Growing up, Joe lived in a small town. When he left for college, the population was 840.
The population has grown by 5% after Joe's first year of college. What is the new
population? Show your work.

The number of words Jack can type in a minute is 73 words.

In seven minutes, Jack types 511 words. To calculate how many words he types per minute, you divide the total number of words by the total time taken:

Words per minute = Total words / Total time

Words per minute = 511 words / 7 minutes

Words per minute = 73 words

Answer:

y= 1.6

Step-by-step explanation:

First you make x=0 and then since x=0 you plug it in the equation

11-5y=3+6(0)

11-5y=3

now you swing the 11 to the other side

-5y=3-11

-5y=-8

now you divide -8 by -5 to isolate the variable

y= 1.6

Answer: right side behavior:

              f(x) is Decreasing

             g(x) is Increasing

             h(x) is Increasing

             j(x) is Decreasing

Step-by-step explanation:

The rules for end behavior are based on 2 criteria: Sign of leading coefficient and Degree of polynomial

Sign of leading coefficient (term with greatest exponent):

Degree of polynomial (greatest exponent of polynomial:

f(x) = -2x²

as x → +∞, f(x) → +∞  Decreasing

as x → -∞, f(x) → -∞   Decreasing

g(x) = (x + 2)³

as x → +∞, f(x) → +∞  Increasing

as x → -∞, f(x) → -∞   Decreasing

[tex]h(x)=-1+x^{\frac{1}{2}}\implies h(x)=x^{\frac{1}{2}}-1[/tex]  

as x → +∞, f(x) → +∞  Increasing

as x → -∞, f(x) → -1    Decreasing to -1

[tex]j(x)=\dfrac{1}{2}(-x)^5\implies j(x)=\dfrac{1}{2}(-1)^5(x)^5\implies j(x)=-\dfrac{1}{2}x^5[/tex]

as x → +∞, f(x) → +∞  Decreasing

as x → -∞, f(x) → -∞   Increasing

Answer:

B. Angle Addition Postulate; Subtraction Property of Equality

Step-by-step explanation:

Given:

[tex]m\angle PQR=x+7\\ \\m\angle SQR=x+3\\ \\m\angle PQR+m\angle SQR=m\angle PQS=100^{\circ}[/tex]

Find: x

Solution:

1. [tex]m\angle PQR+m\angle SQR=m\angle PQS[/tex] - Angle Addition Postulate

2. [tex]x+7+x+3=100[/tex] - Substitution Property

3. [tex]2x+10=100[/tex] - Simplify

4. [tex]2x=90[/tex] - Subtraction Property of Equality

5. [tex]x=45[/tex] - Division Property of Equality

To find the probabilities in this scenario, we will use the information provided in the survey results.

To find the probabilities in this scenario, we will use the information provided in the survey results. Let's go through each question one by one:

a. The prisoner does not take classes: We can find this probability by adding the number of prisoners who do not take high school or college classes and dividing it by the total number of prisoners. In this case, the number of prisoners who do not take classes is 107 + 32 = 139. The total number of prisoners is 107 + 450 + 32 + 367 = 956. So, the probability is 139/956.

b. The prisoner is under 30 and is taking either a high school class or a college class: We can find this probability by adding the number of prisoners who are under 30 and taking high school or college classes and dividing it by the total number of prisoners. In this case, the number of prisoners who are under 30 and taking high school or college classes is 107 + 450 = 557. So, the probability is 557/956.

c. The prisoner is over 30 and is taking either a high school class or a college class: We can find this probability by adding the number of prisoners who are over 30 and taking high school or college classes and dividing it by the total number of prisoners. In this case, the number of prisoners who are over 30 and taking high school or college classes is 32 + 367 = 399. So, the probability is 399/956.

Answer:

Weighted mean grade: 81.2

Letter grade: B

Step-by-step explanation:

5 regular tests:

  (63+91+88+84+79) / 5 * 60%

= 405 / 5 * 0.6

= 48.6

Final exam:

86 * 10% = 8.6

Project:

90 * 15% = 13.5

Homework:

70 * 15% = 10.5

So her weighted mean grade is

48.6 + 8.6 + 13.5 + 10.5 = 81.2

The student's weighted mean grade is 81.2, which corresponds to a letter grade of B.

To calculate the student's weighted mean grade, we must apply the provided weights to each component. The five tests count for 60%, the final exam counts for 10%, the project counts for 15% and the homework counts for 15%.

First, find the mean of the five regular test scores: (63 + 91 + 88 + 84 + 79) / 5 = 81.

Then, calculate individual contributions by multiplying the scores by the corresponding weights:

Add these to find the student's weighted mean grade: 48.6 + 8.6 + 13.5 + 10.5 = 81.2. As her grade is above 80, her letter grade would be B.

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Answer:

A. because 3.7 ×2 is 7.4. so the full answer would be 7.4 ×10^4

Answer:

[tex](14+12)\times (8+12) > (14\times 12)+(8\times 12)[/tex]

Step-by-step explanation:

First let us evaluate the value of both the expressions.

[tex](14+12)\times (8+12) = 26\times 20 = 520[/tex]

[tex](14\times 12)+(8\times 12) = 168 + 96 = 264[/tex]

a) Hence, Larry's claim that both the expressions are equivalent is wrong.

The evaluation of the expressions have been shown above. The second expression was obtained by swapping the addition and multiplication order and that created the difference.

b) Clearly,

520 > 264

Therefore,

[tex](14+12)\times (8+12) > (14\times 12)+(8\times 12)[/tex]

[tex](14+12)\times (8+12)[/tex] is greater by the expression  [tex](14\times 12)+(8\times 12)[/tex] by a value of 520 - 264 = 256.

Final answer:

Larry is incorrect; the expressions (14 + 12) × (8 + 12) and (14 × 12) + (8 × 12) are not equivalent. The first expression equals 520, and the second equals 264, with the first being greater by 256.

Explanation:

No, Larry is not correct. The expressions (14 + 12) × (8 + 12) and (14 × 12) + (8 × 12) are not equivalent because they do not follow the same mathematical rules. The former is calculated using the distributive property of multiplication over addition, while the latter is simply a sum of two products.

To illustrate, let's compute both expressions:

Comparing the results, 520 is evident greater than 264. The difference between them is 256.

The rules of mathematics are universally valid, and incorrect application of these rules can lead to different outcomes, as shown in Larry's claim.

Answer:

{ (7+3) • 5-4} ÷2+2​

7 + 3 = 10

5 - 4 = 1

10 x 1  = 10

10 divided by 2 = 5

5 + 2 = 7

7 is your ansswer

Answer:

25

Step-by-step explanation:

For this, you would use PEMDAS.

PEMDAS stands for parenthesis, exponents, multiplication, division, addition and subtraction. That is the order that you would do those steps.

So first, you would do what is inside the parenthesis, 7+3 which is equal to 10.

So then, you would have { 10• 5-4} ÷2+2.

You next step would be to multiply 10 and 5. This would give you 50.

So your equation would be {50-4}÷2+2

The next step would be to subtract 4 from 50 which would give you 46. And the next step is to divide 46 by 2 which is 23. And the last step would be to add 2 to 23, which is 25.

So, your answer is 25.

Answer:

5/8

Step-by-step explanation:

4- 9/4 × 3/2 = 4 - (9 *3) / (4*2)

                    = 4 - 27/8

                    = 4*8/8  - 27/8

                   =  32/8 - 27/8

                    = ( 32-27) / 8

                   = 5/8

The correct value of the expression is 0.625.

To evaluate the expression 4 - 9/4 × 3/2, follow these steps:

Start with the multiplication and division from left to right:

Calculate 9 / 4, which equals 2.25.

Then multiply 2.25 by 3/2, which is 1.5. So, 2.25 × 1.5 = 3.375.

Subtract the result from 4: 4 - 3.375 = 0.625.

So, the evaluated value of the expression 4 - 9/4 × 3/2 is 0.625.

Greetings!

In division, the number being divided is considered the dividend, and the number dividing is called the divisor. The answer is the quotient.

A total that is divided into equal groups is called the dividend.

Hope this helps!

Answer:A. 10x. B. -2yz

Step-by-step explanation:

A. 4x+7x=11x

11x+(-x) = 11x-1x=10x

B. -5yz+yz=-4yz

-4yz+2yz=-2yz

The simplified expresisons are 10x and -2yz.

An expression is a mathematical statement which consists of variables, constants and mathematical operators.

The expression is

4x +7x + (-x)

To simplify means to reduce the expression into its simplest form, by performing the basic mathematical opertaion as given in the expression.

As the expressions only consist of one variable x,

The coefficients can be added.

(4+7-1) x

The like terms will be added, the sum obtained after Addition is,

10x

The expression is

–5yz + yz + 2yz

The expression has two variables, y and z.

The like terms will be added

( -5 +2+1) yz

The sum obtained after Addition is,

-2yz

Both the expressions are simplified.

Simplified expressions are easier to understand.

To know more about Expression

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Step-by-step explanation:

You must first add 20 to all inqualies, leaving u with 0 is greater than or equal to 2x which is also greater than or equal to 40.

Divde everything by 2 to get rid of the 2 from the x

0 divided by 2 is 0, 2x divded by 2 is x, 40 divided by 2 is 20.

Thats the answers

Answer:

The Value of 9 would be hundredths since it is a decimal, and the value of the 2 that is in front of the 9 would be tenths. the 'th' is always used when numbers are behind the decimal, always remember that :)

Step-by-step explanation:

I hope this helped you!

For this case we must apply distributive property term by term, to simplify the expression:

[tex](6x) (12x) + (6x) (- 9) + (27) (12x) + (27) (- 9) =[/tex]

We have to:

[tex]+ * - = -[/tex]

So:

[tex]72x ^ 2-54x + 324x-243[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]72x ^ 2 + 270x-243[/tex]

ANswer:

[tex]72x ^ 2 + 270x-243[/tex]

Answer:

y=-2x+3

Step-by-step explanation:

Answer:

The triangle with vertices with (3, 5), (-2, 6), and (1, 3) is a right triangle.

Solution:

Given that the vertices of triangle are (3, 5), (-2, 6) and (1, 3)

Let us consider A(3, 5) B(-2, 6) C(1, 3)

If the sum of square of distance between two vertices is equal to the square of distance between third vertices, then the triangle is a right angled triangle.

By above definition, we get  

[tex]BC^{2} + CA^{2} = AB^{2}[/tex] ----- eqn 1

Where AB is the distance between vertices A and B

BC is the distance between vertices B and C

CA is the distance between vertices C and D

Distance between any two vertices of a triangle is given as  

[tex]Distance =  \sqrt{\left(x_{2} -x_{1}\right )^{2} + \left(y_{2} -y_{1}\right)^{2}  }[/tex] ------- eqn 2

Step 1:

Let us find the distance between the vertices A(3,5) and B(-2,6)  

By using equation 2, we get  

[tex]x_{1} = 3, x_{2} = -2, y_{1} = 5 \text { and } y_{2} = 6[/tex]

Distance between vertices A and B =[tex]\sqrt{(-2-3)^{2}+(6-5)^{2}}[/tex]

= [tex]\sqrt{(-5)^{2} + (1)^{2}}[/tex]

= [tex]\sqrt{(-5)^{2} + (1)^{2}}[/tex]

= [tex]\sqrt{25+1}[/tex]

= [tex]\sqrt{26} units[/tex]

Step 2:

Let us find the distance between the vertices B(-2,6) and C(1,3)

By using equation 2, we get  

[tex]x_{1} = -2, x_{2} = 1, y_{1} = 6 \text { and } y_{2} = 3[/tex]

Distance between vertices B and C = [tex]\sqrt{(1-(-2))^{2}+(3-6)^{2}}[/tex]

= [tex]\sqrt{(1-(-2))^{2} + (3-6)^{2}}[/tex]

= [tex]\sqrt{3^{2}+9}[/tex]

= [tex]\sqrt{9+9}[/tex]

= [tex]\sqrt{18} \text { units }[/tex]

Step 3:

Let us find the distance between the vertices C(1,3) and D(3,5)

By using equation 2, we get  

[tex]x_{1} = 1, x_{2} = 3, y_{1} = 3 \text { and } y_{2} = 5[/tex]

Distance between the vertices C and A

= [tex]\sqrt{(3-1)^{2} + (5-3)^{2}}[/tex]

= [tex]\sqrt{2^{2} + 2^{2}}[/tex]

= [tex]\sqrt{4+4}[/tex]

= [tex]\sqrt{8} units[/tex]

Step 4:

By using equation 1,

[tex]BC^{2} + CA^{2} = AB^{2}[/tex]

[tex](\sqrt{18})^{2} + (\sqrt{8})^{2} = (\sqrt{26})^{2}[/tex]

18 + 8 = 26

26 = 26

Hence the condition is satisfied. So the given triangle with vertices with (3,5), (-2,6), and (1,3) is a right triangle.  

Answer:

21

Step-by-step explanation:

Add 5 and 2 together to get 7 and multiply it by 3

Answer:

They are the same size

Step-by-step explanation:

1 cm = .01 m

64 cm = .64 m

Answer:

x = -7

Step-by-step explanation:

The equation of the line in standard form is y=5.

This is a horizontal line, so the perpendicular line will be a vertical line of the form x=a.

Since we are given that the line should pass through the point (−7,−5) then the equation of the line is x=−7.

Answer:

1000 = 160 + 50x

1000 - 160 = 840

840 = 50x

840/50 = 16.8

he can bring up 16.8 approx., but total boxes would be 16.

Step-by-step explanation:

The equation representing the situation is 150 + 50x <= 1000, where x represents the number of boxes of books the delivery person brings up to the office.

To write an equation, we need to represent the information given in the situation. Let's assign a variable, x, to represent the number of boxes of books the delivery person brings up to the office. The weight of the delivery person is fixed at 150 lbs and the weight of each box is 50 lbs. So, the total weight carried by the elevator is 150 + 50x. The equation representing this situation is 150 + 50x ≤ 1000, since the maximum capacity of the elevator is 1000 lbs.

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Answer:

The common denominator you can calculate as the least common multiple of the both denominators - LCM(9, 3) = 9. The fraction result cannot be further simplified by cancelling.

In words - seventeen ninths minus five thirds = two ninths.

Step-by-step explanation:

Answer:

Examples are:

Angle ABC is 65 degrees and Angle DEF is 25 degrees.

Angle MNO is 50 degrees and Angle XYZ is 40 degrees.

Step-by-step explanation:

Complementary angles are any two angles that when added together equal 90 degrees.   Complementary angles do not have to be next to each other, but they must total 90 degrees.

Answer:

the first choice 2 ; -2 ; 6 :-6

Step-by-step explanation:

1) method : you can put this values 2 ; -2 ; 6 :-6 you are 0

2) method  you can solve this equation

x^4-40x^2+144=0

let : x² = t   and t ≥ 0

t² -40t +144 = 0

Δ = b²- 4ac    a= 1           b = - 40         c = 144

Δ =(-40)²- 4(1)(144= 1600 -576 = 1024=32²

t1 = (40+32)/2 = 36 = 6²

t1 = (40-32)/2 = 4 = 2²

but :  x² = t   and t ≥ 0

1)case    :    x² = 6²       x = 6 or x= -6

2() case : x² =2²          x = 2 or x= -2

Answer:

$540

Step-by-step explanation:

You need first to calculate the hour rate that is payment divided to total number of hours done.

297/22 = 13.5

Now we know that she is earning $13.5/1 hour

We just need to multiply by 22 hours and we have 13.5*22 = $540

Answer:

Step-by-step explanation:

2,080

When you divide 1060 by 48, your answer will be 22.08333... (repeated decimal) but when rounded, it will either be 22, 22.1, or 22.08 (just for rounding, you do not have to put this in.)

Hope this helped!

Nate

Answer:

22.0833333333 or 22.083 with the line above 3

Step-by-step explanation:

22.0833333333 or 22.083 with a line above the 3 because 1060 divided by 48 is 22.0833333333 repeating 3s

Mean: Average of the numbers in a set of data.

The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set. If we want to find the mean of the data set shown here, let's begin by adding the numbers.

35 + 40 + 45 + 50 + 55 + 60 + 65 = 350

Now, this will be divided by how many numbers are in the set which is 7.

350 ÷ 7 = 50.

Therefore, the mean of the set of data shown here is 29.2.

Answer: The mean of the data is Option 4. 50

Step-by-step explanation:

Answer:

Problem can not be solved

Step-by-step explanation:

* Lets explain how to solve the problem

- A total of 1000 people attended a benefit concert was held to raise

 money for a children foundation

∴ The number of students and adult is 1000

- Student  ticket cost $2 and an adult ticket cost $3

∴ The cost of the student ticket is $2

∴ The cost of the adult ticket is $3

- The organizer raises a total of $5500

∴ The total money earns fro tickets is $5500

- Assume that the number of students who attended the concert

 is x and the number of adults is y

- There are 1000 students and adults attended the concert

∴ x + y = 1000 ⇒ (1)

- The cost of student ticket is $2

∴ The money earned from students is 2 × x = 2x dollars

- The cost of adult ticket is $3

∴ The money earned from adults is 3 × y = 3y dollars

- The total money earned from students and adults is $5500

∴ 2x + 3y = 5500 ⇒ (2)

* Now lets solve the two equation by elimination method

- Multiply equation (1) by -3 to eliminate y

∴ (-3)x + (-3)y = (-3) × 1000

∴ -3x - 3y = -3000 ⇒ (3)

- Add equations (2) and (3)

∴ -x = 2500

- Multiply both sides by -1

∴ x = -2500

∵ x represents the number of the students and never the number

  of student be negative , then the problem can not be solved