Make g the subject of the formula

Answer:

A

Step-by-step explanation:

Given

a = \(\frac{b+c}{d}\) ( multiply both sides by d to clear the fraction )

ad = b + c ( subtract b from both sides )

ad - b = c → A

Answer: 1st one

Step-by-step explanation:

Answer:

Example 1: Y is directly proportional to x. When x = 5, y = 8. What does y equal when x = 9?

First, we set up our general equation. Because y is directly proportional to x, we have:

y = cx

where c is the constant of proportionality. In other words, when x goes up, y goes up, and when x goes down, y goes down.

The next thing we do is plug our values for x and y into the equation so we can solve for c:

8 = (c)(5)

Solving for c, we get c = 8/5 = 1.6 and we plug this into our equation:

y = 1.6x

Now, we can plug x = 9 into the equation to find out what y equals:

y = (1.6)(9)

y = 14.4

So, our answer is 14.4

Example 2: Y is directly proportional to the square of x. When x = 2, y = 32. What does y equal when x = 5?

This time, our general equation is slightly more complicated because x is squared:

y = cx2

Like before, we solve for our constant:

32 = (c)(22)

32 = (c)(4)

We get c = 8:

y = 8x2

Solving for y when x = 5, we get y = (8)(52) = (8)(25) = 200

Example 3: Y is inversely proportional to x. When x = 2, y = 8. What does y equal when x = 24?

This time, because y is inversely proportional to x, our general equation is different:

xy = c

so when x goes up, y goes down, and vise versa. But, other than that, we solve these kinds of problems the same way as direct proportion problems. Solving for the constant, we get:

(2)(8) = c

So c = 16 and our equation is now:

xy = 16

Solving for y when x = 24 we get y = 16/24 = 2/3

Example 4: Y is inversely proportional to the square root of x. When x = 36, y = 2. What does y equal when x = 64?

As before, we set up our equation:

eq001

Since the square root of 36 is 6, it is easy to solve for c:

(6)(2) = c

We get c = 12 and our equation is now:

eq002

Solving for y when x = 64 we get 8y = 12 or y = 12/8 = 1.5 because the square root of 64 is 8.

Step-by-step explanation:

Example 1: Y is directly proportional to x. When x = 5, y = 8. What does y equal when x = 9?

First, we set up our general equation. Because y is directly proportional to x, we have:

y = cx

where c is the constant of proportionality. In other words, when x goes up, y goes up, and when x goes down, y goes down.

The next thing we do is plug our values for x and y into the equation so we can solve for c:

8 = (c)(5)

Solving for c, we get c = 8/5 = 1.6 and we plug this into our equation:

y = 1.6x

Now, we can plug x = 9 into the equation to find out what y equals:

y = (1.6)(9)

y = 14.4

So, our answer is 14.4

Example 2: Y is directly proportional to the square of x. When x = 2, y = 32. What does y equal when x = 5?

This time, our general equation is slightly more complicated because x is squared:

y = cx2

Like before, we solve for our constant:

32 = (c)(22)

32 = (c)(4)

We get c = 8:

y = 8x2

Solving for y when x = 5, we get y = (8)(52) = (8)(25) = 200

Example 3: Y is inversely proportional to x. When x = 2, y = 8. What does y equal when x = 24?

This time, because y is inversely proportional to x, our general equation is different:

xy = c

so when x goes up, y goes down, and vise versa. But, other than that, we solve these kinds of problems the same way as direct proportion problems. Solving for the constant, we get:

(2)(8) = c

So c = 16 and our equation is now:

xy = 16

Solving for y when x = 24 we get y = 16/24 = 2/3

Example 4: Y is inversely proportional to the square root of x. When x = 36, y = 2. What does y equal when x = 64?

As before, we set up our equation:

eq001

Since the square root of 36 is 6, it is easy to solve for c:

(6)(2) = c

We get c = 12 and our equation is now:

eq002

Solving for y when x = 64 we get 8y = 12 or y = 12/8 = 1.5 because the square root of 64 is 8.

Answer:

y = 8

Step-by-step explanation:

because y is directly proportional to .√x

=> y = a√x

but when x = 100, y = 80

=> 80 = 10a

=> a = 8

=> y = 8√x

Answer:

8x - 1x

Step-by-step explanation:

Just do the stuff in the ()'s  first, for this it's is 4x - 3x, then rewrite the problem and it is  simplified

In order to cut the standard error of the mean in half (to 12.5), you must select a sample size of 612.

To find the new sample size required to cut the standard error of the mean in half, you can use the following formula:

New Standard Error = (Old Standard Error) / √(New Sample Size / Old Sample Size)

We know the old standard error (25) and want to find the new standard error (12.5). So, we can rewrite the formula as:

12.5 = 25 / √(New Sample Size / 153)

First, divide both sides of the equation by 25:

0.5 = 1 / √(New Sample Size / 153)

Next, square both sides of the equation:

0.25 = 1 / (New Sample Size / 153)

Now, take the reciprocal of both sides:

4 = New Sample Size / 153

Finally, multiply both sides by 153 to find the new sample size:

New Sample Size = 4 * 153

New Sample Size = 612
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Answer:

9; the initial fee.

Step-by-step explanation:

Rounding off the answer to the nearest dollar, the amount in the account at the end of 10 years is $377,453.

Given that money is transferred continuously into an account at the constant rate of $230,000 per year, and the account earns interest at the annual rate of 3.7% compounded continuously.

We are to find how much will be in the account at the end of 10 years.

To solve this question, we can use the formula for continuous compound interest, which is given as;

A = Pert,

where

A = the balance in the account at the end of the investment period

P = the principal amount (the initial amount invested)

exp = is Euler’s constant ≈ 2.71828

r = the annual interest rate expressed as a decimal

t = the time the money is invested

Using the formula above to solve the question;

P = $230,000r = 0.037

t = 10 years

A = Pert

A = $230000 * e(0.037*10)A = $377,453.06

Rounding off the answer to the nearest dollar, the amount in the account at the end of 10 years is $377,453.

$377,453

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The probability of the data vale more extreme than 3.65 is 0.000131.

First of all given that x(value) = μ+3.65σ , where μ is the mean and σ is the standard deviation.

we know that z-score = (x - μ)/σ

z-score = (μ+3.65σ - μ)/σ

z = 3.65σ/σ

z = 3.65

From the normal distribution table,

P(z>3.65) = 0.000131

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The rate at which the machine crushes dry fruit is option (D) 4 1/3 kilograms per minute.

To find the rate at which the machine crushes dry fruit, we need to divide the amount of fruit crushed by the time taken. We can convert the mixed number of 3 1/4 kilograms to an improper fraction as follows

3 1/4 = (3 x 4 + 1)/4 = 13/4

So the rate at which the machine crushes dry fruit is

rate = amount of fruit crushed / time taken

= (13/4) / (3/4)

= 13/4 x 4/3

= 13/3

Convert to mixed fraction

= 4 1/3

Therefore, the correct option is (D) 4 1/3

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The given question is incomplete, the complete question is:

A processing machine crushes 3 1/4 kilograms of dry fruits in 3/4 minute. What is the rate, in kilograms per minute, at which the machine crushes dry fruit? A. 3/13 B. 16/39 C. 2 7/16 D. 4 1/3

Hello and Good day,

This question is relating to probability and it can come in percentages and fractions. I will follow directions as the problem states and provide both.

1. There is a 1/20 or 5% chance that the dart would land on section 20.

2. There is a 10/20 or 50% chance that the dart would land on an odd number.

There are 10 odd numbers present on the dart board.

3. 4/20 or 20%

There are 4 numbers greater than 16.

4. 0/20 or 0%

This is because there are no 25's on the dart board

5. 17/20 or 85%

This is because there are 17 numbers that aren't 4, 5, or 6.

6. 7/20 or 35%

There are 7 numbers less than 8.

7. 20/20 or 100% chance

8. 19/20 or 95% chance

I honestly was to lazy to right the rest in complete sentences, but i hope you find this well. Have a great day.

Thank you for your support,

-Oceanbreeze24

Answer:

√63 can be written as

√ 9 × 7 = √ 9 × √7 = 3 × √ 7

= 3√7

Hope this helps you

Answer: \(3\sqrt{7}\)

Step-by-step explanation:

Separate \(\sqrt{63}\) into \(\sqrt{7}\) and \(\sqrt{9}\).  Then simplify \(\sqrt{9}\) into 3.  Thus, the simplified version of \(\sqrt{63}\) is \(3\sqrt{7}\)

The total amount y collected from x students is y = 10x.

The graph is given below.

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The club is charging $10 per student that attends.

This means,

Number of students = x

The total amount y collected from x students.

y = 10x

The graph is given below.

Thus,

y = 10x is the total amount y collected from x students is

The graph is given below.

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Miss Austin is covering the topic of central tendency in statistics, specifically the mean. By giving her class 6 sets of data and asking them to identify which one can be most accurately summarized by the mean, she is testing their understanding of how the mean represents the average value of a set of data.

This also involves understanding how to calculate the mean and interpret its value in relation to the other values in the dataset. Therefore, Miss Austin is helping her class develop skills in data analysis and statistical reasoning. The use of the term "set" is not clear, but assuming it means "sets of data," it is relevant to the topic being covered.

Miss Austin is covering the topic of "Descriptive Statistics" in her class. Specifically, she is focusing on the concept of "mean" as a measure of central tendency to summarize data sets. By asking her students to identify which data set can most accurately be summarized by the mean, she is teaching them how to understand the appropriateness of using the mean for different sets of data.

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Answer:

\(\displaystyle \int^x_0\sin(3t^2)\,dt\approx x^3-\frac{27}{42}x^7\)

Step-by-step explanation:

Recall the MacLaurin series for sin(x)

\(\displaystyle \sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-...\)

Substitute 3t²

\(\displaystyle \displaystyle \sin(3t^2)=3t^2-\frac{(3t^2)^3}{3!}+\frac{(3t^2)^5}{5!}-...=3t^2-\frac{3^3t^6}{3!}+\frac{3^5t^{10}}{5!}-...\)

Use FTC Part 1 to find degree 7 for F(x)

\(\displaystyle \int^x_0\sin(3t^2)\,dt\approx\frac{3x^3}{3}-\frac{3^3x^7}{7\cdot3!}\\\\\int^x_0\sin(3t^2)\,dt\approx x^3-\frac{27}{42}x^7\)

Hopefully you remember to integrate each term and see how you get the solution!

The other wall is 12 feet long can be evaluated using Pythagoras theorem.

What is Pythagoras theorem?

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Here given in the question that one side of the wall 5 feet

So as it is a rectangular bedroom it can be split into 2 right-angled triangles.

So the hypotenuse of the triangle is 13 feet

Now using the Pythagoras theorem we can  find out the length of the other wall

b²=h²-p²

b²=13²-5²

b²=169-25=144

b=√144

b=12 feet

Hence the other wall is 12 feet long.

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Probability that a randomly selected point falls in the white area is; 84.1%

The formula for area of a circle is;

A = πr²

where r is radius.

Thus;

A_circle = π * 4² = 50.265 cm²

Now, formula for area of triangle is;

A_tria = ¹/₂ * base * height

A_tria = ¹/₂ * 4 * 4 = 8 cm²

Thus;

Area of white portion = 50.265 cm² - 8 cm²

Area of white portion = 42.265  cm²

Thus;

Probability that a randomly selected point falls in the white area is;

P(White area) = 42.265/50.265 = 0.8408

= 84.1%

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Answer:

Area of the gym floor = 100.8 square meters

Step-by-step explanation:

Area of the gym floor = Area of rectangle A + Area of rectangle B - Area of the overlap

Area of rectangle A = 105 square meters

Area of rectangle B = 8.4 square meters

Area of the overlap = \(\frac{3}{25}\times (\text{Area of rectangle A})\)

                                = \(\frac{3}{25}\times 105\)

                                = 12.6 square meters

Area of the gym floor = 105 + 8.4 - 12.6

                                    = 100.8 square meters

Therefore, area of the gym floor is 100.8 square meters.  

Answer:

18.9 square meters

Step-by-step explanation:

I think you mean that the area of the Rectangle A is 10.5 not 105.

10.5+ 8.4- 1.26= 18.9

Where I got the 1.26 from?

3/25 the area of Rectangle A is area of the overlap of the rectangles. Which means we have to divide 10.5 by 25 and multiply by 3. That gives us 1.26.

I hope this is helpful.

Answer:

Step-by-step explanation:

Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85 is 7 years

Let the ages be x and x + 2 since they're consecutive odd integers.

We want to find Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85. This will be illustrated as:

x² + 4(x + 2) = 85

x² + 4x + 8 = 85

Collect like terms

x² + 4x + 8 - 85

x² + 4x - 77 = 0

x² + 11x - 7x - 77 = 0

x(x + 12) - 7(x + 11) = 0

x - 7 = 0

x = 0 + 7

Therefore, the age is 7 years.

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Your query has an answer of Extras charges = $999.

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

What is the formula's percentage?

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

Detailed explanation:

Data

Total cost: $11.325

8% state tax

$53 for license plates

$40 for an emissions inspection.

Process

1.- Determine the 8% of the car's cost.

11325 ———————— 100%

x ———————- 8%

x = (8 x 11325)/100

x = 90600/100

x = $1,066.16 in state taxes

2. Determine the entire cost.

Charges total $906 plus $53 plus $40.

= $ 999

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Molly earned $282.37 - $220.00 = $62.37 in interest at the end of six years.

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

To solve this problem, we can use the formula for compound interest:

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

We are given that Molly placed $220.00 in a savings account with an annual interest rate of 4.2%. We are also told that she did not add or take out any money from the account, so the principal remains $220.00. Since we are not given how many times per year the interest is compounded, we will assume it is compounded annually (n = 1).

After 6 years, the formula becomes:

\(A = 220(1 + 0.042/1)^{(1*6)}A = 220(1.042)^6\)

A = 220(1.2835)

A = $282.37

Therefore, Molly earned $282.37 - $220.00 = $62.37 in interest at the end of six years.

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By the principle of mathematical induction, we have shown that P(n) is true for n ≥ 1.

To the proof the mathematical induction for p(n) is true for n≥1 the following steps we have to follow;

Step 1: Base case (n = 1)

We need to prove that P(1) is true:

1 + 4 = 3/4(1 + 1/(-1))

5 = 3/4(2 - 1)

5 = 3/4(1)

5 = 5

Step 2: Inductive hypothesis

Assume that P(k) is true for some positive integer k. That is:

1 + 4 + (4/2) + ... + (4/k) = 3/4(k + 1) - 1

Step 3: Inductive step

We need to prove that P(k + 1) is true using the inductive hypothesis:

1 + 4 + (4/2) + ... + (4/k) + (4/(k + 1)) = 3/4((k + 1) + 1) - 1

Adding (4/(k + 1)) to both sides of the inductive hypothesis:

1 + 4 + (4/2) + ... + (4/k) + (4/(k + 1)) = 3/4(k + 1) - 1 + (4/(k + 1))

Simplifying the right-hand side:

1 + 4 + (4/2) + ... + (4/k) + (4/(k + 1)) = 3/4(k + 1) - 1 + 4/(k + 1)

Combining like terms:

1 + 4 + (4/2) + ... + (4/k) + (4/(k + 1)) = (3(k + 1) - 4 + 4)/(4(k + 1))

Simplifying further:

1 + 4 + (4/2) + ... + (4/k) + (4/(k + 1)) = (3k + 3)/(4(k + 1))

Common denominator on the right-hand side:

1 + 4 + (4/2) + ... + (4/k) + (4/(k + 1)) = (3k + 3)/(4k + 4)

Simplifying the numerator:

1 + 4 + (4/2) + ... + (4/k) + (4/(k + 1)) = 3(k + 1)/(4(k + 1))

Canceling out the common factors:

1 + 4 + (4/2) + ... + (4/k) + (4/(k + 1)) = 3/4(k + 1)

Therefore, P(k + 1) is true.

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Answer:B

Step-by-step explanation:

Transformation involves changing the position of a shape.

To map ΔHJK to ΔLMN, we (b) Translate K to N and reflect across the line containing JK.

ΔHJK and ΔLMN are similar triangles; this means that the following sides are corresponding:

The first translation would be to translate corresponding sides K to N.

Then triangle HJK must be translated across a line that contains point K (i.e. either line JK or line HK)

By comparing the options, the true statement is:

(b) Translate K to N and reflect across the line containing JK.

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The correct answer is (b) all real numbers except odd multiples of π/2. The domain of validity for cscθ (cosecant) is restricted because cosecant is undefined when the sine of an angle is zero.

In the trigonometric identity cscθ = 1/sinθ, the denominator sinθ becomes zero at odd multiples of π/2 (such as π/2, 3π/2, 5π/2, etc.), resulting in a division by zero error. Therefore, the cosecant function is not defined for these values of θ.

For all other real numbers θ, the sine function is non-zero and well-defined, allowing us to calculate the reciprocal of the sine and determine the value of the cosecant. Hence, the domain of validity for cscθ is all real numbers except odd multiples of π/2, as stated in option (b).

It's important to note that in trigonometry, the domain of validity is determined by avoiding any values that would lead to undefined expressions or division by zero errors.

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The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π, because at these points the sine function equals zero, and division by zero is undefined.

In mathematics, the cosecant function (csc), is defined as the reciprocal of the sine function, or 1/sinθ. The domain of a function are all the possible input values that will yield real numbers (output). For the csc function, its domain includes all real numbers except where the denominator is zero because division by zero is undefined.

In the unit circle context, sine equals zero at 0, π, 2π, ..., and the negative counterparts. Basically, these are the multiples of π. Thus, for the csc function, the domain is all real numbers except multiples of π, which matches option d in your choices.

The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π.

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Sean's age is 4 years and his brother's age is 11 years.  

Linear Equations in Two Variables: It is an equation written in the form ax+by +c=0. a, b, and c are real values, whereas x and y are variables. We can say that a and b are not equal to zero. Linear equations are solved when the same number is added to both sides, as well as when both sides are multiplied and divided by the same amount. Linear equations with two variables are denoted by x and y.

Let Sean's age be y years.

Let Sean's brother's age be x years.

Sean is three more than twice as old as brother.

∴ y = 2x + 3      -- (1)

Also, the total of their ages is 15.

∴ x+y = 15

⇒ y = 15 -x     -- (2)

Substitute y from equation (2) in equation (1)

⇒ 2x + 3 = 15 - x

⇒ 3x = 12

∴ x = 4

Put x in equation (2)

⇒ y = 15- 4

∴ y = 11

Thus, Sean's age is 4 years and his brother's age is 11 years.

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Answer:

16=2b+4

12=2b

b=6

.............

Answer:

b = 6

Step-by-step explanation:

16 + 5b = 7b + 4     <-- Subtract 5b from the left

16 = 2b + 4     <-- Subtract 4 from the right

12 = 2b     <-- Divide by 2

b = 6

Two organ systems that help maintain homeostasis after exercise are the respiratory system and the cardiovascular system.

1. Respiratory System:

During exercise, the increased activity of muscles leads to an increased demand for oxygen, and as a result, the cells produce more carbon dioxide (CO2) as a byproduct of cellular respiration. The respiratory system plays a vital role in maintaining homeostasis by regulating the levels of oxygen and carbon dioxide in the body.

After exercise, the respiratory system responds by increasing the rate and depth of breathing. This elevated ventilation allows for a greater intake of oxygen from the inhaled air. The oxygen-rich air enters the lungs, where it diffuses across the thin walls of the alveoli and into the bloodstream. Simultaneously, the increased ventilation facilitates the removal of carbon dioxide from the bloodstream into the alveoli, ready to be exhaled.

By adjusting the rate and depth of breathing, the respiratory system helps restore homeostasis by replenishing oxygen levels and eliminating excess carbon dioxide. This ensures that the body's cells receive the necessary oxygen for energy production while preventing the buildup of carbon dioxide, which can be detrimental if allowed to accumulate.

2. Cardiovascular System:

The cardiovascular system, composed of the heart, blood vessels, and blood, works in conjunction with the respiratory system to maintain homeostasis after exercise. Its primary function is to deliver oxygen and nutrients to the tissues while removing waste products, including carbon dioxide.

During exercise, the cardiovascular system responds to the increased demand for oxygen and the accumulation of carbon dioxide. The heart rate increases, leading to a higher cardiac output. The cardiac output is the amount of blood pumped by the heart per minute, and it increases to meet the heightened oxygen requirements of the active muscles.

As the heart pumps more vigorously, blood flow to the muscles is enhanced. This allows for the delivery of oxygen and nutrients to the working tissues, promoting their optimal function. Simultaneously, the increased blood flow facilitates the removal of carbon dioxide produced during exercise.

The blood vessels also play a role in maintaining homeostasis after exercise. They undergo vasodilation, which means the blood vessels widen to accommodate the increased blood flow to the muscles. This vasodilation helps dissipate heat generated during exercise and allows for efficient oxygen and nutrient delivery to the tissues.

Together, the respiratory system and the cardiovascular system work synergistically to maintain homeostasis after exercise. The respiratory system ensures an adequate supply of oxygen and the elimination of excess carbon dioxide, while the cardiovascular system delivers oxygen and nutrients to the tissues while removing waste products. This coordinated effort helps restore the body's internal balance and supports efficient cellular function.

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The discriminant of g can be positive, zero, or negative, depending on the specific values of the quadratic equation in g.

The discriminant is a term used in the quadratic formula to determine the nature of the roots of a quadratic equation. It is calculated as b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.

If the discriminant is positive, it means that the quadratic equation has two distinct real roots. This occurs when b^2 - 4ac > 0.

If the discriminant is zero, it means that the quadratic equation has one real root with multiplicity. This occurs when b^2 - 4ac = 0.

If the discriminant is negative, it means that the quadratic equation has two complex conjugate roots. This occurs when b^2 - 4ac < 0.

To determine whether the discriminant of g is positive, zero, or negative, we would need to know the specific coefficients of the quadratic equation in g. Without that information, we cannot provide a definitive answer.

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Answer:

=47/36

(Decimal: 1.305556)

Step-by-step explanation:

Answer:

3 1/4

Step-by-step explanation:

3/4 + ( 1/3 / 1/6 ) - (- 1/2)

First, divide within the parenthesis

3/4 + 2 - (- 1/2)

Next, change the double subtraction to an addition

3/4 + 2 + 1/2

Convert to forths

3/4 + 2 + 2/4

Add 3/4 and 2

2 3/4 + 2/4

Add 2 3/4 and 2/4

3 1/4

I hope that this helps :)