Which of the following functions is NOT a linear function?
A y = 5
B
y == 5x
C y = 5(x - 2)
D y == 5x – 2 + x?

Answer:Write x² + 10x + 29 in the form (x + c)² + d, where c

Step-by-step explanation:

Answer:

(x+5)² + 4, so c is 5 and d is 4

Step-by-step explanation:

x² + 10x + 29 is a quadratic equation which can be witten as x² + bx + c, where b is 10 and c is 29.

We need to complete the square to get it in the form

(x + c)² + d

Completing the square uses the form:

[tex](x + \frac{b}{2} ) {}^{2} - ( \frac{b}{2} ) {}^{2} + c[/tex]

substitute b = 10 and c = 29 in this form:

[tex](x + \frac{10}{2}) {}^{2} - ( \frac{10}{2} ) {}^{2} + 29[/tex]

Simplify further:

[tex](x + 5) {}^{2} - 25 + 29[/tex]

[tex](x + 5) {}^{2} + 4[/tex]

c = 5, d = 4

Answer:

I think you forgot to show us the problem

Answer:

The rate is 5 dollars per student.

Step-by-step explanation:

The rate per student can be found with [tex]\frac{dollars}{student}[/tex]:

[tex]\frac{150dollars}{30student}=5\frac{dollars}{student}\\\\\frac{350dollars}{70student}=5\frac{dollars}{student}[/tex]

The rate is 5 dollars per student.

Answer: 6.655 * 10^-3

Step-by-step explanation:

0.006655 in scientific notation

6.655 × 10³

The congruency proofs that can be used for each of the triangles are;

1) SSS Congruency

2) None

3) HL Congruence

1) The SSS congruency postulate states that If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Now, we see that we are shown 2 corresponding sides that are congruent. However, the third side is automatically congruent using the reflexive property of congruence.

Thus, we conclude that the congruency can be proved using SSS Congruency postulate.

2) In this one, we are given 2 congruent sides and the included angle and so it is SAS Congruency and neither SSS nor HL congruency can be used.

3) The HL congruence Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

In this case, we see that the hypotenuse is congruent to itself by reflexive property of congruence while the one leg is also congruent and so we can use HL Congruence Theorem

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Answer:

3.  $42,540

4.  $53,480

Step-by-step explanation:

Income

Gross income = $61,840

Allowances

Head of household (2009) = $8,350

Single with 2 dependents = $3,650 + $3,650 · (2) = $10,950

Total allowances = $8,350 + $10,950 = $19,300

Taxable Income

Gross income - total allowances = $61,840 - $19,300 = $42,540

Income

Gross income = $79,480

Allowances

Married filing jointly (2009) = $11,400

Married with 2 dependents = $7,300 + $3,650 · (2) = $14,600

Total allowances = $11,400+ $14,600 = $26,000

Taxable Income

Gross income - total allowances = $79,480 - $26,000 = $53,480

Answer:

slope = 1/4

Step-by-step explanation:

at a cafeteria the price of a salad depend on it weight in ounces. the graph shows the relationship what is the slope of the line

Find two places where the line neatly intersects the graph. For example, we will use the points: (0 , 0) and (4 , 1)

slope = change in y / change in x

[tex]slope = \frac{(y_{1} -y_{2} )}{(x_{1} -x_{2} )}[/tex]

slope = (0 - 1) / (0 - 4)

slope = -1 / -4

slope = 1/4

Answer: 1/4

Step-by-step explanation:

I just did it

The variance is 206 and standard deviation is 14.353.

In the given question, we have to find the standard deviation and variance from the following frequency distribution X.

Days:                          1         2         3         4         5         6         7

Commodity Price:    240    260    270    245     255     286    264

x                                (x-X)                             (x-X)^2

240                    (240-260) = -20                   400

260                    (260-260) = 0                        0

270                    (270-260) = 10                      100

245                    (245-260) = -15                     225

255                    (255-260) = -5                      25

286                    (286-260) = 26                     676

264                    (264-260) = 4                        16

Total = 1820                                                    Σ(x-X)^2 = 1442

X = Total of x/total number

X = 1820/7

X = 260

Variance = Σ(x-X)^2/n

Variance = 1442/7

Variance = 206

Standard Deviation = √(Variance)

Standard Deviation = √206

Standard Deviation = 14.353

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The total distance is an illustration of a linear function.

(1) Why the relationship is a function

The relationship is a function because all input values of h, have exactly one corresponding output value of d

(2) The function type

The function is a discrete function, because the number of hours is an integer, and it cannot take decimal values (in this case)

(3) The domain for a drive of 8 hours

The domain is the set of time the girls drive.

So, the domain is: [0,8]

(4) The range

The function is given as:

d= 55h + 10

When h = 0,

d = 55(0) + 10 = 10

When h = 8,

d =  55(8) + 10 = 450

So, the range is: [10,450]

(5) The graph

Sorry

(6) The slope

A linear function is represented as:

y = mx + c

Where:

m represents the slope.

So, by comparison:

Slope = 55

The slope in this case represents the distance travelled per hour

(7) The y-intercept

In (6) above, c represents the y-intercept.

So, by comparison:

c = 10

The y-intercept in this case represents the initial distance

(a) The 95% confidence interval for the mean of the compressive strength is 4885.1 < μ < 5054.9.

(b) The 95% confidence interval for the mean of compressive strength is 4975.2 < μ < 5012.4.

a) We have to find the 95% confidence interval for the mean of the compressive strength.

we are given

x = sample mean = 4970

n = sample size = 9

σ = population standard deviation = 130

The 95% confidence interval for population mean is

x - Z​​​​​​a/2*(σ/√n) < μ < x + Z​​​​​​a/2*(σ/√n)

For a = 0.05 Z​​​​​​a/2 = Z​​​​​​0.025 = 1.96

4970 - 1.96*(130/√9) < μ < 4970 + 1.96*(130/√9)

4885.1 < μ < 5054.9

Hence, the 95% confidence interval for the mean of the compressive strength is 4885.1 < μ < 5054.9.

b) We have to find the 95% confidence interval for the mean of the compressive strength.

Since the population's standard deviation is unknown in this instance, the population mean's t confidence interval is used.

From the data n = 9

X = sample mean = 4993.8

s = sample standard deviation = 24.2

For a= 0.05 and degree of freedom = n -1 = 8

t​​​​​​a/2 , n-1 = t​​​​​​0.025,8 = 2.306

x - t​​​​​​a/2*(s/√n) < μ < x + t​​​​​​a/2*(s/√n)

4993.8 - 2.306*(24.2/√9) < μ < 4993.8 + 2.306*(24.2/√9)

4975.2 < μ < 5012.4

Hence, the 95% confidence interval for the mean of compressive strength is 4975.2 < μ < 5012.4.

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The complete question is:

A new cure has been developed for a certain type of cement that should change its mean compressive strength.

a) It is known that the standard deviation of the compressive strength is 130 kg/cm^2 and that we may assume that it follows a normal distribution. 9 chunks of cement have been tested and the observed sample mean is X = 4970. Find the 95% confidence interval for the mean of the compressive strength.

b) Now, assume that we do not know the standard deviation of the normal distribution. 9 chunks of cement have been tested, and the measurements are 5001, 4945, 5008, 5018, 4991, 4990, 4968, 5020, 5003. Find the 95% confidence interval for the mean of the compressive strength.

Answer:

Step-by-step explanation:

To convert a value to a z-score, you need to subtract the mean and divide by the standard deviation. Here is how to convert each value to a z-score:

a. x = 23: (23 - 25) / 3 = -0.67

b. x = 33: (33 - 25) / 3 = 2.33

c. x = 19: (19 - 25) / 3 = -1.67

d. x = 45: (45 - 25) / 3 = 6.67

Therefore, the z-scores are -0.67, 2.33, -1.67, and 6.67 for values a, b, c, and d respectively.

Answer: f(0)=-5

Step-by-step explanation:

f(0) means that x = 0

sub in 0 into the equation

f(0)=-0-5

f(0)=-5

Answer:

f(0) = -5

Step-by-step explanation:

Given f(x) = -x - 5

In order to find f(0), you need to replace x with 0

so f(0) = -(0) - 5

f(0) = -5

25x¹⁰/y⁶ is equivalent to expression to (5x⁻⁵ y³)⁻².

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given

Expression

(5x⁻⁵ y³)⁻²

25x¹⁰ y⁻⁶

25x¹⁰/y⁶

25x¹⁰/y⁶ is equivalent to expression to (5x⁻⁵ y³)⁻².

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With the help of Geometry We would make Australia 200 miles more wider.

What is geometry?

Geometry is a branch of mathematics that is concerned with the study of shapes, sizes, and relative positions of figures and the properties of space. It is one of the oldest branches of mathematics that has been around for centuries and is still relevant today. Geometry is used to explain many aspects of our lives, from the size of buildings and bridges to the path of a baseball in flight. It is a powerful tool for problem solving and understanding the world around us. Geometry is based on axioms, or accepted truths, that are used as the basis for forming logical proofs. These proofs are used to develop theorems and formulas which help us to understand and explain our world.

We would make Australia 200 miles more wider too or just give 200 miles long US to some other country to make their sizes equal.

Hence, we would make Australia 200 miles more wider

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The perimeter of the figure with the varied side length is 52 cm

From the question, we have the following parameters that can be used in our computation:

Shape = composite figure

Smaller shapes = squares and rectangles

Side lengths = varied values

The perimeter of the figure is calculated as

Perimeter = Sum of the sides lengths of the shape

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

Perimeter  = 12 + 7 + 3 + 4 + 3 + 7 + 6 + 10

Evaluate the sum in the above equation

Perimeter  = 52 cm

Hence, the perimeter is 52 cm

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The probability that one has a dog allergy when tested positive will be 0.3311.

What do you mean by probability?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

According to the given question,

We have the given information:

1% of the population has an allergy to dogs.

This will be:

= 1% × 100000

= 1000

So, 1000 people have an allergy to dogs.

The number of people who doesn't have allergy to dogs will be:

= 100000 - 1000

= 99000

Those that have allergies = 2% × 1000 = 20

So, the probability that one has dog allergy will be:

= P(has allergy and test positive)

= (0.01 × 0.98) + (0.098 + 0.0198)

= 0.0098/0.0296

= 0.3311

Therefore, the probability is 0.3311.

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Answer:

Divide by 2

Step-by-step explanation:

Answer:

x > 2

Step-by-step explanation:

8x - 5 > 13 - x             Add x to both sides

8x + x - 5 > 13 - x + x

9x - 5 > 13                   Add 5 to both sides

9x - 5 + 5 > 13 + 5

9x > 18  Divide both sides by 9

[tex]\frac{9x}{9}[/tex] > [tex]\frac{18}{9}[/tex]

x > 2

Answer:

x>2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

324 Miles

If you divide 189 by 7, you get 27. If you then multiply 27(miles per hour) by 12(hours) you get 324.

Answer:

y = total cost

x = mile

Step-by-step explanation:

Answer: y = 5 + 0.75x

Step-by-step explanation:

Answer:

cos x

Step-by-step explanation:

d( 2 + sin x )/DX

= d( 2 )/dx + d( sin x )/dx

= 0 + cos x

= cos x

Note : -

Answer:

A)   The graph of function g(x) is V-shaped and has the following properties:

B)  Translation of 2 units down.

Therefore:

Step-by-step explanation:

The absolute value parent function, f(x) = |x|, is defined as:

[tex]f(x)=\begin{cases}x \; &\text{if}\;x > 0\\0 \; &\text{if} \; x=0\\-x\; &\text{if}\;x < 0\end{cases}[/tex]

Therefore:

Its graph is V-shaped and has the following properties:

Given absolute value function:

[tex]g(x)=|x+3|[/tex]

The graph of function g(x) is the parent function f(x) translated 3 units to the left.

As the graph has only been translated horizontally, the domain and range are the same as the parent function.

Therefore, the graph of function g(x) has:

Given absolute value functions:

[tex]f(x)=|x|[/tex]

[tex]h(x)=|x|-2[/tex]

The graph of function h(x) is the parent function f(x) translated 2 units down.

As the graph has been translated vertically, the domain is the same as the parent function, but the vertex and range are different.

We got the mean value 4.167 and standard deviation 19.56.

In statistics, a mean value is the average value of all the available data. And it can be determined by adding all the data by dividing the amount of data.

A standard deviation is an estimation that implies how far each available data apart from the mean value.

we are given, 4% of the population has a genetic mutation

Total people in the group =600

Now, total number of people who have genetic mutation = (4/100) ×600

                                                                                              = 24

the number of randomly selected people =100= X

Mean = Number of selected people/ people who have mutation

  Mean = X/n = 100/24 = 4.167

the standard deviation = √∑(X-mean) ²/n

                                       = √∑(selected people - mean) ²/ mutation number

                                    =√(100-4.167) ²/24

            standard deviation = 19.56

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By using the given scale, we will see that the real distance is 240km

We know that the scale of the map is 1 cm to 12km, so we just need to take the distance in centimeters on the map, and multiply that number by 12 km.

We know that on the map, the distance between Cardiff and London is 20cm, then the real distance is 12km times that, so we will get:

real distance = 20*12km = 240km

The real distance between Cardiff and London is  240 kilometers.

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Answer:

The graph will be a V shape

Step-by-step explanation:

The graph will be a V shape because of the absolute value

The 99% confidence interval for the population mean cost is 38.37 to 269.97.

What is confidence interval?

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

Given that the standard hotel rooms in the Philadelphia area has a mean nightly cost of $154.17.

The standard deviation of the price of all hotel rooms in Philadelphia is $38.60.

According to the empirical rule,

P(μ - 3σ ≤ X ≤ μ - 3σ) = 99%.

Here μ = 154.17 and σ = 38.60.

Calculating the confidence interval:

154.17 -  (3 × 38.60) ≤ X ≤ 154.17 + (3 × 38.60)

38.37 ≤ X ≤ 269.97

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Answer:

9 ( x + 9 )

Step-by-step explanation:

81 = 9 × 9

9x = 9 × x

9x + 81 = 9 ( x + 9 )

The genre which had the same number of votes in each study is: B. horror.

In Mathematics, there are different types of graph and these include the following:

A pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors.

From the bar chart, the number of votes for horror movie is equal to 40 votes. Next, we would calculate the number of votes for horror movie in the pie chart as follows;

Number of votes = 16/100 × 250

Number of votes = 0.16 × 250

Number of votes = 40 votes.

In conclusion, we can logically deduce that horror is a movie genre that has the same number of votes in each independent study.

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95% confident the population mean is between (9.1,9.9).

We are given the following data set:

9.3, 9.7, 9.2, 9.7

What is Standard Deviation?

Standard Deviation [tex]$=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}}$[/tex]

where[tex]$x_i$[/tex] are data points, [tex]$\bar{x}$[/tex]is the mean and [tex]$\mathrm{n}$[/tex] is the number of observations.

Mean [tex]$=\frac{\text { Sum of all observations }}{\text { Total number of observation }}$[/tex]

Mean [tex]$=\frac{37.9}{4}=9.475$[/tex]

Sum of squares of differences [tex]$=0.2075$[/tex]

S.D[tex]$=\sqrt{\frac{0.2075}{3}}=0.262$[/tex]

[tex]$95 \%$[/tex] Confidence interval:

[tex]$\bar{x} \pm t_{\text {critical }} \frac{s}{\sqrt{n}}$[/tex]

Putting the values, we get,

[tex]$t_{\text {critical }}$[/tex] at degree of freedom 3 and[tex]$\alpha_{0.05}=\pm 3.182$[/tex]

[tex]$9.475 \pm 3.182\left(\frac{0.262}{\sqrt{4}}\right)=9.475 \pm 0.416842=(9.058158,9.891842) \approx(9.1,9.9)$[/tex]

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