calculate the next three numbers of each progression1) 15,-14,13,-12,11...2) 2,5,9,14...

Answer:

≈9.64 gallons

Step-by-step explanation:

To solve, we can figure out how many quarts are in a minute and use that to figure out how many quarts are in an hour. Then, we can convert quarts to gallons.

4.5 quarts = 7 minutes

First, we can find how many quarts equal 1 minute. To do this, we can divide both sides by 7 because anything divided by itself equals 1

4.5/7 quarts = 1 minute

Next, we want to figure out how many quarts go into 60 minutes, or 1 hour. To do this, we can multiply both sides by 60 because 1 * 60 = 60

4.5 * 60 / 7 quarts = 60 minutes = 1 hour

We now know how many quarts are in an hour, so we can now convert quarts to gallons

4 quarts = 1 gallon

divide both sides by 4

1 quart = 1/4 gallons

To get from quarts to gallons, we can divide by 4, so we have

(4.5 * 60 / 7)/4 = 4.5 * 60 / 28

≈9.64 gallons

Step-by-step explanation:

S.i =principal x rate x time/100

7,50000x4x4.5/100

13500000/100

135000

The angles that we have in the image here are:

When two angles are measured, they sum up to 180. They are said to be supplementary angles.

On the question, we have two angles that are 90 degrees on a straight line. Hence they are supplementary.

This is an angle that is at 90 degrees. We have to two right angles on the diagram that we have here.

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Answer: Probability = 0.2

Step-by-step explanation:

Given data:

Mean production time = 32.20 seconds

Standard deviation = 1,05seconds

probability that a full production run will take less than 32 seconds on average to produce

= P(Xbar<32)

= P(Z<-0.8518)

= 0.2

A. The system of equations in standard form is: 4x + 5y = 540 and 3x + 5y = 440.

B. The y-intercept of the equation representing the prices on Saturday night is 108, and the y-intercept of the equation representing the prices at the matinee on the second day is 88.

A) Let's define the variables:

Let x represent the number of children attending.

Let y represent the number of adults attending.

On Saturday night:

The equation for the revenue generated on Saturday night is:

4x + 5y = 540 (since children's tickets cost $4 and adults' tickets cost $5, and the total revenue is $540).

Matinee on the second day:

The equation for the revenue generated at the matinee is:

3x + 5y = 440 (since children's tickets cost $3 and adults' tickets still cost $5, and the total revenue is $440).

Therefore, the system of equations in standard form is:

4x + 5y = 540

3x + 5y = 440

B) Let's rewrite the system of equations in slope-intercept form:

On Saturday night:

4x + 5y = 540

Rearranging the equation, we get:

5y = -4x + 540

Dividing both sides by 5, we get:

y = (-4/5)x + 108

The y-intercept of this equation is 108.

Matinee on the second day:

3x + 5y = 440

Rearranging the equation, we get:

5y = -3x + 440

Dividing both sides by 5, we get:

y = (-3/5)x + 88

The y-intercept of this equation is 88.

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Answer:

108cm³

Step-by-step explanation:

Seeing that the base is a square, we first have to calculate the area of the base. This is equal to 9x9, in other words 81cm squared. Now, we multiply the base area to the vertical height divided by 3, which becomes 81x(4/3), which is then 108cm³.

:))))))))))

Answer:

The equation of line that passes through the point (8,-7) and is parallel to the line 5x+4y=16 is  \(\mathbf{y=-\frac{5}{4}x+3}\)

Step-by-step explanation:

We need to write an equation of the line that passes through the point (8,-7) and is parallel to the line 5x+4y=16.

The equation will be of form \(y=mx+b\) where m is slope and b is y-intercept.

Finding slope of the line:

Since both the lines are parallel, and we know that parallel lines have same slope.

The slope of given line \(5x+4y=16\) can be found by writing in slope-intercept form \(y=mx+b\)

\(5x+4y=16\\4y=-5x+16\\y=-\frac{5}{4}x+16\)

Comparing with \(y=mx+b\) the slope m is: \(m=-\frac{5}{4}\)

So, the slope of required line is: \(m=-\frac{5}{4}\)

Now, finding y-intercept b

y-intercept can be found using slope \(m=-\frac{5}{4}\) and point (8,-7)

\(y=mx+b\\-7=-\frac{5}{4}(8)+b\\-7=-5(2)+b\\-7=-10+b\\b=-7+10\\b=3\)

So, we get y-intercept: b=3

Now, the equation of required line having slope \(m=-\frac{5}{4}\) and y-intercept b=3 is:

\(y=mx+b\\y=-\frac{5}{4}x+3\)

So, the equation of line that passes through the point (8,-7) and is parallel to the line 5x+4y=16 \(\mathbf{y=-\frac{5}{4}x+3}\)

The functions for this problem are defined as follows:

The functions for this problem are given as follows:

The addition and subtraction functions for this problem are given as follows:

At x = -2, the numeric value of the subtraction function is given as follows:

(t - s)(-2) = -2³ - 5(-2)²

(t - s)(-2) = -28.

The product function for this problem is given as follows:

(ts)(x) = \(5x^5\)

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Answer:

$34.00

Step-by-step explanation:

The solution is : Kami sold 28 large figurines.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

from the given information, we get,

Let x represent the number of large figurines that Kami sold.

Let y represent the number of small figurines that Kami sold.

This month kami sold 70 figurines in 2 sizes.

This means that

x + y = 70 - - - - - - - - - - 1

The large figurines sold for $12 each and the small figurines sold for $8 each. The amount of money he received from the sales of the large figurines was equal to the amount of money he received from the sales of the small figurines. This means that

12x = 8y

y = 12x/8

y = 1.5x

Substituting y = 1.5x into equation 1, it becomes

x + 1.5x = 70

2.5x = 70

x = 70/2.5

  = 28

y = 1.5x

 = 1.5 × 28

 = 42

Hence, The solution is : Kami sold 28 large figurines.

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Answer:

1244 DCD

Step-by-step explanation:

Answer:

The math exam.

Step-by-step explanation:

Ir order to compare all these scores, let's convert them to the relative form (a percentage).

Art one is easy, since it's given by the problem: 78%.

English score percentage will be given by this operation: (19/25)=0.76= 76%.

Math is the same concept as in English, 32/40= 0.8= 80%.

Now, compare the 3 results:

Art: 78%.

English: 76%.

Math: 80%.

The math exam was was the one where Maria received the highest score out of the 3 tests.

Step-by-step explanation:

I don't really know the answer 'cause

check the answer in aswer sheet

Answer:

The standard answer for this is 50%.  

Step-by-step explanation:

  However, this is based on the implicit assumption that the coin is fair.

If there are reasonable grounds to doubt that the coin is fair, the theoretical probability must be based on observed statistics.   In this scenario, the probability is 60%.  

Answer:

8910

Step-by-step explanation:

30x297 = 8910

All 3 angles add up to 180 degrees.

so 40 + 2x + 3x = 180

40 + 5x = 180

5x = 140

x = 28

So angle A = 2x = 2(28) = 56 degrees.

Answer: 56°

Step-by-step explanation:

We know that a triangle's angles add up to 180 degrees. We will create an equation to help us solve for x using this information.

     Given:

           2x + 3x + 40 = 180

     Combine like terms:

           5x + 40 = 180

     Subtract 40 from both sides of the equation:

           5x = 140

     Divide both sides of the equation by 5:

           x = 28

Next, we will substitute this value of x into the expression for ∠A.

     ∠A = 2x = 2(28) = 56°

Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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Answer:

9 integers between 2023 and 5757 that have 12, 20, and 28 as factors.

Step-by-step explanation:

An integer that has 12, 20, and 28 as factors must be divisible by the least common multiple (LCM) of these numbers. The LCM of 12, 20, and 28 is 420. So we need to find the number of integers between 2023 and 5757 that are divisible by 420.

The first integer greater than or equal to 2023 that is divisible by 420 is 5 * 420 = 2100. The last integer less than or equal to 5757 that is divisible by 420 is 13 * 420 = 5460. So the integers between 2023 and 5757 that are divisible by 420 are 2100, 2520, ..., 5460. This is an arithmetic sequence with a common difference of 420.

The number of terms in this sequence can be found using the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the number of terms. Substituting the values for this sequence, we get:

5460 = 2100 + (n - 1)420 3360 = (n - 1)420 n - 1 = 8 n = 9

So there are 9 integers between 2023 and 5757 that have 12, 20, and 28 as factors.

The minimum amount of plastic wrap needed to completely wrap 8 containers is  794. 4 in². Option D

The area of each circular end is:

A = πr²

A = 3.14 × (2.75)²

A = 23.68in²

The area of the rectangular side is:

A = h * circumference

circumference = 5.5in * π

circumference = 17.27in

Using the given height of 3 inches, we get:

A = 3in * 17.27

A = 51.81in²

Therefore, the total surface area of each container is:

A = 2 * 23.68 + 51.81

A = 98.17in²

To wrap 8 containers, we need to multiply the surface area of each container by 8:

Total surface area = 8 × 98.17

Total surface area = 794. 4 in²

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Answer:

I think of A

Step-by-step explanation:

is that right

Answer:

ΔSRQ ∼ ΔVUT

Step-by-step explanation:

i got it correct

Answer:

RT = 20

Step-by-step explanation:

Given that,

Point S lies on the line segment RT.

We have, ST = 3x-8, RT = 4x and RS = 4x-7

It is clear that, RT = RS+ST

Putting the values, we get :

4x = 4x-7 + 3x-8

Taking like terms together,

4x-4x-3x = -7-8

-3x = -15

x = 5

Put the value of x in RT = 4x.

So,

RT = 4(5)

RT = 20

Hence, length of RT = 20.

Answer: 42

Step-by-step explanation:

The best way to solve this is to set up an equation. In this problem, we can use "x" for Mikhail's age, so that Gabrielle's age becomes "x+13." Now, we can write, "x+x+13=97," because Mikhail's age (x) plus Gabrielle's age (x+13) is equal to 97. When we solve for x, we get x=42, so Mikhail's age is 42.

Answer:

Here is my Cheese

Step-by-step explanation:

french cheese88

Answer:

LOL you are funny aren’t you

The equation 6y + y = 5 can be written in a slope-intercept form as y = 5/7.

We have,

To write the equation 6y + y = 5 in slope-intercept form (y = mx + b), we need to simplify the equation and isolate the y variable on one side.

Starting with the equation 6y + y = 5:

Combining the like terms on the left side gives us:

7y = 5

To isolate the y variable, we divide both sides of the equation by 7:

y = 5/7

Now the equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.

In this case, since the equation only contains the variable y and no x, the slope (m) is not present, and the y-intercept (b) is 5/7.

Therefore,

The equation 6y + y = 5 can be written in a slope-intercept form as y = 5/7.

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Answer:

4,000 cm³

Step-by-step explanation:

Let x be the length of the sides of the base and h be the height of the box.

The surface area is given by:

\(A=x^2+4xh=1,200\\h=\frac{1,200-x^2}{4x}\)

The volume if the box is:

\(V=hx^2\\V=({\frac{1,200-x^2}{4x}} )*x^2\\V=300x-\frac{x^3}{4}\)

The value of x for which the derivate of the function above is zero will produce the largest possible volume:

\(V=300x-\frac{x^3}{4} \\V'=300-\frac{3}{4}x^2=0\\ x^2=400\\x=20\ cm\)

The height of the box is:

\(h=\frac{1,200-20^2}{4*20}\\h=10\ cm\)

The largest possible volume is:

\(V=10*20^2\\V=4,000\ cm^3\)

The largest possible volume of the box is 4,000 cm³

The volume of the open-top box is the amount of space in it.

The largest possible volume of the box is 4000 cubic centimeters

The surface area of an open-top box is:

\(\mathbf{A = 2lh + 2wh + lw}\)

So, we have:

\(\mathbf{2lh + 2wh + lw = 1200}\)

The box has a square base.

So, we have:

\(\mathbf{l= w }\)

The expression becomes

\(\mathbf{2lh + 2lh + l^2 = 1200}\)

\(\mathbf{4lh + l^2 = 1200}\)

Make  the subject

\(\mathbf{h = \frac{1200 - l^2}{4l}}\)

The volume of the box is:

\(\mathbf{V = lwh}\)

So, we have:

\(\mathbf{V = l^2h}\)

Substitute \(\mathbf{h = \frac{1200 - l^2}{4l}}\)

\(\mathbf{V = l^2 \times \frac{1200 - l^2}{4l}}\)

\(\mathbf{V = l \times \frac{1200 - l^2}{4}}\)

Expand

\(\mathbf{V = \frac{1200l - l^3}{4}}\)

Split

\(\mathbf{V = 300l - \frac{l^3}{4}}\)

Differentiate

\(\mathbf{V' = 300 - \frac{3l^2}{4}}\)

Set to 0

\(\mathbf{ 300 - \frac{3l^2}{4} = 0}\)

Rewrite as:

\(\mathbf{ \frac{3l^2}{4} = 300}\)

Multiply through by 4

\(\mathbf{ 3l^2 = 1200}\)

Divide both sides by 3

\(\mathbf{l^2 = 400}\)

Take square roots of both sides

\(\mathbf{l = 20}\)

Recall that:

\(\mathbf{h = \frac{1200 - l^2}{4l}}\)

So, we have:

\(\mathbf{h = \frac{1200 - 20^2}{4 \times 20}}\)

\(\mathbf{h = \frac{1200 - 400}{80}}\)

\(\mathbf{h = \frac{800}{80}}\)

\(\mathbf{h = 10}\)

Recall that:

\(\mathbf{V = l^2h}\)

So, we have:

\(\mathbf{V=20^2 \times 10}\)

\(\mathbf{V=4000}\)

Hence, the largest possible volume of the box is 4000 cubic centimeters

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Explanation:

Each time x goes up by 1, y goes up by 18

slope = rise/run

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

slope = 18/1

slope = 18

You can also use the slope formula to get the same answer. Let's say we picked the points (2,36) and (3,54). We then would get

m = (y2-y1)/(x2-x1)

m = (54-36)/(3-2)

m = 18/1

m = 18

We get the same result as before.

Since x represents the number of years and y is the number of inches, the slope of 18/1 indicates an increase of 18 inches per 1 year, or just 18 inches per year.

The probability of spinning an even number, flipping tails, then spinning an odd number is:

1/9   (as fraction) or 11.11% (as percent)

To find the probability of spinning an even number, flipping tails, then spinning an odd number. We need to consider the individual probabilities. That is:

We have only one even number in the spinner, and that is 2. Thus,

P(even number) = 1/3

For a coin, the probability of head or tail is 1/2. Thus,

P(tail) = 1/2

We have two odd number in the spinner, and that is 1 and 3. Thus,

P(odd number) = 2/3

Therefore, the probability of spinning an even number, flipping tails, then spinning an odd number will be:

P(even, tail, odd) = 1/3 * 1/2 * 2/3

                            = 2/18

                            = 1/9   (as fraction)

In percent:

P(even, tail, odd) =  1/9 * 100

                            = 11.11%

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Answer:

x=5

Step-by-step explanation:

5x-4+3x=36

combine lke terms

5x+3x-4=36

8x-4=36

    +4. +4

8x=40

/8.  /8

x=5

hopes this helps