Consider the rational equaton [tex]\frac{5}{x-6}\ \textgreater \ \frac{3}{x+2}[/tex]. Determine if each statement is true or false. Explain your answer.

a. [tex]-2 6[/tex] is a solution to the rational inequality.



b. The excluded values of the rational inequality are [tex]x=6[/tex] and [tex]x=-2[/tex] only

8:20 is the same as 2:5.

acc to our question-

hence,8:20 is the same as 2:5.

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Answer:

12.06

Step-by-step explanation:

-5.5+10.63+(-3.7)+10.63

1) Remove parentheses.

-5.5 + 10.63 - 3.7 + 10.63

2) Simplify -5.5 + 10.63 to 5.13.

5.13 - 3.7 + 10.63

3) Simplify 5.13 - 3.7 to 1.43.

1.43 + 10.63

4) Simplify.

12.06

The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We can determine how "spread out" the values in a data set are by looking at the mean absolute deviation.

The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation. Take the absolute value of each digit in the data set, then deduct the mean. Next, add up the absolute values. The mean absolute deviation is then calculated by dividing the aforementioned sum by the total number of values in the data set. Finally, tenths should be rounded.
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Answer: ≈ 18.91 cm

Step-by-step explanation:

r²= 114 ÷ pi/3.14 = 5700/157

r = √r²

≈ 6.025

Circumference = r × pi/3.14

≈ 18,91 cm

Answer:

2w+12

Step-by-step explanation:

twice a number: doubled or multiplied by 2

Increased: means to add

Hopes this helps please mark brainliest

Answer:

W2+12

Step-by-step explanation:

twice a number means to multiply by two

increased by 12 means to add 12

so W2+12 is the answer

Answer:

12.

Step-by-step explanation:

[tex]\text{let } x = \text{ number of people who participated in the survey}[/tex]

3 = 25% of x. We can rewrite that as an equation.
[tex]\frac3x \times 100 = 25 \text{ // Divide by 100}\\ \\\frac3x = \frac14 \text{ // Cross multiply}\\\\12 = x[/tex]

Answer:

-7

Step-by-step explanation:

To solve this system of equations, let's solve for x first. We can move 6y to the other side of the first equation by adding it to both sides. Now we know what x equals:

x = 30 + 6y.

Now, we can substitute that equation in for every x in the 2nd equation, then solve for y.

The second equation becomes:

5(30+6y) - 2y = -46

(150 + 30y) - 2y = -46

Simplify.

150 + 28y = -46

Subtract 150 from both sides

28y = -196

Divide by 28 (to get y by itself)

y = -7

Answer:

y = -7

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}x-6y = 30\\5x-2y =-46\end{cases}[/tex]

Multiply the first equation by -5:

[tex]\implies -5(x-6y)=-5(30)[/tex]

[tex]\implies -5x+30y=-150[/tex]

Add this to the second equation to eliminate the term in x:

[tex]\begin{array}{crcrcl}& 5x & - & 2y & = & \:\:-46\\+&(-5x&+&30y&=&-150)\\\cline{2-6}&&&28y&=&-196\\ \cline{2-6}\end{array}[/tex]

Solve the equation for y:

[tex]\implies 28y=-196[/tex]

[tex]\implies \dfrac{28y}{28}=\dfrac{-196}{28}[/tex]

[tex]\implies y=-7[/tex]

The perimeter (adding up all the sides) of a rectangular piece of land is 228 feet. The length of the land is 74 feet and its width is 154 feet.

The perimeter of a closed plane figure is referred to in geometry. You might have studied perimeter calculations in school. An equilateral triangle has a 27-foot perimeter if each of its nine sides is the same length. The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeter, meters, inches, and feet.

Given,

Perimeter = 228 feet

Length = x

Width = 2x + 6

Perimeter of rectangle = Length + Width

228 = x + 2x + 6

228 = 3x + 6

228 - 6 = 3x

222 = 3x

x = 74

The length of the land is 74 feet and its width is 154 feet.

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The circumference of circle with the diameter is 62.8cm

The Circumference of the circle is the measurement of the boundary of the circle.

If we open a circle and make a straight line out of it , then its length is circumference.

The circumference of a circle = 2πr

where r is radius of circle

we can write circumference in terms of diameter,

diameter of circle = 2r

so , the circumference = πd

Given in the question,

the diameter of circle = 20cm

Therefore , the circumference will be  πd

taking 3.14 value of π

= (3.14)× 20

=62.8 cm

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The option she should choose based on the given condition is Option B 2 math questions and 7 science questions.

What are linear inequalities?

When two linear expressions are compared using the inequality symbols, that is an expression of a linear inequality.

Given, Time is taken for solving single math question = 12 minutes

          Time is taken for solving single science question = 5 minutes

Let 'x' be the total number of math questions and 'y' be the total number of science questions.

Then,

The total time taken for 'x' math questions = 12x minutes

The total time taken for 'y' science questions = 5y minutes

So, as defined in the question, we get

Total time she wants to spend practicing < 60 minutes

i. e. 12x + 5y < 60 .................... (i)

Now, we check this condition for each answer choice

A) x = 3 and y = 5, substituting values in equation (i)

So, 12*3 + 5*5 < 60

or, 36+25 < 60

or, 61 < 60 (Not valid)

B) x = 2 and y = 7, substituting values in equation (i)

So, 12*2 + 5*7 < 60

or, 24+35 < 60

or, 59 < 60 (Valid)

So, Option B is valid.

Hence, the required answer of choice is Option B i.e. 2 math questions and 7 science questions.

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Answer:

-98

Step-by-step explanation:

a negative plus a positive equals a negative .

You basically minus 412 and 314 and add the negative sign

The percentage is used to denote the fraction of a quantity present.

The number of athletics students are 4. The correct answer is option A.

The percentage is defined as the portion of quantity present.

It is converted into fraction by dividing it by 100.

The percentage of students in athletics are 48%.

Total number of students in the class is 25.

The number of students in athletics is given as,

N = 48% of 25

=> N = 48 / 100 × 25

=> N = 48 / 4

=> N = 12.

Hence the number of athletics students in Mrs. Cano's class is 12.

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After solving, the test statistic value of z is -2.65.

In the given question,

Sample Mean x=264.4

Population standard deviation σ=20

sample size (n) = 25

significance level α=0.05

To test  Jean's claim that Jack's driving distance is less than 275 yards

The null and alternative hypothesis are

H(0): μ=275

H(α): μ<275

Test Statistic Z is:

Z = (x-μ)/(σ/√n)

Z = (264.4-275)/(20/√25)

Z = -10.6/(20/5)

Z = -10.6/4

Z = -2.65

Hence, the test statistic value of z is -2.65.

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The right question is:

Jack tells Jean that his average drive of a golf ball is 275 yards. Jean is skeptical, she thinks he has overstated is driving distance and asks for substantiation. So Jack takes a random sample of 25 of his drives. The mean of this sample is 264.4 yards. His driving distance is known to be normally distributed with a population standard deviation of 20 yards. Test Jean's claim that Jack's driving distance is less than 275 yards at a 0.05 significance level. Calculate the test statistic to 2 decimal places.

The solution of the system of equations is

x = -13/20 , y = 9/2 , z = 19/20

Given, a system of equations

x + 5y - 3z = 19

2x - 3y + 4z = -11

4x + y - 2z = 0

On multiplying eq (1) by 2, we get

2x + 10y - 6z = 38

On subtracting eq (1) and (2), we get

13y - 10z = 49 ... (4)

Now, On multiplying eq (2) by 2, we get

4x - 6y + 8z = -22

On subtracting eq (3) and (2), we get

7y - 10z = 22 ... (5)

Now, on subtracting eq (4) and (5), we get

6y = 27

y = 9/2

On substituting the value of y in Eq (5), we get

z = 19/20

Now, On substituting the value of y & z in Eq (1), we get

x + 5(9/2) - 3(19/20) = 19

x + 45/2 - 57/20 = 19

x + 393/20 = 19

x = -13/20

Hence, the solution of the system of equations is

x = -13/20 , y = 9/2 , z = 19/20

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Answer:

56

Step-by-step explanation:

Step-by-step explanation:

54÷3

=18

one is 17

one is 18

the other is 19

The amount owed at the end of the 6 years duration is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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Answer:

51.425

Step-by-step explanation:

Answer:

16 ft

Step-by-step explanation:

We are here given that the side lengths of the state flag are in ratio 4:7 . Let us take the ratio to be [tex] 4x:7x[/tex] .

Now we are given that the flag is 28 ft. long. So ;

[tex]\longrightarrow 7x = 28\\[/tex]

Divide both sides by 7 ,

[tex]\longrightarrow x = 4 [/tex]

Therefore the height of the flag will be ,

[tex]\longrightarrow h = 4x [/tex]

Substitute for x ,

[tex]\longrightarrow h = 4(4) ft [/tex]

Multiply,

[tex]\longrightarrow\underline{\underline{ h = 16ft}} [/tex]

And we are done!

The number of people who bought £4 tickets are 139.

Let £4 tickets be x

Let £5 tickets be y.

Therefore based on the information given, this will be:

x + y = 223 ..... i

4x + 5y = 936 ..... ii

From equation i

x = 213 - y

Put this into equation ii

4x + 5y = 936

4(213 - y) + 5y = 936

852 - 4y + 5y = 936

Collect like terms

y = 84

This implies that the number of £5 tickets is 84.

Recall that x + y = 223

x + 84 = 223

x = 223 - 84

x = 139

The number of £4 tickets is 139

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When the interest rate is 12.75%, your balance at the conclusion of the third month is $3270.06.

When provided,

P=$3168

R=0.1275/12

= 0.010625

n=3

Interest rate = 12. 75%

Using the formula

A=P(1+r)^n

we can now insert the values

A=3168(1+0.010625)^3 and

A=3270.06

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Step-by-step explanation:

Find the attached picture

Answer:

you see that Square on the corner of B use that unit box and trace it and then go to E and Trace two unit boxes at the top

The slope of the graph will be changed. The graph is still a straight line, But it becomes steep.

The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

Slope of a Line :

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.

where "m" represents a line's slope.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

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The equation that could be used to determine the number of dimes, d, in his pocket is: 0.35d + 0.75 =2.50.

Let the number of dimes be d

Let number of quarters be q

Hence,

d + q = 2.50

q = d+3

1 dimes = $0.10

1 quarters = $0.25

0.10d +0.25q = 2.50

Substitute value of  q into 0.10d +0.25q = 2.50

0.10d +0.25 (d+3) = 2.50

0.10d +0.25d +0.75 = 2.50

0.35d + 0.75 =2.50

Hence, the equation is : 0.35d + 0.75 =2.50.

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Answer: y =  4x -11

Remeber  the slope is the gradient -> m

Our equation to find the problem:

Substitude:

y-9 = 4(x-5)                       because y1= 9, x1 = 5 and m = 4

y-9 = 4x - 20                     multiply by 4 with the numbers in  the bracets

y =  4x -11                          - 9 on both sides

therfore our equation that passes through the point (5,9) and has a slope of 4 is y =  4x -11

The value of x that is a counterexample to the student's conjecture is of:

x = 0.

A counter example to a conjecture is a statement that makes the conjecture false.

In the context of this problem, the conjecture is presented as follows:

x + 5 < x².

The conjecture is only true for non-negative numbers, hence the counter example also has to be a non-negative number, meaning that these following options are removed, as they are negative numbers:

For x = 0, the conjecture is given as follows:

0 + 5 < 0²

5 < 0

Which is a false statement, hence x = 0 is the counterexample to the student's conjecture.

At x = 5, the conjecture is given as follows:

5 + 5 < 5².

10 < 25.

Which is true, however, the conjecture has already been shown to be false at x = 0.

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Answer: 8(x2 + 2x) = –3

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

Step-by-step explanation: I hope i did this right?

Answer:

A. 8(x2 + 2x + 1) = –3 + 8

B. x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

E. 8(x2 + 2x) = –3

Step-by-step explanation:

On edge 2022

We reject our null hypothesis, H₀, at a level of significance of =0.01 since the P-value is less than that threshold. There is compelling statistical data to indicate that since 1991, the proportion of drivers who love driving has decreased.

Given,

The Pew Research Center recently polled n=1048 U.S. drivers and found that 69% enjoyed driving their automobiles.

In 1991, a Gallup poll reported this percentage to be 79%. using the data from this poll, test the claim that the percentage of drivers who enjoy driving their cars has declined since 1991.

To report the large-sample z statistic and its p-value,

Null hypothesis,

H₀ : p = 0.79

Alternative hypothesis,

Ha : p < 0.79

Level of significance, α = 0.01

Under H₀

Test statistic,

[tex]Z_0= \frac{\hat p - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

Z₀ = -7.948

The alternative hypothesis(Ha) is left-tailed, so the P-value of the test is given by

P-value = P(z <-7.945)

            = 0.000     (from z-table)

Since the P-value is smaller than given level of significance, α=0.01 we reject our null hypothesis, H₀, at α=0.0.1 level Strong statistical evidence to conclude that the percentage of drivers who enjoy driving their cars has declined since 1991.

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