Simplify the following to a single term, evaluate where possible. If rational exponents change to radical form before you evaluate. х a) (-5a-563) + (4a4b2) c) (811) × (813) b) (n)-3 (nºjº (n-3) (T)*

The probability that a randomly selected college student will find a parking spot in the library parking lot in less than minutes is 0.0668

The formula to calculate the probability of finding a parking spot in less than 3 minutes is as follows:

P(x < 3) = P(Z < (3-4.5)/1)

= P(Z < -1.5)

= 0.0668

Therefore, the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes is 0.0668, rounded to four decimal places.

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Answer:

b

Step-by-step explanation:

Answer:

18.84

Step-by-step explanation:

The formula for circumference is 2(pi)r, I think. The radius is 3. 3 times 2 is 6. 6 times 3.14 is around 18, I think.

hope this helps

Answer:

A

Step-by-step explanation:

The total cost of mower is $10,228.48. The correct option from the following option given is D.

A down payment on a cottage is the money paid in advance by the buyer in a real estate transaction or other large purchase. Down payments are typically a portion of the sales price and can range from 3% to 20% for a primary residence.

The total cost of the mower will be the sum of the down payment and the total amount paid through the loan:

Down payment = $1,000

Total amount paid through the loan = (monthly payment) x (number of months) = $192.26 x 48 = $9,228.48

The total cost of the mower is:

Total cost = Down payment + Total amount paid through the loan

Total cost = $1,000 + $9,228.48

Total cost = $10,228.48

Therefore, the total cost of the mower is $10,228.48.

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Answer:

23 boxes of pasta

A i think maybe

:>..,.h,j.

Therefore, in a 2x2 table, the pattern of cell frequencies that would indicate independence is d. All cell frequencies are exactly the same.

In a 2x2 contingency table, the expected cell frequencies under the null hypothesis of independence are equal for all cells. If the observed cell frequencies in the table are approximately equal to the expected cell frequencies, then we can conclude that there is no significant association between the two variables being studied. In other words, the pattern of observed cell frequencies is consistent with the null hypothesis of independence. Therefore, if all cell frequencies are exactly the same, it suggests that the variables are independent, as each cell has an equal chance of being filled by any observation regardless of the value of the other variable.

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Students raised $225 in the first week and $90 in the second week.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, a student club has a goal to raise $750 to buy new books for a library.

In the first week, the club raised 30% of its goal.

Now, 30% of 750

= 30/100 ×750

= 3×75

= $225

In the second week, the club raised 12% of its goal.

Now, 12% of 750

= 12/100 ×750

= 0.12×750

= $90

Hence, students raised $225 in the first week and $90 in the second week.

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To solve this problem we can draw or circle so:

So to find the area we need to find the hight so we can use the sin propertie so:

and we solve for h so:

So the area will be:

Answer:

3 + 21 = 24 and they are the product to the factors of 63

Step-by-step explanation:

Answer:

The left is -10, 1 the other side is 10, -10

Step-by-step explanation:

Answer:

Step-by-step explanation:

After clockwise rotation 90°, we obtain vertices of image as (-2, -2), (-4, -5) and (2, -4). Therefore, option C is the correct answer.

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

Given that, triangle LMN with vertices L(2, -2), M(5, -4) and N(4, 2).

After clockwise rotation 90° we get

Here, L(2, -2) →L'(-2, -2)

M(5, -4) →M'(-4, -5)

N(4, 2) →N'(2, -4)

Therefore, option C is the correct answer.

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Answer:

x=8

Step-by-step explanation:

Angle bisector means it cute the big angle into two equal, smaller angles (like cutting a piece of cake in half)

therefore, you can set both smaller angles equal to each other, then solve for x

4x+1=33   Subtract 1 from both sides

4x=32      Divide both sides by 4

x=8

You'll get it, keep studying! :)

Answer:

20

Step-by-step explanation:

3/12=4

4x5=20

wooooow

Answer:

$20

Step-by-step explanation:

12/3 = 4

That means each shirt is 4 dollars.

5×4 = 20

Answer:

15.42

Step-by-step explanation:

The formula for finding the perimeter of a semicircle: r(π+2)

Therefore, 3(π+2)

9.42+6 = 15.42

1. The table of values showing the amount Kevin owes his friend after t weeks is as follows:

Week    Amount Owed

0               $90

 1               $85

2               $80

3               $75

4               $70

...

18              $0 ($5 - $5)

2. The equation representing the amount (L) Kelvin owes his friend after t weeks is L = 90 - 5t.

An equation is a mathematical statement showing that two mathematical expressions using the equation symbol (=) are equal or equivalent.

Equations establish the numerical relationship existing between two or more mathematical expressions, numbers, values, or variables.

Week    Amount Owed

0               $90

 1               $85 ($90 - $5)

2               $80 ($85 - $5)

3               $75 ($80 - $5)

4               $70 ($75 - $5)

The total amount borrowed = $90

The amount of repayment = $5

The repayment period = weekly

Let the balance after t weeks of payment = L

L = 90 - 5t

In eighteen weeks, Kevin will complete the repayment of the loan.

Check:

If t = 18

L = 90 - 5t

L = 90 - 5(18)

L = 90 - 90

L = 0

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Answer:

The solution is 18

Step-by-step explanation:

To check which point satisfies the inequality 2x + y > 10, we substitute each value of x and y in the equation.

A. 2(2) + 3 > 10

    7 > 10

  This is incorrect. So the point does not satisfy the expression.

B. 2(3) + 2 > 10

    8 > 10

    This is also incorrect.

C. 2(4) + 3 >10

     11 > 10

     This is correct since 11 is greater than 10. So point (4,3) satisfies the inequality.

D. 2(3) + 4 > 10

    10 > 10

 This is also incorrect.

What is inequality?

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Answer

Step-by-step explanation:

Answer:

\(3b + 4c = a\)

\(3b = a - 4c\)

\( \frac{3b}{3} = \frac{a}{3} + \frac{ - 4}{3} \)

\( \frac{3b}{3} = \frac{a}{3} + \frac{ - 4c}{3} \)

\(b = \frac{a}{3} + \frac{ - 4c}{3} \)

\(b = \frac{a}{3} - \frac{4c}{3} \)

Step-by-step explanation:

Thanks!!!!!

Answer:

The answer is 20 feet.

Step-by-step explanation:

Answer:

20 ft

Step-by-step explanation:

5 : 2 :: x : 8

Product of means  = product of extremes

2*x = 5*8

  2x = 40

     x = 40/2

x = 20

I think the answer is A. I will check if it is wrong

The quotient is 1111. The process continues until the result is less than the divisor.

To perform the division using the restoring-division algorithm with the given divisor and dividend, follow these steps:

Step 1: Initialize the dividend and divisor

Divisor: 00011

Dividend: 1011

Step 2: Append zeros to the dividend

Divisor: 00011

Dividend: 101100

Step 3: Determine the initial guess for the quotient

Since the first two bits of the dividend (10) are greater than the divisor (00), we can guess that the quotient bit is 1.

Step 4: Subtract the divisor from the dividend

101100 - 00011 = 101001

Step 5: Determine the next quotient bit

Since the first two bits of the result (1010) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

Step 6: Subtract the divisor from the result

101001 - 00011 = 100110

Step 7: Repeat steps 5 and 6 until the result is less than the divisor

Since the first two bits of the new result (1001) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100110 - 00011 = 100011

Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100011 - 00011 = 100001

Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100001 - 00011 = 011111

Since the first two bits of the new result (0111) are less than the divisor (00011), we guess that the next quotient bit is 0.

011111 - 00000 = 011111

Step 8: Remove the extra zeros from the result

Result: 1111

Therefore, the quotient is 1111.

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Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

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Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

Answer:

I believe your answer is 5:6

Step-by-step explanation:

because 1 is the only number less than 2 so 1-6=5 and there are a total of 6 numbers so therefore your answer should be 5:6. Hope this helps :)

Drawing 31 tokens ensures that you have at least one odd token, by the Pigeonhole Principle.

To be certain you get at least one token that is odd, you need to draw enough tokens to ensure that you exhaust all possible even numbers. Since there are 30 even numbers between 0 and 60, it follows that you must draw 31 tokens to be certain you get at least one that is odd.

This is known as the Pigeonhole Principle, which states that if there are n pigeonholes and n+1 pigeons, then at least one pigeonhole must contain more than one pigeon. In this case, the even numbers represent the n pigeonholes and the odd numbers represent the n+1 pigeons.

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Answer:

x=1.070833

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4(3x−2) = 4.85

(4) (3x) + (4) (−2) = 4.85 (Distribute)

12x + − 8 = 4.85

12x − 8 = 4.85

Step 2: Add 8 to both sides.

12x − 8 + 8= 4.85 + 8

12x=12.85

Step 3: Divide both sides by 12.

12x/12

=

12.85/12

x = 1.070833

Answer:

x = 277.915...

Step-by-step explanation:

\(4^{4.85} = 3x -2 \\831.746... = 3x - 2\\x = 277.915...\)

The missing par of the triangles are

hypotenuse = 16.43

angle B = 57.26 degrees

angle C = 32.74 degrees

information given in the question

hypotenuse = ?

opposite = 9

adjacent =  14

The hypotenuse is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

hypotenuse² = 9² + 14²

hypotenuse² = 277

hypotenuse = √277

hypotenuse = 16.43

angle B

tan (angle B) = 14/9

angle B = arc tan (14/9)

angle B = 57.26 degrees

angle C

tan (angle C) = 9/14

angle C = arc tan (9/14)

angle C = 32.74 degrees

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The mean and the standard deviation of the sampling distribution of the sample mean  is equal to 4.57 and 0.69 respectively.

Population mean  'μ' = 4.57

Sample size 'n' = 7

Population Standard deviation 'σ' =1.82

Mean of the sampling distribution of the sample mean is equal to the population mean,

which is μ = 4.57.

So, μₓ = μ = 4.57.

Standard deviation of the sampling distribution of the sample mean also known as the standard error of the mean.

Using the formula we have,

σₓ = σ / √(n)

Substituting the given values, we have,

⇒ σₓ = 1.82 / √(7)

⇒ σₓ = 1.82 / 2.646

⇒ σₓ = 0.6878

⇒ σₓ ≈ 0.69

This implies,

The standard deviation of the sampling distribution of the sample mean is σₓ ≈ 0.69.

Therefore, the mean of the sampling distribution of the sample mean and

standard deviation of the sampling distribution of the sample mean  is equal to 4.57 and 0.69 respectively.

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The above question is not complete, the complete question is:

Easy Eats Diner is a large restaurant chain. After paying for a meal at Easy Eats Diner, customers are asked to rate the quality of the food as a 1, 2, 3, 4, or 5, where a rating of 1 means "not good" and 5 means "excellent". The customers' ratings have a population mean of μ = 4.57, with a standard deviation of σ=1.82. Suppose that we will take a random sample of n= 7 customers' ratings. Let x represent the sample mean of the 7 customers' ratings. Consider the sampling distribution of the sample mean x.

Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed.

(a) Find μₓ(the mean of the sampling distribution of the sample mean).  ?

(b) Find σₓ (the standard deviation of the sampling distribution of the sample mean). ?