how to solve percent change and percent error problem

The value of x is 17, y is 2 and length of DF is 20.

Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.

For x

DG = GE ( Given )

DG + GE = DE

DE = 2(DG)

DG/DE = 1/2

hence GH/EF = 1/2

By Basic Proportionality Theorem ( BPT )

(x – 3) / 28 = 1/2

after cross multiplication

2(x – 3) = 28

2x – 6 = 28

2x = 34

x = 17

For y

By Basic Proportionality Theorem (BPT) to side DF

DF = 2(DH)

DH/DF = 1/2

(y + 8) / (y + 8 + x – 7) = 1/2

after cross multiplication

2(y + 8) = y + 8 + x – 7

put x = 17

2(y + 8) = y + 8 + 17 – 7

2(y + 8) = y + 18

2y + 16 = y + 18

2y = y + 2

2y – y = 2

y = 2

DF = 2(2+8)

     = 2(10)

     = 20

Hence, x is 17, y is 2 and DF is 20.

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The inequality will be 3.70x ≤ 145 and the number of items that you can by is  x ≤ 39

Total budget that you have = $145

The price of each item = $3.70

Consider the number of items = x

The inequality will be

3.70x ≤ 145

We have to solve the inequality to find the number of items

3.70x ≤ 145

Divide 3.70 on the both side of the inequality

3.70x / 3.70 ≤ 145 / 3.70

x ≤ 39.18

x ≤ 39

The number of items that you can buy is x ≤ 39

Hence, the inequality will be 3.70x ≤ 145 and the number of items that you can by is  x ≤ 39

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The equation that compares the time (t) with the distance (d) would be; 80 (t) = d

An expression that depicts the relationship between two or more numbers and variables is called an equation. Two or more equations that can be solved to get a singular result are referred to as a system of equations. The equation's power must be in one degree.

Given that A train travels at 80 miles per hour. We need to find the equation that compares the time (t) with the distance (d)

where t means time so if the train travels 2 hours then it will travel;

80 × 2 = 160 miles

Therefore, the equation that compares the time (t) with the distance (d) would be; d = 80t.

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A graph which represents the linear function y = -2x is: graph B.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Generally speaking, the graph of any proportional relationship is characterized by a straight line with the data points passing through the origin (0, 0) because as the values on the x-axis (x-coordinate) either increases or decreases, the values on the y-axis (y-coordinate) increases or decreases simultaneously.

In this context, we can reasonably infer and logically deduce that the relationship between x-values and y-values in the graph of y = -2x is proportional as it passes through the origin (0, 0).

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By using normal distribution, it is obtained that weight of a randomly selected chicken egg is 28.39 grams

What is normal distribution?

Normal distribution is a continuous type probability distribution whose probability density function is

[tex]\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}[/tex]

where,  z = [tex]\frac{x - \mu}{\sigma}[/tex]

[tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation

In case of normal distribution

Formula for z = [tex]\frac{x - \mu}{\sigma}[/tex]

[tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation

Let the weight of the egg be x grams

Here, z = -1.41, [tex]\mu[/tex] = 58 and [tex]\sigma[/tex] = 21

[tex]-1.41 = \frac{x - 58}{21}\\[/tex]

x = -1.41 [tex]\times[/tex] 21 + 58

x = 28.39 grams

Weight of a randomly selected chicken egg is 28.39 grams

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The function rule that gives the height of a stack of cups is h(c) = 8+ 2(c)

Looking at the image,  1 paper cup has a body height of 8cm (total height = 10cm) and the height of the cups increases by 2cm for each cup added.

If you add three cups, for example, the height increases by 6cm (3 x 2cm). If you add n cups the height will increase by 2n and the total height will be 8+2n  

Number of cups, c  >>>>>  Process >>>>>  Height of stack, h(cm)

         c                                  8+ 2(c)                       h

h(c) = 8+ 2(c)

Note: It is h(c) because c is the input and h is the output

Therefore, the function rule that gives the height of a stack of cups in terms of the number of cups in a stack is h(c) = 8+ 2(c)

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Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

you multiply the denominator with the denominator and the numerator with the numerator

[tex]\frac{5}{6}x\frac{2}{5}[/tex]

[tex]\frac{5x2}{6x5}[/tex]

[tex]\frac{10}{30}[/tex]

[tex]\frac{1}{3}[/tex]

Hopes this helps please mark brainliest

The percent increase between the total without Daya's employer contribution and the total with is A. 94%.

From the information, Daya contributes a set percentage of her gross pay towards a 401k account and will have a total of $172,486.00 by retirement and her employer also contributes a set percentage, which will increase her total by $161,531.00.

Therefore, the percentage increase will be:

= Increase in amount / Original amount × 100

= 161,531/172486 × 100

= 94%

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x = -2, n(-2) = -1 - (-2) + 4 = 5

x = 0, n(0) = -1 - 0 + 4 = 3

x = 5, n(5) = -1 - 5 + 4 = -2

Answer:

sin(79°) - cos(11°) = 0

Step-by-step explanation:

Based on the rule sin(90-x) = cos(x), we can transform the expression. See the attached for more details

The amount of tax that Walmart pay annually in FUTA is  $630 million .

In the question ,

it is given that ,

the amount that an employee earns in 1 year(E) = $7000

the tax rate (r) = 6%

number of employees in Walmart = 1.5 million = 1.5 × 10⁶

So , the amount of tax paid by Walmart in Federal Unemployment Tax Act(FUTA) can be calculated using the formula

Amount = r × n × E

Substituting the values of r , n , E in the amount formula ,

we get ,

Amount = 0.06 × 1.5 × 10⁶ × 7000

= 630,000,000

= 630 million .

Therefore , The amount of tax that Walmart pay annually in FUTA is  $630 million .

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Answer:

(- 1, 3 )

Step-by-step explanation:

2x + 3y = 7 → (1)

- 2x + 4y = 14 → (2)

add (1) and (2) term by term to eliminate x

(2x - 2x) + (3y + 4y) = (7 + 14)

0 + 7y = 21

7y = 21 ( divide both sides by 7 )

y = 3

substitute y = 3 into either of the 2 equations and solve for x

substituting into (1)

2x + 3(3) = 7

2x + 9 = 7 ( subtract 9 from both sides )

2x = - 2 ( divide both sides by 2 )

x = - 1

As a check

substitute the values of x and y into the left side of both equations and if equal to the right side in both equations then the values of x and y are true.

(1) 2(- 1) + 3(3) = - 2 + 9 = 7 ← true

(2) - 2(- 1) + 4(3) = 2 + 12 = 14 ← true

then (- 1, 3 ) is the solution to the system

Answer:(- 1, 3 )

Step-by-step explanation:

Answer:

Answer: 2x-12

Step-by-step explanation:

First, you distribute and then combine like terms. :)

Answer:

Step-by-step explanation:

Step 1 : Distribute

The distributive property is a rule in mathematics that is used to help simplify equations by using brackets

-3(x+4) + 5x

-3x - 12 + 5x

Step 2 : combine similar tribes

Similar terms are terms in algebra that have the same variables or constants in algebra. Similar terms of the algebraic form above are. Similar terms are terms in algebra that have the same variables or constants in algebra.

-3x - 12 + 5x

2x - 12

Step 3 : common factor

Common factor is the same factor of two or more numbers. For example, the factors of the numbers 18 and 12 can be determined in the following way. So, the common factors of these two numbers are 2, 3, and 6.

2x - 12

2 (x-6)

Completion

2(x-6)

The cost of each bag of flour is $ 18.85 and the cost of each bag of $ 25.7 which a wholesale food supplier charges for each bag of flour and for each bag of sugar.

Given that:

The cost of each bag of flour = x dollars

The cost of each bag of sugar = y dollars

Bakery A purchases seven bags of flour and five bags of sugar for a total cost of $260.45.

Bakery B purchases five bags of flour and three bags of sugar for a total cost of $171.35.

Making equation from both the above statements. We get,

7x + 5y = 260.45 ...... (1)

5x + 3 y = 171.35 ....... (2)

Multiplying equation (1) by 5 and equation (2) by 7. We get the value,

35x + 25y = 1302.25 ....... (3)

35x + 21y = 1199.45 ........ (4)

Subtracting equation (4) from (3). We get,

4y = 102.80

=> y = $ 25.70

Putting the value of y in equation (1). We get,

7x + 25.70 x 5 = 260.45

7x = 260.45 - 128.5

7x = 131.95/7

=> x = $ 18.85

Hence, we can say that a wholesale food supplier charges 18.85 dollars for each bag of flour and 25.7 dollars for each bag of sugar.

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Answer:

Step-by-step explanation:

$603.5

Answer:39.65

Step-by-step explanation:

turn 6.5% to 0.065

610 x 0.065=39.65

Answer:

x = 0.08

Step-by-step explanation:

2x²+ 8x - 1 = 0

4x + 8x - 1 = 0

12x - 1 = 0

Add 1 to the -1 and to the 0 too

12x = 1

Divide both side

x = 0.08

Volume of the rectangular solid in cubic inches for the given measures of edges 1. 5 feet by 1½ feet by 3 inches is equal to 972 cubic inches.

As given in the question,

Given measures of edges of the rectangular solid is equal to :

1. 5 feet by 1½ feet by 3 inches

Length = 1.5 feet

Conversion 1 feet = 12 inches

1.5 feet = 1.5 × 12

            = 18 inches

Width = 1½ feet

          = 3/2 feet

          = ( 3/2 ) × 12

          = 18 inches

height = 3 inches

Volume of the rectangular solid = length × width × height

                                                     = 18 × 18 × 3

                                                     = 972 cubic inches

Therefore, volume of the rectangular solid in cubic inches for the given measures of edges 1. 5 feet by 1½ feet by 3 inches is equal to 972 cubic inches.

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Answer:

1. Y = 2x

2. 2

3.

Step-by-step explanation:

2. Slope = (y2- y1)/(x2-x1)

(8-4)/(4-2)

4/2

2

3.

The monthly bill for 20 gallons of water is $88.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

A water bottling company charges $8 per month for their water dispenser and $4 for each gallon of water delivered.

If you have g gallons of water delivered in a month.

Then, the equation to represent the  amount of your bill for that month.

8+ 4g

Now, for g=20 the amount of bill would be

= 8 +4(20)

= 8+ 80

= $88

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Answer:

no chart

Step-by-step explanation:

show chart let us see what to use

The integers in the set S:{-24, -6, 12, 24) that will make the inequality 1/3(m - 3) ≤ 1/6(m - 12) false are: S:{12, 24}​.

In order to determine which integers are true and false with respect to a solution of the given inequality, we would have to test the given integers by substituting their values into the inequality as follows;

For integers (-24, 24), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(-24 - 3) ≤ 1/6(-24 - 12)

1/3(-27) ≤ 1/6(-36)

-9 ≤ -6 (True).

For integers (-24, 24), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(24 - 3) ≤ 1/6(24 - 12)

1/3(27) ≤ 1/6(36)

9 ≤ 6 (False).

For integers (-24, -6), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(-6 - 3) ≤ 1/6(-6 - 12)

1/3(-9) ≤ 1/6(-18)

-3 ≤ -3 (True).

For integers (-6, 12), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(12 - 3) ≤ 1/6(12 - 12)

1/3(9) ≤ 1/6(0)

3 ≤ 0 (False).

For integers (12, 24), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(12 - 3) ≤ 1/6(12 - 12)

1/3(9) ≤ 1/6(0)

3 ≤ 0 (False).

1/3(m - 3) ≤ 1/6(m - 12)

1/3(24 - 3) ≤ 1/6(24 - 12)

1/3(27) ≤ 1/6(36)

9 ≤ 6 (False).

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Answer:

Alexa has 13 quarters and 15 dimes.

Step-by-step explanation:

First, we should set up a system of equations using the given information. We can use q to represent the number of quarters and d to represent the number of dimes.

Since quarters are $0.25, dimes are $0.10, and the total is $4.75 we know 0.25q + 0.1d = 4.75

The problem tells us that there are 2 more dimes than quarters, so d = q + 2

To solve for the number of quarters, we can substitute the second equation into the first equation.

0.25q + 0.1 (q + 2) = 4.75

0.25q + 0.1q + 0.2 = 4.75

0.35q = 4.55

q = 13

Then, to solve for the number of dimes, we can substitute q into the second equation.

d = q + 2

d = 13 + 2

d = 15

Answer:

  A.  -5

Step-by-step explanation:

You want the slope of a graphed line that crosses grid points (0, 2) and (1, -3).

The sign of the slope is positive if the line goes up to the right. This line goes down to the right, so the sign of its slope is negative. (Eliminates choices C and D)

The magnitude of the slope is the ratio of vertical distance to horizontal distance between two points. This line drops 5 vertical squares for each square to the right, so its slope is ...

  rise/run = -5/1 = -5

The slope is best represented by -5.

__

Additional comment

From a point on the line that is a crossing of grid lines, if the line crosses the next vertical grid line before it crosses the next horizontal grid line, the magnitude of its slope is less than 1.

Here, the line crosses several horizontal grid lines before it crosses another vertical grid line, so its slope has a magnitude greater than 1. When the choice is between -5 and -1/5, the larger magnitude number is -5.

From two points on the line, you can find the slope using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (-3 -2)/(1 -0) = -5/1 = -5 . . . . . . using points (0, 2) and (1, -3)

The probability that the representation in base-9 and the representation in base-11 are both three-digit numbers is 0.6753 which is approximately 0.7 option E.

Given,

We require the following inputs to determine the probability that both the base-9 representation and the base-11 representation are three-digit numbers:

The base-11's lowest 3-digit number is 100.

The comparable number is 121 when expressed in base 10.

888 is the biggest 3-digit base-9 number.

The corresponding number is 728 when expressed in base 10.

As a result, there are the following possibilities:

Possibilities = 728 - 121 + 1

Possibilities = 608

The total number of 3-digit base-10 numbers is

Count = 999 - 100 + 1

Count = 900

The necessary probability is:

P = 608/900

Evaluate

P = 0.6753 ≈ 0.7

Therefore,

The probability that the representation in base-9 and the representation in base-11 are both three-digit numbers is 0.6753 which is approximately 0.7 option E.

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Answer:

4 Hot dogs packages and 5 hot dog buns packages.

Step-by-step explanation:

This question seems to be regarding the LCM or the least common multiple. Least common multiple is found by figuring out the first time when both numbers, in this case 10 and 8 have the multiple. You can do this by setting up a table with the multiples of each number.

8  | 16 | 24 | 32 | 40

10 | 20| 30 | 40

We can see that the LCM is 40 so we can see that we need 4 Hot Dog packets and 5 buns packets.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

For the given triangle MNO, as per the given measurements the smallest angle among all the three angles is ∠M.

As given in the question,

In the given triangle MNO,

Measure of the sides of the triangle are as follow:

MN = 18 yd

NO = 17 yd

MO = 19 yd

Arrange them in ascending order we have,

17 < 18 < 19

NO < MN < MO

From the given measurement of the sides of the triangle , smallest side is NO.

Angle opposite to side MN = ∠O

Angle opposite to side NO = ∠M

Angle opposite to side MO = ∠N

Angle opposite to the smallest side is the smallest angle.

∠M is the smallest angle.

Therefore, for the given triangle MNO, as per the given measurements the smallest angle among all the three angles is ∠M.

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Answer:

-6

Step-by-step explanation:

to solve you need to substitute the value of x in the equation which is given as 2so if you rewrite the equation it will be

-2(2)+10

=(-2*2)+10

=-4+10

=6