Solve using the quadratic formula.
x² - 4x + 2 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals
rounded to the nearest hundredth.
X =
or x =

After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large, the best recommendation is c. Increase the sample size.

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specific confidence level; the 95% confidence level is the most commonly used, but other levels, such as 90% or 99%, are also used.

Confidence intervals are used by statisticians to quantify uncertainty in a sample variable. A researcher, for example, may randomly select different samples from the same population and compute a confidence interval for each sample to determine how well it may represent the true value of the population variable. The resulting datasets are all unique, with some intervals containing the true population parameter and others not.

In this case, the sample size should be increased when the results are meaningless because the width of the interval is too large.

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Complete questions

After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?

a. Increase the level of confidence for the interval

b. Decrease the sample size

c. Increase the sample size

d. Reduce the population variance

We can write given quadratic expression  2x² + 12x + 8 as  2(x + 3)² - 10

And a = 2, b = 3, c = -10

We have been given an expression  2x² + 12x + 8

We need to write given expression in the form a(a + b)² + c, where a, b and c are numbers.

2x² + 12x + 8

=  2x² + 12x + 18 - 18 + 8

= (√2x + 3√2)² - 10

= (√2)² (x + 3)² - 10

= 2(x + 3)² - 10

Comparing with a(a + b)² + c, where a, b and c are numbers.

a = 2, b = 3 and c = -10

Therefore, we can write given quadratic expression  2x² + 12x + 8 as  2(x + 3)² - 10

And a = 2, b = 3, c = -10

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The domain of the function shown on the graph is given by the following option:

B. All real numbers.

The domain of a function is the set composed by all the input values that are assumed by the function.

On a graph, the meaning of each variable is given as follows:

Hence, considering the graph of the function, the domain of the function is the set that contains all the values of x of the function.

From the image given at the end of the answer, the line continues to left and to right, meaning that it has no spaces in it's definition, and thus the function is defined for all real values and the correct option is given by option b.

The problem containing the graph of the function and the options is given by the image presented at the end of the answer.

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13 72/99 is rational number.

A rational number is a number that can represented in the form p/q where p, q are integers and q ≠ 0. E.g. 3/1, 5/12.

An irrational number is the opposite of a rational number that cannot be represented in the form p/q where p, q are integers and q ≠ 0. E.g. √2

Given, number = 13 72/99

It is a mixed fraction. It can be converted into proper fraction :

(13×99 + 72)/99 = 1359/99

1359/99 is a rational number since numerator and the denominator are both integers.

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Answer:

(11x + 17) = 116°

(13x - 1) = 116°

Step-by-step explanation:

(11x + 17) and (13x - 1) are equal because they are vertically opposite angles.

11x + 17 = 13x - 1

2x = 18

x = 9

Substitute x = 9 into angle measures.

11(9) + 17 = 116°

Since both angles are equal, (13x - 1) is also 116°.

Answer:

-4

Step-by-step explanation:

Simplifying

8(x + 12) = 64

Reorder the terms:

8(12 + x) = 64      (12 * 8 + x * 8) = 64      (96 + 8x) = 64

Solving

96 + 8x = 64

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-96' to each side of the equation.

96 + -96 + 8x = 64 + -96

Combine like terms: 96 + -96 = 0

0 + 8x = 64 + -96

8x = 64 + -96

Combine like terms:

64 + -96 = -32

8x = -32

Divide each side by '8'.

x = -4

Simplifying

x = -4

Answer:

x = 19/2 (or) 9.5

Step-by-step explanation:

The equation is,

→ (8x - 12) = 64

Now the value of x will be,

→ (8x - 12) = 64

→ 8x = 64 + 12

→ x = 76/8

→ x = 19/2

→ [ x = 9.5 ]

Hence, the value of x is 9.5.

The value of f(2) when f(x) = [tex]-x^{2} +6[/tex] will be 2.

According to the question,

We have the following expression:

f(x) = [tex]-x^{2} +6[/tex]

Now, we can easily find the value of f(2) by putting the value of x in the given expression as 2.

So, we will have the following expression:

f(2) = [tex]-(2)^{2} +6[/tex]

f(2) = -4+6

(More to know: the two integers with different signs are subtracted but the sign in the final result remains that of the larger integer. So, in this case, the sign will be positive in the final result.)

f(2) = 2

Hence, the value of f(2) when f(x) = [tex]-x^{2} +6[/tex] will be 2.

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Answer:

m = -96/7

Step-by-step explanation:

5(m - 6) = 10 - 4[2(m - 7) - 5m]

5m - 30 = 10 - 4[2m - 14 - 5m]

5m - 30 = 10 - 4(-3m - 14)

5m - 30 = 10 + 12m + 56

-7m = 96

m = -96/7

The mean is 65 inches and the standard deviation is 3 inches.

Given,

In a group of women, the distribution of heights is roughly normal. Women who are shorter than 62 inches in height make up 16% of the population.

The empirical rule, less than μ - σ of 16% of the data is accurate.

P (x < μ - σ) = 16%

μ - σ = 62 → (I)

Approximately 97.5% of the women are under 71 inches in height,

P (x < μ + 2σ) = 97.5%

μ + 2σ = 71 → (II)

By solving (I) & (II);

μ - σ = 62

μ + 2σ = 71

3σ = 9

σ = 3

From (I);

μ - σ = 62

μ - 3 = 62

μ = 65

Hence, Mean = 65 inches

            Standard deviation = 3 inches

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We can convert a parabola equation from standard form to vertex form. This is in the vertex form and has the formula y = a (x - h)2 + k. The vertex, in this case, is (h, k)=(-1,-6)

Standard Form

A parabola's standard form is: y = ax2 + bx + c

Here, a, b, and c are real numbers (constants), with a = 0. x and y are variables, with (x, y) representing a parabola point.

Vertex Form

A parabola's vertex form is: y = a (x - h)2 + k

Here, a, h, and k are real numbers, with a = 0. x and y are variables, with (x, y) representing a parabola point.

There is a "whole square" in the vertex form, y = a (x - h)2 + k. To convert from standard to vertex form, we simply need to complete the square. Aside from that, we have a formula method for doing this. Let us investigate both methods.

By Finishing the Square

Consider the following standard-form parabola: y = -3x2 - 6x - 9 and complete the square to get the vertex form. First, we must ensure that the x2 coefficient is 1. If the coefficient of x2 is NOT 1, the number will be placed outside as a common factor. We'll get: y = 3x2 6x 9 = 3 (x2 + 2x + 3).

Now, the coefficient of x2 is 1. Here are the steps to convert the above expression into the vertex form.

Determine the x coefficient. 3 (x2 + 2x + 3)

Divide it in half and square the result.

(2/2)^2 = 1^2 = 1

Y= -3(x2+2x+1-1 +3)

Using the appropriate identity, factor the perfect square trinomial formed by the first three terms.

We can use x2 + 2xy + y2 = (x + y) in this case.

x2 + 2x + 1 = (x + 1) in this case.

The preceding expression becomes:

Y= -3 (x2 + 2x + 1-1 +3)

Y= -3(x+1)^2 – 1 +3

The last two numbers should be simplified, and the outside number should be distributed.

Here, -1 + 3 = 2. As a result, the preceding expression becomes:

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

Y = -3(x+1)^2 - 6

This is in the vertex form and has the formula y = a (x - h)2 + k. The vertex, in this case, is (h, k)=(-1,-6)

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The dimensions of the scale drawing is length = 168 inches and width = 126 inches

Scale drawing helps to represent surfaces on earth in a paper by either enlarging its dimension, reducing its dimension by a constant factor called the scale factor.

The conversion or scale factor is 21 inches = 4 meters

If 21 inches = 4 meters,

then 1 meter = 21/4 inches

32 meters inches = 32 x 21/4 = 168 inches

24 meters = 24 x 21/4 = 126 inches.

In conclusion, length of the scale drawing is 168 inches and width of the scale drawing iss 126 inches

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By linear search, We discovered that element 9 is the seventh in the sequence, meaning that number 9 appears on the list in the sequence 1, 3, 4, 5, 6, 8, 9, 11.

A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.

Given,

Sequence = 1, 3, 4, 5, 6, 8, 9, 11

By linear search,

The first element is compared to 9 first. If the element's value is less than nine, we compare the subsequent element with nine, and so on.

Step 1: 9 is not the same as 1.

Step 2: 9 is not the same as 3.

Step 3: 9 is not the same as 4

Step 4: 9 is not the same as 5

Step 5: 9 is not the same as 6

Step 6: 8 and 9 are not the same.

Step 7: 9 equals 9.

We discovered that element 9 is the seventh in the sequence, meaning that number 9 appears on the list.

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Control procedures are those that enable researchers to rule out specific causes for results other than the hypotheses they intend to test.

In a controlled experiment, every factor besides the independent variable is kept under control or constant to ensure that it has no impact on the dependent variable.

This experiment involves the systematic manipulation of an independent variable (the cause) and the measurement of the dependent variable (the effect). This ensures that any extraneous variables are controlled.

This experiment aids the researcher in determining whether the experimental group and control group differ from one another.

For example, during the medication effect test, the group that receives the medication is referred to as the experiment group. Those who don't get any medication are referred to as the control group.

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The number of blue cars is 375.

What is a ratio?

Ratio is a relationship between two values, represented by numbers or percentage Which expresses which of the two value are bigger. And to find that we cancel the common factor between them.

We are given that the ratio of blue cars to red cars is 3:5

Also there are 600 cars in the parking lot

Now, Let the common factor between them be 'x'

Hence the number of red cars is 3x and number of blue cars is 5x

Hence the equation can be given as

3x+5x = 600

8x = 600

Dividing both sides by 8 we get

x= 75

Hence the number of blue cars is 5(75)= 375

The number of blue cars is 375

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Answer: For every 6 chairs sold they sell 1 table

Step-by-step explanation:

After some work this is my answer

Hope this helps :)

Answer:

The equation of the line in fully simplified slope-intercept form is [tex]y=\frac{2}{3}x-6[/tex]

Step-by-step explanation:

The equation of the line in fully simplified slope-intercept form can be calculated as follows

The first step is to calculate the slope [tex]m[/tex] of the given line using the slope formula as follows

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Take two coordinates on the given line

[tex](9, 0)~\text{and}~ (0, -6)[/tex]

Substitute [tex]-6[/tex] for [tex]y_{2}[/tex], [tex]0[/tex] for [tex]x_{2}[/tex] , [tex]0[/tex] for [tex]y_{1}[/tex], [tex]9[/tex] for  [tex]x_{1}[/tex] in the slope formula

[tex]m=\frac{-6-0}{0-9}[/tex]

Simplify the numerator and the denominator at the right side of the equation

[tex]m=\frac{-6}{-9}[/tex]

Simplify the equation

[tex]m=\frac{2}{3}[/tex]

The second step is to find the slope-intercept form of the given line by the point-slope form formula as follows

[tex]y-y_{1}=m(x-x_{1})[/tex]

Take any coordinates on the given line,  take [tex](9,0)[/tex]

Substitute [tex]0[/tex] for [tex]y_{1}[/tex],  [tex]9[/tex] for [tex]x_{1}[/tex], [tex]\frac{2}{3}[/tex]  for [tex]m[/tex]

[tex]y-0=\frac{2}{3}(x-9)[/tex]

Simplify the left side of the equation

[tex]y=\frac{2}{3}(x-9)[/tex]

Expand the right side of the equation

[tex]y=\frac{2}{3}x-\frac{2\times 9}{3}[/tex]

Simplify the right side of the equation

[tex]y=\frac{2}{3}x-6[/tex]

Hence the equation of the line in fully simplified slope-intercept form is

[tex]y=\frac{2}{3}x-6[/tex]

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Answer:

6(p + 5)(p + 10)

Step-by-step explanation:

6p² + 90p + 300 ← factor out 6 from each term

= 6(p² + 15p + 50) ← factor the quadratic

consider the factors of the constant term (+ 50) which sum to give the coefficient of the p- term (+ 15)

the factors are + 5 and + 10 , then

p² + 15p + 50 = (p + 5)(p + 10)

and

6p² + 90p + 300

= 6(p + 5)(p + 10)

The price per gallon will be 2.4 at Miguel's gasoline center.

The slope of the line is represented as the rise of the line.

Here the price per gallon is equal to the slope of the given points

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

we take the two points (4, 10) and (9, 22)

Let

x₁ = 4, y₁ = 10

x₂ = 9, y₂ = 22

∵ Slope m = (y₂ - y₁)/(x₂ -x₁  )

Substitute values in the formula

m = (22 - 10) / (9 - 4)

m = (12)/(5)

m = 2.4

Thus, the price per gallon will be 2.4 at Miguel's gasoline center.

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Cost of Thaddeus camp is $170.00 and total money earned by Thaddeus in raking leaves and shovels snow is $58.35 each then total amount of money Thaddeus required to earn to pay sports camp fee is equal to $53.3.

As given in the question,

Cost of Thaddeus sports camp is equal to  $170.00

Money earned by Thaddeus while raking leaves = $58.35

Money earned by Thaddeus while shovels snow = $58.35

Total amount of money Thaddeus required to earn to pay sports camp fee

= $170 - $(58.35 + 58.35)

= $(170 - 116.7)

= $53.3

Therefore, cost of Thaddeus camp is $170.00 and total money earned by Thaddeus in raking leaves and shovels snow is $58.35 each then total amount of money Thaddeus required to earn to pay sports camp fee is equal to $53.3.

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x = 24

y = 58

Step-by-step explanation:

5x+20 = 6x-4 ( vertically opposite angles)

20+4 = 6x-5x(collect like terms)

x = 24

(y-18)+(5x+20) = 180 (sum of angles on a straight line)

(y-18)+(5×24+20) = 180

(y-18)+140 = 180

y-18 = 180-140(collect like terms)

y-18 = 40

y = 40+18

y=58

Based on the information provided, the equation that can be used to find how much money, c, each charm bracelet cost at full price is 5(c – 4) = 45.

An equation is its simplest form in algebra, refers to a mathematical statement that represents that two mathematical expressions are equal. For example, 2x + 6 = 14 is an equation, where 2x + 6 and 14 are two expressions that are separated by an equal sign. In the given case, as each bracelet cost is reduced by $4 from the full price, and the total cost of 5 identical charm bracelets is $45, the equation that can be used is given by:

5(c – 4) = 45

Solving the equation,

5(c – 4) = 45

c – 4 = 9

c = 9 + 4 = $13

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Answer:

reflection over the y-axis

Step-by-step explanation:

formula for reflection over y is (x,y) -> (x,-y)

The amount is 20 more than 70 that will be 90.

An equation is an expression that shows the relationship between two or more numbers and variables.

A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

We have been given that the statement is "20 more than 70"

WE are asked to find the amount of the given statement.

More means addition therefore,

20 more than 70 = 20 + 70

= 90

Therefore, the amount is 20 more than 70 that will be 90.

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Answer:

Yes

Step-by-step explanation:

You must use the quadratic formula

-b√b^2 -4ac/2a --> -8√-(-8)^2 -4(12)(1)/2(12)

8 +/- 4/24

(1/2, 1/6)

Yes, we can factor 12x²-8x+1=0 and the factors are x=1/6 and x= 1/2.

A factor in maths is one of two or more numbers that divides into a number without a remainder, making it a whole number.

In other words, a factor is a number that divides another number evenly.

   12x² -8x +1=0

⇒ 12x² -2x- 6x+1=0

⇒ 2x (6x-1) -1 (6x-1)=0

⇒ (2x-1) (6x-1)=0

⇒ 2x-1 = 0, 6x-1 = 0

⇒ x=1/2, x=1/6

Therefore, the factors of 12x²-8x+1=0 are 1/2, 1/6.

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The average salary is s(x) = 117400 x + 138600

The average salary in 2005 is $1899600

The average salary in 2010 is $2486600

What is average salary ?

The mean wage earned by a country's working population is known as the national average salary (or national average wage). It is computed by adding together the yearly wages of everyone who is employed and dividing the total by the number of employees.

Let s(x) = mx + b →Linear model in slope-intercept form

at s(1) = $256,000

   s(11) = $1430000

slope [tex]m = \frac{s(11) - s(1)}{11-1}[/tex]

           = (1430000-256000) / 10

           = 117400

To find b we can write

s(1) = 117400 (1) +b

256000 = 117400 + b

b = 256000 - 117400

 = 138600

s(x) = 117400 x + 138600

(b) s(15) = 117400 (15) + 138600

            = $1899600

(c) s(20) =  117400 (20) + 138600

             = $2486600

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Slope of line will be 2 and both the variable quantity charge and time are positively related that means if time will increase cost will also increases.

Slope for two points:

                                   P(x1,y1)   and Q(x2,y2)

             slope of line PQ,

                               [tex]m_{pq}[/tex] = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

while calculating the slope it may comes positive or negative,

              A positive slope means that two variables are positively related to each other.

  while,

            A negative slope means that two variables are negatively related.

from the given graph,

Part A :

              we have two points

                    A(1 , 60)

                    B(3,100)

slope of AB will be,

                               [tex]m_{AB}[/tex] = [tex]\frac{100 - 60 }{3 - 1}[/tex]

                                         = 40 / 2

                                        = 2

         slope of line in graph will be 2

Part B:

              Here slope of line is 2 which is positive, means both the variables charges and hours are positively related.

            that means, if time will increase the cost will also increases.

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Alonzo invests 76,500 in each account.

What is simple interest?

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

Here, we

Let x and y be the amounts invested at 7% and 5% respectively.

then,

x + y = 30,00  for the parts of the Principal

0.07x + 0.05y = 1680  For the rates and total Earnings

x + y = 30,00

y = 30,00 - x

y can be rewritten as 30,00 - x

Using the rates to total earnings we have

0.07x + 0.05(30,00 - x) = 1680

0.07x - 0.05x + 150 = 1680

0.02x = 1680 - 150

0.02x = 1530

x = 76,500

Hence, Alonzo invests 76,500 in each account.

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