Solve the equation. -z/4 = -3/4

Answer:

angle ced is a right ange

so the m angels debate =135 m angle aeb =35

so the answer is 135+35 =170

180 is a all side sim

=180-170=10 answer

Answer:

∠CED is a right angle.

∠CEA is a right angle.

m∠CEB = m∠BEA

m∠DEB = 135°

The value of N that satisfies the following equation, 5!9!= 12N!, is 10.

Factorial notation (n!) means to multiply a series of descending natural numbers. Also stated in the problem that for positive integer n, the factorial notation n! represents the product of the integers from n to 1.

Take for example 6! which can be written as 6 x 5 x 4 x 3 x 2 x 1 = 720.

Given the equation 5!9!= 12N!, expand the factorial notation.

(5 x 4 x 3 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = (4 x 3) N!

N! = (5 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

N! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

N = 10

Therefore, the value of N that satisfies the following equation, 5!9!= 12N!, is 10.

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The answer to the following are below:

Total water area for Alabama and Florida = 2.9 × 10⁷

Total water area for Hawaii and Michigan = 8.5 × 10⁷

Difference of water area of Florida and Hawaii = 3.3 × {10}^{- 1}

Difference of water area of Michigan and Alabama = 2.3 × 10¹

Alabama = 1.7 × 10³

Florida = 1.2 × 10⁴

Hawaii = 4.5 × 10³

Michigan = 4.0 × 10⁴

Total water area for Alabama and Florida = (1.7 × 10³) + (1.2 × 10⁴)

= (1.7 + 1.2) × {10}^{3 + 4}

= 2.9 × 10⁷

Total water area for Hawaii and Michigan = (4.5 × 10³) + (4.0 × 10⁴)

= (4.5 + 4.0) × {10}^{3 + 4}

= 8.5 × 10⁷

Difference of water area of Florida and Hawaii = (4.5 × 10³) - (1.2 × 10⁴)

= (4.5 - 1.2) × {10}^{3 - 4}

= 3.3 × {10}^{- 1}

Difference of water area of Michigan and Alabama = (4.0 × 10⁴) - (1.7 × 10³)

= (4.0 - 1.7) × {10}^{4 - 3}

= 2.3 × 10¹

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Answer:

It takes the electrician 4 hours to complete the job

Step-by-step explanation:

This question can be solved using a rule of three.

In 2/3 of an hour, he completes a sixth of a job. So how many hours does it take for him to complete the job(which is 100% = 6/6 = 1)?

2/3 hour - 1/6 of the job

x hours - 1 of the job

\(\frac{1}{6}x = \frac{2}{3}\)

Applying cross multiplication

\(3x = 6*2\)

\(3x = 12\)

\(x = \frac{12}{3}\)

\(x = 4\)

It takes the electrician 4 hours to complete the job

Answer:

Below

Step-by-step explanation:

Find unit rate (since it starts at 0,0)

at 45 seconds  it is 900 bottles

             900 bottles / 45 seconds = 20 bottle / sec

20 bottles / sec * 80 sec = 1600 bottles

The average rate of change of f(x), represented by the table is 1/7

The formula for calculating the rate of change which is also known as the slope is expressed as;

Rate of change = f(b)-f(a)/b-a

Using the interval [-3 4]

f(b) = f(4) = 7

f(x) = f(-3) = 6

Substitute

Rate of change = 7-6)/4-(-3)

Rate of change= 1/7

Hence the average rate of change of f(x), represented by the table is 1/7

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Answer:

$42

Step-by-step explanation:

Given that,

Galore Super Store buys the latest video game at a wholesale price of $30.00.

The markup rate at Game's Galore Super Store is 40%.

We need to find the price from the store. It can be calculated as follows :

\(C=30+\dfrac{40}{100}\times 30\\\\=30+12\\\\=\$42\)

Hence, we will pay $42.

2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

To express 2 cos 35 sin 67 as a sum, we can use the trigonometric identity for the product of two sine or cosine functions.

Specifically, the identity states that 2 cos A sin B can be written as

sin(A + B) + sin(A - B).

Applying this identity, we have:

2 cos 35 sin 67 = sin(35 + 67) + sin(35 - 67)

Simplifying the expressions inside the sine functions:

sin(102) + sin(-32)

Since the sine function is an odd function,

sin(-x) = -sin(x),

so we can rewrite the equation as:

sin(102) - sin(32)

Therefore, 2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

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Answer:

P(F | D) = 47.26%

There is a 47.26% probability that the foreman forgot to shut off the machine the previous night.

Step-by-step explanation:

A foreman for an injection-molding firm admits that on 23% of his shifts, he forgets to shut off the injection machine on his line.

Let F denote the event that foreman forgets to shut off the machine.

Failure to shut down at night causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 5% to 15%.

Let D denote the event that the mold is defective.

If the foreman forgets to shut off the machine then 15% molds get defective.

P(F and D) = 0.23×0.15

P(F and D) = 0.0345

If the foreman doesn't forget to shut off the machine then 5% molds get defective.

P(F' and D) = (1 - 0.23)×0.05

P(F' and D) = 0.77×0.05

P(F' and D) = 0.0385

The probability that the mold is defective is

P(D) = P(F and D) + P(F' and D)

P(D) = 0.0345 + 0.0385

P(D) = 0.073

The probability that the foreman forgot to shut off the machine the previous night is given by

∵ P(B | A) = P(A and B)/P(A)

For the given case,

P(F | D) = P(F and D)/P(D)

Where

P(F and D) = 0.0345

P(D) = 0.073

So,

P(F | D) = 0.0345/0.073

P(F | D) = 0.4726

P(F | D) = 47.26%

Answer:

m<E = 60 deg

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180 deg.

m<E + m<F + m<G = 180

m<E + 75 + 45 = 180

m<E + 120 = 180

m<E = 60

Answer:

60 is the ans

Step-by-step explanation:

let angle E be x

then add all sides of triangle and subtract it from 180 you will get 60 degree as ans

Answer:

9

Step-by-step explanation:

The explanation is in the picture

Answer:

Average Rate of Change = -0.4145

It means that the amount of CO2 emitted per year will decrease by an averaage rate of 0.4145 (tons - gallon of gas)/mile

Step-by-step explanation:

In order to solve this problem, we can make use of the Average Rate of Change formula, which looks like this:

\(ARC=\frac{A(25)-A(20)}{25-20}\)

So we need to start by finding what A(25) is equal to, so we get:

\(A(25)= 0.0089(25)^{2}-0.0815(25)+22.3\)

so

A(25)=7.4875

next, we can find A(20)

\(A(20)=0.0089(20)^{2}-0.0815(20)+22.3\)

so we get:

A(20)=9.56

so now we can use the average rate of change formula:

\(ARC=\frac{A(25)-A(20)}{25-20}\)

\(ARC=\frac{7.4875-9.56}{25-20}\)

ARC=-0.4145

and It means that the amount of CO2 emitted per year will decrease by an averaage rate of 0.4145 (tons - gallon of gas)/mile

Answer:

I'm sorry but I cannot help you because you have not put a picture

Answer:

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

The margin of error is of:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In a clinical test with 2161 subjects, 1214 showed improvement from the treatment.

This means that \(n = 2161, \pi = \frac{1214}{2161} = 0.5618\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a p-value of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

Margin of error:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(M = 1.96\sqrt{\frac{0.5618*0.4382}{2161}}\)

\(M = 0.0209\)

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

Answer:

\((x,y) = (-1,-2.5)\)

Step-by-step explanation:

Let be \(f(x) = \frac{(x+3)^{2}}{x-2}\) and \(g(x) = \left|\frac{x}{2}\right| -3\), we plot each curve with the help of graphic tool. In this case, we use Desmos and outcome is presented in the image attached below. Mathematically speaking, a solution to the system of equation exists when \(f(x) = g(x)\). Graphically speaking, it means that a solution exists when both curves pass through each other.

According to the graphic tool, we conclude that the only solution to the system of equations is \((x,y) = (-1,-2.5)\).

Answer:

12.5

Step-by-step explanation:

Answer:

5.5inches

Step-by-step explanation:

1331/8=166.375

then length of a side is = cubic root of 166.375

=³√166.375

5.5

Answer:

6,000

Step-by-step explanation:

Since we round to the thousand we look at the place behind there. Since 6 is in the hundreds place we have to round the number up. Meaning that we will round to 6,000.

Answer:

6000

Step-by-step explanation:

Identity the thousandth digit

Then look at the digit, next to the thousandth place. If that digit is less than 5,you then round down to the thousandth digit,but If that digit is greater than or equal to 5, you round up the thousandth digit.

Answer:

By the end of this resource, you will be able to identify domain and range from any given contextual situation.  

Determining the domain and range from a linear or quadratic contextual situation is similar to determining the independent and dependent variables.

Step-by-step explanation:

Suppose you are interviewing for a job. Your employer offers you the choice of two different options for your pay. The first option is to pay you $10.00 per hour and give you a raise of $.50 per hour at the end of the year. The second option is to pay you $11.50 per hour and give you a raise of $.25 per hour at the end of the year.

First, find a function for each option. To do that, you have to know what the domain and range might be. Let y = the amount you will make at the end of the year and x = the number of hours you work. Thinking about what would be reasonable values for x and y will help determine the domain and range.

First, let's think about the domain. Since x represents the numbers of hours you worked for the year, would it be reasonable to have negative values? If you said NO, you would be correct. We can assume the lowest possible value in the domain would equal zero. So, our domain would be {x| x ≥ 0}.

Now, let’s think about the range. Since y represents your earnings at the end of the year, would it be reasonable to have negative values? If you said NO again, you would be correct. You cannot earn a negative amount. We can assume the lowest possible value in the range would also equal zero. So, our range would be {y | y ≥ 0}. You should be able to relate with this situation since you may have to make a decision in comparing two or more job offers in your future.

It's important to realize that every situation is different and you must think about what is reasonable.  

An axiom of predicate calculus is the foundation of predicate calculus that is based on a fundamental and obvious principle or statement

The foundation of predicate calculus is based on a fundamental and obvious principle or statement known as an axiom.

The aforementioned axioms act as a foundation for deducing rational conclusions and evidence within the domain of predicate calculus.

Universally accurate and accepted without the need for additional reasoning is how they are commonly perceived.

The fundamental regulations and connections that oversee quantifiers, predicates, and logical operations, including conjunction, disjunction, and implication, are determined by the axioms of predicate calculus. They offer a sturdy groundwork for rationalizing statements that involve variables, quantification, and logical connectors in formal systems of logic.

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\(\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=\pi \end{cases}\implies \pi =\pi r^2\implies \cfrac{\pi }{\pi }=r^2 \\\\\\ 1=r^2\implies \sqrt{1}=r\implies 1=r\)

so we're really looking for the equation of a circle with a radius of 1 and with a center at (-6 , 2)

\(\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-6}{h}~~,~~\underset{2}{k})}\qquad \stackrel{radius}{\underset{1}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-6) ~~ )^2 ~~ + ~~ ( ~~ y-2 ~~ )^2~~ = ~~1^2\implies (x+6)^2 + (y-2)^2=1\)

The probability distribution for x is:

x P(x)

0 0.214

1 0.571

2 0.214

Since there are 8 cameras in the box, the total number of ways to choose 2 cameras from the box is given by the combination formula:

C(8,2) = 8!/(2!×(8-2)!) = 28

So there are 28 possible ways to choose a sample of 2 cameras.

Now, let's calculate the probability of each possible value of x:

When x = 0, both cameras in the sample are non-defective. The number of ways to choose 2 non-defective cameras from the 4 non-defective cameras in the box is given by the combination formula:

C(4,2) = 4!/(2!×(4-2)!) = 6

So the probability of x = 0 is:

P(x=0) = (number of ways to choose 2 non-defective cameras)/(total number of ways to choose 2 cameras)

= 6/28

= 0.214

When x = 1, one camera in the sample is defective and the other is non-defective. The number of ways to choose 1 defective camera from the 4 defective cameras in the box and 1 non-defective camera from the 4 non-defective cameras in the box is given by the product of the corresponding combinations:

C(4,1) × C(4,1) = 4×4 = 16

So the probability of x = 1 is:

P(x=1) = (number of ways to choose 1 defective camera and 1 non-defective camera)/(total number of ways to choose 2 cameras)

= 16/28

= 0.571

When x = 2, both cameras in the sample are defective. The number of ways to choose 2 defective cameras from the 4 defective cameras in the box is given by the combination formula:

C(4,2) = 4!/(2!×(4-2)!) = 6

So the probability of x = 2 is:

P(x=2) = (number of ways to choose 2 defective cameras)/(total number of ways to choose 2 cameras)

= 6/28

= 0.214

Therefore, the probability distribution for x is:

x P(x)

0 0.214

1 0.571

2 0.214

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\(y = ab^{x} \)

\(y = 3 \times {4}^{x} \)

"a" is the initial amount (3), and "b" is the growth factor (4).

To find "b" plug in the knowns into the exponential function equation and solve.

\(y = ab^{x} \)

\(48 = 3 \times {b}^{2} \)

\(16 = {b}^{2} \)

\( \sqrt{16} = b\)

\(b = 4\)

The coordinates point C of the given line segment AC is C(0, -2) whose midpoint is at B.

To calculate the midpoint of a line segment, find the average for the coordinates of the endpoints of the line segment. I.e.,

Consider a line segment AC, B is its midpoint.

So, the coordinates of B are (Where we have A(x1, y1) and C(x2, y2))

B(x, y) = \((\frac{x1+x2}{2}, \frac{y1+y2}{2})\)

It is given that, B is the midpoint of a line segment AC.

Where A has coordinates as (-3, 4) and B has coordinates as (-1 1/2, 1).

So, the coordinates of the other end point C of the given line segment are calculated as

B(x, y) = \((\frac{x1+x2}{2}, \frac{y1+y2}{2})\)

⇒ (-1.5, 1) = \((\frac{-3+x2}{2}, \frac{4+y2}{2})\)

⇒ -1.5 = (-3 + x2)/2 and 1 = (4 + y2)/2

⇒ -3 = -3 + x2 and 2 = 4 + y2

⇒ x2 = 0 and y2 = 2 - 4 = -2

Therefore, point C has coordinates as (0, -2).

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Answer:

reduced traffic on the road

Step-by-step explanation:

just took the test :)

Answer: C) Reduced traffic on the road

Step-by-step explanation: Ive taken this test

The solutions to the equation 1x² - 16x = 20 are x = 8 + 2√21 and x = 8 - 2√21.

To solve the quadratic equation 1x² - 16x = 20, we need to rearrange it into the standard form ax² + bx + c = 0. Let's simplify the equation step by step:

1x² - 16x = 20

First, move all terms to one side of the equation:

1x² - 16x - 20 = 0

Now we have a quadratic equation in the standard form. To solve it, we can use factoring, completing the square, or the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 1, b = -16, and c = -20. Substituting these values into the quadratic formula:

x = (-(-16) ± √((-16)² - 4(1)(-20))) / (2(1))

Simplifying further:

x = (16 ± √(256 + 80)) / 2

x = (16 ± √336) / 2

x = (16 ± √(16 * 21)) / 2

x = (16 ± 4√21) / 2

Simplifying:

x = 8 ± 2√21

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Answer:

Since we are talking annual interest and, I assume a time period of 1 year:

The interest earned is the sum of the interest earned on the two loans separately

Let x = amount loaned at 14%

18,500-x = amount loaned at 12%

I = prt

p = x and 18500-x

r = 0.14 and 0.12

t = 1

2390 = 0.14x + 0.1(18500-x)

2390 = .14x + 1850 - 0.1x

x = 13500

x = $13,500 loaned at 14%

18500-x = $5,000 loaned at 12%

Answer:

$8,500 was loaned at 14%, and

$10,000 was loaned at 12%.

Step-by-step explanation:

Total loan: $18,500.

Part at 14%

Part at 12%

Let the part at 14% = x.

Let the part at 12% = y.

Equation of amount of loan:

x + y = 18500

x amount at 14% earns 14% of x = 0.14x interest.

y amount at 12% earns 12% of y = 0.12y interest.

Equation of interest charged:

0.14x + 0.12y = 2390

We have a system of equations.

x + y = 18500

0.14x + 0.12y = 2390

Multiply both sides of the first equation by -0.12. Write the second equation below it, and add the equations.

     -0.12x - 0.12y = -2220

(+)    0.14x + 0.12x = 2390

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

      0.02x             = 170

x = 170/0.02

x = 8500

x + y = 18,500

8500 + y = 18,500

y = 10,000

Answer:

$8,500 was loaned at 14%, and

$10,000 was loaned at 12%.

Answer: 7y(3x+2)

Step-by-step explanation:

The greatest-common-factor for the coefficients 21 and 14 is 7

Both 21xy and 14y have the variable y

So the GCF factor is 7y

A. The system of equations in standard form is: 4x + 5y = 540 and 3x + 5y = 440.

B. The y-intercept of the equation representing the prices on Saturday night is 108, and the y-intercept of the equation representing the prices at the matinee on the second day is 88.

A) Let's define the variables:

Let x represent the number of children attending.

Let y represent the number of adults attending.

On Saturday night:

The equation for the revenue generated on Saturday night is:

4x + 5y = 540 (since children's tickets cost $4 and adults' tickets cost $5, and the total revenue is $540).

Matinee on the second day:

The equation for the revenue generated at the matinee is:

3x + 5y = 440 (since children's tickets cost $3 and adults' tickets still cost $5, and the total revenue is $440).

Therefore, the system of equations in standard form is:

4x + 5y = 540

3x + 5y = 440

B) Let's rewrite the system of equations in slope-intercept form:

On Saturday night:

4x + 5y = 540

Rearranging the equation, we get:

5y = -4x + 540

Dividing both sides by 5, we get:

y = (-4/5)x + 108

The y-intercept of this equation is 108.

Matinee on the second day:

3x + 5y = 440

Rearranging the equation, we get:

5y = -3x + 440

Dividing both sides by 5, we get:

y = (-3/5)x + 88

The y-intercept of this equation is 88.

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