An urn contains 4 white balls and 7 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 11 ​balls: ​(a) If 2 balls are white and 1 is​ red? ​(b) If all 3 balls are​ white? ​(c) If all 3 balls are​ red?

Answer:

82 units.

Step-by-step explanation:

The Pythagorean Theorem is a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the legs.

In this case, 18 and 80 are the legs.

18^2 + 80^2 = c^2

324 + 6,400 = c^2

6,724 = c^2

c^2 = 6,724

c^2 = 82^2

c = plus or minus 82

Since measurements cannot be negative, the length of the hypotenuse is 82 units.

Hope this helps!

Answer:

82 units   indeed!

Step-by-step explanation:

c = [tex]\sqrt{ 18^{2} + 80^{2} }[/tex]

c = 82

Answer:

30.7i + 135.9j + 53.4k

Step-by-step explanation:

The ' horizontal ' may act as the x - axis in this case, the airplane taking off at an angle of 173 cos 18 respective to this x - axis. Respectively it travels restricted to an angle of 173 sin 18 from the y - axis. The following shows this angle at vector( s ) j and k relative to the air -

j - ( 173 cos 18 ),

k - ( 173 sin 18 )

Thus, one can assume such -

[tex]0i + ( 173 cos 18 )j + ( 173 sin 18 )k[/tex]

Knowing that, this second bit here should be similar to the first bit above, given that the wind is now blowing  with a velocity of 42 miles per hour at an angle of 47 degrees. Therefore, j = 42 cos 47, i = 42 sin 47 -

[tex]( 42 sin 47 )i + ( 42 cos 47 )j + 0k[/tex]

Adding the two we should get the following -

[tex]30.7i +135.9j + 53.4k[/tex]

Answer:

  30.72i+ 135.89j +53.46k

Step-by-step explanation:

If we measure angle φ up from the horizontal and angle θ CCW from east, the direction vector of the airplane at take-off is ...

  (ρ, θ, φ) = (173 mph, 90°, 18°)

The rectangular expression of this vector will be ...

  (ρ·cos(θ)·cos(φ), ρ·sin(θ)·cos(φ), ρ·sin(φ)) = (0, 164.53, 53.46) . . . mph

__

The wind vector is ...

  (ρ, θ, φ) = (42, -43°, 0°) ⇒ (30.72, -28.64, 0) . . .  mph

And the rectangular coordinate sum of these vectors is ...

  (0, 164.53, 53.46) +(30.72, -28.64, 0) = (30.72, 135.89, 53.46)

The resultant velocity vector of the airplane is ...

  30.72i+ 135.89j +53.46k

Answer:

120

Step-by-step explanation:

480/(1+3)

480/4

= 120

1 × 120 : 3 × 120

120 : 360

Boys to girls are in the ratio 120:360.

There are 120 boys.

Answer: Evaluate the Function, right?

Hello!

~~~~~~~~~~~~~~~~~~

A) 4x = -4 [x=-1] =

4x = -4 =

x = -1 = x = -1

( The steps : Substitute the given value into the function and evaluate.)

B) 2(x-3) =-12 [x=3] =

2 ( x - 3) = -12 = x = -3

x = 3 = x = 3

( The steps : Substitute the given value into the function and evaluate.)

C) 8x - 4x = 24 [x = 1/2] =

8x - 4x = 24 = x = 6

x = 1/2 = x = 1/2

( The steps : Substitute the given value into the function and evaluate.)

D) 9x - 4x = 24 [x=18] =

9x - 4x = 24 = x = 24/5

x = 18 = x = 18

( The steps : Substitute the given value into the function and evaluate.)

~~~~~~~~~~~~~~~~~~

Step-by-step explanation: All the steps are the same. Substitute the given value into the function and evaluate.

Hope this helped you!

Answer:

y=5 or y=-4

Step-by-step explanation:

6y - 3| + 8 = 35

|6y-3|=35-8

|6y-3|=27

either 6y-3=-27 then 6y=27+3

y=30/6=5

or 6y-3=-27

6y=-27+3

y=-24/6

y=-4

I’m not exactly sure what this means.

But you can use “ to abbreviate the labels.

So it would be 6” and 4.5”

Answer:

Step-by-step explanation:

There is some ambiguity in this question. I think you want 4.5 + 6 = 10.5 inches.

Answer:

41.18% probability of drawing a white counter or a green counter

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

There are 3+10+4 = 17 counters.

Of those, 3+4 = 7 are white or green

7/17 = 0.4118

41.18% probability of drawing a white counter or a green counter

Answer:

60 of 24 dollars each and 50 of 25 dollars

Step-by-step explanation:

x= 24 dollars

110 shares, total x at 24 dollars each

110-x at 25 dollars each

24x+25 (110-x)=2690

24x+ 2750 - 25x= 2690

-1x= -60

x= 60

24 multiplied by 60 =1440

2690-1440 =1250

1250 / 25 = 50

can u vote me as brainliest ?

Answer:

  (0, -5)

Step-by-step explanation:

You have (x, f(x)) = (0, 0) and you want (x, f(x) -5).

That would be ...

  (x, f(x) -5) = (0, 0 -5) = (0, -5)

Answer:

4.9 × 10^1

hopefully this helped :3

Answer:

4.9 * 10 ^1

Step-by-step explanation:

We want one digit to the left of the decimal

49

4.9

We moved the decimal one place to the left

One is the exponent.  Since we moved to the left the exponent is positive

4.9 * 10 ^1

Answer:

Option C.

Step-by-step explanation:

The given function is

[tex]y=\dfrac{2x+1}{x^2}[/tex]

We need to find the slope of the function when x=4.

Differentiate the given function w.r.t. x.

[tex]\dfrac{dy}{dx}=\dfrac{x^2\dfrac{d}{dx}(2x+1)-(2x+1)\dfrac{d}{dx}x^2}{(x^2)^2}[/tex]    (Using quotient rule)

[tex]\dfrac{dy}{dx}=\dfrac{x^2(2+0)-(2x+1)(2x)}{x^4}[/tex]

[tex]\dfrac{dy}{dx}=\dfrac{2x^2-4x^2-2x}{x^4}[/tex]

[tex]\dfrac{dy}{dx}=\dfrac{-2x^2-2x}{x^4}[/tex]

[tex]\dfrac{dy}{dx}=\dfrac{-2x(x+1)}{x^4}[/tex]

[tex]\dfrac{dy}{dx}=\dfrac{-2(x+1)}{x^3}[/tex]

Now substitute x=4 in the above equation.

[tex]\dfrac{dy}{dx}_{x=4}=\dfrac{-2(4+1)}{4^3}[/tex]

[tex]\dfrac{dy}{dx}_{x=4}=\dfrac{-2(5)}{64}[/tex]

[tex]\dfrac{dy}{dx}_{x=4}=\dfrac{-10}{64}[/tex]

[tex]\dfrac{dy}{dx}_{x=4}=-0.15625[/tex]

[tex]\dfrac{dy}{dx}_{x=4}\approx -0.16[/tex]

Therefore, the correct option is C.

Answer:

A sample of 385 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

How large a sample:

We need a sample of n.

n is found when M = 0.05.

We dont know the true proportion, so we work with the worst case scenario, which is [tex]\pi = 0.5[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.05}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.05})^{2}[/tex]

[tex]n = 384.16[/tex]

Rounding up

A sample of 385 is needed.

Answer:

c) 0.62

Step-by-step explanation:

In this case, we are required to find the partial correlation, [tex] r_Y_X_1_|_X_2[/tex].

To find the partial correlation, use the formula:

[tex] r_Y_X_1_|_X_2 = \frac{r_Y_X_1 - r_Y_X_2 * r_X_1_X_2}{\sqrt{1 - r_X_1_X_2}^2 - \sqrt{1 - r_Y_X_2}^2} [/tex]

[tex] r_Y_X_1_|_X_2 = \frac{0.64 - 0.72 * 0.32}{\sqrt{1 - 0.32}^2 - \sqrt{1 - 0.72}^2} [/tex]

[tex] = \frac{0.410}{0.657}[/tex]

[tex] r_Y_X_1_|_X_2 = 0.62 [/tex]

The partial correlation is 0.62.

Option C

Answer:

Step-by-step explanation:

We will apply the vertical line test in the given graphs to test them for a function.

Option (1) [First in top row]

If we draw a vertical line from any point, none other point of the graph passes through it.

Therefore, Graph (1) is a function.

Option (2) [2nd in the top row]

When we draw a vertical line through (2, 1), another point (2, -1) will pass through this line.

Therefore, Graph (2) is not a function.

Option (3) [1st in the second row]

In this option when a vertical line is drawn from (2, 1) two more points (2, 2) and (2, 3) pass through this line.

Therefore, graph (4) is not a function.

Option (4). [2nd in the 2nd row]

In this graph only one point lie on the vertical lines drawn.

Therefore, Graph (4) is a function.

Answer:

paper = $4 and stapler = $7

Step-by-step explanation:

let p represent paper and s represent stapler, then

3p + 4s = 40 → (1)

5p + 6s = 62 → (2)

Multiplying (1) by 5 and (2) by - 3 and adding will eliminate p

15p + 20s = 200 → (3)

- 15p - 18s = - 186 → (4)

Add (3) and (4) term by term to eliminate p

2s = 14 ( divide both sides by 2 )

s = 7

Substitute s = 7 into either of the 2 equations and evaluate for p

Substituting into (1)

3p + 4(7) = 40

3p + 28 = 40 ( subtract 28 from both sides )

3p = 12 ( divide both sides by 3 )

p = 4

Thus package of paper costs $4 and stapler costs $7

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Trigonometry.

so here, we gonna use the cosine ratios.

so here, we also use the Pythagoras Theorem.

[tex] {h}^{2} + {k}^{2} = {r}^{2} [/tex]

so we here, we get

h= 1 ,

[tex]h = 1 \: r = 2 \: k = \sqrt{3} \: \\ \alpha = 60 \: \beta = 30[/tex]

Answer:

W+6 = Y.

Or

Y -6 = W

Step-by-step explanation:

Let's call the length of the rectangle L.

And let W represent the width of the rectangle.

Let's write an expression to determine the width of the rectangle relative to the length of the rectangle.

From the question, the width W is 6 less than the length L of the rectangle.

It means the length is greater than the width with 6 units.

The expression is

W+6 = Y.

Or

Y -6 = W

Answer:

86.53

Step-by-step explanation:

Area of Triangle Formula: A = 1/2bh

Pythagorean Theorem: a² + b² = c²

Step 1: Draw altitude and label numbers

If we draw a line down the middle, we can see that we get a perpendicular bisector and that we get 2 right triangles with a hypotenuse of 29 and a leg of 3. We need to find h using Pythagorean Theorem in order to use area formula:

3² + b² = 29²

b² = 29² - 3²

b = √832 = h

Step 2: Plug in known variables into area formula:

A = 1/2(√832)(6)

A = 3√832

A = 86.5332

Answer:

[tex]slope:1/8y-intercept:-7\\COORDINATES(x,-7)\\\\(56,0)[/tex]

Step-by-step explanation:

Answer:

The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.

Step-by-step explanation:

The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.

We reject the null hypothesis if the p-value of a statistic is lower than the level of significance α.

And we fail to eject the null hypothesis if the p-value of a statistic is greater than the level of significance α.

A lower p-value indicates that the result is statistically significant.

And a higher p-value indicates that the result is not statistically significant.

Answer:

[tex]\text{The implicit solution:} \frac{1}{81} e^{9x}(9x - 1) + \frac{3}{e^t} = C[/tex]

Step-by-step explanation:

It is given that there is arbitrary constant C and we have to find the implicit solution. Therefore, first separate the variable that is given in equation and then use integration to find the implicit solution. Here, below is the calculation.

 The given equation is:

[tex]\frac{dx}{dt} = \frac{3}{xe^{t-9x}}[/tex]

Now, if we use separation of variable.

[tex]\frac{dx}{dt} = \frac{3}{xe^{t-9x}} \\\frac{dx}{dt} = \frac{3}{xe^{9x}e^{t}} \\xe^{9x}dx = \frac{3}{e^{t}}dt \\[/tex]

Now integrate both side:

[tex]\int xe^{9x} dx = \int \frac{3}{e^{t}} dt \\\frac{e^{9x}}{9}(x) - \int \left [ \frac{e^{9x}}{9} \right]dx = -3e^{-t} + C \\[/tex]

[tex]\frac{xe^{9x}}{9} - \frac{e^{9x}}{81} = -3e^{-t} + C \\\frac{1}{81} e^{9x}(9x - 1) + \frac{3}{e^t} = C \\[/tex]

Thus, the implicit solution is:

[tex]\frac{1}{81} e^{9x}(9x - 1) + \frac{3}{e^t} = C[/tex]

Answer:

The first one

Step-by-step explanation:

Took the test

Answer: 1/10 of the store's total sales last month were in appliances (lower right corner)

Step-by-step explanation:

Let's go through the four possible answers

In the upper left corner it says "Total mobile phone sales is likely 27,000" which is a paraphrase of what is given. The chart gives 9000 as the phone sales for that one particular store. If all stores are identical in performance, then we have 4*9000 = 36000 in total mobile phone sales. Of course, it's impossible to know for sure how the other stores did. So we can eliminate this as one of the answers.

In the upper right corner, it says "13% of the stores sales was in car electronics" (also paraphrased). We have 13 thousand in car electronics out of 17+13+6+9+15 = 60 thousand total. Divide the two values: 13/60 = 0.2167 = 21.67% approximately. So we can eliminate this as an answer.

In the lower left corner, it says "the total sales is likely greater than $300,000" but we don't know for sure because again we don't have the other charts for the three other stores. Assuming the four stores perform the same, then we'd have 4*60 = 240 thousand as the total and not 300 thousand. It's safe to say we can eliminate this as an answer.

In the lower right corner, it says "1/10 of the stores sales were appliances". This statement is true. Why? Because 6 thousand is the sales figure for appliances out of 60 thousand total. Divide the values: 6/60 = 1/10. So this is why the lower right corner is the answer.

Answer:

a) x-4+9

b) x-2

For part b, I am not 100% sure about my answer, but I am sure about part a.

Answer:

99.48% probability that the sample mean would be greater than 64.8 kilograms.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 67, \sigma = \sqrt{121} = 11, n = 164, s = \frac{11}{\sqrt{164}} = 0.86[/tex]

What is the probability that the sample mean would be greater than 64.8 kilograms?

This is 1 subtracted by the pvalue of Z when X = 64.8.

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

By the Central Limit Theorem

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

[tex]Z = \frac{64.8 - 67}{0.86}[/tex]

[tex]Z = -2.56[/tex]

[tex]Z = -2.56[/tex] has a pvalue of 0.0052

1 - 0.0052 = 0.9948

99.48% probability that the sample mean would be greater than 64.8 kilograms.

Answer:

i think its 1259712.

Step-by-step explanation:

when we find3^3 and 6^6 we get, 27×46656

and by multiplying them we get, 1259712...

is answer

Answer:

  1,259,712

Step-by-step explanation:

Follow the order of operations, evaluating exponents first:

  3^3 × 6^6 = 27 × 46,656 = 1,259,712

_____

When in doubt, the Google calculator can be relied upon to follow the order of operations. (Use an asterisk (*) for multiplication.)

Answer:

Step-by-step explanation:

While the pareto distributions are continuous in nature, they are sometimes used to model discrete data in fields such as Social Sciences, Humanities, Geophysics, and Actuarial Sciences.

The Pareto Distribution is a power-law probability distribution used in studies of observable phenomena.

The probability density function (PDF) for a Pareto Distribution is:

Xn = 1

for various Alpha levels

Where Xn is the probability value of X

As Alpha tends to infinity, the pareto distribution tends to ¶ [X-Xn]

Where ¶ is the Dirac Delta function.

Answer: 4.21596 x 10⁴⁷

Step-by-step explanation:

  (3.346 x 10²⁶) (1.26 x 10²¹)

= (3.346 x 1.26) x 10²⁶⁺²¹

= 4.21596 x 10⁴⁷

Answer:4541(Rounded) 4541.99779(Unrounded)

Step-by-step explanation:

A= P(1 + r)^T

A= answer

P=principle(amount of money)

r=Rate(percent / 100)

T=Time(Annually)

1030(1 + .077)^20

Brainliest would be appericiated!