According to this diagram, what is sin 28°?
62
17
00
289
90°
15
A.
15
17.
B.
17
15
c.
17
D. 8
17
E. 15
8

Answer:

90% confidence interval is ( -149.114, -62.666   )

Step-by-step explanation:

Given the data in the question;

Sample 1                                Sample 2

x"₁ = 259.23                            x"₂ = 365.12

s₁  = 34.713                              s₂ = 48.297

n₁ = 5                                       n₂ = 10

With 90% confidence interval for μ₁ - μ₂ { using equal variance assumption }

significance level ∝ = 1 - 90% = 1 - 0.90 = 0.1

Since we are to assume that variance are equal and they are know, we will use pooled variance;

Degree of freedom DF = n₁ + n₂ - 2 = 5 + 10 - 2 = 13

Now, pooled estimate of variance will be;

[tex]S_p^2[/tex] = [ ( n₁ - 1 )s₁² + ( n₂ - 1)s₂² ] / [ ( n₁ - 1 ) + ( n₂ - 1 ) ]

we substitute

[tex]S_p^2[/tex] = [ ( 5 - 1 )(34.713)² + ( 10 - 1)(48.297)² ] / [ ( 5 - 1 ) + ( 10 - 1 ) ]

[tex]S_p^2[/tex] = [ ( 4 × 1204.9923) + ( 9 × 2332.6 ) ] / [  4 + 9 ]

[tex]S_p^2[/tex] = [ 4819.9692 + 20993.4 ] / [  13 ]

[tex]S_p^2[/tex] = 25813.3692 / 13

[tex]S_p^2[/tex] = 1985.64378

Now the Standard Error will be;

[tex]S_{x1-x2[/tex] = √[ ( [tex]S_p^2[/tex] / n₁ ) + ( [tex]S_p^2[/tex] / n₂ ) ]

we substitute

[tex]S_{x1-x2[/tex] = √[ ( 1985.64378 / 5 ) + ( 1985.64378 / 10 ) ]

[tex]S_{x1-x2[/tex] = √[ 397.128756 + 198.564378 ]

[tex]S_{x1-x2[/tex] = √595.693134

[tex]S_{x1-x2[/tex] = 24.4068

Critical Value = [tex]t_{\frac{\alpha }{2}, df[/tex] = [tex]t_{0.05, df=13[/tex] = 1.771  { t-table }

So,

Margin of Error E =  [tex]t_{\frac{\alpha }{2}, df[/tex] × [ ( [tex]S_p^2[/tex] / n₁ ) + ( [tex]S_p^2[/tex] / n₂ ) ]

we substitute

Margin of Error E = 1.771 × 24.4068

Margin of Error E = 43.224

Point Estimate = x₁ - x₂ = 259.23 - 365.12 = -105.89

So, Limits of 90% CI will be; x₁ - x₂ ± E

Lower Limit = x₁ - x₂ - E = -105.89 - 43.224 = -149.114

Upper Limit = x₁ - x₂ - E = -105.89 + 43.224 = -62.666

Therefore, 90% confidence interval is ( -149.114, -62.666   )

Answer:

45 mph

251 ft

Step-by-step explanation:

[tex] s = \sqrt{30fl} [/tex]

a.)

[tex] s = \sqrt{30(0.85)(80)} [/tex]

[tex] s = \sqrt{2040} [/tex]

[tex] s = 45 [/tex]

Answer: 45 mph

b.)

[tex] 80 = \sqrt{30(0.85)l} [/tex]

[tex] 80^2 = (\sqrt{25.5l})^2 [/tex]

[tex] 25.5l = 6400 [/tex]

[tex] l = 251 [/tex]

Answer: 251 ft

Answer:

A and E

Step-by-step explanation:

Answer:

ANS.1

Freshmen F = 32

Sophomore S = 48

Total students = 80 students

P(F) = Favorables cases/Total cases

   = 32/80

Hope this helps!

Answer:

32/80 or 2/5 simplified

Step-by-step explanation:

P(Freshman) = 32/80 or 2/5 simplified

Answer:

1979

91%

Step-by-step explanation:

Given the relation :

P = (318t + 6792) / (1.19t + 107.36)

P = % of household with PC

t = years since 2000

1.) We need to find t, when P = 85%

P = 0.85

0.85 = (318t + 6792) / (1.19t + 107.36)

0.85(1.19t + 107.36) = (318t + 6792)

1.0115t + 91.256 = 318t + 6792

Collect like terms :

1.0115t - 318t = 6792 - 91.256

−316.9885t = 6700.744

t = 6700.744 / - 316.9885

t = - 21.138760

t = - 21 years

2000 - 21 years = 1979

Percentage who had computer in 2014

t = 2014 - 2000 = 14

P = (318(14) + 6792) / (1.19(14)+ 107.36)

P = (4452 + 6792) / (16.66 + 107.36)

P = 11244 / 124.02

P = 90.6627

P = approximately 91%

Answer:

Step-by-step explanation:

y=x^2+x-30

y=x^2-(6-5)x-30

y=x^2-6x+5x-30

y=x(x-6)-5(x-6)

y=(x-5)(x-6)

Answer:

(x+6)(x-5)

Step-by-step explanation:

The product is -30 and the sum is 1.

Factors of -30 are

-1  and 30

-2 and 15

-3 and 10

-5 and 6

-5 + 6 = 1

Answer:

Infinitely Many Solutions

Step-by-step explanation:

Given

[tex]\left[\begin{array}{cccccc}1&2&3&4&5&6\\7&6&5&4&3&2\\8&8&8&8&8&8\end{array}\right][/tex]

Required

Determine the type of solution

From the matrix, we have:

3 non-zero rows and 5 variables (the last column is the result)

When the number of variables is more than the number of non-zero rows, then such system has infinitely many solutions

i.e.

[tex]Variables > Non\ zero\ rows[/tex]

[tex]5 > 3[/tex]

Answer:

32 are in California and 8 are in Nevada.

Step-by-step explanation:

You multiply 40 by 0.80. You then get 32. That's your answer.

Answer:

see below

Step-by-step explanation:

y = x²-8x+ 15

Let x = -2

y = (-2)²-8(-2)+ 15

  = 4 +16 +15

   = 35

Let x = 1

y = (1)²-8(1)+ 15

     1 -8+15

   =8

The vertex is (4,-1)

Answer:

x+.017x= 203.90

1.017x = 203.90

x = 203.90/1.017

x = 200.49

Answer:

I got 200.49

Step-by-step explanation: I used a graphing calculator. hoped this helps!!!

Answer:

Graph B

Step-by-step explanation:

Hope this helps

There is no solution.

Step-by-step explanation:

Given:

y = 2x + 1

4x - 2y = 4

Substitute y = 2x + 1 into 4x - 2y = 4

4x - 2(2x + 1) = 4

4x - 4x - 2 = 4

0x = 4 + 2

0x = 6

Anything to the multiple of zero is zero. Hence 0x = 0, and 0 ≠ 6

So there is no solution to the equation.

Answer:

[tex] x_{1} = 3 + \sqrt {6} [/tex]

[tex] x_{2} = 3 - \sqrt {6} [/tex]

Step-by-step explanation:

Given the quadratic equation;

x² - 6x + 3 = 0

To find the roots of the quadratic equation, we would use the quadratic formula;

Note: the standard form of a quadratic equation is ax² + bx + c = 0

a = 1, b = -6 and c = 3

The quadratic equation formula is;

[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]

Substituting into the formula, we have;

[tex] x = \frac {-(-6) \; \pm \sqrt {-6^{2} - 4*1*(3)}}{2*1} [/tex]

[tex] x = \frac {6 \pm \sqrt {36 - (12)}}{2} [/tex]

[tex] x = \frac {6 \pm \sqrt {36 - 12}}{2} [/tex]

[tex] x = \frac {6 \pm \sqrt {24}}{2} [/tex]

[tex] x = \frac {6 \pm 2 \sqrt {6}}{2} [/tex]

[tex] x_{1} = \frac {6 + 2 \sqrt {6}}{2} [/tex]

[tex] x_{1} = \frac {6}{2} + \frac {2 \sqrt {6}}{2} [/tex]

[tex] x_{1} = 3 + \sqrt {6} [/tex]

Or

[tex] x_{2} = \frac {6 - 2 \sqrt {6}}{2} [/tex]

[tex] x_{2} = \frac {6}{2} - \frac {2 \sqrt {6}}{2} [/tex]

[tex] x_{2} = 3 - \sqrt {6} [/tex]

Answer:

i got (-10/7, -44/7)

Answer:

3 and - 4

Find the gradient by picking any 2 points on the line then dy/dx

The gradients of line A is 3 and gradient of line B is -4.

Gradient of line is known as slope of line.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The line A passes through the points (0, -2) and (1, 1).

Gradient of line A = 1-(-2)/1

=3/1

=3

The line B passes through the points (1, 1) and (0, 5).

Gradient of line B = 5-1/0-1

=-4

Hence, the gradients of line A is 3 and gradient of line B is -4.

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Answer:

x+113=180

Step-by-step explanation:

it's because of parallelogram property that opposite sides are parallel so being parallel this indicates co interior angle and it's sum is 180 so ,x+113=180,x=180_113,x=67 ans

Answer:

David had x amount of M&M's. He then ate 15 of them for snack. Now David only has 35 M&M's left. How many M&M's did David have in the beginning?

Step-by-step explanation:

Answer:

X= 20

Step-by-step explanation:

Hannah has 35 marbles. Hannah gives away 15 marbles. How many marbles does Hannah have left? Solve the equation X- 15=35.

Answer:3

Step-by-step explanation:

Answer:                                                                                                                                                      

2                                                                                                                                                       Step-by-step explanation:

in the places there is X you put -3 , -3 squared minus 7 is equal to 9 , 9-7 is equal to 2

Answer:

[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]

[tex] \large{ \tt{❁ \: LET'S \: START}} : [/tex]

[tex] \large{ \tt{⋆ \: f( - 3) = {( - 3)}^{2} - 7}}[/tex]

[tex] \large{ \tt{↦ \: f( - 3) = ( - 3) \times ( - 3) - 7}}[/tex]

[tex] \large{ \tt{↦f( - 3) = 9 - 7}}[/tex]

[tex]↦ \large{ \tt{f( - 3) = \boxed{ \tt{2}}}}[/tex]

[tex] \tt{✺ \: COMFORT \: IS \: THE \: ENEMY \: OF \: ACHIEVEMENT\: ♪}[/tex]

♡ Hope I helped! ♕

☃Have a wonderful day / evening ! ☼

# StayInAndExplore ! ☂

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

A = $29,201.97

A = P + I where

P (principal) = $20,000.00

I (interest) = $9,201.97

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 9.5/100

r = 0.095 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 20,000.00(1 + 0.095/12)(12)(4)

A = 20,000.00(1 + 0.007916667)(48)

A = $29,201.97

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $20,000.00 at a rate of 9.5% per year compounded 12 times per year over 4 years is $29,201.97

Answer:

800

Step-by-step explanation:

50% of 400 = 200

1995-1999= 4 years

200x4= 800

Answer:

Question 1)

Cristina is traveling 11 miles per hour and Kori is traveling 20 miles per hour.

Question 2)

Four hours.

Question 3)

Paige spent two hours biking and six hours walking.

Step-by-step explanation:

Question 1)

Let Cristina's speed be x.

Kori travels 9 miles per hour faster than Cristina. So, Kori's speed is (x + 9).

After six hours, Cristina would have traveled 6x miles and Kori would have traveled 6(x + 9) miles.

Since Kori traveled in the opposite direction, we can place a negative to represent this. So, after six hours, Kori is -6(x + 9) miles away from the restaurant while Cristina is 6x miles away from the restaurant.

Since the distance between them is 186 miles, the difference of the two expressions is 186. Hence:

[tex](6x)-(-6(x+9))=186[/tex]

Distribute:

[tex]6x-(-6x-54)=186[/tex]

Distribute:

[tex]6x+6x+54=186[/tex]

Simplify:

[tex]12x=132[/tex]

Hence:

[tex]x=11[/tex]

Cristina's speed is 11 miles per hour. Thus, Kori's speed is 20 miles per hour.

Question 2)

Let h represent the amount of time that has passed in hours.

Carrie left the restaurant traveling 12 miles per hour.

Four hours later, Leah left traveling in the same direction at 24 miles per hour.

After four hours, Carrie would have traveled 12(4) = 48 miles.

Carrie would still be traveling at 12 miles per hour. So, her distance from the restaurant is given by:

[tex]12h+48[/tex]

Since Leah just left and is traveling at a rate of 24 miles per hour, her distance from the restaurant is given by:

[tex]24h[/tex]

Leah will catch up when the two expressions are equivalent. Hence:

[tex]12h+48=24h[/tex]

Solve for h:

[tex]12h=48\Rightarrow h=4[/tex]

Leah will catch up with Carrie in four hours.

Question 3)

Let x represent the amount of hours spent biking and y represent the amount of hours spent walking.

The total trip to the mall took eight hours. Hence:

[tex]x+y=8[/tex]

The mall is a total of 46 miles away. Since Paige bikes at a rate of 8 miles per hour and walks at a rate of five miles per hour:

[tex]8x+5y=46[/tex]

Solve the system. We can use elimination. Multiply the first equation by -5:

[tex]-5x-5y=-40[/tex]

We can add this to the second equation:

[tex]3x=6[/tex]

Hence:

[tex]x=2[/tex]

Using the first equation again:

[tex](2)+y=8\Rightarrow y=6[/tex]

So, Paige spent two hours biking and six hours walking.

Answer:

D

Step-by-step explanation:

shaped like a cone

Cone = 1/3

v = 1/3 x 3.14 x 2.5^2 x 4.2

v =27.475

The equation should the artist use to calculate the volume of the

cone is, 4. V=1/3π (2.5)²(4.2)

A cone is a three-dimensional geometric object with a smooth, curved top and a flat base. As a cone's height increases, its radius gradually decreases until it reaches a particular point.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, An artist is making a sculpture shaped like a cone having a radius of 2.5 inches and a height of 4.2 inches.

We know The volume of a cone is (1/3)πr²h.

Therefore, The volume of the cone would be,

= (1/3)π(2.5)²×4.2 cubic inches.

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9514 1404 393

Answer:

  F ∪ H = [2, ∞)

  F ∩ H = (6, ∞)

Step-by-step explanation:

Graphs of the two sets are shown in the attachment. Set F is shown in red; set H is shown in blue. The solid dot means the point is included in the set, equivalent to a square bracket in interval notation. The open dot means the point is not included in the set, equivalent to a round bracket (parenthesis) in interval notation.

F ∪ H

The union of two sets is the set that contains elements that are members of either set. Here, set F includes all of the elements of set H, so the union of the to sets is simply set F.

  F∪H = F = [2, ∞)

__

F ∩ H

The intersection of two sets is the set of elements that are common to both sets. Here, every element of set H is also an element of set F, but not vice versa. So, the intersection of the sets is equivalent to set H.

  F∩H = H = (6, ∞)

Answer:

B = 31.6

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan B = opp / adj

tan B = 28.2 / 45.8

taking the inverse tan of each side

tan ^ -1 ( tan B) = tan ^-1 (28.2/45.8)

B =31.62145

Rounding to the nearest tenth

B = 31.6

Answer:

37.1666666667

Step-by-step explanation:

brainiest please

Answer:

Answer:

Step-by-step explanation:

(a) A = 23°

(b) A=99°

(c) A = 53°

(d) A= 36°

Answer:

65 miles

Step-by-step explanation:

y=55+0.15x

64.75=55+0.15x

9.75=0.15x

x=9.75/0.15

x=65 miles

Cora, her sister, and four friends. So there are 6 people, 120 candies are divided equally in the bag, so each person gets 20 candies

Each person will get 20 candles.

The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication.

Now it is given that,

Number of candles in the bag = 120

Cora, her sister, and four friends are going to share.

So, Number of person = 6

Thus, candles each person gets = Number of candles in the bag / Number of person

⇒ candles each person gets = 120 / 6

⇒ candles each person gets = 20

Thus, each person will get 20 candles.

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