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Answer:

2 gallons converted to liters is 7.57 or 8 liters rounded

Answer: The graph of a quadratic function is called a parabola. ... There is an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.

Step-by-step explanation:

Answer:

y = (5/7)x + (75/7)

Step-by-step explanation:

If you ever find yourself in a math class where you have to write the equation of a line that goes through a certain point and has a certain slope, don't panic. There is a simple formula that can help you out. It's called the point-slope form and it looks like this:

y - y1 = m (x - x1)

It may look scary, but it's actually pretty easy to use. All you have to do is plug in the values that you know and solve for the ones that you don't. For example, let's say you have a line that passes through the point (-1, 10) and has a slope of 5/7. You can use the point-slope form to write the equation of the line like this:

y - 10 = (5/7) (x - (-1))

See? That wasn't so bad. Now you can simplify the equation by distributing the 5/7 and adding 10 to both sides. You get:

y = (5/7)x + (75/7)

And that's it! You have written the equation of the line in slope-intercept form, which is another way of writing the equation of a line. You can check your answer by plugging in the values of x and y from the original point and seeing if they make the equation true. If they do, you're good to go. If not, you made a mistake somewhere and you should go back and fix it.

Congratulations! You have learned how to use the point-slope form to write the equation of a line. Now you can impress your math teacher and your friends with your skills.  Remember, with great power comes great responsibility.

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

The function g(x) = 2f(6x) + 8 is a function transformation of the function f(x)

The function g(x) is given as:

g(x) = 2f(6x) + 8

The table is not given.

So, I will provide a general explanation

Using the following values of x:

x = 0, 1, 2, 3......

We have:

g(0) = 2f(6 *0) + 8

g(0) = 2f(0) + 8

g(1) = 2f(6 *1) + 8

g(1) = 2f(6) + 8

g(2) = 2f(6 *2) + 8

g(2) = 2f(12) + 8

g(3) = 2f(6 *3) + 8

g(3) = 2f(18) + 8

Next, we assume the following values

f(0) = 4, f(6) = 5; f(12) = 6 and f(18) = 7

The values become:

g(0) = 2f(0) + 8 = 2 * 4 + 8 = 16

g(1) = 2f(6) + 8 = 2 * 5 + 8 = 18

g(2) = 2f(12) + 8 = 2 * 6 + 8 = 20

g(3) = 2f(18) + 8 = 2 * 7 + 8 = 22

So, the table of values would be:

x     g(x)

0     16

1     18

2   20

3   22

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The factor of the polynomial is P(x) = (x² - 4)(x² + 1) and the zeros are x = i, x = -i, x = 2 and x = 4

From the question, the polynomial expression is given as

P(x) = x⁴ - 3x² - 4

Start by expanding the polynomial

So, we have

P(x) = x⁴ - 4x² + x² - 4

Group the expanded expression as follows

So, we have

P(x) = (x⁴ - 4x²) + (x² - 4)

Factor each group

So, we have

P(x) = x²(x² - 4) + 1(x² - 4)

Factor out (x² - 4)

P(x) = (x² - 4)(x² + 1)

Set to 0

(x² + 1)(x² - 4) = 0

This gives

x² + 1 = 0 or x² - 4 = 0

Solve for x

x² = -1  or x² = 4

So, we have

x = i, x = -i, x = 2 and x = 4

The graph of the function is added as an attachment

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Length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

The area of Rectangle is length times of width

Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.

Here, the dimensions of the rectangles are the same.

The width of the two rectangles is W=2W+2W=4W

The length of the two rectangles is L=L+L+L=3L

Because the adjacent side has a common length.

3L+4W=200

3L=200-4W

Divide both sides by 3

L=(200-4W)/3

Let us form an equation using the area of rectangle formula:

A=2LW

=2(200-4W)/3.W

A=400-8W²/3

Let us differentiate to get the area to be maximized dA/dW=0

1/3×(400-8W²)=0

1/3(400-16W)=0

400-16W=0

400=16W

Divide both sides by 16

W=25

The width is 25 feet.

Substitute W value in equation to get L value:

L=200-4×25/3

=200-100/3

=100/3

=33.33

The length is 33.33 feet.

Now let us find the maximum area

A=2LW

=2×33.33×25

=1666.66

Hence, length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

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To set up the amortization table, we can use the mortgage and interest formulas as follows:

Mortgage formula:

M = P [ i(1 + i)^n / (1 + i)^n - 1]

where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (APR divided by 12), and n is the total number of payments (20 years multiplied by 12 months per year).

Interest formula:

I = P * i

where I is the monthly interest payment, P is the remaining principal balance, and i is the monthly interest rate.

Using these formulas, we can set up the following amortization table for the first two months:

Month Payment Principal Interest Balance

1    $400,000

2    

To fill in the table, we need to calculate the monthly payment (M) and the monthly interest payment (I) for the first month, and then use these values to calculate the principal payment for the first month. We can then subtract the principal payment from the initial balance to get the balance for the second month, and repeat the process to fill in the remaining columns.

To calculate the monthly payment (M), we can use the mortgage formula:

M = P [ i(1 + i)^n / (1 + i)^n - 1]

where P is the principal amount, i is the monthly interest rate, and n is the total number of payments.

Plugging in the given values, we get:

M = 400,000 [ 0.00279 (1 + 0.00279)^240 / (1 + 0.00279)^240 - 1]

M = $2,304.14

Therefore, the monthly payment is $2,304.14.

To calculate the interest payment for the first month, we can use the interest formula:

I = P * i

where P is the remaining principal balance and i is the monthly interest rate.

Plugging in the values for the first month, we get:

I = 400,000 * 0.00279

I = $1,116.00

Therefore, the interest payment for the first month is $1,116.00.

To calculate the principal payment for the first month, we can subtract the interest payment from the monthly payment:

Principal payment = Monthly payment - Interest payment

Principal payment = $2,304.14 - $1,116.00

Principal payment = $1,188.14

Therefore, the principal payment for the first month is $1,188.14.

To calculate the balance for the second month, we can subtract the principal payment from the initial balance:

Balance = Initial balance - Principal payment

Balance = $400,000 -$1,188.14

Balance = $398,811.86

Therefore, the balance for the second month is $398,811.86.

Using these values, we can complete the first two rows of the amortization table as follows:

Month Payment Principal Interest Balance

1 $2,304.14 $1,188.14 $1,116.00 $398,811.86

2    

To fill in the remaining columns for the second month, we can repeat the process using the new balance of $398,811.86 as the principal amount for the second month. We can calculate the interest payment using the same method as before, and then subtract the interest payment from the monthly payment to get the principal payment. We can then subtract the principal payment from the balance to get the new balance for the third month, and repeat the process for the remaining months of the amortization period.

a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

a) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.

In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.

Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.

b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.

For Scooter, with x = 20 (number of shirts sold):

f(x) = 200 + 15x

f(20) = 200 + 15 * 20

f(20) = 200 + 300

f(20) = 500

For Karissa, with x = 12 (number of repairs):

f(x) = 80 + 35x

f(12) = 80 + 35 * 12

f(12) = 80 + 420

f(12) = 500

Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

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The statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The question is: Consider the function f(x) = (-2/3)x - 24  Which conclusions can be drawn about f⁻¹(x) Select two options:

f⁻¹(x) has a slope of -2/3

f⁻¹(x) has a restricted domain.

f⁻¹(x) has a y-intercept of (0, –36).

f⁻¹(x) has an x-intercept of (–36, 0).

f⁻¹(x) has a range of all real numbers.

f(x) = (-2/3)x - 24

To find the inverse of a function:

interchange the x and y

x = (-2/3)y - 24

y = (-3/2)(x + 24)

y = (-3/2)x - 36

The slope of a function f⁻¹(x) is -3/2

From the graph, we can see the y-intercept is (0, -36) and the range will be all real numbers.

Thus, the statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.

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Answer:

D and  E

Step-by-step explanation:

did the test

Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 \(S_{n}\)​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is \(a_{1}\) = 4000, second term is \(a_{2}\) = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

\(d = a_{2} - a_{1} = 5000 - 4000 = 1000\)

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and \(S_{n}\) = 165000 in “ \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) “ which can be represented as:

Determining, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\)

⇒ 165000 = \(\frac{n}{2}\) [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + \(1000n^2\)

⇒ \(1000n^2\) + 7000n - 330000 = 0

⇒ \(1000n^2\) ( \(n^2\) + 7n - 330 ) = 0

⇒  \(n^2\) + 7n - 330 = 0

⇒ \(n^2\) + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.

Answer:

17 FT

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

if 1 friend = 3 sandwiches, and you have 4 friends, you multiply the 3 by 4 and get 12

Step-by-step explanation:

The perpendicular line that goes through the midpoint of another line in a triangle is the angle bisector.

m<BCD = m<ACB / 2 = 134.76 / 2 = 67.38°

The test scores 78,90,94,72,80,68,72,88,94,98,86,96 for students in Mr.Garcia's study group arranged as box-whisker-plot in option D is the correct form.

What is box-whisker-plot?

It is a type of data representation which is also known as box plot. It shows the main 5 pointed data which includes maximum value of given data, minimum value of the given data, median of the data, upper quartile and the lower quartile. The upper and lower extremes are indicated using end point of the lines. The box indicates the inter quartile range and the whisker inside the box indicates the median of the data.

The observations given are:78,90,94,72,80,68,72,88,94,98,86,96

On arranging the data in ascending order, we get:

68, 72, 72, 78, 80, 86, 88, 90, 94, 94, 96, and 98

As the number of observations are even, the median will be the average of \(\frac{N}{2} and \frac{N}{2}+1\) terms{where N=number of observations}

Median= mean of \(\frac{12}{2} and \frac{12}{2} + 1\) terms

           =mean of 6th and 7th term of the sequence

           =mean of 86 and 88   {6th term=86 and 7th term=88}

Median =87

First quartile Q1: Median of all terms before median{68, 72, 72, 78, 80, 86}

Quartile 1= mean of 3rd and 4th term { \(\frac{N}{2} and \frac{N}{2}+1\) }

               =mean of 72 and 78  {3rd term=72 and 4th term=78}

               =75

Quartile 3=Median of all terms after median{88, 90, 94, 94, 96, 98}

Quartile 3= median of terms {88, 90, 94, 94, 96, 98}

               = mean of 3rd and 4th term { \(\frac{N}{2} and \frac{N}{2}+1\) }

               =mean of 94 and 94  {3rd term=94 and 4th term=94}

               =94

Inter quartile range=quartile 3 - quartile1

                               =94 - 75

                                =19

The 5 points to check the correct box-whisker-plot are:

Minimum observation=68

Lower quartile=75

Median=87

Upper quartile=94

Maximum observation=98

The correct option is D.

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Refer to the figure attached below for options.

The part of the foot will the photo collage cover is 1/5 square foot

Recall that an area of a lawn is an area of soil-covered land planted with grasses and other durable plants such as clover which are maintained at a short height with a lawnmower (or sometimes grazing animals) and used for aesthetic and/or recreational purposes

The given parameters are

Area of the Poster =1 sq.ft.

The collage will cover a part of the poster that is

1/5ft wide and 3/5ft long

Area of the Photo Collage Section

=Length X Width

= 1/3 * 3/5

= 3/15 ft = 1/5foot

In conclusion,  the photo cover will cover 1/5  of a square foot

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The scaled triangle will be larger than the initial size by a factor 2.

The scaled square will be smaller than the initial side by a factor 4.

Dilation refers to a transformation that changes the size of a geometric figure without altering its shape.

Dilation involves scaling an object by a certain factor, that might result in  enlarging or reducing its dimensions uniformly in all directions.

Based on the given diagram, the new length and size of the object is calculated as follows;

For the triangle, (measure the length with ruler)

For the square; (measure the length with ruler)

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Answer:

20x+8

Step-by-step explanation:

Answer:

y = 3. last option is correct answer for 2nd question.

Step-by-step explanation:

f(x) just means y.

horizontal asymptote is y = 'something.'

the graph crosses y = 4, so y = 4 cannot be asymptote.

y = 3 is since the graph never quite touches it.

as for ∞, we see that as x approaches -∞, y almost reaches 3. but not quite. also, as x approaches +∞, y approaches +∞.

so the last option is the correct answer.

Answer:

13/10

Step-by-step explanation:

Its 13/10...

please give brainliest

Answer:

13/10

Step-by-step explanation:

Answer:

Except for -1 (12w - 6).

Answer:

h(x) = 0.5x + 8

Step-by-step explanation:

We are being asked to write an equation where h(x) represents the soil depth in inches and x describes the number of bags. To do this, we need to find b (our y-intercept, ie the value of h(x) or y when x=0) and m (our slope).

"The depth of the soil is currently 8 inches": this means before any bags are added (ie when x=0), the soil depth starts at 8. This makes 8 our y-intercept (b in h(x)=mx+b) as we have to add it on to however much the bagged soil adds in order to get the total depth.

"For each bag of soil he adds, the depth will increase by 1/2 of an inch": this means that the soil depth from added bags is equal to the amount of bags times 0.5, which makes 0.5 our slope (m in h(x)=mx+b).

Therefore our answer is:

h(x) = 0.5x + 8

Answer:

Step-by-step explanation:

(19/3)+(7/2)

(11/2)+(13/3)

=> 6.33 + 3.5   /   5.5 + 4.33  = 1

Answer:

2 1/20 m

Step-by-step explanation:

3/5 + 3/4 + 7/10  Turn into common denominators:

12/20 + 15/20 + 14/20 = 41/20

= 2 1/20 m

Answer:

a) Null hypothesis (H0): the mean guest bill for a weekend is $600.

Alternative hypothesis (Ha): the mean guest bill for a weekend is significantly bigger than $600.

b) When H0 can not be rejected, the conclusion is that there is no enough evidence to claim that the mean guest bill had increased from $600.

c) When the H0 is rejected, they have enough evidence to claim that the mean guest bill is significantly bigger than $600.  

Step-by-step explanation:

a) The accountant, as he wants to see if there is evidence to support the claim that the mean guest bill has increased significanty, should write the hypothesis like that:

Null hypothesis (H0): the mean guest bill for a weekend is $600.

Alternative hypothesis (Ha): the mean guest bill for a weekend is significantly bigger than $600.

A sample of bills of the period in study needs to be taken in order to have a representation of the actual population of bills and then perform a t-test, as the sample mean and standard deviation will be used to perform the test.

b) When H0 can not be rejected, the conclusion is that there is no enough evidence to claim that the mean guest bill had increased from $600. If the P-value was low but not enough, they may take another sample to perform the test again or leave it like that.

c) When the H0 is rejected, they have enough evidence to claim that the mean guest bill is significantly bigger than $600.  

The equation is 3x - 8 = 0.

So, 5 is a solution if we replace x by 5 and we get 0 on the left side of the equation.

Then, replacing x by 5, we get:

3x - 8 = 0

3*5 - 8 = 0

15 - 8 = 0

7 = 0

Since 7 is different from 0, 5 is not a solution.

Answer: 5 is not a solution