Compute the total pay:

Hours worked: 8
Hourly wage: $7.25
Plus Tips: $54.65


$112.65

$109.85

$108.65

$105.40

Answer:  the fifth term in the sequence is 25√5

Step-by-step explanation:

b₁=√5     b₂=5            b₅=?

Denominator of the geometric sequence q is:

\(\displaystyle\\q=\frac{b_2}{b_1} \\\\q=\frac{5}{\sqrt{5} } \\\\q=\frac{5(\sqrt{5}) }{\sqrt{5}(\sqrt{5}) } \\\\q=\frac{5(\sqrt{5}) }{5} \\\\q=\sqrt{5}\)

b₅=b₁*qⁿ⁻¹

b₅=√5(√5)⁵⁻¹

b₅=√5(√5)⁴

b₅=√5(5)²

b₅=25√5

A cost that varies depending on the values of decision variables is a variable cost. This type of cost changes in proportion to changes in the production or sales volume.

Variable costs are expenses that fluctuate with changes in the level of production or sales. These costs are directly tied to the quantity of goods or services produced or sold, and they increase or decrease as the production or sales volume changes. Common examples of variable costs include materials, labor, and direct expenses associated with producing a product or providing a service. As the production or sales volume increases, the variable cost per unit decreases, due to economies of scale. Conversely, as production or sales volume decreases, the variable cost per unit increases, due to diseconomies of scale. Understanding variable costs is essential for businesses to accurately calculate their costs of goods sold, determine their break-even point, and make informed decisions about pricing and production levels.

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Answer:

6x2 + 16x = 672

Reorder the terms:

16x + 16x2 = 672

Solving

16x + 16x2 = 672

Solving for variable 'x'.

Reorder the terms:

-672 + 16x + 16x2 = 672 + -672

Combine like terms: 672 + -672 = 0

-672 + 16x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.

16(-42 + x + x2) = 0

Factor a trinomial.

16((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying

-7 + -1x = 0

Solving

-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1x = 0 + 7

-1x = 0 + 7

Combine like terms: 0 + 7 = 7

-1x = 7

Divide each side by '-1'.

x = -7

Simplifying

x = -7

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying

6 + -1x = 0

Solving

6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.

6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0

0 + -1x = 0 + -6

-1x = 0 + -6

Combine like terms: 0 + -6 = -6

-1x = -6

Divide each side by '-1'.

x = 6

Simplifying

x = 6

Solution

x = {-7, 6}

Step-by-step explanation:

The given quadratic function models the projectile of the object as it is

launched off the top of the building.

The interpretation of the function values are;

The appropriate domain is 0 ≤ x ≤ 7

Reasons:

The given function for the height of the object is f(x) = -16·x² + 16·x + 672

The domain is given by the values of x for which the value of y ≥ 0

Therefore, when -16·x² + 16·x + 672 = 0, we get;

-16·x² + 16·x + 672 = 0

16·(-x² + x + 42) = 0

-x² + x + 42 = 0

x² - x - 42 = 0

(x - 7)·(x + 6) = 0

x = 7, or x = -6

The minimum value of time, x is 0, which is the x-value at the top of the

building, and when x = 7, the object is on the ground.

Therefore;

The maximum value of f(x) = a·x² + b·x + c, is given at \(x = -\dfrac{b}{2 \cdot a}\)

Therefore;

We have;

\(x = -\dfrac{16}{2 \times (-16)} = \dfrac{1}{2}\)

Which gives;

\(f \left(\frac{1}{2} \right) = -16 \times \left(\dfrac{1}{2} \right)^2 + 16 \times \left(\dfrac{1}{2} \right)+ 672 = 676\)

The height of the building is given when the time, x = 0, as follows;

Height of building, f(0) = -16 × 0² + 16 × 0 + 672 = 672

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Statement: ∠ABC ≅ ∠EDC

Reason: Given (or Angle equality postulate)

In line 5, we can state that ∠ABC is congruent to ∠EDC because it is given in the paragraph proof. The reason for this statement is the "Given" or "Angle equality postulate," which states that if two angles are given to be congruent, then they are congruent.

Statement: Triangle ABC and Triangle EDC are congruent.

Reason: ASA (Angle-Side-Angle) congruence criterion.

In a two-column proof, each line consists of a statement and a reason. To complete the proof, we need to determine the appropriate statement and reason for line 5.

The given paragraph proof should provide information leading to the conclusion that Triangle ABC and Triangle EDC are congruent. The most likely reason for this congruence would be the ASA (Angle-Side-Angle) criterion.

The ASA criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Therefore, in line 5, we can state "Triangle ABC and Triangle EDC are congruent" and provide the reason as "ASA (Angle-Side-Angle) congruence criterion." This indicates that the two triangles are congruent based on the given information and the ASA criterion.

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Answer:

It's gonna be C and good luck!

The total surface area of the prism will be 290.125 Square units.

The surface area of a rectangular prism is the measure of how much-exposed area a prism has. Surface area is expressed in square units.

The surface area of a rectangular prism is given by:

SA = 2 (lh +wh + lw )

where

l = 3

w = 4.25

h = 18.25

SA = 2 (3x18.25 + 4.25x18.25 + 3x4.25)

SA = 2 (54.75 + 77.5625 + 12.75)

SA = 2 (146.0625)

SA = 290.125 square units

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The probability of getting four of a kind in a hand of 7 cards is approximately 0.0001813.

To calculate the probability of getting four of a kind in a hand of 7 cards, we can break it down into two steps:

Step 1: Calculate the probability of getting four cards of the same value.

The first card can be any value, so the probability is 1. The second card must match the value of the first card, so the probability is 3/51 (there are 3 remaining cards of the same value out of the remaining 51 cards). The third and fourth cards must also match the same value, so the probabilities are 2/50 and 1/49, respectively.

Step 2: Calculate the probability of getting three different cards for the remaining three cards.

After getting four cards of the same value, there are 48 cards remaining. The first of the remaining three cards can be any value other than the four of a kind, so the probability is 48/48. The second card must be a different value than the first card, so the probability is 36/47. The third card must be different from the first two, so the probability is 24/46.

Multiplying the probabilities from Step 1 and Step 2 together, we get:

(1) × (3/51) × (2/50) × (1/49) × (48/48) × (36/47) × (24/46) = 0.0001813

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According to the information we can infer that the probability that the hand will contain four of a kind in the given card game is approximately 0.0015.

To calculate the probability of obtaining a four of a kind hand, we need to consider the number of ways to get a four of a kind hand divided by the total number of possible hands.

First, let's calculate the number of ways to get a four of a kind hand. We have 13 different card values (Ace, 2, 3, ..., 10, Jack, Queen, King), and for each value, we need to choose 4 cards out of the 4 available in the deck. So, there are 13 ways to choose the four cards of the same value.

Next, we need to calculate the number of ways to choose the remaining 3 cards with different values. We have 12 remaining card values (excluding the one used for the four of a kind), and for each value, we need to choose 1 card out of the 4 available. Therefore, there are 12 * 4 * 4 = 192 ways to choose the remaining 3 cards.

Now, let's calculate the total number of possible hands. In this card game, each player starts with a hand of 2 cards and then draws 5 more, so the total number of possible hands is given by the combination of 7 cards taken from a deck of 52 cards, which is denoted as C(52, 7) = 133,784,560.

Finally, we can calculate the probability by dividing the number of ways to get a four of a kind hand by the total number of possible hands:

So, we can conclude that the probability of obtaining a four of a kind hand in the given card game is approximately 0.0015, rounded to four decimal places.

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Answer:

C(h) = 50h + 25

$425

Step-by-step explanation:

Et the plumber works for h hours.

Cost of one hour = $50

Therefore, cost of h hours = $50h

Total cost = cost of h hours + plumber service call charge

C(h) = 50h + 25 (required equation)

Plug h = 8

C(8) = 50* 8 + 25 = 400 + 25 = $425

a) Probability that the time headway will be less than 10 seconds is 0.0228.

b) Probability that the time headway will be more than 9 seconds is 0.8737.

c) Probability that the time headway will be between 5 and 8 seconds (inclusive) is 0.2331.

(a) The probability that the time headway will be less than 10 seconds can be found by using the Poisson distribution formula and substituting λ = 3.5 (since the traffic flow is 210 veh/h, which corresponds to an average of 3.5 veh/min). Thus,

(b) The probability that the time headway will be more than 9 seconds is equal to 1 minus the probability that the time headway will be less than or equal to 9 seconds. Thus,

(c) The probability that the time headway will be between 5 and 8 seconds (inclusive) can be found by subtracting the probability that the time headway is less than or equal to 4 seconds from the probability that the time headway is less than or equal to 8 seconds, i.e.,

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The short-run aggregate supply (SRAS) curve has a positive slope because it represents the relationship between the price level and the quantity of goods and services supplied in the economy in the short run.

As the price level rises, firms are incentivized to increase production to maximize profits, leading to a higher quantity supplied. In the short run, some input prices, such as wages, are sticky and do not adjust immediately to changes in the overall price level. Therefore, when the price level rises, firms can sell their output at higher prices without incurring significant cost increases.

This allows firms to increase production and supply more goods and services in response to higher prices, leading to a positive slope of the SRAS curve.

In the long run, however, input prices become more flexible and adjust to changes in the overall price level. Wages, for example, may increase as workers negotiate higher salaries in response to inflation.

As input prices adjust, firms' costs increase, reducing their profitability. In the long run, firms cannot sustain higher levels of production solely based on higher prices, resulting in a vertical long-run aggregate supply (LRAS) curve.

The LRAS curve represents the economy's potential output, determined by factors such as technology, resources, and the size of the labor force, which are unaffected by changes in the overall price level.

Thus, the vertical LRAS curve indicates that in the long run, changes in the price level do not affect the economy's overall level of output, but only result in changes in the price level itself.

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The error term is a random variable with an expected value of zero.2. The error term is normally distributed

The assumptions underlying the simple linear regression model `y = Bo + B1x + e` are: 1.

The variance of the error term e is constant across all values of x.Thus, the assumptions that are underlying the simple linear regression model `y = Bo + B1x + e` are the second and the third options, which are "The error term is normally distributed." and "The variance of the error term e is constant across all values of x." respectively.

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A sample is said to be picked in such a way that any potential subset of the same size has an equal chance of being chosen is known as simple random sample.

What is  simple random sample ?

A simple random sample, also known as an SRS, is a subset of people (also known as a sample) taken from a larger group of people (also known as a population), where the subset is selected at random and with an equal probability. This procedure involves choosing a sample at random. In SRS, the probability of selecting any subset of k individuals as a sample is the same for all subsets of k individuals.

Therefore, A sample is said to be picked in such a way that any potential subset of the same size has an equal chance of being chosen is known as simple random sample.

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Answer:

I believe the answer is B

\(\overline{AB}\)1) The proof for to show that ΔJKN ≅ΔMKL is given as follows:

Given:

∠N≅∠L

\(\overline{JK}\) ≅ \(\overline{MK}\)

Thus,

ΔJKN ≅ΔMKL:

Reason: Angle - Angle - Side Theorem

Note that Vertical ∡s are ≅ (Congruent)

2) Given:

\(\overline{DE}\) || \(\overline{FG}\)

∠E ≅ ∠G

Since

\(\overline{DE}\) || \(\overline{FG}\), it means that ∠EDF ≅ ∠GFD, is because Alternate Angles of parallel lines are ≅ (Congruent). Given that ∠E ≅ ∠G. On the basis of reflexive property, \(\overline{DF}\) ≅ \(\overline{FD}\).

Hence, by the rule of Angle - Angle - Side, ΔFDE ≅ΔDFG.

In geometry, the reflexive property of congruence asserts that every angle, line, and figure/shape is congruent to itself.

This characteristic is commonly utilized in proofs such as establishing two triangles are congruent and parallel lines are parallel.

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Answer:

(4, - 5 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 270°

a point (x, y ) → (- y, x ) , thus

(- 5, - 4 ) → (4, - 5 )

Answer:

Step-by-step explanation:

The amount (quantity) of water can be calculated if you use percent conversion.

Given:

Total amount - 10lb

Sugar syrup - 25%

Find 25% of 10 (in this situation, pounds):

\(10\) ×\(\frac{25}{100} =2.5\) lbs

Nina has to make 10%, so:

\(\frac{2.5}{10}\) × \(100=25\) lbs

Find the amount of water that you will need to add:

\(25\) lbs \(- 10\) lbs \(= 15\) lbs

The predicted values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350, therefore, the correct option is IC.

Given,

Mean of X = 600

Standard deviation of X = 10

Mean of Y = $5000

Standard deviation of Y = 1000

Correlation r= 0.9

Future value of X = 595

Z score of X = (X- Mean of X) / Standard deviation of X= (595-600) / 10 = -0.5

Using the formula, Predicted y = average of y+ r* (Z score of X)* standard deviation of y

Predicted y = $5000 + 0.9 * (-0.5) * 1000 = $4750

The predicted value of Y for X = 595 is $4750.

Now, to find the values of A, B, C, and D; we need to calculate the Z score of X = 615 and find the corresponding predicted value of Y.

Z score of X = (X- Mean of X) / Standard deviation of X= (615-600) / 10 = 1.5

Predicted y = average of y+ r* (Z score of X)* standard deviation of y

Predicted y = $5000 + 0.9 * (1.5) * 1000 = $6350

The predicted value of Y for X = 615 is $6350.

Hence, the values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350

Therefore, the correct option is IC.

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Answer:

The Properties of parallelogram are

a) Opposite sides are equal

b) All angles are not 90°

The Properties of trapezium are

a) One pair of opposite side is parallel

b) side of adjacent angle and non parallel side

of trapezium is 180°

The Properties of rhombus are

a) All sides are equal

b) All angles are not 90°

The length οf οne side οf the cube is 4 cm.

In geοmetry, a cube is a three-dimensiοnal sοlid shape that has six square faces οf equal size, and all its angles are right angles (90 degrees). A cube is a regular pοlyhedrοn, which means that all its faces are cοngruent (i.e., identical) regular pοlygοns and its edges have the same length.

The surface area οf a cube with edge length "s" is given by the fοrmula:

\(SA = 6s^{2}\)

We are given that the surface area οf the cube is \(96 cm^2\). Therefοre, we can set up the equatiοn:

\(96 = 6s^{2}\)

Dividing bοth sides by 6, we get:

\(16 = s^{2}\)

Taking the square rοοt οf bοth sides, we get:

s = 4

Therefοre, the length οf οne side οf the cube is 4 cm.

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Answer:

i believe the answer is c aka 51.84

Answer:

(6, 8)

Step-by-step explanation:

Use the section formula.

The amount of water drank in 12 hours will be 180 ounces.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jim drinks 15 ounces of water each hour. The amount of water drank by Jim in 12 hours will be,

Amount of water = 15 x 12

Amount of water = 180 ounces

Hence, the amount of water drank in 12 hours will be 180 ounces.

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There should be neither underfilling or overfilling, according to the manufacturer. The appropriate hypotheses to test are  H0: μ = 5.8 Ha: μ ≠ 5.8.

On average, a machine with 5.8 oz of toothpaste is made to feel toothpaste tubes. it is the producer. No one ever does either an inadequate or excessive amount of the proper hypothesis to be tested. Saddam is our no hypothesis since our current estimate of the population mean is that it equals 2,5.8. The manager responded by saying that manufacturers do not want any underfilling, overfilling, or filling that is less than required. It doesn't want to be overfilled or to be filled to the brim. This merely suggests that the value of our alternate hypotheses won't be much higher than 5.8. This is untrue. It won't be brand-new. fewer than 5.8. This is untrue. It won't be brand-new. fewer than 5.8, This is untrue. It will be struck. The alternative will be 5.8 is not equal. So, this is our alternative theory and our reason why we don't agree with the protesters.

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Answer:

Solution is in the attached photo.

Step-by-step explanation:

Take note for this question we can use the Sine rule to straightaway find the unknown value.

Answer:

256 train or 80% of the trains arrived on time

Step-by-step explanation:

Total trains that arrived in a week = 320 trains

Late = 5% of 320

early = 15% of 320

On time = 320 - (15 + 5% of 320)

=> 320 - (20% * 320)

=> 320 - 64

=> 256

Therefore, 256 train or 80% of the trains arrived on time

Hope my answer helps :)

Answer:

D

Step-by-step explanation:

Given a quadratic function in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

• If a > 0 then minimum value

• If a < 0 then minimum value

For

f(x) = x² + 16x + 3

a = 1 > 0 then f(x) has a minimum value

The minimum is the value of the y- coordinate of the vertex.

The x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

Here a = 1 and b = 16 , then

\(x_{vertex}\) = - \(\frac{16}{2}\) = - 8

To find the y- coordinate of the vertex, substitute x = - 8 into f(x)

f(- 8) = (- 8)² + 16(- 8) + 3 = 64 - 128 + 3 = - 61

Thus the function has a minimum value of - 61 → D

The cosine of 150° is -0.866 and the sine of 150° is 0.5. we can use the trigonometric functions.

To determine the cosine and sine of the angle θ = 150°, we can refer to the unit circle and the trigonometric ratios. In the unit circle, the cosine of an angle is the x-coordinate of the point on the circle corresponding to that angle, and the sine is the y-coordinate.

For θ = 150°, we can locate the corresponding point on the unit circle. At 150°, the x-coordinate is -0.866 and the y-coordinate is 0.5. Therefore, the cosine of 150° is -0.866 and the sine of 150° is 0.5.

The negative cosine value indicates that the angle is in the second quadrant, where the x-coordinate is negative. The positive sine value indicates that the angle is also in the second quadrant, where the y-coordinate is positive.

In summary, for the angle θ = 150°, the cosine is -0.866 and the sine is 0.5. These values represent the x-coordinate and y-coordinate, respectively, of the point on the unit circle corresponding to the given angle.

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Answer:

where is it?

Step-by-step explanation: