Wyatt just got his commercial driver's license and is starting a new career as a truck driver.
Getting trained and licensed involved a one-time cost of $500. Gas and insurance end up
costing him $4 per mile. For his first delivery, Wyatt will get paid $400 plus $6 per mile that
he drives. If he drives a certain distance on this delivery, Wyatt will break even, making back
all the money he had to spend. How much would both the costs and the earnings be?

Write a system of equations, graph them, and type the solution.

Answer: x = 1/2 , -3/2

Step-by-step explanation:

Use the quadratic formula:

a=4

b=4

c=-3

x= -4 +- sqrt16-4(4)(-3) / 8

= -4 +- sqrt16+48 / 8

= -4 +- sqrt64 / 8

= -4 +- 8 / 8

Split it to (-4 + 8) / 8 and (-4 - 8) / 8

4/8 and -12/8 = 1/2 and -3/2

The number of red marbles in the bag is 12.

We are given a bag. The bag contains two types of marbles. There are red and blue marbles in the bag. The ratio of marbles is four red marbles to thirteen more blue marbles than red marbles. Let the ratio of the number of red marbles to that of blue marbles be denoted by the variable "r".

r = 4/(13 + 4) = 4/17

The number of red marbles and blue marbles in the bag is 4x and 17x, respectively, where "x" is a variable. We know that the number of blue marbles in the bag is 51. We can write the following equation to find the value of "x".

17*x = 51

x = 51/17 = 3

Hence, the number of red marbles is 4x = 4*3 = 12.

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The speed of the fish in still water is 5 Km/h.

The speed of the current is 1 km/hr.

For the given question.

Total distance travelled by fish = 12 miles.

Let the speed of the fish in still water be 'x km/h.'

Let the speed of the current be 'y km/hr'.

Time taken by fish in moving down steam is 2 hours.

Time taken by fish in moving up steam is 3 hours.

Use formula;

Distance = speed x time

Part a:  system of linear equations

Down steam; 2(x + y) = 12   ...eq 1

Up steam; 3(x - y) = 12   ...eq 2

Part b: speed of the fish in still water.

Solve equation 1 an d 2 by elimination.

2(x + y) = 12

3(x - y) = 12

Divide equation 1 by 2 and multiply it by 3, Then add to eq 2.

6x = 30

x = 5

Speed of fish in still water = 5 Km/h.

Part c: speed of the current

Put value of x in eq 1.

x = 5

2y = 12 - 10

2y = 2

y = 1

Thus, speed of the current is 1 km/hr.

Part d: If the speed of the current is not constant than, then the value of speed of the fish in still water can not be found.

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Answer: If the graph of a relationship is a line or a ray through the origin, then it is proportional. If it is a line or ray that does not pass through the origin, then it is not proportional. Also, if it is not linear, then it is not proportional.

Step-by-step explanation:

Answer:

Step-by-step explanation:

See the attached image

The temperature when the plane reaches an altitude of 7,000ft is 47.3 degree.

What is temperature?

Temperature, measure of hotness or coldness expressed in terms of any of several arbitrary scales and indicating the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).

Given,

there is temperature decrease in every thousand feet = 1.7f

temperature decrease in 7000 ft = 7(1.7) = 11.9 f

Therefore, temperature = 59.2- 11.9

=47.3

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Distance between starting and end point. The hiker descends the distance is [tex]124.1m[/tex]

What is depth?

The distance between the nearest end and farthest end of an object is its depth.

Here given that, the depth of the mammoth cave is [tex]-124.1m[/tex].

When the hiker is at the maximum depth it is traveling to the bottom of the cave.

As it is given the depth of the cave [tex]-124.1m[/tex]. Since the hiker is traveling down to the bottom and covering the total depth and the hiker must have covered the same distance corresponding to the depth in the cave which would be [tex]124.1m[/tex].

Hence, the hiker must have descended the distance that is [tex]124.1m[/tex]

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Answer:

Integer, Rational, Real

Step-by-step explanation:

Let's go through and define what each of these are:

Integer:

An integer is any number (including zero) that is positive or negative. Please note that it cannot be a decimal / fraction.

-1 is a whole, negative number. So, it is an integer.

Rational:

A rational number is any number that can be written as a ratio of 2 numbers. Ex: 1.5 can be 3/2

-1 can be written as -1/1, so it is a rational number.

Real

A real number is *any* number that is not imaginary (the number i is imaginary. i is [tex]\sqrt{-1}[/tex])

-1 has no i so it is a real number

Irrational

An irrational number is any number with a radical at it's end. Ex: 3 [tex]\sqrt{5}[/tex], and [tex]2\sqrt{2}[/tex]

-1 has no radical attached to it, so it is not an irrational number.

Whole:

A whole number is any number that has no decimal and is positive (though zero is included)

-1 has no negative, but is a negative number so it would not be counted as a whole number.

Natural:

Natural numbers were always confusing to me, but I hope this will help you. A natural number is any positive number starting at 1, and going forever. They always increase in a multiple of 1. Examples of natural numbers: 1, 2, 3, 4... It is called a natural number, because counting in multiples of ones is natural to us, like counting the amount of apples in a basket.

-1 is a negative number, so doesn't qualify for the characteristics of a natural number.

Let's go back through all of these explanations and see which ones we said -1 is:

Integer, Rational, Real

Using the ideal gas law, pv=nrt we can find the number of moles (n), pressure (P), volume (V), Kelvin (T).

The relationship between pressure (P), volume (V), amount of gas (n), and temperature (T) is represented by the ideal gas equation, PV=nRT (T). Because it assumes that gas is functioning in an ideal or theoretical way and can therefore be written as a universal gas constant, it is known as "the ideal gas law" (represented by R in the equation).

It is believed that the gas is perfect.

In many cases, pressure (P) is measured in atmospheres (atm). Liters are commonly used to measure volume (V) (L). Mole amounts (n) are frequently used as units of measurement (mol). The unit of temperature is Kelvin (T) (K).

R is the universal constant. The SI value is 8.31 J/mol∗K

The ideal gas law is helpful for comprehending and computing the characteristics and actions of gas, such as when developing cars or airplanes. It is also crucial for understanding thermodynamics. For instance, the pressure can be determined when the temperature, volume, and quantity of gas are known. When the variables are unknown, the ideal gas law equation can be changed to provide a solution for each one.

Hence by using the ideal gas law, pv=nrt compute the characteristics and actions of gas.

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Answer:

Step-by-step explanation:

The y-intercept is the y-coordinate with x = 0, this is 2 on the table:

Use one more of points, (2, 6.5) to find the slope:

The line is:

Correct choice is A.

Answer:

25

Step-by-step explanation:

5x5 =25 25-5=20

The expression of the given volume formula for the l will be 1 and l, in general, will be V/(wh).

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

As per the given volume expression,

V= lwh

a)

l = V/(wh)

l = 8/(2 × 4) = 1

b)

V= lwh

l = V/(wh)

Hence "The expression of the given volume formula for the l will be 1 and l, in general, will be V/(wh)".

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Answer:

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

and

TThe 95% confidence interval for the mean spent on books at this university is (160.711, 179.289).

In the given question we have to find the 95% confidence interval for the mean spent on books at this university.

A sample of 50 students was taken from the local university.

So n=50

These students spent an average of $170 on books this semester, with a standard deviation of $25.50.

So x=$170 and σ = $25.50

So the 95% confidence interval for the mean spent on books at this university.

CI=x ± [tex]z_{\alpha /2}[/tex]× σ/√n

Now finding the value of [tex]z_{\alpha /2}[/tex] for 99%=0.99 confidence interval.

[tex]\alpha[/tex] =1−0.99 = 0.01

[tex]\alpha[/tex]/2 = 0.01/2 = 0.005

[tex]z_{\alpha /2}=z_{0.005}[/tex]

[tex]z_{\alpha /2}[/tex] = 2.576

The z critical value at 99% confidence interval is 2.576.

Putting the value

CI=170 ± 2.576× 25.50/√50

CI=170 ± 2.576× 25.50/7.071

CI=170 ± 2.576×3.606

CI=170 ± 9.289

CI=(170 − 9.289, 170 + 9.289)

CI =(160.711, 179.289)

Hence, the 95% confidence interval for the mean spent on books at this university is (160.711, 179.289).

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At Letter2go, Betsie can purchase the 250 envelopes. As an example, 250 envelopes cost £31.9 in the Letter2go store but £33.17 in the Value World store.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.

From Letters 2 go:

Pack of 25 envelopes for £3.19

If we look at the price of envelopes at shop 1, which is Value World,

The cost of a pack of 10 envelopes is £1.99.

Also, buy 2, get one is free

Which means that 1 pack = £1.99

2 packs = 2×£1.99 = £3.98

Also, with 2 packs Betsie get 1 pack free

So, Betsie gets 3 packs for £3.98.

1 pack = 10 envelopes

3 packs = 30 envelopes.

Hence,

In shop Value World:

30 envelopes = £3.98

1 envelope = £3.98/30

250 envelopes = (3.98/30)×250

So, 250 envelopes will cost £33.17 in Shop Value World.

From shop Letter 2 go:

25 envelopes = £3.19

1 envelope = £3.19/25

250 envelopes = (3.19/25)×250

Therefore, 250 envelopes in Store Letter 2 go should cost £31.9.

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The different ways used to display misleading information on a graph is done by skipping a number or doesn't begin at zero. There are incorrect labels on the graph. Data is missing.

A misleading graph also referred to as a distorted graph, is one that presents data inaccurately, abusing statistics in the process and potentially leading to an incorrect conclusion.

Sometimes deceptive graphs are created on purpose, and other times it's just a matter of people not comprehending the data that goes into the graph. The "classic" varieties of deceptive graphs include those in which:

The vertical scale does not begin at zero, is too large or too little, skips digits, or all of the above.

The graph's labels need to be updated.

Data is omitted.

Thus, the different ways used to display misleading information on a graph are done by skipping a number or doesn't begin at zero. There are incorrect labels on the graph. Data is missing.

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Answer:

2

Step-by-step explanation:

we can try 2 to distribute since 18 divided by 9 is 2

2(4x+9)

2(4x)+2(9)

8x+18

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

 -3x^2 + 24x + 5 in the form 5 (6x - 3)^2 + 18

Answer:

3

It should be 3 because well how to explain

Answer:1174.5

Step-by-step explanation:

.13 times 1350= 175.5$ so 1350-175.5= 1,174.5$

Step-by-step explanation:

function 1 :

simple, you put 3 into every place of x and then calculate.

y = -4×3 + 2 = -12 + 2 = -10

function 2 :

the only one where we need to think a little.

so, x = 3.

from the center of the coordinate axes we go on the x-axis to 3.

from there we go up out down to intersect the line. then we look to the left to the y-axis and see what value we have there : -1

y = -1 when x = 3

function 3 :

the solution is already written there in full sight.

input = 3.

so, we look in the table. where is the line with input = 3 ?

it is the last but one line. what value is in the output column of that line ? -3

output = -3

Answer:

MN = 130

Step-by-step explanation:

since M is at the midpoint of LN , then

LM = MN

7x - 24 = 6x - 2 ( subtract 6x from both sides )

x - 24 = - 2 ( add 24 to both sides )

x = 22

Then

MN = 6x - 2 = 6(22) - 2 = 132 - 2 = 130

Answer:

Plug all of the X values on the left of the table in to the equations one by one and calculate.

-2(-4)—5= 3

-2(-2)—5= -1

-2(0)—5= -5

-2(2)—5= -9

Step-by-step explanation:

Answer:

nStep-by-stepkbexplanation:

Answer:their equal to 150

Step-by-step explanation:

took the test

The recipe  that  will only make 1 dozen cookies is as follows:

.18 cups of peanut butter

.12 cups of vegetable shortening

.30 cups packed light brown sugar

.72 tablespoons of milk

.66 teaspoon vanilla extract

.24 large eggs

.36 cups of flour

.18 teaspoons of baking soda

.6 teaspoons of salt.

This refers to the ingredients for baking a snack or dessert.

From the question:

Original cookie recipe =

1 1/2 cups of peanut butter

1 cup of vegetable shortening

2 1/2 cups packed light brown sugar

6 tablespoons of milk

5 1/2 teaspoon vanilla extract

2 large eggs

3 cups of flour

1 1/2 teaspoons of baking soda

1/2 teaspoon of salt

Note: 1 dozen= 12

The recipe that will only make 1 dozen cookies will be = Original cookie recipe * 12

1 1/2 cups of peanut butter * 12 =

3/2 *12= 18

1 cup of vegetable shortening *12

1 * 12 = 12

2 1/2 cups packed light brown sugar * 12

3/2 * 18 = 30

6 tablespoons of milk *12

6 * 12 = 72

5 1/2 teaspoon vanilla extract * 12

11/2 *12 = 66

2 large eggs * 12

2*12 = 24

3 cups of flour *12

3*12 = 36

1 1/2 teaspoons of baking soda * 12

3/2 *12 = 18

1/2 teaspoon of salt * 12

1/2 * 12= 6

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Answer: Gradient is 3 and y-intercept is 15

Step-by-step explanation:

by rearranging the equation so y is on 1 side we get:

y = 3x + 15

the gradient is the number before the x (coefficient)

the y intercept is the number that is not multiplied by the x, in this case 15

It will take 96.7 days for the whole US population to get infected.

Given information;

The number of people infected with coronavirus doubles every 3.3 days as following;

1 → 2 →  4 → 8 → 16 → 32 → 64 → . . . . . . . . . . . . → 333,000,000

Let 'x' denotes number of 3.3 days passed the for cases 333,000,000.

⇒ [tex]2^x = 333,000,000[/tex]

For the above equation applying log on both sides. we get;

x(In 2) = In (330,000,000)

x =  In (330,000,000)/(In 2)

x = 28.3

Therefore;

So, total no. of 3.3 days passed = 1 + x

                                                     = 1 + 28.3

                                                     = 29.3

And number of days for 1 to 330,000,000 = 29.3 * 3.3 days

                                                                      = 96.7 days

Hence, it will take 96.7 days to infect the total population in US.

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