The quality control manager of at Long John Silver's restaurant wants to analyze the length of time that a car spends at the drive-thru window waiting for an order. It is determined that the mean time spent at the window is 59.3 seconds with a standard deviation of 13.1 seconds. The distribution of time at the window is skewed right. The quality control manager wishes to use a new delivery system designed to get cars through the drive-thru system faster. A random sample of 40 cars results in a sample mean time spent at the window of 56.8 seconds. There is a 15% chance that the mean time spent at the window of a random sample of 50 cars will exceed what value?

The sum z1 + z2 gives the point with coordinates (1, - 4), so option A is the correct one.

We know that these two points have the coordinates:

z1 = (3, 1)

z2 = (-2, - 5)

And we want to find the addition of the two points.

To add them, we just need to add the correspondent coordinates:

(3, 1) + (-2, -5) = (3 - 2, 1 - 5) = (1, - 4)

That point is the sum of z1 and z2, and we know that it is the point A, so point A is the correct option.

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5, 8, 8, 5 has a population standard deviation of 3

Given,

The population is

{5, 8, 8, 5}

The population's mean is calculated as follows:

Sum of terms / Number of terms

Calculate the values and then replace them in the equation.

Sum equals 5 + 8 + 8 + 5 = 26

Number of terms = 4

The population's average is 26 / 4 = 6.5

The population's variance is equal to (5 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (5 - 6.5)²

= (-1.5) (-1.5)² + (1.5) (1.5)² + 1.5² + (-1.5) (-1.5)²

= 2.25 + 2.25 + 2.25 + 2.25

= 9

The population's standard deviation is equal to

= 3

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Answer:

Ms. Sunshine needs to make 62.5 cookies.

Step-by-step explanation:

25 * 2.5 = 62.5

Answer:

The answer is the third option

Step-by-step explanation:

When an exponent is raised to the power of another exponent, both exponents are multiplied.
Recall that a number without an exponent is thought to be raised to the power of 1.

So after multiplying the exponents of all of the variables by 4, we are left with a solution identical to the third option.

The sentence that uses the word "obstinancy" incorrectly is: if we eat out too often, its result in obstinancy and poor health. The Option C is correct.

Obstinancy is a noun that refers to the quality of being stubborn or resolutely unyielding. It describes a person's refusal to change their views, opinions, or actions, even in the face of compelling evidence or persuasive arguments. Example of its use: despite the pleas of his family, the man's obstinancy led him to continue his dangerous lifestyle.

We often use the word "obstinancy" for the followings:

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In a case whereby In 1950, a U.S. population model was y = 151. (1.013)^t-1950 million people, where t is the year, the model predict the U.S. population would be 288 million in the year 2000.

Population models are mechanical theories that link alterations in population structure and density to responses at the individual level (life history features in eco-evolutionary theory or vital rates in demographic theory).

The model was given as y=151x(1.013)^t-1950

where the future time t = 2000

Then we can substitute the given year 2000 as the value of 't'

then we will have y=[151x(1.013)^(2000-1950)] = 288 million

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Answer:

x=24 or 25

Step-by-step explanation:

90% is x=24

89.999999 repeat% is x =25

115° is the value of external angle.

Where is exterior angle?

Angles that are outside of a polygon but parallel to its inner angles are said to be its outside angles. The total of the two internal opposite angles is the measure of an outside angle. A triangle's one side is extended to form the triangle's exterior angle.

                        Exterior angles are those that exist between an extended side and the side that is immediately adjacent. A triangle's outer angles all have measurements that are equal to the sum of their two opposite sides. inner perspectives.

  AD ║EG

∠BFC= 75°

∠EFB = 40°

∠FCD =  ( 40+75)

          = 115°

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Answer:

289 and 324

Step-by-step explanation:

first find the root of 300 then the number you get is 17.3205.... then look in the line and look at the points in between 17 and 18 then find the square root of 17 and you'll get your answer

Area of triangle shape

Area A = BxH/2 = [ 8 x (5+1/2) ]/2

. = 4 x 5.5

. = 22

Then answer is

Area of logo = 22 inches2

OPTION B)

Answer:

The answer is: 4y(2x+y)

Step-by-step explanation:

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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a) The organization of ledger accounts under an accounting equation and journal entries are as follows:

                         Assets                               =  Liabilities + Equity

            Cash +   Inventory + A/Receivable                    C.Stock  R/Earnings

1.       $43,000                                                                 $43,000

2.       -28,000   $28,000

3.                                                $42,000                                          42,000 S/Revenue

4.                        -20,000                                                                  -20,000 COGS

5.        37,000                            -37,000

6.        -9,800                                                                                     -9,800 Op Exp.

Bal. $42,200      $8,000           $5,000                      $43,000    $12,200

Debit Cash $43,000

Credit Common Stock $43,000

Debit Inventory $28,000

Credit Cash $28,000

Debit Accounts Receivable $42,000

Credit Sales Revenue $42,000

Debit Cost of goods sold $20,000

Credit Inventory $20,000

Debit Cash $37,000

Credit Accounts Receivable $37,000

Debit Operating expenses $9,800

Credit Cash $9,800

b1)

Jana's Flowers

For the year ended December 31, Year 1

Sales Revenue           $42,000

Cost of goods sold    $20,000

Gross profit                $22,000

Operating expenses   $9,800

Net income                $12,200

b2) Jana's Flowers

December 31, Year 1

Cash                           $42,200

Accounts Receivable  $5,000

Inventory                     $8,000

Total assets             $55,200

Common Stock        $43,000

Retained Earnings      12,200

Total equity            $55,200

b3) Jana's Flowers

For the year ended December 31, Year 1

Net income                $12,200

Changes in working capital:

Accounts Receivable  (5,000)

Inventory                      (8,000)

Operating cash flow     ($800)

Financing activities:

Common Stock       $43,000

Cash flows              $42,200

c) I do not agree with this statement.  It does not necessarily flow that Jana selling $42,000 in goods will be able to recover more than half of the $43,000 she invested in her business.  So far, she has made $12,200 from her investment.

Cash $43,000 Common Stock $43,000

Inventory $28,000 cash $28,000

Accounts Receivable $42,000 Sales Revenue $42,000

Cost of goods sold $20,000 Inventory $20,000

Cash $37,000 Accounts Receivable $37,000

Operating expenses $9,800 Cash $9,800

Thus, it will take time for Jana to recover her investment in the business.

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\(\left(2+\sqrt{10} \right)\left(2-\sqrt{10} \right)\\\\=2^2-\left(\sqrt{10} \right)^2\\\\=4-10\\\\=-6\)

The principal in this scenario is $ 8000.

Simple Interest can be defined as the sum paid back for using the borrowed money, over a fixed period of time.

Compound Interest can be defined as when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time.

It is Given that:

Priscilla invested 20,000 that means the total amount she invested.

Amount= $ 20,000

Rate of interest=12%

Time= 5 year

Interest= $12,000.

By the formula;

Amount =  principal + Interest

Principal = Amount - Interest

Principal= $ 20,000- $12,000

Principal=$ 8000

Hence, the principal in this scenario is $ 8000.

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Answer:

V=(22*22)/2*42

=10164 in

B is true, so we can conclude ~~A by disjunctive syllogism.

This proof is based on the inference rules you provided.

D Proof: Premises:

C ---> (~D ---> ~X)

The Modus Ponens Rule was used.

Finally, X /D

Explanation: Using Modus Ponens, we can conclude that D ---> X from premises 1 and 2.

Because premise 2 is true, we can conclude X via modus tollens.

We can conclude that D must be false because X is true.

Evidence for C:

Conditions: A ---> B B

Modus Tollens is the rule that was used.

Finally, C / A

Explanation: Using Modus Tollens, we can conclude from premises 1 and 2 that A.

Because A is false in premise 1, we can conclude that B is true.

Because premise 2 is true, we can conclude C using disjunctive syllogism.

Proof for ~~A:

Premises:

A ---> ~D

~D ---> (~B v ~~A)

A

B

Rule used: Modus Ponens

Conclusion:

~~A /B

Explanation:

From premise 1 and 3, using Modus Ponens, we can conclude that ~D.

From premise 2 and ~D, using Modus Ponens, we can conclude that ~B v ~~A.

From premise 4, B is true, so we can conclude ~~A by disjunctive syllogism.

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Answer: $1.92??

Step-by-step explanation:

The amplitudes of functions are a) 8 and b) 6.

Given are the functions we need to determine the amplitude of function,

a) y = 8 Sin (x/2) + 3

b) y = 6 Cos x + 2

So,

To determine the amplitude of a trigonometric function, you can follow these steps:

For a sine function of the form y = A×sin(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

For a cosine function of the form y = A×cos(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

Let's apply these steps to the given functions:

a) y = 8×sin(x/2) + 3

The coefficient of sin in this function is 8, so the amplitude is |8| = 8.

Therefore, the amplitude of function a) is 8.

b) y = 6×cos(x) + 2

The coefficient of cos in this function is 6, so the amplitude is |6| = 6.

Therefore, the amplitude of function b) is 6.

Hence the amplitudes of functions are a) 8 and b) 6.

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The length of the third side is 2√34 + 6.

We can use the triangle inequality theorem to solve this problem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.

Let x be the length of the third side. Then we have:

2√34 + 6 > x

Subtracting 6 from both sides, we get:

2√34 > x - 6

Adding 6 to both sides, we get:

x < 2√34 + 6

Therefore, the length of the third side must be less than 2√34 + 6.

To find the exact length of the third side, we need to check if the triangle inequality is satisfied for an equality. In other words, we need to check if:

2√34 + 6 = x

If this is true, then the given sides can form a triangle.

Simplifying the equation, we get:

x = 2√34 + 6

The exact length is 2√34 + 6 if the triangle inequality is satisfied for an equality.

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The degree of the provided polynomial is 18, and the leading term is √7.

It is defined as the combination of constants and variables with mathematical operators.

We have given an expression:

\(= \rm \sqrt{7}x ^{18} + 12.1x^{ 15} + \pi 4 x^ 6 + 1 9\)

As we can see in the expression the greatest degree is 18.

So the degree of the polynomial is 18

And the coefficient of the variable which has a height degree is the leading term.

The leading term = √7

Thus, the degree of the provided polynomial is 18, and the leading term is √7.

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Answer: LCM=672; HCF=12

Step-by-step explanation:

LCM=Least Common Multiple

HCF=Highest Common Factor

Factor of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Factor of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

From the list we can see, the highest common factor between 84 and 96 is 12.

The easiest way to find least common multiple is to time the numbers together and then divide it by their highest common factor.

84×96÷12=672

The following answers are given as:

2.1)

2 teaspoons of vinegar are needed for 5 teaspoons of olive oil.

2.2)

8 teaspoons of vinegar are needed for  20 teaspoons of olive oil.

2.3)

There are 12 teaspoons of vinegar and 30 teaspoons of olive oil in the 42 teaspoons of salad.

2.4)

There are 4 teaspoons of vinegar and 10 teaspoons of olive oil in the 14 teaspoons of salad.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

6 teaspoons of vinegar = 15 teaspoons of olive oil.

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Now,

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 2 on both sides.

2 teaspoons of vinegar = 5 teaspoons of olive oil.

Now,

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 8 on both sides.

8 teaspoons of vinegar = 20 teaspoons of olive oil.

Now,

Total number of teaspoons = 42

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 12 on both sides.

12 teaspoons of vinegar = 30 teaspoons of olive oil.

12 + 30 = 42 teaspoons

Now,

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 4 on both sides.

4 teaspoons of vinegar = 10 teaspoons of olive oil.

4 + 10 = 14 teaspoons

Thus,

2 teaspoons of vinegar are needed for 5 teaspoons of olive oil.

8 teaspoons of vinegar are needed for  20 teaspoons of olive oil.

There are 12 teaspoons of vinegar and 30 teaspoons of olive oil in the 42 teaspoons of salad.

There are 4 teaspoons of vinegar and 10 teaspoons of olive oil in the 14 teaspoons of salad.

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Answer:

4.9 .................................

Answer:

The correct awnser is A : )

Step-by-step explanation: