Why is it a problem to find the square root of a negative number, for example √-4?

Answer: B.

Step-by-step explanation: Remember, circumfrence is 2 pi r. multiply 6.1 and 2. That is 12.2. Then, use a calculator to multiply that to get approx 76.65. Round that up to 76.7.

Answer:

B

23

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

\(24^{2} + 7^{2}\) = 625

\(\sqrt{625\\}\) = 25

Therefore, the length of BD in rectangle ABCD is 25mm. I just did the test and it is correct. 23 is wrong.

Each cross-section perpendicular to the x-axis is an equilateral triangle. The volume of the solid is\((sqrt(3)/36) × s^3.\)

To find the volume of a solid whose each cross-section perpendicular to the x-axis is an equilateral triangle, we need to use calculus. Let us denote the area of an equilateral triangle with side length s as A(s).

Hence, the volume of the solid will be∫baf(x)dx, where f(x) is the function that gives the area of the cross-sectional triangle whose base is the x-axis and b and a are the limits of the interval over which we want to find the volume.

As each cross-section is an equilateral triangle, the area of the triangle whose base is the x-axis will be

\(A(f(x)) = (\sqrt{(3)/4)} \times(f(x))^2.\)

We have to find the limits of the interval for which we need to find the volume. As we are finding the volume of a solid, we know that the interval will be in the x-direction. Hence, we need to find the limits of the interval of the x-axis. We can see that the cross-sectional triangles are equilateral triangles.

Hence, they will be similar, and we can set up a proportion to find the value of x for which the triangle has side length s. We know that the height of an equilateral triangle with side length s is \((sqrt(3)/2) × s.\) As the cross-sectional triangles are perpendicular to the x-axis, their height will be equal to the value of x.

Hence, we can set up a proportion to find the value of x. We know that:

\((sqrt(3)/2) × s = x. => s = (2/sqrt(3)) × x.\)

Hence, the limits of the interval will be x = 0 and \(x = (sqrt(3)/2) × s. => x = 0\)and \(x = s/(2 × sqrt(3)).\)

Now, let us find the volume. We know that \(f(x) = (sqrt(3)/4) × x^2.\)

Hence, the volume will be: \(V = ∫(s/(2 × sqrt(3))0(sqrt(3)/4) × x^2dx => V = (sqrt(3)/36) × s^3\)

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Answer:

b. 8.6

Step-by-step explanation:

lmk if it was right

Answer:

6 + 6y + 6 = 12 + 6

Step-by-step explanation:

2(3) + 6y = 12

Multiply 2(3).

6 + 6y = 12

Subtract 6 on both sides, so y variable is isolated.

6 + 6y - 6 = 12 - 6

6y = 6

Divide by 6 on both sides.

6y/6 = 6/6

y = 1

Answer:

a) 60,000 cubic cm

b)600,000 cubic mm

c)60 L

Step-by-step explanation

To find the volume, you would have to multiply the height length and width.

50*40*30 and that equals to 60,000 cm. 10 mm=1cm.

So 60,000*10=b, b=600,000,  1,000 cm=1 L

60,000/1,000=L, L=60

Hope this helps. If it does, please rate 5 stars!

The domain of the function h(x)=\(10x^{2} -6x\) is all real numbers.

Given function h(x)=\(10x^{2} -6x\).

We are required to find the domain of the given function.

Function is basically relationship between two or more variables that are expressed in equal to form. The values that we entered in the function are known as a part of domain and the values that we get from the function are known as a part of range of function.

The function is h(x)=\(10x^{2} -6x\).

We have not given any range of the function, so we donot know the limit under which the values of that  function lies. Because we donot know the limit so we can put any real number in the function. So the domain of the function h(x)=\(10x^{2} -6x\) is all real numbers.

Hence the domain of the function h(x)=\(10x^{2} -6x\) is all real numbers.

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Answer: 41,472

Step-by-step explanation:

Answer:

16 feet long

Step-by-step explanation:

If the tree's shadow length is 15 and you want to find the tree which is 30, you multiply by two and you have to multiply the 8 as well by two and you get 16.

Answer:

Your answer is: 16ft

Step-by-step explanation:

I had to answer because it wouldn't let me comment. You have no clue how good it feels to know I'm not forgotten.

Answer:

20%

Step-by-step explanation:

Percentage discount on the cost of the sofa = 20%

Percentage discount = (Absolute discount / Cost price) × 100

Given,

             Cost price =  $600

Absolute discount  =  Cost price - Selling price

Absolute discount  =  $600 - $480

                                = $120

Percentage discount = (Absolute discount / Cost price) × 100

                                   = (120/600) × 100

                                   = 120/6

                                   = 20%

Hence, percentage discount on the cost of the sofa = 20% .

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Using Simple Interest formula ,

The rate percent on amount of Rs.300 is 5.5 .

At same rate, R = 5.5 the principle 800 will be Rs1120 in next 7 years .

In first case we have given that ,

principle = Rs.350

time = 4 years

Amount = Rs 1120

simple interest = 1120-350 = Rs.770

let rate of interest be R% .

Using the formul of simple interest

S.I = P×R×t /100

=> 770 = 350×4×R/100

=> R = 5.5 %

In Second case , rate of interest is same as in first case. So,

Amount = Rs. 1120

Principle = Rs. 800

rate of interest (R)= 5.5

Again simple interest formula Used:

Simple Interest = (P × R × T)/100

Simple interest = 1120 - 800 = Rs. 320

Simple Interest = (P × R × T)/100

⇒ 320 = 800×5.5 ×T/100

=> T = 7.27 ~ 7

∴ In the given principle Rs 800 with same rate of interest will be 1120 in 7 next years .

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Answer:

Below in bold.

Step-by-step explanation:

∛-12

The nearest cube  to -12 is -8    ( -27 is the next after -12)

a) The answer is -2.

b) we can do this by trial and improvement

It must be between -2 and -3, closer to -2 than 3 so first we guess -2.1

(-2.1)^3 = -9.261

(-2.2)^3 = -10.648

(-2.3)^3 = `2.167  - very close

Answer is -2.3 .

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Answer:

Book = $8 each

CD = $5 each

8 x 5 = 40

2 x 5 = 10

= 50

8 x 2 = 16

5 x 3 = 15

= 31

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Answer:

One book equals $8 and one CD equals $5

Step-by-step explanation:

Let books be denoted as 'x' and CDs as 'y'

5x + 2y = 50    ...1

2x + 3y = 31    ...2

I usually eliminate the y variable, and to do this, you multiply the first equation by 3 and the second equation by 2, because the lowest common multiple between 2 and 3 is 6.

...1*3    and    ...2*2

15x + 6y + 150    ...3

4x + 6y = 62    ...4

Eliminate y by taking ...4 away from ...3

15x - 4x = 150 - 62

11x = 88

x = 8

Sub this value into ...1

5(8) + 2y = 50

40 + 2y = 50

Rearrange

2y = 50 - 40

2y = 10

y = 5  

This means that one book is $8 and one CD equals $5

Answer:

Area : 27

Perimeter : 24

Step-by-step explanation:

Area : Just count the number of squares in the box

Perimeters : Count the number of squares surrounding the box

The probability of x being greater than 18 (p(x > 18)) is equal to the probability of x being less than 18 (p(x < 18)) in a normal distribution.

In a normal distribution, the probability of an event happening to the left of the mean (μ) is equal to the probability of the event happening to the right of the mean. This means that if we know the probability of x being less than 18 (p(x < 18)), we can use the property of symmetry to determine the probability of x being greater than 18 (p(x > 18)).

Since the probability distribution of x is symmetric around the mean, the area under the probability density function (PDF) to the left of the mean is the same as the area to the right of the mean. Therefore, we can say:

p(x > 18) = p(x < 18)

In other words, the probability of x being greater than 18 is equal to the probability of x being less than 18 in a normal distribution.

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Both statements are false. Consumer surplus decreases when the price is increased above the equilibrium, and producer surplus decreases when the price is decreased below the equilibrium.

(a) False.

The statement is not necessarily true. Consumer surplus is the difference between what consumers are willing to pay for a good or service and what they actually pay. At the equilibrium price, consumer surplus is maximized. However, if the price is increased above the equilibrium price, consumer surplus will generally decrease.

This is because as the price increases, fewer consumers are willing to purchase the good or service, resulting in a decrease in consumer surplus. T

herefore, at any price higher than the equilibrium price, the consumer surplus will generally be less than the consumer surplus at the equilibrium price.

(b) False.

Similar to the previous statement, the statement is not necessarily true. Producer surplus is the difference between the price producers receive for a good or service and the minimum price they are willing to accept. At the equilibrium price, producer surplus is maximized.

However, if the price is decreased below the equilibrium price, producer surplus will generally decrease. This is because as the price decreases, fewer producers are willing to supply the good or service, resulting in a decrease in producer surplus.

Therefore, at any price lower than the equilibrium price, the producer surplus will generally be less than the producer surplus at the equilibrium price.

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The maximum number of relative extrema of the given polynomial is; 3

When trying to find the maximum number of relative extrema of a polynomial, we usually use the formula;

Maximum number of relative extrema contained in a polynomial = degree of this polynomial - 1.

We are given the Polynomial as;

f(x) = 3x⁴ - x² + 4x - 2

Now, the degree of the Polynomial would be 4. Thus;

Maximum number of relative extrema = 4 - 1

Maximum number of relative extrema = 3

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The probability that the first person picked will be female is 2/5.

Two quantities are compared to form a ratio. Discover how to calculate the ratio of two items, such as apples to oranges.

Total audience = 120

Ratio of males to females; 3:2

Total males : 3*120/ 5 = 72

Total females: 2*120/5 = 48

Probability that the first person picked will be female = total females / total audience

Probability = 48 / 120

Probability = 2/5

Thus, the probability that the first person picked will be female is 2/5.

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Answer:

4y - x = 20

Step-by-step explanation:

Y= x/4 + 5/1

Cross multiply to get = y= (x+20/4)

4y = x+20

4y - x =20

According to the information we can infer that the estimated mean qualifying speed with 90% confidence is 224.78 mph.

To estimate the mean qualifying speed with a 90% confidence level, we can use the formula for a confidence interval:

Where:

Using the given data, the sample mean (X) is calculated by finding the average of the seven speeds:

Next, we calculate the sample standard deviation (s) using the data:

Now, we can plug these values into the confidence interval formula:

Calculating the confidence interval gives us:

The lower bound of the confidence interval is approximately 223.52 mph, and the upper bound is approximately 226.04 mph. So, we can estimate the mean qualifying speed with 90% confidence to be approximately 224.78 mph.

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It would take approximately 60 years for Keenan to double his money with an APY of 1.2%. Therefore, the answer is (a) 60 years.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To determine how long it would take for Keenan to double his money with an annual percentage yield (APY) of 1.2%, we can use the "Rule of 72." This rule is a quick and easy way to estimate the time it takes for an investment to double in value.

The rule of 72 states that to find the number of years it takes for an investment to double, we divide 72 by the annual interest rate. So, in this case, we would divide 72 by 1.2 to get:

72 / 1.2 = 60

Therefore, it would take approximately 60 years for Keenan to double his money with an APY of 1.2%. Therefore, the answer is (a) 60 years.

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The formula V₂ = Vmax [S] / (Km + [S]) can be rearranged algebraically to solve for [S] in terms of V₂, Vmax, and Km.

To rearrange the formula V₂ = Vmax [S] / (Km + [S]) to solve for [S], we can follow these steps:

Multiply both sides of the equation by (Km + [S]) to eliminate the denominator:

V₂ (Km + [S]) = Vmax [S]

Expand the left side of the equation:

V₂ Km + V₂[S] = Vmax [S]

Distribute Vmax to both terms on the right side:

V₂ Km + V₂[S] = Vmax [S]

Move the term V₂[S] to the other side of the equation:

V₂[S] - Vmax [S] = -V₂ Km

Factor out [S] from the left side:

[S] (V₂ - Vmax) = -V₂ Km

Divide both sides of the equation by (V₂ - Vmax) to solve for [S]:

[S] = (-V₂ Km) / (V₂ - Vmax)

Therefore, the rearranged formula for [S] in terms of V₂, Vmax, and Km is [S] = (-V₂ Km) / (V₂ - Vmax).

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Answer:

twenty percent are grapes

Step-by-step explanation:

The polynomial expansion evaluates to n for x = 1, we can conclude that the sum of the reciprocals of all these products is also equal to n.

The sum of the reciprocals of all products of k distinct positive integers (a1, a2,..., ak) is denoted by the expression "a1,...,ak," where each ai is selected from the set "1,2,...,n."

To show that this aggregate equivalents n, we can consider the polynomial extension of (1 + x)(1 + x^2)(1 + x^3)...(1 + x^n). Each term in this extension addresses a result of unmistakable powers of x, going from 0 to n.

Presently, assuming we assess this polynomial at x = 1, each term becomes 1, and we acquire the amount of all results of k unmistakable positive numbers, where every whole number is browsed the set {1,2,...,n}.

Since the polynomial development assesses to n for x = 1, we can infer that the amount of the reciprocals of this multitude of items is likewise equivalent to n.

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Brian ordered 3 large cheese pizzas and a salad. the salad cost $4.95. if he spent a total of $47.60 including the $5 tip, each pizza cost $12.55.

To find out how much each pizza cost, we need to subtract the cost of the salad and the tip from the total amount Brian spent. Let's calculate it step by step.

1. Subtract the cost of the salad from the total amount spent:
  $47.60 - $4.95 = $42.65

2. Subtract the tip from the result:
  $42.65 - $5 = $37.65

3. Divide the remaining amount by the number of pizzas ordered:
  $37.65 ÷ 3 = $12.55

Therefore, each pizza cost $12.55.

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