Tammie wondered how her friends felt about their cell phone service. She randomly selected 10 of her friends who used company A and another 10 of her friends who used company B and asked if they felt their service was​ excellent, good,​ fair, or poor. Why should Tammie not use the​ chi-square test?

Answer:

Parents = 36

Sudents = 31

Step-by-step explanation:

x + y = 67............ (1)

x = 67 - y

2.75x + 3.25y = 202.25

2.75 (67-y) + 3.25y = 202.25

184.25 - 2 75y + 3.25y = 202.25

0.5y = 18

y = 36

From (1)

x + 36 = 67

x = 67-36 = 31

Answer:

The theoretical probability is smaller than the relative frequency

Step-by-step explanation:

6-sided cube rolled 200 times

Probability of an even number is 1/2= 0.5

200*1/2= 100- theoretical probability

Experimental frequency= 115

Relative frequency= 115/200= 0.575

0.575 > 0.5

The theoretical probability is smaller than the relative frequency

Answer:

The theoretical probability is smaller than the relative frequency.

Step-by-step explanation:

Answer:

8x-7y

Step-by-step explanation:

(–2y – x) – (5y – 9x)

Distribute the minus sign

-2y -x -5y +9x

Combine like terms

-x +9x - 2y -5y

8x-7y

Answer:

[tex]8x-7[/tex]

Step-by-step explanation:

[tex](-2y - x) - (5y - 9x)[/tex]

Distribute the negative sign.

[tex](-2y - x)-5y+9x[/tex]

[tex]-2y - x-5y+9x[/tex]

[tex]-2y -5y+9x- x[/tex]

Add or subtract like terms.

[tex]-7y+8x[/tex]

Answer:

Year 7 = 75 students

Year 9 = 25 students

Step-by-step explanation:

Year 7 has 3/8 of the total since the circle is divided into 8 sections and has 3 of the 8 sections

3/8 * 200 students = 75

Year 9 has 1/8 of the total since the circle is divided into 8 sections and has 1 of the 8 sections

1/8 * 200 =25

Answer:

C.6x³-33x² + 45x-6

Step-by-step explanation:

(3x-6)(2x^2-7x+1)

= 3x(2x² - 21x +1) -6(2x² - 7x+1)

= (6x³ - 21x² + 3x) - (12x² - 42x+6)

= 6x³ - 21x² + 3x -12x² + 42x -6

= 6x³-33x² + 45x-6

Answer:

x = -2

y = -5

Step-by-step explanation:

We can solve this algebraically (substitution or elimination) or graphically. I will be using elimination:

Step 1: Add the 2 equations together

-8y = 40

y = -5

Step 2: Plug y into an original equation to find x

-3(-5) + 10x = -5

15 + 10x = -5

10x = -20

x = -2

And we have our final answers!

Answer:

[tex]\boxed{\sf \ \ \ x=-2 \ \ \ and \ \ \ y=-5 \ \ \ }[/tex]

Step-by-step explanation:

let s solve the following system

(1) -5y-10x=45

(2) -3y+10x=-5

let s do (1) + (2) it comes

-5y-10x-3y+10x=45-5=40

<=>

-8y=40

<=>

y = -40/8=-20/4=-5

so y = -5

let s replace y in (1)

25-10x=45

<=>

10x=25-45=-20

<=>

x = -20/10=-2

so x = -2

Answer:

[tex] 1 \frac{1}{24} [/tex]

Step-by-step explanation:

[tex] \frac{5}{6} + \frac{1}{3} . \frac{5}{8} \\ \\ = \frac{5}{6} + \frac{5}{24} \\ \\ = \frac{5 \times 4}{6 \times 4} + \frac{5 }{24} \\ \\ = \frac{20}{24} + \frac{5 }{24} \\ \\ = \frac{20 + 5}{24} \\ \\ = \frac{25}{24} \\ \\ = 1 \frac{1}{24} \\ [/tex]

Answer:

Step-by-step explanation:

z = (X - μ) / σ, where X = date, μ = mean, σ = standard deviation

z = (28.9 - 18.1) / 3.7

z = 18.6

0.06681 is the area for this z.

6.681% shall be shorter than 18.6 inches.

Answer:

The approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

Step-by-step explanation:

The equation of the parabola is:

[tex]y=0.00035x^{2}[/tex]

Compute the first order derivative of y as follows:

 [tex]y=0.00035x^{2}[/tex]

[tex]\frac{\text{d}y}{\text{dx}}=\frac{\text{d}}{\text{dx}}[0.00035x^{2}][/tex]

    [tex]=2\cdot 0.00035x\\\\=0.0007x[/tex]

Now, it is provided that |x | ≤ 605.

⇒ -605 ≤ x ≤ 605

Compute the arc length as follows:

[tex]\text{Arc Length}=\int\limits^{x}_{-x} {1+(\frac{\text{dy}}{\text{dx}})^{2}} \, dx[/tex]

                  [tex]=\int\limits^{605}_{-605} {\sqrt{1+(0.0007x)^{2}}} \, dx \\\\={\displaystyle\int\limits^{605}_{-605}}\sqrt{\dfrac{49x^2}{100000000}+1}\,\mathrm{d}x\\\\={\dfrac{1}{10000}}}{\displaystyle\int\limits^{605}_{-605}}\sqrt{49x^2+100000000}\,\mathrm{d}x\\\\[/tex]

Now, let

[tex]x=\dfrac{10000\tan\left(u\right)}{7}\\\\\Rightarrow u=\arctan\left(\dfrac{7x}{10000}\right)\\\\\Rightarrow \mathrm{d}x=\dfrac{10000\sec^2\left(u\right)}{7}\,\mathrm{d}u[/tex]

[tex]\int dx={\displaystyle\int\limits}\dfrac{10000\sec^2\left(u\right)\sqrt{100000000\tan^2\left(u\right)+100000000}}{7}\,\mathrm{d}u[/tex]

                  [tex]={\dfrac{100000000}{7}}}{\displaystyle\int}\sec^3\left(u\right)\,\mathrm{d}u\\\\=\dfrac{50000000\ln\left(\tan\left(u\right)+\sec\left(u\right)\right)}{7}+\dfrac{50000000\sec\left(u\right)\tan\left(u\right)}{7}\\\\=\dfrac{50000000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+5000x\sqrt{\dfrac{49x^2}{100000000}+1}[/tex]

Plug in the solved integrals in Arc Length and solve as follows:

[tex]\text{Arc Length}=\dfrac{5000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+\dfrac{x\sqrt{\frac{49x^2}{100000000}+1}}{2}|_{limits^{605}_{-605}}\\\\[/tex]

                  [tex]=1245.253707795227\\\\\approx 1245.25[/tex]

Thus, the approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

Answer:

We conclude that this is an unusually high number of faulty modems.

Step-by-step explanation:

We are given that while conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems.

The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013.

Let p = population proportion.

So, Null Hypothesis, [tex]H_0[/tex] : p = 0.013      {means that this is an unusually 0.013 proportion of faulty modems}

Alternate Hypothesis, [tex]H_A[/tex] : p > 0.013      {means that this is an unusually high number of faulty modems}

The test statistics that would be used here One-sample z-test for proportions;

                             T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~  N(0,1)

where, [tex]\hat p[/tex] = sample proportion faulty modems= [tex]\frac{10}{367}[/tex] = 0.027

           n = sample of modems = 367

So, the test statistics  =  [tex]\frac{0.027-0.013}{\sqrt{\frac{0.013(1-0.013)}{367} } }[/tex]

                                     =  2.367

The value of z-test statistics is 2.367.

Since, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since our test statistics is more than the critical value of z as 2.367 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that this is an unusually high number of faulty modems.

Answer:

  1.896

Step-by-step explanation:

You can answer this just using your number sense.

  [tex]\log_7{(40)}\approx 1.896[/tex]

You know that 49 = 7², so log₇(49) = 2. The log function has a fairly small slope, so log₇(40) will not be far from 2.

_____

If you want to use your calculator, you can use the "change of base formula".

  log₇(49) = log(49)/log(7) ≈ 1.602060/0.845098 ≈ 1.896

Answer:

47.25 pounds

Step-by-step explanation:

[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex]

First, we determine the Rate In

Rate In=(concentration of salt in inflow)(input rate of brine)

[tex]=(0.5\frac{lbs}{gal})( 6\frac{gal}{min})\\R_{in}=3\frac{lbs}{min}[/tex]

Change In Volume of the tank, [tex]\frac{dV}{dt}=6\frac{gal}{min}-4\frac{gal}{min}=2\frac{gal}{min}[/tex]

Therefore, after t minutes, the volume of fluid in the tank will be: 100+2t

Rate Out

Rate Out=(concentration of salt in outflow)(output rate of brine)

[tex]R_{out}=(\frac{A(t)}{100+2t})( 4\frac{gal}{min})\\\\R_{out}=\frac{4A(t)}{100+2t}[/tex]

Therefore:

[tex]\dfrac{dA}{dt}=3-\dfrac{4A(t)}{100+2t}\\\\\dfrac{dA}{dt}=3-\dfrac{4A(t)}{2(50+t)}\\\\\dfrac{dA}{dt}=3-\dfrac{2A(t)}{50+t}\\\\\dfrac{dA}{dt}+\dfrac{2A(t)}{50+t}=3[/tex]

This is a linear differential equation in standard form, therefore the integrating factor:

[tex]e^{\int \frac{2}{50+t}dt}=e^{2\ln|50+t|}=e^{\ln(50+t)^2}=(50+t)^2[/tex]

Multiplying the DE by the integrating factor, we have:

[tex](50+t)^2\dfrac{dA}{dt}+(50+t)^2\dfrac{2A(t)}{50+t}=3(50+t)^2\\\{(50+t)^2A(t)\}'=3(50+t)^2\\$Taking the integral of both sides\\\int \{(50+t)^2A(t)\}'= \int 3(50+t)^2\\(50+t)^2A(t)=(50+t)^3+C $ (C a constant of integration)\\Therefore:\\A(t)=(50+t)+C(50+t)^{-2}[/tex]

Initially, 20 pounds of salt was dissolved in the tank, therefore: A(0)=20

[tex]20=(50+0)+C(50+0)^{-2}\\20-50=C(50)^{-2}\\C=-\dfrac{30}{(50)^{-2}} =-30X50^2=-75000[/tex]

Therefore, the amount of salt in the tank at any time t is:

[tex]A(t)=(50+t)-75000(50+t)^{-2}[/tex]

After 15 minutes, the amount of salt in the tank is:

[tex]A(15)=(50+15)-75000(50+15)^{-2}\\=47.25$ pounds[/tex]

Following are the solution to the given question:

Using formula:

[tex]\to \frac{dA}{dt} =R_{in}-R_{out}\\\\[/tex]

Find:

[tex]\to R_{in}\ and \ R_{out}\ =? \\\\[/tex]

Solution:

[tex]\to R_{ in} = \text{(concentration of salt in inflow)}[/tex][tex]\times \text{(i\1nput rate of brine)}\\[/tex]

[tex]\therefore\\ R_{in} = (\frac{1}{2}\frac{lb}{gal})\cdot (3\frac{gal}{min}) = 3\frac{lb}{min}\\[/tex]

Since in this question the solution is pumped out at a slower rate, therefore the water amount in the tank accumulates at the rate of[tex](6- 4) = 2 \ \frac{gal}{min} Thus,[/tex]

after t minutes there will be [tex]100+ 2t[/tex]gallons in the tank.

[tex]\because R_{out}=\text{(concentration of salt in outflow)}\cdot \text{(o\1utput rate of brine)}[/tex]

[tex]\therefore R_{out} =\frac{A(t)}{100+2t} \frac{lb}{gal} \cdot (4\frac{gal}{min})= \frac{4A(t)}{100+2t}\ \frac{lb}{min}[/tex]

Now, we substitute these results in the DE to get

[tex]\to \frac{dA}{dt}=3-\frac{4A(t)}{100+2t}\\\\\to \frac{dA}{dt}= 3 -\frac{2A(t)}{50+t} \\\\\to \frac{dA}{dt}+\frac{2}{50+t}\ A(t) -3\\\\[/tex]

Which is a linear DE in the standard form Thus, the integrating factor is

[tex]e ^{\frac{2}{ 50+t} \ dt} + e^{2\ln|(50+t)|} =e^{\ln(50 + t)^2}=(50+t)^2[/tex]

Multiplying the DE by integrated factor:

[tex](50+t)^2 \frac{dA}{dt} +2(50 + t) A(t) = 3(50 +t)^2\\\\ \therefore \frac{d}{dt}(50+t)^2 \frac{dA}{dt}-3(50+t)^2\\\\\therefore (50+t)^2\ A(t) -3(50+t)^2 \ dt \\\\\therefore (50+t)^2\ A(t) -\frac{3}{3}(50+t)^3 + c \\\\\therefore \ A(t) -(50+t) + c(50+t)^{-2} \\\\[/tex]

Now, applying the initial condition [tex]A(0) = 20[/tex]to get

[tex]\to 20 = (50) +\frac{c}{2500}\\\\\to 20 - 50=\frac{c}{2500}\\\\[/tex]

[tex]\therefore \\\\\to \frac{c}{2500} = -30\\\\ \to c= -30 \times 2500 \\\\\ \to c= -75000\\\\[/tex]

Now, substitute by this result in the solution to get

[tex]\to A(t) = (50 +t) - \frac{-75000}{(50 +t)^2}[/tex]

Now, after 15 minutes we find that

[tex]\to A(30) = 50 + 15-\frac{-75000}{(50+15)^2 } = 65+\frac{75000}{65^2} \\\\[/tex]

therefore

[tex]\to A(30)=65 +\frac{75000}{4225} \\\\[/tex]

            [tex]=65 +\frac{15000}{845} \\\\ =65+\frac{3000}{169}\\\\= 65+17.75 \\\\= 82.75 \ \frac{lb}{gal} \\\\[/tex]

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Answer:

Correct statement: "the number is divisible by 3".

Step-by-step explanation:

The statement provided is:

When a number is divisible by 9, the number is divisible by 3.

The general form of a conditional statement in if-then form is:

[tex]p\rightarrow q[/tex]

This implies that if p, then q.

The part after the "if" is known as the hypothesis and the part after the "then" is known as the conclusion.

The if-then form of the provided statement is:

If a number is divisible by 9, then the number is divisible by 3.

So, the conclusion is:

"the number is divisible by 3"

Answer:

a

Step-by-step explanation:

Answer:

f=10

Step-by-step explanation:

I don't know a formula for this but I can see that <CRE is a 90° angle so 7f+2f=90 and if f=10 7f=70 and 2f=20 which fits

The measure of angle of each is 70° and 20°.

Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.

Angles are usually measured in degrees or radians.

The given angles are complementary.

That is, ∠CRE is complementary, which means the angle is 90 degrees.

∠CRT + ∠TRE = 90°

(7f)° + (2f)° = 90°

9f = 90°

f = 90 / 9

f = 10

Hence ∠CRT = (7f)° = 70°

∠TRE = (2f)° = 20°

Hence the measure of each of the angle is 70° and 20°.

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Answer:

Check below, please

Step-by-step explanation:

Hello!

1) In the Newton Method, we'll stop our approximations till the value gets repeated. Like this

[tex]x_{1}=2\\x_{2}=2-\frac{f(2)}{f'(2)}=2.5\\x_{3}=2.5-\frac{f(2.5)}{f'(2.5)}\approx 2.4166\\x_{4}=2.4166-\frac{f(2.4166)}{f'(2.4166)}\approx 2.41421\\x_{5}=2.41421-\frac{f(2.41421)}{f'(2.41421)}\approx \mathbf{2.41421}[/tex]

2)  Looking at the graph, let's pick -1.2 and 3.2 as our approximations since it is a quadratic function. Passing through theses points -1.2 and 3.2 there are tangent lines that can be traced, which are the starting point to get to the roots.

We can rewrite it as: [tex]x^2-2x-4=0[/tex]

[tex]x_{1}=-1.1\\x_{2}=-1.1-\frac{f(-1.1)}{f'(-1.1)}=-1.24047\\x_{3}=-1.24047-\frac{f(1.24047)}{f'(1.24047)}\approx -1.23607\\x_{4}=-1.23607-\frac{f(-1.23607)}{f'(-1.23607)}\approx -1.23606\\x_{5}=-1.23606-\frac{f(-1.23606)}{f'(-1.23606)}\approx \mathbf{-1.23606}[/tex]

As for

[tex]x_{1}=3.2\\x_{2}=3.2-\frac{f(3.2)}{f'(3.2)}=3.23636\\x_{3}=3.23636-\frac{f(3.23636)}{f'(3.23636)}\approx 3.23606\\x_{4}=3.23606-\frac{f(3.23606)}{f'(3.23606)}\approx \mathbf{3.23606}\\[/tex]

3) Rewriting and calculating its derivative. Remember to do it, in radians.

[tex]5\cos(x)-x-1=0 \:and f'(x)=-5\sin(x)-1[/tex]

[tex]x_{1}=1\\x_{2}=1-\frac{f(1)}{f'(1)}=1.13471\\x_{3}=1.13471-\frac{f(1.13471)}{f'(1.13471)}\approx 1.13060\\x_{4}=1.13060-\frac{f(1.13060)}{f'(1.13060)}\approx 1.13059\\x_{5}= 1.13059-\frac{f( 1.13059)}{f'( 1.13059)}\approx \mathbf{ 1.13059}[/tex]

For the second root, let's try -1.5

[tex]x_{1}=-1.5\\x_{2}=-1.5-\frac{f(-1.5)}{f'(-1.5)}=-1.71409\\x_{3}=-1.71409-\frac{f(-1.71409)}{f'(-1.71409)}\approx -1.71410\\x_{4}=-1.71410-\frac{f(-1.71410)}{f'(-1.71410)}\approx \mathbf{-1.71410}\\[/tex]

For x=-3.9, last root.

[tex]x_{1}=-3.9\\x_{2}=-3.9-\frac{f(-3.9)}{f'(-3.9)}=-4.06438\\x_{3}=-4.06438-\frac{f(-4.06438)}{f'(-4.06438)}\approx -4.05507\\x_{4}=-4.05507-\frac{f(-4.05507)}{f'(-4.05507)}\approx \mathbf{-4.05507}\\[/tex]

5) In this case, let's make a little adjustment on the Newton formula to find critical numbers. Remember their relation with 1st and 2nd derivatives.

[tex]x_{n+1}=x_{n}-\frac{f'(n)}{f''(n)}[/tex]

[tex]f(x)=x^6-x^4+3x^3-2x[/tex]

[tex]\mathbf{f'(x)=6x^5-4x^3+9x^2-2}[/tex]

[tex]\mathbf{f''(x)=30x^4-12x^2+18x}[/tex]

For -1.2

[tex]x_{1}=-1.2\\x_{2}=-1.2-\frac{f'(-1.2)}{f''(-1.2)}=-1.32611\\x_{3}=-1.32611-\frac{f'(-1.32611)}{f''(-1.32611)}\approx -1.29575\\x_{4}=-1.29575-\frac{f'(-1.29575)}{f''(-4.05507)}\approx -1.29325\\x_{5}= -1.29325-\frac{f'( -1.29325)}{f''( -1.29325)}\approx -1.29322\\x_{6}= -1.29322-\frac{f'( -1.29322)}{f''( -1.29322)}\approx \mathbf{-1.29322}\\[/tex]

For x=0.4

[tex]x_{1}=0.4\\x_{2}=0.4\frac{f'(0.4)}{f''(0.4)}=0.52476\\x_{3}=0.52476-\frac{f'(0.52476)}{f''(0.52476)}\approx 0.50823\\x_{4}=0.50823-\frac{f'(0.50823)}{f''(0.50823)}\approx 0.50785\\x_{5}= 0.50785-\frac{f'(0.50785)}{f''(0.50785)}\approx \mathbf{0.50785}\\[/tex]

and for x=-0.4

[tex]x_{1}=-0.4\\x_{2}=-0.4\frac{f'(-0.4)}{f''(-0.4)}=-0.44375\\x_{3}=-0.44375-\frac{f'(-0.44375)}{f''(-0.44375)}\approx -0.44173\\x_{4}=-0.44173-\frac{f'(-0.44173)}{f''(-0.44173)}\approx \mathbf{-0.44173}\\[/tex]

These roots (in bold) are the critical numbers

Answer:

It may look simple to the owner because he is not the one losing a job. For the three machinists it represents a major event with major consequences

Answer:

54

Step-by-step explanation:

The pink parts are 9 out of total 11 parts.

9/11

Multiply with 66.

9/11 × 66

= 54

Hey there! :)

Answer:

P(Pink) = 54.

Step-by-step explanation:

Begin by calculating the possibility of the spinner landing on pink:

[tex]P(pink) = \frac{pink}{total}[/tex]

Therefore:

[tex]P(Pink) = \frac{9}{11}[/tex]

In this question, the spinner was spun 66 times. Since we have solved for the probability, we can set up ratios to find the probability of the spinner landing on pink out of 66.

[tex]\frac{9}{11}= \frac{x}{66}[/tex]

Cross multiply:

594 = 11x

Divide both sides by 11:

x = 54.

P(Pink) = 54.

Answer:

y= -5/2

x -7

x+2y=4

Step-by-step explanation:

Answer:

c. x > 7 / 5 or x < 1 / 5

Step-by-step explanation:

2 | 5x − 4 | > 6

| 5x - 4 | > 3

So combining the 2 above we get:

Correct choice is c.

Answer:

x>7/5                 or            x <1/5

Step-by-step explanation:

2 | 5x − 4 | > 6

Divide by 2

2/2 | 5x − 4 | > 6/2

 | 5x − 4 | > 3

There are two solutions one positive and one negative ( the negative flips the inequality)

5x-4 >3      or         5x-4 < -3

Add 4 to each side

5x-4 +4>3+4   or              5x-4+4 < -3+4

5x >7                  or            5x <1

Divide by 5

x>7/5                 or            x <1/5

Answer:  Measure of angle T = 25 degrees and Measure of angle U = 45 degrees

Step-by-step explanation:

Measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.

" Triangles are said to be congruent if the corresponding sides and angles of the one triangle are equals to the other triangles."

According to the question,

In triangle KLM,

KM =27millimeters

LM = 20millimeters

KL = 12 millimeters

∠K= 45degrees

∠M= 25 degrees

∠L = 110degrees

From the given measurements of the triangle we have,

side with measure 27millimeters is opposite to angle 110° .

side with measure 12millimeters is opposite to angle 25° .

side with measure 20millimeters is opposite to angle 45°.

From the conditions in triangle TUV to be congruent to triangle KLM ,

Measure of angle T = 25 degrees and TU = 12  is against the given condition of congruent triangle.

As angle T and side TU are adjacent to each other, which is against the correspondence of the given triangle.

Hence, measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.

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Answer:

c- the right triangle altitude theorem

Step-by-step explanation:

i did it on edge! ; )

The missing statement in Step 6 is ,c- The right triangle altitude theorem.

We have given that,

In △ABC, AD ⊥ BC

Prove: StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction.

Triangle A B C is shown.

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two-line segments it creates on the hypotenuse

Therefore we have,

A perpendicular bisector is drawn from point A to point D on side C B forming a right angle.

The length of A D is h, the length of C B is a, the length of C A is b, and the length of A B is c.

So the missing statement in Step 6

b = c

c=The right triangle altitude theorem.

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Answer:

25%

Step-by-step explanation:

less than 30 is from minimum to lower quartile. so, 25%

Answer:

  (x, y) = (7, 4) meters

Step-by-step explanation:

The area of the floor without the removal is x^2, so with the smaller square removed, it is x^2 -y^2.

The perimeter of the floor is the sum of all side lengths, so is 4x +2y.

The given dimensions tell us ...

  x^2 -y^2 = 33

  4x +2y = 36

From the latter equation, we can write an expression for y:

  y = 18 -2x

Substituting this into the first equation gives ...

  x^2 -(18 -2x)^2 = 33

  x^2 -(324 -72x +4x^2) = 33

  3x^2 -72x + 357 = 0 . . . . write in standard form

  3(x -7)(x -17) = 0 . . . . . factor

Solutions to this equation are x=7 and x=17. However, for y > 0, we must have x < 9.

  y = 18 -2(7) = 4

The floor dimension x is 7 meters; the inset dimension y is 4 meters.

Answer:

You didn't state it but you need to find Angle A.

From the Pythagorean Theorem, we calculate side ac

side ac^2 = 5^2 - 3^2  =25 -9 = 16 Side AC = 4

arc tangent angle A = 3 / 4 = .75

angle A =  36.87 Degrees

Step-by-step explanation:

Answer:

tan∅ = -1517/817

Step-by-step explanation:

tan∅ = sin∅/cos∅

Answer:

Step-by-step explanation:

Answer:

The sequence can be represented by the formula of its nth term:

[tex]a_n=\frac{(-1)^n}{n}[/tex]

Step-by-step explanation:

Notice that we are in the presence of an alternate sequence (the values alternate from negative to positive. Therefore we need to take into account that there should be a factor "-1" raised to the "n" value for the sequence. Also, given that the sequence looks in absolute value like the harmonic sequence, we conclude upon the following general form for the "nth" term of the sequence:

[tex]a_n=\frac{(-1)^n}{n}[/tex]

Answer:

50 to 60 seconds is the answer

Answer:

34

Step-by-step explanation:

F(x) = 2x^3 - 7x + 1

Let x= 3

F(3) = 2* 3^3 - 7*3 + 1

      = 2 * 27 -21+1

      = 54 -21 + 1

      = 34

Answer: 34

Step-by-step explanation:

Answer:

Step-by-step explanation:

The most expensive ticket is the adult ticket, so we'll use "a" to represent the number of those sold. Then (299-a) student tickets were sold, and total revenue was ...

  4a +1(299-a) = 587

  3a = 288

  a = 96

96 adult tickets and 203 student tickets were sold.

Answer: 4h4hj4h44 n4

Step-by-step explanation: b4jb4j 4 n4