The set of data in the table below represents a linear function.
X
-4
-2
0
2
4
y
2
2.5
3
3.5
4
Which is an equation for this function?

Answer:

It is a polynomial, the standard form is -1.6[tex]x^{2}[/tex]-5x+7, and the degree is 2.

Step-by-step explanation:

1. Polynomials can be positive, negative, a zero, a whole number, decimals, or a fraction.

2. When writing a polynomial in standard form arrange the terms from least degree to greatest degree.

3. In this instance the degree of the polynomial is 2 because the term with the highest degree only has x to the second power.

;)

The given equation, -x + 3(1 + x) = 3(x +2), solved for x, is x = -3

From the question, we are to solve the given equation.

The given equation is

-x + 3(1 + x) = 3(x +2)

To solve this equation, we will determine the value of the variable in the equation.

The variable in the equation is x.

Thus, we will solve for x in the equation.

-x + 3(1 + x) = 3(x +2)

Clear the parentheses by applying the distributive property

-x + 3 + 3x = 3x + 6

Collect like terms

-x + 3x - 3x = 6 - 3

-x = 3

Multiply both sides of the equation by -1

-1 × -x = -1 × 3

x = -3

Hence, the value of x is -3

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Equation of the line passing through the given points is y = -1/5(x) + 29/5.

Given points:

(-1,6) and (-2,11)

slope m = 11 - 6 / -2 - (-1)

= 5/-2+1

= 5/-1

m = -1/5.

substitute m and (-1,6) in y=mx+c.

y = mx + c

6 = -1/5(-1) + c

6 = 1/5 + c

c = 6 - 1/5

= 30 - 1 / 5

c = 29/5.

y = mx + c

y = -1/5(x) + 29/5.

Therefore equation of the line passing through the given points is y = -1/5(x) + 29/5.

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The sum of the measures of the exterior angles of a triangle, one at each vertex, is 360° and it proved.

Exterior angle

The the angle that is formed with one side and the adjacent extended side of a triangle is known as exterior angle.

Given,

Here we use linear pairs to find the sum of all the angles labeled in the triangle.

And then use what you know about the interior angles of a triangle to show that the sum of the measures of the exterior angles of a triangle, one at each vertex, is 360°.

While we looking into the following figure, we can see that R and Y are the interior and exterior angles of the triangle respectively.

Therefore, here the angles Y and R form a linear pair.

So, we can written it as,

=> Y + R = 180°

Then the value of y is

=> Y = 180° - R

Therefore, when we calculate the value of the full triangle, then we get

=> (Y + R) + (Y + R) + (Y + R) = 180° + 180° + 180°

When we simplify this one,

=> 3Y + 3R = 540° --------- (1)

We already know that,  the sum of interior angles of the triangle is as follows,

=> R + R + R = 180°

By using angle sum property of a triangle,

WE can written this like the following,

=> 3R = 180° --------- (2)

Now, substituting the value from equation(2) in equation(1) we get,

Then,

=> 3Y + 180° = 540°

=> 3Y = 540° - 180°

=> 3Y = 360°

Therefore, the sum of exterior angles = 360°

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The 99% confidence interval is ( 255.157, 262.843 ).

The subset chosen from the larger set to make assumptions is known as a random sample. A range of values is a confidence interval.

According to the given question,

n = number of pregnant women who are smokers

n   =   115

μ = average pregnancy length for the sample

μ   =   259

σ = standard deviation

σ   =   16

At a 99% confidence level,

α   =   0.01

z(α/2)   =   2.576

The confidence interval is

CI    =   μ ± z(α/2).(σ/√n)

      =   259 ± (2.576)(16/√115)

      =   259 ± (2.576)(16/10.724)

      =   259 ± (2.576)(1.492)

      =   259 ± 3.843

      =   ( 259 - 3.843, 259 + 3.843)

CI   =   ( 255.157, 262.843 )

Therefore, the 99% confidence interval to estimate the length of pregnancy for women who smoke is ( 255.157, 262.843 ).

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The complete question is

Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 115 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 259 days. From a large body of research, it is known that the length of human pregnancy has a standard deviation of 16 days. The researchers assume that smoking does not affect the variability in pregnancy length.

Find the 99% confidence interval to estimate the length of pregnancy for women who smoke.

Note: The critical z-value to use is 2.576

Another advantage of using Anova is that it arranges the means so the significant differences can be located and interpreted easily.

The ANOVA test is a type of statistical test used to determine whether there is a statistically significant difference between two or more categorical groups by testing mean differences using variance.

Another important part of the ANOVA is the splitting of the independent variables into two or more groups.

The assumptions for the ANOVA test are the same as those for general parametric tests.

Advantages of ANOVA:

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The measure of each of the missing angles is m<1 = 40°, m<2 = 61°, m<3 = 119°, m<4 = 61°, m<5 = 58°, m<6 = 122°, m<7 = 58°, m<8 = 82° and m<9 = 98°

To solve this problem, we need some angle geometry knowledge:

Since the sum of angles on a straight is 180°. Thus:

m<1 + 82° + 58° = 180°

m<1 = 180° -82° - 58° = 40°

The sum of angles on a triangle is 180°:

m<2 + 58° + 61° = 180°

m<2 = 180° - 58° - 61° = 61°

m<2 + m<3 = 180° (angles on a straight )

61°+ m<3 = 180°

m<3 = 180°-61° = 119°

m<4 = m<2 = 61° (alternate angles)

m<5 + m<4 + 61 = 180° (angles on a straight )

m<5 + 61° + 61 = 180°

m<5 = 180°- 61°-61° = 58°

m<5 + m<6 =  180° (angles on a straight )

58°+ m<6 =  180°

m<6 =  180°-58° = 122°

m<7 =  58°  (alternate angles)

m<1 + m<7 +m<8 = 180° (angles on a triangle )

40+58°+m<8 = 180°

m<8 = 180°-40-58° = 82°

m<8+m<9 = 180° (angles on a straight )

82+m<9 = 180°

m<9 = 180°-82° = 98°

The measure of the missing angles m<1, m<2, m<3, m<4, m<5°, m<6, m<7, m<8 and m<9 are 40°, 61°, 119°, 61°, 58°, 122°, 58°, 82° and 98° respectively

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Answer:

im not sure if this helps but you can write it with letter like this y = mx + b

Step-by-step explanation:

Answer:

Urban

Step-by-step explanation:

4y = -3x-12 the equation of a line perpendicular to y= 4/3 ​x−1 that passes through the point (-4,-8).

A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis.

The slope of parallel lines is the same. The slopes of perpendicular lines are opposing reciprocals. To put it another way, if m=a/b, then m⊥= -b/a.

y= 4/3 x - 1

Slope = 4/3

Equation of line perpendicular to this line

y= -( 3/4) x+b

As slope is -1/m

Now as line passes through (-4,-8)

Plug it in

-8 = (-3/4)(-4) +b

-8= 3+ b

Gives b = -12

So the equation of line will be

y = (-3/4) x -12

or 4y = -3x-12

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Answer:

x = 5; m<1 = 69

Step-by-step explanation:

We know that the two angles with degrees 20x+11 and 25x-14 are vertical angles and are thus congruent or equal.  Therefore, we can set the two angles equal to each other to find x:

[tex]20x+11=25x-14\\20x+25=25x\\25=5x\\5=x[/tex]

If we plug in x into any of the two angles, we find the measure of both angles is 111.

The most probable relationship between angle 1 and the other two angles is supplementary, which means that the measure of angle 1 and any of the two angles beside it is 180.

To find m<1, represented as x, we can use the equation:

[tex]180=20(5)+11+x\\180=111+x\\69=x[/tex]

Researchers developed a blood test which is quite fair. It gives a positive reaction of 97% people who have that disease and 5% who don't have that disease.

Therefore, the Probability of Type I error if the new blood test is used is 0.025.

H₀ : "the individual does not have the disease"

(a) Probability of Type I error of rejecting  when  is true =

Probability of concluding the individual has the disease when in fact the individual does not have the disease = 0.025 because the blood test erroneously gives a positive reaction in 2.5% of the people who do not have the disease.

(b) Probability of Type II error = Probability of fail to reject  when  is true= Probability of concluding the individual does not have the disease when in fact he has the disease = 0.05 because the blood test gives a positive reaction in 97% of the people who have the disease, this implies that the test gives a negative reaction in 5% of the people who have the disease.

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Their covariance is -0.0151

Given;

The expected return on security x is 9%, whereas the standard deviation is 18%. The expected return on security y is 12%, and the standard deviation is 21%. If the correlation between the two securities is 0.4

Security X:

Expected return E(Rx) = 9% = 0.09

Standard deviation (σx) = 18% = 0.18

Security Y:

Expected return E(Ry) = 12% = 0.12

Standard deviation (σy) = 21% = 0.21

and

Corr(X,Y) = -0.4

We know that,

Corr(X,Y) = Cov(X,Y)/ σx*σy

Substituting the above-given values, we get;

-0.4 = Cov(X,Y)/ 0.18*0.21

-0.4 = Cov(X,Y)/ 0.0378

Cov(X,Y) = -0.4*0.0378

Cov(X,Y) = -0.0151

Therefore, the covariance is -0.0151.

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By using the equation of the line and the perpendicular line relationship, the equation of the perpendicular line y = (8 / 3) · x - 5

Mathematically speaking, lines are represented by equations of the form:

y = m · x + b

Where:

And two lines perpendicular to each other observe the following relationship:

m · m' = - 1

Where:

First, determine the slope of the perpendicular line by perpendicular line relationship:

m = - 3 / 8

m' = - 1 / (- 3 / 8)

m' = 8 / 3

Second, calculate the intercept of perpendicular line by the equation of the line:

b = y - m · x

b = 3 - (8 / 3) · 3

b = 3 - 8

b = - 5

Third, write the equation of the perpendicular line:

y = (8 / 3) · x - 5

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The measure of side P to the nearest degree is 79 degrees.

Given:

ΔOPQ ,

O = 700 cm,

P = 840cm

Q = 620cm.

To find:

The measure of angle P.

According to the Law of Cosines:

In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. The law of cosines states:

                                   [tex]cos A = b^{2} +c^{2} - a^{2} / 2bc[/tex]

Using Law of Cosines ΔOPQ, we get,

           cos P = o² +q²- p² / 2oq

       ⇒ cos P = (700)² + (620)² -(840)² /2×700×620

       ⇒ Cos P = 490000 + 384400 - 705600 / 868000

       ⇒ Cos P = 168800/868000

on further simplification, we get,

Cos P = 0.19447

P = Cos⁻¹ (0.19447)

P = 78.786236

P = 79.

∴ the measure of angle P is 79 degrees.

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Therefore, the measure of angle P is 79 degrees.

Answer:

k = 5

Step-by-step explanation:

substitute the values of x into 3x + k and equate with the corresponding value, that is

x = 1

3(1) + k = 8

3 + k = 8 ( subtract 3 from both sides )

k = 5

x = 3

3(3) + k = 14

9 + k = 14 ( subtract 9 from both sides )

k = 5

x = 5

3(5) + k = 20

15 + k = 20 ( subtract 15 from both sides )

k = 5

the value of k is therefore 5

Side-Side-Side can be used to prove this pair of triangles is congruent.

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent. When two or more triangles are taken that are similar to one another, their corresponding sides and angles are also similar to one another.

According to this question,

Two respective sides of triangles are equal.

One side is common between these two triangles.

Therefore, the third side of the triangles is equal as well.

As all respective sides of the triangles are equal, we can say that the triangles are congruent by Side-Side-Side.

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Answer:

A square number is always nonnegative. So a quantity squared must be nonnegative.

Answer:

X = -4

Step-by-step explanation:

25^(x+3) = 1/5

5^2^(x+3) = 5^(-2)

5^(2x+6) = 5^(-2)

2x+6 = -2

2x = -8

x = -4

Answer:

x = -7/2

or can be written,

x = -3.5

Step-by-step explanation:

25 is a power if 5 and so is 1/5. If you can write both sides as 5 to "some" power. Then the equation is just getting those two exponents equal. See image.

 Using logarithms is a nice shortcut. But then you need need a calculator. See image.

The arithmetic sequence that has the given features is presented as follows:

[tex]a_n = 2 + 3(n - 1)[/tex]

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and called common difference d.

The nth term of an arithmetic sequence is obtained by the following rule:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term of the sequence.

The sum of the first n terms is presented as follows:

[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]

The sum of the first nine terms is of 126, hence:

[tex]S_9 = 126[/tex]

[tex]\frac{9(a_1 + a_9)}{2} = 126[/tex]

[tex]4.5(a_1 + a_9) = 126[/tex]

The ninth term is written as follows:

[tex]a_9 = a_1 + 8d[/tex]

Hence:

[tex]4.5(a_1 + a_1 + 8d) = 126[/tex]

[tex]9a_1 + 36d = 126[/tex]

[tex]a_1 + 4d = 14[/tex]

The sum of the second nine terms is of 369, hence:

[tex]S_{18} = 126 + 369[/tex]

[tex]S_{18} = 495[/tex]

Then:

[tex]\frac{18(a_1 + a_{18})}{2} = 495[/tex]

[tex]a_{1} + a_{18} = 55[/tex]

The 18th term is:

[tex]a_{18} = a_1 + 17d[/tex]

Hence:

[tex]2a_1 + 17d = 55[/tex]

From the first equation, it is found that:

[tex]a_1 = 14 - 4d[/tex]

Hence the common difference is obtained as follows:

2(14 - 4d) + 17d = 55

28 - 8d + 17d = 55

9d = 27

d = 3.

Hence the first term is of:

[tex]a_1 = 14 - 4(3) = 2[/tex]

Thus the definition of the sequence is:

[tex]a_n = 2 + 3(n - 1)[/tex]

The problem asks for the definition of the arithmetic sequence.

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The following are the answers:

23. The cost for 7 lessons is $82, and the cost of 11 lessons is $122, we have;

The total cost of lessons is;  f(x) = y = 10·x + 12 and one lesson costs $22

24. The equation of population of Laredo, Texas is :

p = 92500t/17 + 123000

25. The linear equation to represent the temperature T at an elevation of x, where x is in thousands of feet is T = -(2000/3)x + (4228/3).

26. The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;

⇒ R = 4c

Given:

23. Lydia wants  to purchase guitar lessons.

7 lessons = $82

11 lessons = $122

we are asked to determine the linear equation which finds the total cost C for d lessons.

The general equation for the total cost of lessons is;

Let a represent the cost of 7 guitar lessons, and let b represent the cost of 9 guitar lessons, given that the cost increases linearly with the number of lessons, we have;

The cost increase per lesson = The slope of the linear function representing the total cost of a guitar lesson

Therefore,

slope = b-a/11-7 = b-a/4

Expressing the equation in slope and intercept form, we get:

(y-a) = b-a/4 . (x-7)

y = b-a/4 . x-7 × b-a/4 + a = b-a/4 . x + 11.a-7.b/4

y = b-a/4 . x + 11.a-7.b/4 = 1/4.((b-a).x+11.a-7.b

where a=$82 and b=$122 we ahve:

y = 1/4 . (122-82) . x+1/4 . (11×82-7×122) = 10x+12

The total cost of a lesson is:

y = 10×1+12

= 22

24. Given:

t = the number of years after 1990.

So, for 1990, t = 0. So the coordinate is (0, 123000).

For 2007, t = 17. So the coordinate is (17, 215500).

using point slope formula:

m = 215500-123000/17-0

m = 92500/17

⇒ p = 92500t/17 + 213000

25. The equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at

x = 0.

We know the slope is (y₂ - y₁)/(x₂ - x₁).

∴ Here the temperature is y and the height is x.

And the points are (6000, 76) and (12000, 49)

So, slope =(12000 - 6000)/(49 - 76).

Slope = (6000/-27).

Slope = -(2000/9).

Now we have to determine the y-intercept by putting any of the points in y = mx + b.

So, 76 = -(2000/9)×6000 + b.

76 = -(12000/9) + b.

76 = -(4000/3) + b.

b = 4000/3 + 76.

b = 4228/3.

∴ y = -(2000/3)x + (4228/3) or T = -(2000/3)x + (4228/3).

26. The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

he friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale.

On first day, they collect = $60

On second day, they collect = $88

Now,

We have to find the equation as;

⇒ R = mc + b

We need to find the value of m and b.

Since, The first point = (15, 60)

The second point = (22, 88)

Hence, Slope (m) = (88 - 60) / (22 - 15)

m = 28 / 7

m = 4

And, To find b substitute R = 60 , c = 15 and m = 4 in above equation,

⇒ R = mc + b

⇒ 60 = 4 x 15 + b

⇒ b = 0

Thus, Substitute m = 4 and b = 0 in equation (i) we get;

⇒ R = mc + b

⇒ R = 4c + 0

⇒ R = 4c

Therefore, The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;

⇒ R = 4c

Hence we get the required answers.

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The mean price of one of Henry's stamp is $34.7.

The mean number of plays is 6.33.

The mean length of phone call is 11.79.

Mean is the average of a set of numbers.

Mean = ∑(midpoint x frequency) / frequency

Midpoint = (upper boundary + lower boundary) / 2

Stamp price   Frequency   Midpoint                   (Midpoint x frequency)

20 - 26               24            (20 + 26) / 2 = 23                 552

27 - 33                39            (27 + 33) / 2 = 30                  1170

34 - 40                50            (34 + 40) / 2 = 37                   1850

41 - 47                  37            (41 + 47) / 2 = 44                    1628

Sum                     150                                                          5200

Mean = 5200 / 150 = 34.7

Number of weeks   Frequency      Midpoint               Midpoint x Frequency

1 - 3                              4                 (1 + 3) / 2 = 2                        8

4 - 6                             27               (4 + 6) / 2 = 5                      135

7 - 9                             16                (7 + 9) / 2 = 8                     128

10 - 12                            4               (10 + 12) / 2 = 11                  44

13 - 15                             1               (13 + 15) / 2 = 14                  14

Sum                               52                                                         329

Mean = 329 / 52 = 6.33

Length of call   Frequency  Midpoint                        Midpoint x frequency

1 - 4                     3                 (1 + 4) / 2 = 2.5                    7.5

5 - 8                    32              (5 + 8) / 2 = 6.5                     208

9 - 12                   30              (9 + 12) / 2 = 10.5                   315

13 - 16                  45              (13 + 16) / 2 = 14.5                   652.50

17 - 20                  17               (17 + 20) / 2 = 18.5                  314.50

Sum                     127                                                              1,497.50

Mean = 1497.50 / 127 = 11.79

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To write our number as a fraction, the order of the steps is:

First, we define our number:

x = 0.1717...

So we start with the step 3.

Now notice that there are two repeating decimals, so we need to multiply both sides by 100 (as many zeros as repeating decimals)

100*x = 10*0.1717... = 17.1717...

This is step 5.

Now we can subtract the original number in both sides so we remove the repeating decimals:

100*x - 0.1717... = 17.1717... - 0.1717...

99*x = 17

These are steps 4 and 2.

Finally, we divide both sides by 99 to get:

x = 17/99

Which is step 1.

And that is our number written as a fraction.

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Answer:

319 would be the sum

Step-by-step explanation:

The fraction of the teacups that are either indigo or teal in Cassie's Tea Shop are 1/2.

The fraction of teacups in Cassie’s Tea Shop which will either be indigo or teal can be found by adding the fractions of the tea cups which are indigo, to those which are teal.

Fraction of teacups which are indigo = 1/12

Fraction of teacups which are teal = 5/12

The fraction of teacups which are indigo or teal is:

= 1 / 12 + 5 / 12

= 6 / 12

In the simplest form, this is:

= (6 / 6) / (12 / 6)

= 1 / 2

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Answer: The answer to this problem is 1/2.

Step-by-step explanation:

The first thing you do is to add 1/12 and 5/12 together.

1/2 + 5/12 = 6/12

Then you simplify 6/12 to get the answer.

6/12 = 1/2

6/6 = 1

12/6 = 2

This is how you get the answer!

The equation of the polynomial equation with a fifth degree is P(x) = (x  + 4)³(x - 4)²

The given parameters are

The sum of multiplicities of the polynomial equation must be equal to the degree.

This means that the multiplicity of the zero -4 is 3

The equation of the polynomial is then calculated as

P(x) = (x - zero)^multiplicity

Substitute the known values in the above equation, so, we have the following representation

P(x) = (x - (-4))³ * (x - 4)²

Open the inner brackets

P(x) = (x  + 4)³ * (x - 4)²

This gives

P(x) = (x  + 4)³(x - 4)²

Hence, the equation is P(x) = (x  + 4)³(x - 4)²

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Answer:

Step-by-step explanation:

First, find the slope of 4x - 5y = 7

Simplify it down to a readable form:

5y = 4x - 7

y = (4x - 7)/5

y = 4/5 x - 7/5

slope = 4/5

slope perpendicular to 4/5 is its opposite reciprocal, which would be -5/4.

given the point (2,3), we can get the equation using point slope form for linear equations: y-k = m(x-h) for point (h,k).

now plug:

y-3 = (4/5)(x-2)

y-3 = (4/5)x - 8/5

Answer: x+x+y.y.y = 2x+y^3 ( y cube)

Step-by-step explanation:

Answer:

2x+y^3

Step-by-step explanation:

x's are added while y's are multiplied