student throws 3 coins in the air. Find the probability that exactly 2 landed on heads, given that at least 2 landed on heads.

Answer:

[tex]\frac{dy}{dx}[/tex] = - 21[tex]x^{6}[/tex] + 6x² + 1

Step-by-step explanation:

Differentiate each term using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

Given

y = - 3[tex]x^{7}[/tex] + 2x³ + x , then

[tex]\frac{dy}{dx}[/tex] = (7 × - 3 )[tex]x^{6}[/tex] + (3 × 2)x² + (1 × 1 )[tex]x^{0}[/tex]

    = - 21[tex]x^{6}[/tex] + 6x² + 1

Hey there! :)

Answer:

[tex]({\frac{-9\sqrt{3} }{2}, 9/2) }[/tex]

Step-by-step explanation:

In rectangular coordinates, the form is:

(r·cosθ, r·sinθ)

In this instance:

Polar coordinates: (9, 150°). Use the coordinates above to solve for the rectangular coordinates.

(r · cos 150°, r· sin 150°)

(9 · cos 150°, 9· sin 150°)

cos 150° = -√3/2

sin 150° = 1/2

Plug these values into the equation:

(9 · (-√3/2), 9 · 1/2)

Multiply and simplify:

(-9√3/2, 9/2)

Therefore, the coordinates in rectangular form are:

[tex]({\frac{-9\sqrt{3} }{2}, 9/2) }[/tex]

Answer:

Slope: 1

y-intercept: 8

Step-by-step explanation:

x, y

-8,0

0,8

Answer:

  3 square units

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic.

  A = 12(1/2)² = 12(1/4) = 3 . . . square units

__

Comment on the working

It might be helpful to you to see how this works when the units of the number are attached to the number.

  A = 12(1/2 unit)² = 12(1/2 unit)(1/2 unit) = 12(1/2)(1/2)(unit)(unit) = 3 unit²

I often choose to keep the units with the numbers, just to make sure that the numbers and units are correct. For example, you can multiply inches by feet, but you get in·ft, which is not square inches and not square feet. You have to do a conversion to get the result in square units.

Answer:c is the correct ans

Step-by-step explanation:

Feel pleasure to help u

Answer:

B-. More than one unique triangle exists with the given side lengths.

Step-by-step explanation:

according to to tringle inequality theorem he sum of the length of two sides of a triangle should be greater than the third side”. In order to verify the mentioned theorem, some cal. are preforemed below

12+15>18

15+18>12

Answer: B. f is always negative on the interval

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

Explanation:

-1/5 = -0.2

Pick any number for x that will make the interval -0.2 < x < 2 to be true. I find x = 0 to be easiest.

Plug it into f(x)

f(x) = (5x+1)(4x-8)(x+6)

f(0) = (5(0)+1)(4(0)-8)(0+6)

f(0) = (1)(-8)(6)

f(0) = -48

We get a negative result.

So we can rule out choice A which says that f is always positive. Either f is always negative on this interval, or it's a mix of being positive and negative.

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

Note that the roots of f(x) are -1/5, 2 and -6. This is from solving f(x) = 0

Use the zero product property to solve (5x+1)(4x-8)(x+6) to find the three roots mentioned.

The roots of -1/5 and 2 form the boundary of the interval mentioned at the top of the problem. There are no roots in between -1/5 and 2, so this means that f(x) stays entirely negative on this interval. There is no way f(x) becomes positive on this interval because it would have to cross over the x axis, thus forming another root. But again there are no roots between -1/5 and 2.

A graph confirms we have the correct answer. Check out the image attached below. Note the portion from x = -0.2 to x = 2 is entirely below the x axis.

Answer:

$36

Step-by-step explanation:

30 is 5/6 of the game, so we can think that 1/6 is equal to 6, since 5(6) is 30.

If we add another sixth, we get 36, which will be the total cost of the game.

Answer: 72 arrangements

Step-by-step explanation:

The books are:

Statistics,  calculus, geometry, algebra, and trigonometry.

So we have 5 books.

We want that algebra and trigonometry are not together.

Suppose that we have 5 positions:

Now, we can start with algebra in the first position.

Now, we have 3 positions for trigonometry (3rd, 4th and 5th).

Now, once those two books are in position, we have 3 other positions and 3 other books, so for the first selection we have 3 options, for the second position we have 2 options, and for the last option we have 1 option.

The number of combinations is equal to the number of options in each selection:

3*(3*2*1) = 18

Now, if Algebra is in the second place, then for trigonometry we have only 2 possible options (4th and 5th)

and for the other 3 books again we have 3*2*1 combinations:

the total number of combinations is:

2*(3*2*1) = 12

If algebra is in the 3rd position, trigonometry has 2 options (1st and 5th)

For the other 3 books, we have 3*2*1 combinations.

The total number of combinations is:

(3*2*1)*2 = 12

in the fourth position is the same as the second position, so here we have again 12 combinations.

For the fifth position is the same as for the first position, so we have 18 combinations.

The total number of combinations is:

C = 18 + 12 +12 +12 +18 = 72

Answer:

Step-by-step explanation:

This is a combination question. Combination has to do with selection. For example if r objects are to be selected from n pool of oblects, this can be done in nCr number of ways.

nCr = n!/(n-r)r!

According to the question, if a radio show can only play 10 records out of 12 records available, this can be done in 12C10 number of ways.

12C10 = 12!/(12-10)!10!

= 12!/2!10!

= 12*11*10!/2*10!

= 12*11/2

= 6*11

= 66 different ways

Answer:

A.

Step-by-step explanation:

B is wrong because irrational numbers can include pie.

C and D are wrong because irrational numbers don't get a whole number, and instead gives a decimal numbers.

Answer:

1050 in total, 52.50 for each athlete

Step-by-step explanation:

We can start by writing an equation with x as the number of athletes

250+40x= Total cost

Now we can substitute 20 for x

250+40(20)

250+800

1050

The total cost is 1050

If you need the amount that each athlete is paying individually, just divide it by 20

1050/20=52.50

52.50 for each athlete

Answer:

0.0885 = 8.85% probability that the sample mean will exceed 2,500.

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 [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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]\mu = 2400, \sigma = 210, n = 8, s = \frac{210}{\sqrt{8}} = 74.25[/tex]

Calculate the probability that the sample mean will exceed 2,500.

This is 1 subtracted by the pvalue of Z when X = 2500. So

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

By the Central Limit Theorem:

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

[tex]Z = \frac{2500 - 2400}{74.25}[/tex]

[tex]Z = 1.35[/tex]

[tex]Z = 1.35[/tex] has a pvalue of 0.9115

1 - 0.9115 = 0.0885

0.0885 = 8.85% probability that the sample mean will exceed 2,500.

Answer:

C. (2, -3)

Step-by-step explanation:

Easiest and fastest way to get the solution set is to graph the systems of equations and analyze where the graphs intersect.

Answer:

Step-by-step explanation:

Hello!

Given the variable

X:  Ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloth.

The researcher's claim is that the ratio of the SC of the sloths is more variable than in other animal species that are more active.

For more active species the standard deviation of the ratio is σ= 0.09

1)

To calculate the sample standard deviation you have to calculate the sample variance first:

[tex]S^2= \frac{1}{n-1} [sumX^2-\frac{(sumX)^2}{n} ][/tex]

n=7; ∑X= 8.91; ∑X²= 11.8599

[tex]S^2= \frac{1}{6} [11.5899-\frac{(8.91)^2}{7} ]= 0.0287= 0.029[/tex]

S= √S²= √0.029= 0.169≅ 0.17

The sample standard deviation of the ratio is 0.17

2)

The parameter of interest is the population standard deviation. To calculate a confidence interval for the standard deviation of a population you have to estimate the population variance first. Then calculate the square root of both limits of the interval for the variance to obtain the interval for the standard deviation.

The statistic to use is the Chi-Square and the formula for the interval is:

[tex][\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ][/tex]

[tex]X^2_{n-1;\alpha /2}= X^2_{6; 0.025}= 1.2373[/tex]

[tex]X^2_{n-1;1-\alpha /2}= X^2_{6; 0.975}= 14.449[/tex]

[tex][\frac{6*0.029}{14.449} ;\frac{6*0.029}{1.2373} ]\\[/tex]

[0.0120; 0.1406]

Using a 95% confidence level you'd expect the interval [0.0120; 0.1406] to include the true value of the population variance of the ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloths.

Now you have to calculate the square root of each limit:

[√0.0120; √0.1406]

[0.1097; 0.3750]

Using a 95% confidence level you'd expect the interval [0.1097; 0.3750] to include the true value of the population standard deviation of the ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloths.

3)

As you can see the calculated interval doesn't include the value obtained for the other species.

I hope this helps!

Answer:

first term = -2

fourth term = -16

eighth term = -256

Step-by-step explanation:

Given;

A sequence with function;

A(n) = -2x2^(n-1)

The first, fourth, and eighth terms of the sequence can be calculated by substituting their corresponding values of n;

First term A(1); n = 1

A(1) = -2x2^(1-1) = -2×1 = -2

Fourth term A(4); n = 4

A(4) = -2x2^(4-1) = -2×8 = -16

Eighth term A(8); n = 8

A(8) = -2x2^(8-1) = -2×128 = -256

Therefore,

first term = -2

fourth term = -16

eighth term = -256

Answer:

  4 blue fish for every 5 orange fish

Step-by-step explanation:

(orange fish) = (1 1/4)·(blue fish) . . . . . the given relation

(orange fish) = (5/4)·(blue fish) . . . . . write as improper fraction

(orange fish)/(blue fish) = 5/4  . . . . .  divide by "blue fish"

There are 4 blue fish for every 5 orange fish.

Answer:

b. 1.69

Step-by-step explanation:

So to solve this problem we need to simply find the percentage increase from 11.8 to 12 =>

to solve this we would do 12 - 11.8 = 0.2 --> 0.2 is our "difference in the increase" -->

now we divide this by our amt. which is 11.8 --> 0.2/11.8 = approx. 0.0169

--> finally multiply that by 100 which is simply moving the decimal places 2 places right giving us the final answer of 1.69

Hope this helps!

Answer:

B. 1.69%

Step-by-step explanation:

If Ross calculated the countertop for a laundry room to be 12 square feet but turns out to be actually 11.8 square feet, we need to find out how much percentage error Ross has made!

In order to solve this question,

1) We need to create proportions:

Ross' calculations              x

______________ =   _________

   actual area                   100

x represents the percentage error.

100 is the total percentage.

2) Now we plug in the numbers:

We plug in 12 for Ross' calculations. We plug in 11.8 for the actual area. So, it will look like this:

   12                x

______ = _______

   11.8           100

3) Time for cross multiplication:

12 times 100 is 1,200

11.8 times x is 11.8x

So,

1,200 = 11.8x

4) Now we divide:

1,200 divided by 11.8 equals to 101.69 %

5) We are not done! We still have to subtract:

101.69

-100.00

_______

    1.69

Finished!!

Our answer is 1.69%, which is B.

Hope this was helpful !!!

Answer:

45°

Step-by-step explanation:

The diagram for this question has been attached to this response. Please check.

The angle of elevation is the angle between a horizontal line from a viewer and the line of sight to an object being viewed which is above the horizontal line.

From the diagram;

θ is the angle of elevation

x = height of the tree

y = length of the shadow of the tree = x

Therefore,

tanθ = [tex]\frac{x}{y}[/tex]           [Remember that y = x? Then substitute into the equation]

tanθ = [tex]\frac{x}{x}[/tex]

tanθ = 1

θ = tan⁻¹(1)

θ = 45°

Therefore, the angle of elevation is 45°

Answer:

20

Step-by-step explanation:

224÷4 = 56+40 = 96÷2 = 48+12 = 60÷3 = 20

If Ronnie goes to the racetrack with his buddies on a weekly basis. How much did he start with the first week is $20.

Hence:

4 [2 (3x - 12) -40] = 224

4 [6x - 24 - 40] = 224

Collect like term

24x - 256= 224

24x/24 = 480/24

Divide both side by 24

x=480/24

x=$20

Therefore How much did he start with the first week is $20.

Learn more about How much did he start with here:https://brainly.com/question/25870256

#SPJ2

Answer:

20 Lizard lollies.

Step-by-step explanation:

There are 10 lizard lollis.  This is out of 10+4+6 = 20 total treats.  This makes the probability of drawing a lizard lollis 10/20 = 1/2.

This means out of 40 treats handed out, we can expect him to give out 1/2(40) = 20 lizard lollis.

Answer:

34.99

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The equation must be equal to c since that is the total cost.

c = 1.18v

Plug in 98 for v to find the answer.

c = 1.18(98)

c = $115.64

Answer:

1/5k-2/3j and -2/3j+1/5k

Step-by-step explanation:

This is because the sign of both of the terms stay the same and the fractions and variables stay the same for each term as well.

Answer:

y=-3

Step-by-step explanation:

If the line is perpendicular to the y- axis, that means that it must be a horizontal line. Any horizontal line must be in the form y=b. Since the y-value of the point is -3, the equation of the line must be y=-3

Answer:

y = -3

Step-by-step explanation:

A line perpendicular to the y-axis is a horizontal line.

The equation of a horizontal line is of the form

y = k,

where k is the y-coordinate of all points on the line. Since point (-5, -3) is on the line, then the y-coordinate of all points on the line is -3.

Answer: y = -3

Answer:

Solve for y in the first equation.

Step-by-step explanation:

Given

3x+y=9

15x-3y = 1

Required

Determine the first step to avoid fractions

From the list of given options, the option that best answered the question is to Solve for y in the first equation.

Solving for y will let you substitute the expression for y in the second equation

Going by that:- Solve for y in the first equation.

[tex]3x + y = 9[/tex]

Subtract 3x from both sides

[tex]3x - 3x + y = 9 - 3x[/tex]

[tex]y = 9 - 3x[/tex]

Substitute 9 - 3x for y in the second equation

[tex]15x - 3y = 1[/tex] becomes

[tex]15x - 3(9 - 3x) = 1[/tex]

[tex]15x - 27 + 9x = 1[/tex]

Collect like terms

[tex]15x + 9x = 1 + 27[/tex]

[tex]24x = 28[/tex]

Divide both sides by 24

[tex]\frac{24x}{24} = \frac{28}{24}[/tex]

[tex]x = \frac{28}{24}[/tex]

Divide numerator and denominator by 4

[tex]x = \frac{7}{6}[/tex]

Substitute 7/6 for x in the [tex]y = 9 - 3x[/tex]

[tex]y = 9 - 3 * \frac{7}{6}[/tex]

[tex]y = 9 - \frac{7}{2}[/tex]

Solve fraction

[tex]y = \frac{18-7}{2}[/tex]

[tex]y = \frac{11}{2}[/tex]

Answer:

It's B (the one above is right)

Step-by-step explanation:

Answer:

The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:

[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]

Step-by-step explanation:

The general form of a regression equation is:

[tex]y=\alpha +\beta_{1}x_{1}+\beta_{2}x_{2}+...+\beta_{n}x_{n}[/tex]

Here,

α = y-intercept

βi = regression coefficients, (i = 1, 2, ..., n)

A regression analysis is performed to determine whether the predictor variables are statistically significant or not.

The output of the regression analysis consists of two tables.

One is the regression output and the other is the ANOVA table.

The regression output table is used to display which predictor variables are statistically significant and which are not.

The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:

[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]

And the ANOVA table displays overall regression analysis.

The F-test statistic is used to for the overall regression analysis.

Thus, the test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:

[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]

Answer:

  D.  65°

Step-by-step explanation:

The measure of the angle at crossed chords is the average of the measures of the intercepted arcs:

  m∠XYZ = (1/2)(arc XZ +arc WV)

  m∠XYZ = (1/2)(86° +44°) = 130°/2

  m∠XYZ = 65°

Answer:

see explanation

Step-by-step explanation:

Given that p varies directly as s² and inversely as r then the equation relating them is

p = [tex]\frac{ks^2}{r}[/tex] ← k is the constant of variation

To find k use the condition when s = 6, r = 3 and p = 48, that is

48 = [tex]\frac{6^2k}{3}[/tex] ( multiply both sides by 3 to clear the fraction

144 = 36k ( divide both sides by 36 )

4 = k , thus

p = [tex]\frac{4s^2}{r}[/tex] ← equation of variation

When s = 10 and r = 5 , then

p = [tex]\frac{4(10)^2}{5}[/tex] = [tex]\frac{400}{5}[/tex] = 80

Answer:

200√3

Step-by-step explanation:

The triangle given here is a special right triangle, one with angles measuring 30-60-90 degrees. The rule for triangles like these are that the side opposite the 30° angle can be considered x, and the side opposite the 60° angle is x√3, while the hypotenuse, or side opposite the right angle, is 2x. All we need to know here are the two legs to find the area.

Since b is opposite the 30° angle, it is x, while side RS is opposite the 60° angle, meaning it is equal to x√3, meaning that the area of the triangle is 1/2*x*x√3. We can substitute in 20 for x, making our area 1/2*20*20√3. Multiplying we get 10*20√3, or 200√3.