The equilateral triangle shown has a perimeter of 30 inches and a height of a inches.
What is the value of a?
O 5 in
O 5√3 in
O10 in
•10√3 in

The correct option that shows the associative property is D:

[tex](\left[\begin{array}{ccc}4\\2\end{array}\right] + \left[\begin{array}{ccc}3\\5\end{array}\right]) + \left[\begin{array}{ccc}1\\3\end{array}\right] = \left[\begin{array}{ccc}4\\2\end{array}\right] + (\left[\begin{array}{ccc}3\\5\end{array}\right] + \left[\begin{array}{ccc}1\\3\end{array}\right] )[/tex]

The associative property of addition says that we can perform sums in any order we want:

A + (B + C) = (A + B) + C

The option that shows this property is the one at D, where we have 3 vectors and we can select any order in which we add them, such that the sum is written as:

[tex](\left[\begin{array}{ccc}4\\2\end{array}\right] + \left[\begin{array}{ccc}3\\5\end{array}\right]) + \left[\begin{array}{ccc}1\\3\end{array}\right] = \left[\begin{array}{ccc}4\\2\end{array}\right] + (\left[\begin{array}{ccc}3\\5\end{array}\right] + \left[\begin{array}{ccc}1\\3\end{array}\right] )[/tex]

That expression shows the associative property of the addition with matrices.

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The division expressions to the quotients and remainders are

Expression (a)

The expression is given as

(x² - x - 30) ÷ (x - 6)

The synthetic set up is

6 |   1  -1  30

   |__________

Bring down the first coefficient, which is 1 and repeat the process

6 |   1  -1  30

   |___6_-30_____

      1   -5   0

This means that

Quotient = x - 5 with no remainder

Expression (b)

The expression is given as

(x³ - 2x² - 7x - 4) ÷ (x² + 2x + 1)

Using a graphing tool, we have

(x³ - 2x² - 7x - 4) ÷ (x² + 2x + 1) = x - 4 with no remainder

This means that

(x³ + 2x² - 1) ÷ (x² - x + 1) = x + 3 R 2x - 4

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The total area Cydney painted on the display stand is 416 square inches, excluding the bottom of the larger cube.

5. To solve the problem, we need to find the total area that Cydney painted on the display stand.

Plan for solving the problem:

6. Solving the problem:

The surface area of a cube is given by the formula: [tex]6 * (side length)^2[/tex].

For the larger cube:

Surface area of the larger cube =[tex]6 * (8 inches)^2[/tex] = 6 * 64 square inches = 384 square inches.

For the smaller cube:

Surface area of the smaller cube = [tex]6 * (4 inches)^2[/tex]= 6 * 16 square inches = 96 square inches.

Since the bottom of the display stand was not painted, we need to subtract the area of the bottom face of the larger cube:

Area of the bottom face of the larger cube = [tex](side length)^2[/tex] =[tex](8 inches)^2[/tex] = 64 square inches.

Finally, we can calculate the total area Cydney painted by adding the surface area of both cubes and subtracting the area of the bottom face of the larger cube:

Total area painted = (Surface area of the larger cube + Surface area of the smaller cube) - Area of the bottom face of the larger cube

= (384 square inches + 96 square inches) - 64 square inches

= 480 square inches - 64 square inches

= 416 square inches

Therefore, Cydney painted a total area of 416 square inches on the display stand.

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Part 1a) An exponential function is a better model to represent the data because the rate of change is not constant instead of using a linear function, whose rate of change (slope) is constant.

Part 1b) The slope between each points are different.  So, the data is best represented by an exponential function.

Part 2a) The estimated number of college degrees earned in the United States in 2050 is about 2 million.

Part 2b) The estimated number is more likely to be an under-estimation.

Exponential equations increase by a constant exponent or power, written in the form of $$f(x) = ab{x}$$.

Linear equations or functions increase by a constant slope, written in the form of y = mx + b, where m is the slope.

Year    College degrees

            (  thousands)

1910                37

1930             122

1950            432

1970            792

1990          1,051

2010          1,650

Using exponential smoothing in Excel, the result of the prediction shows that 2,237,000 college degrees will be earned in 2050.

The number of college degrees earned in the United States in 2050 = 2,237,000 ≈ 2 million.

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Area of the figure is 402.8 ft².

We have,

Rectangle area = Length x Width

Area of sector = π r² x angle / 360

Now,

There are two rectangles and one sector.

So,

Area of one rectangle.

= 8 x 2

= 16 ft²

Area of another rectangle.

= 5 x 2

= 10 ft²

Area of the sector.

= π x r² x {360 - (150 + 90 + 90)}

= 3.14 x 2² x 30

= 376.8 ft²

Now,

The area of the figure.

= 16 + 10 + 376.8

= 402.8 ft²

Thus,

The area of the figure is 402.8 ft².

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Answer:

$27.69

Step-by-step explanation:

39 - (39)(0.29) = 39 - 11.31 = 27.69

The circumference of the given circle is approximately 47.3 inches.

Since the length of the arc KL and the measure of the central angle ∠KOL are known, we can use the formula for arc length to find the circumference of the circle:

arc length = (central angle / 360°) x circumference

Plugging in the known values, we have:

4.6 in = (35° / 360°) x circumference

Solving for the circumference, we get:

circumference = 4.6 in / (35° / 360°)

circumference = 4.6 in x (360° / 35°)

circumference ≈ 47.3 in (rounded to the nearest tenth)

Therefore, the circumference of the circle is approximately 47.3 inches.

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The probabilities are given as follows:

a) x is less than 60: 0.9495 = 94.95%.

b) x is greater than 16: 0.9909 = 99.09%.

c) x is between 16 and 60: 0.9404 = 94.04%.

d) x is greater than 60: 0.0505 = 5.05%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 42, \sigma = 11[/tex]

The probability of a value less than 60 is the p-value of Z when X = 60, hence:

Z = (60 - 42)/11

Z = 1.64

Z = 1.64 has a p-value of 0.9495.

Hence the probability of a value greater than 60 is of:

1 - 0.9495 = 0.0505 = 5.05%.

The probability of a value greater than 16 is one subtracted by the p-value of Z when X = 16, hence:

Z = (16 - 42)/11

Z = -2.36

Z = -2.36 has a p-value of 0.0091.

1 - 0.0091 = 0.9909 = 99.09%.

The probability of a value between 16 and 60 is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 16, hence:

0.9495 - 0.0091 = 0.9404 = 94.04%.

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We can match the numbers in Column I with their square roots in Column II as follows:

1. √844 = C. 29.1

2. √900 = H. 30

3. √650 = G. 25.5

4. √784 = E. 28

5. √699 = B. 26.4

6. √805 = D. 28.4

7. √729 = A. 27

To find the square roots of the numbers, we can simply punch the sign into the calculator and insert the figures in it. For instance, to find the square root of 900, we can simply insert the figure into the calculator while inputting the square root sign before it.

To determine if your answer is correct, try squaring the numbers. The output should be the original numbers provided.

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Answer:

7.7

Step-by-step explanation:

Find the third angle that is not given:

180 - (120 + 37) = 23.

Draw a line that cuts the 120 degree angle and makes two 90 degree angles with the opposite side. We will call this line h.

You can find the length of h by using sine of 37 degrees. We get:

sin(37 deg) = h/5

h = 3.01

Because we have already found the third angle, 23 degrees, we can use sine of 23 degrees to find the missing side length (x):

sin(23 deg) = 3.01/x

x = 7.7

Answer is 7.7

The graph could be the graph of exponential function of option b)

[tex]F(x) = 2 • (0.5)^{x} [/tex]

The general form of an exponential function is

[tex]f(x) = {ab}^{x} [/tex]

Here, a is the function's starting value and b is its growth factor.

F(x) is an increasing function if b > 1, and if b<1, then f(x) is a decreasing function

The function's initial value is 2 as can be seen from the provided graph. Therefore, a has a value of 2.

Given that the graph indicates that the function is decreasing, b must be less than 1.

It indicates that the necessary function is in the form of

[tex]f(x) = 2(b)^{x} [/tex]

Where it is b<1

By checking option B, b=0.5<1. Hence, option B is the correct answer

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Note that the full question is:

(check the attached image)

Justification:

(1) BP | Premise

(2) (RDP) | Premise

(3) RD B | Modus Ponens (1), (2)

(4) ROP | Premise

(5) T | Modus Ponens (3), (4)

T | Conclusion (the desired statement to be proved)

The given proof is presented in the format of a deductive argument, where each line represents a statement that either follows logically from previous statements (i.e., by a rule of inference) or is assumed to be true (i.e., a premise). The objective of the proof is to demonstrate that the conclusion, represented by the symbol "/T", is a logical consequence of the premises.

The justification column of the proof provides an explanation of why each statement in the argument is true or valid. In this proof, the first four lines are premises that are assumed to be true, and their justifications are simply labeled as "Premise". The last two lines of the proof represent the application of a rule of inference called modus ponens, which states that if we have two statements A and A -> B, we can infer B. The justification for line 3 is modus ponens with lines 1 and 2 as antecedent and consequent respectively, and the justification for line 5 is modus ponens with lines 3 and 4 as antecedent and consequent respectively.

The conclusion of the proof, represented by "/T", is reached by applying modus ponens with lines 3 and 4 as antecedent and consequent respectively. The conclusion follows logically from the premises and the application of the modus ponens rule, which justifies the truth of the conclusion. Therefore, we can conclude that the argument is valid, and the conclusion can be accepted as true.

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The cost of the items indicates that the inequality that represents the cost or amount spent is; 18 + 5n ≤ 50, therefore, yes Mai is correct, because the total amount spent depends on the amount with Priya

An inequality is a comparison between two expressions, variables, or quantities that are of different values, using the symbols, '<', '≤', '≠', '≥', and '>'.

The amount Priya has to spend = $50

The cost the gift she finds for her parents = $18

The number of siblings Priya has = 5

Therefore;

The cost of the items she thinks each of her 5 siblings would like = 5 × n

The total cost of the items Priya intends to buy = 18 + 5·n

The inequality that indicates the possibility of Priya buying all the items she finds is therefore;

18 + 5·n ≤ 50

Therefore, May is correct as the amount or the cost of items Priya buys should be less than or equivalent to the $50 Priya has

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Answer: center: (5,-5) radius: 8

Step-by-step explanation:

found it online:)

Using MACRS rates, the book value of the $2,500 computer after 3 years is $720.

MACRS (Modified Accelerated Cost Recovery System) rates are prearranged percentages used for the purposes of tax.

They compute how much an asset depreciates each year based on its class and expected lifespan.

Using MACRS rates, we shall calculate the book value of a $2,500 computer after 3 years in this way.

First, we shall apply the respective depreciation rates to the initial cost and subtract the accumulated depreciation each year.

Year 1:

Depreciation = Year 1 MACRS Rate x Initial Cost

Depreciation = 20.0% × $2,500 = $500

Year 2:

Depreciation = Year 2 MACRS Rate x Initial Cost

Depreciation = 32.0% × $2,500 = $800

Year 3:

Depreciation = Year 3 MACRS Rate x Initial Cost

Depreciation = 19.2% × $2,500 = $480

Next, subtract the accumulated depreciation from the initial cost to have the book value for each year:

Year 1:

Book Value = Initial Cost - Depreciation

Book Value = $2,500 - $500 = $2,000

Year 2:

Book Value = Year 1 Book Value - Year 2 Depreciation

Book Value = $2,000 - $800 = $1,200

Year 3:

Book Value = Year 2 Book Value  - Year 3 Depreciation

Book Value = $1,200 - $480 = $720

Therefore, the book value of the $2,500 computer after 3 years is $720.

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The batting average for Brett is of 0.25 = 25%.

The batting average is obtained applying the proportions in the context of the problem.

A proportion is applied as the batting average is given by the division of the number of hits by the number of at bats.

Brett got 10 hits in 40 at bats, hence his batting average is calculated as follows:

10/40 x 100% = 0.25 x 100% = 25%.

From the image given at the bottom, we have that he got 10 hits on 40 at bats, hence the batting average calculated above is of 25%.

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The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

Option A is the correct answer.

We have,

The problem states that a student must work on i-Ready for at least 4 hours per month to receive a grade of 100.

Since Sophia received a math grade of 100, it means that she has met the requirement of working on i-Ready for at least 4 hours in the last month.

And,

The symbol "≥" means "greater than or equal to," indicating that Sophia worked for at least 4 hours.

Therefore,

The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

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Answer:

332.88

Step-by-step explanation:

To find the median of this data set, we first need to determine the total number of observations. This is given by the last cumulative frequency, which is 189.

Since the total number of observations is an odd number, we can find the median by identifying the middle value. The middle value is the observation that has half the data below it and half the data above it.

To find this value, we can divide the total number of observations by 2:

189 ÷ 2 = 94.5

This means that the median observation falls in the 330-339 range, since the cumulative frequency at the end of this range is 38, which is the smallest cumulative frequency greater than 94.5.

To find the exact median value, we can use the following formula:

Median = L + ((N/2 - CF) / f)

where:

L = lower limit of the median class (in this case, 330)

N = total number of observations (in this case, 189)

CF = cumulative frequency of the class preceding the median class (in this case, 20)

f = frequency of the median class (in this case, 24)

Plugging in the values, we get:

Median = 330 + ((94.5 - 20) / 24)

= 330 + (74.5 / 24)

≈ 332.88

Therefore, the median of the given scores is approximately 332.88.

In order to convert the base of the logarithm from base 10 to any other base and calculate intensities, we need the change of base formula.

To solve this problem, we need to use the logarithmic property known as the "change of base formula" which states that:

log_a (b) = log_c (b) / log_c (a)

This formula allows us to change the base of a logarithm from one value to another.

In this case, we want to find the ratio of the intensity of the first speaker to that of the second speaker, which is given by:

ratio = intensity of the first speaker/intensity of the second speaker

To calculate this ratio, we need to first convert the decibel values to intensities using the formula:

intensity = 10^(dB/10)

where dB is the decibel value.

For the first speaker, the intensity is:

intensity of the first speaker = [tex]10^{(85/10)} = 7.94 *10^8[/tex]

For the second speaker, the intensity is:

the intensity of the second speaker [tex]= 10^{(75/10)} = 1.78 * 10^7[/tex]

Now we can calculate the ratio of intensities:

[tex]ratio = (7.94 * 10^8) / (1.78 * 10^7) = 44.66[/tex]

This means that the sound from the first speaker is 44.66 times more intense than the sound from the second speaker.

Therefore, we need the change of base formula to change the base of the logarithm from 10 to any other base to calculate the intensities.

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The mass of the frying pan in grams is 52 grams.

In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.

Generally speaking, there are one (1) kilogram in one hundred (100) grams. This ultimately implies that, a proportion or ratio for the conversion of 0.52 kilogram to grams would be written as follows;

Conversion:

1 kilogram = 100 grams

0.52 kilogram = x grams

By cross-multiplying, we have the following:

x = 0.52 × 100

x = 52 grams.

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Complete Question:

The mass of Stewart's favorite frying pan is 0.52 kilograms. What is the mass of the frying pan in grams?

The required amount of rent be $4,850.19.

The original rent of apartment per month = $1700

And the interest = 11%

Time = 10 years.

To determine the apartment's rent during the tenth year:

Rent is calculated as Initial = Rent x [tex](1 + Increase Rate )^{year}[/tex] .

We plug the values and compute the rent for the tenth year using the provided data,

Rent = $1700 x (1 + 0.11)¹⁰

Rent = $1700 x 2.85

Rent = $4,850.19

Thus,

The apartment's rent in the tenth year would be about $4,850.2 per month.

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The solution of the equation using Cramer's rule is x = -3, and y = 2.

The solution of the equation using Cramer's rule is calculated as follows;

x + 2y = 1

-3x - 2y = 5

Find the determinant of the matrix;

[1     2]

[-3   -2]

Δ = -2 - (-6) = 4

Find the x determinant;

[1      2]

[5     -2]

Δx = -2 - 10 = -12

Find the y determinant;

[1      1]

[-3   5]

Δy = 5 - (-3) = 8

The value of x = Δx/Δ  = -12/4 = -3

The value of y = Δy/Δ  = 8/4 = 2

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Answer:

To determine which bank is more cost-effective, we need to consider how many transactions we will make per month. Let's call the number of transactions "t".

Bank A charges a flat fee of $45 per month, regardless of how many transactions we make. So the total cost of using Bank A for one month is:

Total cost for Bank A = $45

Bank B charges a monthly fee of $20, plus $0.70 for each transaction. So the total cost of using Bank B for one month is:

Total cost for Bank B = $20 + ($0.70 x t)

To determine which bank is more cost-effective, we need to find the value of "t" that makes the total cost of Bank B equal to the total cost of Bank A.

$45 = $20 + ($0.70 x t)

$25 = $0.70 x t

t = $25 / $0.70

t ≈ 36

So if we make 36 or more transactions per month, Bank A is more cost-effective. If we make fewer than 36 transactions per month, Bank B is more cost-effective.

Answer:

x < 6

Step-by-step explanation:

3x < 18 ( divide both sides by 3 )

x < 6

Yes, Both diagonal are equal in length with √ 80 units.

We have to given that;

The coordinates of rectangle PQRS are P(1, 6), Q(1, 2), R(9, 2), and S(9, 6).

Hence, The length of diagonal are PR and QS.

Since, We know that;

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, Length of PR is,

PR = √ (x₂ - x₁)² + (y₂ - y₁)²

PR = √ (9 - 1)² + (2 - 6)²

PR = √ 64 + 16

PR = √ 80

And, Lenght of QS is,

QS = √ (x₂ - x₁)² + (y₂ - y₁)²

QS = √ (9 - 1)² + (2 - 6)²

QS = √ 64 + 16

QS = √ 80

Thus, Both diagonal are equal in length with √ 80 units.

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The location of the center and the radius will be (-1.5. -2) and 3, respectively. Thus, the correct option is A.

Given that:

Equation: (x + 1.5)² + (y + 2)² = 9

Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,

(x - h)² + (y - k)² = r²

Compare the equation, then we have

Center: (-1.5, -2)

Radius: r² = 9 ⇒ r = 3

Thus, the correct option is A.

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The probability that 12 or more bikes will be returned out of 335 stolen bikes is approximately 0.1747 (17.47%).

Let X be the random variable representing the number of bikes returned out of 335 stolen bikes.

We are given that the probability of a single bike being returned which is:

p = 0.03 (3% written as a decimal).

We can use the binomial distribution to calculate the probability of X bikes being returned:

P(X = k) = [tex]335C_{k} * p^{k} * (1-p)^{335-k}[/tex]

where [tex]335C_{k}[/tex] reads 335 combination k.

To find the probability that fewer than 12 bikes will be returned, we can calculate the cumulative probability:

P(X < 12) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 11)

Using a calculator, we find that:

P(X < 12) = 0.8253.

The probability of 12 or more bikes being returned can be calculated as the complement of the probability of fewer than 12 bikes being returned:

P(X ≥ 12) = 1 - P(X < 12) = 1 - 0.8253 = 0.1747

Therefore, the probability that 12 or more bikes will be returned out of 335 stolen bikes is approximately 0.1747 or 17.47%.

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If two variables are directly proportional, this means that the ratio of the two variables is constant. In other words, if x and y are directly proportional, then there exists some constant k such that:

y = kx

To find the missing value in the table, we can first calculate the value of k using any set of corresponding values for x and y. For example, we can use the first row of the table:

y = kx 9 = k(-3) k = -3

Now that we know k, we can use it to find the missing value for the second row:

y = kx y = (-3)(-5) y = 15

Therefore, the missing value in the table is 15.

The correct statement regarding the transformations to [tex]f(x) = 10^x[/tex] to create [tex]g(x) = 3(10)^x - 2[/tex] is given as follows:

A vertical dilation by a factor of 3 and a vertical shift down 2 units

The parent function for this problem is given as follows:

[tex]f(x) = 10^x[/tex]

The transformed function for this problem is given as follows:

[tex]g(x) = 3(10)^x - 2[/tex]

Hence the transformations are given as follows:

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