a. Your food total for dinner is $32.50.
leave a 20% tip on the food total. Find
Sales tax is an additional $1.95. You
total and the total amount you pay for
the percent of sales tax on the food
dinner.

If the workers' union at a particular university is quite strong.  the probability that exactly 4 of the workers interviewed are union members is 0.1699.

You must count all conceivable outcomes as well as favourable outcomes in order to compute probability. The number of favourable outcomes divided by the total number of possible outcomes yields the chance that an event will occur.

Using this formula to the probability

P(X = k) = (n choose k) * [tex]p^{k}[/tex] * [tex](1-p)^{n-k}[/tex]

Where:

X = random variable

n = 5

p = 0.96

k = 4

Let plug in the formula

P(X = 4) = (5 choose 4) *[tex]0.96^{4}[/tex] *[tex](1-0.96)^{5-4}[/tex]

= 5 *[tex]0.96^{4}[/tex] * 0.04

= 0.1699

Therefore the probability is 0.1699.

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The mean of the distribution in this problem is given as follows:

19.5625 pounds.

The mean of a data-set is given by the sum of all observations in the data-set divided by the cardinality of the data-set, which represents the number of observations in the data-set.

The dot plot shows the absolute frequency of each observation in the context of the problem.

Considering the dot plot, the sum of the observations in this problem is given as follows:

2 x 12 + 4 x 15 + 1 x 16 + 1 x 18 + 2 x 20 + 1 x 22 + 3 x 25 + 2 x 29 = 313.

The number of observations is given as follows:

2 + 4 + 1 + 1 + 2 + 1 + 3 + 2 = 16.

Hence the mean is given as follows:

313/16 = 19.5625 pounds.

The problem is given by the image presented at the end of the answer.

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Answer: To plot ratios and rates as ordered pairs on the coordinate plane, you can follow these steps:

Understand the ratio or rate: Make sure you understand the meaning and value of the ratio or rate you are working with. A ratio compares two quantities, while a rate compares two quantities with different units.

Choose a coordinate system: Set up a coordinate system on the plane with an x-axis and a y-axis. Determine the range of values you want to plot on each axis based on the given ratio or rate.

Determine the values for the axes: Assign the x-axis and y-axis values based on the given ratio or rate. For ratios, you can assign the values of the ratio to the x and y axes directly. For rates, you will need to convert the rate into a ratio by choosing a unit for one of the quantities.

Plot the points: Use the values obtained from step 3 as the x and y coordinates for each ordered pair. Plot the points on the coordinate plane.

Connect the points (if applicable): If you have multiple points, you can connect them with a line to show the relationship between the ratios or rates.

Label the axes and title the graph (if applicable): Add labels to the x and y axes to indicate the quantities being compared. You can also add a title to the graph to describe the relationship being represented.

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

12/8=x/2

12×2=8x

24=8x

x=24/8

x=3

Answer:

Step-by-step explanation:

17

5 divided by 135

The length of the side AB of the given triangle is 210.5cm.

Let us assume that AB = BC, then we can use the Sine Rule to find the length of AB.

Sine Rule states that:

[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex] = [tex]\frac{c}{SinC}[/tex]

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides.

In this case, we have:

a = BC = c

b = AC = 44

c = AB = x

B = 12°

A + B + C = 180 (sum of angles in a triangle)

but b = c, therefore angle A = angle C

A + 12 + C = 180°

2C + 12 = 180°

C = (180 - 12)/2

C = 84°

Using the Sine rule,

b/SinB = c/SinC

44/Sin 12° = x/Sin 84°

x = (44 Sin 84°)/Sin12

x = (44)(0.9945)/0.2079

x = 43.754/0.2079

x = 210.476

Therefore the side AB = 210.5cm

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If a subset A of natural numbers (N) satisfies the conditions 0 ∈ A and if n ∈ A, then n+1 ∈ A, then A must be equal to the set of all natural numbers (N).

We will use a proof by contradiction to demonstrate this.

Assume that there exists a subset A of natural numbers that satisfies the given conditions, but A is not equal to N.

This means there exists a natural number k that is not in A.

Let B = N - A be the set of natural numbers that are not in A.

B is non-empty because it contains at least k.

Since 0 ∈ A, but k ∉ A, there must be a smallest natural number in B. Let's denote it as b.

Now, according to the given conditions, if n ∈ A, then n+1 ∈ A.

We can apply this repeatedly to obtain n+1, (n+1)+1, (n+1)+1+1, and so on.

Considering b-1, it is a natural number that is not in B because b is the smallest natural number in B. So, b-1 ∈ A.

Using the condition that if n ∈ A, then n+1 ∈ A, we can apply it repeatedly to b-1 to get (b-1)+1, (b-1)+1+1, and so on.

This implies that b, b+1, b+2, and so on, all belong to A.

However, this contradicts the fact that b is the smallest natural number in B, and A is defined such that it includes all natural numbers greater than or equal to 0.

Therefore, our assumption that A is not equal to N is false, and we can conclude that A = N.

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Answer:

43.07

Step-by-step explanation:

remove the decimals and divide them as whole numbers then after the successful division return the decimal places according to the number of decimal places in each that is minus the number of decimal places in the divisor from the numbers of decimal places in the dividend

A quadrilateral with double arrows going in the same direction for one pair of the opposite sides is a Parallelogram, and it is the shape that has two pairs of parallel sides.

The shape that has two pairs of parallel sides is the third option: a quadrilateral with double arrows going in the same direction for one pair of the opposite sides.

This shape is called a parallelogram, which is a type of quadrilateral where opposite sides are parallel and congruent. In a parallelogram, each pair of opposite sides has the same length and the same arrow direction, which is what is represented by the double arrows in the description.

The other options do not fit the definition of a parallelogram. The first option describes a shape with four right angles, but only two pairs of parallel sides, which would make it a trapezoid. The second option describes a shape with only one pair of parallel sides, which is not enough to be a parallelogram. The fourth option describes a shape with sides of different lengths and in the shape of an arrow, which does not fit the definition of a parallelogram.

Parallelograms have many interesting properties, such as opposite angles being congruent and diagonals bisecting each other. They are also the basis for other geometric shapes, such as rectangles and rhombuses, which have additional properties due to their specific angles and side lengths.

A quadrilateral with double arrows going in the same direction for one pair of the opposite sides is a parallelogram, and it is the shape that has two pairs of parallel sides.

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mathworldwolfram

SOHCAHTOA

sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent

Quadrants

2 1

4 3

for a 1,2,√3 TRIANGLE

where a = 1 o = √3 h = 2

π = 180

tan 60 = 180/3 = π/3

tan 60 = π/3 in radians = √3/1 in degrees

tan 225 = (5*180)/4 = 5π/4 = -√2/2 in degrees

sin90 = π/2 in radians = soh = 1/2

sin150 = 5π/6 in radians = soh -√3/2

cos 90 = π/2 in radians = cah 1/2

tan 240 = 4π/3 in radians = toa = -√3/1

The total surface area of the triangular prism is equal to 520 square centimeters. (Correct choice: D)

In this problem we find the case of a triangular prism, which has two triangular faces and three rectangular faces. We must determine the total surface area with the help of the following area formulas:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

Now we proceed to determine the total surface area of the prism:

A = 2 · 0.5 · (15 cm) · (8 cm) + (10 cm) · (8 cm) + (17 cm) · (10 cm) + (15 cm) · (10 cm)

A = 120 cm² + 80 cm² + 170 cm² + 150 cm²

A = 520 cm²

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PART A: Linda has $4.41 more than Enrique after one year.

PART B: Enrique has $12.10 more than Linda after the second year.

PART A: After one year, we can calculate the amount of money each person has in their respective accounts.

For Linda's account:

Principal amount = $610

Interest rate = 1.2%

[tex]Interest $ earned = Principal $ amount \times (Interest rate/100) = $610 \times (1.2/100) = $7.32[/tex]

[tex]Total $ amount after one year = Principal amount + Interest earned = $610 + $7.32 = $617.32[/tex]

For Enrique's account:

Principal amount = $590

Interest rate = 3.9%

[tex]Interest $ earned = Principal amount \times (Interest rate/100) = $590 \times (3.9/100) = $22.91[/tex]

Total amount after one year = Principal amount + Interest earned = $590 + $22.91 = $612.91

Comparing the two amounts, after one year Linda has more money.

The difference in the amount is:

$617.32 - $612.91 = $4.41

Therefore, Linda has $4.41 more than Enrique after one year.

PART B: After a second year, we need to calculate the amounts again.

For Linda's account:

Principal amount = $617.32

Interest rate = 1.2%

[tex]Interest earned = Principal amount \times (Interest rate/100) = $617.32 \times (1.2/100) = $7.41[/tex]

Total amount after the second year = Principal amount + Interest earned = $617.32 + $7.41 = $624.73

For Enrique's account:

Principal amount = $612.91

Interest rate = 3.9%

[tex]Interest earned = Principal amount \times (Interest rate/100) = $612.91 \times (3.9/100) = $23.92[/tex]

Total amount after the second year = Principal amount + Interest earned = $612.91 + $23.92 = $636.83

Comparing the two amounts, after the second year Enrique has more money.

The difference in the amount is:

$636.83 - $624.73 = $12.10

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Answer:

24

Step-by-step explanation:

As x is now equal to 5, all you have to do is substitute it into were x is in the f(x) formula given.

x^2-1 turns into (5)^2-1=

25-1=

24

The expression for the calculation is:

[tex]\sf 3+12\times(14+19)[/tex]

Let us focus on "product of... and the sum of..." first. Whenever you have procedures arranged in an order similar to this, always remember that the second keyword tells you to put a mathematical operation inside grouping symbols, while the first keyword tells you to keep an operation isolated on the outside. In this exercise, the product of 12 tells you that you will be distributing it amongst another individual or set inside grouping symbols, which in this case is a "set inside grouping symbols" because the sum of 14 and 19 tells you that in order to complete the produced expression, the additive expression must be placed inside grouping symbols. Now, all we have left is 3, which can be added on either side of the entire expression because according to the order of operations, in this case, multiplication is performed before addition.

Hence the expression for the calculation is

[tex]\sf 3+12\times(14+19)[/tex]

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The amount of fencing you will get is 5 feet.

Math operations include division as one of its types. This technique involves splitting the phrases or numbers into the same amount of components.

If $18 is the cost for every 3 feet of fencing, then as per the division operation the cost per 1 foot of fencing is,

$18/3 = $6.

So, if it costs $30, then the amount of fencing you will get is $30/$6 = 5 feet.

Therefore, the required amount of fencing is 5 feet.

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The zeros of the polynomial p(x) = x³ + x² + 8x - 60 will be (- 2 + √4 i), (- 2 - √4 i) and 3.

Given that:

Polynomial, p(x) = x³ + x² + 8x - 60

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

At x = 3, then we have

p(3) = 3³ + 3² + 8(3) - 60

p(3) = 60 - 60

p(3) = 0

The one zeros are 3. Then the other two zeros are given as,

(x³ + x² + 8x - 60) / (x - 3) = 0

[(x - 3)(x² + 4x + 20)] / (x - 3) = 0

x² + 4x + 20 = 0

x = [-4 ± √(4² - 4 × 1 × 20)] / (2 × 1)

x = - 2 ± √4 i

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Answer:

[tex]\frac{13}{145}[/tex]

Answer:

W=26........

Step-by-step explanation:

26+9+10=45

The value of P(B) is 0.7.

We are given that there are two events A and B which are independent of each other. It means that they are mutually exclusive. We are also given the value of P(A) = 0.26 and [tex]P(B|A)[/tex] = 0.7. We have to determine the value of P(B).

We will use the formula of conditional probability to solve this question.

The formula for conditional probability;

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

As we know that A and B are independent events, Therefore

P( A [tex]\cap[/tex] B ) = P(A). P(B)

Substituting the value of [tex]P(A \cap B)[/tex] in the formula of conditional probability,

Therefore,

[tex]P(B|A)[/tex] = [tex]\frac{P(A) P(B)}{P(A)}[/tex]

We are given that [tex]P(B|A)[/tex] is 0.7, we will substitute this value.

0.7 = P(B)

Therefore, the value of P(B) is 0.7 after rounding it to the nearest thousandth.

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The maximum amount Lauren should budget for housing is $445.50 per month.

Now, A good rule of thumb is that housing expenses should not exceed 30% of her income.

So, We get;

30% of Lauren's monthly income of $1485 would be:

= 30% x $1485

= $445.50

Therefore, the maximum amount Lauren should budget for housing is $445.50 per month.

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The fair price for the smaller box should be $1.00.

From the question, we have that the larger box of popcorn sells for $3.00 and the two boxes have congruent openings and equal heights, we then can make the assumption  that the only difference between them is their volume.

The volume of a pyramid is found using the formula:

V = (1/3) B* h,

where 'B'=  base area

'h' = height of the pyramid

In conclusion, we can say that The fair price for the smaller box should be $1.00 because a pyramid is 1/3 the volume of a prism.

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The complete question is attached

Answer: add image

Step-by-step explanation:

That value being n = 2

============================================================

Explanation:

The only even prime number is n = 2. This leads to n^2+3 = 2^2+3 = 7 which is also prime. So far we found one such value of n that fits the criteria.

-----------

If n is odd, then n^2 is also odd.

The quick proof goes like this: let n = 2k+1 for some integer k. This guarantees n to be odd. Then n^2 = (2k+1)^2 = 4k^2+4k+1 = 2(2k^2+2k)+1 = 2*(some integer)+1 = some odd integer.

------------

If n is prime and n isn't equal to 2, then n must be odd.

If n was even and n > 2, then it would be a multiple of 2 by definition, and would rule out it being prime. Example: n = 16 is not prime since 2 is a factor.

So n must be odd if we want to find more numbers to fit the given criteria. That makes n^2 being odd as well from the previous section's proof.

But then we use the idea that:

odd + odd = even

I'll leave the proof of this to the reader.

The sum of any two odd numbers gives an even number. An example would be 3+5 = 8.

There are no odd values of n that are prime and n^2+3 is prime.

We therefore can conclude there's only one value of n that is prime and n^2+3 is also prime. That value being n = 2.

Hannah needs to invest approximately $3173.79 now to have $6500 in 10 years at an interest rate of 7% compounded continuously.

Use the formula for continuous compounding to solve this problem:

[tex]A = Pe^{(rt)[/tex]

where A is the future value, P is the present value (the amount Hannah needs to invest), r is the annual interest rate (as a decimal), and t is the time in years.

We want to find P, so we can rearrange the formula as:

[tex]P = \dfrac{A}{e^{(rt)}}[/tex]

Substituting the given values, we get:

[tex]P = \dfrac{6500}{e^{(0.07\times10)}}[/tex]

P≈ $3173.79

Therefore, Hannah needs to invest approximately $3173.79 now to have $6500 in 10 years at an interest rate of 7% compounded continuously.

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The composition (f o g)(x) = 10/(x+10) and its domain is all real numbers except x = -10.

a) To find (f o g) (x), we need to substitute g(x) into f(x) wherever we see x. That is,

(f o g) (x) = f(g(x)) = f(10/x) = (10/x) / (10/x + 1)

b) To find the domain of (f o g) (x), we need to look for any values of x that make the denominator of the expression equal to zero, since division by zero is undefined. Thus, we solve the equation:

10/x + 1 = 0

10/x = -1

x = -10

Therefore, the domain of (f o g) (x) is all real numbers except x = -10, since that value makes the denominator equal to zero. In interval notation, the domain is:

(-∞, -10) U (-10, ∞)

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The molarity of the resulting solution is 0.42 M (rounded to two significant figures), which is option C.

To solve this problem, we can use the equation:

M₁V₁= M₂V₂

where M₁ is the initial molarity, V₁ is the initial volume, M₂ is the final molarity, and V₂ is the final volume.

We are given that the initial volume is 50.0 mL and the initial molarity is 1.25 M. We are also told that 100.0 mL of water is added to the solution, so the final volume is 50.0 mL + 100.0 mL = 150.0 mL.

Plugging these values into the equation, we get:

(1.25 M)(50.0 mL) = M2(150.0 mL)

Solving for M₂, we get:

M₂ = (1.25 M)(50.0 mL) / (150.0 mL) = 0.4167 M

Therefore, the molarity of the resulting solution is 0.42 M (rounded to two significant figures), which is option C.

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The arithmetic sequence is solved and the nth term is aₙ = 5n - 4

Given data ,

The formula for the nth term of an arithmetic sequence is:

aₙ = aₙ1 + (n - 1)d

where a₁ is the first term, d is the common difference, and n is the term number.

In this case, a₁ = 1 and d = 5, so the formula becomes:

aₙ = 1 + (n - 1)5

Simplifying, we get:

aₙ = 5n - 4

Hence ,  the formula for the nth term of the arithmetic sequence with first term 1 and common difference 5 is aₙ = 5n - 4

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The area of the rectangle is 1632/3 square feet.

To calculate the area, we need to multiply the length and width of the given rectangle. The length is 51 feet, and the width is 10 2/3 feet, which can be expressed as an improper fraction as 32/3 feet.

Multiplying these values, we have:

Area = length × width

= 51 ft × (32/3) ft

= (51 × 32)/(3)

= 1632/3 square feet

So, the area of the rectangle is 1632/3 square feet.

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Decentralization is a management approach that involves the delegation and assignment of decision-making rights from top levels of management to lower levels of management. Option A

It is an effective way to empower employees and to improve decision-making processes within an organization. The benefits of decentralization include the following:

It empowers more employees at lower levels of management: Decentralization allows employees to take ownership of their work, to be more accountable, and to make decisions that are in the best interest of the organization. This, in turn, leads to improved job satisfaction, employee engagement, and better overall performance.

It allows for better and more timely decision-making: Decentralization ensures that decisions are made closer to where the work is being done. This leads to faster decision-making, improved responsiveness to changes in the market, and better coordination between different departments and teams.

It trains future managers: Decentralization provides employees with the opportunity to gain valuable management experience, which can help prepare them for future leadership roles within the organization.

However, one benefit of decentralization that is not accurate is that it forces top levels of management to focus on individual units. In fact, decentralization can free up top management to focus on the big picture and long-term strategy, rather than getting bogged down in day-to-day operations.

In conclusion, decentralization is a useful management approach that can help organizations improve decision-making, empower employees, and train future managers.

By delegating decision-making rights to lower levels of management, organizations can improve overall performance and become more adaptable to changes in the market.

So Option A is correct.

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complete question:

The benefits of decentralization i.e. delegation and assignment of decision rights include all of the following except:

a it forces top levels of management to focus on individual units

b it empowers more employees at lower levels of management

c it allows for better and more timely decision making

d it trains future managers