation from the second one to eliminate d

That's

100c - 50c + d - d = 38,000 - 27,000

50c = 11,000

Divide both sides by 50

We have the final answer as

Hope this helps you

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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The quotient when 6+8i is divided by 2i is given by -3i+4.

We know that, complex number \(i^1=-1\).

Given the divisor is = 2i and dividend is = 6+8i

Dividing the dividend by divisor we get,

(6+8i)/2i = 6/2i + 8i/2i = 3/i + 4 \(=\frac{3i}{i^2}+4\) = 3i/(-1)+4 = -3i+4

Hence the quotient is = -3i+4.

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Answer:

The interval from -12 to -7

The interval from 6 to 12.

Step-by-step explanation:

The equation is log(x + 9) + log(x 9) = log[(x + 9)(x 9)]. = log(x² − 81)

Here is the equation:

log(x² - 81) = 0.47712

This can be expressed in exponential form:

x² - 81 = 10^(0.47712)

x² = 81 + 3.02343

x² = 84.02343

x ≈ ± 9.1658

The answers are therefore x -9.1658 and x 9.1658.

These intervals are where these solutions occur:

The answer, x -9.1658, can be found in the range from -12 to -7.

- The answer x = 9.1658 is found in the range of 6 to 12.

The appropriate choices are:

- The range between -7 and -12; - The range between 6 and 12.

Answer:

$8515.13

Step-by-step explanation:

Given :

Interest rate, r =. 1.25% = 0.0125 compounded quarterly

Principal = 8000

Number of years, t = 5 years

Compound interest :

A = P(1 + r/n)^nt

A = final amount ; n = number of compounding times per period

n = 4 (quarterly)

A = 8000(1 + 0.0125/4)^4*5

A = 8000(1 + 0.003125)^20

A = 8000(1.003125)^20

A = 8000 * 1.0643907

A = 8515.1258

Final. Amount to. Be repaid = $8515.13