2cos2+cos2(2)−2cos2cos2=1​

Answer:

25

Step-by-step explanation:

40/24 = x/15

x = 15•40/24

x = 25

Answer:

25

Step-by-step explanation:

just use the facts that both triangles are similar

Answer:

1 / 9

Step-by-step explanation:

Choosing with replacement means that the first draw from the lot is replaced before another is picked '.

Number of Blue marbles = 2

Number of red marbles = 4

Total number of marbles = (2 + 4) = 6

Probability = required outcome / Total possible outcomes

1st draw :

Probability of picking blue = 2 / 6 = 1 /3

2nd draw :

Probability of picking blue = 2 / 6 = 1/3

P(1st draw) * P(2nd draw)

1/3 * 1/3 = 1/9

sfddssdfa63434daasfdfddfsa

Answer:

true the question is true and wait for others my could be wrong also

Answer:

3/2,  -1.1

Step-by-step explanation:

the probability cannot be greater than 1. probability is between 0 and 1

Answer:

khai niem hinh cat don gian?

Answer:

1/4

Step-by-step explanation:

White = w

Black = B

Blue = b1

Tan = t

Wb1

Wt

Bbi

Bt

The answer will be 1/4, because there are 4 ways it can work and only 1 way it can be white shirt and tan pants.

Answer:

1/4

Step-by-step explanation:

it would be 1/4 because there are 4 different clothing pieces in total and there is only one way it would work the way the problem says.

9514 1404 393

Answer:

  a) Lahulspiti: -8; Srinigar: -2; Shimla: 5; Ooty: 14; Bengahuru: 22

  b) 30

  c) 6

  d) yes; no

Step-by-step explanation:

a) The values are read from the graph.

__

b) 22 -(-8) = 22 +8 = 30 . . . . difference between highest and lowest

__

c) -2 -(-8) = -2 +8 = 6 . . . positive difference

(Technically, the difference between L and S is L - S = (-8) -(-2) = -6.)

__

d) -2 + 5 < 5 . . . . true

  -2 + 5 < -2 . . . . false

Answer:

b. The actual count of bike riders is too small.

d. n*p is not greater than 10.

Step-by-step explanation:

Confidence interval for a proportion:

To be possible to build a confidence interval for a proportion, the sample needs to have at least 10 successes, that is, [tex]np \geq 10[/tex] and at least 10 failures, that is, [tex]n(1-p) \geq 10[/tex]

Of the 123 students surveyed 5 ride a bike to campus.

Less than 10 successes, that is:

The actual count of bike riders is too small, or [tex]np < 10[/tex], and thus, options b and d are correct.

Answer:

No

Step-by-step explanation:

If we use the Pythagorean theorem, we can find if it is a right triangle. To do that, set up an equation.

[tex]6^{2}+8^{2}=c^2[/tex]

If the triangle is a right triangle, c would equal 11

Solve.

[tex]36+64=100[/tex]

Then find the square root of 100.

The square root of 100 is 10, not 11.

So this is not a right triangle.

I hope this helps!

Answer:

cos theta  = adj / hyp is positive (+/+)

Step-by-step explanation:

In this open interval, the hypotenuse (radius) is always positive, whereas the adjacent side is positive and the opposite side negative.

in this interval:

sin theta = opp / hyp is neg (-/+)

cos theta  = adj / hyp is positive (+/+)

tan theta = opp / adj = (-/+) :  negative

Answer:

A) Neither function A nor function B has an x-intercept.

Step-by-step explanation:

Answer:

f

Step-by-step explanation:

Answer:

S = 62.9

Step-by-step explanation:

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

tan S = opp side / adj side

tan S = sqrt(42)/ sqrt (11)

tan S = sqrt(42/11)

Taking the inverse tan of each side

tan ^ -1( tan S) =  tan ^-1(sqrt(42/11))

S=62.89816

Rounding to the nearest tenth

S = 62.9

9514 1404 393

Answer:

  x = 10/3 = 3 1/3 ≈ 3.33

Step-by-step explanation:

Triangles ABC and ADE are similar, so corresponding sides are proportional.

  DE/DA = BC/BA

  x/(4+6) = 2/6

  x = 10(2/6) = 10/3 = 3 1/3

Given:

Distance traveled by sprinter = 200 m

Time taken by sprinter = 20.03 seconds

To find:

The sprinter's average speed rounded to 4 sf.

Solution:

We know that,

[tex]\text{Average speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

It is given that, the sprinter travels a distance of 200 m in a time of 20.03 seconds.

[tex]\text{Average speed}=\dfrac{200}{20.03}[/tex]

[tex]\text{Average speed}=9.985022466[/tex]

[tex]\text{Average speed}\approx 9.985[/tex]

Therefore, the average speed of the sprinter is 9.985 m/sec.

Answer:

9.985

Step-by-step explanation:

Answer:

2.5%

Step-by-step explanation:

Thorazine is available in the strength of 25mg/mL.

To find out the percentage strength,

W/V = g/mL  (weight in grams of solute/milliliters of solute.)

1mL of Thorazine contains 25mg.

Dissolve Thorazine with the 100mL solution.

Therefore, 25 x 100 = 2500mg

Which is equals to 2.5g

100mL solution contains 2.5g of Thorazine.

Percentage Strength (W/V) = 2.5 / 100 x 100 = 2.5%.

The percentage strength of Thorazine 25mg/mL has 2.5%

Answer:

The answer is "".

Step-by-step explanation:

Please find the complete question in the attached file.

We select a sample size n from the confidence interval with the mean [tex]\mu[/tex]and default [tex]\sigma[/tex], then the mean take seriously given as the straight line with a z score given by the confidence interval

[tex]\mu=3.87\\\\\sigma=2.01\\\\n=110\\\\[/tex]

Using formula:

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]  

The probability that perhaps the mean shells length of the sample is over 4.03 pounds is

[tex]P(X>4.03)=P(z>\frac{4.03-3.87}{\frac{2.01}{\sqrt{110}}})=P(z>0.8349)[/tex]

Now, we utilize z to get the likelihood, and we use the Excel function for a more exact distribution

[tex]=\textup{NORM.S.DIST(0.8349,TRUE)}\\\\P(z<0.8349)=0.7981[/tex]

the required probability: [tex]P(z>0.8349)=1-P(z<0.8349)=1-0.7981=\boldsymbol{0.2019}[/tex]

If 6ˣ = 5, then

(6ˣ)³ = 6³ˣ = 5³ = 125,

and

6³ˣ⁺² = 6³ˣ × 6² = 125 × 6² = 125 × 36 = 4500

Answer:

Amount gained = $900

Step-by-step explanation:

Let the cost price be = x

Given selling price = 8400

And profit% = 12%

Profit = selling price - cost price

        = 8400 - x

[tex]Profit \ \% = \frac{profit}{cost \ price} \times 100\\\\12\% = \frac{8400 - x}{x} \times 100\\\\\ 12 \times \frac{1}{100} = \frac{8400 - x}{x}\\\\\frac{12 \ x}{100} = 8400 - x \\\\\frac{12x}{100} + x = 8400\\\\12x + 100x = 8400 \times 100\\\\112x = 8400 \times 100\\\\x = \frac{8400 \times 100}{112} = 7500[/tex]

Therefore , cost price of the radio $7500

The amount she gained = 8400 - 7500 = $ 900

"RS tangent to circle a..." is first statement          Reason: Given

Second Reason: "Radius perpendicular to tangent"

Second Statement: "AR is parrallel to BS"      Reason: "2 lines perpendicular..."

Answer:

a) 0.321 = 32.1% probability of obtaining a negative daily return, on any given day.

b) 0.103 = 10.3% probability of having a negative daily return for two days in a row.

c) (-$1449.68, $3109.68)

d) A bonus of $4,488.174 is needed.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normal distribution with mean = $830 and standard deviation = $1,781.

This means that [tex]\mu = 830, \sigma = 1781[/tex]

(a) What is the probability of obtaining a negative daily return, on any given day?

This is the p-value of Z when X = 0, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0 - 830}{1781}[/tex]

[tex]Z = -0.466[/tex]

[tex]Z = -0.466[/tex] has a p-value 0.321.

0.321 = 32.1% probability of obtaining a negative daily return, on any given day.

(b) Assuming the returns on successive days are independent of each other, what is the probability of having a negative daily return for two days in a row?

Each day, 0.3206 probability, so:

[tex](0.321)^2 = 0.103[/tex]

0.103 = 10.3% probability of having a negative daily return for two days in a row.

(c) Give the boundaries of the interval containing the middle 80% of daily returns

Between the 50 - (80/2) = 10th percentile and the 50 + (80/2) = 90th percentile.

10th percentile:

X when Z has a p-value of 0.1, so X when Z = -1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.28 = \frac{X - 830}{1781}[/tex]

[tex]X - 830 = -1.28*1781[/tex]

[tex]X = -1449.68[/tex]

90th percentile:

X when Z has a p-value of 0.9, so X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 830}{1781}[/tex]

[tex]X - 830 = 1.28*1781[/tex]

[tex]X = 3109.68[/tex]

So

(-$1449.68, $3109.68)

d) As part of its incentive program, any trader who obtains a daily return in the top 2% of historical returns receives a special bonus. What daily return is needed to get this bonus?

The 100 - 2 = 98th percentile, which is X when Z has a p-value of 0.98, so X when Z = 2.054.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.054 = \frac{X - 830}{1781}[/tex]

[tex]X - 830 = 2.054*1781[/tex]

[tex]X = 4488.174 [/tex]

A bonus of $4,488.174 is needed.

Answer:

x = 6

Step-by-step explanation:

15 more represents “+15”

3 times a number represents “3*x” which is written as “3x”

So fifteen more than 3 times a number is 33 would be written as;

3x + 15 = 33

Now solve for x using algebra;

3x = 33 - 15

3x = 18

x = 18 / 3

x = 6

Hope this helps!

Step-by-step explanation:

Since the ratio of monthly income to savings of the family is 7:2, we assume that the income be 7t and savings be 2t

Now, we are given that the savings is =Rs 500

So, According to our assumption, 2t=500

⇒t=250

Hence, the income of the family is =7×250=Rs 1750

And the expenditure is =Income−Savings

=Rs 1750−Rs 500

=Rs 1250

Answer:

Angle A = Angle D = 69° 30'

Angle B = Angle C = 110° 30'

Step-by-step explanation:

     B ___ C

    /              \

  /                  \

A ________ D

AB and CD are 10

BC is 6

AD is 14

If we divide the trapezoid, we can imagine a line.

     B_ F_C

    /      |      \

  /        |         \

A ___E____ D

AE = ED = 7 (14/2)

BF = FC = 3

So now, we draw another line from B or C to AE or ED

     B_ F_ C

    /      |     | \

  /        |     |    \

A ___E_ G_ D

EG = GD = 3.5 (7/2)

There is a right triangle now, GCD

GD is 3.5 and CD is 10. To determine angle D, we can apply trigonometric function:

CD is H, and GD is A

cos D = A/H

cos D = 3.5/10 → 0.35

angle D = 69° 30'

By theory, we know that angle D and angle A, are the same so:

Angle D = Angle A = 69° 30'

Angle B = Angle C

We also make a cuadrilateral, which is EFCD.

Angle D is 69° 30', Angle E is 90°, Angle F is also 90°

Sum of angles in cuadrilateral is 360°

360° - 69° 30' - 90° - 90° = Angle C = Angle B

Angle C = Angle B = 110° 30'

Let's confirm the angles in the trapezoid:

69° 30' + 110° 30' + 69° 30' + 110° 30' = 360°

A + B + C + D

Answer:

2x + 1.

Step-by-step explanation:

Average = sum of the expression / number of expressions

= [(4 - 2x) + (-7 - 3x) + (11x + 6)] / 3

= (-2x - 3x + 11x + 4 - 7 + 6) / 3

= 6x + 3 / 3

= 2x + 1

Answer:

2x+1

Step-by-step explanation:

(4-2x), (-7-3x),(11x+6)

Add the three expressions

(4-2x)+ (-7-3x)+(11x+6)

Combine like terms

-2x-3x+11x+4-7+6

6x+3

Divide by the number of expressions which was 3

(6x+3)/3

2x+1

The average is 2x+1

The transformation set of [tex]y[/tex] values for function [tex]f[/tex] is [tex][-1,1][/tex] this is an interval to which sine function maps.

You can observe that the interval to which [tex]g[/tex] function maps equals to [tex][-2,0][/tex].

So let us take a look at the possible options.

Option A states that shifting [tex]f[/tex] up by [tex]\pi/2[/tex] would result in [tex]g[/tex] having an interval [tex][-1,1]+\frac{\pi}{2}\approx[0.57,2.57][/tex] which is clearly not true that means A is false.

Let's try option B. Shifting [tex]f[/tex] down by [tex]1[/tex] to get [tex]g[/tex] would mean that has a transformation interval of [tex][-1,1]-1=[-2,0][/tex]. This seems to fit our observation and it is correct.

So the answer would be B. If we shift [tex]f[/tex] down by one we get [tex]g[/tex], which means that [tex]f(x)=\sin(x)[/tex] and [tex]g(x)=f(x)-1=\sin(x)-1[/tex].

Hope this helps :)

Answer:

B

Step-by-step explanation:

substitute the values in the eq. Ot is also arithmetic progression.