The legths of the sides of a rectangle are in a ratio of 4:7. If the length is 31.5 in., find the width, perimeter an area of this rectangle.

Based on the numbers that Joe selected, the people selected were D) Alan, Eugene, Martin, Sam.

The 17th person was selected and if we assigned numbers from 1 to 20 to the alphabetized list, we would find that number 17 is Sam.

The 5th person is Eugene and the 1st person is Alan. The 12th person is Nathan.

In conclusion, option D is correct.

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Answer:

-2.5

Step-by-step explanation:

Answer:

-5/2 or -2.5

you can type it in a calculator

Answer:

-726

Step-by-step explanation:

So whenever you have a fraction raised to some power, you can distribute the exponent: [tex](\frac{a}{b})^n=\frac{a^n}{b^n}[/tex] the reason for this can be explained, using the definition of an exponent. You can see: [tex](\frac{a}{b})^n[/tex] as [tex]\frac{a}{b} * \frac{a}{b} * \frac{a}{b}... \text{ n amount of times}[/tex] multiplying fractions simply multiplying the numerators by the other numerators, and the denominators by the other denominators. So you're going to have the fraction: [tex]\frac{a * a * a \text{ n amount of times...}}{b * b * b\text{ n amount of times...}}[/tex] which can be rewritten as an exponent, since this is the very definition of an exponent. This simplifies to: [tex]\frac{a^n}{b^n}[/tex].

Anyways now that you hopefully understand that, let's simplify the expression

The first step is to distribute the exponent to get the fraction:

[tex]\frac{6}{2}-\frac{81^2}{3^2}[/tex]

Now square both values to get

[tex]\frac{6}{2}-\frac{6,561}{9}[/tex]

The fraction simplifies to:

[tex]\frac{6}{2}-729[/tex]

the left fraction simplifies to 3, so you get

[tex]3-729[/tex]

This simplifies to

-726

According to the dilation formula, the location of the four vertices of the quadrilateral A'B'C'D' are A'(x, y) = (0, 0), B'(x, y) = (0, 7.5), C'(x, y) = (12.5, 7.5) and D'(x, y) = (12.5, 0).

Dilation are a kind of rigid transformations defined by the following formula:

P'(x, y) = O(x, y) + r · [P(x, y) - O(x, y)]     (1)

Where:

If we know that r = 2.5, O(x, y) = (0, 0), A(x, y) = (0, 0), B(x, y) = (0, 3), C(x, y) = (5, 3) and D(x, y) = (5, 0), then the resulting points are obtained:

A'(x, y) = (0, 0) + 2.5 · [(0, 0) - (0, 0)]

A'(x, y) = (0, 0)

B'(x, y) = (0, 0) + 2.5 · [(0, 3) - (0, 0)]

B'(x, y) = (0, 7.5)

C'(x, y) = (0, 0) + 2.5 · [(5, 3) - (0, 0)]

C'(x, y) = (12.5, 7.5)

D'(x, y) = (0, 0) + 2.5 · [(5, 0) - (0, 0)]

D'(x, y) = (12.5, 0)

Lastly, we proceed to graph the two figures.

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Answer:

x = 55°

Step-by-step explanation:

given 2 inscribed angles intercept the same arc then they are congruent, so

x = 55°

Answer:

A

Step-by-step explanation:

[f(x) + g(x)]=x²+3x-6+1

=x2+3x-5

The value of the composite function is A: x² + 3x - 5.

Option A is the correct answer.

We have,

To find (f + g)(x), you simply need to add the two functions f(x) and g(x) together.

So, (f + g)(x) = f(x) + g(x).

Given:

f(x) = 3x + 1

g(x) = x² - 6

Now, add the two functions:

(f + g)(x) = (3x + 1) + (x² - 6)

Now, combine like terms:

(f + g)(x) = 3x + 1 + x² - 6

Finally, rearrange the terms in descending order of powers of x:

(f + g)(x) = x² + 3x - 5

Thus,

The value of the composite function is A: x² + 3x - 5.

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The area of wood needed for the frame is 5. 5 + 106 square inches. Option A

The amount of wood needed for the window frame will be equal to area of window frame.

It is important to note that the upper part of window is semicircle

Area of the upper part = π [tex]\frac{R^2 - r^2}{2}[/tex]

where,

R = Outer radius,

r = Inner radius.

Area of upper part = π ×  [tex]\frac{6^2 - 5^2}{2}[/tex]

Area of upper part = 11π/2

Area of upper part = 5. 5π

To find the area of the lower part, it is important to note that the area of lower part of frame will be area of 3 different rectangles. Two are the same rectangles with length 48 inches and width 1 inch and one rectangle with length 10 inches (12-2) and width 1 inch.

Area of lower part = 2 × 48 × 1 + 10 × 1

Area of lower part = 96 + 10

Area of lower part  = 106 inches

Thus, the area of wood needed for the frame is 5. 5 + 106 square inches. Option A

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x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000. This can be obtained by understanding the question and observing the equations.

Given that total number of seats is 10,000 and there are two levels pricing.

Thus by observing the equation, x + y = 10,000,

10,000 is the sum of 2 variable which obviously will be the number of tickets in level 1 and number of tickets in level 2.

Since there are two level pricing,

50x + 150y = 75,000 represent the addition of total cost of tickets of level 1 and 2.

Hence x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000.

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Answer:graph b

Step-by-step explanation:

Answer:

The product is the difference of squares is [tex]$$(7w+10x)(7w-10x)=49{{w}^2}-100{{x}^2}$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(7 w+10 x)(7 w-10 x)=(7 w)^{2}-(10 x)^{2} \\&(7 w+10 x)(7 w-10 x)=49 w^{2}-100 x^{2}\end{aligned}$$[/tex]

Answer:

- Please see the attached picture for full solution!:)

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The value of x in the triangle is (a) 30√2

The complete question is in the attached image.

From the attached image of the triangle, we can see that the triangle is a right triangle, and x can be solved using the following sine function

[tex]\sin(45) = \frac{30}{x}[/tex]

Evaluate sin(45)

[tex]\frac 1{\sqrt 2} = \frac{30}{x}[/tex]

Solve for x

[tex]x = 30 * \sqrt 2[/tex]

Evaluate

[tex]x = 30 \sqrt 2[/tex]

Hence, the value of x in the triangle is (a) [tex]30 \sqrt 2[/tex]

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Answer:

B.) y = x² + 3, x < 4
          x + 4, x ≥ 4

Step-by-step explanation:

Remember, the x-values associated with closed dots are not included in the function. Therefore, only greater than/less than signs can be applied to these points.

The exponential function includes all x-values before x = 4. Therefore, the domain for the parabola is x < 4.

The linear function includes all x-values after and including x = 4. Therefore, the domain for the linear portion of the function is x ≥ 4.

The company cannot build  10 child bikes and 12 adult bikes No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 , Option A is the correct answer.

System of inequality represent system of inequalities that satisfies common condition.

It is given that

Each child bike requires 4 hours to build and 4 hours to test.

Each adult bike requires 6 hours to build and 4 hours to test.

Total building hours = 120

Total testing hours = 100

If c represents child bikes and a represents adult bikes, can the company build 10 child bikes and 12 adult bikes in a week.

6a + 4c ≤ 120

4a +4c ≤100

On solving this system of Inequality

a ≤ 10

which is less than required , and so

No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

Therefore Option A is the correct answer.

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Answer:

no it does not pass the vertical line test choose D

Step-by-step explanation:

Answer:

A quadratic equation can be solved using the quadratic formula, the factoring method, or completing the square. You expect to get either one or two answers.

Step-by-step explanation:

First, we have to understand how to solve a quadratic equation. There are three methods, the first of which is the quadratic formula. For any quadratic equation that takes the standard form of

[tex]f(x)=ax^2+bx+c[/tex]

you can solve for x by using the following formula:

x=(-b±√(b^2-4ac))/2a

Sometimes, however, the quadratic expression is factorable, meaning it can be converted into a product of two smaller expressions. For example:

[tex]x^2-4=(x-2)(x+2)[/tex]

As you can see, factoring gives you the roots easily (set each smaller expression to 0 and solve for x). If the quadratic is factorable, it would be easiest to use this method first.

Completing the square is another method that can be used to solve a quadratic function. It is often preferred because it converts the function into something factorable. In order to complete the square, you have to first ensure that the quadratic term's coefficient is 1. After that, you can take the linear term's coefficient, divide it by 2, and square it. Take the new term you found and add it to the equation. Because you are adding something to an equation, you must also subtract. Now, you can complete the square and factor. An example can be found below:

[tex]x^{2}-6=0\\\\(x^2-6+9)-9=0\\\\(x-3)^2-9=0\\\\(x-3-3)(x-3+3)=0\\\\x(x-6)=0\\\\x=0, x=6[/tex]

A quadratic equation can only have up to two solutions. You can imagine the graph of a quadratic. It looks like a parabola and only changes directions once. This means that it only crosses the x-axis two times. You can also look at the examples given and see that factoring only gives you two smaller expressions (leading to 2 roots). Sometimes, however, you might get a double root, leading to an equation with only one solution. This happens when the discriminant of the quadratic equation is 0. You can calculate this in advance to save yourself some time.

We can use the following identity:

(Xm, Ym) = X1+X2/2, Y1+Y2/2, where Xm and Ym are the midpoints of X and Y.

So, let's use it.

For question 11, X1 is -3, Y1 is 9, X2 is 3, and Y2 is -7.

Plugging in the points, we get:

-3 + 3 = 0 / 2 = 0 for x, and 9 + (-7) = 2 / 2 = 1 for y. Thus the midpoint is (0,1).

For question 12, X1 is -9, Y1 is -4, X2 is 1, and Y2 is 6. Plugging in the values we get:

-9 + 1 = -8 / 2 = -4 for x, and -4 + 6 = 2 / 2 = 1 for y. So the midpoint is (-4,1)

Answer:

Step-by-step explanation:

#11 (first photo): M = (0, 1)

basically, if you just count the units out (like i went from (-3,9) to (0,9) so i went 3 units to the right) and then do the same for the other point (making sure the number of units is equal so you would want to move 3 left) and then draw a line, you can then connect the other 2 points to create 2 triangles and where they intersect is the midpoint.

so in the picture, the bold green line is the original line, the purple line is the line created when you move units for both points, and the blue lines are the lines created when you fill in the blanks to make the triangles

#12 (picture 2): M = (-4, 1)

and the process is the exact same just change it for the points used

Total 36 outcomes are possible on rolling two dices simultaneously

A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment

A dice has 6 possibilities (1,2,3,4,5,6) , thus two when dices thrown together will have 36 outcomes in it's sample space. It's sample space is shown in picture attached below.

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The sum of the square root of -2 and -18 is 4i√2

From the information given,

The sum square root of -2

√-2 + √-18

√-2 = √(-1*2) =  √-1 * √2 = i√2   Note that the square root of -1 = i

√-18 = √(-1*18) =  √-1 * √1`8 = i√18  Note that the square root of -1 = i

But we have that

√18 = √(9*2)

Using surd form. we have

= √9 * √2= 3√2

Then,

√-18 = i√18= i(3√2) = 3i√2

Let's add the sum of square root, we have

√-2 + √-18 = i√2 + 3i√2 = (i + 3i)√2 = 4i√2

Therefore, the sum of the square root of -2 and -18 is 4i√2

The complete question is;

What is the sum of square root of -2 and square root of -18?

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Answer:

Step-by-step explanation:

The domain of an exponential function is all real numbers.

The range of an exponential function that has not been vertically shifted is [tex](0, \infty)[/tex].

The domain of the function is all the real numbers and the range of the function is set of all positive real numbers

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

The domain of the given function is all real numbers. In other words, there are no restrictions on the possible values of x that we can plug into the function.

To see why, note that we can raise any real number to any power, so there are no values of x that are off-limits for this function.

The range of the function is all positive real numbers.

This is because the base of the exponential function is 5, which is positive, and raising 5 to any power results in a positive number. Multiplying a positive number by 3 also results in a positive number, so the function output is always positive.

Hence , we can write the domain and range of the function as:

Domain: all real numbers

Range: y > 0 (all positive real numbers)

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If the radius of the smaller gear is 1.5 inches and the radius of the large gear is 4.5 inches then the bicycles can travel a distance of 62.83 inches.

Given radius of the small gear=1.5 inches and radius of the larger gear=4.5 inches.

Number of rotation of the small gear for each rotation of the larger gear=4.5/1.5=3

Distance which the bicycle can travel=3*2πr.

=3*2*π*10

=60π inches.

Difference in distance travelled=60π inches-40π inches.

=20π inches

put π=3.14

=20*3.14

=62.83 inches.

Hence the distance that the bicycle travels is 62.83 inches if the radius of smaller gear is 1.5 inches and radius of the larger gear is 4.5 inches.

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Question is incomplete as it should includes:

Description about the question that person is travelling through bicycle. That's why radius of gears has been given.

Answer:

Step-by-step explanation:

what-if analysis

What-if analysis is a technique used to determine how the expected performance is affected by changing the assumptions underlying the prediction. Use What-if analysis to compare different scenarios and their possible outcomes based on fluctuating conditions.

What-if analysis allows project managers to identify event options and impacts, as well as change assumptions. When used properly, project managers can make more informed decisions and more accurately predict the outcome of those decisions.

Sensitivity analysis determines how different values ​​of the independent variable affect a particular dependent variable under certain assumptions. In other words, sensitivity analysis examines how the causes of various uncertainties in a mathematical model contribute to the overall uncertainty of the model.

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Answer:

Negative linear relationship

Step-by-step explanation:

the answer is 30 because 3*4=12/2=6 and for the other triangle it is 8*6=48/2 =24 and 24+6=30

The number of dimes is 13.

The system of equation for the situation is as follows;

x + y = 24

0.1x + 0.05y = 1.85

The coins are 24.

Therefore, they are all dimes and nickel.

Total value of the coins is $1.85.

Hence, let

x = number of dimes

y = number of nickels

Therefore,

x + y = 24

0.1x + 0.05y = 1.85

0.1x + 0.1y = 2.4

0.1x + 0.05y = 1.85

0.05y = 0.55

y = 0.55 / 0.05

y = 11

x = 24 - 11

x = 13

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A P-value of 0.0086 is sufficient evidence to refute the manufacturer's claim.

Suppose a particular vehicle gets 50 miles per gallon on the freeway and a simple random sample of 30 cars.

Let μ indicates the average number of miles per gallon of highway for a particular car model

Let [tex]\bar{x}[/tex] indicates the sample mean, σ indicates the population standard deviation and n indicates the sample size.

Given; [tex]\bar{x}[/tex]=49, σ= 2.3 and n = 30,μ₀ = 50

The significance level is α= 5%

Hypotheses: To test the null hypothesis: H₀: μ₀ = 50 Alternative hypothesis: H₁: μ <50

The test statistic can be written as:

[tex]z=\frac{\sqrt{n}(\bar{x}-50)}{\sigma}[/tex]

It follows a standard normal distribution under H₀.

Decision rule / rejection range: P-value <0.05 or because there is a test on the left

z <Ф⁻¹ (0.05) d. H. Z <-1.6449d. H.

[tex]\bar{x}[/tex] < μ₀+(σ÷√n )×-1.6449 = 49.3092725599558

Test statistic: Observations value of the test statistic,

[tex]\begin{aligned}Z_{stat}&=\frac{\sqrt{n}(\bar{x}-50)}{\sigma}\\ Z_{stat}&=\frac{\sqrt{30}(49-50)}{2.3}\\ Z_{stat}&=-2.3814\end[/tex]

critical value = Z critical = Z0.05 = -1.6449

P-value= P(Z < -2.3814)

P-value= P(Z < -2.3814)

P-value= (–2.3814)

P-value= 0.0086

Therefore, p-value = 0.0086 <0.05 and  test statistic observations Zstat critical value  [tex]\nleq[/tex] -1.6449, there is enough evidence to reject the null hypothesis.

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Since the length of the ladder is 40ft, the length of the zip line Z will be 222.47m.

Note that: one has to derive b using the law of sine.

[tex]\frac{b}{sin (15)} = \frac{40}{sin 90}[/tex]

b  = [40  x  Sin (15)] / sin (90)

So:

Sin (15) = √3−1)/(2√2

= 0.2588190451

Then: Sin (90)  = 1

So,  b  = (0.2588190451 *40)/1

= 10.35/1

= 10.35

So one has to also derive for h

= [tex]\frac{b}{sin (15)} = \frac{h}{sin 75}[/tex]

Note that b = 10.35

Hence : h = 10.35 * [(√3 + 1) / 2√2] / [(√3−1)/(2√2)]

h  = 10.35 * 3.73

h = 38.62

Using  simple trigonometric analysis, we can say that:

∠ GJH = 90°; and

∠ GHJ = 10°

Therefore, to obtain Z

Z/ Sin (90) = h/Sin (10)

(Then make Z the subject of the formula)

Thus Z = h * Sin (90)/ Sin (10)

Z = 38.62 * 1/ 0.1736

Z = 222.47m

Therefore, Since the length of the ladder is 40ft, the length of the zip line Z will be 222.47m.

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