Select the correct answer from each drop-down menu. ∆abc has side lengths of 10 units, 20 units, and 24 units. ∆xyz is similar to ∆abc, and the length of its longest side is 60 units. the perimeter of ∆xyz is units. if the height of ∆abc, with respect to its longest side being the base, is 8 units, the area of ∆xyz is square units.

Answer:

1. 3

2. 1

3. 2

4. 4

5. 5

Step-by-step explanation:

Answer:

The third answer is correct.

Step-by-step explanation:

You are going to translate the smaller quadrilateral (4 sided figure) to the larger quadrilateral.  Then you need the scale factor from the smaller figure to the larger.  

Side EF times the scale factor will give you side AB.  Let's call the scale factor s then our equation would be:

EF x s = AB  To find s divide both sides by EF

\(\frac{EF(s)}{EF}\) = \(\frac{AB}{EF}\)

s = \(\frac{AB}{EF}\)  This is our scale factor.

Helping in the name of Jesus.

Answer:

-5/2

Step-by-step explanation:

for perpendicularity;

\(m1 = \frac{ - 1}{m2} \)

where m1 is first slope

and m2 is second slope

so here, let m1 be green line slope

and m2 be red line slope

thus,

\(m2 = \frac{ - 1}{m1} \)

\(m2 = \frac{ - 1}{ \frac{2}{5} } = - 1 \div \frac{2}{5} \)

\( = - 1 \times \frac{5}{2} = \frac{ - 5}{2} \)

Answer:

16

The simplest way to do it is:

5 x 2 = 10

8 x 2 = 16

The cost of the company and the profit functions indicates;

Part A; The profit, P(x) = -0.5·x² + 40·x - 300

Part B; x = 20 and x = 60

Part C; The company can impossibly make a profit of $15,000

The profit is the difference between the revenue and the cost of the goods and services sold by the company.

Part A; The cost, C(x) = 40·x + 300

The revenue function is; R(x) = 80·x - 0.5·x²

(Therefore, the profit, P(x) = R(x) - C(x)

P(x) = 80·x - 5·x² - (40·x + 300) = -0.5·x² + 40·x - 300

P(x) = -0.5·x² + 40·x - 300

Part B; When the profit, P(x) = 300, we get;

P(x) = -0.5·x² + 40·x - 300 = 300

-0.5·x² + 40·x - 300 - 300 = 0

-0.5·x² + 40·x - 600 = 0

x² - 80·x + 1200 = 0

(x - 20) × (x - 60) = 0

x = 20, and x = 60

The values of x at which the profit will be $300 are x = 20, and x = 60

Part C; When the profit is $1,500, we get;

P(x) = -0.5·x² + 40·x - 300 = 1,500

-0.5·x² + 40·x - 300 = 1,500

-0.5·x² + 40·x - 1,800 = 0

x² - 80·x + 3,600 = 0

The discriminant indicates that we get;

D = (-80)² - 4 × 1 × 3,600) = -8000

The discriminant is -8,000, therefore, there are no real result, and the company can not make a profit of $15,000

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The vertex form of the given equation, y = -6x² + 3x + 2, is expressed as: y = -6(x - 0.25)² + 2.375.

The vertex form of an equation is expressed as, y = a(x - h)² + k, where:

(h, k) = vertex of the parabola.

Given the equation, y = -6x² + 3x + 2, factor the equation:

y = -6(x² - 0.5x) + 2

y = -6(x² - 0.5 + 0.0625) + 2.375

Rewriting the equation as perfect squares, we would have:

y = -6(x - 0.25)² + 2.375

The vertex form of y = -6x² + 3x + 2 is, y = -6(x - 0.25)² + 2.375.

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Answer:

c y = -6(x-1/4)^2+19/8

Step-by-step explanation:

Answer:

It's C.

Step-by-step explanation:

12x+4+9x+8=180

Combine like terms 21x+12=180

Subtract 12 from both sides 21x=168

Divide each side by 21 21x/21=168/21

x=8

Since we need to round up to the next integer, the required sample size for this experiment is 284 people for the confidence level.

To find the required sample size for NASA's experiment, we can use the following formula for the sample size estimation in a proportion experiment:

\(n = (Z^2 * p * (1-p)) / E^2\)

where:
- n is the sample size
- Z is the z-score corresponding to the desired confidence level (85% in this case)
- p is the estimated population proportion (0.33)
- E is the margin of error (0.04)

First, we need to find the z-score for an 85% confidence level. We can look this up in a z-table, or use an online calculator. The z-score for an 85% confidence level is approximately 1.44.

Next, we can plug the values into the formula:
\(n = (1.44^2 * 0.33 * (1-0.33)) / 0.04^2\)
n ≈ (2.0736 * 0.33 * 0.67) / 0.0016
n ≈ 283.66

Since we need to round up to the next integer, the required sample size for this experiment is 284 people.

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A checking account is used for daily basis transaction and a debt and is usually associated with it.Saving accounts is just used for saving money.It has a time limit then you can withdraw your money.It is not on daily basis.

A bank account that allow the user to withdraw the money ,pay bill,transfer money to other person or make a purchase anything by writing checks.Check accounts typically don't earn interest.By checking accounts we can easily deposit and withdraw money for daily transaction.

Saving accounts are intended for storing your money which you don't plan to use daily.saving accounts earns interest at your money.saving account is designed for the accumulation of money in a safe place for future use.saving accounts offer easy access to your money in any emergency.so keeping your money in a saving account means that your money is safe for your future use.

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The correct answer is options A and E.

f(x) = 6x + 4

f(1) = 6(1) + 4 = 10

f(2) = 6(2) + 4 = 16

f(3) = 6(3) + 4 = 22

Clearly, options A and E are the same sequences.

S_10 is an affine geometry, S_14 is a projective geometry, S_15 is neither an affine nor projective geometry and S_21 is a projective geometry.

For each of the following finite incidence structures, draw a picture and determine which are affine geometries, which are projective geometries, which are neither.

(a) S_10 is an affine geometry because each line has two points, and every pair of points lies on a unique line. The structure is symmetrical since each point is connected to the other three points.

(b) S_14 is a projective geometry because it contains a set of three pairwise disjoint lines (lines with no common points) {A, B, R}, {C, D, R}, {R, T, U}. It also satisfies the axiom that any two points have a unique line passing through them.

(c) S_15 is neither an affine nor projective geometry. Although every pair of points lies on a unique line, it doesn't satisfy the other axioms of affine or projective geometries, like the existence of a set of pairwise disjoint lines.

(d) S_21 is a projective geometry. It has three sets of pairwise disjoint lines: {A, B, C}, {D, E, F}, {G, H, I}, and each pair of points has a unique line passing through them.

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In mathematics, "\(a^2\)" denotes the square of a number or variable "a." It is calculated by multiplying "a" by itself.

4For example, if "a" is 5, then a^2 would be 5*5, which equals 25. When "a" represents a positive number, its square is always positive.

If "a" is negative, its square is still positive since a negative multiplied by a negative results in a positive.

In geometrical terms, if "a" represents the length of the side of a square, then a^2 represents the area of that square. This notation is part of the general concept of exponentiation.

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The Question in English

What does a^2 mean in mathematics

Answer:

x=4

y=5

Step-by-step explanation:

inform me if u cant open the image

Answer:

(4,5)

Step-by-step explanation:

I solved through substitution

3x+2y=22

x-2y=-6 ----> -2y=-6-x ----> -2y=-x-6 -----> y=1/2x+3

Solving for x:

3x+2y=22

3x+2(1/2x+3)=22

3x+x+6=22

4x+6=22

4x=16

x=4

Solving for y:

x-2y=-6

4-2y=-6

-2y=-10

y=5

(4,5)

The component of statistical methodology that encompasses the collection, organization, and summarization of data is referred to as descriptive statistics.

Descriptive statistics is a fundamental aspect of statistical methodology that focuses on the initial stages of data analysis. It involves the collection of data through various methods such as surveys, experiments, or observational studies. This data is then organized and structured in a systematic manner to facilitate a comprehensive understanding of its characteristics.

The first step in descriptive statistics is data collection. This can involve various techniques such as sampling, where a subset of the population is selected to represent the entire group. The collected data can be quantitative (numerical) or qualitative (categorical), depending on the nature of the study.

Once the data is collected, it needs to be organized in a meaningful way. This can involve sorting, categorizing, and arranging the data into different groups or categories. For quantitative data, measures such as frequency distributions, histograms, and scatter plots can be used to organize and display the data. For qualitative data, methods such as tables, charts, or graphs may be employed to summarize the information.

Finally, descriptive statistics involves summarizing the collected and organized data to extract key insights and characteristics. This can include measures such as central tendency (mean, median, mode), variability (range, variance, standard deviation), and correlation. These measures provide a concise summary of the data, enabling researchers to gain a better understanding of its overall patterns, trends, and distribution.

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Answer:

The average was 259.24 in 1996.

Step-by-step explanation:

In order to find the year that the average, "y", is 259.24 we need to apply this value on the given expression, as done below:

\(259.24 = 0.15*x + 255.34\\0.15*x = 259.24 - 255.34\\0.15*x =3.9\\x = \frac{3.9}{0.15}\\x = 26\)

The average was 259.24 after 26 years, therefore it was in 1996.

The real numbers can be classified as either rational or irrational numbers.

1. Rational Numbers:
Rational numbers can be expressed as the ratio (or fraction) of two integers. They can be written in the form p/q, where p and q are integers and q is not equal to zero. Rational numbers can be positive, negative, or zero. Some examples of rational numbers include 1/2, -3/4, and 5.

2. Irrational Numbers:
Irrational numbers cannot be expressed as the ratio of two integers. They are non-repeating and non-terminating decimals. Irrational numbers can be positive or negative. Some examples of irrational numbers include √2, π (pi), and e (Euler's number).

It is important to note that the set of real numbers contains both rational and irrational numbers. Every rational number is a real number, but not every real number is a rational number. This means that there are real numbers that cannot be expressed as a fraction.

In summary, the classification of real numbers as rational or irrational depends on whether they can be expressed as a ratio of integers (rational) or not (irrational). The set of real numbers contains both rational and irrational numbers, providing a comprehensive representation of all possible values on the number line.

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Using the binomial distribution, it is found that there is a 0.864 = 86.4% probability that at most 5 seniors will attend the prom.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem, we have that:

The probability that at most 5 seniors will attend the prom is given by:

\(P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)\)

In which:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{20,0}.(0.18)^{0}.(0.82)^{20} = 0.0189\)

\(P(X = 1) = C_{20,1}.(0.18)^{1}.(0.82)^{19} = 0.0829\)

\(P(X = 2) = C_{20,2}.(0.18)^{2}.(0.82)^{18} = 0.1730\)

\(P(X = 3) = C_{20,3}.(0.18)^{3}.(0.82)^{17} = 0.2278\)

\(P(X = 4) = C_{20,4}.(0.18)^{4}.(0.82)^{16} = 0.2125\)

\(P(X = 5) = C_{20,5}.(0.18)^{5}.(0.82)^{15} = 0.1493\)

\(P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0189 + 0.0829 + 0.1730 + 0.2278 + 0.2125 + 0.1493 = 0.864\)

0.864 = 86.4% probability that at most 5 seniors will attend the prom.

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The difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

According to the given question.

We have a function

f(x) = -1/(5x -12)

As we know that, the difference quotient is a measure of the average rate of change of the function over and interval.

The difference quotient formula of the function y = f(x) is

[f(x + h) - f(x)]/h

Where,

f(x + h) is obtained by replacing x by x + h in f(x)

f(x) is a actual function.

Therefore, the difference quotient formual for the given function f(x)

= [f(x + h) - f(x)]/h

= \(\frac{\frac{-1}{5(x+h)-12} -\frac{-1}{5x-12} }{h}\)

= \(\frac{\frac{-1}{5x + 5h -12}+\frac{1}{5x-12} }{h}\)

= \(\frac{\frac{-1+5h}{5x + 5h-12} }{h}\)

= \(\frac{-1+5h}{(5x +h-12)(h)}\)

= \(\frac{-1+5h}{5xh + h^{2} -12h}\)

= \(\frac{h(-\frac{1}{h}+5) }{h(5x+h-12)}\)

= \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\)

Hence, the difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

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Answer:

  305 miles

Step-by-step explanation:

You want to know how far Dylan travelled if he drove 50 mph for 3.5 hours and 65 mph for 2 hours.

Distance is the product of speed and time. The total distance Dylan travelled will be the sum of lengths of the legs of his trip.

  distance = speed · time

  total distance = speed1 · time1 + speed2 · time2

  = (50 mi/h)(3.5 h) +(65 mi/h)(2 h) = 305 mi

Dylan travelled a total of 305 miles.

Answer:

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

Using the Commutative property of addition, which states that the order of addends does not affect the sum, you can rewrite:

Now, the expression becomes:

Next, apply the Associative property of addition, which states that the grouping of addends does not affect the sum.

You can rearrange the terms as follows:

Then, combine the like terms:

Now the expression matches the given form:

This shows that the two expressions are equivalent using the Commutative and Associative properties of addition.

Option C is the correct choice as it accurately describes the chi-square test for independence. The chi-square test for independence is used to determine if there is a relationship between two categorical variables. It is similar to neither a single-sample t test nor a correlation because it involves categorical variables, not continuous ones.

Option C accurately describes the chi-square test for independence. It states that the test is similar to an independent-measures t test because it compares separate samples to evaluate the difference between separate populations.

The chi-square test for independence involves creating a contingency table that displays the observed frequencies of the two categorical variables. Then, it calculates the expected frequencies under the assumption of independence. The test compares the observed and expected frequencies using the chi-square statistic. If the observed frequencies significantly differ from the expected frequencies, we reject the null hypothesis and conclude that there is a relationship between the variables.

In contrast, options A, B, and D do not accurately describe the chi-square test for independence. Option A refers to a single-sample t test, which is not applicable to the chi-square test. Option B mentions a correlation, which assesses the relationship between continuous variables, not categorical ones. Option D combines elements of both a correlation and an independent-measures t test, which are not applicable to the chi-square test.

Therefore, option C is the correct choice as it accurately describes the chi-square test for independence.
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Answer:

27 days

Step-by-step explanation:

15% of 180 = 27

Answer: 8

Step-by-step explanation:

Right on edge!

Answer: D

Step-by-step explanation: Just solve for perimeter of a rectangle by just plugging the side length in with these equations.

Answer -2,3. 2,3 3,-3 -4 -3

Step-by-step explanation:

Answer:

Q (-2, 3)
R (2, 3)

S (3, -3)

T (-4, -3)

Step-by-step explanation:

Good luck kiddos :)

Answer

15 to 2

Step-by-step explanation:

Answer:

\(\Huge \boxed{x=8}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

E ———— F ———— G

EG = EF + FG

27 = (2x - 8) + (4x - 13)

Combining like terms.

27 = 6x - 21

Adding 21 to both sides.

48 = 6x

Dividing both sides by 6.

8 = x

\(\rule[225]{225}{2}\)

The value of the variable x will be 1.

A line segment in mathematics has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a path that joins two places.

If EF = 2x - 8, FG = 4x - 13, and EG = 27.

Point F lies on the line segment EG. Then we have

EG = EF + FG

27 = 2x - 8 + 4x - 13

27 = 6x - 21

6 = 6x

x = 1

Then the value of the variable x will be 1.

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