Use the tangent to find the unknown side lengths.

Answer:

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Step-by-step explanation:

A={1,2,3,4,5,6}

R={(x,y):y is divisible by x}

We know that any number (x) is divisible by itself.

(x,x)∈R

∴R is reflexive.

Now,(2,4)∈R [as 4 is divisible by 2]

But,(4,2)∈ /

R. [as 2 is not divisible by 4]

∴R is not symmetric.

Let (x,y),(y,z)∈R. Then, y is divisible by x and z is divisible by y.

∴z is divisible by x.

⇒(x,z)∈R

∴R is transitive.

Hence, R is reflexive and transitive but not symmetric.

Answer:

The p-value of the test is 0.1017, which is greater than the standard significance level of 0.05, which means that this is not good evidence that the mean real compensation μ of all CEOs increased that year.

Step-by-step explanation:

At the null hypothesis, we test if there was no increase, that is, the mean is 0, so:

[tex]H_0: \mu = 0[/tex]

At the alternative hypothesis, we test if there was an increase, that is, the mean is greater than 0, so:

[tex]H_1: \mu > 0[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

104 companies, adjusted for inflation, in a recent year. The mean increase in real compensation was x¯=6.9%, and the standard deviation of the increases was s=55%.

This means that [tex]n = 104, X = 6.9, s = 55[/tex]

Value of the test-statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{6.9 - 0}{\frac{55}{\sqrt{104}}}[/tex]

[tex]t = 1.28[/tex]

P-value of the test:

The p-value of the test is a right-tailed test(test if the mean is greater than a value), with 104 - 1 = 103 df and t = 1.28.

Using a t-distribution calculator, this p-value is of 0.1017.

The p-value of the test is 0.1017, which is greater than the standard significance level of 0.05, which means that this is not good evidence that the mean real compensation μ of all CEOs increased that year.

Answer:

Total earning last month with x articles is:

This is same amount as 2000

The equation is:

Solution :

Using the TI-84 PLUS calculator

a). Area : 0.41

μ = 75

σ = 9

InvNorm(0.41,75,9)

= 72.95209525

Therefore, the 41st percentile of the scores is 72.95209525

b).  Area : 0.74

μ = 75

σ = 9

InvNorm(0.74,75,9)

= 80.79010862

Therefore, the 74st percentile of the scores is 80.79010862

c). 8%

So,  Area : 0.92

μ = 75

σ = 9

InvNorm(0.92,75,9)

= 87.64564405

Therefore, X =  80.79010862

Answer:

The actual dimensions of the floor are 12,5m by 1,8m.

Step-by-step explanation:

Scale problems are solved by proportions, using a rule of three.

Scale of 1:50

This means that each cm on the cupboard has a real dimension of 50 cm

25 cm on the cupboard:

So the real dimension is:

25*50 = 1250 cm = 12,5m

3.6 cm

The real dimension is:

3.6*50 = 160 cm = 1,8 m

The actual dimensions of the floor are 12,5m by 1,8m.

Answer:

It should be the top right one

(with 6ft as the height)

Step-by-step explanation:

Answer:

It must be the lower to the left choice.

Step-by-step explanation:

As you can see, the net we have is composed of only triangles.

So we should be choosing a figure with a triangular base.

Our answers are narrowed down into the top right and lower left choices because both figures have triangular bases.

The other person down there chose the top right choice and was incorrect, so the answer should be the lower to the left figure.

Also, its the lower left figure because look at the triangular base, it is an isosceles meaning that two sides have the same length.

If the net says that the long side measures 9 ft, then the other two sides should be the same length and shorter than 9 ft. So the answer is the lower left figure.

Hope this helps

Step-by-step explanation:

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Answer:

2x + 3y -3=0

Step-by-step explanation:

The given equation of the line is ,

[tex]\implies 2x - 3y = 13 [/tex]

Now convert it into slope intercept form to get the slope , we get ,

[tex]\implies 3y = 2x - 13 \\\\\implies y =\dfrac{2}{3}x -\dfrac{13}{2}[/tex]

Therefore the slope is ,

[tex]\implies m = \dfrac{2}{3} [/tex]

We know that the product of slope of perpendicular lines is -1 . Therefore the slope of the perpendicular line will be ,

[tex]\implies m_{perpendicular}= -\dfrac{2}{3} [/tex]

Now one of the point is (-6,5) .On Using point slope form , we have ,

[tex]\implies y-y_1 = m( x - x_1) \\\\\implies y - 5 = -\dfrac{2}{3}( x + 6 ) \\\\\implies 3y - 15 = -2x -12

\\\\\implies 2x + 3y -15+12=0 \\\\\implies \underline{\underline{ 2x + 3y -3=0 }}[/tex]

Answer:

y = - [tex]\frac{3}{2}[/tex]x - 4

Step-by-step explanation:

2x – 3y = 13

3y = 2x + 13

y = [tex]\frac{2}{3}[/tex]x + [tex]\frac{13}{3}[/tex]

slope = 2/3

negative reciprocal = -3/2

y = -3/2x + b

(-6, 5)

5 = (-3/2)(-6) + b

5 = 9 + b

b = -4

y = -3/2x - 4

Answer:

the probability that we hit the bullseye at least 100 times is 0.0113

Step-by-step explanation:

Given the data in the question;

Binomial distribution

We find the probability of hitting the dart on the disk

⇒ Area of small disk / Area of bigger disk

⇒ πR₁² / πR₂²

given that; disk-shaped board of radius R² = 5, disk-shaped bullseye with radius R₁ = 1

so we substitute

⇒ π(1)² / π(5)² = π/π25 = 1/25 = 0.04

Since we have to hit the disk 2000 times, we represent the number of times the smaller disk ( BULLSEYE ) will be hit by X.

so

X ~ Bin( 2000, 0.04 )

n = 2000

p = 0.04

np = 2000 × 0.04 = 80

Using central limit theorem;

X ~ N( np, np( 1 - p ) )

we substitute

X ~ N( 80, 80( 1 - 0.04 ) )

X ~ N( 80, 80( 0.96 ) )

X ~ N( 80, 76.8 )

So, the probability that we hit the bullseye at least 100 times, P( X ≥ 100 ) will be;

we covert to standard normal variable

⇒ P( X ≥  [tex]\frac{100-80}{\sqrt{76.8} }[/tex] )

⇒ P( X ≥ 2.28217 )

From standard normal distribution table

P( X ≥ 2.28217 ) = 0.0113

Therefore, the probability that we hit the bullseye at least 100 times is 0.0113

I can't see the diagram sorry.

Step-by-step explanation:

Is there supposed to be a picture attached?

Answer:

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Answer:

cf

=41

5 f-46

Step-by-step explanation:

thiis is the answer

Answer:

To find the inverse, switch the y(F(C)) and the x(C) variables.

So this function:

[tex]y=\frac{9}{5}x+32 \\[/tex]

Will become this function:

[tex]x=\frac{9}{5}y+32 \\[/tex]

You will then solve for y:

[tex]x=\frac{9}{5}y+32 \\x-32=\frac{9}{5}y\\5(x-32)=5(\frac{9}{5}y)\\5x-160=9y\\y=\frac{5x-160}{9}\\y=\frac{5x}{9}-\frac{160}{9}[/tex]

Substitute in the variables of this problem:

[tex]C(F)=\frac{5C}{9}-\frac{160}{9}[/tex]

Answer: This problem is a fraction since we have several equal parts that make up one whole. The problem asks us to talk about the relationship of white pieces to the whole. Since we know the whole is made up of 7 pieces (4 blue parts and 3 white parts = 7 total parts), then 7 will be our denominator (number on the bottom of the fraction).

Now that we have our number on the bottom, we need to look back at the question to carefully decide what parts of the whole we are looking at. The question wants to know how many of the parts are white. We know that 3 of the parts are white, so that is our numerator (number of the top of the fraction).

Our final answer is 3/7 or "three-sevenths." Said another way, three of the seven pieces are white.

Step-by-step explanation:

Answer:

Translation

Step-by-step explanation:

A translation is when the triangle is moved around on the graph without it being reflected or changed in any way. I will be the same exact triangle, just with different coordinates.

Hope this helps!

Answer:

The alternative hypothesis is [tex]H_1: \mu_M - \mu_W \neq 0[/tex], considering M for men and W for women.

Step-by-step explanation:

He uses the data to conduct a hypothesis test to determine if the mean percent of expenditures that goes toward housing (including fuel and light) is different for men and women.

At the null hypothesis, we test if there is not difference, that is, the difference of the mean is 0, so:

[tex]H_0: \mu_M - \mu_W = 0[/tex]

At the alternative hypothesis, we test if there is a difference, that is, the difference of the means is different of 0, so:

[tex]H_1: \mu_M - \mu_W \neq 0[/tex]

Answer:

5,5,6,6,13

Step-by-step explanation:

Mode means most often.  The 5 numbers has 2 modes 5 and 6

This means that 4 of the numbers must be 5,5,6,6

Median means the middle number must be 6

5,5,6,6,x is the only way to to get the middle number to be 6

We need to average to 7

(5+5+6+6+x) /5 = 7

(5+5+6+6+x) /5  *5= 7*5

(5+5+6+6+x) =35

22+x = 35

x = 35-22

x = 13

The other number is 13

The sample statistic that must have changed after the correction was made is mean. Because mean is based on all the observation in the data. So changing any value in the data will impact mean.

Changing the highest salary in the data will have no impact on median because median lies at the center of data.

Changing the highest salary in the data will have no impact on mode because mode is the most frequently occurring value in the data.

Changing the highest salary in the data will have no impact on minimum because minimum is the smallest value in the data.

Hence the only statistic which will change is mean.

Answer: A-Mean

Step-by-step explanation:

A.) Mean

B.) Median

C.)  Mode

D.)  Minimum

Answer:

$36.5 money ms.weaver spent for the items

Answer:

1/4 = x

Step-by-step explanation:

x - 2( 3x - 1 ) = 3x

Step 1 :- Distribute 2

x - 2 × 3x - 2 × 1 = 3x

x - 6x + 2 = 3x

Step 2:- Combine like terms

-5x + 2 = 3x

Step 3 :- Add 5x to both sides

-5x + 5x + 2 = 3x + 5x

2 = 8x

Step 4 :- Divide both side by 8

2/8 = 8x / 8

1/4 = x

Answer:

a) 0.15 / 0.09

b) 0.15 / 1

c) 0.15 / 0.23

Answer:

Hence the value of p is 0.04746.

Step-by-step explanation:

The test statistic is

[tex]Z=(\bar x-\mu)/(s/vn)\\\\=(355-390)/(115/ \sqrt(30))\\\\=-1.667[/tex]

The p-value= P(Z<-1.67) =0.04746. (from standard distribution table)

Therefore p-value =0.04746.

9514 1404 393

Answer:

  x = 30 2/3

Step-by-step explanation:

Angles 4 and 5 are complementary, so we have ...

  m∠4 +m∠5 = 90°

  (2x +4) +(x -6) = 90

  3x -2 = 90 . . . . . . . . . collect terms

  3x = 92 . . . . . . . . . . add 2; next, divide by 3

  x = 92/3 = 30 2/3

Answer:

Pvalue = 0.1505

y = 0.550x1 + 3.600x2 + 7.300

Step-by-step explanation:

Given the data :

Study Hours GPA ACT Score

5 4 27

5 2 18

5 3 18

1 3 20

2 4 21

Using technology, the Pvalue obtained using the Fratio :

F = MSregression / MSresidual = 30.228571/ 8.190476 = 3.69

The Pvalue for the regression equation is:

Using the Pvalue from Fratio calculator :

F(1, 3), 3.69 = 0.1505

Using the Pvalue approach :

At α = 0.01

Pvalue > α ; Hence, we fail to reject H0 and conclude that ; There is not enough evidence to show that the relationship is statistically significant.

The regression equation :

y = A1x1 + A2x2 +... AnXn

y = 0.550x1 + 3.600x2 + 7.300

x1 and x2 are the predictor variables ;

y = predicted variable

Answer:

No it is not since there is 15 defectice parts in 2machines and there is 8 broken parts in the one machine

Hope This Helps!!!

Answer:

Step-by-step explanation:

(x+3)(x+1)=1

x²+3x+x+3=1

x²+4x+2=0

x²+4x+4=-2+4

(x+2)²=2

x+2=±√2

x=2+√2

and x=2-√2

so x≠-3

and x≠-1

Answer:

14.077 feet to the nearest thousandth.

Step-by-step explanation:

First let's work out the multiplier:

6 + 5 + 2 = 13.

61/2 = 30.5

- so the multiplier is 30.5/13 = 2.34615

The longest piece refers to the 6 in the ratio its length

= 6 * 2.34615

= 14.0769 ft.

9514 1404 393

Answer:

  x = 7

Step-by-step explanation:

Vertical angles have the same measure, so ...

  m∠A = m∠B

  (5x -9)° = (8x -30)°

  21 = 3x . . . . . . . . . divide by °, add 30-5x

  7 = x . . . . . . . . . . divide by 3

Answer:

$370,881

Step-by-step explanation:

firstly we we multiply 1,5% by 2yrs. the answer we get is 3,0%. we then multiply 3 % by $123,627 and get $370,881

If Lisa bought a house The value of the house increased by 1.5% each year for 2 years.  The value of the house was £123,627. The initial amount of the house is  95120.7.

Percentage, a relative value indicating hundredth parts of any quantity.

Given,

Lisa bought a house The value of the house increased by 1.5% each year for 2 years

By the end of 2 years, the value of the house was £123,627.

A=P(1+rt)

A is the final amount,

r is rate of interest

t is the time

P is principle amount.

123,627=P(1+1.5/100 (2))

123657=P(1+0.15(2))

123657=P(1+0.3)

123657=1.3P

Divide both sides by 1.3

P=95120.7

The initial amount of the house when Lisa bought is 95120.7

To learn more on Percentage click:

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Answer:

La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].

Step-by-step explanation:

Considerando que se tratan de dos matrices de igual dimensión y cuyos elementos son números reales, conocemos que la adición entre dos matrices consiste en las sumas de los elementos de igual posición, esto es, los elementos que están localizados en las mismas filas y columnas, entonces, la suma es:

[tex]\vec A = \left[\begin{array}{cc}1&2\\-1&0\end{array} \right][/tex], [tex]\vec B = \left[\begin{array}{cc}-2&9\\3&5\end{array}\right][/tex]

[tex]\vec U = \vec A + \vec B = \left[\begin{array}{cc}1 + (-2)&2+9\\-1 + 3&0 + 5\end{array}\right][/tex]

[tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex]

La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].