Penny works at a local
amusement park.
She earns $9.80 per hour.
She is also paid $7.00 for
meals and $3.00 for
transportation each day.
Last Friday, Penny earned
$88.40. Write and solve an
equation to determine how
many hours Penny worked
on Friday.

The graph of the new function compared to the first one will be shifted down.

Vertical translation describes the movement of a function graph upward or below. The function's form is preserved in this case. The graph moving or shifting along the y-axis is another name for it. Each point on the graph moves k units vertically during vertical translation, and the graph is said to have translated k units.

The two functions are

f(x) = x + 2

g(x) = x - 1

You can see that all you need to do to transform f into g is just take 3 off of it.

f(x) - 3 = (x+2) - 3

= x + 2 - 3

= x - 1

= g(x)

Every transformation, such as f(x) f(x) + k, now produces a vertical translation, which is translated upward if k > 0 and downward if k 0. The correct response is C since the function is translated three units down in our situation where k = -3.

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The complete question is:

"If y = x + 2 were changed to y = x - 1, how would the graph of the new function compare with the first one?

A. It would be shifted up.

B. It would be shifted left.

C. It would be shifted down.

D. It would be less steep."

Answer: Angle 3

Step-by-step explanation:

The height the anchor begins to drop is 17.5 m

Since a Naval Carrier dropped anchor off the coast. The massive anchor drops at 3.5 m/s and will be 52.5 meters under the surface of the water after 20 seconds.

Let

The total height the anchor drops is thus H = h + h'

Now, the total height the anchor drops H = vt where

So, equating both equations, we have

vt = h + h'

Making h subject of the formula, we have that

h = vt - h'

Given that

Substituting the values of the variables into the equation, we have that

h = vt - h'

h = 3.5 m/s × 20 s - 52.5 m

h = 70 m - 52.5 m

h = 17.5 m

So, the anchor drops 17.5 m

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Answer:

Step-by-step explanation:

7x + 3= 24

7x= 24-3

7x= 21

x= 21/7

x= 3

Then we have that

5-4x

5-4(3)

5-12

Answer= -7

Answer:

The 1 liter bottle is better value

Step-by-step explanation:

Cost of 750 ml = £1.90

Cost of 1 liter = £2.50

1000 ml = 1 liter

Cost per 250 ml

750 ml / 3 = £1.90 / 3

250 ml = £0.6333333333333

Approximately,

£ 0.633

Cost per 250 ml

1 liter / 4 = £2.50 / 4

250 ml = £0.625

The 750 ml bottle is not a better value

The 1 liter bottle is better value

Answer:

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

Total hours worked is x + y.

Earning from the part time job is 24x, from the internship is 12y.

Inequality for the number of hours:

Inequality for the earning:

This can be simplified by dividing all terms by 12:

Answer:

\(\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}\)

\(\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}\)

Step-by-step explanation:

Part-time job

Internship

The student needs to work less than 15 hours a week:

\(\implies x+y < 15\)

The student needs to earn at least $240 a week:

\(\implies 24x+12y \geq 240\)

Therefore, the system of inequalities is:

\(\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}\)

The second inequality can be simplified by dividing each term by 12:

\(\implies \dfrac{24x}{12}+\dfrac{12y}{12} \geq \dfrac{240}{12}\)

\(\implies 2x+y \geq 20\)

Therefore, a second system of inequalities is:

\(\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}\)

To solve the system of equalities, graph both inequalities and shade the overlapping region.  

Any (x, y) point in the overlapping region is a solution to the system of inequalities.

Answer:

(4,6)

Step-by-step explanation:

Since its reflected just remove the signs

The reflected coordinate points along the y-axis is C'(4, - 6).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

We know reflection over the y-axis changes (x, y) to (- x, y).

Given, Point C(-4, -6) is reflected over the y-axis.

∴ The reflected coordinate points C'(4, - 6).

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The equation that represents the same relationship is D. 3x−4y=2

It should be noted that the equation of the line in slope-intercept form is:

y = (3/4)x - 1/2

Multiplying both sides of this equation by 4 to eliminate the fraction, we get:

4y = 3x - 2

Rearranging this equation to the standard form, we get:

3x - 4y = 2

Therefore, the answer is D. 3x - 4y = 2.

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200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

The absolute difference between the predicted and actual values must be determined, added together, and divided by the total number of periods.

Forecasted values are as follows: 1,500 and 1,400

Values in actuality: 1,200 and 1,500

Absolute differences:

|1,500 - 1,200| = 300

|1,400 - 1,500| = 100

Now, we calculate the MAD:

MAD = (300 + 100) / 2 = 400 / 2 = 200

Therefore, 200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

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Answer:

he pays 3$ less with his card

heart or brain if this helps!

Since we know that Melvin pays 1,679 dollars per liter and 1,439 dollars per liter using the loyalty card.

To solve this problem, we need to subtract 1,439 from 1,679. We get:

1,679 – 1,439 = 240

We get the final answer as: $240 or 240 dollars.

Hope this helps :)

Answer:

700$ more

Step-by-step explanation:

Food: \(.34*7000=2380\)

Clothing and Entertainment: \(C=.11*7000=770\\E= .13*7,000=910\\Both = 1680\)

\(2380-1680= 700\)

The fraction  12/3+3/4÷(−1/3)−1/2is evaluated to give -114/10

A fraction can be defined as part of a whole element, variable or number

The several  types of fractions in mathematics are;

From the information, we have that;

12/3+3/4÷(−1/3)−1/2

The fraction given is a mixture of proper fractions and improper fractions

Expand the bracket, we get;

12/3 + 3/4 ÷ -1/3 -1/2

Find the lowest common denominator

48 + 9 /12 ÷ -2 - 3 /6

Add the numerators

57/12  ÷ -5/6

Take the inverse of the divisor and multiply

57/12 × 6/-5

-114/10

Hence, the value evaluated from the fraction is -114/10

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The formula for the variance of the MLE estimator of β₀ is:

Var(β₀) = {σ²}{n} [ 1 + x²} / {∑{i=1}ⁿ (x_i - x²}

For the simple linear regression model, we have:

\(y_{i} = \beta_{0} + \beta _{1} x_{i} + epsilon_{i}\)

where y(i) is the response variable, x (i) is the predictor variable, β₀ and β₁ are the intercept and slope parameters, and ∈(i) is the error term.

To find the variance of the MLE estimators of β₀ and β₁, we first need to derive the MLEs for these parameters:

β₁= {sum{i=1}ⁿ (xi - {x})(y_i - {y})}/{{i=1}ⁿ (x_i - {x})²}

β₀ = {y} -  β₁x

where x and y are the sample means of the predictor and response variables, respectively.

Next, we need to find the variances of these estimators. The formula for the variance of the MLE estimator of β₁ is:

$Var( β₁) = σ²∑{i=1}ⁿ (x_i - x²)

where , σ² is the variance of the error term.

And, the formula for the variance of the MLE estimator of β₀ is:

Var(β₀) = {σ²}{n} [ 1 + x²} / {∑{i=1}ⁿ (x_i - x²}

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Answer:i think its 115 degres

Step-by-step explanation:

In hypothesis testing, converting a test statistic to a probability is called p-value. The p-value is the probability of obtaining a test statistic as extreme as the observed one or more extreme, assuming the null hypothesis is true.

If the p-value is less than the chosen level of significance, typically 0.05 or 0.01, the banker would reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis, which is that the proportion of banking customers with a money market savings account has decreased. If the p-value is greater than the chosen level of significance, the banker would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the proportion has decreased.

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The probability that a carpet that is 7 ft × 12 ft contains no flaws is 0.732  

The Normal, Binomial, and Poisson Distributions are the three types of continuous and discrete data-based distributions used in probability and statistics. The distribution of unusual occurrences is another name for the Poisson distribution. This is mostly used to forecast the likelihood of future events based on how frequently the past events occurred. It offers the chance that a specific number of events might happen during a particular time frame.

The formula for Poisson distribution is given below:

       P(x) = (e^-x * m^x) / x!  

Here we have,

flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet  

Given the dimensions of carpet = 7 feet × 12 feet  

=> area of the carpet = 84 feet²

=> the expected mean of defects m = [1/270]*84 = 0.311

Now use the Poisson formula  

P[x] = e^-m × m^x / x!

=> P(x = 0) = e^-(0.31) × 0.31^(0) / 0!

= (0.732 × 1)/1 = 0.732

Therefore,

The probability that a carpet that is 7 ft × 12 ft contains no flaws is 0.732  

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Answer: 63

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

Angle B should be 37°

Step-by-step explanation:

All i fugured out was the angle measure, which should be 90+53=143 and 180-143=37°, I’m just not sure what the other stuff means/needs.

Answer:

$117.6

Step-by-step explanation:

Formula:

I = Prt

Given:

P = 210

r = 8% = 0.08

t = 7

Work:

I = Prt

I = (210)(0.08)(7)

I = 117.6

Answer:

Step-by-step explanation:

So with 8% interest, Jim will have to pay 8% more each year. For the first year we need to multiply 210 with 1.08 to find the amount that Jim would have had to pay to his sister if he had gotten an 8% interest for 1 year. Every time the year increases we need to multiply the previous number with 1.08 because we are looking for the 8% increased value of the previous one, therefore our equation is:

P(t) = 210*(1.08)^t --> (t=time in years, P(t)=amount of money Jim need to pay back with respect to time)

Since Jim gets an 8% interest for 7 years we have to put in 7 for t.

P(7)=210*(1.08)^7

which is approximately $359.903

Comparing the rates of change, we see that Mr. Mole's altitude decreases by 0.6 meters per minute, while Bugs Bunny's altitude decreases by larger amounts per minute (-1.6 meters and -5.6 meters). Therefore, Bugs Bunny dug faster than Mr. Mole.

To determine who dug faster, we need to compare the rates of change of their altitudes over time.

For Mr. Mole, the equation for his altitude (A) as a function of time (t) is given as A = -4 - 0.6t. This means that his altitude decreases by 0.6 meters per minute.

For Bugs Bunny, we can observe the change in altitude from the table of values. The change in altitude between 2 minutes and 9 minutes is -1.6 meters, and the change in altitude between 9 minutes and 16 minutes is -5.6 meters.

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9514 1404 393

Answer:

  P = 250 +50t

Step-by-step explanation:

We are given two pairs of time and price:

  (t, P) = (0, 250)  and  (5, 500)

We can put these into the 2-point form of the equation for a line:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  P = (500 -250)/(5 -0)(t -0) +250

  P = 250/5t +250

  P = 50t +250 . . . . Madelyin's cost equation

Answer:

need

Step-by-step explanation:

The measures of the angle and it's supplement are144°  and 36° respectively.

The measure of the supplement of an angle is four times the measure of the angle. (given)

Let us consider the value of the supplement be X°.

Therefore the value of the angle  is 4X°

 180 - X = 4X

  X = 36° (The value of supplement)

180°-X = 144°( The value of angle)

Hence the angles are 36° and 144° .

The measures of the angle and it's supplement are144°  and 36° respectively.

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Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

sin²x + cos²x = 1 ⇒ 1 - sin²x = cos²x

cot x = \(\frac{cosx}{sinx}\)

Consider the left side

\(\frac{(1-sin0)(1+sin0)}{sin^20}\) ← expand numerator using FOIL

= \(\frac{1-sin^20}{sin^20}\)

= \(\frac{cos^20}{sin^20}\)

= cot²Θ = right side

If you are trying to earn the most money possible on your investment, you should invest in Account Cas it has the highest interest rate and compounds annually.
i. Account A: $5255.61
ii. Account B: $5221.53
iii. Account C: $5169.31
a. To determine the value of your investment after 12 years for each account, we can use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

i. Account A:
A = $1150(1 + 0.139/1)^(1*12)
A = $1150(1.139)^12
A ≈ $5908.52

ii. Account B:
A = $1150(1 + 0.133/12)^(12*12)
A = $1150(1.011083)^144
A ≈ $6122.64

iii. Account C:
A = $1150(1 + 0.13/365)^(365*12)
A = $1150(1.000356)^4380
A ≈ $6150.15

b. If you are trying to earn the most money possible on your investment, you should invest your money in:

Account C

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Answer:

2/5 = c/145

Step-by-step explanation:

2/5 = c/145

Cross multiply

5c = 290

c = 58 computers needed for 145 students

The magnitude is approximately 186 pounds.

A mathematical object's magnitude, often known as its size, is a quality that indicates whether it is bigger or smaller than other things of the same sort. Formally speaking, an object's magnitude represents the ordered (or ranked) outcome of the class of objects it belongs to.

We have to assume that the notation starts South and then moves 76 degrees East.

The 70-pound force is going at an angle down and to the right.

The down one is negative and the right one is positive.

We have to use the vectors as the hypotenuse of a rectangle.

70 cos(76) = vertical = 16.93 down

70 sin(76) = horizontal = 67.92 right

120 cos(80) = vertical = 20.83 up

120 sin(80) = horizontal =118.17 right

We have to add up all the values vertically and horizontally, and we get

-16.93 + 20.83 =3.9 up

67.92 + 118.17= 186.09 right

Here, the magnitude is the hypotenuse.

sqrt(15.21+34629.49) =186.13 pounds.

Direction is cos⁻¹(3.9/186.13) = 88.802  

Remember this is North then 88.802 degrees East

Therefore, the magnitude is approximately 186 pounds.

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To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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The critical value for a chi-square test with a table of 3 rows and 2 columns and an alpha level of 0.05 is 5.991.

The chi-square test is used to determine if there is a significant association between two categorical variables.

The critical value is a threshold value that helps us make a decision about the null hypothesis. In this case, we have a table with 3 rows and 2 columns, indicating that we are analyzing the relationship between two categorical variables, each with 3 and 2 levels, respectively.

To find the critical value, we need to specify the alpha level, which represents the level of significance or the maximum probability of rejecting the null hypothesis when it is true. In this case, the alpha level is given as 0.05.

By consulting the chi-square distribution table with appropriate degrees of freedom (DF), which is calculated as (number of rows - 1) * (number of columns - 1), we can find the critical value. With 3 rows and 2 columns, the DF is (3-1) * (2-1) = 2.

Looking up the critical value for a chi-square distribution with 2 degrees of freedom and an alpha level of 0.05, we find that the critical value is 5.991.

Therefore, the critical value for this chi-square test is 5.991, which means that if the calculated chi-square statistic is greater than this value, we would reject the null hypothesis.

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