Solve the system of equations by the substitution method.
x+y=8
y=-3x

The value of x is -1 for equation -4x = -x + 3

Two or more expressions with an Equal sign is called as Equation.

The given equation is -4x = -x + 3

In the given equation minus four times of x equal to minus x plus three

x is the variable

Plus and minus are operators

-4x = -x + 3

Take the variables to one sides

Add +x on both sides

-4x+x=-x+x+3

-3x=3

Divide both sides by -3

x=-1

Hence, the value of x is -1 for equation -4x = -x + 3

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Answer:

5

Step-by-step explanation:

:)

Answer:5

Step-by-step explanation:|-10|-|-5|

                                             10-5

                                              5

Probability that S assumes a value between 280 and 320 inclusive is 0.853.

S = Σ[tex]X_{i}[/tex] where  [tex]X_{i}[/tex] has a uniform distribution on 1, 2, 3, 4, 5, with mean 3 and variance (25 – 1)/12 = 2 (result known, or calculated via E[[tex]X^{2}[/tex]] = 11, or from book of formulae, p10, with a = 1, b = 5, h = 1).

So S ~ N(300, 200) approximately.

P(280 ≤ S ≤ 320) = [tex]P(\frac{279.5-300}{\sqrt{200} } < Z < \frac{320.5-300}{\sqrt{200} })[/tex]

                           = [tex]P(-1.450 < Z < 1.450)[/tex]

                           = 0.853.

Hence, probability is 0.853.

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Answer:

Classification - Right Scalene

Perimeter - 30ft

Area - 30ft

Step-by-step explanation:

Classification - There's a right angle, and 3 unequal sides.

Perimeter - 5 + 13 + 12 = 30

Area = 5*12=60, 60/2 = 30

The composition f(4) has a value of -27

The definition of the functions is given as

f(x) = -2x^2 + 5

Rewrite the above function properly

So, we have the following representation

f(x) = -2x² + 5

To find the function f(4), we set the value of x in the equation f(x) = -2x² + 5

This is represented by

Calculate f(x), when x = 4

Substitute 4 for x in the equation f(x) = -2x² + 5

So, we have the following equation

f(4) = -2(4)² + 5

Evaluate the exponents

This gives

f(4) = -2 * 16 + 5

Evaluate the products

This gives

f(4) = -32 + 5

Evaluate the sum

f(4) = -27

Hence, the value of the function is -27

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Rectangular coordinates are x = -3.5 , y = 7[tex]\sqrt{3}[/tex]/2 by using the relation between rectangular and polar coordinates

What do you mean by rectangular coordinates?

Rectangular coordinates, commonly known as cartesian coordinates, are a way to represent graphs and show where points are located on a two-dimensional surface or in three-dimensional space.

The origin is the intersection of the two perpendicular axes that make up the Cartesian plane.

The xy plane is another name for the Cartesian plane.

Given polar coordinates are (-7,5π/3)

To change polar coordinates to recatngular coordinate use

x = rcosθ , y = rsinθ

here r = -7 and θ = 5π/3

x = -7cos5π/3 = -7 × 1/2 = -7/2 = -3.5

y = -7sin5π/3 = -7 × -[tex]\sqrt{3}[/tex]/2 = 7[tex]\sqrt{3}[/tex]/2

Therefore, rectangular coordinates are x = -3.5 , y = 7[tex]\sqrt{3}[/tex]/2

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The equation of the relationship is 2x + 4y = 45 and the graph is attached

From the question, we have the following parameters:

This means that

Price of each drink = Half $4

Evaluate

Price of each drink = $2

Represent the number of drinks with x and the number of bucket of popcorn with y

So, we have the following representation

Total amount of popcorn + Total amount of drinks = Total amount

This gives

2x + 4y = 45

Next, we sketch the graph

See attachment for the graph of the equation

The graph is represented by a straight line

This means that it is a linear equation

Also, the graph touches the axes at (0, 11.25) and (22.5, 0)

This means that the highest number of drinks and buckets are 11.25 and 22.5 respectively

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a. The annual base premium when Danielle cecils driver rating factor is 1.60 and her car is in age group is $709.

b. The annual premium is $1134.40

It should be noted that the annual premium simply refers to the amount of premium that's paid yearly by the entity. The insurance company has premium payment options for the clients.

The annual base premium will be:

= Liability premium + Collision premium + Comprehensive premium

= $383 + $240 + $86

= $709

The annual premium will be:

= Annual base premium × Driver rating factor

= $709 × 1.60

= $1134.40

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Answer:

5:6

Step-by-step explanation:

The entire class is 11/11.

Girls: 5/11 of the class.

Boys: 11/11 - 5/11 = 6/11

Ratio of girls to boys:
5/11 / 6/11 = 5/11 × 11/6 = 5/6

Answer: 5:6

The expression [tex](\frac{1}{4^{-3 } } )^{-2}[/tex] is less than 1.

The sign to change to make the expression greater than 1 is changing the sign of the exponential value which will make the new expression as

[tex](\frac{1}{4^{-3 } } )^{2}[/tex]

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).

In other words, an algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.)

Therefore, let's simplify the expression to know if it's equals to 1, greater than 1 or less than 1.

[tex](\frac{1}{4^{-3 } } )^{-2}[/tex]

using law of indices,

[tex](\frac{1}{4^{-3 } } )^{-2}[/tex] = 1 × [tex](4^{-3} )^{2}[/tex]

4⁻⁶  = 1 / 4⁶ = 1 / 4096

Hence,

1 / 4096 = 0.00024414062

Therefore,  the value is less than 1.

Let's change one sign to make the expression greater than 1.

Therefore, the expression will be [tex](\frac{1}{4^{-3 } } )^{2}[/tex]

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Answer:

The distance between two points on a 2D coordinate plane can be found using the following distance formula. d = √ (x2 - x1)2 + (y2 - y1)2. where (x 1, y 1) and (x 2, y 2) are the coordinates

Step-by-step explanation:

Answer:

two times x plus two

Step-by-step explanation:

The required net income of the companies is given as 49,000.

Given that,
Accounts receivable of 88000 and accounts payable of 39000 and have revenues of 121000 and expenses of 83000 what is the company's net income is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Total income = 88000 + 121000 = 209000
Total outflow = 39000 + 83000 = 122000
Net income = 209000 - 122000 = 49000

Thus, the required net income of the companies is given as 49,000.

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Required values are to be put in blank space,

a. 99

b. 10

c. 5

after using logarithmic properties.

The other technique to write exponents in mathematics is using logarithms. A numbers  base based logarithms is equal to other number. A logarithm performs exponentiation's exact opposite function

For example:

If 10² = 100 then log₁₀¹⁰⁰ = 2.

Some logarithmic properties used are:

All of the questions are based on simple logarithmic properties:

a. In this properties used are,

   logₐˣ + logₐⁿ = logₐˣⁿ

   log₅⁹ + log₅¹¹ = ?

   comparing with general form, we get

   log₅⁹ + log₅¹¹ = log₅⁹⁹

b. In this properties used are,

   logₐˣ - logₐⁿ = logₐ[tex]^{x/n}[/tex]

   ? - log₉⁷ = log₉[tex]^{10/7}[/tex]

   comparing with general form, we get

   log₉¹⁰ - log₉⁷ = log₉[tex]^{10/7}[/tex]

c. In this properties used are,

   logₐ⁽ˣ⁾ⁿ = n logₐˣ

   log₂[tex]^{1/25}[/tex] = log₂⁽[tex]^{1/5}[/tex]⁾² = -2 log₂⁽⁵⁾

   Comparing with general form, we get

   log₂[tex]^{1/25}[/tex] = -2log₂⁵

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The way the decrease in confidence affect the sample size​ required is: A. Decreasing the confidence level decreases the sample size needed.

Using this formula to find the decrease in sample size

n = [zs/E]^2

Where:

n = Sample size

zs = z-score

E=  margin of error

Confidence coefficient for 99% = 2.58

Hence,

2.58 × 13.8/sqrt(n) = 0.04

2.598 × 13.4 /0.04 = sqrt(n)

( 2.598× 13.8 /0.04)^2  = n

n=803,371.6

So,

Confidence coefficient for 90% = 1.64

n= (1.64× 13.8/0.04)^2

n =320,129.64

Therefore the correct option is A.

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The complete question is:

A doctor wants to estimate the mean HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 4 points with 99% confidence assuming S=13.8 based on earlier​ studies? Suppose the doctor would be content with 90 confidence. How does the decrease in confidence affect the sample size​ required?

How does the decrease in confidence affect the sample size required

A. Decreasing the confidence level decreases the sample size needed.

B. The sample size is the same for all levels of confidence.

C. Decreasing the confidence level increases the sample size needed.

The distance between the two point of the line segment is 26.07

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

Distance between two points is the length of the line segment that connects the two given points. Distance between two points in coordinate geometry can be calculated by finding the length of the line segment joining the given coordinates

d = √((x₂ – x₁)² + (y₂ – y₁)²

Substituting the values into the equation;

d = 2√170 = 26.07.

Kindly find the attached graph of the two points.

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24.

[tex](6x+3y)-\frac{z^{2}}{(2x)}[/tex]

[tex](6(3)+3(4))-\frac{(6)^{2}}{(2(3))}[/tex]

a) Solve parenthesis.

[tex](18+12)-\frac{(6)^{2}}{6}\\ \\30-\frac{(6)^{2}}{6}[/tex]

b) Solve the exponent.

[tex]30-\frac{36}{6}[/tex]

c) Divide.

[tex]30-6[/tex]

d) Subtract.

[tex]24.[/tex]

The elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.

According to the question,

We have the following information:

A = {6,7,8,11} and B = {7,6,7,9}

Now, we know that the elements of AUB means that all the elements which are there in both sets but the elements are not supposed to be repeated.

(Please that AUB can also be found using Venn diagram and questions are asked where the question has to be solved by making Venn diagram and representing all the elements in it.)

So, we have the following expression:

AUB = {6,7,8,9,11}

(Now, note that numbers however repeated in sets are not repeated here.)

Hence, the elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.

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Answer:

[tex]\frac{50}{50\\}[/tex] [tex]= \frac{65}{50}[/tex]

Now cross-multiply

Let p represent the percentage

50(50) = 50(65) ; 2500p = 3250

now divide 2500 on both sides to find p

2500p/2500 and 3250/2500

p = 1.3 ; percentage change is equal to %1.3 increase

Marissa will have $720 in 7 years when she has $48 in her saving account that earns 2% simple interest per year.

where

Calculation

From, A = P(1 + RT)

where, p = $48

R = 2%

T= 7 years

A = 48(1 + 2*7)

A = $720

Hence, Marissa will have $720 in her bank account after 7 years.

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The difference of 20 and 3 times a number x is represented by 20 - 3x , the correct option is (c) .

In the question ,

it is given that

the number is x ,

we have to find the expression , that represents the difference of 20 and 3 times a number .

three times the number x is denoted by 3x .

and the difference of 20 and three times the number x is 20 - 3x .

the expression is (20 - 3x).

Therefore , The difference of 20 and 3 times a number x is represented by 20 - 3x , the correct option is (c) 20 - 3x .

The given question is incomplete , the complete question is

Which answer choice represents the difference of 20 and 3 times a number x ?

(a) 3x + 20

(b) 20(3x)

(c) 20 – 3x

(d)  (20 · 3)x

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Answer:

1350 ml

Step-by-step explanation:

(1800 : 4) * 3

450 * 3

1350 ml

Answer:

4

Step-by-step explanation:

aint no way...this is literally 1st grade math...anyways

7(x)=28

divide both sides by 7

x=4

According to the solving the percent error = 11.764%

The percent error is the distinction between the estimated value and the real value in relation to the actual value. In those other words, the relative error is multiplied by 100 to calculate the percent error.

The difference between an approximate number and an exact value is measured in percent error. The bigger the percentage error, the further your estimated value deviates from the known value; conversely, the smaller the percentage error, more closer your approximation to the true value.

Actual value = 408

Expected value = 456

We know that the percent error :

= (expected value - actual value)/actual value.

= (456 - 408)/ 408

= 48/408

= 11.764

= 11.764%

According to the solving the percent error = 11.764%

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The value of the current assets is $44500.

Plants asset = $27000

Equity = $81000

The value of the current asset will be:

Cash $7,500

Prepaid Rent $12,000

Accounts Receivable $6,000

Merchandise Inventory $19,000,

Current asset = $44500

Plant assets will be:

Land $16,000

Building $11,000.

Plant asset = $16000 + $11000 = $27000

Stockholders equity will be:

Common stock = $30000

Retained earnings = $51000

Equity = $81000

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A solution to this inequality |y + 4| < 1 in as an interval is: A. −5 < y < –3.

An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:

Adding -1 to both sides of the inequality, we have:

|y + 4| + (-1) < 1 + (-1)

|y + 4| - 1 < 0

Evaluating the absolute value function, we have the following:

y + 4 < ±1

For the positive interval, we have:

y < -4 + 1

y < -3

For the negative interval, we have:

y < -4 - 1

y < -5

Finally, we would express the solution to this inequality as an interval as follows:

-5 < y < -3.

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Complete Question:

What is a solution to this inequality |y + 4| < 1?

A. −5 < y < –3

B. –3 < y < 5

C. –4 < y < 1

D. 1 < y < 4

60% of the fruit punch is orange juice.

In this question, we have been given 3/5 of a fruit punch is orange juice.

We need to find the percentage of the fruit punch is orange juice.

3/5 of a fruit punch is orange juice, means 3 of 5 fruit punch is orange juice.

Using the percentage formula,

3/5 * 100

= 0.6 * 100

= 60%

Therefore, 60% of the fruit punch is orange juice.

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For the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.

As given in the question,

Ratio of orange juice in the given fruit juice = 3/5

From the given ratio it indicates out of 5 fruits 3 are orange

Percentage of fruit punch is orange juice in the given juice is equal to

= ( 3 / 5 ) × 100

= ( 3 × 100 ) / 5

= 300 / 5

= 60%

60% of the fruit punch is orange juice.

Therefore,  for the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.

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Answer:

4/15

Step-by-step explanation:

[tex]\frac{3}{5}=\frac{9}{15} \\ \\ \frac{1}{3}=\frac{5}{15} \\ \\ \frac{3}{5}-\frac{1}{3}=\frac{9}{15}-\frac{5}{15}=\frac{4}{15}[/tex]