Joe has 80 video games and ally has 3 times as many.
How many video games do they have in all?

In  sequence ,

(1) (B) y = x and

(2) (D) Rotation 90° counter-clockwise, then translation 4 units left.

What do "sequence" and "example" mean?

An ordered list of numbers is referred to as a sequence. To go forward in the defined pattern, three dots are shown. A phrase is used to refer to each number in the series.

                               One is the first word, three is the second, five is the third, and so on, in the series 1, 3, 5, 7, 9,...

Since we are given that ΔA'B'C' is formed after a sequence of transformations applied to ΔABC.

The first is a reflection across a line and second is a translation.

The co-ordinates of point C are (-4, -2). After reflection from the line y = x, the co-ordinates becomes  (2, -4).

Also, the coordinates of point C' are (12, 0).

So, to reach point C' from point C, we should add 10 units to the x-coordinate and 4 units to the y-coordinate.

That is, the translation of 10 units right and 4 units up.

Thus, the complete transformation is

The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the line y = x followed by a translation 10 units right and 4 units up.

Thus, the correct answer is (1) y = x and (2) 10 units to the right and 4 units up.

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Answer:

f(0) = 1

f(x) = f(x-1) - 3

Step-by-step explanation:

probably use the style of your teacher

Answer:

x = 2

Step-by-step explanation:

First distribute:

-3 (x+4) = 6(-x-1)

-3x -12 = -6x -6

Isolate the variable:

-6 = -3x

Simplify:

-6/3 = x

x = 2

Hope this helps!

Answer:

The best chart to show how your department's expenses compare to the total company's expenses, and hopefully save employee jobs, would be:

Pie Chart

Step-by-step explanation:

Answer: 63 < N ≤ 66

Step-by-step explanation:

We have the set:

(66, 64, 65, 66]

First.

When we have an end with the signs "(" or ")" means that the element near the sign does not belong to the set, this would be an "open" end. Usually used for the symbols > and <

While the sign "[" or "]" (in some cases the symbols { and } are used instead)

means that the value next to it are included in the set. Usually used for the symbols ≤ and ≥.

Then in the set: (63, 64, 65, 66} the value 63 does not actually belong, and value 66 does belong.

Then this set is written as:

63 < N ≤ 66

Such that N is an integer number.

Answer:

x=67.4

Step-by-step explanation:

well sin30:1/2

So y is not 30 since 5/13 doesn’t equal 1/2

So it’s either the the third or fourth option

And x>y

So option 4 is correct

Answer:

The constant of propotionality between y and x is 3.5.

Step-by-step explanation:

Step-by-step explanation:

There are FOUR queens in a deck of 52 cards

4/52 chance of selecting a queen =  1/13  chance  = .07692 chance

If Jenny worked the same shifts as Susan and had the same income of $7,000 last year, then she do not need to file a tax return because  her total income is below the filing threshold.

Whether Jenny needs to file a tax return or not depends on her total income and the types of income she received.

If Jenny had the same income of $7,000 last year as Susan and is single with no dependents,

She will not be required to file a federal tax return for the 2022 tax year as long as her total income is below the filing threshold because for tax year 2022, the filing threshold for single taxpayers under the age of 65 is $12,950.

Therefore , Jenny do not need to file a tax return .

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Answer:

24 machines

Step-by-step explanation:

36*54= x*81

x=36*2/3

x=24

Answer:

24

Step-by-step explanation:

We can set up a simple equation and solve for x to get our answer

36 machines for 54 days = x machines for 81 days

we know that they will produce the same amount of toys as the end result, so we can set both equations equal to each other and solve for x

so,  

\(36*54=81x\\\\\frac{(36*54) }{81} =x\\\\\frac{1944}{81}=24 \\\\x=24\)  

first, divide both sides by 81

then multiply 36 with 54 and divide by 81

and we get x=24

So it'll take 24 machines to produce the same number of toys in 81 days

Feel free to ask questions if you need further help

Answer:

angle R =70

Step-by-step explanation:

angles in a triangle add up to 180°

to find angle TQP add known angles and subtract from 180

57+75=132

180-132=48

angles in a straight line add up to 180°

use new found angle and known angle to find angle SQR

48+48=96

180-96=84

angles in a triangle add up to 180°

to find angle R add known angles and subtract from 180

26+84=110

180-110=70

Answer:

-260

Step-by-step explanation:

-75+-85+-100

Answer:

62.5%

Step-by-step explanation:

the question is worded weirdly but basically since they're saying "given that a state does not use nuclear power", you can ignore the ones that do use nuclear power.

20 + 12 = 32

and then u have to find the percentage that do use coal (20). to do that all you have to do is divide then move the decimal place backwards 2 times

20 ÷ 32 = 0.625

62.5%

a) Hypothesis test:

Null hypothesis (H0): The percentage of graduate students looking for housing on campus is equal to 15%.

Alternative hypothesis (Ha): The percentage of graduate students looking for housing on campus is greater than 15%.

To test the hypothesis, we can use a one-sample proportion test. We will calculate the test statistic and compare it to the critical value or p-value to make a decision.

The observed proportion of graduate students looking for housing on campus is 78/433 = 0.1804.

Using a significance level (α) of 0.05, we will conduct the test and calculate the test statistic and p-value.

Plan:

Test statistic: z = (p - p) / sqrt(p(1-p)/n)

where p is the observed proportion, p is the hypothesized proportion (0.15), and n is the sample size (433).

Do:

Calculating the test statistic:

z = (0.1804 - 0.15) / sqrt(0.15 * 0.85 / 433)

z ≈ 2.07

Conclude:

Since the test statistic is 2.07, we compare it to the critical value or calculate the p-value.

The critical value for a one-sided test with a significance level of 0.05 is approximately 1.645. Since 2.07 > 1.645, the test statistic falls in the rejection region.

The p-value associated with the test statistic of 2.07 is less than 0.05. Therefore, we reject the null hypothesis.

Based on the survey data, there is evidence to suggest that the percentage of graduate students looking for housing on campus is greater than 15%. The housing office should consider increasing the amount of housing available to graduate students.

b) The p-value obtained in part a) represents the probability of obtaining a test statistic as extreme as the one observed (or more extreme), assuming the null hypothesis is true.

In this case, the p-value is less than 0.05, which suggests strong evidence against the null hypothesis. It indicates that the observed proportion of graduate students looking for housing on campus is significantly higher than the hypothesized proportion of 15%.

c) Including the 21 non-respondents would change the sample size and potentially affect the estimated proportion. If these additional respondents had similar characteristics to the 433 who responded, it is possible that the recommendation might still remain the same.

However, the exact impact depends on the responses of the non-respondents, so it is difficult to determine the precise effect without their data.

d) Type II error in this study would occur if the housing office fails to increase the amount of housing on campus when it is actually necessary (i.e., the percentage of graduate students looking for housing on campus is higher than 15%).

This means the null hypothesis would not be rejected when it should have been. A consequence of this type of error would be the unmet demand for housing, potentially causing dissatisfaction among graduate students and a shortage of available housing options.

e) Type I error in this study would occur if the housing office increases the amount of housing on campus when it is not necessary (i.e., the percentage of graduate students looking for housing on campus is not higher than 15%). This means the null hypothesis would be rejected incorrectly.

A consequence of this type of error would be allocating resources and efforts towards increasing housing capacity unnecessarily, which could result in wastage of resources and potentially impact other areas of the university's operations.

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Answer:

transversal

Step-by-step explanation:

1. In geometry any line which passes through or intersects  2 or more line are called a transversal.

2.Transversal are generally used in geometry of Euclidean plane to  decide whether the given set of lines  through which transversal passes are parallel or not.

The complex numbers are solved using De Moivre's Theorem and then are matched with their respective solutions.

What is De Moivre's Theorem?

De Moivre's formula, also known as the theorem and identity of de Moivre, says that for any real number x and integer n, holds -

(cos x + i sin x)^n=cos nx + i sin nx

where i is the imaginary unit (i^2 = 1).

Also, [r(cos x + i sin x)]^n = r^n(cos nx + i sin nx) or [r cis x]^n = [r^n cis nx].

The first complex number is (1+i)^5.

Solve using De Moivre's formula -

(1+i)^5 = [√2{(1/√2)+(i/√2)}^5]

=(√2)^5[cos(π/4)+i sin(π/4)]^5

=(√2)^5[cos(5π/4)+i sin(5π/4)]

=(√2)^5[(-1/√2)-(i/√2)]

=4(-1-i)

=-4-4i

The second complex number is (-1+i)^6.

Solve using De Moivre's formula -

(-1+i)^6=(1-i)^6

=[√2{(1/√2)-(i/√2)}^6]

=(√2)^6[cos(-π/4)+i sin(-π/4)]^6

=(√2)^6[cos(-6π/4)+i sin(-6π/4)]

=8(0+1i)

=8i

The third complex number is 2[cos(20)+i sin(20)]^3.

Solve using De Moivre's formula -

2[cos(20)+i sin(20)]^3=2^3[cos(60)+i sin(60)]

=8[(1/2)+{(√3)i/2}]

=4+4√3i

The last complex number is 2[cos(π/4)+i sin(π/4)]^4.

Solve using De Moivre's formula -

2[cos(π/4)+i sin(π/4)]^4=2^4[cos(4π/4)+i sin(4π/4)]

=16[cos(π)+i sin(π)]

=16(-1+i(0)]

=-16

Therefore, the complex numbers are solved using the theorem.

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Answer:

see explanation

Step-by-step explanation:

The given angles are adjacent and supplementary, thus

149 + 13x + 5 = 180

154 + 13x = 180 ( subtract 154 from both sides )

13x = 26 ( divide both sides by 13 )

x = 2

Thus

13x + 5 = 13(2) + 5 = 26 + 5 = 31°

Answer:

C. 39 ft²

Step-by-step explanation:

Area of the outer rectangle which includes the white triangle

= length x width

= 5 x 9

= 45  ft²

Area of the white triangle

= 1/2 x base x height

= 1/2 x 4 x 3

= 6 ft²

Area of shaded region
= Area of rectangle - Area of triangle

= 45 - 6

= 39 ft²

Answer:

Hope it helps!

Step-by-step explanation:

The general form of a cubic function is y = ax3 + bx + cx + d where a , b, c and d are real numbers and a is not zero. We can graph cubic functions by plotting points.

A cubic function is any function of the form y = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants, and a is not equal to zero, or a polynomial functions with the highest exponent equal to 3. These types of functions are extremely prevalent in applications involving volume.

Credits;

Graphs of Cubic Functions (solutions, examples, videos)

Cubic Function: Definition, Formula & Examples - Video & Lesson

If a random walk Sn is recurrent when started from position x and has a positive probability of eventually visiting another site y, then the random walk will indeed visit y infinitely often when started from x.

To prove this statement, we can use a proof by contradiction and leverage the Law of Large Numbers. Assume that the random walk Sn, when started from x, visits y only finitely often. This implies that there exists a finite number of visits to y, say N visits. However, since the random walk is recurrent, it will eventually return to x with probability 1.

Now, consider the event that the random walk Sn returns to x after the Nth visit to y. This event has a positive probability due to the recurrence of the random walk. However, once the random walk returns to x, it has a positive probability of visiting y again. This contradicts our assumption that the random walk visits y only finitely often.

By contradiction, we conclude that if a random walk is recurrent when started from x and has a positive probability of visiting another site y, it will visit y infinitely often when started from x.

This argument shows that the property of recurrence guarantees that the random walk will revisit visited sites infinitely often, providing a connection between recurrence and infinite visits.

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Formula of simple interest rate is:

Where,

So the interest rate is:

So the simple interest rate is:

4% interest rate.

The difference between the two localities is 1 speaker.

Let's solve the problems step by step:

a) To determine which of the two locations has a higher number of speakers of a language other than Spanish, we need to compare the ratios of speakers in El Cerrito and El Paseo.

In El Cerrito, 3 out of every 4 people speak a different language than Spanish. This can be written as a ratio: 3:4.

In El Paseo, 5 out of every 7 people speak a different language than Spanish. This can be written as a ratio: 5:7.

To compare the two ratios, we can find a common denominator. In this case, the least common multiple of 4 and 7 is 28.

In El Cerrito, the ratio becomes 21:28 (multiplying both sides by 7).

In El Paseo, the ratio becomes 20:28 (multiplying both sides by 4).

From the ratios, we can see that in El Cerrito, there are 21 out of 28 people who speak a different language than Spanish, while in El Paseo, there are 20 out of 28 people who speak a different language than Spanish.

Since 21 is greater than 20, El Cerrito has a higher number of speakers of a language other than Spanish.

b) The difference between the two localities can be calculated by subtracting the number of speakers in El Paseo from the number of speakers in El Cerrito.

In El Cerrito, there are 21 speakers of a different language than Spanish.

In El Paseo, there are 20 speakers of a different language than Spanish.

The difference is obtained by subtracting 20 from 21, resulting in a difference of 1 speaker.

Therefore, the difference between the two localities is 1 speaker.

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Answer:

The initial weight of the candle is 8 oz.

D.the candle's initial weight

Step-by-step explanation:

To find rate of change:

\(\sf \frac{change \ in \ weight}{ time \ taken}\)

take two points: (0,8),(5,7)

rate:

\(\rightarrow \sf \frac{y1-y}{x1-x}\)

\(\hookrightarrow\sf \sf \frac{7-8}{5-0}\)

\(\hookrightarrow\sf-\frac{1}{5}\)

\(\hookrightarrow\sf -0.2\) is the rate of change.

The relative risk of being alive at 5-years after diagnosis associated between white men and black men is 2.03.

In the US, among a representative group of 6,006 white men and 1,126 black men, ages 70-79 years at diagnosis of stage IV prostate cancer: 2,337 white men and 344 black men were alive after 5 years of follow-up.

In order to calculate the relative risk of being alive at 5-years after diagnosis associated between white men and black men, we can use the following formula:

Relative risk = [ (number of white men alive after 5 years) / (total number of white men) ] ÷ [ (number of black men alive after 5 years) / (total number of black men) ]

Therefore, substituting the values given in the formula we get;

[ (2,337) / (6,006) ] ÷ [ (344) / (1,126) ] = 0.63 ÷ 0.31 = 2.03

Therefore, the relative risk of being alive at 5-years after diagnosis associated between white men and black men is 2.03.

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The division of 78 by 13 will gives 78/13 as reduced fractions

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division, can be interpreted as equally dividing the number WHICH is being divided in total x parts, where x is the number of parts the number is divided.

WE have to divide the number 78 by 13 to find the fraction form first.

78 divided by 13 means 78÷ 13

Therefore, 78/13 in reduced fractions

78/13 = 6 in whole number

Hence, The division of 78 by 13 will gives 78/13 AS reduced fractions

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The complete question is;

Find 78 divided by 13. Input your answer as a reduced fraction.

Answer:

D. \( Cos(Z) = \frac{5}{13} \)

Step-by-step explanation:

Using trigonometric ratios formula, thus:

\( Cos(Z) = \frac{Adjacent}{Hypotenuse} \)

Reference angle = Z

Adjacent = 10

Hypotenuse = 26

Plug in the values into the formula

\( Cos(Z) = \frac{10}{26} \)

Simplify

\( Cos(Z) = \frac{5}{13} \)

A threat to internal validity occurs only if a potential design confound varies systematically with the independent variable.

In experimental research, an independent variable is a variable that the researcher manipulates or systematically varies in order to study its effect on the dependent variable. It is called "independent" because it is not influenced by any other variables in the experiment, and its effects on the dependent variable can be observed and measured independently of any other factors.

Only when a possible design confound fluctuates systematically with the independent variable does internal validity come under threat. In other words, it might be challenging to distinguish between the effects seen on the dependent variable and the independent variable if there is a component that fluctuates consistently or predictably with changes in the independent variable. Internal validity is less likely to be threatened by random or unplanned variation.

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A threat to internal validity occurs only if a potential design confound varies systematically with the independent variable. This means that if the confound varies randomly or haphazardly, it is less likely to affect the results of the study.

This means that the confound is consistently related to the independent variable, making it difficult to determine if the observed effects are due to the independent variable or the confound. If the confound varies spontaneously or haphazardly, it is less likely to pose a threat to internal validity, as it would not be consistently associated with the independent variable.

However, if the confound is related to the independent variable in a consistent and predictable way, it can introduce bias and undermine the internal validity of the study. It is important for researchers to carefully control for potential confounds and ensure that any observed effects are truly due to the independent variable and not some other factor.

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Answer:

18, 24, 8, 3

Step-by-step explanation:

8a = 42 - 18

8a = 24

a = 24 / 8

a = 3

To check, plug 3 into the equation

8(3) = 42-18

24 = 24

Answer:

8a = 42 - 18

8a = 24

a = 24 ÷ 8

a = 3

Step-by-step explanation:

To find the steps to the equation, we must solve the equation.

Step 1: Subtract 18 from both sides.

Step 2: Divide both sides by 8.

Therefore, the answers are 18, 24, 8, and 3.

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