You have just used the network planning model and found the critical path length is 30 days and the variance of the critical path is 25 days. The probability that the project will be completed in 33 days or less is equal to:_______.

Answer:

DC = 10.93 cm ,  AC = 9.8 cm

Step-by-step explanation:

From trigonometry;

⇒ Tan 60 = AB/BD

⇒AB = BD Tan 60 ( where BD = 4 cm )

⇒ AB = 6.93 cm

Also, AB=BC , therefore;

⇒ BC = 6.93 cm

⇒ Cos 60 = BD/AD

⇒ AD = BD/ Cos 60 = 4/Cos 60

⇒ AD = 8 cm

From Pythagoras theorem;

⇒ [tex]AC^{2}[/tex] = [tex]AB^{2}[/tex] + [tex]BC^{2}[/tex] = [tex](6.93)^{2}[/tex] + [tex](6.93)^{2}[/tex]

⇒ AC = [tex]\sqrt{96.05}[/tex] = 9.80 cm

⇒ DC = BD + BC = 4 + 6.93

⇒ DC = 10.93 cm

Answer: 623 inches

Step-by-step explanation:

We can model this escalator as a right triangle, in which its length is the hypotenuse and its vertical rise ([tex]x[/tex]) is on of the sides of the triangle (as shown in the figure).

So, if we want to find [tex]x[/tex] we have to use the trigonometric function sine:

[tex]sin(15\°)=\frac{opposite-side}{hypotenuse}[/tex] (1)

Here, the opposite side is [tex]x[/tex] and the hypotenuse is [tex]200 ft 9 in[/tex].

Now we have to transform  [tex]200 ft 9 in[/tex] to inches, in this case we only have to convert [tex]200 ft[/tex] to inches, knowing that [tex]1 ft=12 in[/tex]:

[tex]200 ft \frac{12 in}{1 ft}=2400 in[/tex]

[tex]200 ft + 9 in=2400 in+ 9 in=2409 in[/tex]

Substituting this value in (1):

[tex]sin(15\°)=\frac{x}{2409 in}[/tex] (2)

Isolating [tex]x[/tex]:

[tex]x=frac{sin(15\°)}{2409 in}[/tex]

Finally:

[tex]x=623.49 in \approx 623 in[/tex]

Step-by-step explanation:

(a) If g is the number of gallons left in the tank, and t is the time in hours since 8AM:

g = 8 gal − (1 gal / 24 mi) (60 mi / 1 hr) (t hr)

g = 8 − 2.5t

(b) If d is the distance traveled:

d = 60 mi/hr × t hr

d = 60t

(c) When George runs out of gas, g = 0.

0 = 8 − 2.5t

t = 3.2

The distance he travels is:

d = 60(3.2)

d = 192

George travels 192 miles.

3.2 hours after 8AM, the time is 11:12AM.

well, we know the sine, and we also know that we're on the II Quadrant, let's recall that on the II Quadrant sine is positive whilst cosine is negative.

[tex]\bf sin^2(\theta)+cos^2(\theta)=1~\hspace{10em} tan(\theta )=\cfrac{sin(\theta )}{cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ sin^2(a)+cos^2(a)=1\implies cos^2(a) = 1-sin^2(a) \\\\\\ cos^2(a) = 1-[sin(a)]^2\implies cos^2(a) = 1-\left( \cfrac{3}{4} \right)^2\implies cos^2(a) = 1-\cfrac{3^2}{4^2} \\\\\\ cos^2(a) = 1-\cfrac{9}{16}\implies cos^2(a) = \cfrac{7}{16}\implies cos(a)=\pm\sqrt{\cfrac{7}{16}}[/tex]

[tex]\bf cos(a)=\pm\cfrac{\sqrt{7}}{\sqrt{16}}\implies cos(a)=\pm\cfrac{\sqrt{7}}{4}\implies \stackrel{\textit{on the II Quadrant}}{cos(a)=-\cfrac{\sqrt{7}}{4}}\\\\[-0.35em]~\dotfill\\\\tan(a)=\cfrac{sin(a)}{cos(a)}\implies tan(a)=\cfrac{~~\frac{3}{4}~~}{-\frac{\sqrt{7}}{4}}\implies tan(a)=\cfrac{3}{4}\cdot \cfrac{4}{-\sqrt{7}}\\\\\\tan(a)=-\cfrac{3}{\sqrt{7}}\implies \stackrel{\textit{rounded up}}{tan(a) = -1.13}[/tex]

Answer:

Step-by-step explanation:

Let h represent the number of hours that Jamarcus can rent the truck.

To rent a truck, the charge is $16 per hour and also a fueling fee of $25

The total cost of renting the truck for x hours would be

16h + 25

Since Jamarcus wants to rent the truck and can spend no more than $125, the inequality representing the situation would be

16h + 25 ≤ 125

16h ≤ 125 - 25

16h ≤ 100

h ≤ 6.25

2) 3x - 5 ≥ - 11

3x ≥ - 11 + 5

3x ≥ - 6

x ≥ - 6/3

x ≥ - 2

The correct graph is option A

Answer:

a

Step-by-step explanation:

The answer is in the attachment

Answer: the length if the ramp is 47.17 feet

Step-by-step explanation:

The wheelchair ramp makes an angle of 11 degrees with the ground and forms a right angle triangle. The length of the ramp becomes the hypotenuse of the right angle triangle.

The distance of the platform from the ground level forms the opposite side of the right angle triangle.

To determine the length of the ramp, h, we would apply the Sine trigonometric ratio. It is expressed as

Sin θ = opposite side/hypotenuse

Therefore,

Sin 11 = 9/h

h = 9/Sin 11 = 9/0.1908

h = 47.17 feet

Answer:

g6h12

Step-by-step explanation:

Answer:  mmmmm.

Step-by-step explanation:

Answer:question 1)$6.66.67

Question2) Rent and expenses =$760

Rent and expenses are too high for the budget

Step-by-step explanation:

1)$2000×(1/3)= $666.67

2)Rent and expenses =$(650+60+10+20+20)= $760

$2100×(1/3)= $700

Rent and expenses should not exceed one third of $2100, which is $700 but it exceeded by$60. Therefore budget is too high.

Final answer:

These Mathematics questions involve calculating budgets to manage income and expenses. For budgeting housing costs, the recommendation is not to exceed one-third of income. A budget table is used to track all monthly expenses against income to determine savings potential and necessary adjustments.

Explanation:

The subject of these questions is Mathematics, specifically focusing on budgeting and personal finance. In these scenarios, students are learning to apply mathematical operations to real-life situations involving income, expenses, and budget planning.

For question 1, you would calculate the maximum amount you should spend on housing from a $2,000 monthly budget by dividing $2,000 by 3, which gives you $666.67. This is because it's recommended to spend no more than one-third of your income on housing.

For question 2, adding together the rent and housing expenses ($650 + $60 + $10 + $20 + $20), you get a total of $760. If you have an income of $2,100, you should not spend more than $700 on housing (which is one-third of your income), so $760 is indeed too high for the budget.

Creating a budget table is an essential skill for financial literacy. When constructing one, you list your monthly income and subtract all your expenses, including housing, utilities, groceries, and any other costs, to see what is left for savings and discretionary spending. For example, with an after-tax monthly income of $2,589.10, if you spend $790 on rent, $75 on a cell phone, and have other listed expenses, you'd subtract all these from your income to see if you can save the desired 10%.

Answer:

The question continues ; Which of the following is true ;

Jaylan basis in the partnership is $12,00 and Caspers is 10,000

Jaylan and Casper each have a basis in the partnership of 12,000

Jaylan will have a larger share of the profits than Casper

The first and third answers are both correct

Answer ; Jaylan and Casper each have a basis in the partnership of 12,000

Step-by-step explanation:

Both Jaylan and casper will have a partnership basis of $12,000 , it was mentioned initially in the question that (Jaylan and casper are equal partners in J&C racoon hats), equal partners implies both Jaylan and casper with have equal profit and equal losses as the case maybe Irrespective of the amount each contributed. Hence Jaylan and Casper each have a basis in the partnership of 12,000.

The stiffness of one short spring is 13500 N/m

Solution:

We are given a chain with number of spring N = 30 and linked end to end ( in series) and stiffness of this chain is 450 N/m

We have to find the stiffness of one short spring

The springs are identical, which means they have same stiffness

The stiffness of one spring in series is given as:

[tex]k_i = N \times k_s[/tex]

Where,

N is the number of springs

[tex]k_i[/tex] is the stiffness of one spring

[tex]k_s[/tex] is the stiffness of this chain

Substituting,

[tex]N = 30\\\\K_s = 450[/tex]

Therefore,

[tex]k_i = 30 \times 450\\\\k_i = 13500[/tex]

Thus the stiffness of one short spring is 13500 N/m

If a chain of 30 identical short springs linked end-to-end has a stiffness of 450 N/m , The stiffness of one short spring is 13500 N/m

Given : Stiffness = 450 N/m,

To find : the stiffness of one short spring

According to the given question,

We knows that,

The springs are identical, by which means they have the same stiffness

Hence, The stiffness of one spring will be given as:

              [tex]\rm k_i=N \times k_s[/tex]  

Where,

On substituting the values in the formula we will get,

        N = 30

        [tex]\rm k_s[/tex] = 450

Then,

           [tex]\rm k_i =30 \times450\\\\k_i = 13500[/tex]

Therefore, The stiffness of one short spring is 13500 N/m

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Answer:

Step-by-step explanation:

Part 1:

An equation of sine wave can be written as y = 5 Sin(2x + 3).

The amplitude of the above equation is 5.

The period of the function is [tex]\frac{2\pi }{2} = \pi[/tex].

The frequency of the function is [tex]\frac{1}{\pi }[/tex].

Part 2:

[tex]y = 2 Sin(3x + 5) + 9.......(1)\\y = 5 Sin(4x + 8) + 12.....(2)\\y = 3 Sin(x + 6) + 2......(3)[/tex]

The above given equations numbered 1, 2 and 3 represents three different sound waves.

For (1), the frequency is [tex]\frac{1}{\frac{2\pi }{3} } = \frac{3}{2\pi }[/tex].

For (2), the frequency is [tex]\frac{4}{2\pi } = \frac{2}{\pi }[/tex].

For (3), the frequency is [tex]\frac{1}{2\pi }[/tex].

Frequency of sounds refers the speed of vibration.

The taken three siounds has different frequencies.

Answer:

a) 21.2%

b)  $176.05 or more

c) 15.87%    

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $155

Standard Deviation, σ = $25

We are given that the distribution of spending amounts is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

a) P(spends more than $175 per week on groceries)

P(x > 175)

[tex]P( x > 175) = P( z > \displaystyle\frac{175 - 155}{25}) = P(z > 0.8)[/tex]

[tex]= 1 - P(z \leq 0.8)[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(x > 175) = 1 - 0.788 = 0.212 = 21.2\%[/tex]

b) P(X > x) = 0.2

We have to find the value of x such that the probability is 0.2

P(X > x)  

[tex]P( X > x) = P( z > \displaystyle\frac{x - 155}{25})=0.2[/tex]  

[tex]= 1 -P( z \leq \displaystyle\frac{x - 155}{25})=0.2 [/tex]  

[tex]=P( z \leq \displaystyle\frac{x - 155}{25})=0.8 [/tex]  

Calculation the value from standard normal z table, we have,  

[tex]P(z < 0.842) = 0.8[/tex]

[tex]\displaystyle\frac{x - 155}{25} = 0.842\\\\x = 176.05[/tex]  

A consumer has to spend approximately $176.05 or greater to be in the top 20% of the distribution.

c) My family spends on average $130 dollars on groceries.

P(less than $130)

[tex]P( x < 130) = P( z < \displaystyle\frac{130 - 155}{25}) = P(z < -1)[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(x < 130) = 0.1587 = 15.87\%[/tex]

Thus, my family percentile is 15.87%

a) 21.2%
b)  $176.05 or more
c) 15.87%    

We are given the following information in the question:
Mean, μ = $155
Standard Deviation, σ = $25
We are given that the distribution of spending amounts is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_(score) = \displaystyle(x-\mu)/(\sigma)[/tex]
a) P(spends more than $175 per week on groceries)
[tex]P(x > 175)P( x > 175) = P( z > \displaystyle(175 - 155)/(25)) = P(z > 0.8)= 1 - P(z \leq 0.8)[/tex]
Calculation the value from standard normal z table, we have,  
[tex]P(x > 175) = 1 - 0.788 = 0.212 = 21.2\%\\[/tex]

b) [tex]P(X > x) = 0.2[/tex]
We have to find the value of x such that the probability is 0.2
[tex]P(X > x) \\P( X > x) = P( z > \displaystyle(x - 155)/(25))=0.2 \\= 1 -P( z \leq \displaystyle(x - 155)/(25))=0.2 \\=P( z \leq \displaystyle(x - 155)/(25))=0.8[/tex]
Calculation the value from standard normal z table, we have,  
[tex]P(z < 0.842) = 0.8\\\displaystyle(x - 155)/(25) = 0.842\n\nx = 176.05[/tex]
A consumer has to spend approximately $176.05 or greater to be in the top 20% of the distribution.

c) My family spends on average $130 dollars on groceries.
P(less than $130)
[tex]P( x < 130) = P( z < \displaystyle(130 - 155)/(25)) = P(z < -1)[/tex]
Calculation the value from standard normal z table, we have,  
[tex]P(x < 130) = 0.1587 = 15.87\%[/tex]
Thus, my family percentile is 15.87%

Answer: the value of y is 180

Step-by-step explanation:

If y varies directly as x, then as y increases,x increases and as y decreases, x decreases.

We would introduce a constant of proportionality, k. Therefore,

y = kx

When y = - 18, x = - 2

Therefore,

- 18 = - 2 × k

Dividing the left hand side and the right hand side of the equation by

- 2, it becomes

- 2k/ -2 = - 18/-2

k = 9

The expression becomes

y = 9x

Therefore, when x = 20,

y = 9 × 20 = 180

Yo sup??

since y varies directly with x we can say

y=kx

at y=-18, x=-2 then

-18=k*(-2)

k=9

therefore

y=9x

at x=20

y=9*20

=180

Hope this helps.

Answer:

(1) ADB = CDB = 90°

(2) c sinA

(3) (sinA)/a = (sinB)/b

Step-by-step explanation:

1. ADB = CDB = 90°

2. c sinA

since,

sin A = x/c , sin C = x/a

so x = c sinA and a sinC

3. from reflective property of x,

since x = c sinA

and x = a sinC

we substitute each equivalently

that is,

c sinA = a sinC

dividing each sides of the equation by ac we have ,

(c sinA)/ac = ( a sinC)/ac

simplifying we have,

(sinA)/a = (sinB)/b

Therefore the above equation is referred to as the SINE RULE.

Answer: The larger rug is 4 times larger

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

The small circular rug covers an area of approximately 67 square feet. This means that

67 = πr²

r² = 67/π = 67/3.14 = 21.34

r = √21.34 = 4.62

If a large size rug has twice the dimensions of a small rug, it means that the radius of the larger rug would be

2 × 4.62 = 9.24

The area of the larger rug would be

3.14 × 9.24² = 268.06ft²

Therefore

268.06/67 = 4

The larger rug is 4 times larger

Answer: $4.50 per candle

Step-by-step explanation:

$32.55 - $17.50 - $1.55 = $13.50 for all the candles

To find the price of a single candle we divide our answer by 3

13.50/3 = $4.50

Answer:

4%

Step-by-step explanation:

Let the stock be $10

A 20% decline = 80/100 * 10

= 8

A 30% increase = 30/100 * 8

= 2.4 + 8 = 10.4.

Overall increase = 10.4 - 10 = 0.4

Percentage overall increase = 0.4/10 * 100

= 4%

Answer:

$ 270

Step-by-step explanation:

Do 250 X 1.08 to get the answer

Using the percentage increase formula, John's bank account value of $250 will increase by 8% to $270 after one year.

To find the future value of John's bank account, we will use the percentage increase formula. If his account increased by 8% this year to $250, we can calculate next year's balance by multiplying $250 by 1.08 (which represents a 100% principal plus an 8% increase).

Step-by-step calculation:

Therefore, the value of John's bank account if it increases by the same percentage over the next year will be $270.

Answer:

A

Step-by-step explanation:

Answer: the cost of Parker's tuition is $17955

Step-by-step explanation:

Let x represent the cost of Parker's tuition.

Parker was able to pay 44% of his college tuition with his scholarship. This means that the amount that he was able to pay with his scholarship would be

44/100 × x = 0.44 × x = 0.44x

The amount that is remaining for him to pay would be

x - 0.44x = 0.56x

If he paid the remaining $10,054.52 with a student loan, it means that

0.56x = 10054.52

x = 10054.52/0.56

x = 17954.5

Rounding up to the nearest whole number, it becomes

x = $17955

Final answer:

The statistic concerning the number of siblings would be the mean number of siblings for the randomly selected students, not the entire school population.

Explanation:

The question posed by the student pertains to determining the mean number of siblings for students in a school. Anna collected data by randomly selecting 75 students and recording the number of siblings for each student. The statistic in this context is d. the mean number of siblings for the randomly selected students. This is because the statistic refers to a summary measure that is calculated from a sample of data. Therefore, the statistic is the calculated average number of siblings from just those 75 students and not the entire school population.

When discussing sampling methods, one could use a completely random method or use systematic sampling with a tool such as a random number generator for selection. Regardless of the method, the primary criterion is that every member of the population has an equal chance of being included in the sample.

Final answer:

The statistic refers to the mean number of siblings for the randomly selected students, computed by dividing the sum of siblings reported by the 75 students by 75.

Explanation:

The statistic in this scenario is the mean number of siblings for the randomly selected students. The mean, or average, will be calculated by adding up the total number of siblings reported by the 75 students and then dividing that sum by 75. This statistic will serve as an estimate for the mean number of siblings for each student in the whole school. Although option b attempts a similar approach with systematic sampling by selecting every 50th student, the actual calculated mean from the 75 randomly selected students (which is the result of the random sampling method described in option a) is the statistic we are referring to. Option c is asking for a different kind of statistic related to stress scores.

Answer: 233,168

Step-by-step explanation:

Formula: 1 + 2 + 3 + ... + n = n(n+1)/2

Sum of all the numbers below 1000 that is divisible by 3:

3 + 6 + 9 + ... + 999 = 3 (1 + 2 + 3 + ... + 333) = 3 x 333 x 334 / 2 = 166,833

Sum of all the numbers below 1000 that is divisible by 5:

5 + 10 + 15 + ... + 995 = 5 (1 + 2 + 3 + ... + 199) = 5 x 199 x 200 / 2 = 99,500

As we add up 166,833 and 99,500, the numbers that are divisible by 3*5 = 15 would be counted double. Therefore, subtract the result for numbers divisible by 15 just once:

Sum of all numbers below 1000 that is divisible by 15:

15 + 30 + 45 + ... + 990 = 15 (1 + 2 + 3 + ... + 66) = 15 x 66 x 67 / 2 = 33165

Therefore, [ 166,833 + 99,500 ] - 33,165 = 233,168

To find the sum of all the multiples of 3 or 5 below 1000, you need to find the sum of the multiples of 3 and 5 separately and then subtract the sum of the multiples of 15. The sum is 233,003.

To find the sum of all the multiples of 3 or 5 below 1000, we can use the concept of arithmetic series. First, we need to find the sum of the multiples of 3 and the sum of the multiples of 5 below 1000. Then, we need to subtract the sum of the multiples of 15 (since numbers that are multiples of both 3 and 5 have been counted twice).

Using the formula for the sum of an arithmetic series, the sum of the multiples of 3 below 1000 is given by:

3 + 6 + 9 + ... + 999 = (1/2)(3 + 999)(333) = 166,833

Similarly, the sum of the multiples of 5 below 1000 is:

5 + 10 + 15 + ... + 995 = (1/2)(5 +995)(199) = 99,500

Finally, the sum of the multiples of 15 below 1000 is:

15 + 30 + 45 + ... + 990 = (1/2)(15 + 990)(66) = 33,330

Now, we can calculate the sum of all the multiples of 3 or 5 by adding the sum of the multiples of 3 to the sum of the multiples of 5 and then subtracting the sum of the multiples of 15:

166,833 + 99,500 - 33,330 = 233,003

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Step-by-step explanation:

The given four sides of quadrilateral = (1,3), (5,3), (7,-1) and (1,-1)

To find, the area of the shape (quadrilateral) = ?

We know that,

The area of quadrilateral = [tex]\dfrac{1}{2} [x_{1}( y_{2}-y_{3})+x_{2}( y_{3}-y_{4})+x_{3}( y_{4}-y_{1})+x_{4}( y_{1}-y_{2})][/tex]

= [tex]\dfrac{1}{2} [1( 3+1)+5( -1+1)+7( -1-3)+1}( 3-3)][/tex]

= [tex]\dfrac{1}{2} [1(4)+5( 0)+7( -4)+1}( 0)][/tex]

= [tex]\dfrac{1}{2} [4+0-28+0][/tex]

= [tex]\dfrac{1}{2} [32][/tex]

= 16 square units.

Thus, the area of the shape (quadrilateral) is 16 square units.

Answer:

Aidan got 56% of votes.

Step-by-step explanation:

Given:

Aidan is running for student body president. In today's election, he received 462 votes out of a total of 825 votes cast.

Now, to find the percent of votes did Aidan get.

Total votes cast = 825 votes.

Votes he received = 462 votes.

Now, to get the percent of votes Aidan get:

[tex]\frac{Votes\ he\ received}{Total\ votes\ cast} \times 100[/tex]

[tex]=\frac{462}{825} \times 100[/tex]

[tex]=0.56\times 100[/tex]

[tex]=56\%.[/tex]

Therefore, Aidan got 56% of votes.

Answer:

56%

Step-by-step explanation:

Aidan got fifty-six percent of the votes.

To solve this problem, start by letting p represent the unknown percent and write the percent as the fraction p over one hundred.

Write a second ratio that expresses the part-whole relationship between the numbers four hundred sixty-two over eight hundred twenty-five.

Set up a proportion between the two ratios.

Write the cross product equation. Eight hundred twenty-five p equals one hundred times four hundred sixty-two, or eight hundred twenty-five p equals forty-six thousand two hundred.

Divide each side of the equation by eight hundred twenty-five to solve for p.

p equals fifty-six.

Aidan received fifty-six percent of the votes cast.

Answer:

C) ¼ ∫ u⁵ du, where u = sin(4x)

Step-by-step explanation:

∫ cos(4x) sin⁵(4x) dx

Using u substitution:

u = sin(4x)

du = 4 cos(4x) dx

¼ du = cos(4x) dx

¼ ∫ u⁵ du

Answer: A. Approximately 0.017 pounds

Step-by-step explanation:

Formula to find the margin of error :

[tex]E=z^*\dfrac{s}{\sqrt{n}}[/tex] , where z* = critical value for confidence interval , s= standard deviation , n= sample size.

As per given , we have

s= 0.15 pound

n= 300

Critical value for 95% confidence = 1.96

Then, Margin of error for 9%% confidence interval will be :

[tex]E=(1.96)\dfrac{0.15}{\sqrt{300}}\\\\=0.0169740979142\approx0.017[/tex]

Hence, they can expect a margin error of 0.017 pound (approximately.)

Thus , the correct answer is A. Approximately 0.017 pounds

Answer:

48 bags are needed by George to fill his sandbox.

Step-by-step explanation:

Given:

Total capacity of the sandbox (V) = 32 cubic feet

Capacity of each bag = (B) = [tex]\frac{2}{3}[/tex] cubic feet

Now, number of bags required (N) = ?

The formula to find the total number of bags required to fill the sandbox is given as:

[tex]Number\ of\ bags=\frac{Total\ capacity\ of\ sandbox}{Capacity\ of\ each\ bag}\\\\N=\frac{V}{B}[/tex]

Now, plug in the given values and solve for 'N'. This gives,

[tex]N=32\div\frac{2}{3}[/tex]

In order to multiply a whole number with a fraction, we replace the division sing by multiplication and take the reciprocal of the fractional number. This gives,

[tex]N=32\times \frac{3}{2}\\\\N=\frac{32\times 3}{2}\\\\N=16\times 3=48[/tex]

Therefore, 48 bags are needed by George to fill his sandbox.

George needs 48 bags of sand, each holding 2/3 cubic feet, to fill his sandbox that requires 32 cubic feet of sand.

To determine how many bags of sand are required to fill George's sandbox that has a volume of 32 cubic feet, when each bag holds 2/3 cubic feet of sand, we need to perform a division operation. We divide the total volume (32 cubic feet) by the volume each bag holds (2/3 cubic feet).

The calculation is as follows:

Find the inverse of 2/3 which is 3/2.

Multiply the total volume by the inverse. 32 × (3/2) = 32 × 1.5 = 48.

Thus, George would need 48 bags of sand to fill his sandbox.

The correct answer would be B.

The lower e is used for continuous compounding and it is raised by the interest rate times the amount of time

Formula  that describes the value of an initial investment of [tex]\$300[/tex] growing at an interest rate of [tex]6\%[/tex] compounded continuously is equals to [tex]A(t) = 300e^{.06t}[/tex].

" Compounded continuously is defined as the interest calculation and reinvestment of the amount over infinite period."

Formula used

[tex]A(t) = P e^{rt}[/tex]

[tex]A(t) =[/tex] Final amount

[tex]P =[/tex] Principal amount

[tex]t =[/tex]  time period interest is applied

[tex]r=[/tex] rate of interest

According to the question,

Given,

Principal amount [tex]= \$300[/tex]

Rate of interest [tex]= 6\%[/tex]

As per the given condition interest compounded continuously,

Substitute the value in the formula of interest compounded continuously  we get,

[tex]A(t) = 300 e^{\frac{6}{100} t}\\\\\implies A(t) = 300 e^{.06 t}[/tex]

Hence, Option (B) is the correct answer.

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Answer:

Step-by-step explanation:

Ben's car gets between 18 and 21 miles per gallon of gas. If his car's tank holds 15 gallons, it means that the least distance that Ben can drive on one tank of gas would be

18 × 15 = 270 miles.

Also, the most distance that Ben can drive on one tank of gas would be

21 × 15 = 315 miles.

Therefore the the range of distance that Ben can drive on one tank of gas is between 270 miles and 315 miles. If d represents the distance, then the range is

270 ≤ d ≤ 315)

Answer:

Step-by-step explanation:

p = 120 ± 4