A parallelogram has an AREA of 7 square units. If the height that corresponds to a base is 14 units, what is the base?

The conversion of  730 km into miles is 456.70 miles so Maria drives 456.70 miles.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.

Distance = 730 kilometers.

Since given that,

1 mile =1.609 kilometers

So,

1 kilometer = 1/1.609 miles

So,

730 kilometers = 730 × 1/1.609 miles

⇒ 456.70 miles

Hence "The conversion of  730 km into miles is 456.70 miles so Maria drives 456.70 miles".

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Answer:

The answer is 30

Step-by-step explanation:

12÷2×5

6×5

=30

The study is a randomized controlled trial (RCT) study.

In an RCT study, participants are randomly assigned to either the treatment group or the control group. The treatment group receives the intervention (in this case, one of the two surgery procedures) being studied, while the control group does not receive the intervention.

The participants are then followed to observe the outcome of interest (in this case, the hours to recovery after surgery).

The goal of an RCT study is to determine if the intervention has an effect on the outcome. By randomly assigning participants to the treatment and control groups, any observed differences in the outcome between the two groups can be attributed to the intervention.

This helps to control for other factors that may influence the outcome and reduces the risk of bias in the results.

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The corporation should deposit $4,298.46 at the end of each month into the sinking fund.

The amount of interest earned over the life of the account is: $47,616.64.

The value of the fund after 2, 4, 6 are $56,243.62, $115,263.54, $178,155.28 respectively.

The interest earned during the second month of the 7th year is $317.13

To determine the amount that should be placed in the sinking fund at the end of each month, we can use the formula for present value of an annuity:

PV = R[(1-(1+i)^(-n))/i]

where:

PV = present value of the sinking fund

R = monthly deposit

i = monthly interest rate

n = number of months

We know that the sinking fund needs to have a future value of $460,000 in 8 years. If we assume monthly deposits and monthly compounding, we have:

PV = 0

FV = $460,000

i = 6.5%/12 = 0.00541667

n = 8 years * 12 months/year = 96 months

Using the formula, we can solve for R:

R = (FV*i)/((1+i)^n - 1) = ($460,000 * 0.00541667)/((1+0.00541667)^96 - 1) = $4,298.46

Therefore, the corporation should deposit $4,298.46 at the end of each month into the sinking fund.

To determine the amount of interest earned over the life of the account, we can subtract the total amount deposited from the total amount in the sinking fund at the end of 8 years:

Total amount deposited = $4,298.46/month * 96 months = $412,383.36

Total amount in sinking fund after 8 years = $460,000

Interest earned = $460,000 - $412,383.36 = $47,616.64

To determine the value of the fund after 2, 4, and 6 years, we can use the formula for future value of an annuity:

FV = R[((1+i)^n - 1)/i]

where:

FV = future value of the sinking fund

R = monthly deposit

i = monthly interest rate

n = number of months

After 2 years, we have:

FV = $4,298.46[((1+0.00541667)^(2*12)) - 1]/0.00541667 = $56,243.62

After 4 years, we have:

FV = $4,298.46[((1+0.00541667)^(4*12)) - 1]/0.00541667 = $115,263.54

After 6 years, we have:

FV = $4,298.46[((1+0.00541667)^(6*12)) - 1]/0.00541667 = $178,155.28

To determine the interest earned during the second month of the 7th year, we can first calculate the total amount in the sinking fund at the beginning of the 7th year:

FV = $4,298.46[((1+0.00541667)^(6*12)) - 1]/0.00541667 = $178,155.28

Then, we can calculate the amount of interest earned during the first month of the 7th year:

Interest earned = $178,155.28 * 0.00541667 = $964.11

Finally, we can calculate the amount of interest earned during the second month of the 7th year by subtracting the interest earned during the first month from the total interest earned during the 7th year:

Interest earned during second month = $47,616.64 * (0.065/12) - $964.11 = $317.13

Therefore, the interest earned during the second month of the 7th year is $317.13

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Answer:

2(x-3)² - 11 where a = 2, b = -3, c = -11

Step-by-step explanation:

Taking the first 2 terms,

2x² - 12x ==> 2(x² -6x)   [1]

x² -6x can be rewritten as (x -3)² - 9 [2]

since (x-3)² = x² -6x + 9  

Substituting for x² -6x in [1] we get

2(x² -6x) = 2((x -3)² - 9 ) = 2(x-3)² -18

Therefore substituting for 2x² - 12x in the original equation we get

2x² - 12x + 7 = 2(x-3)² -18 + 7 ==> 2(x-3)² -11

this is in the form (a(x+b) + c where a = 2, b = -3 and c= -11

Cross-check
2(x-3)² - 11 ==> 2 (x² -6x +9) -11 ==> 2x² -12x +18 - 11 ==> 2x² -12x + 7

if the value of x doubles, the value of y will also double, since y is directly proportional to x with a constant of 5. Therefore, the answer is 28. So correct option is A.

In mathematics, an equation is a statement that shows that two expressions are equal to each other. An equation typically consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equals sign (=).

Equations are used to represent mathematical relationships and to solve problems in a variety of fields, including physics, engineering, economics, and finance. They can be linear or non-linear, and they may involve one or more variables.

If the equation is y = 5x, and the value of x doubles, then the new value of x would be 2x. To find the corresponding value of y, we can substitute 2x for x in the equation:

y = 5(2x)

y = 10x

So if the value of x doubles, the value of y will also double, since y is directly proportional to x with a constant of 5. Therefore, the answer is 28.

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The volume of the pot is = 731.2 cubic inches.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured.

The space occupied within an object's borders in three dimensions is referred to as its volume.

It is sometimes referred to as the object's capacity.

Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.

Since the forms of various three-dimensional objects vary, so do their volumes.

According to our answer-

volume of a pot is = πr²h + 2πr³

22/7 * 698/3

731.2 cubic inches

Hence, The volume of the pot is = 731.2 cubic inches.

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Step-by-step explanation:

finding volume of pyramid

\( \frac{1}{3} (12 \times 18)(13) \\ \frac{1}{3} (216)(13) \\ \frac{1}{3} (2808) \\ 936 {ft}^{3} \)

volume of the rectangular prism

\((12)(18)(11) \\ (216)(11) \\ 2376 {ft}^{3} \)

volume of the shape

\(936 + 2376 \\ 3312 {ft}^{3} \)

Answer:

8

Step-by-step explanation:

215-175=40

40÷5=8

Answer:

$8 should be your answer

Step-by-step explanation:

215 - 175 = 40

40 ÷ 5 = 8

Answer:

225 cm^3

Step-by-step explanation:

(a) There are 81 possible answer sequences for the four questions.

(b) The probability of getting all four answers correct when guessing is approximately 0.01235 when rounded to five decimal places.

(c) The probability of answering at least one question correctly when guessing is approximately 0.51775 when rounded to five decimal places.

(a) Since there are three possible answers for each of the four questions, there are a total of 3^4 = 81 possible answer sequences for the four questions.

(b) If you are guessing on each question, the probability of getting one question correct is 1/3. Since there are four questions, the probability of getting all four correct is (1/3)^4 = 1/81, which is approximately 0.01235 when rounded to five decimal places.

(c) The probability of not getting any question correct is (2/3)^4, since there are two incorrect answers for each question and we are guessing on all four questions. Therefore, the probability of getting at least one question correct is 1 - (2/3)^4, which is approximately 0.51775 when rounded to five decimal places.

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The missing term in the provided quadratic equation is 10x if the roots of a quadratic equation are 5 ± 3i.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have the roots of a quadratic equation:

5 ± 3i

To find the quadratic equation:

(x - (5+3i))(x - (5-3i))

\(\rm =x^2+x\left(-\left(5-3i\right)\right)-\left(5+3i\right)x-\left(5+3i\right)\left(-\left(5-3i\right)\right)\)

= x² -10x + 34

The missing value is 10x

The quadratic equation is:

= x² -10x + 34

Thus, the missing term in the provided quadratic equation is 10x if the roots of a quadratic equation are 5 ± 3i.

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60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

According to the question,

We have the following information:

3 digits integers are to be made from 1,2,3,4 and 5

So, we will use permutation to find the possible number of digits that can be made if we apply all the given conditions.

Now, we have:

Total number of digits = 5

Number of digits to be made = 3

So, we have:

\(^{5} P_{3}\)

Solving this expression:

5*4*3

60

Hence, 60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

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Answer: See explanation

Step-by-step explanation:

Diameter = 8 inches

Radius = Diameter/2 = 8/2 = 4 inches

Height of the cylinder = 3 inches

Height of the cone = 18 inches

Volume of a cylinder = π r² h

= 3.14 × 4² × 3

= 3.14 × 16 × 3

= 150.72

Volume of a cone = 1/3 π r² h

= 1/3 × 3.14 × 4² × 18

= 1/3 × 3.14 × 16 × 18

= 301.44

From the answer gotten, we can deduce that the volume of the cone is twice the volume of the cylinder.

Answer:

- Yes, They agree

Step-by-step explanation:

Do Rachel and Dylan argree?

- Yes, They agree

Prove your answer using the values of the ratio.

100 of your friends listen to it

- Total Number = 100

Rachel said the ratio of the number of the people who liked the playlist to the number of people who did not like the playlist is 75:25.

The ratio can be simplifies further by diving all through by 25;

75/25  : 25/25

3 : 1

Dylan said that for every three people who liked the playlist, one person did not.

This simplifies to 3 : 1.

Same thing with what rachel said, so they both agree

20 + 2 + 2 + 9,  20 + 4 + 9 add 24+9 by making tens.

What is an example of tens and ones?

There are always tens and ones in two-digit numerals. As an illustration, the tens place of the number 56 is represented by 5 and the ones place by 6, respectively.

                      Here, each rod is one ten and is made up of ten ones. First fact: As 1 ten, 2 tens, 3 tens, 4 tens, and so on, the numbers 10, 20, 30, 40, and so forth can be written.

Where do the ones and tens go?

A location with a value of 1 in the system of places and values. In the number 23, the one's place is occupied by 3. a place with a value of 10 in the system of place-values. 2, which is in the tens place, is the number 23.

24+9 by making tens

= 20 + 2 + 2 + 9

    20 + 4 + 9

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The surface area of the  gas tank capsule represented to 1 dp is about 9079.2 cm²

The surface area of a solid object is the area of all the faces of the object.

Part of the dimension of the gas tank obtained from a similar question on the website is; Total length of the gas tank = 85 cm

Therefore;

Radial length of the tank = (85 cm - 51 cm)/2 = 17 cm

The surface area of the tank can be found as the surface area of a composite figure. The extreme right and left part of the tank together form a sphere, while the middle portion is a cylinder. Therefore, we get;

Surface area = 4 × π × 17² + 2 × π × 17 × 51 = (1734 + 1156) × π = 2890·π

Surface area of the figure = 2890·π cm² ≈ 9079.2 cm²

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The new volume (V₂) will be twice the initial volume (V₁) when the absolute temperature is doubled at constant pressure.

According to Charles's Law, which states that the volume of a gas is directly proportional to its absolute temperature when pressure is held constant, if the absolute temperature of a given amount of gas is doubled, the new volume will also double.

V₁ / T₁ = V₂ / T₂

Where:

V₁ and T₁ are the initial volume and absolute temperature respectively,

V₂ and T₂ are the final volume and absolute temperature respectively.

If the absolute temperature is doubled (T₂ = 2T₁),

V₁ / T₁ = V₂ / (2T₁)

By cross-multiplying and simplifying,

V₂ = 2V₁

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Using Green's Theorem to evaluate ∫ C → F ⋅ d → r , where → F = 〈 √ x + 6 y , 2 x + √ y 〉 and C consists of the arc of the curve y = 3 x − x 2 from (0,0) to (3,0) and the line segment from (3,0) to (0,0).The orientation of C is counterclockwise, so the integral evaluates to:

              ∫ C → F ⋅ d → r = ∫ 0 3 ∫ 0 3 x − 2 y dx dy = −2/3.

Let's understand this in detail:

1. Parametrize the curve C

Let x = t and y = 3t - t2

2. Calculate the area enclosed by the curve

A = ∫ 0 3 (3t - t2) dt

       = 9 x 3/2 - x2/3 + 10

3. Check the orientation of the curve

Since the curve and the line segment are traced in the counterclockwise direction, the orientation of the curve will be counterclockwise.

4. Use Green's Theorem

∫ C → F ⋅ d → r  = ∇ x F(x,y) dA

            = 9 x 3/2 - x2/3 + 10

5. Simplify the Integral

∫ C → F ⋅ d → r = [ √ (3t - t2) + 6 (3t - t2) ] [6t - 2t2] dt

                 = [ 3 (3t - t2) + 6 (3t - t2) ] (36t2 - 12t3 + 2t4)

                 = −2/3.

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Riemann sum approximation ol L (4ln + 2) dx with n subintervals of equal length is Σ[(4(i/n) + 2)]Δx, not 02(n(' %)2)" as it seems to contain typographical errors.

To find the left Riemann sum approximation of the integral ∫(4ln(x) + 2) dx using n subintervals of equal length, we need to divide the interval of integration into n equal subintervals and evaluate the function at the left endpoint of each subinterval, then sum up the areas of the rectangles formed.

Let's rewrite the given options in a more readable format:

Option 1: Σ[2((8i) + 2)]Δx

Option 2: Σ[(4i + 2)]Δx

Option 3: Σ[(4(i/n) + 2)]Δx

Option 4: Σ[(4(i/n) + 2)]Δx^2

To determine the left Riemann sum, we want to use the left endpoints of the subintervals, which are given by (i/n) for i = 0, 1, 2, ..., n-1.

The correct option for the left Riemann sum approximation is:

Option 3: Σ[(4(i/n) + 2)]Δx

In this option, (i/n) represents the left endpoint of each subinterval, (4(i/n) + 2) represents the function evaluated at the left endpoint, and Δx represents the width of each subinterval.

Note:

A left Riemann sum approximation of L (4ln + 2) dx with n subintervals of equal length is given by the following formula:

LRS = h/n * [2(x0 + 2) + 2(x1 + 2) + 2(x2 + 2) + ... + 2(xn-1 + 2) + 2(xn + 2)]

where h is the length of the interval (4/n) and xi is the ith subinterval (xi = 4i/n). Thus, the left Riemann sum approximation of L (4ln + 2) dx with n subintervals of equal length is given by:

LRS = (4/n) * [2(0 + 2) + 2(4/n + 2) + 2(8/n + 2) + ... + 2(4(n-1)/n + 2) + 2(4n/n + 2)]

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Answer:

Area of sector = 21.21

Step-by-step explanation:

Answer:

Area of sector = ½ r² ∅

1/2 ( 9^2) pi/6

81 x pi/6 x 1/2

81 x (0.52359877559) x 1/2

Area of sector = 21.21

Step-by-step explanation:

Answer:A

Step-by-step explanation:

if total is 90 and one part is 62,

90-62=28=CAT

The percentage of money spent on books to that of cost for last semester is 16%

The cost for last semester was 2000.

The cost books was 320.

The percentage formula = part/whole × 100

Part = 320

Whole = 2000

Equation = 320/2000× 100

               = 32/20

               = 16%

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The increase in the minimum wage from $8.10 to $15, indicates that the percentage increase in the minimum wage is 85.\(\overline{185}\)%

A percentage represent the number, amount, proportion or ratio of an item to another (possibly larger) item per hundred (100) units of the comparison or larger item.

Percentages, quantitatively describes the idea of the amount of a substance. It is a measure of the amount or occurrence of an item.

The specified original minimum wage at Ben's Burger = $8.10

The new amount to which the minimum wage is increased = $15

The percentage increase can be obtained using the formula;

\(\% \ increase = \frac{New - Original}{Original} \times 100\)

The percentage increase is therefore; ((15 - 8.10)/8.1) × 100 = 85.\(\overline{185}\) %

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Answer:

See below.

Step-by-step explanation:

1.) False - It contains 6 sig figs, not 2.

2.) False - It goes up to 2 decimal places, not 3.

3.) True

4.) False - It goes up to 1 sig fig, not 4.

a) The 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b) The 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

To calculate the confidence intervals for the population proportion, we can use the formula:

Confidence Interval = sample proportion ± margin of error

The margin of error can be calculated using the formula:

Margin of Error = critical value * standard error

where the critical value is determined based on the desired confidence level and the standard error is calculated as:

Standard Error = \(\sqrt{((p * (1 - p)) / n)}\)

Given that the sample proportion (p) is 0.81 and the sample size (n) is 500, we can calculate the confidence intervals.

a. 90% Confidence Interval:

To find the critical value for a 90% confidence interval, we need to determine the z-score associated with the desired confidence level. The z-score can be found using a standard normal distribution table or calculator. For a 90% confidence level, the critical value is approximately 1.645.

Margin of Error = \(1.645 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0323

Confidence Interval = 0.81 ± 0.0323

≈ (0.7777, 0.8423)

Therefore, the 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b. 95% Confidence Interval:

For a 95% confidence level, the critical value is approximately 1.96.

Margin of Error = \(1.96 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0363

Confidence Interval = 0.81 ± 0.0363

≈ (0.7737, 0.8463)

Thus, the 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

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As a result, for the same data set, a 99% confidence interval would have a greater margin of error than a 90% confidence interval.

Answer: If a 90% confidence interval is constructed based on a sample of data, and it is 74% + 3%, a 99% confidence interval based on this same sample of data would have a larger margin of error and probably a different center.

What is a confidence interval? A confidence interval is a statistical technique used to establish the range within which an unknown parameter, such as a population mean or proportion, is likely to be located. The interval between the upper and lower limits is called the confidence interval. It is referred to as a confidence level or a margin of error.

The confidence level is used to describe the likelihood or probability that the true value of the population parameter falls within the given interval. The interval's width is determined by the level of confidence chosen and the sample size's variability. The confidence interval can be calculated using the standard error of the mean (SEM) formula

.A 90% confidence interval indicates that there is a 90% chance that the interval includes the population parameter, while a 99% confidence interval indicates that there is a 99% chance that the interval includes the population parameter.

When the level of confidence rises, the margin of error widens. The center, which is the sample mean or proportion, will remain constant unless there is a change in the data set. Therefore, alternative A is the correct answer.

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Answer:

2 seconds later

Step-by-step explanation:

Since the required equation is lacking, let the equation modeled by the height be expressed as y = -16t² + 64

The ball hits the ground at y =0. Substitute y = 0 into the expression and find t;

Since y = -16t² + 64

0 =  -16t² + 64

16t² = 64

t² = 64/16

t² = 4

t = ±√4

t = 2 and -2

Time cannot be negative, hence the ball hits the ground 2 seconds later.

Note that the equation used was assumed. Similar solution can be applied for any given equation.

The correct answer is option c. Cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the opposite side in a right triangle.

In a right triangle, the hypotenuse is the side opposite the right angle, the opposite side is the side opposite the angle of interest, and the adjacent side is the side adjacent (next to) the angle of interest.

To understand why cosine is defined as adjacent/ opposite, let's consider a right triangle:

In the triangle above, the angle of interest is θ (theta). The adjacent side is the side adjacent to θ, and the opposite side is the side opposite to θ. The hypotenuse is the side opposite the right angle.

The cosine of θ is defined as the ratio of the length of the adjacent side to the length of the opposite side:

cos(θ) = adjacent / opposite

This definition stems from the trigonometric ratios in right triangles. By dividing the adjacent side by the opposite side, we can determine the cosine of an angle, which represents the ratio of the lengths of these two sides.

Therefore, option c, "Adjacent / opposite," correctly represents the definition of cosine in the context of a right triangle.

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