Which of the following is equivalent to the expression x² - 64?
A) (x-8)²
B) (x-64)²
C)(x-8)(x-8)
D) (x+8) (x-8)

I believe the scale factor is 3. The x coordinate is at 3 for the pre-image and for the image it is 9 so we can conclude that the scale factor is 3.

Answer:

34 cm

Step-by-step explanation:

the gap in the middle is 2 cm because 9 - ( 4 + 3 ) = 2

4 + 2 + 2 + 3 + 3 + 6 + 9 + 5 = 34

The profitability index for Aryan Company's new machine investment is 0.96.

The profitability index is a ratio used to measure the profitability of an investment by comparing the present value of future cash flows to the initial investment cost. It is calculated by dividing the present value of future cash flows by the initial investment cost.

In this case, the present value of the future cash flows can be calculated by multiplying the expected cash flow of $24,000 per year by the present value of an annuity for 3 periods at 12%, which is given as 2.40183. Therefore, the present value of future cash flows is $57,644.32.

The initial investment cost is $60,000.

To calculate the profitability index, we divide the present value of future cash flows by the initial investment cost: $57,644.32 / $60,000 = 0.96074. Rounded to one decimal place, the profitability index is 0.96.

The profitability index indicates that the present value of the expected future cash flows is approximately 96% of the initial investment cost. Generally, a profitability index greater than 1 indicates a favorable investment, while a value less than 1 suggests an unfavorable investment. In this case, the profitability index of 0.96 suggests that the investment is not expected to be highly profitable.

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The complete question is :

Aryan Company p o buy a new machine for $60.000 that will have an estimated useful site of 3 years and no savage value. The expected cash tom $24,000 annually Company has a cost of capital of 12% Given that the present value of $1 after 3 periods at 12% 071172 and the present valu of an annuity for 3ds at 12% is 2.40183, the profitability index is

1.96

1.04

0.28

0.96

0.04

Answer:

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

hope this helps

Using the properties of percentages we can calculate that there are 200 kids in the archery camp that summer.

Long before the decimal numeral system, Ancient Rome routinely computed in fractions as multiples of 1/100.

A percentage is a dimensionless (pure) number; it has no unit of measurement.

The % value is determined by multiplying the numerical value of the ratio by 100. To calculate 50 apples as a percentage of 1250 apples, first compute 50/1250 = 0.04, then multiply by 100 to get 4%.

Let the total number of kids in the camp be x.

The number of kids who took archery = 25%

But 50 students took archery.

hence 25% of x = 50

Solving we infer:

x = 200

Therefore there are 200 kids in the camp.

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In order to revise the second sentence for a presentation, the best thing to do would be to break it up into two sentences.

The second sentence is quite long and so would not be the best fit for a presentation.

We can solve this by breaking it into two sentences such as:

This makes the presentation more readable and ensures that the information is better passed on.

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Answer:

B - Breaking into two sentences

Step-by-step explanation:

Edge 2023

Answer:

Step-by-step explanation:

X       Y                    X           Y    

0       3                     0           5

1        7                     1              8

2        11                    2           11

3        15                   3          14

4         19                   4            17  

Answer:

The slope is 8

Step-by-step explanation:

Answer:

Monomial is the expression that has maximum variable power 1.

so you can add any number or variable in the expression to make it monomial but the over power of variable must be 1.

Step-by-step explanation:

example;    3x2y + 1

Aggregate Demand (AD) is a macroeconomic concept that represents the total demand for goods and services in an economy. The X factor in the AD equation represents exports, which are an important part of the economy.

AD is calculated by adding up the individual components of demand, which include consumer spending (C), investment spending (I), government spending (G), and net exports (X-M). The X-M component represents the difference between exports (X) and imports (M).

The X component in the equation represents exports, which are the goods and services produced domestically and sold to foreign countries. Exports are an important part of the economy as they generate income and create jobs. The M component in the equation represents imports, which are the goods and services purchased from foreign countries and consumed domestically. Imports can have a negative impact on the economy as they represent a drain on resources and can lead to a trade deficit. The X factor in the equation is used to represent exports because it is a variable that can change over time. Factors that can affect exports include exchange rates, tariffs, and global demand for certain products. If the exchange rate between two currencies changes, it can make exports more or less expensive for foreign buyers, which can affect the level of exports. Tariffs are taxes on imports, which can make domestic products more competitive in foreign markets.

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Answer:

D.

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

There are 3 out of 8 shaded in the box, and there are two whole ones, making it:

2 × 3/8

----------------------------------------------------------------------------------------------------------------

Have a good day :)

Answer/Step-by-step explanation:

Given that the side length of a squared field is represented by the expression 3 - 7x,

a. Perimeter of the squared field (expressed as a sum):

Permimeter of a square = s + s + s + s

All sides of a square are of equal length.

s = side length of the squared field = 3 - 7x

Thus,

Perimeter expressed as a sum = (3-7x) + (3-7x) + (3-7x) + (3-7x)

b. Permitted of squared field expressed as a product:

Perimeter of square expressed as product = 4(s)

s = side length of squared field = 3 - 7x

Permimeter of squared field expressed as a product = 4(3 - 7x)

c. An equivalent expression for the product in (b) can be written using the distributive property as follows:

Perimeter = 4(3 - 7x)

Perimeter = 4(3) - 4(7x)

Answer:

80 magazines sold

Step-by-step explanation:

120*2/3=80

Answer:

Ml is 30 ft beco it help in pi

Emma earns approximately $419,000 in total in the first 10 years of her career. The correct option is D.

Emma's total earnings in the first 10 years of her career is the sum of her salary for each year.

In the first year, Emma earns $39,000.

For the subsequent years, she gets a 5% raise. This means her salary increases by 5% each year.

To calculate her salary for each year, we can use the formula:

Salary = Previous Year's Salary + (Previous Year's Salary * 0.05)

Let's calculate her earnings for each year:

Year 1: $39,000

Year 2: $39,000 + ($39,000 * 0.05) = $41,000

Year 3: $41,000 + ($41,000 * 0.05) = $43,050

Year 4: $43,050 + ($43,050 * 0.05) = $45,202.50

Year 5: $45,202.50 + ($45,202.50 * 0.05) = $47,462.63

Year 6: $47,462.63 + ($47,462.63 * 0.05) = $49,835.76

Year 7: $49,835.76 + ($49,835.76 * 0.05) = $52,326.55

Year 8: $52,326.55 + ($52,326.55 * 0.05) = $54,939.88

Year 9: $54,939.88 + ($54,939.88 * 0.05) = $57,680.87

Year 10: $57,680.87 + ($57,680.87 * 0.05) = $60,554.91

Now, let's sum up her earnings for the first 10 years:

Total Earnings = Year 1 + Year 2 + Year 3 + ... + Year 10

Total Earnings = $39,000 + $41,000 + $43,050 + ... + $60,554.91

Total Earnings = $419,478.82.

Therefore, Emma earns approximately $419,000 in total in the first 10 years of her career.

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Geometric series is convergent if the |r|<1 where r is the common ratio.

Let Sn=∑ni=0(−3/4)i then

Sn=(−3/4)n+1−1(−3/4)−1

Now take n→∞ then

Sn→0−1(−3/4)−1=4/7

because |−3/4|<1 and so (−3/4)n→0. Now note that your sum is

lim ∑i=1n+1(−3)i−14i=lim 14∑i=1n+1(−3)i−14i−1=1/4.lim Sn=1/7.

Geometric series: A geometric series is the result of adding together geometric sequences indefinitely. Depending on the sequence given to us, such infinite sums can either be finite or infinite. A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series frequently reach, reach, or avoid a particular number.

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Probability refers to the measure of the likelihood that a particular event will occur. It is represented as a value between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

The probability of an event "A" is denoted as P(A). The probability of an event can be determined based on the following formula:

P(A) = (Number of favorable outcomes)/(Total number of possible outcomes)

We are given that the probability of rolling an even number is twice the probability of rolling an odd number. Thus, the probability of rolling an even number is 2/3, and the probability of rolling an odd number is 1/3. Now we will solve the given questions.1. Pr (B) = 1/3Option d, 1/32. Pr (A n B) = Pr (B) × Pr (A | B)

Here, we know that the probability of rolling an even number is 2/3, and the probability of rolling an odd number is 1/3. Thus, Pr(B) = 1/3We also know that the probability of rolling a number less than 4, given that an odd number shows up is 1/2.

Thus, Pr(A | B) = 1/2Therefore,Pr(A n B) = Pr(B) × Pr(A | B)= (1/3) × (1/2)= 1/6Option c, 1/93. Pr (B) = 1/3Option d, 1/34. Pr (A) = Pr (A n B) + Pr (A n B')From part (2), we know that Pr(A n B) = 1/6

We also know that the probability of rolling a number less than 4, given that an even number shows up is 1/2.

Thus, Pr(A | B') = 1/2Therefore,Pr(A n B') = Pr(B') × Pr(A | B')= (2/3) × (1/2)= 1/3

Hence, Pr(A) = Pr(A n B) + Pr(A n B')= (1/6) + (1/3)= 1/2

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We have an unfair die. When we roll the die, the probability that an even number shows up is twice the probability that an odd number shows up.

The correct options are:

1. Pr(B) = 1/3

2. Pr(AnB) = 1/3

3. Pr(B) = 1/3

4. Pr(A) = 2/3

We define two events A and B as follows:

A = a number smaller than four shows up B = an odd number shows up. The correct options are:

1. Pr(B) = 1/3,

2. Pr(AnB) = 1/3,

3. Pr(B) = 1/3,

4. Pr(A) = 2/3.

To find: Probability of the events (Pr).

Solution: Let's assume the probability of getting odd number be x, then the probability of getting even number will be 2x.

We know, the sum of all the possible outcomes of the die should be equal to 1.

Therefore, the probability of getting odd number + probability of getting even number = 1

⇒ x + 2x = 1

⇒ 3x = 1

⇒ x = 1/3

So, the probability of getting odd number = 1/3 and the probability of getting even number = 2/3.

1) Pr(B) = probability of getting odd number

= 1/3

2) Pr(AnB) = Probability of getting a number smaller than four and odd number

= probability of getting 1 + probability of getting 3

= 1/6 + 1/6

= 1/3

3) Pr(B) = probability of getting odd number

= 1/3.

4) Pr(A) = probability of getting a number smaller than four

= probability of getting 1 + probability of getting 2 + probability of getting 3

= 1/6 + 1/3 + 1/6

= 2/3

Hence, the correct options are:

1. Pr(B) = 1/3

2. Pr(AnB) = 1/3

3. Pr(B) = 1/3

4. Pr(A) = 2/3

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Step-by-step explanation:

2x + 1 + x - 13 = 180° because these angles are supplementary

3x - 12 = 180°

3x = 180 + 12

3x = 192 divide both sides by 3

x = 64

2x + 1 ➡ 2 × 64 + 1 = 129°

x - 13 ➡ 64 - 13 = 51°

It is stated that the two triangles have two sides that are proportional and the angle between them is congruent. This aligns with the conditions of the SAS similarity theorem, making option C the correct choice.

The triangles can be proven similar by the SAS (Side-Angle-Side) similarity theorem, which states that two triangles are similar if and only if two pairs of corresponding sides are proportional and the included angles are congruent.

To understand why option C is the correct answer, let's break down the conditions of the SAS similarity theorem. The theorem states that if two triangles have sides that are proportional (i.e., the corresponding sides have a constant ratio) and the angle between those sides is congruent (i.e., they have the same measure), then the triangles are similar.

In the given question, option C satisfies these conditions. It states that the two triangles have two sides that are proportional, indicating that the corresponding sides have a constant ratio. Additionally, it mentions that the angle between these sides is congruent, meaning it has the same measure in both triangles.

By meeting the requirements of the SAS similarity theorem, option C concludes that the triangles can be proven similar. Therefore, it is the correct choice among the given options.

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Answer:

4 units

Step-by-step explanation:

Answer:

look below

Step-by-step explanation:

Shape A is congruent to shape ___F___, as shown by a reflection across the y-axis and then a translation down __3___ units. B is congruent to shape __D__, as shown by a reflection across the y-axis and then a translation down __2___ units​

Answer:

24

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

5+3=8

8+4=12

Step-by-step explanation:

100% = 12 throws

what are 150% ?

so, the question really is, what do I need to multiply 100(%) with to get 150(%) ?

100×x = 150

x = 150/100 = 1.5

so, since 100% and 12 throws are equivalent, we need to multiply the number of throws with the same factor x :

12×1.5 = 18

so,

150% = 18 throws.

she made 18 throws.

Answer:

$12.50

Step-by-step explanation:

$100 divided by 8 hours = $12.50

Step 1

Find the angles

Hence,

The margin of error for this interval can be calculated by taking the difference between the upper and lower bounds of the confidence interval and dividing it by 2. In this case, the difference between 0.333 and 0.397 is 0.064. Dividing that by 2 gives us a margin of error of 0.032.

This means that if we were to take multiple samples of 500 American households and calculate a confidence interval for each sample, about 95% of those intervals would contain the true proportion of American households that own a dog. However, each interval would differ slightly due to sampling variability, and the true proportion may fall outside the given interval. It is important to note that the margin of error is influenced by the sample size. Larger sample sizes tend to produce smaller margins of error, while smaller sample sizes result in larger margins of error. Therefore, it is crucial to have a sufficient sample size to ensure that the estimate is accurate and the margin of error is small.

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a) the total number of ordered triples in relation R is: 5 * 4 * 3 = 60

b) the cardinality of relation R is |R| = 10.

c) Since the product is not equal to 6, (2, 1, 3, 2) is not in relation R. The answer is "no".

d) Since 1 < 3 < 4 and all elements are integers between 0 and 6, (1, 3, 4) satisfies the conditions and is in relation R. The answer is "yes".

What is cardinality?

In mathematics, cardinality is a concept that refers to the "size" or "number of elements" in a set. It is a measure of the quantity of elements present in a set, disregarding any specific order or arrangement.

a) To count the number of ordered triples in relation R, we need to consider the given conditions: 0 < i < j < k < 6.

Since i, j, and k are integers, we have 5 choices for k (1, 2, 3, 4, or 5). For each choice of k, we have (k-1) choices for j (as j must be smaller than k). Finally, for each choice of j, we have (j-1) choices for i.

Therefore, the total number of ordered triples in relation R is:

5 * 4 * 3 = 60

b) To find the cardinality of relation R, we need to count the number of ordered quadruples (a, b, c, d) that satisfy the condition a * b * c * d = 6.

The prime factorization of 6 is 2 * 3, and since a, b, c, and d are positive integers, we have the following possibilities:

(2, 1, 1, 3), (2, 1, 3, 1), (2, 3, 1, 1)

(1, 2, 1, 3), (1, 2, 3, 1), (1, 3, 1, 2), (1, 3, 2, 1)

(3, 1, 1, 2), (3, 1, 2, 1), (3, 2, 1, 1)

Therefore, the cardinality of relation R is |R| = 10.

c) To determine if (2, 1, 3, 2) is in relation R, we need to check if the product of the four elements equals 6:

2 * 1 * 3 * 2 = 12

Since the product is not equal to 6, (2, 1, 3, 2) is not in relation R. The answer is "no".

d) To determine if (1, 3, 4) is in relation R, we need to check if the three elements satisfy the condition 0 < i < j < k < 6:

Since 1 < 3 < 4 and all elements are integers between 0 and 6, (1, 3, 4) satisfies the conditions and is in relation R. The answer is "yes".

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Answer:

100

Step-by-step explanation:

In a 45-45-90 triangle, the hypotenuse is always larger than either of the legs by a factor of \(\sqrt{2}\). x is therefore:

\(100\sqrt{2}\div \sqrt{2}=100\)

Hope this helps!