Which is the last sentence of the proof? because f + e = 1, a2 + b2 = c2. Because f + e = c, a2 + b2 = c2. Because a2 + b2 = c2, f + e = c. Because a2 + b2 = c2, f + e = 1.

well, let's noticed, the original amount is $271 and 12 years later it turned to $417, so

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$417\\ P=\textit{initial amount}\dotfill &271\\ r=rate\to r\%\to \frac{r}{100}\dotfill &0\\ t=years\dotfill &12\\ \end{cases}[/tex]

[tex]417=271(1 + \frac{r}{100})^{12}\implies \cfrac{417}{271}=\left( \cfrac{100+r}{100} \right)^{12} \implies \sqrt[12]{\cfrac{417}{271}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[12]{\cfrac{417}{271}}=100+r\implies 100\sqrt[12]{\cfrac{417}{271}}-100=r\implies {\Large \begin{array}{llll} \stackrel{\%}{3.657\approx r} \end{array}}[/tex]

The equation for the line of best fit to predict the salary for an employee with 6 years of experience is $58,587.

The letter m is frequently used to represent slope; the reason for this is unclear, although it is first used in English by O'Brien in 1844, who wrote the equation for a straight line as "y = mx + b," and by Todhunter in 1888, who wrote it as "y = mx + c."

Finding the ratio of "vertical change" to "horizontal change" between any two unique locations on a line yields the slope. When the ratio is stated as a quotient ("rise over run"), the result is the same for each

We have to take any two points in the given information and find the value of slope.

Let the two points are (0, 52000), (1, 53,150)

m=(53150-52000)/(1-0)

m=1150

Therefore, slope=1150

Now, the equation of the line is y=mx+b

52000=1150(0)+c

c=52000

Therefore, y=1150x+52000

For 6 years experience,

Take x=6 then,

y=1150(6)+52000

y=6900+5200

y=58,900

y=$58,900≈58,587

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Answer:

$58,587.

Step-by-step explanation:

Adjacent angles of a parallelogram are supplementary.

[tex]3x+10+8x+5=180 \\ \\ 11x+15=180 \\ \\ 11x=165 \\ \\ \boxed{x=15} \\ \\ \\ \\ 5y+3(15)+10=180 \\ \\ 5y+55=180 \\ \\ 5y=125 \\ \\ \boxed{y=21}[/tex]

The answer is 10,000

Answer:

7

Step-by-step:

2 * 7 =14 first due to PEMDAS

3 + 14 = 17

Answer:

7

Step-by-step explanation:

Let "x" be denoted as the variable for "what".

The question posted is: 3 + 2x = 17

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, subtract 3 from both sides of the equation:

2x + 3 = 17

2x + 3 (-3) = 17 (-3)

2x = 17 - 3

2x = 14

Next, divide 2 from both sides of the equation:

(2x)/2 = (14)/2

x = 14/2

x = 7

7 is your answer.

~

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 18}}{\left( \cfrac{30}{100} \right)18}\implies 5.4[/tex]

The player who has the better record between Jamal and Brian as required in the task content is; Jamal.

It follows from the task content that the player who has the better record between Jamal and Brian is to be determined.

Since it is given that Jamal and Brian 7/9 and 5/8 of their free throws respectively;

It follows that when expressed as a percentage; we have;

For Jamal;

7 / 9 × 100% = 77.78%

For Brian;

5 / 8 × 100% = 62.5%.

Ultimately, the player who has the better record for free throws is; Jamal since he has a greater percentage success rate for free throws.

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Answer:

25.12  pulgadas

Step-by-step explanation:

Answer:

12.78

Step-by-step explanation:

He has 25.65, sold 3.87. 25.65-3.87=21.78

The scale factor from the scale drawing to the actual triangle is; 1/3

The area of a triangle is calculated using the formula;

A = ¹/₂bh

Where;

A is area.

b is base.

h is height.

The two sides of the rectangle are 6 units and 3 units. Use the measurements in the formula. "u" is for units.

Thus;

A = ¹/₂(6)(3)  

A = 9 square units

The scale factor, represented by the variable "k", tells you how much a shape enlarged or reduced. If "k" is greater than 1, the shape enlarged. If "k" is greater than 0 and less than 1, the shape reduced

In this case, since the drawing is smaller than the actual triangle, the scale factor will be a fraction less than 1 and greater than 0.

The scale factor is used for side length. When it's used to find a side length, we use "k" multiplied by a side. Since the information we know is area, we find k² first, then isolate "k".

Divide the depicted triangle area by the actual area.

k² = 9 ÷ 81

k² = 1/9

√k² = √(1/9)

k = 1/3

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(a) The probability that there will be exactly 3 eruptions in the next 200 years is 0.1404

(b) The probability the next eruption occurs between 25 and 50 years is 0.2488

Let X be the random variable denoting the volcanic eruptions as follows

Poisson distribution with parameters  λ.

the average of the eruption is  λ=2.5 per year.

Also for 200 eruptions the average of the eruptions is  λ=2.5 per year.

Also, for 200 eruptions, the average of the eruptions is  λ=5 per year.

The probability is:

P(X=3) = e⁻³(5)³/3!

= 0.0067×125/3×2×1

= 0.8422/6

= 0.1404

(b) Let X be the random variable denoting the volcanic eruptions as follows

Poisson distribution with parameters  λ and also let 2.5 eruptions in 100 years is same as waiting time of:

100/2.5

= 40 years per eruption

therefore, X ~ Exp(β=40)

the probability density function of X is:

f(x) = { 1/40 e⁻¹/⁴⁰ , x>0

          0 ,  otherwise}

And cumulative distribution function is:

P(X≤x) = 1 - e, x>0

the probability is:

P(25<X<50) = P(X<50)-P(X<25)

P(25<X<50) = e²⁵/⁴⁰ - e⁵⁰/⁴⁰

= e⁻°·°²⁵ - e⁻¹·²⁵

= 0.5353 - 0.2865

= 0.2488

Hence we get the required answer.

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Q=1,Q'=0 as an active-high input s-r latch has a 1 on the s input and a 0 on the r input.

An SR latch (Set/Reset) is an asynchronous device that solely depends on the state of the S and R inputs and does not require any input from the control signals. The illustration demonstrates how two NOR gates with a cross-feedback loop may be used to build an SR latch. Set-reset, or S-R, latches are therefore the most basic type of bistable device. We can connect two NOR gates so that the output of one feeds back into the input of the other, and vice versa, to create an S-R latch, as shown below: The Q and not-Q outputs are supposed to be in opposing states.

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Answer:

CPCTC

Step-by-step explanation:

BD is perpendicular to AC, forming two right triangles. The hypotenuses are congruent, as is our leg that we will call b. If we use Law of Sines to find our angles a and c (no matter the values), we would find that because b is the same leg in both triangles and the hypotenuses are congruent, angles a and c are congruent, so therefore your missing angle in both triangles is congruent, and using a trig function will find that AD and CD are congruent, making all of both triangles congruent.

Answer:

i suggest using -2 to multiply the figures in the bracket as a first step

Step-by-step explanation:

then you'll have something like this

-2x - 10 - 4 = 5x

-2x - 14 = 5x

-14 = 5x + 2x

-14 = 7x

x = -14/7

x = -2. hope this helps

Answer:

A ; D ; F

Step-by-step explanation:

32 - 4(5) = 12

32 - 20 = 12 (ok)

11 + 6(5) = 22

11 + 30 = 22

41 = 22 (false)

18-2(5) = 9

18 - 10 = 9

8 = 9 (false)

5/5 + 5 = 6

1 + 5 = 6

6 = 6 (ok)

3(5)+ 1 = 9

15 + 1 = 9

16 = 9 (false)

25/5 + 4 = 9

5 + 4 = 9

9 = 9 (ok)

The function in the graph is y = x² - 1 and the inverse of the function is y = √(x + 1) and the graph is attached

Examining the graph the vertex is v(h, k) = (0, -1)

Quadratic equation is of the form

y = a(x + h)² + k

using the vertex we write the equation as

y = a(x + 0)² - 1

using point (1, 0) a is calculated

0 = a(1 + 0)² - 1

a = 1

The equation of the graph is

y = a(x + 0)² - 1

y = x² - 1

The domain of the equation is all real numbers and the range is calculated from the inverse

x = √(y + 1)

y + 1 ≥ 0

y ≥ -1

Inverse function

y = x² - 1

x² = y + 1

x = ±√(y + 1)

exchanging the variables

y = ±√(x + 1)

taking the positive function

y = √(x + 1)

here the domain and range is exchanged

range: all real numbers

domain: x  ≥ -1

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Answer:

17.85

Step-by-step explanation:

You first divide 12.75 by 5, to see the price for one pound of pretzels. Then, you times that by 7, because you want to know how much it would cost for Lupita to but 7 pounds of pretzels. That would equal 47.85, which is your answer.

Answer:

x=2

Step-by-step explanation:

x/2 = 1 (multiply by 2 both sides)

x= 2

99.7% of the Manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.

On Subtracting 1 from your sample size, we get

100 – 1 = 99.

On Subtracting confidence level from 1, and then divide by two.

(1 – .997) / 2 = 0.0015

Now, df = 99 and α = 0.0015

from the table at df = 99 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

28 / √(100) = 2.8

Now, 2.262 × 2.8 = 6.33

So, the confidence interval be,

(100 - 6.33 , 100 + 6.33) = (44.67 , 56.33)

Hence, 99.7% of the Manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.

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The 1.9 × 103 is 2.15 times smaller than 4.085 × 105. (Option B)

In order to determine a number is how many times smaller than the other number, the second number is divided by the first number. Division and multiplication, both used in the situation are basic arithmetic operations. In the give case, the in order to determine how many times smaller 1.9 x 103 is than 4.085 x 105, is given by

4.085 x 105/1.9 x 103

First simplifying by multiplying the terms in the numerator and denominator

4.085 x 105/1.9 x 103

428.925/195.7

Dividing the numerator by denominator,

428.925/195.7 = 2.15

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The simple interest on the amount $198,562 mortgage at 3.99% will be $7922.62.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.

Unlike compound interest, which adds the interest from the principal of prior years to determine the interest of the following year, the principal amount in simple interest remains constant.

As per the given,

Principle amount P = $198,562

Rate = 3.99%

Interest amount = 3.99% of $198,562

⇒ (3.99/100)198562 = $7922.62

Hence "The simple interest on the amount of $198,562 mortgage at 3.99% will be $7922.62".

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1) $9.27  (far store), $9.87 (near store)

2) $0.169 per mile

3) 4.6 miles , 16.8 miles

4) $0.78, $2.84

5) $10.05 to the far store, $12.71 to the near store

What is Cost?

A mathematical formula known as the cost function is used to graph how production costs will change depending on the output level. To put it another way, it calculates the overall cost of production based on the quantity that is produced.

1) Let's compare chicken costs:

$3.09 * 3 = $9.27  (far store)

$3.29 * 3 = $9.87 (near store)

2) Now let's look at how much it costs to travel in your car:

    [tex]\frac{3.87}{23} = 0.169\ per \ mile[/tex]

           = $0.169 per mile.

3) Next, let's look how much it costs to travel to each store from the gas used. Multiply by 2 because you not only have to drive there, but also back home for the round trip:

2.3 miles * 2 = 4.6 miles

8.4 miles * 2 = 16.8 miles

4) Now to find the cost of gas for the respective trips:

$0.169 * 4.6 = $0.78

$0.169 * 16.8 = $2.84

5) We can just eyeball it from here that it's not worth it to travel, but for completion's sake, let's add the gas and chicken costs together:

$9.27 + $0.78 = $10.05 to the far store

$9.87 + $2.84 = $12.71 to the near store

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Answer: I think the answer is A.

The total number of games would be 15 games.

What are the Permutation and Combination?

Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.

Consider each team playing with the other team once

Total number of games scheduled = Number of ways of selecting 2 from 6 teams

               [tex]=^nC_r\\\\=^6C_2\\\\=\frac{6!}{2!*4!}\\\\=15[/tex]

Hence the total number of games would be 15 games.

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Slope of y = 2x +80 is 2, y-intercept is 80, x-intercept is -40.

Slope is defined as how much the y-coordinate changes with respect to the x-coordinate. Slope remains constant anywhere on the line.

Given equation is y = 2x + 80, where y is total amount of spending by tourist in Florida, in billions of dollars and x represents the number of years since 2013.

Equation of a line in slope-intercept form is,

y = mx + c, where m is the slope of the line and c is the y-intercept.

Comparing the given equation with slope-intercept form, we get,

m = 2 and c = 80

Domain of the equation includes number of years from 2013 - 2017 and the range of the equation is the corresponding y values.

Since slope is positive, as x value increases, y value also increases.

x- intercept is the point where the line touches the x-axis. y-coordinate will be zero at that point.

0 = 2x + 80 ⇒ x = -40

For the equation y = 2x +80, slope = 2, y-intercept = 80, x-intercept = -40.

Domain is the set of all number of years from 2013 - 2017 and range is the corresponding amount spend by tourist in the years from 2013-2017. As x value increases, y value also increases.

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Answer:

there's no picture

The point of the coordinate plane is ( 0.5 , 1 )

what is coordinate plane ?

The definition of a coordinate plane is as follows: A coordinate plane, often referred to as a rectangular coordinate plane grid, is a two-dimensional plane made up of the Y-axis, a vertical line, and the X-axis, a horizontal line.

solution:

A( -3, -5) and B( 2, 7 ), m:n = 1:1

using section formula

P = [ { (mx2+nx1)/ (m+n) , { (my2+ny1)/ (m+n) }]

  = [ 1(2) + 1(-3) / 2 , 1( 7 ) + 1(-5) / 2 ]

  = ( 0.5 , 1 )

Hence the coordinate plane point is ( 0.5 , 1 )

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The number of ways that the teacher can arrange the row is  185328000

Given,

Number of male students = 12

Number of female students = 13

Number of students teacher needs to select = 8

The row arrangement is like; 4 men in the middle and  2 women on each end;

Here,

Order of the arrangement is considered.

So, permutation can be used.

Female students selected = ¹³P₂

Male students selected = ¹²P₄

Then,

Number of ways for the arrangement =  ¹³P₂ × ¹²P₄

= 15600 × 11880

= 185328000

That is,

The teacher can arrange a row with 4 men in the middle and 2 women on each end in 185328000 ways.

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This fails to reject the null Hypothesis.

What is z test?

If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.

a recent survey reported that small businesses spend 24 hours a week marketing their business.

these businesses are spending less than 24 hours a week on marketing. the chamber conducts a survey of 58 small businesses within their state and finds that the average amount of time spent on marketing is 22.7 hours a week.

assuming that the population standard deviation is 6.1 hours.

z = x'- u / α(/√n) = (5.05-4.50/1.83/√38) = 1.85

Hence, This fails to reject the null Hypothesis.

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Answer:

The solution to the given expression would be 23.

Step-by-step explanation:

1. Remove the parentheses:

[tex]2.3*6+2.3*4[/tex]

2. Multiply the numbers 2.3 by 6: 13.8

[tex]13.8+4*2.3[/tex]

3. Multiply the numbers 2.3 by 4: 9.2

4. Add the numbers 13.8 by 9.2: 23

= [tex]23[/tex] ←Our Final Solution

____________________________________________

Hope this helps!