COMMON CORE REVIEW
1. Find the percent of change from 32 feet to 79 feet. Round to the nearest tenth, if necessary. Then state whether the percent of change is percent of increase or percent of decrease.
2. Factor this expression: 27+108n
3. Factor this expression: 56x + 16

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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 expected change in the dependent variable for a change in one of the explanatory variables in a nonlinear model is given by Delta Y = f(x_1 + Delta x_1, x_2, ...., x_k) - f(x_1, x_2, .... x_k).

Any attribute that can have different values, such as height, age, temperature, or test results, is referred to as a variable in research.

To assess the causality of relationships, researchers frequently modify or measure independent and dependent variables in studies.

The cause is the independent variable. Its value is unaffected by the other study variables.

The effect is the dependent variable. Changes in the independent variable affect its value.

A dependent variable is one that is altered as a result of the modification of an independent variable. Your independent variable "depends" on the outcome you're interested in measuring.

Dependent variables are also referred to as:

.response elements (they respond to a change in another variable)

.outcome factors (they represent the outcome you want to measure)

.Left-side parameters

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The expected change in the dependent variable for a change in one of the explanatory variables in a nonlinear model is given by Delta Y = f(x_1 + Delta x_1, x_2, ...., x_k) - f(x_1, x_2, .... x_k).

Any attribute that can have different values, such as height, age, temperature, or test results, is referred to as a variable in research.

To assess the causality of relationships, researchers frequently modify or measure independent and dependent variables in studies.

The cause is the independent variable. Its value is unaffected by the other study variables.

Effect is the dependent variable. Changes in the independent variable affect its value.

A dependent variable is one that is altered as a result of the modification of an independent variable. Your independent variable "depends" on the outcome you're interested in measuring.

Dependent variables are also referred to as:

.response elements (they respond to a change in another variable)

.outcome factors (they represent the outcome you want to measure)

.Left-side parameters

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The time at which the two cars will be 170 miles apart is; 1.619 hours

Let us write an equation for each car as;

d₁ = r₁*t₁ (northbound)

d₂ = r₂*t₂ (southbound)

They both start at the same time, and will stop them both when they are 170 miles apart. Thus;

t = d₁/r₁

t = d₂/r₂

Thus, the equation to find their times is;

d₁/r₁ = d₂/r₂

d₁ = d₂r₁ /r₂

Thus;

d₁ + d₂ = 170

d₁ = 170 - d₂

Similarly, r₁ = 45 mph and r₂ = 40 mph

170 - d₂ = d₂(45/60)

4(170 - d₂) =3d₂

7d₂ = 680

d₂ = 680/7

d₂ = 97.143 miles

d₁ = 170 - 97.143

d₁ = 72.857 miles

t₁ = d₁/r₁ = 72.857/45 = 1.619 hours

This represents the time that they will be 170 miles apart

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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 : -

(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: 14.9

Step-by-step explanation:

Pythagoras Theorem States that for any right angled triangle.

a ^ 2 + b^2 = c ^2.

a = 10

b = 11

x = unknown

x^2 = a ^ 2 + b^2

x^2 = (10 * 10) + (11 * 11)

x = sqrt(100 + 121)

x = sqrt(221)

x = 14.9

A geometric series is one in which there is a constant between two successive numbers in the series.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Suppose the series is given as

2,4,8,16,32,64.........

The common difference is defined as the ratio of the next term to the previous term.

From the above series, the common ratio is calculated as,

Common ratio = 4 / 2

Common ratio = 2

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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

If a rental car agency charges $15 per day plus 11 cents per mile to rent a certain car. The number of  miles you have to be driven for the cost of the car from the first agency to equal the cost of a car from the second agency is 100 miles.

First step is to set the equation that will be used to find the number of miles

Equation

15+.11x=18+.08x

So,

Number of miles

15+.11x=18+.08x

Collect like terms

.03x=3

Divide both side by  0.03

x=3/.03

x =100 miles

Therefore we can conclude that the number of miles is 100 miles.

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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

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

Answer:

I think you forgot to show us the problem

Therefore ,  [tex]-4|x|[/tex]   is the square root of [tex]-\sqrt{16x^{2} }[/tex]

When a number is multiplied by itself, the result is known as the square root of the number. To represent the square root, use the radical symbol. For illustration, [tex]\sqrt[/tex]16 = 4. Another name for the radical sign is the root symbol or surds.

given

- [tex]\sqrt{16x^{2}[/tex] when [tex]x[/tex] < 0,

In order to solve the given expression we will take the square root of the term inside the root.

Perfect squares (squares of integers) make up the word in the square root, thus we can express it as a square of the numbers.

⇒  [tex]-\sqrt{(4x)^{2} }[/tex]    [ as [tex](4x)^{2}[/tex] = [tex]16x^{2}[/tex]]

On taking square root the square gets removed. So, we have,

[tex]-|4x|[/tex]  =[tex]-4|x|[/tex]

Since , so the value would be negative.

Therefore , [tex]-4|x|[/tex] is the square root of [tex]-\sqrt{16x^{2} }[/tex]

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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:

A

Step-by-step explanation:

bait left = 20 - 2x     where x = hours      slope = -2   answer A

Answer:

D 448

multiply -4×16×-7

= 448

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: 6.655 * 10^-3

Step-by-step explanation:

0.006655 in scientific notation

6.655 × 10³

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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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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Answer:

2 370 / 6 = 395

Step-by-step explanation:

(x,y,z)=(19,14,3)

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Answer:

y = total cost

x = mile

Step-by-step explanation:

Answer: y = 5 + 0.75x

Step-by-step explanation:

Answer:

Divide by 2

Step-by-step explanation:

Answer:

At $800,000 of sales the offers are equal.  Anything over 800,000 makes the second deal a better deal.

Step-by-step explanation:

Let y equal the total money earned.

Let x equal the total sales.

y = .01x + 42000

y = .025x + 30000  Set these two equations equal to each other.

.01x + 42000 = .025x + 30000  Subtract .01x  from both sides

.01x -.01x + 42000 = .025x - .01x + 30000

42000 = .015x + 30000   Subtract 30000 from both sides

12000 = .015x   Divide both sides by .015

[tex]\frac{12000}{.015}[/tex] = [tex]\frac{.015x}{.015}[/tex]

800,000 = x

Answer:

job 1 , y = 42 000 + 0.01x

job 2 , y = 30 000 + 0.025x

42 000 + 0.01x < 30 000 + 0.025x

42 000 - 30 000 < 0.025x - 0.01x

12 000 < 0.015x

x < 800 000

example of u get 900 000 total sales

42 000 + 0.01(900 000) < 30 000 + 0.025(900 000)

42 000 + 9000 < 30 000 + 22 250

51 000 < 52 500

Step-by-step explanation: