Find the value of x in the triangle below.

Answer:

mean = 77

Step-by-step explanation:

We have a confidence interval of (59, 95) with a confidence of  99.7 percent

99.7 is 6 standard deviations from the mean, 3 on each side of the mean

mean - 3 sigma = 59

mean + 3 sigma = 95

We can use elimination to eliminate sigma.  Add these equations together

mean - 3 sigma = 59

mean + 3 sigma = 95

---------------------------------

2 * mean = 154

Divide each side by 2

2 * mean/2 = 154/2

mean = 77

Based on a sample where the 99.7% confidence interval for the mean of a population is (59,95), 77 is the mean

Answer:

$3.08

Step-by-step explanation:

Answer:

B). −2√6/5

Step-by-step explanation:

tan theta = sin theta/ cos theta

Multiply each side by cos theta

tan theta * cos theta = sin theta

Divide each side by tan theta

cos theta = sin theta/ tan theta

We know that the sin (- theta) = - sin theta  since sin is and odd function

sin theta  = - (  sin (-theta))

Putting this into the above equation,

cos theta =  - (  sin (-theta)) / tan theta

cos theta = - 1/5 / (sqrt(6)/12)

Remember when dividing fractions, we use copy dot flip

cos theta =   -1/5  * 12/ sqrt(6)

cos theta = -12/ (5 sqrt(6))

We cannot leave a sqrt in the denominator, so multiply the top and bottom by sqrt(6)/sqrt(6)

cos theta = -12/ (5 sqrt(6))  * sqrt(6)/sqrt(6)

cos theta = -12 sqrt(6) / 5*6

Simplify the fraction.

cos theta = -2 sqrt(60/5

Given sin(−θ)=1/5, we know sin(θ)=−1/5, and tan(θ)=√6/12 is positive, indicating that cos(θ) must be positive in the fourth quadrant. Using the Pythagorean identity, we find that cos(θ)=2√6/5, which corresponds to option (D).

The question asks for the value of cos(θ) given sin(−θ) = 1/5 and tan(θ) = √6/12.

First, recognize that sin(−θ) = −sin(θ), which means that sin(θ) = −1/5. Then, use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 to find cos(θ).

sin^2(θ) = (1/5)^2 = 1/25
cos^2(θ) = 1 − (1/25) = 24/25
cos(θ) = ±√(24/25)

Since tan(θ) = √6/12 is positive, and tangent is the ratio of sine to cosine, and we know sine is negative (sin(θ) = −1/5), then cosine must be positive for the tangent to be positive. So, cos(θ) is the positive root.

cos(θ) = √(24/25) = 2√6/5. This matches with option D).

Answer:u got to multiply

Step-by-step explanation:

To find the remainder when dividing the polynomial f(x) = x^10-8x^8-8x^3+12x^2-5x-5 by x^2-1, we can use synthetic division. Carrying out the synthetic division process, the remainder is -10x + 7.

To find the remainder when dividing the polynomial f(x) = x^{10}-8x^8-8x^3+12x^2-5x-5 by x^2-1, we can use polynomial long division. However, since we want to avoid this method, we can use synthetic division instead.

After performing synthetic division, we find that the remainder is -10x + 7. Therefore, the remainder when dividing f(x) by x^2 - 1 is -10x + 7.

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Answer:

A

Step-by-step explanation:

Trust the spam

Question

(98 x2) + (69 x52) =

4 + (34 x 19) + 987 =

Answer:

Step-by-step explanation:

(98 x2) + (69 x52) =

196 + 3588 =

3784

---------------

4 + (34 x 19) + 987 =

4 + 646 + 987 =

1637

Answer: <

Step-by-step explanation: The top triangle (1) has a smaller area than triangle 2.

Answer:

Angle 1 < Angle 2

Step-by-step explanation:

This is a short answer, but I promise that its 100% correct.

Hope it helps.

Answer: 85 meters

Step-by-step explanation:

The maximum height is the y-value of the vertex.

h(t) = -4.9t² + 20t + 65

      a=-4.9   b=20  c=65

[tex]t=\dfrac{-b}{2a} = \dfrac{-(20)}{2(-4.9)} =\dfrac{-20}{-9.8}=2[/tex]

h(2) = -4.9(2)² + 20(2) + 65

      = -19.6 + 40 + 65

      = 85.4

Answer: [tex]\bold{\dfrac{16}{33} = 48\%}[/tex]

Step-by-step explanation:

  Red  or  Green

[tex]=\dfrac{red}{total}+\dfrac{green}{total}[/tex]

[tex]=\dfrac{9}{33}+\dfrac{7}{33}[/tex]

[tex]=\dfrac{16}{33}[/tex]

≈ 48%

Answer:

2x² +4x +11 +20/(x-2)

Step-by-step explanation:

The synthetic division is in the attachment. It shows the above quotient is the result of the division.

Problem 1

Answer: choice D) 84% of the wage earners earn less than $14,000 each

------------

The empirical rule states that 95% of the area under a normal curve is within 2 standard deviations (approximately), so 100-95 = 5% is found in the two tails combined, leaving 5/2 = 2.5% in each tail. Because the top 2.5% earns $18000 or more, this means 18000 is roughly 2 standard deviations above the mean, so z = 2

If z = 2 corresponds to with x = 18000, with mean mu = 10000, then the standard deviation sigma is...

z = (x-mu)/sigma

2 = (18000 - 10000)/sigma

2 = 8000/sigma

2sigma = 8000

sigma = 8000/2

sigma = 4000

So mu+sigma = 10000+4000 = 14000 is the cutoff mark for the earners 1 standard deviation above the mean.

Check out the attached image figue 1 for the diagram for the empirical rule. Add up the values that are to the left of z = 1, so 2.35+13.5+34+34 = 83.85 which rounds to 84

===============================================

Problem 2

Answer: choice D) 2.5%

-----------

x = 250, mu = 190 and sigma = 30

z = (x-mu)/sigma

z = (250-190)/30

z = 60/30

z = 2

According to the emprical rule, roughly 95% of the distribution is within 2 standard deviations. So 100-95 = 5% is in the combined tails leaving 5/2 = 2.5% is in the upper tail.

===============================================

Problem 3

Answer: Choice D) 4,4,4,5,5,6,7,7,8,8,8

------------

Plot each of the values on a dot plot. See the attached image figure 2 for each dotplot. Notice how plot D is bimodal with two hill features, so this distribution is non-normal. Normal distributions only have one mode (one hill).

Answer:

You didn't input the function, but the cosine of 90 degrees is zero.

Cosine values of zero also occur when an angle equals

270 degrees 450 degrees 630 degrees and 810 degrees.

Step-by-step explanation:

Answer:

That would be 0, 180, 360, 540, and 720.

Step-by-step explanation:

If the value of sine is 0. Add 180 five times and we get the five numbers for the answer.

Answer:

The Answer is a Prime polynomial, it cannot be further factorized.

Step-by-step explanation:

Answer:

180 grams

Step-by-step explanation:

Mitchell has to use more coffee than usual for two reasons: First, he's making a larger pot than usual (15(15left parenthesis, 15 cups rather than 10)10)10, right parenthesis. And second, he's using the Arabica coffee, which requires 20\%20%20, percent more coffee for the same strength.

2

Instead of brewing \blue{10}10start color blue, 10, end color blue cups, Mitchell wants to brew \red{15}15start color red, 15, end color red cups, which means he has to use \dfrac{\red{15}}{\blue{10}}=\purple{1.5}  

​  =1.5start fraction, start color red, 15, end color red, divided by, start color blue, 10, end color blue, end fraction, equals, start color purple, 1, point, 5, end color purple times more coffee.

3

As his friend said, Mitchell also has to use \pink{20\%}20%start color pink, 20, percent, end color pink more coffee than usual, so he'll have to multiply the amount of coffee by \green{1.2}1.2start color green, 1, point, 2, end color green, or \green{120\%}120%start color green, 120, percent, end color green.

4

The total amount of coffee he has to use is 100100100 grams \times×times \purple{1.5} \times \green{1.2} = 1801.5×1.2=180start color purple, 1, point, 5, end color purple, times, start color green, 1, point, 2, end color green, equals, 180 grams.

Answer: (13, 47)

The expression t = 4 means that 4 units of time have come off the clock (possibly 4 seconds). Plug this value into each equation given for x and y

x = 2*t + 5 = 2*4 + 5 = 8 + 5 = 13

y = 3*t^2 - 1 = 3*4^2 - 1 = 3*16 - 1 = 48 - 1 = 47

In short, if t = 4 then it leads to x = 13 and y = 47 at the same time. These x and y values pair up to get the final answer (13,47)

--------------

Here's an update:

If t = 2, then,

In short, if t = 2, then x = 9 and y = 11

The point on the graph at time [tex]\(t = 4\) is \((13, 47)\)[/tex].

To find the point on the graph at time [tex]\(t = 4\)[/tex] given the parametric equations [tex]\(x = 2t + 5\)[/tex] and [tex]\(y = 3t^2 - 1\)[/tex], substitute [tex]\(t = 4\)[/tex] into both equations.

1. For [tex]\(x\)[/tex]:

[tex]x = 2t + 5[/tex]

[tex]x = 2(4) + 5[/tex]

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

[tex]x = 13[/tex]

So, at [tex]\(t = 4\), \(x = 13\)[/tex].

2. For [tex]\(y\)[/tex]:

[tex]y = 3t^2 - 1[/tex]

[tex]y = 3(4)^2 - 1[/tex]

[tex]y = 3(16) - 1[/tex]

[tex]y = 48 - 1[/tex]

[tex]y = 47[/tex]

So, at [tex]\(t = 4\), \(y = 47\)[/tex].

Therefore, the point on the graph at time [tex]\(t = 4\) is \((13, 47)\)[/tex].

Answer:

x = 8

y = 1

Step-by-step explanation:

Slope = difference in y values / corresponding difference in x values

Slope =  (9 - 5) / (x - 10) = -2

-2x + 20 = 4

x = -16 / -2 = 8  (answer)

Question 4

(y - 6) /(1 - 2) = 5

y - 6 = -5

y = 1  (answer).

Answer: D

Step-by-step explanation:

The x-intercepts of the graph are: x = -2 , x = -1, and x = 3

-->                                                 x + 2 = 0, x + 1 = 0, and x - 3 = 0

-->                                                           (x + 2) (x + 1) (x - 3)

Answer:

Gil is not correct.    

Step-by-step explanation:

We have been given that Gil borrows $8,000 for college expenses. He will pay a total of $10,280 after 6 years. Gil says the interest rate is at least 5%.

We will use simple interest formula to check whether Gil is right or not.

[tex]A=P*(1+r*t)[/tex], where

A= Final amount after t years.

P= Principal amount.

r= Interest rate in decimal form.

Let us substitute our given values in above formula to find the interest rate.

[tex]10280=8000*(1+r*6)[/tex]  

[tex]10280=8000+48000*r[/tex]

[tex]2280=48000*r[/tex]  

[tex]r=\frac{2280}{48000}[/tex]

[tex]r=0.0475[/tex]

Since r is in decimal form, so let us convert interest rate in percent by multiplying by 100.

[tex]0.0475*100=4.75[/tex]

Therefore, the original interest rate is 4.75% which is less than 5%, so Gil is not correct.  

Answer:

The answer is gill is incorrect he will pay 2280 interest, which corresponds to  an interest rate of 4.75

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

[tex]g(x) = 3x + 1 \\\ y = 3x + 1[/tex]

Changing x to y and y to x:

[tex]x = 3y + 1 \\\ 3y = x - 1 \\\ y = \frac{x - 1}{3} \\\ g^{-1}(x) = \frac{x - 1}{3} \\\ g^{- 1} (1) = \frac{1 - 1}{3} \\\ g^{- 1} (1) = 0[/tex]

I hope I helped you.

Answer:

0

Step-by-step explanation:

Hope this helps.

Answer: Yes they do.

Step-by-step explanation:

This because the ratio 10:1 means that for every 10 students that ride the bus only one walks. So if you had 30 students riding he bus you would only have 3 students that walked. So no matter what you will have more kids riding the bus.

Answer:

1. [tex]\dfrac{3}{8}[/tex]

2. 240 km

Step-by-step explanation:

Anna drives [tex]\dfrac{1}{8},[/tex] Irina drives [tex]\dfrac{3}{8},[/tex] Vlad drives [tex]\dfrac{1}{8},[/tex] then Avel drives

[tex]1-\dfrac{1}{8}-\dfrac{3}{8}-\dfrac{1}{8}=\dfrac{8}{8}-\dfrac{1}{8}-\dfrac{3}{8}-\dfrac{1}{8}=\dfrac{8-1-3-1}{8}=\dfrac{3}{8}.[/tex]

If the road trip involves 640 km of driving, then Avel drives

[tex]640\cdot \dfrac{3}{8}=80\cdot 3=240\ km.[/tex]

Answer:

False

Step-by-step explanation:

To determine whether the statemaent "If [tex]a\Rightarrow b[/tex] is true, then [tex]\neg a\Rightarrow b[/tex] is also true" holds, you can form the truth table:

[tex]\begin{array}{ccccc}a&b&a\Rightarrow b&\neg a&\neg a\Rightarrow b\\1&1&1&0&1\\1&0&0&0&1\\0&1&1&1&1\\0&0&1&1&0\end{array}[/tex]

When the result of the column [tex]a\Rightarrow b[/tex] takes value 1 (true), the result of the column  [tex]\neg a\Rightarrow b[/tex] is not always 1, then the statement is false.

Answer:

46 boxes

Step-by-step explanation:

So for a total of 20 boxes, the cost is [tex]75+55=130[/tex]

We have remaining [tex]221-130=91[/tex]

Each additional box costs 3.5, so for 91 dollars, we can get:

[tex]\frac{91}{3.5}=26[/tex] boxes

So, total [tex]10+10+26=46[/tex] boxes can be bought for $221.00

Given the budget of $221 and the stipulated price rates, the company can buy a total of 46 boxes of paper clips.

To solve this problem, we first need to calculate how many boxes the company can buy with $221 considering the different rates. The first 10 boxes cost $7.50 each, so ten boxes would cost $75. The next 10 boxes cost $5.50 each, so these together would cost $55. This means that 20 boxes cost $130. Subtract this amount from the total budget, which leaves $91.

Since each additional box over 20 boxes costs $3.50, we divide our remaining fund, $91, by $3.50 to determine how many more boxes can be purchased. This comes out to roughly 26 boxes.

So, adding up all the boxes, the company can buy 10 boxes (at $7.50) + 10 boxes (at $5.50) + 26 boxes (at $3.50) = 46 boxes with $221.

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Answer:

The ladder from the base of the building is 5.18 ft (Approx)

Step-by-step explanation:

As given

A ladder that is 20 ft. Long is leaning against the side of a building.

If the angle formed between the ladder and the ground is 75.

Now using the trignometric property .

[tex]cos\theta = \frac{Base}{Hypotenuse}[/tex]

As shown in the figure.

[tex]\theta = 75^{\circ}[/tex]

Base = CB

Hypotenuse = AC = 20 ft.

Put in the trignometric identity .

[tex]cos75^{\circ} = \frac{CB}{AC}[/tex]

[tex]cos75^{\circ} = \frac{CB}{20}[/tex]

[tex]cos\ 75^{\circ} = 0.259[/tex]

Put in the above

[tex] 0.259= \frac{CB}{20}[/tex]

[tex]0.259 = \frac{CB}{20}[/tex]

CB = 0.259 × 20

CB = 5.18 ft (Approx)

Therefore the ladder from the base of the building is 5.18 ft (Approx) .