Suppose a square had an area measured in square inches, with a numerical value that is 12 more than that of its perimeter, measured in inches.


Write an equation that can be used to find the dimensions of the square

Answer:

Step-by-step explanation:

Height of the triangle = apothem = 9 inches

Base = 6 inches

\(Area \ of \ triangle = \frac{1}{2}bh\\\\=\frac{1}{2}*6*9\\\\= 3*9\\\\= 27 \ in^{2}\)

Area of regular polygon = Area of 5 triangle.

                                        = 5 * 27

                                        = 135 square inches

Answer:

If the amount is P, with the interest rate of 12%, the interest over the year is:

In this case the quarterly interest rate is:

With the same amount and 3% quarterly rate, the yearly interest would be:

The quarterly interest rate in this case is:

If the quarterly interest rate is r, it should be little less than 3% to yield a 12% yearly rate.

So Kraig is wrong.

A, B, D are your answers

AP E X

Point H is the midpoint of FG, Line t intersects FG at a right angle and Line t is perpendicular to FG are true statements.

A system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

A. Point H is the midpoint of FG: This statement must be true because line t is the perpendicular bisector of FG, which means it passes through the midpoint of FG and intersects FG at a right angle.

Therefore, H is the midpoint of FG.

B. Line t intersects FG at a right angle: This statement must be true because line t is the perpendicular bisector of FG, which means it intersects FG at a right angle.

C. FG = FH: This statement is not necessarily true.

While H is the midpoint of FG, the length of FH depends on the position of point H along line t. It could be greater than, less than, or equal to half the length of FG.

D. Line t is perpendicular to FG

This statement must be true because line t is the perpendicular bisector of FG, which means it is perpendicular to FG.

E. Line t is parallel to FG: This statement is not true. If line t were parallel to FG, it would not intersect FG at all, let alone at a right angle as required for a perpendicular bisector.

Therefore, Point H is the midpoint of FG, Line t intersects FG at a right angle and Line t is perpendicular to FG are true statements.

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The system of equations has infinite solutions, both equations represent the same line.

Here we have the following system of equations:

-3x+6y=12

2y=x+4

And we want to solve this by substitution, first, we can rewrite the first equation as:

-3x + 3*(2y) = 12

Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:

-3x + 3*(x + 4) = 12

Now we can solve this for x.

-3x + 3x + 12 = 12

12 = 12

So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).

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The change in volume (dv) is equal to 1221.45 cm³ if the radius of the sphere changes from 18 cm to 18.3 cm.

The change in the volume of the sphere can be represented by the following formula;

dV = 4πr²(dr)

Here dV is the change in the volume, r represents the radius and dr represents the change in the radius of the sphere.

As the radius of this sphere changes from 18 cm to 18.3 cm, we first calculate the change in radius by subtraction;

change in radius = 18.3 - 18 = 0.3 cm

Now substituting the values in the equation;

dV = 4π(18²)(0.3)

dV = 4π(324)(0.3)

dV = 4π(97.2)

dV = 1221.45

Therefore, the change in the volume of the sphere is 1221.45 cm³

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Answer:

The equation of a straight line is always \(y=mx+b\), where m is a constant which is the slope and b is a constant which is the y-intercept.

Substitute these values in:

\(y=3x-7\)

The graph would look like the image attached.

Answer:

The financial incentive had a significant effect on the proportion of individuals who quit smoking

Step-by-step explanation:

To determine if the financial incentive had a significant effect on the proportion of individuals who quit smoking, we can conduct a hypothesis test.

Null hypothesis: The proportion of individuals who quit smoking in the financial rewards group is the same as the proportion who quit smoking in the traditional group.

Alternative hypothesis: The proportion of individuals who quit smoking in the financial rewards group is greater than the proportion who quit smoking in the traditional group.

We can use a one-tailed z-test for proportions to test this hypothesis, with a significance level of 0.05.

First, we calculate the pooled proportion of individuals who quit smoking:

p = (number of individuals who quit smoking in financial rewards group + number of individuals who quit smoking in traditional group) / (total number of individuals in both groups)

p = \(\frac{(0.15 * 439 + 0.05 * 439)}{878}\)

p = 0.1

Next, we calculate the standard error of the difference between the two proportions:

SE = \(\sqrt{(p(1-p) * ((1/n1) + (1/n2)))}\)

where n1 is the sample size of the financial rewards group (439) and n2 is the sample size of the traditional group (439).

SE = \(\sqrt{(0.1 * 0.9 * ((1/439) + (1/439)))\)

SE = 0.022

Finally, we calculate the test statistic:

z = (p1 - p2) / SE

where p1 is the proportion of individuals who quit smoking in the financial rewards group (0.15) and p2 is the proportion of individuals who quit smoking in the traditional group (0.05).

z = (0.15 - 0.05) / 0.022

z = 4.55

The critical z-value for a one-tailed test with a significance level of 0.05 is 1.645.

Since our calculated z-value is greater than the critical z-value, we reject the null hypothesis and conclude that the proportion of individuals who quit smoking in the financial rewards group is significantly greater than the proportion who quit smoking in the traditional group.

Therefore, we can say that the financial incentive had a significant effect on the proportion of individuals who quit smoking.

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"Monica swam 9/16 of a mile on Tuesday. She swam 1 5/8 of a mile on Wednesday. She swam approximately 2 miles in all" is the true statement.

This a problem on addition and subtraction of fractions

Since Hope's dad gives her 7/8 of a chocolate bar one day and then gives her 6/12 of a chocolate bar the next day. Hope received approximately 1 chocolate bar. Total chocolate  received will be:

Total chocolate received = 7/8  + 6/12 = 1 3/8

This statement is not true

Since Dee has 10/12 of a cake and gives 4/8 to her neighbor. Dee has approximately 1 cakes left. The cakes left will be:

cakes left = 10/12 - 4/8 = 1/3

This statement is not true

Since Joe ran 8/15 of a mile on Thursday. He ran 4/5 of a mile on Friday. Joe ran approximately 1/2 mile in all. The total mile ran will be:

total mile ran =  8/15 + 1/2 = 2 1/10

This statement is not true

Monica swam 9/16 of a mile on Tuesday. She swam 1 5/8 of a mile on Wednesday. She swam approximately 2 miles in all.

mile swam =  9/16 +  1 5/8 = 2 3/16

This statement is true

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Answer:

3×0+1=1

Step-by-step explanation:

i hope that helps

Answer:

2762.5

Step-by-step explanation:

Answer:

34.5

Step-by-step explanation:

21,23,27,28, 31, 38, 48, 50, 52, 57

31+38=69

69/2=34.5

Answer:

(0, ∞ )

Step-by-step explanation:

Basic exponential functions always take on values ranging from (but not touching) 0 upward.

Thus, the range of this particular exponential function is (0, ∞ )

Answer:

14.86 is the answer..............

Answer:

-14.86

hope this helps :)

The Riemann sum for the function f(x) = -1, with the sample points chosen to be the right-hand endpoints of each sub-interval, is given by Rn = -(b - a), and limit of Rn as n approaches infinity also equal to -(b - a).

A Riemann sum is a method for approximating the area under a curve by dividing the area into a number of rectangles and summing their areas.

The function f(x) = -1 is constant function.

We want to calculate the Riemann sum Rn for this function, where the sample points are chosen to be the right-hand endpoints of each sub-interval. Let [a, b] be the interval of integration and let Δx = (b - a)/n be the width of each sub-interval.

Then, the right-hand endpoints of the sub-intervals are given by xi = a + iΔx for i = 1, 2,.., n. The corresponding function values are f(xi) = -1 for all i.

The Riemann sum Rn is given by:

Rn = Σ[i=1 to n] f(xi)Δx

Substituting f(xi) = -1 for all i, we get:

Rn = Σ[i=1 to n] (-1)Δx

Rearranging the terms, we get:

Rn = -Σ[i=1 to n] Δx

Since Δx = (b - a)/n, we have:

Rn = -Σ[i=1 to n] (b - a)/n

Expanding the summation, we get:

Rn = -[(b - a)/n + (b - a)/n + ... + (b - a)/n]

There are n terms in the summation, each equal to (b - a)/n.

Rn = -n(b - a)/n = -(b - a)

we get:

limn→∞ Rn = -limn→∞ (b - a) = -(b - a)

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Answer:

-33

-20

-4

6

3

Step-by-step explanation:

I apologize if I get any wrong

Answer:

(D) 2

Step-by-step explanation:

The scale factor of the enlargement of ΔABC to ΔA'B'C' is given by the ratio of the length of the corresponding sides of ΔA'B'C' and ΔABC

Therefore, we have;

\(The \ scale \ factor = \dfrac{Length \ of \overline {B'C'}}{Length \ of \overline {BC}} = \dfrac{Length \ of \overline {A'C'}}{Length \ of \overline {AC}} = \dfrac{Length \ of \overline {A'B'}}{Length \ of \overline {AB}}\)

\(\dfrac{Length \ of \overline {B'C'}}{Length \ of \overline {BC}} = \dfrac{2 \ units}{1 \ unit} = 2\)

\(\dfrac{Length \ of \overline {A'C'}}{Length \ of \overline {AC}} = \dfrac{4 \ units}{2 \ units} = 2\)

\(\dfrac{Length \ of \overline {A'B'}}{Length \ of \overline {AB}} = \dfrac{2 \cdot \sqrt{5} \ units}{\sqrt{5} \ units} = 2\)

Therefore, the scale factor = 2

Answer:

47 degrees

Step-by-step explanation:

142-95 will come to an answer of 47  .

The compound inequality for the graph shown above is :

It's important to use the least common denominator when adding or subtracting rational expressions, to ensure that the resulting expression is in its simplest form.

What is Algebraic expression ?

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

The main disadvantage of adding two rational expressions using a common denominator that is not the least common denominator is that the resulting expression may not be in its simplest form.

For example, consider the following two rational expressions:

2     3

- + -----

x     x + 1

If we use a common denominator of x(x+1), we get:

2(x+1)     3x

------- + -----

x(x+1)    x(x+1)

However, the least common denominator of these two expressions is x(x+1), and we can simplify the expression by multiplying the first term by (x+1)/(x+1):

2(x+1)       3

------- + -------

x(x+1)    x(x+1)

= (2x+2+3x)/(x(x+1))

= (5x+2)/(x(x+1))

So, if we had used the common denominator x^2 + x, we would have obtained the following expression:

2(x+1)(x)     3(x+1)

---------- + ----------

x(x+1)    x(x+1)

= (2x^2+2x+3x+3)/(x^2+x)

= (2x^2+5x+3)/(x^2+x)

which is not in its simplest form, since we can factor the numerator to get:

(2x+1)(x+3)/(x(x+1))

Therefore, it's important to use the least common denominator when adding or subtracting rational expressions, to ensure that the resulting expression is in its simplest form.

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As given by the question

There are given that the table for the survey.

Now,

From the table, the new vehicle that is driven by juniors and seniors is 37 and 74.

And,

The total number of drives is 199.

So,

The percentage of the new vehicle is :

Then,

Hence, the correct option is B.

Answer:

0.72 repeat

Step-by-step explanation:

              __

8 ÷ 11 =0.72

Answer:

P(0 < X < 1, 1 < Y < 2) = 0

P(X ≥ 1, Y ≥ 1) = 0

Step-by-step explanation:

To compute P(0 < X < 1, 1 < Y < 2), we need to evaluate the joint cumulative distribution function (CDF) within the given range.

First, let's break down the problem into two cases:

Case 1: 0 < X < 1, 1 < Y < 2

In this case, both X and Y fall within the specified ranges.

P(0 < X < 1, 1 < Y < 2) = FX,Y(1, 2) - FX,Y(1, 1) - FX,Y(0, 2) + FX,Y(0, 1)

To calculate these probabilities, we can refer to the given joint CDF:

FX,Y(x, y) =

0 if x < 0 or y < 0

min(x, y) if 0 ≤ x, y < 1

x if 1 ≤ x, y ≤ 2

Plugging in the values, we get:

P(0 < X < 1, 1 < Y < 2) = min(1, 2) - min(1, 1) - min(0, 2) + min(0, 1)

= 1 - 1 - 0 + 0

= 0

Therefore, P(0 < X < 1, 1 < Y < 2) equals zero.

Note: The joint CDF is discontinuous at (1, 1) and (0, 2), which is why the probability is zero in this particular range.

Case 2: X ≥ 1, Y ≥ 1

In this case, both X and Y are greater than or equal to 1.

P(X ≥ 1, Y ≥ 1) = 1 - FX,Y(1, 1)

Using the given joint CDF, we have:

P(X ≥ 1, Y ≥ 1) = 1 - min(1, 1)

= 1 - 1

= 0

Therefore, P(X ≥ 1, Y ≥ 1) equals zero.

In summary:

P(0 < X < 1, 1 < Y < 2) = 0

P(X ≥ 1, Y ≥ 1) = 0

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Denote by X the arrival time of the first guest. The time of arrival of the first guest at a bank is modeled by the Poisson distribution, where the arrival rate is λ. Thus, the number of arrivals during time t is Poisson(λt).

Therefore, the distribution of X is Exponential(λ), which means that its probability density function is

f(x) = λe−λx, x > 0.

The expected value of X is E[X] = 1/λ and the variance is Var(X) = 1/λ².

b. Denote by Y the arrival time of the second guest.

The number of arrivals during time t is Poisson(λt). The first guest arrived at time X, so the number of arrivals from time X to time t is Poisson(λ(t - X)).

Thus, the arrival time of the second guest has the conditional probability density function:

f(y | X) = λe^(−λ(y−x)), y > x

Therefore, the unconditional probability density function of Y is obtained through the law of total probability:

f(y) = ∫f(y | x)f(x)dx

= ∫λe^(−λ(y−x))λe^(−λx)dx

= λ²e^(−λy), y > 0

Therefore, the distribution of Y is Exponential(λ), which is the same as that of X.

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Step-by-step explanation:

the answer will be zero 0

Answer: -1.5

Step-by-step explanation:

took the test

The z-score of a bag of almonds weighing 12.2 ounces will be negative 1.5.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

A machine packages bags of almonds.

The weights of the bags are normally distributed with a mean of 14 ounces and a standard deviation of 1.2 ounces.

Then the z-score of a bag of almonds weighing 12.2 ounces will be

z-score = (x - mean) / SD

z-score = (12.2 - 14) / 1.2

z-score = -1.8 / 1.2

z-score = -1.5

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Answer:To evaluate the exponential expression 6(4+2)² - 32, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, we simplify the expression inside the parentheses:

4 + 2 = 6

Next, we square the result:

6² = 36

Now, we substitute the squared result back into the expression:

6(36) - 32

Next, we perform the multiplication:

6 * 36 = 216

Finally, we subtract 32:

216 - 32 = 184

Therefore, the value of the given exponential expression 6(4+2)² - 32 is 184.

Answer:

Step-by-step explanation:

In exponents division, if base are same then subtract the powers.

\(\frac{a^{m}}{a^{n}}=a^{m-n}\)    when m > n

\(\frac{a^{m}}{a^{n}}=\frac{1}{a^{n-m}}\)     when n > m

\(\frac{19^{23}}{19^{41}} = \frac{1}{19^{41-23}} = \frac{1}{19^{18}}\)

Answer:

Sheesh they r correct lol

Step-by-step explanation:

a. The most that they could expect to sell it for is $19,3026.00.

b. If you purchase a home for $435,500.00, then you can expect to sell it for $670,432.00 after 11 years

c. for the first two months, the interest portion of the payment is $39.55 and the principal portion of the payment is $89.51.

It is the amount of money that a borrower pays to a lender for the use of the lender's money or asset.

a. A holiday trailer depreciates in value approximately 10% per year.

If your family purchases a holiday trailer for $29,000.00 and they plan on selling in the 4th year, then the most that they could expect to sell it for is $19,3026.00.

To calculate this, we can use the following equation:

Amount after n years = Original Amount x (1 - Depreciation Rate)ⁿ

= 29,000.00 x (1 - 0.10)⁴

= 29,000.00 x 0.6561

= $19,3026.00

b. In some housing markets, it is predicted that homes will continue to appreciate at 4% per year into the future.

If you purchase a home for $435,500.00, then you can expect to sell it for $670,432.00 after 11 years, if this appreciation percentage is correct.

To calculate this, we can use the following equation:

Amount after n years = Original Amount x (1 + Appreciation Rate)ⁿ

= 435,500.00 x (1 + 0.04)¹¹

= 435,500.00 x 1.5394

= $670,432.00

c. Huan accepted an in-store loan on a computer she just purchased. The monthly payment is $64.53 on the $2,000 computer with a 12% APR for 3 years. To determine the portion of the monthly payment that will go towards interest and principal for the first two months, we can use the following equation:

Interest Payment = (Principal Balance x Monthly Interest Rate)

Principal Payment = Monthly Payment - Interest Payment

For the first month:

Interest Payment = (2,000.00 x 0.12/12)

= $20.00

Principal Payment = 64.53 - 20.00

= $44.53

For the second month:

Interest Payment = (1,955.47 x 0.12/12)

= $19.55

Principal Payment = 64.53 - 19.55

= $44.98

Therefore, for the first two months, the interest portion of the payment is $39.55 and the principal portion of the payment is $89.51.

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