A videoke machine can be rented for 1,000 for three days, but for the fourth day onwards, an additional cost of 400 per day is added. Represent the cost of renting videoke machine as a piecewise function of the number of days it rented.

Answer:

1/2

Step-by-step explanation:

3/8 + 2/8 is 5/8, 1/2 is equal to 4/8, so 5/8 is only 1/8 away from 1/2 while 5/8 is also 3/8 away from 1 or 8/8 therefore, it is closer to 1/2

Division involves dividing a dividend by a divisor to obtain a quotient. The division equation can incorporate a remainder if the dividend is not evenly divisible by the divisor.

However, when the remainder is zero, the quotient can be found by dividing the dividend by the divisor directly.

Division is an arithmetic operation that involves dividing a number, known as the dividend, by another number, known as the divisor. The result of division is the quotient, which represents how many times the divisor can be evenly divided into the dividend. However, division can also yield a remainder, which is the amount left over when the dividend cannot be divided by the divisor evenly.

The division method can be represented by the equation: Dividend = Quotient × Divisor + Remainder. This equation highlights that the dividend can be expressed as the product of the quotient and the divisor, plus any remaining amount, which is the remainder. When the remainder is zero, it indicates that the dividend is divisible by the divisor without any remainder.

In such cases, the equation can be simplified to: Dividend = Quotient × Divisor. This implies that the quotient represents the exact number of times the divisor can be divided into the dividend. Therefore, when the remainder is zero, the quotient can be determined simply by dividing the dividend by the divisor using the division symbol (÷ or /).

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Answer:

80.13

Step-by-step explanation:

Answer:

80.13

Step-by-step explanation:

Since a rectangle being cut by a diagonal forms a right triangle, the Pythagorean theorem is applicable. The Pythagorean theorem states;

\(a^{2} + b^{2} = c^{2}\)

Where "a" and "b" are the legs, or sides of the triangle, and "c" is the hypotenuse or diagonal.

The sides or legs are, 70 and 39, all one simply has to do now is substitute them into the formula and solve for "c".

\(70^{2} + 39^{2} = c^{2}\\4900 + 1521 = c^2\\6421 = c^2\\c = \sqrt{6421}\\\)

c ~ 80.13

The length of the line segment is given by the distance equation

D = 7.2 units

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the distance of the line segment between two points be D

Now , the equation will be

Let the first point be represented as P ( 1 , 6 )

Let the second point be represented as Q ( 7 , 2 )

Now , distance between P and Q is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

D = √ ( 1 - 7 )² + ( 6 - 2 )²

On simplifying the equation , we get

D = √ ( -6 )² + ( 4 )²

D = √ ( 36 + 16 )

D = √ 52

D = 7.2 units

Hence , the distance is 7.2 units

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Candles we light total in all 120 birthdays is 7260.

Arithmetic Progression is defined as the sequence of numbers where the difference is constant .

According to the given question

No of candle on 1st birthday = 1

no of candle on 2nd birthday =2

.

.

No of candle on 120th birthday= 120

The given situation can be represented in the form of sequence .

1,2,3,4,5,...,120.

The above sequence forms an Arithmetic Progression as the common difference is same that is 1.

To find the total candles we need to find the sum of the above AP.

Sum of AP \(=\frac{n}{2}[2a+(n-1)d]\)       ...where a=first term , n=total number of terms , d=common difference  .

a=1 , d=1 , n=120

Substituting the value we get

\(=\frac{120}{2} [2(1)+(120-1)1]\\ \\ =60[2+119] \\ \\ =60*121\\ \\ =7260\)

Therefore , Total of 7260 candles  will be light in all 120 birthdays.

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Answer:

the price of the vanilla flavored coffee per pound is $8.50

the price of the espresso flavored coffee per pound is $9.00

Step-by-step explanation:

Let's give letters to the unknowns, so we can generate equations easily:

cost of espresso coffee beans per pound:  "E"

cost of vanilla flavored coffee beans per pound : "V"

Now, the first statement:

18 pounds of E plus 17 pounds of V cost $306.50, can be written as:

18 E + 17 V = 306.5

The second statement:

19 pounds of E plus 15 pounds of V cost $298.50, can be written as:

19 E + 15 V = 298.5

Now, in order to solve this system of linear equations we can use substitution for example:

E = (306.5 -17 V)/18

and use this expression to substitute for E in the second equation:

19  (306.5 - 17 V)/ 18 + 15 V = 298.5

multiplying by 18 on both sides to eliminate denominators, we get:

19 (306.5 - 17 V) + 270 V = 5373

5823.5 - 323 V +270 V = 5373

5823.5 - 53 V = 5373

5823.5 - 5373 = 53 V

450.5 = 53 V

V = 8.5

Therefore the price of the vanilla flavored coffee per pound is $8.50

Now we use this found value in the substitution equation:

E = (306.5 -17 V)/18

E = (306.5 - 17 (8.5))/18

E = 9

Therefore the price of the espresso flavored coffee per pound is $9.00

The estimated value of the explanatory variable is not statistically significant at the 5%-level if a. the t-statistic is greater than 2.5.

The t-test is a hypothesis testing technique used to decide whether the estimated coefficient of a linear regression model is statistically significant or not. The t-value is used to measure the size of the difference between the estimated coefficient and the hypothesized value. When the t-value exceeds a critical value, such as 2.5, the estimated value of the explanatory variable is not significant at the 5%-level. It implies that the null hypothesis, which assumes that the explanatory variable's coefficient is zero, cannot be rejected.

The p-value is a measure of the probability of obtaining a more extreme value of the test statistic than the observed value if the null hypothesis is true. A small p-value implies that the null hypothesis should be rejected. When the p-value is less than 0.05, it means that the estimated value of the explanatory variable is significant at the 5%-level.

The confidence interval is a range of values that is expected to include the true value of the population parameter with a specified level of confidence. A 95% confidence interval means that the true value of the population parameter lies within the range 95% of the time. The 95% confidence interval does not contain zero implies that the estimated value of the explanatory variable is statistically significant at the 5%-level since it suggests that the population parameter is different from zero at the 5%-level. Conversely, if the 95% confidence interval contains zero, the estimated value of the explanatory variable is not statistically significant at the 5%-level since it means that the population parameter is not different from zero at the 5%-level. Therefore, it is essential to examine the t-statistic, p-value, and confidence interval while conducting hypothesis testing to make an informed decision.

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Answer:

7

Step-by-step explanation:

PLZ TELL ME IF IM WRONG

Answer

47.56468797565 in years

Step-by-step explanation:

im not sure what her age is in seconds with scientific notation though sorry :(

We have proved the statement (Vn ∈ Z) (2 | n² iff 2 | n).

To prove the statement (Vn ∈ Z) (2 | n² iff 2 | n), we will consider both directions separately.

Direction 1: If 2 divides n², then 2 divides n.

Assume that 2 divides n². This means that there exists an integer k such that n² = 2k.

Taking the square root of both sides, we have √(n²) = √(2k).

Since n is an integer, we know that n ≥ 0. Therefore, we can write n = √(2k).

To show that 2 divides n, we need to prove that there exists an integer m such that n = 2m.

Substituting the value of n from above, we have √(2k) = 2m.

Squaring both sides, we get 2k = 4m².

Dividing both sides by 2, we have k = 2m².

Since m² is an integer, let's denote it as p, where p = m².

Now, we can rewrite the equation as k = 2p.

This shows that 2 divides k, which means 2 divides n.

Direction 2: If 2 divides n, then 2 divides n².

Assume that 2 divides n. This means that there exists an integer m such that n = 2m.

To prove that 2 divides n², we need to show that there exists an integer k such that n² = 2k.

Substituting the value of n from above, we have (2m)² = 2k.

Expanding the equation, we get 4m² = 2k.

Dividing both sides by 2, we have 2m² = k.

Since m² is an integer, let's denote it as p, where p = m².

Now, we can rewrite the equation as 2p = k.

This shows that 2 divides k, which means 2 divides n².

In both directions, we have shown that if 2 divides n², then 2 divides n, and if 2 divides n, then 2 divides n². Therefore, we have proved the statement (Vn ∈ Z) (2 | n² iff 2 | n).

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Answer:

he could have been thinking of 1/2 + 1/2 or 4/8 + 4/8 or maybe 5/10 + 5/10

because 2/2=1 and so does 8/8 and 10/10

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(5\frac{1}{6}=\frac{(5*6)+1}{6}=\frac{31}{6}\)

Answer:

31/6 (improper fraction).

Step-by-step explanation:

5 1/6 = (6 × 5) + 1/6 = 31/6

31/6 is the improper fraction.

There were 47 children who attended the party. To determine the number of children who attended the party, we need to consider the preferences for each drink and the number of children who liked each combination ( can be solved by set theory as well).

Let's break down the information given:

5 children liked all three drinks (coke, fanta, and sprite).

9 children liked both fanta and coke.

7 children liked both fanta and sprite.

8 children liked both coke and sprite.

16 children liked fanta.

18 children liked coke.

17 children liked sprite.

4 children liked none of the drinks.

To find the total number of children who attended the party, we need to add up all the individual preferences and subtract those who liked none of the drinks. Total number of children who attended the party:

= Number of children who liked fanta + Number of children who liked coke + Number of children who liked sprite - Number of children who liked none of the drinks

= 16 + 18 + 17 - 4

= 47.

Therefore, there were 47 children who attended the party.

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Answer:

It should be D.

Answer:

\(6\sqrt{5}\)

Step-by-step explanation:

In any right triangle, the Pythagorean theorem states:

\(a^2+b^2=c^2\), where \(a\) and \(b\) are two legs of the triangle and \(c\) is the hypotenuse.

Plugging in given values, we have:

\(12^2+VU^2=18^2,\\144+VU^2=324,\\VU^2=180,VU=\sqrt{180}=\sqrt{36}\cdot \sqrt{5}=\boxed{6\sqrt{5}}\)

Answer:

A' ( 2,3)

B' ( 5,5)

C ( 7,3)

D'(5,2)

In the given question;

The purchase price of the car is $21,000.00.

The interest rate = 8.5% compounded quarterly.

Part 1: Function which represents the situation;

The formula for calculation the amount is;

A = P(1 + r/n)∧nt

A = total amount after adding interest.

r = rate of interest 8% per annum.

n = number times of compounds per years(quarterly) = 4

t = time duration (in years)

t = 6 months  = 0.5 years.

Thus, the function is given as; A = P(1 + r/n)∧nt

Part 2: The interest rate after the 8.5% interest rate is compounded quarterly

Compound interest = amount - principal

CI = P(1 + r/n)∧nt - P

Put the values;

CI = $21,000.00(1 + 8/4×100)∧(4×0.5) -  $21,000.00

Solving the equation;

CI = $21,000.00×1.0404 - $21,000.00

CI = $848.4

The compound int interest after 6 months will be $848.4.

Part 3: Sean's balance at the end of 5 years.

Amount for  5 years;

A =  P(1 + r/n)∧nt

Put t = 5 and other values same.

A = $21,000.00(1 + 8/4×100)∧(4×5)

A = $31204.89

The Sean's balance amount balance after 5 years is $31204.89.

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The interval is known as a prediction interval when it is created using the estimated regression equation to forecast the mean for all units that satisfy a specific set of supplied criteria.

A prediction Interval is a statistical interval that provides a range of values within which a future observation is likely to fall. It takes into account both the variability of the data and the uncertainty in the estimates of the regression coefficients.

In contrast, a confidence interval is a statistical interval that provides a range of values within which a population parameter is likely to fall. It is used to estimate the true value of a population parameter based on a sample of data.

Therefore, a prediction interval is specific to the individual unit being predicted, while a confidence interval is specific to the population parameter being estimated.

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Answer:

\(\cos(\theta)=\frac{4}{5}\)

Step-by-step explanation:

Step 1:

Let us find the missing side. We know this is a right triangle, so we can use the pythagorean thereom to find the last side. Let us set 12 as variable a, 20 as variable c, and the unknown side as variable b.

\(a^2+b^2=c^2\\12^2_b^2=20^2\\b^2=400-144\\b^2=256\\b=\pm16\)

We do know that a length can never be negative, so the side b would be 16.

Step 2:

According to SOHCAHTOA, cosine is utilizes the adjacent and hypotenuse of the given angle theta. Let us write the equation:

\(\cos(\theta)=\frac{adjacent}{hypotenuse} \\\\\cos(\theta)=\frac{16}{20} \\\\\cos(\theta)=\frac{4}{5}\)

I hope this helps! Let me know if you have any questions :)

Answer:

Step-by-step explanation:

-1+4+4x=83

4x =83-3

4x=80

x=20

Answer: 1 and 3

Step-by-step explanation: For the fractions 3/4 and 7/12, let's list the factors of each numerator and denominator:

Factors of 3: 1, 3

Factors of 4: 1, 2, 4

Factors of 7: 1, 7

Factors of 12: 1, 2, 3, 4, 6, 12

From the lists above, we can see that the common factors of 3/4 and 7/12 are 1 and 3.

Step-by-step explanation:

the area of a triangle :

baseline × height / 2

it does not matter, if the height is inside or outside (like in this case) of the triangle.

the baseline and height pair is always determined by the right angle between them. if there is no right angle, it is not the height to that side (or the side to that height).

so,

the area is

3 × 2/3 / 2 = 1 ft²

Answer:

20

Step-by-step explanation:

vertical angles are equal. meas. of angle a = meas. of angle b

x=5x-80

x+80=5x

80=4x

20=x

Answer:

A = 80

Step-by-step explanation:

If they are vertical angles, they are equal.

5x - 80 = x                      Add 80 to both sides

5x - 80 + 80 = x + 80

5x = x + 80                     Subtract x from both sides

5x - x = x - x + 80

4x = 80                           Divide by 4

4x/4 = 80/4

x = 20

Answer:

12,342,000,065

Step-by-step explanation:

yeah-ya

The values of a, h and k on the function are given as follows:

The meaning of the transformations is given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

y = 1/x.

Hence the meaning of the transformations is given as follows:

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Answer: 14

Step-by-step explanation: I solved the equation

Answer:

14 dollars

Step-by-step explanation:

Answer:

8 11/100

Step-by-step explanation:

8.11 is the same thing as 8 whole numbers and since the .11 is in the hundreths place, it becomes 11/100.

Step-by-step explanation:

The square root of 0.0144 is 0.12.

To find the square root of 0.0144, we can use a calculator or estimate it manually. One way to estimate the square root of 0.0144 is to recognize that it is very close to 0.01, which has a square root of 0.1. Since 0.0144 is slightly larger than 0.01, we can expect its square root to be slightly larger than 0.1.

To get a more precise answer, we can use a calculator or long division. Here's one way to do it:

- Write 0.0144 as a fraction: 0.0144 = 144/10000

- Take the square root of the numerator and denominator separately: sqrt(144)/sqrt(10000)

- Simplify the square roots: 12/100

- Reduce the fraction: 3/25

Therefore, the square root of 0.0144 is 0.12 or 3/25.