A player pays $2 to randomly draw a card from a standard deck of playing cards. He wins $10 if he draws a black 2, and $5 if a 10 or ace is picked. Determine the probability of each possible value of X (the amount won or lost) to complete the probability distribution for the game. Give each value as a fraction with a denominator of 52.

Answer:

The radius of the silo is 3.49 m.

Step-by-step explanation:

We have,

Height of the cylinder, h = 30 ft

Volume of cylindrical shaped grain silo, [tex]V=1152\ ft^3[/tex]

It is required to find the radius of silo. The formula of volume of cylinder is given by :

[tex]V=\pi r^2h[/tex]

r is radius

[tex]r=\sqrt{\dfrac{V}{\pi h}} \\\\r=\sqrt{\dfrac{1152}{\dfrac{22}{7}\times 30 }} \\\\r=3.49\ m[/tex]

So, the radius of the silo is 3.49 m.

Answer:

Hector will pay $74.25 interest on the loan.

Step-by-step explanation:

Hector took out a loan of $900 for 18 months at a rate of 5.5% annually.

Principal amount = $900

Rate of interest = 5.5%

Time = 18 months = 1.5 years

Formula for interest :

[tex]I=\frac{P\times R\times T}{100}[/tex]

  [tex]=\frac{900\times 5.5\times 1.5}{100}[/tex]

 = 74.25

Hector will pay $74.25 interest on the loan.

Given:

The radius of the circle is 12 units.

The central angle of the shaded region is 90°

We need to determine the arc length of the shaded region.

Arc length:

The arc length of the shaded region can be determined using the formula,

[tex]Arc \ length=(\frac{\theta}{360} ) 2 \pi r[/tex]

substituting [tex]\theta=90[/tex] and r = 12, we get;

[tex]Arc \ length=(\frac{90}{360} ) 2 (3.14)(12)[/tex]

Multiplying the terms, we have;

[tex]Arc \ length=\frac{6782.4}{360}[/tex]

Dividing, we get;

[tex]Arc \ length=18.84[/tex]

Rounding off to the nearest tenth, we get;

[tex]Arc \ length =18.8[/tex]

Thus, the arc length of the shaded region is 18.8 units.

(arrange the data set from least to greatest)

0, 0, 2, 2, 3, 4, 6, 8

(find the median: *the middle number*)

Median: 2.5

Lower quartile: 1

Upper quartile: 5

Interquartile range : upper quartile - lower quartile = answer

Interquartile range: 5 - 1 = 4

So the IQR or interquartile for the following data set is 4.

Answer 144 ft2

Step-by-step explanation:

Answer:

The surface area is 81 feet squared

Step-by-step explanation:

IM SO SORRY! the answer is 33 feet squared

Answer:

0% probability that less than 76 in the sample keypads pass inspection.

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using 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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 181, p = 0.8[/tex]

So

[tex]\mu = E(X) = np = 181*0.8 = 144.8[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{181*0.8*0.2} = 5.38[/tex]

Find the probability that less than 76 in the sample keypads pass inspection.

Using continuity correction, this is [tex]P(X < 76 - 0.5) = P(X < 75.5)[/tex], which is the pvalue of Z when X = 75.5.

So

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

[tex]Z = \frac{75.5 - 144.8}{5.38}[/tex]

[tex]Z = -12.88[/tex]

[tex]Z = -12.88[/tex] has a pvalue of 0

0% probability that less than 76 in the sample keypads pass inspection.

Answer:

[tex]0.56749[/tex].

Step-by-step explanation:

We have been given that the wait times in line at a grocery store are roughly distributed normally with an average wait time of 7.6 minutes and a standard deviation of 1 minute 45 seconds. We are asked to find the probability that the wait time is less than 7.9 minutes.

First of all, we will convert 45 seconds into minutes by dividing by 60 as:

[tex]45\text{ Seconds}=\frac{45}{60}\text{ minutes}=0.75\text{ minutes}[/tex]

So 1 minute 45 seconds will be equal to 1.75 minutes.

Now, we will find z-score corresponding to 7.9 minutes using z-score formula.

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

z = z-score,

x = Random sample score,

[tex]\mu[/tex] = Mean,

[tex]\sigma[/tex] = Standard deviation.

[tex]z=\frac{7.9-7.6}{1.75}[/tex]

[tex]z=\frac{0.3}{1.75}[/tex]

[tex]z=0.17142\approx 0.17[/tex]

Now we will use normal distribution to find area under normal curve that corresponds to a z-score of 0.17 that is [tex]P(z<0.17)[/tex].

[tex]P(z<0.17)=0.56749[/tex]

Therefore, the probability that wait time is less than 7.9 minutes would be 0.56749.

Answer:21 (2 sf)

Step-by-step explanation:

10%0f 520=52

1%0f 520=52 divide by 10 =5.2

5.2x4=20.8

=21 to 2sf

I am going to assume 10.42 is 10 minutes 42 secons.

10 min * 60 seconds / per minute, = 600 seconds

600 + 42 = 642 seconds starting

-

8 min * 60 seconds / per minute, = 480 seconds objective

To solve for how long this will take set up an equation,

642 - 1.6t = 480

162 = 1.6t

t = 101.25 days

Since time has a decial, it needs to be rounded up in order for her to be fully below 8 minutes.

Therefore the answer is 102 days.

Answer:

D

Step-by-step explanation:

please like and Mark as brainliest

don't mind my messy handwriting

We can build a polynomial given it's degree and zeros. Below I am going to show how we do that, and then I will solve the question, finding that one example of a desired polynomial is:

[tex]f(x) = x^3 - 15x^2 + 54x - 40[/tex]

Zeros of a function:

Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.

In this question:

Polynomial of degree 3, so 3 roots.

All positive, I will choose:

[tex]x_1 = 1, x_2 = 4, x_3 = 10[/tex]

I will choose the leading coefficient as a = 1.

Thus

[tex]f(x) = a(x - x_1)(x - x_2)(x - x_3)[/tex]

[tex]f(x) = (x-1)(x-4)(x-10)[/tex]

[tex]f(x) = (x^2-5x+4)(x-10)[/tex]

[tex]f(x) = x^3 - 15x^2 + 54x - 40[/tex]

The image shown in the end of this question shows that this polynomial has three positive roots, also all whole numbers.

Another similar example is given at https://brainly.com/question/21328461

Answer: she should use 13 pounds of birdseed and 27 pounds of sunflower seeds.

Step-by-step explanation:

Let x represent the number of pounds of birdseed that she should use.

Let y represent the number of pounds of sunflower seeds that she should use.

Angela​ Leinenbachs' pet store wishes to make a 40​-pound mixture of birdseed and sunflower seeds. It means that

x + y = 40

Birdseed costs ​$0.52 a pound and sunflower seeds cost ​$0.82 a pound. If the mixture would sell for ​$0.72 per a pound, then the total cost of the mixture would be 0.72 × 40 = $28.8

The equation would be

0.52x + 0.82y = 28.8- - - - - - - - - -1

Substituting x = 40 - y into equation 1, it becomes

0.52(40 - y) + 0.82y = 28.8

20.8 - 0.52y + 0.82y = 28.8

- 0.52y + 0.82y = 28.8 - 20.8

0.3y = 8

y = 8/0.3 = 27

x + y = 40

x + 27 = 40

x = 40 - 27

x = 13

Answer:

hope this helps

please like and Mark as brainliest

Answer:

[tex]P(8)=700\cdot(1.1)^8\approx 1500[/tex], where t is the number of years since 2010.

Step-by-step explanation:

See my attached image for an explanation!

Answer: p = X/(1-X)X + Y/(1-Y)Y

Step-by-step explanation:

Answer: (-2, 3)

Step-by-step explanation:

Answer:

The point-slope form of a linear equation is a formula that allows a person to calculate the slope and point of intercept of a line, and then once you calculate the linear equation, you can calculate the x and y coordinate of any point on the line!

1. Choose two points on a line.

2. Indicate the y1 (the y coordinate of the first point) and y2 (the y coordinate of the second point).

3. Indicate the x1 (the x coordinate of the first point) and the x2 (the x coordinate of the second point)

4. Plug the previously identified variables into the slope formula where the slope is equal to (y2-y1)/(x2-x1)

5. Subtract y2 and y1.

6. Subtract x2 and x1.

7. Divide the quantity in #5 by the quantity in #6. This is your slope.

8. Observe the equation: y=mx+b where "m" is the slope calculated in #7.

9. Plug in the slope for "m"

10. Using one of the points identified earlier, plug in y1 into "y" and x1 into "x". Rearrange and solve for b.

11. Then plug in the value "b" into y=mx+b. Make sure to leave the unknown variables "x" and "y", but make sure to still plug in the "m" calculated earlier!

Answer:

Step-by-step explanation:

let the quadratic eq. be ax²+bx+c=0

or x²+b/a x+c/a=0

or x²+b/ax=-c/a

to complete the square add both sides (b/2a)²or b²/4a²

x²+b/a x+(b/2a)²=b²/4a² -c/a

(x+b/2a)²=(b²-4ac)/(4a²)

taking square root

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

now you must know why -b and not +b

Final answer:

The expression ± √(b² - 4ac) in the quadratic formula refers to the discriminant and cannot be rewritten as b ± √(-4ac) because it would incorrectly separate b from the discriminant and alter the expression's meaning, leading to incorrect solutions.

Explanation:

The student is asking about the quadratic formula, which is used to find the solutions to a quadratic equation of the form at² + bt + c = 0. The formula for the solutions is given by:

-b ± √(b² - 4ac) / 2a

The term ± √(b² - 4ac) cannot be rewritten as b ± √(-4ac) because it alters the original expression's meaning. The square root is taken of the entire expression b² - 4ac, which represents the discriminant of the quadratic equation. It provides information on the nature and number of roots of the equation. Separating b from the discriminant before taking the square root would calculate a different value and therefore lead to incorrect solutions.

Example:

When you substitute the given values, say a = 1, b = 0.0211, and c = -0.0211, into the quadratic formula, you will get:

-0.0211 ± √((0.0211)² - 4(1)(-0.0211)) / (2(1))

Changing the formula to b ± √(-4ac) incorrectly suggests that you can separate b from the discriminant and take the square root of -4ac alone, which would not yield a correct solution.

Answer:

y = 1.8x + 32

or

y = 9/ 5x  + 32

Step-by-step explanation:

Used a slope calculator

Answer:

There is 8% (P=0.08) that Frances concludes that the new equipment increases the average daily jewelry production when in fact the new equipment has no effect.

Step-by-step explanation:

We have one-sample z-test with a significance level of 0.08 and a power ot the test of 0.85.

In this test, the null hypothesis will state that the new equipment has the same  productivity of the older equipment. The alternative hypothesis is that there is a significative improvement from the use of new equipment.

The probability that Frances concludes that the new equipment increases the average daily jewelry production when in fact the new equipment has no effect is equal to the probability of making a Type I error (rejecting a true null hypothesis).

The probability of making a Type I error is defined by the level of significance, and in this test this value is α=0.08.

Then, there is 8% that Frances concludes that the new equipment increases the average daily jewelry production when in fact the new equipment has no effect.

Answer:

44

Step-by-step explanation:

if 88 is the right angle degree, that means the acute angle would be half of 88.

88÷2=44

Answer:

V = [tex]\frac{1}{3}[/tex]π(8 - [tex]\frac{8}{3}[/tex])[tex]\sqrt{\frac{8}{3} }[/tex] = 9.11 [tex]m^{3}[/tex]

r = 4[tex]\frac{\sqrt{3} }{3}[/tex]

h = [tex]\sqrt{\frac{8}{3} }[/tex]

Step-by-step explanation:

Given that the right triangle whose hypotenuse is [tex]\sqrt{8}[/tex]

We know that:

[tex]r^{2} + h^{2} = 8[/tex]

<=> [tex]r^{2} = 8 - h^{2}[/tex]

The volume of the cone is:

V = π[tex]r^{2} \frac{1}{3} h[/tex]

<=> V = π[tex]\frac{1}{3}(8 - h^{2} )h[/tex]

Differentiate w.r.t h

[tex]\frac{dV}{dh}[/tex] = π [tex]\frac{1}{3}[/tex] (8 - [tex]3h^{2}[/tex])

For maximum/minimum: [tex]\frac{dV}{dh}[/tex] = 0

<=> π [tex]\frac{1}{3}[/tex] (8 - [tex]3h^{2}[/tex])  = 0

<=> [tex]h^{2}[/tex] = [tex]\frac{8}{3}[/tex]

<=> h = [tex]\sqrt{\frac{8}{3} }[/tex]

=> [tex]r^{2}[/tex] = [tex]\frac{16}{3}[/tex]

<=> r = 4[tex]\frac{\sqrt{3} }{3}[/tex]

So the volume of the cone is:

V = [tex]\frac{1}{3}[/tex]π(8 - [tex]\frac{8}{3}[/tex])[tex]\sqrt{\frac{8}{3} }[/tex] = 9.11 [tex]m^{3}[/tex]

Answer:

k is also 109 degrees bcoz they are corresponding angles

Answer:

V = 10,240mm^3

Step-by-step explanation:

The volume of pyramid is given by the following formula:

[tex]V=\frac{1}{3}bh[/tex]  (1)

b: base of the pyramid = (32mm)^2

h: height

Thus, it is necessary to find the value of h, by using the Pitagoras's theorem, one half of the base and the slant height (which forms a rectangle triangle with h):

[tex]h=\sqrt{(34)^2-(16)^2}=30mm[/tex]

by replacing in (1) you obtain:

[tex]V=\frac{1}{3}(32mm)^2(30mm)=10,240\ mm^3[/tex]

hence, the volume is 10240mm^3

Answer:

Step-by-step explanation:

The ordered pairs are

The slope is:

Answer is 2

Answer:

4

Step-by-step explanation:

The graph is:

x    y

1/4  2

1/2  4

Slope formula is (y2-y1/x2-x1)

4-2/0.5-0.25

2/0.25

4

Best of Luck!

Answer:

The answer is A, C and D

Step-by-step explanation:

a

c

d

The correct answer is a) The sample needs to be random but we don’t know if it is.

Calculate success by multiplying the sample % by the sample size to make sure the sample size is adequate.

The situation at random we receive impartial population data from random sampling. It might be dangerous to draw conclusions about a community from data that was not randomly chosen samples since such data typically contains some type of bias.

Calculate success by multiplying the sample % by the sample size to make sure the sample size is adequate, and calculate failure by multiplying one less than the sample percentage by the sample size. The condition is satisfied if both of these items are larger than ten.

To learn more about random condition refer to:

https://brainly.com/question/251701

#SPJ2

Answer:

i. The amount made in interest is $65,000.

ii. Yes, because her expenses is lesser that her interest.

Step-by-step explanation:

i. The woman puts $1,000,000 in a savings account with an interest rate of 6[tex]\frac{1}{2}[/tex]%.

Interest rate = 6[tex]\frac{1}{2}[/tex]% = [tex]\frac{13}{200}[/tex]

The amount she would make in interest = [tex]\frac{13}{200}[/tex] × 1,000,000

                                                                   = 65,000

The amount made in interest is $65,000.

ii. The total of her expenses last year is $47,0000 which is lesser than the amount made in inerest.

After her total expenses, should would have a remainder of;

                                   = $65,000 - $47,0000

                                  = $18,000

Therefore, she would be able to live off the interest.

Answer:

42 over 100

Step-by-step explanation:

Answer:21/38

Step-by-step explanation:

Answer: Im 75% sure the answer is A. Its either A or B.

Step-by-step explanation: