Students on a campus of a college in California were asked "What will most likely help you to succeed in
college?" The results of this survey are tabulated below.
Reason
have a good roommate
study hard
live on campus
supportive family
always go to class
have a goal in mind
other
(a) What is the relative frequency for the reason "study hard"? (Write your answer as a fraction.)
Answer:
Frequency
583
620
187
163
558
645
439
(b) What is the relative frequency for the reason "have a goal in mind"? (Write your answer as a fraction.)
Answer:

We get that value of AC after adding AB and BC as 12 x + 20.

We are given that:

AB = 8 x + 2 and BC = 4 x + 18

We need to find AC.

For this, we will add AB and BC.

Adding AB and BC, we get that:

AB + BC = AC

Substituting the values of AB and BC in the equation which are given to us:

AC = 8 x + 2 + 4 x + 18

Combining the like terms, we get that:

AC = 12 x + 20.

Therefore, we get that value of AC after adding AB and BC as 12 x + 20.

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The student's GPA is of 2.33.

Grade Point Average (GPA) is the measure used to summaries your academic achievement at Griffith.

Given:

A worth 4​ points,

B worth 3​ points,

C worth 2​ points,

D worth 1 point

The GPA is

= 3(3) + 1(3) + 2(4) + 2(2)/9+3+4+2

=9+3+8+4/18

=2.33

Hence, The student's GPA is of 2.33.

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Answer:

10x + 7(10x)

Step-by-step explanation:

X is the unknown number

Answer: -2.25

Step-by-step explanation:-2.25 because it is closer to 0

The number 67 and 113 are not the multiples of 3,6 and 7.

Multiples are the results of multiplying one whole number from another whole number.

Now, for the given question;

As, 67 and 113 are not completely divisible by 3. They are not multiple of 3.

67 and 113 are not entirely divisible by 6. So, they are also not the multiple of 6.

Now, 67 and 113 are also not entirely divisible by 7. Thus, they are also not the multiple of 7.

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The measurement of the given angle is a 90 degree.

According to the statement

We have to find that the measurement of this angle.

So, For this purpose, we know that the

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

From the given information:

In the given figure, the measurement of the angle we have to find.

A 90-degree angle is a right angle and it is exactly half of a straight angle. It always corresponds to a quarter turn.

And from the figure it is clearly visible that the line of the angle exactly matches with the 90 degree.

Then the angle is 90 degree.

So, The measurement of the given angle is a 90 degree.

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The equation of teh second line is y = -1/3x + 5/3

The first equation is given as

y = -1/3x + 14

The slope of the above equation is

m = -1/3

Parallel lines have equal slope

So, the slope of the other line is

m = -1/3

The equation is then calculated as

y = m(x - x1) + y1

So, we have

y = -1/3(x + 7) + 4

Expand

y = -1/3x - 7/3 + 4

Evaluate

y = -1/3x + 5/3

Hence, the equation of teh second line is y = -1/3x + 5/3

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Answer:  380.5

Step-by-step explanation: you can type it into desmos graphing calculator

Expression for given numerical is: 9+ (2/x)

Given that we have an word equation that is 9 more than the quotient of 2 and  x

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

Quotient of 2 and x is [tex]\frac{2}{x}[/tex].

Nine(9) more  than 2/x is = 9+ (2/x)

So we have an expression that is:

              9+ (2/x)                          

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From the example that if a = 3 and b = 3 so the value of n = 6. It means that a ≤ n/2 and b ≤ n/2.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that all integers a, b, and n, if n = a + b, then a ≤ n/2 or b ≤ n/2. Let the value of a = 3 and b = 3 now the value of n will be:-

n = a + b

n = 3 + 3 = 6

a = 3, n = 6 then a ≤ n/2.

b = 3, n = 6 then  b ≤ n/2.

Therefore, the example that if a = 3 and b = 3 so the value of n = 6. It means that a ≤ n/2 and b ≤ n/2.

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Hi 

let call "a number" X.

then we have: 4-13X = X + 8 ..

Answer:

see explanation

Step-by-step explanation:

using the rules of exponents

[tex]\frac{1}{a^{m} }[/tex] = [tex]a^{-m}[/tex]

then

[tex]\frac{1}{32}[/tex] = [tex]\frac{1}{2^5}[/tex] = [tex]2^{-5}[/tex]

and

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , so

[tex](2^{-5}) ^{-3x}[/tex]

You didn't provide a lot of info regarding the given question, however if you are looking to solve for t:

_______________________________________________

Isolate the variable by dividing each side by factors that do not contain the variable.

Solution's Exact Form:

[tex]t=-\frac{1}{243},-\frac{243}{32}[/tex]

_______________________________________________

Hope this helps! If not, please provide further info if you can regarding this question and I'll see what else I can do to help. If this did help however, lmk! Thanks and good luck!

Answer: B. 100

C. 400

D. 300

Step-by-step explanation:

A=area of square. s=side length of square.

B. A=s^2

A=10^2

A=100

C. A=20^2

A=400

D. I=Increase in Area

I=20^2 -10^2

I=400-100

I=300

Answer:

The room should be 460.65 [tex]m^{2}[/tex].

Step-by-step explanation:

First, you have to convert the percentage to a fraction.

11% = 0.11

Then add one to that number.

0.11 + 1 = 1.11

Multiply the number with the original room size.

415 * 1.11 = 460.65 ([tex]m^{2}[/tex])

The cost of the dryer will be $450

In the given sum the combined cost of the washer and dryer is $813

let the cost of the dyer be x

the cost of the washer will be (87 - x) as it is mentioned in the question washer costs $87 less than the dryer

According to the problem :

∴  x + (x-87) = 813

=> x+x-87 = 813

=> 2x - 87 = 813

=> 2x = 813 +87

=> 2x = 900

=> x = 900/2

=> x = 450

So the cost of the dryer is $450

The cost of the washer is = x - 87 = 450 - 87 = $363

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Answer:use demos cauculator

Step-by-step explanation:

Answer:

2.4 hours or 2 hours and 24 minutes

Step-by-step explanation:

Distance = rate times time

d = rt

1200 = 500t  Divide both sides by 500

2.4 = t

It will take 2.4 hours.  We can convert the .4 into minutes by using a unit multiplier 60 minutes = 1 hour.

[tex]\frac{.4hours}{1}[/tex] x [tex]\frac{60minutes}{1hour}[/tex]  The words hours cancel out and we are left with

.4 x 60 = 24 minutes.

The number of different digits that appear when [tex]\frac{1}{110}[/tex] is written as a recurring decimal is two digits i.e 9,0.

Given the fraction [tex]\frac{1}{110}[/tex]

Recurring decimal:  

A repeating decimal, also known as a recurring decimal, is a decimal representation of a number whose digits are periodic (repeating at regular intervals) and whose infinitely repeated portion is not zero. It is possible to demonstrate that a number is rational if and only if its decimal representation repeats or terminates.

⇒[tex]\frac{1}{110}[/tex]=0.0090909090.....

Therefore,The number of different digits that appear when [tex]\frac{1}{110}[/tex] is written as a recurring decimal is two digits i.e 9,0.

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Answer:

[tex]\dfrac{4+\sqrt{3}}{4}-\dfrac{(3+4\sqrt{3})}{12}i[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{4+\sqrt{3}}{3+\sqrt{-3}}[/tex]

[tex]\textsf{Apply radical rule}:\quad \sqrt{-a}=\sqrt{a}\sqrt{-1}[/tex]

[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}\sqrt{-1}}[/tex]

[tex]\textsf{Apply imaginary number rule}:\quad \sqrt{-1}=i[/tex]

[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}i}[/tex]

Multiply by the conjugate of the denominator:

[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}i} \cdot \dfrac{3-\sqrt{3}i}{3-\sqrt{3}i}[/tex]

[tex]\implies \dfrac{(4+\sqrt{3})(3-\sqrt{3}i)}{(3+\sqrt{3}i)(3-\sqrt{3}i)}[/tex]

[tex]\implies \dfrac{12-4\sqrt{3}i+3\sqrt{3}-\sqrt{3}i\sqrt{3}}{9-3\sqrt{3}i+3\sqrt{3}i-\sqrt{3}i\sqrt{3}i}[/tex]

[tex]\implies \dfrac{12+3\sqrt{3}-4\sqrt{3}i-3i}{9-3i^2}[/tex]

[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{9-3i^2}[/tex]

[tex]\textsf{Apply imaginary number rule}:\quad i^2=-1[/tex]

[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{9-3(-1)}[/tex]

[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{12}[/tex]

Separate the fractions:

[tex]\implies \dfrac{12+3\sqrt{3}}{12}-\dfrac{(3+4\sqrt{3})i}{12}[/tex]

Simplify:

[tex]\implies \dfrac{4+\sqrt{3}}{4}-\dfrac{(3+4\sqrt{3})}{12}i[/tex]

What number is 15% of 43?

43% of 300 is what number?

12% of what number is 43?

43 is what percent of 106?

What percent of 43 is 6?

The base as used in the question refers to the main number that is a=to say the number on which other calculation are focused on.

Percent is a term used in mathematics to refer to a fraction with a denominator of one hundred. Numbers in percent is accompanied with the percent symbol which is %. Any number having that symbol means that the number is a fraction with a denominator of one hundred.

The term amount as used refers to the result gotten when some mathematical operation is being done on the base.

The calculations to the questions asked are below:

What number is 15% of 43?

= 15/100 x 43

= 6.45

43% of 300 is what number?

= 43/100 x 300

= 129

12% of what number is 43?

= 12/100 x 43

= 5.16

43 is what percent of 106

= 43/106 * 100

= 40.56%

What percent of 43 is 6

= 6/43 x 100

= 13.95%

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Points A, B, C, D, and E are collinear and in that order. The value of Ac is 18.

According to the segment addition postulate, if two points on a line segment, A and C, are given, a third point, B, will only be found on line segment AC if and only if the distances between the points satisfy the conditions of the equation AB + BC = AC.

Keep in mind that a line segment is a portion of a line that has two distinct end points. There are many points between the two end points that make up the object.

The segment addition postulate can be stated more simply by saying that if point B lies on line segment AC, then AB + BC will equal AC.

by the segment addition postulate,

AC + CE = AE so AC = AE - CE

AC = (x+50) - (x+32)

AC = x+50-x-32

AC = 18

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The best description for the elevation of Kristianstad is below sea level.

The elevation of Kristianstad, Sweden, a city founded by King Christian IV of Denmark, is -2 meters .

The best option that describes the elevation of Kristianstad is as follows:

Therefore,

At sea level the elevation will be at 0 meters.

Above sea level the elevation will be above 0 meters. That will make the elevation to be positive

Below sea level the elevation will be below 0 meters. That will make the elevation to be negative.

Therefore, the best description for the elevation of Kristianstad is below sea level.

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Answer:

6

Step-by-step explanation:

The union is defined as the set of all elements in at least one of the sets.

[tex]A \cup B=\{1,2,3,4,5,7\}[/tex]

So, there are 6 elements.

Answer:

x=6

Step-by-step explanation:

2(x+3)-8=10

use 2 to multiply the one in the bracket

(2x+6)-8=10

group like terms

2x-2=10

send all constant terms to one side of the equation

2x=10+2

2x=12

divide both side by the coefficient of x

2x/2=12/2

x=6

Answer:

[tex]\frac{350}{11} weeks[/tex]

Step-by-step explanation:

Let V be the volume of water in the lake and w be the number of weeks to empty the lake

Since it takes 14 weeks to empty the lake by water release, the empty rate = V/14

But at the same time the river is replenishing the lake at a rate of V/25 since it will take 25 weeks to fill the empty lake

               [tex]\frac{1}{14} - \frac{1}{25} = \frac{1}{w}[/tex]

              [tex]25 - 14 = \frac{350}{w}[/tex]  ==> [tex]11 = \frac{350}{w}[/tex]

                  11w = 350

                    w = [tex]\frac{350}{11 }[/tex] weeks

The solution for the given system of equations is (3,5) and (-4,12).

Given two systems of equations i.e. x+y=8 and y=[tex]x^{2}[/tex]-4 and asked to solve them.

⇒x+y=8; let's assume this equation as A

⇒ y=[tex]x^{2}[/tex]-4; let's assume this equation as B

From equation A

⇒y=8-x

From equation B

⇒y=[tex]x^{2}[/tex]-4

Equating both the values of y

⇒8-x=[tex]x^{2}[/tex]-4

⇒[tex]x^{2}[/tex]-8-4+x=0

⇒[tex]x^{2}[/tex]-12+x=0

{solving quadratic equation}

⇒[tex]x^{2}[/tex]-12+4x-3x=0 { factorizing the quadratic equation}

⇒[tex]x^{2}[/tex]+4x-3x-12=0

⇒x(x+4)-3(x+4)=0

⇒(x-3)(x+4)=0

Therefore, the value's of x=3,-4

⇒if x=3

From  equation A

⇒y=8-3=5

For x=3 ; y=5

⇒if x=-4

From  equation A

⇒y=8-(-4)=12

For x=-4 ; y=12

Therefore,The solution for the given system of equations is (3,5) and (-4,12).

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Answer:

225 students

Step-by-step explanation:

600 students, and [tex]\frac{3}{8}[/tex] of students walk to school

[tex]600 * \frac{3}{8} = 225[/tex]

225 students can be expected to walk to school

Answer:

Yes

Step-by-step explanation:

It is a function look at the numbers