For the line y = 1 - 3x, create a table to show the values of x and y where x is from -2 to 2.​

The tanker has been filling the reservoir for 0.0288 minutes or 1.728 seconds as the rate of filling is 1212 gallons per minute using the estimation concept.

As per the question statement, A tanker truck fills the gas station’s reservoir at the rate of 1212 gallons per minute and the reservoir was empty and it is now 35 gallons full. We are supposed to find out for how long has the tanker been filling the reservoir. We will use the concept of estimation.

Rate of filling gas = 1212 gallons per minute

i.e., 1212 gallon of gas taken 1 minute for transfer.

1 gallon of gas will take = (1/1212) minutes

Hence 35 gallons of gas will take = (1/1212)*35 minutes = 0.0288 min.

So, the  tanker has been filling the reservoir for 0.0288 minutes or 1.728 seconds as the rate of filling is 1212 gallons per minute.

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Answer:

first one is 80

Step-by-step explanation:

i did it

The total area for the parallelogram-shaped tiles Felix needs to buy exists 80cm² at the price of $40.

In calculating the area of a parallelogram, the base exists multiplied by the height, in an exact way as computing the area of a rectangle.

Given that, the base of one parallelogram-shaped tile exists 4cm with a height of 2 cm.

Area of one parallelogram shaped tile = 4cm × 2cm

Area of one parallelogram-shaped tile = 8cm²

Total area for the 5black and 5white tiles = 10 × 8cm²

Total area for the 5black and 5white tiles = 80cm²

Therefore, Felix must buy a total area of 80cm² of 10 parallelogram-shaped tiles.

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Answer:

242.

Step-by-step explanation:

Basically, you have to put the 2 numbers "1936" and "8" down. After you put the 2 numbers down, you have to figure out how many times 8 goes into 19 which is 2 times.

You put the 2 above the 1 in 1936. After you put the 2 up there, you have to figure out 2 x 8 which is 16. You have to put the 16 below the 19 and subtract 19 by 16 which is 3.

After you finish that equation, you must bring the 3 down next to the 3 you wrote down on 19 - 16. The number turns into 33 and you have to figure out how many times 8 goes into 33 which is 4 times. You put the 4 next to the 2 above and then do 4 x 8 which is 32. You do 33 - 32 which is 1.

You bring the 6 down in 1936. It turns into a 16. You now have to figure out how many times 8 goes into 16 which is 2 times. You put 2 next to the 2 and the 4 above and that turns the number into 242.

You then have to do 2 x 8 which is 16 and put 16 under the 16 from 33 - 32. That'll make an equation which is 16 - 16 which is 0. There is no remainder and all the numbers were added above so 242 is your answer.

Hopefully, this has helped, tried my best!

=================================

Long Division - Solution and Process    

=================================

We are given the Divisor 8 and the Dividend 1,936.

     242  ← Our Final Solution

8 | 1936

     16

     ___

       33

       32

      ____

          16

           16

            0

The quotient of the given problem would be 242 with a remainder of 0, or simply 242.

Hope this helps!

Answer:

All of them work.

Step-by-step explanation:

An invertible function can be tested for by the horizontal line test. An function is not invertible is a horizontal line drawn anywhere crosses two or more points. A straight line is an invertible function as long as the slope is not equal to 0. With that, let's check A. From x = -6 to -4, the horizontal line test does not cross two points anywhere. A works. Let's check B. B also works because it passes the horizontal line test. C also works.

She cannot afford to buy the car with monthly instalments of $350. She needs to make a downpayment of $856.44 to afford the car

The total amount of the car loan = 13456.44

Number of instalments = 36 monthly payments

Affordable installment per month = $350

EMI: A fixed payment is made by a borrower to a lender at a specific time each month, known as an equated monthly instalment (EMI). The loan is repaid in full over a predetermined period of time by making equal monthly payments to the principal and interest.

Total payment that can be made using the instalments = Monthly instalments * Number of instalments

= 350*36

Total payment that can be made using the instalments = 12600

The amount remaining after paying instalments = 13456.44 - 12600

= 856.44

Downpayment required = $856.44

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In elimination method one equation is multiplied by the negative coefficient of the other

so then in this case y have coefficient 3, the other equation have coefficient y is 1 . Then divide 3/1 = 3 and change sign ,gives -3.

Then the final answer is -3, option c)

Answer:

18.25

Step-by-step explanation:

From the quadratic equation given, the time it will take till the arrow hits the ground is 22.75 seconds

To determine when the arrow hits the ground, we need to find the value of x when the height, f(x), is equal to 0. In other words, we need to solve the equation:

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a),

where a, b, and c are the coefficients of the quadratic equation

In this case, a = -16, b = 24, and c = 16. Substituting these values into the quadratic formula:

x = (-(24) ± √((24)² - 4(-16)(16))) / (2(-16)).

Simplifying further:

x = (-24 ± √(576 + 1024)) / (-32),

x = (-24 ± √(1600)) / (-32),

x = (-24 ± 40) / (-32).

x = -101/4 or x = 101/4

Since x≠  negative;

x = 101/4 = 22.75 seconds

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to find the slope of a line select the two points given.

in this case the point to the left will be (-4,-1) and the one to the right will be (3,1)

use the formula of the slope to calculate

replace the points into the formula

the slope of the line will be 2/7

2=-8-x Equation

x=-10

Explanation

Step 1

the scale is in balance, that indicates that the weights to the right and left are equal

Let

left side=2 squares of 1 each

then

left side=2

Step 2

rigth side=8 times (1) plus -x

rigth side=(8*-1)-x

rigth side=-8-x

Step 3

finally

Step 4

finally solve equation (1) for x

I hope this helps you

The probability of a horse winning a race is

The probability of the horse losing will be calculated as

By substituting the value, we will have

The formula used to calculate the odds of winning is given below as

By substituting the values, we will have

Hence,

The odds of winning = 1 : 24

EXPLANATION

Let's see the facts:

Plan A --> $35 + $0.25/minute

Plan B --> $20 + $0.5/minute

Let's call "x" to the number of minutes that a person could talk.

Here we have two equations as follows:

(1) 35 + 0.25x

(2) 20 + 0.5x

Where x represents the number of minutes a person talks on the phone.

We need to equal both equations in order to obtain the same cost.

35 + 0.25x = 20 + 0.5x

Now, we need to solve this equality as shown as follows:

-Subtracting -35 to both sides:

35 + 0.25x -35 = 20 + 0.5x -35

-Adding similar terms:

0.25x = 0.5x - 15

-Subtracting -0.5x to both sides:

0.25x - 0.5x = -15

-Adding similar terms:

-0.25x = -15

-Dividing both sides by -0.25:

x = -15/-0.25

-Simplifying:

x= 60 minutes

So, when a person talks for 60 minutes the cost of both plans is the same.

EXPLANATION

Let's see the facts:

The angles of symmetry in point A is 60 degrees because the plane in point A is divided in 6 parts, so dividing 360° by 6 give us 60°. The same reasoning applies for the point B dividing it by 3 parts.

The angles of symmetry in point B is 120 degrees.

The cost for 1 liter of premimum gasolinz is 1. 182 times greater

A ratio can be described as the ordered pair of numbers, like x and y, written in the form of a rational numbers, x/y with the denominator greater than zero.

It is also described as the number of times a number or element would contain another one.

It is also known to compare two quantities, elements or numbers.

From the information given, we have that;

To determine the value, we have;

Cost of 1 liter of 25 liters in permimum gasoline/Cost of 1 liter of 25 liters in regular gasoline

substitute the values

$69.73/ $58.98

Find the quotient

1. 182

Hence, the value is 1. 182

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Data

Starting hour = 2:50

Time = 3 h 30 min

Addition

1

2:50

+ 3:30

6:20 Use the hexadecimal system to solve this problem.

Answer:

[tex]y < \frac{5}{3} x - 3 \\ [/tex]

Step-by-step explanation:

- General linear equation of a line passing through point (x, y) with a gradient m and y-intercept (0, c) is ;

[tex]{ \rm{y = mx + c}}[/tex]

- As finding gradient, m; consider points (0, -3) and (3, 2) from the graph;

[tex]{ \rm{slope \: m = \frac{2 - ( - 3)}{3 - 0} }} \\ \\ { \rm{m = \frac{5}{3} }}[/tex]

- Then our equation becomes y = 5/3x + c

- Consider point (0, -3), relate it with (0, c) hence c is -3;

[tex]{ \rm{y = \frac{5}{3}x - 3 }}[/tex]

- If you see the format of the coordinates, x coordinates are greater than y coordinates, hence y < x

[tex]{ \rm{y < \frac{5}{3}x - 3 }} \\ [/tex]

Answer:

[tex]y < \dfrac{5}{3}x-3[/tex]

Step-by-step explanation:

All given answer options have the same linear equation:

[tex]y=\dfrac{5}{3}x-3[/tex]

Therefore, there is no need to work out the equation of the line for this question as it is already given.

When graphing inequalities:

From inspection of the graph there is:

Therefore, the inequality that is represented by the graph is:

[tex]y < \dfrac{5}{3}x-3[/tex]

Using a system of equations, it is found that Sheldon's number is of 37.

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the problem.

For this problem, we have to consider that:

The sum of these numbers is given by:

x + x + 1 = 2x + 1 (combining the like terms).

The sum is equals to 75, hence we can solve for the natural number x as follows:

2x + 1 = 75

2x = 74

x =74/2

x = 37. (which is Sheldon's natural number).

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h(t) = -16t^2+h^0

object falls untill height becomes 0, so h(t) =0, h^0 = 18.9feet

0 = -16t^2 + 18.9

-18.9= -16t^2

-18.9/-16 = -16t^2/-16

t^2=1.18125

ANSWER= OPTION B

Finding slope and y-intercept

for this equation.

-5x - y = 14

we know that

the equation of the line in slope intercept form is equal to

y=mx+b

where

m is the slope

b is the y-intercept

In this problem we have

-5x-y=14

Isolate the variable y

y=-5x-14

therefore

The amount of money should be invested to obtain interest of amount 50000$ is 34,000$(approximately)

The practice of adding interest to the principal amount of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. Reinvesting interest, or adding it to the lent capital rather than paying it out or seeking repayment from the borrower, results in interest being received on the principal amount plus interest collected previously.

[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]

Where,A is the total sum.

P equals the initial principal amount.

The nominal yearly interest rate is r.

The compounding frequency is n.

t is the total amount of time that the interest is charged (expressed using the same time units as r, usually years).

The final value less the beginning investment yields the entire compound interest.

On substituting the values we get that initial investment of approximately 34000$

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Given data:

Population Mean = 346

Standard Deviation = 72

Expected Value of e(x) = population mean = 346

Sample Size = 216

In this case, if many random samples of 216 are taken, then the mean of the sample mean numbers per week is 346. (Option C)

To solve for the variance of x or var(x), we follow the formula below:

In this case, the given standard deviation is 72 and the sample size is 216. Therefore, we have:

One of the properties of the Sampling Distribution of the Mean is that the sampling distribution of the mean is approximately normally distributed so long as the sample size is 30 or higher. Our sample mean here is 346 with a sample standard deviation of √24 or 4.899.

How likely is it to observe a sample mean number of sags per week that exceeds 390?

For this one, we have this formula to use:

Our bar "x" is 390. The "myu" symbol is our population mean which is 346. This σ symbol is the population standard deviation 72 and n is our sample size = 216.

Under a normal curve, the areas defined are between z = -3.5 to z = +3.5. Since our z should exceed > 8.98 and thus far greater than +3.5, then we can say that the probability of having a sample mean that exceeds 390 is zero.

Answer:

{48, 55,73}

Explanation:

To determine if any three side lengths can form a right triangle, we check if it satisfies the Pythagorean Theorem.

Therefore, the side lengths that could form a right triangle are {48, 55,73}.

a. The linear Equations :

3x + (x+42)= 90

⇒4x +42 =90

b. ∠ 1 = 36° and ∠2 =54°

Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the provided equations on a graph and locate the point(s) where they all cross to solve a problem by graphing. You may find the values of the variables you are working for by finding the coordinate of this point.

here

4x+42 = 90 ⇒ x=12

∠1 =4 x 12=36 and ∠2 = 12+42=54

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The money she will have after 4 months would be 31.50 dollars.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of the principal amount, rate, and period.

Simple Interest = (Principal × Rate × Time) / 100

If the initial amount (also called as principal amount) is given as 30, and the interest rate is 15% annually, and it is left for 4 months for that simple interest, then the interest amount earned is given by:

4 month = 0.333 year

Therefore,

Simple Interest = (Principal × Rate × Time) / 100

Simple Interest = (30 × 15× 0.333) / 100

Simple Interest = 31.50

Hence, the money she will have after 4 months would be 31.50 dollars.

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Answer:

54 x 5

Step-by-step explanation:

the first figure out the brackets, then multiply by 5.

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Answer:

the answer is 6 ^ 15 you are very welcom

Answer:

The expression is given below as

Concept:

We will have to explain the options so we can figure out what the final answer is

Sum:

The result is obtained by adding numbers

Quotient:

a quotient is a quantity produced by the division of two numbers.

Product:

A product is the result of multiplication,

Factor:

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.

Step 1:

We will then have to deal with the parenthesis

We will then have to multiply 7 by 16 before adding to 10

Hence,

7 in the expression above represents a factor because after adding 3 and 13, you would need to multiply 2 and 5. Then, you will multiply 7 and 16 which shows that 7 in the expression above represents a factor. 7 is a factor common to both 3 and 16

Therefore,

The final answer is OPTION A

Given a table represents the number of eggs that hatched at 3 different temperature:

The total number of eggs = 14 + 11 = 25

There are just 25 eggs in each time to make the experiment

The number of eggs was not hatched at room temperature = 11

so, the percentage will be =

So, the answer will be = 44

You have to find a line perpedicular to the line y=1/2x-3 that passes through the point (-5,2)

Given one line, to find another one perpedicular to it, you have to keep in mind that the slope of the perpedicular line is the negative inverse of the slope of the first one, that is:

Let the given line be:

And the perpendicular line

The slope of the perpendicular line will be:

So for the line

The slope is

For the perpedicular line it will be:

Now that the slope of the perpendicular is determined, use the point slope form to find the equation of the perpedicular line:

Replace the with m=-2 and (-5,2)

The equation perpendicular to

is

Now you can draw both lines:

To find the percent we are looking for we can use the rule of three:

then:

This means that 51 is 85% of 60.

Therefore 51 is 15% less than 60.