Which of these triangle pairs can be mapped to each other using a reflection and a translation?

Answer:

7x + 2y = - 6

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

y = - \(\frac{7}{2}\) x - 3 ( multiply through by 2 to clear the fraction )

2y = - 7x - 6 ( add 7x to both sides )

7x + 2y = - 6 ← in standard form

Answer:

32

Step-by-step explanation:

Totally there are 50 tosses.  

Let the number of tosses which resulted head be x.  

Therefore the number of tosses which resulted tail is 50−x.

We get x×1+(50−x)×(−1)=14

x−(50−x)=14

x−50+x=14

x=32

Answer:a and b

Step-by-step explanation:

The pair of functions which are inverses of each other from the provided function is given in option A and B. Option A and B is correct.

A function assigns the value of each element of one set to the other specific element of another set.

When a function has the point (x,y), then the inverse of this function has the points (y,x).

\((x,y)^{-1}=(y,x)\)

For example, if a function has point (1,2). Then its inverse has the points (2,1).

The first pair of function given in the problem is,

\(f(x)={(-5.-9).(-3,-4), (0, 1), (3, 7), (6, 13)}\\g(x) = {(-9,-5),(-4,-3), (1.0), (7,3), (13,6)}\)

In this pair, each point of function g(x) is an inverse of the respective point of function f(x).

In the second pair, the function is given as,

\(f(x) = x +7\)

Let, f(x) as y,

\(y = x +7\)

Change the points of x and y

\(x = y +7\\x-7=y\\y=x-7\)

Put f(x) on place of y,

\(f(x) = x -7\)

This is equal to the function g(x)=x-7. Thus, the functions are inverse. In the third pair, the inverse of the f(x) is not equal to the g(x).

Thus, the pair of functions which are inverses of each other from the provided function is given in option A and B. Option A and B is correct.

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Answer:

Step-by-step explanation:

1. x is inversely proportional to y

x=k/y

k is the constant of proportionality

x =60/y

2. x=60/y

x=60/12

x=5

Answer:

Step-by-step explanation:

Answer:

500 dollars

Step-by-step explanation:

Final answer:

At 10% interest, $1 000 was invested.

At 6% interest, $9 000 was invested.

Let "x" be the amount invested at 10%. The annual interest for this investment would be $ 0.1x

Now, the investment at 6% is (10 000 - x), and it would have an annual interest of 0.06(10 000 - x)

We will use the following equation to solve for this

interest 1 = 0.1x

interest 2 = 0.06(10 000 - x)

total interest = 640

Substitute these values

Solve for x

Divide both sides by 0.04

Since the investment at 6% is equal to 10000-x,

Final answer:

At 10% interest, $1 000 was invested.

At 6% interest, $9 000 was invested.

To check,

My dream car is a 2022 Audi RS7 Sportback. The asking price for the 2022 Audi RS7 Sportback is $125,000.

To calculate the down payment required for the car loan, I need to multiply the asking price by the down payment percentage:

Down payment = Asking price x Down payment percentage

Down payment = $125,000 x 0.20

Down payment  = $25,000

Therefore, the down payment required for the car loan would be $24,000.

For the third question, to determine the monthly payment with a 20% down payment, 4% interest rate compounded monthly for 5 years, I would use the following formula:

P = (A - DP) x  r ÷ (1 - (1 + r)⁻ⁿ)

Where P is the monthly payment, A is the total loan amount, DP is the down payment, r is the monthly interest rate (4% divided by 12), and n is the total number of months (5 years * 12 months per year).

A = $125,000 - $25,000 = $100,000

r = 0.04 / 12 = 0.00333

n = 5 years x  12 months per year = 60

P = ($100,000 - $25,000) x  0.00333 / (1 - (1 + 0.00333)⁻⁶⁰)

P = $1,734.58

Therefore, the monthly payment with a 20% down payment, 4% interest rate compounded monthly for 5 years, would be $1,734.58.

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Answer:

20 + 35x

Step-by-step explanation:

We have the expression 5(4 + 7x) and are asked to distrbute it.

When distributing, it's very simple, all you have to do is multiply the number outside the parenthesis with the numbers inside the parenthesis.

Therefore :

(5(4) + 5(7x))

20 + 35x

the empire state building weighs 7.3 x 10^8 pounds

The one world trade centre building weighs about 88200, 000 pounds or 0.8 x 10^8 pounds

sum up the weighs

7.3 x 10^8 + 0.8 x 10^8

8.1 x 10^8

so the value of a is 8.1 and the value of b is 8.

With the help of percentage increase information, we conclude that,  Americans spent approximately $1,141.31 on summer vacation in 2014.

What is percenatge increase?

Percentage increase is a measure of how much a value has increased in comparison to the original value, expressed as a percentage.

To find what Americans spent in 2014, we need to use the percentage increase and the 2015 amount.

Let X be the amount spent in 2014.

We know that the increase from 2014 to 2015 is 3.4%, which can be expressed as:

3.4% = 0.034 (as a decimal)

We also know that the amount spent in 2015 is $1,180.

Using this information, we can set up an equation:

X + 0.034X = 1180

Simplifying the left side:

1.034X = 1180

Dividing both sides by 1.034:

X = 1141.31

So Americans spent approximately $1,141.31 on summer vacation in 2014.

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The Canal's price/earnings ratio is 2.92.

To calculate Canal's price/earnings ratio, we need to find the earnings per share (EPS) first. The EPS can be calculated by dividing the net income by the weighted average number of common shares outstanding.

The weighted average number of common shares outstanding can be calculated as follows:

Weighted average number of common shares outstanding = Total number of common shares - Weighted average number of treasury shares

Weighted average number of common shares outstanding = 24,200 - 4,200 = 20,000

EPS = Net income / Weighted average number of common shares outstanding

EPS = $260,000 / 20,000 = $13

Finally, the price/earnings ratio can be calculated by dividing the market price per share by the EPS:

Price/earnings ratio = Market price per share / EPS

Price/earnings ratio = $38 / $13 = 2.92

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Answer:

0.28

Step-by-step eplanation:

Answer:

0.28

Step-by-step explanation:

Use a calculator

Answer:

65.49*0.065 = 4.26

Step-by-step explanation:

65.49*0.065 = 4.26

65.49+4.26 = $69.75

Answer:

$69.75

Step-by-step explanation:

65.49x6.5%= 4.26

65.49+4.26= 69.75

Don't forget your label!

Hope this helps!

-AxekickNebulite

A possible starting point:

Split up the limit as

\(\displaystyle \lim_{n\to\infty} \frac{1 + \sqrt[3]{2} + \cdots + \sqrt[3]{n}}{n^{4/3}} \times \lim_{n\to\infty} \frac1{n \left(\frac1{(an+1)^2} + \frac1{(an+2)^2} + \cdots + \frac1{(an+n)^2}\right)} = 54\)

Consider the first limit,

\(\displaystyle \lim_{n\to\infty} \frac{1 + \sqrt[3]{2} + \cdots + \sqrt[3]{n}}{n^{4/3}}\)

Refer to the Stolz-Cesàro theorem, which says

\(\displaystyle \lim_{n\to\infty} \frac{a_n}{b_n} = \lim_{n\to\infty}\frac{a_{n+1}-a_n}{b_{n+1}-b_n}\)

where \(a_n\) and \(b_n\) are two real sequences, with \(b_n\) monotone and divergent. In this case,

\(a_n = 1+\sqrt[3]{2}+\sqrt[3]{3}+\cdots+\sqrt[3]{n}\)

\(b_n = n^{4/3}\)

Applying S-C, we get

\(\displaystyle \lim_{n\to\infty} \frac{\sqrt[3]{n+1}}{(n+1)^{4/3} - n^{4/3}} = \lim_{n\to\infty} \frac{(n+1)^{1/3}}{(n+1)^{4/3} - n^{4/3}}\)

Recalling the difference of cubes identity,

\(a^3 - b^3 = (a - b) (a^2 + ab + b^2)\)

we can rewrite the limit as

\(\displaystyle \lim_{n\to\infty} \frac{(n+1)^3 + (n+1)^{5/3} n^{4/3} + (n+1)^{1/3} n^{8/3}}{(n+1)^4 - n^4}\)

and dividing uniformly through the limand by (n + 1)³ yields

\(\displaystyle \lim_{n\to\infty} \frac{1 + \left(\frac n{n+1}\right)^{4/3} + \left(\frac n{n+1}\right)^{8/3}}{(n+1) - \frac{n^4}{(n+1)^3}}\)

Now,

\(n^4 = (n+1)^4 - 4n^3 - 6n^2 - 4n - 1\)

\(\implies \dfrac{n^4}{(n+1)^3} = (n+1) - \dfrac{4n^3+6n^2+4n+1}{(n+1)^3}\)

so the denominator in the limit reduces to a degree-1 polynomial with leading coefficient +4. The numerator converges to 1 + 1 + 1 = 3, so this first limit evaluates to

\(\displaystyle \lim_{n\to\infty} \frac{1 + \sqrt[3]{2} + \cdots + \sqrt[3]{n}}{n^{4/3}} = \frac34\)

It remains to determine the value of a such that

\(\displaystyle \lim_{n\to\infty} \frac1{n \left(\frac1{(an+1)^2} + \frac1{(an+2)^2} + \cdots + \frac1{(an+n)^2}\right)} = \frac43\times54 = 72\)

We have a natural choice of lower and upper bounds for the sum in the denominator:

\(\displaystyle \frac1{(an+n)^2} + \cdots + \frac1{(an+n)^2} \\\\ ~ ~ ~ ~ \le \frac1{(an+1)^2} + \cdots + \frac1{(an+n)^2} \\\\ ~ ~ ~ ~ ~ ~ ~ ~ \le \frac1{(an+1)^2} + \cdots + \frac1{(an+1)^2}\)

\(\implies \displaystyle \frac{n}{(an+n)^2} \le \frac1{(an+1)^2} + \cdots + \frac1{(an+n)^2} \le \frac{n}{(an+1)^2}\)

and

\(\displaystyle \lim_{n\to\infty} n\times\frac{n}{(an+n)^2} = \frac1{(a+1)^2}\)

\(\displaystyle \lim_{n\to\infty} n\times\frac{n}{(an+1)^2} = \frac1{a^2}\)

so that by the squeeze/sandwich theorem,

\(\displaystyle \frac1{(a+1)^2} \le \lim_{n\to\infty} n \left(\frac1{(an+1)^2} + \frac1{(an+2)^2} + \cdots + \frac1{(an+n)^2}\right) \le \frac1{a^2}\)

\(\implies \displaystyle a^2 \le \lim_{n\to\infty} \frac1{n \left(\frac1{(an+1)^2} + \frac1{(an+2)^2} + \cdots + \frac1{(an+n)^2}\right)} \le (a+1)^2\)

and if the middle limit is supposed to evaluate to 72, solving the inequality for a puts it in the interval [6√2 - 1, 6√2] ≈ [7.48528, 8.48528].

Checking against a computer, the solution appears to be a = 8, which agrees with the analysis above. Just not sure how to bridge the gap yet...

Answer:

(2, 4)

Step-by-step explanation:

Anytime you rotate a point 180° about the origin, the x-coordinate and y-coordinate become their opposites.

(x,y) becomes (-x,-y)

Increasing the probability of a type I error generally leads to a decrease in the probability of a type II error, and vice versa.

If your data have statistical significance, this suggests that even if the null hypothesis is correct, they are extremely improbable to occur. You would then reject your null hypothesis in this situation. Yet occasionally, this may be a Type I mistake.

If your results are not statistically significant, the null hypothesis is likely to be correct and they have a high probability of occurring. As a result, your null hypothesis is not rejected. Yet occasionally, this may be a Type II mistake.

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Women’s life expectancy in a country is equals to 63.8 years when men’s life expectancy is 60 years.

A random sample of non-industrialized countries was selected, and study the life expectancy in years is listed for both men and women.

let X - Men and Y - Women

Mean for men , X- bar =52.367 ;

Standard deviations, σₓ = 11.9271

Mean for women, Y- bar=55.317 ;

Standard deviations, σᵧ = 13.30

regression cofficient rₓᵧ = 0.997

Significant at 0.05 level. Consider the regression line equation, of Y on X ,

( Y - Y-bar) = bₓᵧ (X - X-bar) --(1)

bₓᵧ = rₓᵧ ( σᵧ /σₓ) = 0.997(13.3046/11.9271)

= 1.1121

from (1), ( Y - 55.317) = 1.1121 (X - 52.367)

=> Y = - 2.9228 + 1.1121 X

If X = 60 then Y = - 2.9228 + 1.1121 ×60

=> Y = 63.8 yrs.

Hence, women life expectancy is 63.8 yrs.

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Complete question:

Life Expectancies A random sample of non-industrialized countries was selected, and the life expectancy in years is listed for both men and women. If the correlation is significant to at least 0.05 significance, then find women’s life expectancy in a country where men’s life expectancy = 60 years. Otherwise, enter zero

Men 59.7 72.9 41.9 46.2 50.3

Women 63.8 77.8 44.5 48.3 54.0

Answer:

7:4 that would be the ratio

The base of the pyramid is a square. If the crosssection is parallel to the base, the shape formed would be that of the base and it is a square

If the crosssection is perpendicular to the base, the shape formed would be that of the triangular face and it is a traingle

The other shape that can be formed when the cross section is perpendicular to the base but not actually at the vertex, the shape formed is a trapezoid

The shapes are

square

triangle

trapezoid

The following mathematical expression matched with its translation:

1. x + y = 6 (the sum of two numbers is six)

2. x + y (the sum of x and y)

3. xy (the product of two numbers)

4. x ÷ y (x divided by y)

5. y ÷ x (y divided by x)

6. y = x - 6 (six less than a number is y)

7. x - y (x minus y)

8. 6 x = y (six times a number equals y)

9. xy = 6 (the product of two numbers is six)

10. y - x (x subtracted from y)

Mathematical expression can be translated as thus;

the sum of two numbers is six

Let the unknown numbers be x and y respectively

So,

x + y = 6

six less than a number is y

x - 6 = y

also written as

y = x - 6

six times a number equals y

6 × x = y

6x = y

also written as

y = 6x

Therefore, mathematical expressions are algebraic representation of mathematics in words.

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Answer:

%Step-by-step explanation:

283.Modifying Above 3 with bar is the answer

Answer:

The answer is 85/1. To calculate 5 × 17, first multiply 5 × 10 = 50, then add 5 to the result to get 50 + 5 = 55. Finally, divide the result by 1 to get 55/1 = 85/1.

Answer:

The fraction is 5/7

Step-by-step explanation:

5 * 1/7

Multiplying a whole number times a fraction

Multiply the whole number times the numerator.

5 * 1 = 5

Divide by the denominator

5/7

The fraction is 5/7

The graph which shows the solution to the system of inequalities is attached in the picture below :

Given the inequalities :

y ≥ 2x + 1

y ≤ 2x - 2

From y ≥ 2x + 1 ;

Since the inequality sign is ≥, a solid line is used to draw the straight line graph of  y ≥ 2x + 1

From :

y = mx + c

Where, m = slope ; c = intercept

Hence, a straight line graph with ;

Intercept, c = 1 (where the line crosses the y-intercept)

Slope, m = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality :

0 ≥ 2(0) + 1

0 ≥ 0 + 1

0 ≥ 1

This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.

From : y ≤ 2x - 2

Since the inequality sign is ≤, a solid line is used to draw the straight line graph of  y ≤ 2x - 2

Graph the line y ≤ 2x - 2, with ;

Intercept, c = - 2

Slope = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality y ≤ 2x - 2:

0 ≤ 2(0) - 2

0 ≤ 0 - 2

0 ≤ - 2

This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.

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Answer:

Its graph B on edge 2022

Step-by-step explanation:

Answer:

\( \boxed{ \bold{{ \boxed{ \sf8 {x}^{7} + 3 {x}^{6} + {x}^{5} + 5 {x}^{4} - 2 {x}^{3} }}}}\)

Step-by-step explanation:

Here, we have to arrange the polynomial from higher power to lower power.

So, Option C is the correct option

Hope I helped!

Best regards! :D

The value of x is 70 degrees.

To find the value of x, we can use the properties of angles in a circle.

In the given circle, we have a diameter AB passing through the center of the circle, labeled as point C. Point D is located at 2 o'clock, point B at 3 o'clock, and point A at 9 o'clock.

We are given that angle ABD is labeled as 70 degrees. Since angle ABD is an angle formed by a chord (AB) and a tangent (BD), we can apply the property that the measure of an angle formed by a tangent and a chord is equal to half the measure of the intercepted arc.

In this case, angle ABD intercepts the arc AB. Since AB is a diameter, it subtends a 180-degree arc. Therefore, the measure of angle ABD is equal to half the measure of the intercepted arc AB, which is 180 degrees divided by 2, resulting in 90 degrees.

Now, let's focus on angle DAB, labeled as x. Since angle DAB and angle ABD are vertical angles (angles formed by the intersection of two lines), they have the same measure. Therefore, x is also equal to 70 degrees.

In conclusion, the value of x is 70 degrees.

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The sample IQR is a biased estimator of the population IQR. The sample IQR appears to be centered below 16.

A sample that does not accurately reflect the true value of a population parameter is considered to be biased. Even though a biased sample may still be useful if its bias is known, an unbiased sample is one that exactly matches the true value of the population parameter.

Matilda wanted to determine if the sample interquartile range (IQR) was an unbiased estimator of the population IQR. She performed an experiment by placing ping pong balls numbered from 0 to 32 in a drum and thoroughly mixing them. The IQR of the population was determined to be 16.

She then randomly selected 5 balls, calculated their sample IQR, and repeated this process 50 times. The results were summarized in a dot plot, where each dot represented the sample IQR from a sample of 5 balls.

The sample IQR appeared to be biased as it consistently underestimated the population IQR. The dot plot showed that the sample IQR was centered below 16.

Therefore, it can be concluded that the sample IQR is a biased estimator of the population IQR.

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Answer: Sample IQR appears to be a biased estimator since it consistently underestimated the population IQR

Step-by-step explanation: