Use multiplication. 4 times what number is about 35? 35÷4

Answer:

The amount paid as VAT is $ 12800.

Step-by-step explanation:

Sales = $ 80,000

VAT = 16 %

The amount of VAT paid to the government is

= 16 % of $ 80,000

= 0.16 x $ 80,000

= $ 12800

The amount paid as VAT is $ 12800.

The dimensions of the outdoor enclosure with the most area is 250 feet and 125 feet.

One side of the store is 270 feet long

There are 500 feet of fencing available for the other three sides of the enclosure.

The Perimeter of rectangular outdoor storage = 2x + y

2x + y = 500

To maximize the area

y = 500 - 2x...............(1)

Area of rectangle;

A = xy

Now putting the value of y

A = x(500 - 2x)

Solve

A = 500x - 2x^2...................(2)

To finding the value of x differentiating on both side with respect to x.

dA/dx = 500 - 4x...................(3)

Equating dA/dx = 0

500 - 4x = 0

Subtract 4x on both side, we get

4x = 500

Divide by 4 on both side, we get

x = 125

Now putting the value of x in equation 1

y = 500 - 2(125)

y = 500 - 250

y = 250

Differentiating equation 3 again with respect to x

d^2A/dx^2 = -4 < 0 (Maximum)

Hence, for the maximum storage area

Length parallel to the store wall = 250 feet

Length perpendicular to the store wall = 125 feet

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The grade resistance of the 2900-pound car traveling on a 1.8° uphill grade is approximately 90.446 pounds.

To calculate the grade resistance of a car, we can use the equation:

Grade Resistance (F) = Weight of the car (W) * sin(θ)

Given that the weight of the car is 2900 pounds and the uphill grade is 1.8 degrees, we can calculate the grade resistance:

F = 2900 * sin(1.8°)

Using a calculator, the value of sin(1.8°) is approximately 0.031246.

F ≈ 2900 * 0.031246

F ≈ 90.446 pounds

Therefore, the grade resistance of the 2900-pound car traveling on a 1.8° uphill grade is approximately 90.446 pounds.

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Answer:

x=17 degrees

Step-by-step explanation:

All 3 angles = 180 degrees

So 90 + 54 + (x+19) = 180

Combine like terms

163 + x = 180

Subtract 163 from both sides

x = 180-163

x = 17

Answer:

he descends only 57 feet ,as the mine is 10 feet below the surface befor descending

Answer:

Answer:

70 miles

Step-by-step explanation:

Subtracting ten minutes from the elapsed time 94 minutes tells us that the travel (at constant average speed) took 84 minutes.  We convert 84 minutes to 84/60 hour.

distance = rate•time = 50 mi/hr (84/60 hour) = 50(1.4) = 70 miles

The solution to the linear equation can be found to be :

To solve this system of linear equations, first, we'll eliminate the fractions by finding the least common multiple (LCM) of the denominators and then multiplying each equation by the LCM.

x + 2y = 24

x + 8y = 48

Subtract equation (1) from equation (2) to eliminate x:

(8y - 2y) = (48 - 24)

6y = 24

Now, we can solve for y:

y = 24 / 6

y = 4

Now that we have y, we can substitute it into equation (1) to solve for x:

x + 2(4) = 24

x + 8 = 24

x = 24 - 8

x = 16

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In constructing the circle graph, the angle measure was used for the Wanda section is 54 degree,

Hence option A is correct.

From the circular graph,

We can see that,

Wanda represent 15% area of circle.

Since we know that

There are total 360 degree angle in a circle.

Since we also know that,

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Thus,

Angle measure was used for the Wanda section = 360x15/100

                                                                                 = 54  degree

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Answer:

75 seconds or 1 minute and 15 seconds

Step-by-step explanation:

300 meters/4 mps = 75 seconds

The quadratic equation with the roots  1/α and 1/β using the given equation is equal to

As given in the question,

Given equation is:

2x²−5x−6=0

Roots of the given equations are α and β

Compare with standard quadratic equation:

ax² + bx + c = 0

a = 2 , b= -5 , c = -6

Sum of the roots are:

α + β = -b/a

        = -( -5/2)

        = 5/2

Product of the roots

αβ = c/a

    = -6/2

    = -3

Now ,

( α + β )/ αβ = (5/2) / -3

⇒1/ β + 1/α = -5/6

⇒ 1/α + 1/β = -5/6

And ,

1/αβ = -1/3

Quadratic equation with roots 1/α and 1/β is given by:

x² - ( 1/α + 1/β)x + 1/αβ =0

⇒x² - (-5/6)x + (-1/3) = 0

⇒x² + (5/6)x -(1/3) =0

Therefore, the quadratic equation with roots 1/α and 1/β is equal to

x² + (5/6)x -(1/3) =0

The complete question is :

Suppose the roots of the equation 2x²−5x−6=0 are α and β.Find the quadratic equation with roots 1/α and 1/β.​

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Answer:5566

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

4 books

Step-by-step explanation:

We are told that: Hugh bought some magazines that cost 3.95 each

Hugh bought 3 magazines.

Hence, total cost of magazines = 3 magazines × 3.95

= 11.85.

Total cost of magazines = 11.85

From the question, we know that, the total amount Hugh spent = 47.65

Hence, The total cost for books =

Total amount spent - Total cost of magazines

= 47.65 - 11.85

= 35.80

Therefore, the total cost of books = 35.80

We are told in the question that the cost of books is 8.95 each or 8.95 per book.

Hence, the number of books that Hugh bought is calculated as :

35.80/8.95

= 4 books

Therefore, Hugh bought 4 books

The given series are both geometric series with a common ratio of 7/3. We can use the formula for the sum of a geometric series to determine whether the series converges to a finite value or diverges.

The first series has a common ratio of 7/3. The formula for the sum of a geometric series is S = a/(1 - r), where 'a' is the first term and 'r' is the common ratio. In this case, 'a' is 7/3 and 'r' is 7/3. Substituting these values into the formula, we have S = (7/3)/(1 - 7/3). Simplifying further, S = (7/3)/(3/3 - 7/3) = (7/3)/(-4/3) = -7/4. Therefore, the sum of the series is -7/4, indicating that the series converges.

The second series also has a common ratio of 7/3. Again, using the formula for the sum of a geometric series, we have S = a/(1 - r). Substituting 'a' as 7/3 and 'r' as 7/3, we get S = (7/3)/(1 - 7/3). Simplifying further, S = (7/3)/(3/3 - 7/3) = (7/3)/(-4/3) = -7/4. Hence, the sum of the series is -7/4, indicating that this series also converges.

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Step-by-step explanation:

Final account amount will be  ( using compound interest formula)

90 000 (1 + .10)^3 = 119 790       <===     ( 1-% is .10 in decimal)

 subtract original amount to find interest =  £ 29 790.

Answer: £29,791.00

Step-by-step explanation:

Use the Equation \(A = P(1+r/n)^(nt)\)

P represents principal which is the starting amount.

R represents rate which is the percent increase represented in decimal form.

N represents the number of times compounded per year.

T represents the total time.

The question is asking us to solve for A which is the total amount and we just have to plug in all the other variables given to us and solve and subtract from the original.

A = 90,000(1 + 0.1/1)^(1*3)

A = 90,000(1.1)^3

A = 119,791.00

We have the amount, and now we have to subtract it from the original.

119,791-90,000 = 29791

Answer:

7238 units^3

Step-by-step explanation:

The formula for the volume of a sphere of radius 12 units is

V = (4/3)(pi)r^3.  

Here, with r = 12 units,

V = (4/3)(pi)(12 units)^3 = 7238 units^3

Answer:

V = 2304π units³

Step-by-step explanation:

V = (4/3)πr^3

V = (4/3)π(12)^3

V = (4/3)π(1728)

V = 2304π units³

Answer:

You would need to Quadruple the length.

Step-by-step explanation:

In this picture, the scaled drawing's perimeter is equal to 12. So if you quadruple the length, the actual perimeter would be 48.

Answer:

8

Step-by-step explanation: 8

The solution to the given set of equations is, No solution.

We have to given that;

A set of equations is given below:

Equation C: y = 6x + 9

Equation D: y = 6x + 2

Now, We can see that;

y = 6x + 9

y = 6x + 2

Equate both equations, we get;

6x + 2 = 6x + 9

2 ≠ 9

Hence, We get;

The solution to the given set of equations is, No solution.

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That day the number of adults was 95 and the number of children was 38

Let's define the variables:

x = number of adults.

y = number of children.

We know that 133 people used the public swimming pool. then we can write:

x + y = 133

We also know that the receipts for admission totaled 270.75, then we can write other equation as:

2.25x + 1.5y = 270.75

Then the system of equations is:

x + y = 133

2.25x + 1.5y = 270.75

In the first equation we can isolate x to get:

y = 133 - x

Now replace that in the other equation to get:

2.25x + 1.5*(133 - x) = 270.75

0.75x + 199.5 = 270.75

0.75x = 270.75 - 199.5

x = 71.25/0.75 = 95

Then the value of y is:

y = 133 - 95 = 38

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Answer:

The solution to the system of equations is (x, y). To find the value of x, we need to solve for x in one of the equations, and then substitute that value into the other equation to check if it holds.

One way to solve the first equation is to add 6y to both sides and then divide both sides by 5:

5x - 6y = 2.7

5x = 2.7 + 6y

x = (2.7 + 6y)/5

We can then substitute this expression for x into the second equation:

10((2.7 + 6y)/5) + 7 = 1.6

Simplifying this equation we get:

8.4 + 3y = 1.6

3y = -6.8

y = -2.27

Now we can substitute y = -2.27 back into the first equation to find the value of x:

5x - 6(-2.27) = 2.7

5x + 13.62 = 2.7

5x = -10.92

x = -2.184

So the value of x is approximately -2.184 .

Answer:

a=7 b=11 c=9

Step-by-step explanation:

-2-(9)      -2-(9) = -2+9=7 b -2-9=-11 c -2-(-9)-(-2) = -2+9+2=9

Answer:

Is the other answer correct?

Step-by-step explanation:

the probability that at least flights are on time is

P(7) + P(8) + P(9) + P(10)

To calculate the probability that at least a certain number of flights are on time using the binomial distribution, we need the probability of success (p), the number of trials (n), and the desired number of successful trials.

Let's assume we have the following information:

Probability of a flight being on time: p = 0.8 (80%)

Number of flights: n = 10

To find the probability that at least a certain number of flights are on time, we need to sum the probabilities of the desired number of successful trials and all higher numbers of successful trials.

Let's say we want to find the probability of at least 7 flights being on time.

P(at least 7 flights on time) = P(7) + P(8) + P(9) + P(10)

Using the binomial probability formula: P(x) = C(n, x) * p^x * (1-p)^(n-x)

where C(n, x) represents the number of combinations of n items taken x at a time.

Calculating the probabilities: P(7) = C(10, 7) * (0.8)^7 * (0.2)^(10-7) P(8) = C(10, 8) * (0.8)^8 * (0.2)^(10-8) P(9) = C(10, 9) * (0.8)^9 * (0.2)^(10-9) P(10) = C(10, 10) * (0.8)^10 * (0.2)^(10-10)

Finally, we sum up these probabilities to get the probability of at least 7 flights being on time.

P(at least 7 flights on time) = P(7) + P(8) + P(9) + P(10)

Performing the calculations will give us the specific probabilities and the final probability.

Complete Question :- According to an​ airline, flights on a certain route are on time 75​% of the time. Suppose 24 flights are randomly selected and the number of​ on-time flights is recorded.

​(a) Explain why this is a binomial experiment.

​(b) Find and interpret the probability that exactly 14 flights are on time.

​(c) Find and interpret the probability that fewer than 14 flights are on time.

​(d) Find and interpret the probability that at least 14 flights are on time.

​(e) Find and interpret the probability that between 12 and 14 flights, inclusive, are on time.

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Simplifying further:dy/dx = 4x / yTherefore, dy/dx = 4x / y.

To find dy/dx using implicit differentiation, we'll differentiate both sides of the equation with respect to x, treating y as a function of x.

Differentiating the equation \(4x^2 - y^2 = 5\) with respect to x, we get:

8x - 2y * dy/dx = 0

Now, let's solve for dy/dx:

2y * dy/dx = 8x

dy/dx = (8x) / (2y)

Simplifying further:

dy/dx = 4x / y

Therefore, dy/dx = 4x / y.

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A hypothesis test is the significance test we will do.

Given;

Our goal is to find out whether students' self-reported grade point averages and their transcript-reported GPAs differ from one another. What kind of significant test will you administer to your class of 50 SRS students?

hypothesis test:

To decide or judge the value of a parameter, such as the population mean, hypothesis tests are utilized. A hypothesis test can be conducted using either the critical value approach or the P-value approach. There are two sorts of errors made when doing a hypothesis test: Type I Error and Type II Error. Because a sample statistic is being used to make conclusions or judgments about the value of a parameter, the decision obtained may be incorrect.

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Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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The factor form of the quadratic equations are listed below:

Case 13: (b - 4) · (b - 2)

Case 14: (n + 4) · (n + 2)

Case 15: 2 · (n + 9) · (n - 6)

Case 16: 5 · (n + 2)²

Case 17: 2 · (k + 5) · (k + 6)

Case 18: (a - 10) · (a + 9)

Case 19: (p + 10) · (p + 1)

Case 20: 5 · (v - 2) · (v - 4)

Case 21: 2 · (p + 2) · (p - 1)

Case 22: 4 · (v - 2) · (v + 1)

Case 23: (x - 10) · (x - 15)

Case 24: (v - 5) · (v - 2)

Case 25: (p + 6) · (p - 3)

Case 26: 6 · (v + 10) · (v + 1)

In this problem we find quadratic equations of the form a · x² + b · x + c, whose factor form is introduced below:

a · x² + b · x + c = a · x² + a · (- r₁ - r₂) · x + a · r₁ · r₂ = a · (x - r₁) · (x - r₂)

Where r₁, r₂ are real roots.

Now we proceed to present the factor form of each quadratic equation:

Case 13

b² - 6 · b + 8 = (b - 4) · (b - 2)

Case 14

n² + 6 · n + 8 = (n + 4) · (n + 2)

Case 15

2 · n² + 6 · n - 108 = 2 · (n² + 3 · n - 54) = 2 · (n + 9) · (n - 6)

Case 16

5 · n² + 10 · n + 20 = 5 · (n² + 2 · n + 4) = 5 · (n + 2)²

Case 17

2 · k² + 22 · k + 60 = 2 · (k² + 11 · k + 30) = 2 · (k + 5) · (k + 6)

Case 18

a² - a - 90 = (a - 10) · (a + 9)

Case 19

p² + 11 · p + 10 = (p + 10) · (p + 1)

Case 20

5 · v² - 30 · v + 40 = 5 · (v² - 6 · v + 8) = 5 · (v - 2) · (v - 4)

Case 21

2 · p² + 2 · p - 4 = 2 · (p² + p - 2) = 2 · (p + 2) · (p - 1)

Case 22

4 · v² - 4 · v - 8 = 4 · (v² - v - 2) = 4 · (v - 2) · (v + 1)

Case 23

x² - 15 · x + 50 = (x - 10) · (x - 15)

Case 24

v² - 7 · v + 10 = (v - 5) · (v - 2)

Case 25

p² + 3 · p - 18 = (p + 6) · (p - 3)

Case 26

6 · v² + 66 · v + 60 = 6 · (v² + 11 · v + 10) = 6 · (v + 10) · (v + 1)

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Answer:

27850

Step-by-step explanation:

5% of 29,000=1450

2900-1450=27850

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