A $30 shirt is marked, "Get 1/3 off. What is the sale price of the shirt?

The profit made on the 600 grapefruit with a cost price of \(12^{1/2}\) cent each  is 12500 cents.

Profit is the money a business pulls in after accounting for all expenses.

To calculate the profit made on the 600 grapefruit, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the profit made on the 600 grapefruit is 12500 cents.

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The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D

We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.

If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.

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700 cubic inches

Step-by-step explanation:

is known :

V = πr²h

V = 3.14 · 5² · 9

V = 3.14 · 25 · 9

V = 78.5 · 9

V = 706.5 cubic inches → Round to the nearest hundredth

V ≈ 700 cubic inches

The Volume of Cylinder is 1271.7 in³.

The volume of a cylinder is the amount of space that it occupies. It is a measure of the total capacity or content enclosed by the cylindrical shape.

The formula for calculating the volume of a cylinder is:

Volume = πr²h

We have, Radius= 5 in

Height= 9 inch

So, the Volume of Cylinder

= πr²h

= 3.14 x 5 x 5 x 9

= 3.14 x 5 x 81

= 3.14 x 405

= 1271.7 in³

Thus, the Volume of Cylinder is 1271.7 in³.

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Given

ZA and ZB are supplementary angles. If mZA= (3x + 9)° and m ZB = (6x + 27)°,

Solution

Two angles are called supplementary when their measures add up to 180 degrees

Now,

There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

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A line's steepness can be determined by looking at its slope. Slope is determined mathematically as increase over run.

According to the slope equation, the slope of a line may be calculated by dividing the rise of the line between any two places by the run of the same line between the same two sites.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

Slope of y =f(x)

Slope (m) = ΔY / ΔX = 14 / 1 = 14

y = 14x + 22

When x=0, y = 22

When y=0, x = -1.5714285714286

Slope of y = g(x)

Slope (m) =ΔY / ΔX = 14 / 1 = 14

y = 14x + 24

When x=0, y = 24

When y=0, x = -1.7142857142857

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A point that represent a striking deviation in the box plot above include the following: C. P.

In Mathematics and Statistics, a box plot can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

In conclusion, we can logically deduce that point P represent a striking deviation in the box plot because it is an outlier (it is significantly far from all of the other data points).

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the inductive step in her proof 1+2+3+…+k+(2k+1)=k2+(2k+1)=> 1+2+3+…+k+(2k+1)=(k+1)2…

a mathematician wishes to prove the following proposition using a proof by induction: the sum of the first n consecutive odd numbers equals n2. the following can be used as part of the inductive step in her proof:

We have:

1=12

true

1+3=4=22

true

1+3+5=9=32

true

We assume that for n=k

:

1+3+5+…+2k−1=k2…(1)

We will show that for n=k+1

:

1+3+5+…+2k−1+2(k+1)−1=(k+1)2=>

1+3+5+…+2k−1+2k+1=(k+1)2…(2)

We now add the term 2k+1

to both sides of (1)

and we take:

1+2+3+…+k+(2k+1)=k2+(2k+1)=>

1+2+3+…+k+(2k+1)=(k+1)2…(3)

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Answer: Between 8 and 9, they have made 20.

Between 9 and 10, then have made 26

Step-by-step explanation: since im in midddle school and you probaly wouldnt want to get an answer from a child i can assure you this is correct and to get my answer i just added some of the numbers with its exponets

The exponential function through (4, 1250) is y = 2.5ˣ.

The formula for exponential growth is \(y = y_0.e^{(kt)}.\)

The formula for exponential decay is \(y = y_0e^{(-kt)}.\)

Given, An exponential function passes through (4, 1250).

Let, The function be y = abˣ.

1250 = ab⁴.

125×10 = ab⁴.

25×5×5×2 = ab⁴.

5×5×5×5×2 = ab⁴.

5⁴×2 = ab⁴.

ab⁴ = 2.5⁴.

y = 2.5⁴.

y = 2.5ˣ.

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Answer:

$0.23 per minute

$2.30 every 10 minutes

Step-by-step explanation:

there are 60 minutes in an hour so we divide 60 from 13.50

13.5/60= $.23

you make $.23 a minute and $2.30 every 10 minutes

Hopes this helps please mark brainliest

Answer:

Every minute you'll get $0.225 and per 10 minutes, you'll get $2.25.

Step-by-step explanation:

To find out how much you make per minute, divide $13.50 by 60. 60 because that is how many minutes is in 1 hour.

13.50 divided by 60 = $0.225

To find the amount you'll get for 10 minutes, multiply the last answer by 10, or just move the decimal sign over once:

$2.25

Brainliest please! I am so close to getting my next rating! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

800 books

problem solving steps：

adults:60%

young people:5%

children=100%-60%-5%

=35%

35%=280 books

1%=280÷35

=8

100%=800

so,there are 800 books

Answers:

20hr=100$

50hr=2500$

Step-by-step explanation:

Answer:

Step-by-step explanation:

The approximate height of the tree is given as follows:

45.6 ft.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

14.5 ft.

The bases are given as follows:

5.2 ft and x ft.

Hence the value of x is given as follows:

5.2x = 14.5²

x = 14.5²/5.2

x = 40.4 ft.

Hence the height of the three is given as follows:

5.2 + 40.4 = 45.6 ft.

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The standard deviation of the restaurant profits in 2021 is given by $71181.

Restaurant profit for outcome 'move to A' = $ 260000

Restaurant profit for outcome 'move to B' = $ 120000

Restaurant profit for outcome 'stay in C' = $ 100000

The mean of restaurant profits = $(260000 + 120000 + 100000)/3 =$ 160000.

Standard deviation of the restaurant profits in 2021 is given by

= $ √({(260000 - 160000)² + (120000 - 160000)² + (100000 - 160000)²}/3)

= $ √(((100000)² + (40000)² + (60000)²)/3)

= $ √(15200000000/3)

= $ √5066666667

= $ 71181 (rounded to the nearest dollar)

Hence standard deviation of the restaurant profits in 2021 is given by $71181.

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The question is incomplete. The complete question will be -

c) Mode: 15 (appears 6 times)

Mean: 15.25

Median: 15

d) Probability of being 13 years old: 2/20 = 0.1 or 10%

e) Probability of being 14 or 16 years old: 6/20 = 0.3 or 30%

f) Probability of not having 15 years old: 1 - (6/20) = 14/20 = 0.7 or 70%

a) To create a table and calculate the absolute frequency, relative frequency, and percentual frequency, we organize the given ages in ascending order:

13 13 14 14 15 15 15 15 15 16 16 17 17 17 18 18

Age Absolute Frequency Relative Frequency Percentual Frequency

13 2 2/16 12.5%

14 2 2/16 12.5%

15 5 5/16 31.25%

16 2 2/16 12.5%

17 3 3/16 18.75%

18 2 2/16 12.5%

b) To represent the data graphically with a histogram, we plot the ages on the x-axis and the absolute frequency on the y-axis:

c) To calculate the mode, mean, and median:

Mode: The mode is the most frequently occurring age in the dataset. In this case, the mode is 15, as it appears 5 times.

Mean: The mean is the average of all the ages. To calculate it, we sum up all the ages and divide by the total number of ages:

(13 + 13 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 17 + 17 + 17 + 18 + 18) / 20 = 306 / 20 = 15.3

Median: The median is the middle value in the dataset when arranged in ascending order. In this case, the median is 15 since it falls in the middle.

d) To calculate the probability of having 13 years old, we divide the absolute frequency of 13 (2) by the total number of ages (20):

Probability of 13 years old = 2/20 = 0.1 or 10%

e) To calculate the probability of having 14 or 16 years old, we add the absolute frequencies of 14 and 16 (2 + 2 = 4) and divide by the total number of ages (20):

Probability of 14 or 16 years old = 4/20 = 0.2 or 20%

f) To calculate the probability of not having 15 years old, we subtract the absolute frequency of 15 (5) from the total number of ages (20):

Probability of not having 15 years old = (20 - 5)/20 = 0.75 or 75%

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The ratio of EG = 36.

Let's assign variables to the lengths of the line segments:

EF = x

FG = 5x

GH = 3x

We know that EH = EF + FG + GH.

Substituting the given values, we have:

54 = x + 5x + 3x

Combining like terms, we get:

54 = 9x

To isolate x, we divide both sides of the equation by 9:

54/9 = x

Simplifying, we find:

6 = x

EF = 6, FG = 5(6) = 30, and GH = 3(6) = 18.

Since EG is the sum of EF and FG, we can calculate it as follows:

EG = EF + FG = 6 + 30

= 36

EG = 36.

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With regards to the rigid transformations, Yes, it is true to state that ∠ABD is congruent to ∠EFM. This can be justified by translating ∠ABD by superimposing it on ∠EFM.

It is also true to state that ∠ ABD is congruent to ∠GFHG. To justify this, rotate ∠ABD by 180°

A rigid transformation in mathematics is a geometric transformation of a Euclidean space that retains the Euclidean distance between each pair of points. Rotations, translations, reflections, and any combination of these are examples of rigid transformations.

Hence, the above statements are true. Note that rigid transformations do not modify the distance angles, size or shape.

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Answer:

196 miles

Step-by-step explanation:

if he goes 140 miles with 5 gallons, each gallon lets him go 28 miles.

140miles/5gallons=28miles/1gallon

then 7 gallons lets you go 196 miles

brainliest please :)

Answer: 5 or 5 \(\frac{0}{3}\)

Step-by-step explanation:

3*1=3 ==> 1st box value

3*2/3=6/3=2 ==> 2nd box value

3+2=5

5=5 \(\frac{0}{3}\)

Answer:

9.95h + 5  ≤ 125

Step-by-step explanation:

let 'h' = number of hats

Answer: 1.96

2

Step-by-step explanation:

Answer:

tan B =  12 /5

sin B =  12/13

cos B =  5/13

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan B = opp/ adj = 12 /5

sin B = opp/hyp = 12/13

cos B = adj/hyp = 5/13

Answer:

Sine of B = 12/13

Cos of B = 5/13

Tan of B = 12/5

Step-by-step explanation:

In this case, the opposite is 12, the adjacent is 5 and the hypotenuse is 13.

sin is opposite/hypotenuse

cos is adjacent/hypotenuse

and

tan is opposite/adjacent

When a graph is translated to the right by a units, the x-coordinate of each point on the graph increases by a units. So the equation of the transformed function will have x - a in it.

When a graph is translated down by b units, the y-coordinate of each point on the graph decreases by b units. So the equation of the transformed function will have y - b in it.

Given f(x) = |x| + 5 and the graph of f(x) is transformed into the graph of g(x) by a translation of 4 units right and a translation of 3 units down, the equation of the transformed function g(x) will be:

g(x) = f(x - 4) - 3

This is because the x-coordinate increases by 4 units and the y-coordinate decreases by 3 units.

So the equation of g(x) is:

g(x) = |x-4| + 5 - 3

g(x) = |x-4| + 2

This function g(x) will have the same shape as f(x) but shifted 4 units to the right and 3 units down.

Answer:

This function g(x) will have the same shape as f(x) but shifted 4 units to the right and 3 units down.

Step-by-step explanation:

The domain of the function above is [-2, 3].

The range of the function above is [-2.5, 2].

The intervals over which the function is increasing is [-2, 1.5] U [-2.5, 2].

The intervals over which the function is decreasing is [1.5, -2.5].

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of this rational expression (function)   shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = [-2, 3] or -2 ≤ x ≤ 3.

Range = [-2.5, 2] or -2.5 ≤ y ≤ 2.

Additionally, the intervals over which the function is increases over the interval [-2, 1.5] and [-2.5, 2], while it decreases over the interval [1.5, -2.5].

In conclusion, the given function is not constant over any interval.

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