A linear equation is graphed

Answer:

x = 11.5  This is the answer to the equation.

Step-by-step explanation:

2 · (x - 8) = 7  This is the equation as it is written.

x - 8 = 7/2

The right side of the equation 9 - 3x +6+8 + 3x+7 can be simplified by combining like terms as: 30.

2(x - 5) can be simplified using the Distributive Property as: 2x - 10.

In Mathematics, the distributive property of multiplication states that when the sum of two or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

Next, we would combining like terms in the right side of the equation as follows;

9 - 3x +6+8 + 3x+7 = (9 + 8 + 6 + 7) + (3x - 3x)

9 - 3x +6+8 + 3x+7 = 30.

By applying the distributive property of multiplication to left side of the equation, we have:

2(x - 5) = 2x - 10.

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Answer:

The radian measure of a central angle of a circle can be found using the formula:

Radian measure = Arc length / Radius

In this case, the radius is 22 centimeters, and the arc length is x. So,

Radian measure = x / 22

Step-by-step explanation:

Answer:

Step-by-step explanation:

d

Answer:

-3

Step-by-step explanation:

Write the equation in slope -intercept form: y = mx + b

where m is the slope.

       y - 5 = -3x

            y = -3x + 5

Slope = -3

[tex]y-5 =-3x[/tex]

[tex]y-5+5 =-3x+5\\ \\y=-3x+5[/tex]

The slope of a linear equation will always be the coefficient of the "x" variable when the equation is equalled to "y". The coefficient is just the number that multiplies the variable. Hence, the coefficient of this line is "-3". Check the attached image.

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The regrouping column is used to carry numbers from the ones column to the tens column. In this case, there is a 1 that must be carried from the ones column to the tens column. The sum of 48 + 689 is 737.

A column is a vertical structure that acts as a support for a building or is used as a decorative object. It is commonly used in architecture and comes in many different styles, shapes, and sizes. Columns can be made from a variety of materials such as stone, marble, iron, and brass. They are often adorned with intricate carvings and detailed designs. Some ancient structures like the Parthenon in Athens, Greece, are famous for their impressive use of columns.

Hundreds

Tens

Regrouping

First Addend

Second Addend 6

Sum

4

8

Ones

7

7

The regrouping column is used to carry numbers from the ones column to the tens column. In this case, there is a 1 that must be carried from the ones column to the tens column. The sum of 48 + 689 is 737.

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Slope intercept form is written as follows:

[tex]y=mx+b[/tex]

With this information, isolate y on the left side of the provided equation:

[tex]4y=10x-14[/tex]

Now, divide both sides of the equation by 4:

[tex]y=\frac{10}{4} x-\frac{7}{2}[/tex]

This equation cannot be simplified anymore, and is therefore the answer!

[tex]y=\frac{10}{4} x-\frac{7}{2}[/tex]

Answer:

y = (5/2)x - (7/2)

Step-by-step explanation:

–10x + 4y + 14 = 0

                 -14     -14

-----------------------------

-10x + 4y = -14

+10x                 + 10x

--------------------------------

4y = 10x - 14

÷4    ÷4     ÷4

----------------------

y = (10/4)x - (14/4)

simplified

y = (5/2)x - (7/2)

I hope this helps!

The area of the octagon is 11+ 12√2 square units.

The length of the sides of an equiangular octagon is 1, 2, 3, 4, 1, 2, 3 and 4 in that order clockwise.

Suppose it is in a rectangle where the 4 unit sides and the 2 unit sides lie on the sides of the rectangle.

The area of the outer rectangle is shown in the upper-right corner of the sketch.

As per the question, the octagon is equiangular, so all its internal angles are 135 degrees. This means it fits neatly in a rectangle of dimension 3+3√2 by 1+3√2. The area of the octagon is the area of the rectangle minus the area of the four right isosceles triangular corners = 11+12√2.

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5+2+3+7+2=19:19 is the perimeter

The class intervals would be:

Class 1: 2-10

Class 2: 11-19

Class 3: 20-28

Class 4: 29-37

Class 5: 38-46

Class interval can be determined by dividing the range of the data by the desired number of intervals (also known as classes).

First, we need to find the range of the data:

Maximum value: 47

Minimum value: 2

Range: 47 - 2 = 45

For this example, let's choose 5 classes.

Class interval = Range / Number of classes = 45 / 5 = 9

The class intervals would be:

Class 1: 2-10

Class 2: 11-19

Class 3: 20-28

Class 4: 29-37

Class 5: 38-46

Note: The upper limit of each class is always rounded up.

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Step-by-step explanation:

The equation being

D = -65m

They provides us with m

We can plug it in to find out the value of D

The first one is 0

D = -65(0) = 0m

The second is 1

D = -65(1) = -65m

And the last one is 2

D = -65(2) = -130m

The relative change in the annual salaries when comparing Fort Wayne to New York City is 66. 7 %

The relative change in the annual salaries when Fort Wayne and New York City are compared can be found by the formula :

= Difference between the annual salaries of both cities / Salary in Fort Wayne

Difference between the annual salaries of both cities:

= 92, 190 - 55, 300

= $ 36, 890

The relative change is:

= 36, 890 / 55, 300

= 66. 7 %

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The equation in slope - intercept form would be y = 0.6x + 1.1.

Given is that Mr. Phan fills a portion of his pool with water on Monday. Then on Tuesday, he fills the pool with water coming from a hose at a constant rate. The table shows the number of feet of water in the pool as a function of time on Tuesday -

Time on Tuesday after 9 AM (hr) →   0    1      2

Amount of Water in Pool (ft) →          1.1   1.7   2.3​

Let the equation be -

y = mx + c

We can write the slope as -

{m} = (1.7 - 1.1)/(1 - 0)

{m} = 0.6

and

{c} = 1.1        

So, the equation in slope - intercept form would be -

y = 0.6x + 1.1

Therefore, the equation in slope - intercept form would be y = 0.6x + 1.1.

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Answer:

  y = 4

Step-by-step explanation:

You want the equation of the horizontal line containing the point (-1, 4).

On a horizontal line, the y-coordinates of every point are the same. The equation can be written ...

  y = constant

In order for the horizontal line to go through a point with y-coordinate 4, the constant must be 4. The equation is ...

  y = 4

<95141404393>

A sample space the set of all the possible outcomes in a probability experiment.

The sample space in probability theory is the set of all possible outcomes of a random experiment.

It is the set of all possible results of an action, experiment, or random process. In other words, it is the set of all possible values that a random variable can take.

For example, in a coin flip experiment, the sample space could be defined as the set {heads, tails}.

In a dice roll experiment, the sample space could be defined as the set {1, 2, 3, 4, 5, 6}.

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The method of moment estimators of a and b are [tex]\hat{a}=\bar{X}-\sqrt{3}S_x[/tex] and[tex]\hat{b}=\bar{X}+\sqrt{3}S_x[/tex] . And, the maximum likelihood estimators of a and b are  [tex]\hat{b}=x(n)[/tex] and [tex]\hat{a}=x(1)[/tex].

The random sample given is X₁, X₂, X₃,..........., Xₙ from the uniform distribution on [a, b]. The probability density function (pdf) of this is written as,

[tex]f(x)=\begin{cases} \frac{1}{b-a},&a < x < b\\0,&\text{otherwise} \end{cases}[/tex]

a) Now, let's calculate the expected value of X E(X). We get,

[tex]\begin{aligned}\mu _1=E(X)&=\int_a^b x\cdot\frac{1}{b-a}\;dx\\&=\frac{1}{b-a}\left[\frac{x^2}{2}\right]_a^b\\&=\frac{b+a}{2}\end{aligned}[/tex]

Let's calculate the second moment of X. We get,

[tex]\begin{aligned}\mu_2=E(X^2)&=\int^b_ax^2\cdot\frac{1}{b-a}\;dx\\&=\frac{1}{b-a}\left[\frac{x^3}{3}\right]_a^b\\&=\frac{b^3-a^3}{3(b-a)}\\&=\frac{b^2+a^2+ab}{3}\end{aligned}[/tex]

From the above values, variance is calculated as follows,

[tex]\begin{aligned}\mu_2-\mu_1^2=E(X)-E(X^2)&=\frac{b^2+a^2+ab}{3}-\frac{a^2+b^2+2ab}{4}\\&=\frac{4(b^2+a^2+ab)-3(a^2+b^2+2ab)}{12}\\&=\frac{b^2-2ab+a^2}{12}\\&=\frac{(b-a)^2}{12}\end{aligned}[/tex]

Now, using the method of moment, we denote [tex]E(X^2)=\mu_r[/tex] and [tex]M_n=\frac{1}{n}\sum_{i=1}^{n}X_i^2[/tex]. Then, [tex]\hat{\mu_r}=\frac{1}{n}\sum_{i=1}^{n}{X_i} ^r[/tex].

When [tex]\hat{a}[/tex] and [tex]\hat{b}[/tex] are the method of moment estimator of a and b, then, [tex]\hat{\mu_1}=\frac{\hat{a}+\hat{b}}{2}=\bar{X}[/tex] and [tex]\hat{\mu_2}=\frac{1}{n}\sum_{i=1}^{n}{X_i}^{2}[/tex].

Then,

[tex]\begin{aligned}\hat{\mu_2}-\hat{\mu_1^2}&=\left(\frac{1}{n}\sum_{i=1}^{n}({X_i}^{2}\right)-\bar{X}^2\\&=\frac{1}{n}\sum_{i=1}^{n}(X_i-\bar{X})^2\\&={S_x}^{2}\\\frac{(\hat{b}-\hat{a})^2}{12}&={S_x}^{2}\end{aligned}[/tex]

From [tex]\hat{b}+\hat{a}=2\bar{X}[/tex] and [tex]\hat{b}-\hat{a}=\sqrt{12{S_x}^{2}}=2\sqrt{3}S_x[/tex].

Then, the moment estimators of a and b are [tex]\hat{a}=\bar{X}-\sqrt{3}S_x[/tex] and[tex]\hat{b}=\bar{X}+\sqrt{3}S_x[/tex] .

b) Using the joint distribution of [tex]X=(X_1,........, X_n)[/tex] be

[tex]\begin{aligned}L(x_i\; a,b)&=\frac{1}{(b-a)^n}, a < x_i < b\\&=\frac{1}{(b-a)^n}, a < x(1) < x(n) < b\\&=\frac{1}{(b-a)^n}\cdot I\{x(n) < b\}\cdot I\{x(1) > a\}\end{aligned}[/tex]

where [tex]I_A=\begin{cases}1\;\text{if A is true}\\0\;\text{if not}\end{cases}[/tex]

The joint distribution of likelihood is maximum when b-a is minimum under the constraints b>x(n) and a<x(1). Then, [tex](b-a) > x(n)-x(1)[/tex]. So the minimum value is attained when [tex]b-a=x(n)-x(1)[/tex] that is [tex]\hat{b}=x(n)[/tex] and [tex]\hat{a}=x(1)[/tex]. Hence, the maximum likelihood estimate of a and b.

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The total receipts after the end of 1,5,7 years are 124 , 604, 844 million respectively.

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The function T(x)= 120x²+4

Thus after 1 year the receipts is T(1)=120×1+4

                                                          =124 million

After 5 years T(5)=120×5+4

                            =600+4

                            =604 million

Similarly for t=7 years T(7)=840+4

                                          =844 million

Hence, The total receipts after the end of 1,5,7 years are 124 , 604, 844 million respectively.

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The number of terms in the nth row is n + 1. The sum of the terms in the first n rows is equal to the sum of the first n + 1 triangular numbers, which is given by the formula n(n + 1)(n + 2)/6.

So to find m and n, we need to solve the following two equations simultaneously:

n(n + 1)(n + 2)/6 + m = 123000

n + 1 = 2m

Substituting the second equation into the first equation, we get:

m(2m + 1)(2m + 2)/6 = 123000

We can then solve for m using a numerical method, such as the bisection method or Newton-Raphson method. The solution is approximately m = 142.

So the values of m and n are 142 and 284, respectively.

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Answer:

The most the couple can spend for the meal is $82.82 to the nearest cent.

Step-by-step explanation:

Let x be the greatest amount (in dollars) that the couple can spend for the meal.

If a sales tax of 5% is added to the bill, then the bill will be:

[tex]x+0.05x=1.05x[/tex]

If a tip of 15% is then added to the bill, the bill will be:

[tex]1.05x+0.15 \cdot 1.05x=1.2075x[/tex]

If the maximum the couple can spend is $100 then:

[tex]1.2075x\geq100[/tex]

Solve the equation for x:

[tex]\begin{aligned}1.2075x &\geq 100\\\\x&\geq \dfrac{100}{1.2075}\\\\x&\geq 82.8157349...\end{aligned}[/tex]

Therefore, the most the couple can spend for the meal is $82.82 to the nearest cent.

1. The function is continuous everywhere because it is defined for all values of x, and there are no points where f(x) is undefined or where the limit as x approaches a specific value does not exist.

2. Interval of continuity: (-∞, ∞)

Discontinuities: None

Conditions of continuity not satisfied: None

Hence, option (d) is correct.

If and only if a function is continuous on every point in the open interval (a,b), it is continuous over that interval (a,b).

If and only if it is continuous on (a,b), then is continuous over the closed interval [a,b].

The right-sided limit of at x=a is (a), while the left-sided limit of at x=b is (b).

If a function is continuous across the whole open interval, it is said to be continuous over the interval. If it is continuous at each point in its interior and at both of its ends, it is continuous over a closed interval.

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The function represents an exponential decay, as it is a decreasing function.

A function is classified as exponential growth if it is an increasing function, that is, the function is increasing over it's entire domain.

A function is classified as exponential decay if it is an decreasing function, that is, the function is decreasing over it's entire domain.

As the function in this problem is decreasing, it is an exponential decay function.

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Answer:

at least 160 students have to buy a ticket to cover the show's cost.

Step-by-step explanation:

1200 divided by 7.50 = 160.

A two-way table is a statistical tool used to summarize and display the relationship between two categorical variables.

Below is a two-way table that shows the data from the question:

                Popcorn            No Popcorn    Total

Drink            84 - 10 = 74            15              89

No Drink      10                            6              16

Total            84                           21              105

It is a table that displays frequencies (counts or percents) for all possible combinations of two categorical variables which are popcorn and no popcorn and also drink and no drink.

The above table shows that 74 people had both popcorn and a drink, 10 had popcorn but no drink, 6 had neither drink nor popcorn, and 15 had a drink but no popcorn.

The total number of people who had popcorn is 84, and the total number who had a drink is 89.

The total number  of people who's not had popcorn is 21, and the total of  people who's not had dring is 21

The total number of people in the theater is 105.

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For a, the percentage of given angle with respect to whole rotation is 0.36% and 1.3° is equivalent to 0.0072π radian.

What is the percentage?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”.

Examples of percentages are:

10% is equal to 1/10 fraction.

20% is equivalent to ⅕ fraction.

25% is equivalent to ¼ fraction.

Now,

Given angle=1.3°

Total rotation = 360°

So, percentage of given angle=1.3/360*100=0.36%

and 1.3° in radian=1.3*π/180=0.0072π

Hence,

            the percentage of given angle with respect to whole rotation is 0.36% and 1.3° is equivalent to 0.0072π radian.

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The percentage multiplier to find 26% of an amount is, 0.26.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We know that;

Percentage multiplier calculates the percentage of an amount. It is also used to increase or decrease an amount by a percentage.

Now, In order to find the percentage multiplier of 26% of an amount we can multiply the number by a multiplier.

⇒ 26%

⇒ 26/100

⇒ 0.26

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ABC has vertices A (0, -1), B (3,4), and C (3,1). The coordinates of the image after reflection over the x axis is

Reflection is a method of transformation that creates mirror image.

The transformation rule for reflection over the x axis is as below

(x, y) → (x, -y)

Applying the rule we have

A (0, -1), B (3, 4), and C (3, 1) will result to

A' (0, 1), B' (3, -4), and C' (3, -1)

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In the weights of seven people, the 36th percentile is 135.

The following are the weights (in pounds) of seven people:

100, 115, 135, 140, 180, 197, 230

We have to determine the 36th percentile.

The term "percentile" describes how a score contrasts with other scores from the same collection. The percentage of values in a set of data scores that fall below a specific value is a typical way to represent percentile, despite the fact that there is no single meaning for this term.

The formula is:

= Percentile/100 × Total number of weights

There have total weights of 7 people and percentile is 36.

Now putting the value

= 36/100 × 7

= 2.52

= 3(approx)

To find the percentile value we count from left to right.

The 3rd number from left to right is 135.

So the 36th percentile is 135.

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Answer: L=3, W=

Step-by-step explanation: Considering it is a rectangle

P = 2 (l+b) where L equals length and B breadth width)

10 = 2( L + (2/3×L)

Divide by 2

5= x + 2/3×x

5= x/1 + 2/3×x

5= x/1 + 2x/

expand the fraction to get the MCD

3x/3×1 + 2x/3

3x/3 + 2x/3

3x + 2x / 3

5x/3

5= 5x/3

multiply them by 3/5

3/5×5 = 3/5×5/3x.

cancel first 5s

3=3/5 × 5/3x.

cancel 3s

3= 1/5 ×5x

cancel 5s

3=x.

3 is length, so let's add everything up.

p = 2.(l+b)

10= 2. (3+b)

Divide this by

5=3+x

highlight the x by changing order of the numbers.

-x=3-5

-x = -2

then multiply by (-1) to make them positive:

x=

Therefore, length is 3 and width is 2.

The solution for the equation 2cos4x - 1 = 0 is x = 3π/35.

For the values:

x = π/5 + 2kπ and also;

x = π/7 + kπ

then we can solve for k as follows:

π/5 + 2kπ = π/7 + kπ

collect like terms

2kπ - kπ = π/7 - π/5

kπ = (5π - 7π)/35 {simplifying the right hand side to a single fraction}

kπ = -2π/35

k = -2/35 {divide through by π}

put -2/35 for k in the equation x = π/7 + kπ to get the value of x;

x = π/7 - 2π/35 {simplifying the right hand side to a single fraction}

x = (5π - 2π)/35

x = 3π/35

Therefore, the solution for the equation 2cos4x - 1 = 0 is x = 3π/35.

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