in a standard deck there are 52 cards. If Event A is "the card is black" and Event B is "the card is a king," demonstrate the equation holds true.

__ / 52 = __ / 4 × __ / 52​

Answer:

21 miles which is b

Step-by-step explanation:

no other answer makes sense besides that one.

Answer:

The fourth one! (2,-8).

Answer:

Exponential .

Step-by-step explanation:

If you have x with that symbol ^ then it is a exponet, which makes it a exponential.

Answer:

0.0027 = 0.27% probability that the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes

Step-by-step explanation:

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

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.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

At a large state university, the heights of male students who are interscholastic athletes is approximately Normally distributed with a mean of 74.3 inches and a standard deviation of 3.5 inches. Sample of 10:

This means that [tex]\mu_I = 74.3, s_I = \frac{3.5}{\sqrt{10}}[/tex]

Those who are "non-interscholastics" have mean of 70.3 inches and a standard deviation of 3.2 inches. Sample of 12.

This means that [tex]\mu_N = 70.3, s_N = \frac{3.2}{\sqrt{12}}[/tex]

What is the probability that the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes?

This is the probability that:

N - I > 0

Distribution N - I:

[tex]\mu = \mu_N - \mu_I = 70.3 - 74.3 = -4[/tex]

[tex]s = \sqrt{s_I^2+s_N^2} = \sqrt{(\frac{3.5}{\sqrt{10}})^2+(\frac{3.2}{\sqrt{12}})^2} = 1.44[/tex]

Probability:

One subtracted by the p-value of Z when X = 0.

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

By the Central Limit Theorem

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

[tex]Z = \frac{0 - (-4)}{1.44}[/tex]

[tex]Z = 2.78[/tex]

[tex]Z = 2.78[/tex] has a p-value of 0.9973

1 - 0.9973 = 0.0027

0.0027 = 0.27% probability that the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes

The probability for the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes in state university is 0.0027.

Normally distributed data is the distribution of probability which is symmetric about the mean.

The mean of the data is the average value of the given data. The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

For the above data, the value of mean would be

[tex]m=70.3-74.3\\m=-4[/tex]

The selected sample size are 10 interscholastic athletes and 12 non-interscholastics. The value of standard deviation is,

[tex]\sigma=\sqrt{(\dfrac{3.5}{\sqrt{10}})^2+(\dfrac{3.2}{\sqrt{10}})^2}\\\sigma=1.44[/tex]

The Z score can be find out using the following formula.

[tex]Z=\dfrac{X-\mu}{\sigma}\\Z=\dfrac{0-(-4)}{1.44}\\Z=2.78[/tex]

The z score of 2.78 has the p value equal to 0.9973. For sample mean of non-interscholastics to be greater, the probability,

[tex]P=1-0.9973\\P=0.0027[/tex]

Thus, the probability for the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes in state university is 0.0027.



Learn more about the normally distributed data here;

https://brainly.com/question/6587992

Answer:

(28 x 28 x 3.14) - (18 x 18 x 3.14)

=

1444.4

The result of the expression (28 x 28 x 3.14) - (18 x 18 x 3.14) is 20940.80.

Given that:

Expression:

(28 x 28 x 3.14) - (18 x 18 x 3.14)

To calculate the given expression, follow these steps:

First, evaluate the expressions inside each set of parentheses.

Next, perform the arithmetic operations based on the calculated values.

Step 1:

(28 x 28 x 3.14)

The 28 × 28 is equal to 784, then

(28 x 28 x 3.14) = 784 × 3.14

(28 x 28 x 3.14) = 2461.76

(18 x 18 x 3.14)

The 18 x 18 is equal to 324, then

(18 x 18 x 3.14) = 324 × 3.14

(18 x 18 x 3.14) = 1017.36

Step 2:

21952.64 - 1011.84 = 20940.80

So, the result of the (28 x 28 x 3.14) - (18 x 18 x 3.14) is 20940.80.

Learn more about Expression here:

https://brainly.com/question/34132400

#SPJ6

We are given:

Speed of the train = 90 km/h

Converting the speed to km per minute:

[tex]90\frac{km}{h}* \frac{h}{60 min}[/tex]           [since 1 hour = 60 minutes, h/60 minutes is equal to 1]

The 'h' in numerator and denominator will cancel out

90km / 60 min

1.5 km/min

Distance travelled in 2 minutes:

Distance = Speed * time

Distance = [tex]1.5\frac{km}{min}* 2 min[/tex]

Distance = 3 km

Answer:

If the coin is fair, then the odds of getting heads or tails should be equal, 12. Then 3 tosses of tails will have a chance of 12⋅12⋅12=18.

Answer:

1/8 or 12.5%

Step-by-step explanation:

The odds of getting heads is 50% (1/2) each time.

So putting the odds to the power of three will provide the odds of getting heads 3 times.

1/2 * 1/2 * 1/2 = 1/8 or 12.5%

Answer:

350 pounds

Step-by-step explanation:

Assuming three of the turtles are Pinta Island Tortoise, then:

3 turtles -- 1050

1 turtle -- 1050/3 = 350

Thenks and mark me brainliest :))

Answer:

the answer is 350

Step-by-step explanation:

1050 divided by 3 equals 350!!! hope this helps

Answer:

y = 1/x-5 + 2

Step-by-step explanation:

Adding 2 will shift the graph up 2 units

Adding numbers to the x will shift the graph left, so subtract 5 to shift the graph to the right

Answer:

(5x - 4) = 2(2x + 1)

Step-by-step explanation:

Since Ancilla is twice as old as Christabel

Ancilla's age (5x - 4) is twice Christabel (2x + 1) so,

(5x - 4) = 2(2x + 1)

Answer:

you know that the coefficient of x is one so to find x the real equation is x+27= -12 so u cross over 27 to the right it will be -12-27=-39.

Answer:

its just D or its D and E

Step-by-step explanation:

Answer:

Total cost of the trip = 243 + 72x

Step-by-step explanation:

Cost of airfare = $243

Amount spent per day = $72

Which expression can he use to help him find the cost of the trip?

Let

x = number of days spent in Alaska

Total cost of the trip = Cost of airfare + (Amount spent per day * number of days spent in Alaska)

= 243 + (72 * x)

= 243 + 72x

Total cost of the trip = 243 + 72x

If he spent 4 days on the trip

Total cost of the trip = 243 + 72x

= 243 + 72(4)

= 243 + 288

= $531

Answer:

See below

Step-by-step explanation:

1)

[tex] \frac{11 + x}{(2 - x)(x - 3)} = \frac{A}{2 - x} + \frac{B}{x - 3} \\ \\ \therefore \: \frac{11 + x}{(2 - x)(x - 3)} = \frac{A(x - 3) +B(2 - x) }{(2 - x)(x - 3)} \\ \\ \therefore \: 11 + x = Ax - 3A + 2B - Bx \\ \\ \therefore \: 11 + x = - 3A + 2B + Ax - Bx\\ \\ \therefore \: 11 + x = - 3A + 2B + (A - B)x \\ \\ equating \: the \: like \: terms \: on \: both \: sides \\ A - B = 1 \\ \therefore \: A = B + 1.....(1) \\ \\ - 3A + 2B = 11....(2) \\ from \: eq \: (1) \: and \: (2) \\ - 3(B + 1) + + 2B = 11 \\ \\ - 3B - 3 + 2B = 11 \\ \\ - B = 11 + 3 \\ \\ B = - 14 \\ A = - 14 + 1 = - 13 \\ \\ \frac{11 + x}{(2 - x)(x - 3)} = \frac{ - 13}{2 - x} + \frac{ - 14}{x - 3} \\ \\ \frac{11 + x}{(2 - x)(x - 3)} = - \frac{ 13}{2 - x} - \frac{ 14}{x - 3}[/tex]

2)

[tex] \frac{12x + 11}{x^2 +x - 6}[/tex]

[tex] =\frac{12x + 11}{x^2 +3x-2x - 6}[/tex]

[tex] =\frac{12x + 11}{x(x +3) -2(x +3)}[/tex]

[tex] \therefore \frac{12x + 11}{x^2 +x - 6}=\frac{12x + 11}{(x +3) (x - 2)}[/tex]

[tex] \therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A}{(x +3)}+\frac{B}{(x - 2)}[/tex]

[tex] \therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A(x-2)+B(x+3)}{(x-2)(x+3)}[/tex]

[tex] \therefore 12x + 11 = A(x-2)+B(x+3)[/tex]

[tex] \therefore 12x + 11 = Ax-2A+Bx+3B[/tex]

[tex] \therefore 12x + 11 = Ax+Bx-2A+3B[/tex]

[tex] \therefore 12x + 11 = (A+B) x-2A+3B[/tex]

Equating like terms on both sides:

[tex] A + B = 12\implies A = 12-B... (1)[/tex]

[tex] - 2A + 3B = 11... (2)[/tex]

Solving equations (1) & (2), we find:

A = 5, B = 7

[tex] \therefore \frac{12x + 11}{x^2 +x - 6}=\frac{5}{(x +3)}+\frac{7}{(x - 2)}[/tex]

Answer:

961.327 square inches

hundreth = 961.328

Step-by-step explanation:

if u want I can show you the steps

Answer:

V = approx 2035.75

Answer:

True

Step-by-step explanation:

One is the opposite of the other

Answer:

true

Step-by-step explanation:

Answer:

x equals 14 - 7y

Step-by-step explanation:

x + 7y = 14

From this, take 7y to the other side. On shifting it to the other side of the equation, its sign changes to negative.

x = 14 - 7y

Then, we get x equals 14 - 7y.

Answer:

I just did this question I got confused for a second maybe you have a classmate or someone on here lol! x = 6 measure EJF: 64 HOPE THAT HELPS!

Answer:

the answer is 12

i used 5 12 13 special trangle

and there is 2 angle 56 and 34

so the biggest angle meet the 12

and the little angle meet the 5

hopefully its correct

Answer:

[tex] sin \theta = \frac{\sqrt {19}}{10} [/tex]

Step-by-step explanation:

[tex] ( \sin \theta) ^{2} + ( \cos \theta) ^{2} = 1 \\ \\ \therefore \:( \sin \theta) ^{2} + { \bigg( \frac{{9} }{10} \bigg)}^{2}= 1 \\ \\( \sin \theta) ^{2} + \frac{81}{100}= 1 \\ \\ ( \sin \theta) ^{2} = 1 - \frac{81}{100} \\ \\ ( \sin \theta) ^{2} = \frac{100 - 81}{100} \\ \\ ( \sin \theta) ^{2} = \frac{19}{100} \\ \\ \sin \theta = \sqrt{\frac{19}{100} } \\ \\ \sin \theta = \frac{\sqrt {19}}{10} [/tex]

Answer:

hi

there was 3 Elmos and 1 Ellie how much cuteness is there

alot

.

Depends on how cute each one is. then add your math.

-Elizabeth Rodrigo

-YT: Lizzy Playz (with an icon of a cte anime girl with round glasses)

-Dis Cord: Your.Local.Lizzy.Afton

Answer:

Y= PV*(1 + g)^t

Step-by-step explanation:

Giving the following information:

Number of Restaurants (PV)= 2,000

Growth rate (g)= 3%

To calculate the number of restaurants after t years, we need to use the following formula:

Y= PV*(1 + g)^t

For example, for 10 years:

Y= 2,000*(1.03^10)

Y= 2,688

Answer:

The combined area of the shaded triangles in Figure 1 is equal to the combined area of the shaded triangles in Figure 2.  The area of the unshaded square in Figure 1 can be represented by 4c. The combined area of the two unshaded squares in Figure 2 can be  4a+4b. The areas of the squares in Figure 1 and Figure 2 show that 4a+4b=4c.

Step-by-step explanation:

iReady math diagnostic.

Answer:2,097.80

Step-by-step explanation: If you multiply the 2,468.00 to 0.85% you will get the answer of 2,097.80.

Answer:

$2,097.80

Step-by-step explanation:

$2,468.00 - 15%

$2,468.00 * 0.15 = $370.20

$2,468.00 - $370.20 = $2,097.80

(Just another way to do it)

Step-by-step explanation:

if x = 7 and y = 4

a) x + 2y

= 7 + 2 . 4

= 7 + 8

= 15

b) (2x - y)/5

= (2 . 7 - 4)/5

= (14 - 4)/5

= 10/5

= 2

Answer:

The first equation is 15 and the second equation is 2.

Step-by-step explanation:

You have to use substitution. For the first equation it would be: 7 + 2(4),which is 7 + 8,which is 15. For the second equation it would be: 2(7) - 4 divided by 5,which is also 14 - 4 divided by 5,which is 10/5, which is 2.

Answer:

a

Step-by-step explanation:

a is the answer

Answer:

Area = 1514 m^2

Step-by-step explanation:

Total Area = area of rectangle + area of circle

= (60 m × 20 m) + πr^2

= (1200 m^2) + (3.14)(10 m)^2

= (1200 m^2) + (314 m^2)

= 1514 m^2

Answer:

c sorry if im wrong

Step-by-step explanation:

soryy if im wrong please forgive me if i am

Answer:

D.the diagonal bisect each other.Since bisectors divide the diagonals equally in two parts.