1. use the equation to answer these questions. (a) what is the solution to the equation? (b) what is the extraneous solution? why? (c) in general, what is an extraneous solution?

The required function of the line would be y = 2x + 1.

A coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis.

The slope-intercept form is one rule to represent linear function rules. f(x)=mx + b is sometimes used. In any scenario, m and b describe the line's overall features. The slope is denoted by m, while the y-intercept is denoted by b.

According to the given figure,

We clearly see that the coordinates of the y-intercept would be (0, 1).

The value of the x-coordinate is 1 when y-coordinate is 3.

Here the line passes through points (0, 1) and (1, 3).

Let the required linear function would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]

x₁ = 0, y₁ = 1

x₂ = 1, y₂ = 3

⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

⇒ y - 3 = (3 - 1)/(1 - 0 )[x -1]

⇒ y - 3 = (2)[x -1]

⇒ y - 3 = 2x - 2

⇒ y = 2x - 2 + 3

⇒ y = 2x + 1

Therefore, the required function of the line would be y = 2x + 1 .

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The correct expression that is equivalent to the algebraic expression -5x - 15 + 25x - 30 is -5(-4x + 9).

We shall simplify the given algebraic expression by carrying out basic mathematics operations as follows;

Given: -5x - 15 + 25x - 30

we group like terms together

25x - 5x - 15 - 30

20x - 45

the number 5 is a common factor of 20x and 45, so we have that;

5 × 4x - 5 × 9

by factoring out 5

5(4x - 9)

also;

5(4x - 9) = -5(-4x + 9)

Therefore, -5(-4x + 9) is an equivalent expression to the algebraic expression -5x - 15 + 25x - 30

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The college sophomores analysed by Parker represent demographics.

Demographics is defined as the statistics concerned with characteristics and population of any particular group. Inspecting the question, we see the Parker travels multiple countries focussing on sophomores.

Hence, sophomores are specific population being studied thus representing demographics. They will be represented as statistical data. There are multiple examples of demographics characteristics such as age, religion, gender, ethnicity, disability status, home ownership, income, education, psychiatric diagnosis and many others.

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Answer: 4:1

Step-by-step explanation:

We know that there are 16 squares in 4 circles, so the ratio is 16:4 and we can simplify this ratio by dividing by 4 which equal 4:1

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There are 62 number of ways in which classes to these students can be assigned. It can be solved by using the fomula of combination.

What is the formula of combination?

Following is the fomula of combination:

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Here, n is the total objects available and r is the number of object need to choose from n objects.

Let six friends are A, B, C, D, E, and manoj.

Consider all 6 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_6[/tex]

Consider 5 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_5[/tex]

Consider 4 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_4[/tex]

Consider 3 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_3[/tex]

Consider 2 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_2[/tex]

Consider 1 friend is in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_1[/tex]

Consider no friend is in chemistry class all are in biology class. Hence, number of ways in which it can be is,

[tex]^6C_0[/tex]

Hence, total number of ways in which classes can be assigned to 6 students is,

[tex]^6C_6+^6C_5+^6C_4+^6C_3+^6C_2+^6C_1+^6C_0=64[/tex]

Now, the number of ways in which mnoj is alon. There are two ways. Either he will be in the chemistry class or he will be in the physics class.

Hence, subtract 2 from 64 to get the answer.

[tex]64-2=62[/tex]

Hence, there are 62 number of ways in which classes to these students can be assigned.

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Answer:

2 cm and 6 cm

Step-by-step explanation:

x = first leg

y = second leg

y = 4 + x

xy/2 = 6

y = 4 + x

xy = 12

x(4+x) = 12

x²+4x - 12 = 0

(x+6)(x-2) = 0

x = -6 (impossible because a length can’t be negative)

x = 2 cm

y = 2 + 4 = 6 cm

The steps that are used to solve the above equation by substitution include the following:

1.) X = 11 + 2y

2.) -7 ( 2y + 11) -2y = -13

3.) -14y -77- 2y = -13

4.) -16y - 77 = -13

5.) -16y = 64

6.) y= -4

7.) X = 2(-4) + 11 --> X = 3

8.) (3, -4)

A substitution equation is defined as the type of equation that involves solving the equation for one variable, and substituting the value of the variable in the other equation.

The given equation is as follows;

-7x -2y = -13

X - 2y = 11.

To solve for X the following is done;

X = 2y + 11

Substitute X = 2y + 11 into equation 1

-7 ( 2y + 11) -2y = -13

Multiple out to open the brackets;

= -14y -77- 2y = -13

= -16y - 77 = -13

= -16y = 64

= y= -4

Then substitute y = -4 into equation two as follows;

X = 2(-4) + 11

X = 3

Therefore, y = -4, while X = 3 that is ( 3,-4)

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The equation for the parabola is  y = (5/3)(x + 2)(x - 1.2)

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about mathematical equations.

Remove parentheses from each side of the equation and combine similar terms to make it simpler.

To separate the variable term on one side of the equation, use addition or subtraction.

To find the variable, use division or multiplication.

y = A [x - (-2)] (x - 1.2)

y = A(x + 2)(x - 1.2)

At the y-intercept,

-4 = A(0 + 2)(0 - 1.2)

-4 = -2.4A

A = 4/2.4 = 5/3

y = (5/3)(x + 2)(x - 1.2)

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Answer:

y-3= -11/6(x+1)

Step-by-step explanation:

y-3 = -11/6(x-(-1)

y-3 = -11/6(x+1)

Answer:

x-intercept: (7/5, 0)

y-intercept: (0, 14)

Step-by-step explanation:

The x intercept is when y is equal to 0.

1/2(0) + 5x = 7

5x = 7

x = 7/5

Put this into point form, where x is 7/5 and y is 0.

(7/5, 0)

The y intercept is when x is equal to 0.

1/2y + 5(0) = 7

1/2y = 7

y = 14

Put this into point form, where x is 0 and y is 14.

(0, 14)

Answer:0.56

Step-by-step explanation:

First multiply $3.92 from 1 pound

Next dived the answer by 7 which will give you 0.56

If the surface area of the cylinder is 8cm , then the largest possible volume of such cylinder is (16/3)√(2/3π)  cubic units  .

In the question ,

it is given that ,

the cylinder is an open top ,

given that surface area = 8cm² ,

So , the surface area is = 2πrh + πr²,

8 = 2πrh + πr²

So , h = (8 - πr²)/2πr ,

the volume of the cylinder is (V) = πr²h ,

Substituting the value of h ,

we get ,

V = (8r - πr³)/2,

to find the largest volume , we differentiate it with respect to "r" and equate to 0 ,

we get ,

(8r - πr³)/2 = 0

On Simplifying we get ,

r = √(8/3π) ,

the volume is maximum when r = √(8/3π) ,

So , Volume is = ( 8(√8/3π) - π√(8/3π)³)/2

V = 4(√(8/3π)) - (4/3)(√(8/3π))

V = (8/3)√(8/3π)

V = (16/3)√(2/3π)  cubic units .

Therefore , the maximum volume is (16/3)√(2/3π)  cubic units  .

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Answer:

Step-by-step explanation: 12

Answer:  The correct answer is b = √13 or b = −√13

Step-by-step explanation:

When factoring squared variables or numbers, use the square root

b^2 = 13

Take the square root of both sides

√b^2 = √13

b = √13 or b = −√13

Answer:

x = 10

y = 15

Step-by-step explanation:

Start with y.

The smaller triangle has a right angle and two congruent legs.

Since the legs are congruent, then the opposite angles are also congruent.

The measures of the 3 angles of the right triangle are:

3y, 3y, 90

The sum of the measures of the angles of a triangle is 180°.

3y + 3y + 90 = 180

6y + 90 = 180

6y = 90

y = 15

The larger triangle has 2 congruent sides. The opposite angles are congruent. Each of the congruent angles measures 2x + 3y. The angle above measures 50°.

2x + 3y + 2x + 3y + 50 = 180

4x + 6y + 50 = 180

4x + 6y = 130

We know from above that y = 15.

4x + 6(15) = 130

4x + 90 = 130

4x = 40

x = 10

Answer: 8 phones sold and 24 accessories

Answer:

15 weeks.........

Step-by-step explanation:

3×15=45

The foot be moving away from the wall when the top is 10 feet above the ground is 2.4077

How to solve word problems?

It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach.

The ladder against the wall is a right triangle:

x² + y² = 15²

Top slips down => dy/dt = -2 ft/s. When y = 10 ft.  dx/dt = ?

1) Take the derivative with respect to time:

2x (dx/dt) + 2y (dy/dt) = 0

2) Substitute y = 10, x =sqrt(69) z =15

2(sqrt(69)) (dx/dt) + 2(10) (-2) = 0

dx/dt = 40/2(sqrt(69))

dx/dt = 20/(sqrt(69))

= 20/8.30

=2.4077

Hence, the foot be moving away from the wall when the top is 10 feet above the ground is 2.4077.

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Answer of the following questions for given mean and standard deviation along with sample size are:

a. Null hypothesis , H₀: μ = 4.00

   Alternative hypothesis, H₁ : μ > 4.00

b. Value of test statistic is 1.647

c. Conclusion is no evidence to conclude mean wait time for customer is longer than 4.00 minutes.

As given in the question,

Wait time for customer is at most 4.00 minutes

a. Null hypothesis is given by

H₀: μ = 4.00

Mean time is not exceeding the requirement

Alternative hypothesis is given by:

H₁ : μ > 4.00

b. Value of test statistic is given by :

([tex]\bar{x}[/tex] - μ₀) ÷ ( s/√n )

Sample mean [tex]\bar{x}[/tex] = 4.14

Population mean μ₀ = 4.00

Standard deviation 's' = 0.55 minutes

Sample size 'n' = 42

Substitute the value in the formula we get,

(4.14 - 4.00) ÷ (0.55/ √42)

= 0.14 / (0.55/ 6.5)

=0.14/ 0.085

= 1.647

c. α = 1 - 98%

   = 1 - 0.98

   = 0.02

Decision value limit :

Reject H₀ ; if P value < α

Using table ,

P value = P(Z < 1.647)

              = 0.04997

⇒P value = 0.04997

0.04997 > 0.02

Here P value > α

Fail to reject Null hypothesis .

Therefore, from the given standard deviation and mean conclusion is that there is no sufficient evidence to prove that mean wait time for customers is longer than 4.00.

The complete question is:

The board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 4.00 minutes. to make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 42 randomly selected calls. the mean wait time was calculated to be 4.14 minutes. assuming the population standard deviation is 0.55 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 4.00 minutes with a 98% level of confidence?

1. State the null and alternative hypotheses for the test.

2. Compute the value of the test statistic.

3. Draw a conclusion and interpret the decision.

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Extrapolation is the process of making predictions outside the range of numbers by using the regression line.

Extrapolation refers to using the regression line to produce predictions outside of the data's range.

Thus,despite the correlation maybe having a linear shape within the range being observed, this method can be risky because it's possible that it wouldn't hold true over a wider range.

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In multiple linear regression analysis, the correlation among independent variables is termed multicollinearity i.e. option C.

Definition:

a) Homoscedasticity: Homoscedasticity, also known as homogeneity of variances, is the presumption that variations in various groups being compared are equivalent or comparable.

b) Linearity: A mathematical relationship (function) that can be graphically represented as a straight line is said to be linear. Proportionality and linearity are closely linked concepts.

c) Multicollinearity: Multiple independent variables in a model that are correlating from a statistical concept known as multicollinearity.

d) Adjusted Coefficient of Determination: The number of variables in a data collection is taken into account when calculating the adjusted coefficient of determination (also known as adjusted R-squared). Additionally, it penalizes you for any points that deviate from the model.

Hence, the required choice is Option C.

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The predicted income for a 43-year- old who left school after the 10th grade is in option (A) i.e.  $35,700.

Given that:

Educational status is a dummy variable with 0 = high school or less and 1 = some education beyond high school

Regression equation = 14.2 + 0.5 X1 + 1.7X2 + 0.1X3 + e

X1 => Age; X3→ (0 if high school or less and 1 if some education beyond high school)

X2 => (X2 * X3)→ (0 if high school or less and X1 if some education beyond high school)

Given: X1 = 43, X2 and X3 = 0

Putting these values in the below equation.

y = 14.2 + 0.5 X1 + 1.7X2 + 0.1X3 + e

y = 14.2 + (0.5 x 43) + 1.7 x 0 + .1 x 0 + e

y = 14.2 + (0.5 x 43) + 0 + 0 + e

y = 14.2 + 21.5 + e

y = 35.7 + e

The value of e can be neglected as it is a constant value.

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The number of sequence of 0s and 1s of length 19 are there that begin with a 0, end with a 0 are 65 .

In the question ,

After any particular 0, the next 0 in sequence must appear exactly 2 or 3 positions down.

In this case, we start at position 1 and end at position 19,

that is , we move a total of 18 positions down the line.

So , we must add the series of 2s and 3s to get 18.

There are several number of ways to do this:

Case 1: nine 2s - there is only 1 way to arrange them.

Case 2: two 3s and six 2s - there are ⁸C₂ ways = 28 ways

Case 3: four 3s and three 2s - there are ⁷C₄ ways = 35 ways

Case 4: six 3s - there is only 1 way to arrange them.

So , the number of sequences is = 1 + 28 + 35 + 1 = 65 .

Therefore , the total number of sequence is = 65 .

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The number of ways to paint the pots can be found using permutations and is found to be 15120 ways.

What are permutations?

An arrangement of all or a portion of a collection of items, taking into account the arrangement's order, is referred to as a permutation.

Here, we know that there are 9 different paints to choose from, so we are required to find the number of ways we can paint 5 pots without repeating any color.

This can be given by [tex]9P_{5}[/tex] ways.

[tex]=\frac{9!}{(9-5)!} \\=\frac{9!}{4!} \\=15120\space\ ways[/tex].

Therefore, the number of ways to paint the pots is 15120 ways.

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It has been suggested that 4% of all cars on the freeway are going 70 mph. If 4 cars are examined, the probability that at least 1 is going 70 miles per hour is 0.151.

A probability is a numerical representation of the likelihood or possibility that a particular event will occur. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here, it is said that 4% of all vehicles on the roadway are going more than 70 mph.

P(speed excess of 70 mph) = 0.04. Radar is used to determine the speeds of four random cars. Then, n = 4. Then, X = the number of cars going over 70 mph.

Then, the probability that at least one car is going over 70 mph

= P(x = 1, 2, 3, 4)

= 1 - P(x = 0)

= [tex]1 - 4_{C}_{0} (0.04)^{0} (1 - 0.04)^{4-0}[/tex]

= 1 - 0.849

= 0.151

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Answer:

m = -3

Step-by-step explanation:

4(4m - 3) - 1(m - 5) = -52

Distribute both expressions (don't forget that the 1 is -1, so distribute -1.)

16m - 12 - m + 5 = -52
Add like terms

15m - 7 = -52

Add 7 on both sides

15m = -45

Divide by 15 on both sides

m = -3

Answer: The answers to the first page

Step-by-step explanation:

Question 1

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

6

−48

​ >x

Divide −48 by 6 to get −8.

−8>x

Swap sides so that all variable terms are on the left-hand side. This changes the sign direction.

x<−8

Question 2

−3x+8>11

Subtract 8 from both sides.

−3x>11−8

Subtract 8 from 11 to get 3.

−3x>3

Divide both sides by −3. Since −3 is negative, the inequality direction is changed.

x<

−3

3

​Divide 3 by −3 to get −1.

x<−1

Question 3

15x+60>240

Subtract 60 from both sides.

15x>240−60

Subtract 60 from 240 to get 180.

15x>180

Divide both sides by 15. Since 15 is positive, the inequality direction remains the same.

x>

15

180

​Divide 180 by 15 to get 12.

x>12

Question 4

3rd answer choice

Question 5

First, let's calculate how many miles he has left.

80 - 14 = 66

Now, to figure out how many miles a day in 6 days, divide.

66/6 = 11

Xavier should bike 11 miles on each of the 6 remaining days.

Answer:

Step-by-step explanation:

the 2nd one