Pick two cards at random from a well-shuffled deck of 52 cards (pick them simultaneously so they are not the same card). There are 12 cards considered face cards. There are 4 cards with the value 10. Let X be the number of face cards in your hand. Let Y be the number of 10's in your hand. Explain why X and Y are dependent.

Answer:

second option

Step-by-step explanation:

x / x - 1 + 3x / x + 2

= x(x + 2) / (x - 1)(x + 2) + 3x(x - 1) / (x - 1)(x + 2)

= (x² + 2x) / (x² + x - 2) + (3x² - 3x) / (x² + x - 2)

= (4x² - x) / (x² + x - 2)

Answer:

add up c

Step-by-step explanation:

Answer:

IJ= 4.98

Step-by-step explanation:

EF = 12

KF = 6

LF = 7.8

LK = sqrt(7.8^2-6^2) = 4.98

IJ = LK (4.98)

Answer:

253°

Step-by-step explanation:

The central angle whose rays intercept a diameter of the circle has measure 180 deg.

m<AOD = 73 deg

m<DOB = 180 deg

m<ADB = m<AOD +m<DOB = 73 deg + 180 deg = 253 deg

The measure of an arc of a circle is equal to the measure of the central angle that subtends it.

m(arc)AOD = m<AOD = 253 deg

Answer: 253°

The solution is, the measure of Arc A D B is 253°.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

Here, we have,

given that AC and BD are diameters of circle O.

AC and BD intersect at point C the centre of the circle.

The central angle of a circle is the angle based at the circle's center. In other words, the vertex of the angle must be at the center of the circle. A central angle is formed by two radii that start at the center and intersect the circle itself.

The central angle whose rays intercept a diameter of the circle has measure 180 deg.

m<AOD = 73 deg

m<DOB = 180 deg

m<ADB = m<AOD +m<DOB = 73 deg + 180 deg = 253 deg

The measure of an arc of a circle is equal to the measure of the central angle that subtends it.

m(arc)AOD = m<AOD = 253 deg

Answer: the measure of Arc A D B is 253°.

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Answer:

B. The fact that two variables are strongly correlated does not in itself imply a​ cause-and-effect relationship between the variables.

Step-by-step explanation:

The term "correlation does not imply causation", simply means that because we can deduce a link between two factors or sets of data, it does not necessarily prove that there is a cause-and-effect relationship between the two variables. In some cases, there could indeed be a cause-and-effect relationship but it cannot be said for certain that this would always be the case.

While correlation shows the linear relationship between two things, causation implies that an event occurs because of another event. So the phrase is actually saying that because two factors are related, it does not mean that it is as a result of a causal factor. It could simply be a coincidence. This occurs because of our effort to seek an explanation for the occurrence of certain events.

Answer: B. The fact that two variables are strongly correlated does not in itself imply a​ cause-and-effect relationship between the variables.

Step-by-step explanation:

Hi,

f°g means :  apply first g then f . so calculate  "g" and then use result as "x" in f.  

g°f  means :   you apply first  f then g  

so :  f°g =    2(3x²-x) -5  =   6x²-2x- 5

To improve in math, you need practice. have a try with  g°f  :)

give the answer in comments, and I will tell you if you are correct.

good luck.

Answer:

B. Y = 6/4 X

Step-by-step explanation:

Well to find its parallel line we need to put,

2y - 3x = 4 into slope-intercept.

+3x to both sides

2y = 3x + 4

Now we divide everything by 2,

y = 3/2x + 2

So a line that is parallel to the given line will have the same slope but different y intercept, meaning we can cross out choices A and C.

To check look at the image below ↓

Thus,

answer choice B. Y = 6/4 X is correct.

Hope this helps :)

Answer:

The standard error of the mean is  [tex]\sigma _{\= x } = 1.581[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  250

      The standard deviation is  [tex]\sigma = 25[/tex]

          The sample mean is  [tex]\= x = 20[/tex]

The standard error of the mean is mathematically represented as

        [tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

        [tex]\sigma _{\= x } = \frac{25 }{\sqrt{250} }[/tex]

       [tex]\sigma _{\= x } = 1.581[/tex]

Answer:

Increase the sample size.

Step-by-step explanation:

Increasing the sample size is the best way to reduce the likelihood of a type II error.

The type II error occurs when a hypothesis test accepts a false null hypothesis. That is, it fails to reject the null hypothesis that is false.

In such a situation, to increase the power of the test, you have to increase the sample size used in the test. The sampling size has the ability to detect the differences in a hypothesis test.

We have a bigger chance of capturing the difference if the sample size is larger, and it also increases the power of the test.

Answer:

The 95% confidence interval for the average number of units that students in their college are enrolled in is :

Confidence Interval ( 11.76, 12.84).

Step-by-step explanation:

The formula for a Confidence Interval is:

C. I = μ ± z × σ/√n

Where

z = z score

μ is the sample mean

σ is the sample standard deviation

n = number of samples

We were given a 95% confidence interval

The z score for a 95% confidence interval = 1.96

μ = 12.3 units

σ = 1.9

n = 47 students

C. I = μ ± z × σ/√n

C.I = 12.3 ± 1.96 × 1.9/√47

C.I = 12.3 ± 0.5432012283

Hence,

Confidence interval = 12.3 ± 0.5432012283

12.3 - 0.5432012283 = 11.756798772 Approximately ≈ 11.76

12.3 + 0.5432012283 = 12.843201228

Approximately ≈ 12.84

Therefore, the 95% confidence interval for the average number of units that students in their college are enrolled in is :

Confidence Interval ( 11.76, 12.84).

Answer:

option B is the right option.

Step-by-step explanation:

[tex] \frac{bc}{ab} = \frac{ab}{bd} [/tex]

Plug the values:

[tex] \frac{20}{12} = \frac{12}{x} [/tex]

Apply cross product property

[tex]20 \times x = 12 \times 12[/tex]

Calculate the product

[tex]20x = 144[/tex]

divide both sides of the equation by 20

[tex] \frac{20x}{20} = \frac{144}{20} [/tex]

Calculate:

[tex]x = 7.2[/tex]

hope this helps..

Good luck...

this is another type of lazy.... : )

Step-by-step explanation:

Explanation:

1. CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC — given

2. ∆CRH ~ ∆HSC — AA similarity theorem

3. ∠SCH ≅ ∠RHC — corresponding angles of similar triangles are congruent

4. CH ≅ HC — reflexive property of congruence

5. ∆CRH ≅ ∆HSC — SAS congruence theorem

6. CR ≅ HS — CPCTC

Answer:

Step-by-step explanation:

Hello!

For the rectangle ABCD

AB= DC= 11

BC= AD= 2

Point E lies halfway between AB and CD

The shaded are forms two triangles, I'll refer to the upper triangle as "Triangle one" and the lower triangle will be "triangle 2"

The area of a triangle is calculated as

[tex]a= \frac{bh}{2}[/tex]

b= base

h= height

Triangle 1

b₁= AB= 11

[tex]h_1= \frac{BC}{2}= \frac{2}{2}= 1[/tex]

[tex]a_1= \frac{b_1h_1}{2}= \frac{11*1}{2}= 5.5[/tex]

Triangle 2

b₂= DC= 11

[tex]h_2= \frac{BC}{2}= \frac{2}{2} = 1[/tex]

[tex]a_2= \frac{b_2h_2}{2}= \frac{11*1}{2}= 5.5[/tex]

Now you add the areas of both triangles to get the area of the shaded region:

a₁ + a₂= 5.5 + 5.5= 11

Since point E is halfway to all sides of the rectangle, even tough it doesn't see so, the shaded area is equal to half the area of the rectangle:

area= bh= DC*AD= 11*2= 22

area/2= 22/12= 11

I hope this helps!

Answer:

[tex]\frac{x^2}{169} +\frac{y^2}{25}=1[/tex]

If we compare this to the general expression for an ellipse given by:

[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2}=1[/tex]

We can see that the vertex is [tex] V=(0,0)[/tex]

And we can find the values of a and b like this:

[tex] a=\sqrt{169}=13, b=\sqrt{25}=5[/tex]

in order to find the foci we can find the value of c

[tex] c =\sqrt{169-25}=\sqrt{144}=12[/tex]

The two focis are (12,0) and (-12,0)

The convertices  for this case are: (13,0) and (-13,0) on the x axis

And for the y axis (0,5) and (0,-5)

Step-by-step explanation:

For this problem we have the following equation given:

[tex]\frac{x^2}{169} +\frac{y^2}{25}=1[/tex]

If we compare this to the general expression for an ellipse given by:

[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2}=1[/tex]

We can see that the vertex is [tex] V=(0,0)[/tex]

And we can find the values of a and b like this:

[tex] a=\sqrt{169}=13, b=\sqrt{25}=5[/tex]

in order to find the foci we can find the value of c

[tex] c =\sqrt{169-25}=\sqrt{144}=12[/tex]

The two focis are (12,0) and (-12,0)

The convertices  for this case are: (13,0) and (-13,0) on the x axis

And for the y axis (0,5) and (0,-5)

Answer:

Identify what you want to prove and you can test using ANOVA, Chi Square, F test ..... among many.

Step-by-step explanation:

Null and alternative hypothesis are always understood in terms of experiments.

In simple words,

  null hypothesis =    The results of your experiment are due to chance  

  alternative hypothesis = The results of your experiments are NOT due to chance

Therefore, identify what you want to prove and you can test using ANOVA, Chi Square, F test ..... among many.

Answer:

[tex]x+y =14\\x-y =4[/tex]

Step-by-step explanation:

[tex]Let -the -unknown- numbers -be ; x -and; y\\x+y =14\\x-y =4[/tex]

Answer:

487 divide by 14

Step-by-step explanation:

have a nice day

Answer:

125

Step-by-step explanation:

30+25+x=180

55+x=180

x=180-55

x=125

Answer:

Step-by-step explanation:

To find x we use tan

tan ∅ = opposite / adjacent

From the question

x is the adjacent

30 is the hypotenuse

So we have

tan 25 = 30/x

x = 30/tan 25

x = 64.33

x = 64.3 to the nearest tenth

Hope this helps you

Answer:

$15,842

Step-by-step explanation:

We use the Present value formula

Present Value = Future value/(1 + r)ⁿ

r = 6% = 0.06

n = 4 years

Future value = $20,000

Present value = 20,000/(1 + 0.06)⁴

= $15841.873265

≈ $15,842

Answer:

The number of passcodes possible is 1,100,000

Step-by-step explanation:

Here , we want to calculate the number of different possible passcodes.

For the five digit code,

each number in the code has a possibility of choosing from the digits 0 to 9, so this means that each of the numbers in the code has 10 options.

So for a five digit code, the number of possible choices would be 10 * 10 * 10 * 10 * 10 = 10^5

For a six digit code, the number of possible choice would be 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10^6

So for 5 or 6 digits code, the number of possible choices would be;

10^5 + 10^6 = 10^5(1 + 10)

= 11(10^5) = 1,100,000

The number of passcodes possible is 1,100,000

For the five-digit code, the no of possible choices should be [tex]10^5[/tex]

For the six-digit code, the no of possible choices should be [tex]10^6[/tex]

So, the possible choices should be

[tex]10^5 + 10^6 = 10^5(1 + 10)\\\\= 11(10^5)[/tex]

= 1,100,000

Hence, The number of passcodes possible is 1,100,000

Learn more about code here: https://brainly.com/question/24418415

Answer: [tex]\dfrac{5}{2}.[/tex]

Step-by-step explanation:

To find: The number if  [tex]\dfrac{7}{3}[/tex] of it is [tex]5\dfrac{5}{6}[/tex].

Let x be the number.

Then, as per the statement, we have

[tex]\dfrac{7}{3}x=5\dfrac{5}{6}[/tex]

Simplify [tex]5\dfrac{5}{6}[/tex] as [tex]\dfrac{5\times6+5}{6}=\dfrac{35}{6}[/tex]

Then, [tex]\dfrac{7}{3}x=\dfrac{35}{6}[/tex]

Multiply 3 on both sides, we get

[tex]7x=\dfrac{35}{2}[/tex]

Divide both sides by 7, we get

[tex]x=\dfrac{35}{2\times7}\\\\\Rightarrow\ x=\dfrac{5}{2}[/tex]

Hence, the number is [tex]\dfrac{5}{2}.[/tex]

We will see that the mixed number is:

N = 2 + 1/2

We want to find a number N such that 7/3 times N is equal to 5 + 5/6.

So we just need to solve:

(7/3)*N = (5 + 5/6)

If we multiply both sides by 3/7, we get:

(3/7)*(7/3)*N = (3/7)*(5 + 5/6)

N = 15/7 + 15/42

If we multiply and divide the first fraction by 6, we get:

N = (6/6)*15/7 + 15/42 = 90/42 + 15/42

N = 105/42

Now we can write:

105 = 42 + 42 + 21

Replacing that in the fraction we would get:

N = 105/42 = (42 + 42 + 21)/42 = 42/42 + 42/42 + 21/42 = 2 + 21/42

N = 2 + 1/2

If you want to learn more about mixed numbers, you can read:

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Answer:

Step-by-step explanation:

Equation of the line has been given as,

[tex]y=\frac{3}{2}x-5[/tex]

By comparing this equation with the y-intercept form of the equation,

y = mx + b

Slope of the line 'm' = [tex]\frac{3}{2}[/tex]

and y-intercept 'b' = -5

Table for the points to be plotted on a graph will be,

x              y

-4           -11

-2           -6

0            -5

2            -4

4            -3

By plotting y-intercept (0, -5) and any one of the points given in the table we can get the required line.

Answer: actually the answer to this question is (0, -5) and ( 2, -2)

Step-by-step explanation: I just took the test on Plato and got it right :)

Answer:

Probability distribution

Step-by-step explanation:

Probability distribution is the function which describes the likelihood of possible values assuming a random variable. Alternative hypothesis is a statement which we accept or reject based on the null hypothesis. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

Answer:

x = -8, 8

Step-by-step explanation:

Set y = 0 to find the x intercepts

0 = x^2 -64

Add 64 to each side

64 = x^2

Take the square root of each side

±sqrt(64) = sqrt(x^2)

±8  =x

Answer:

Step-by-step explanation:

[tex]\mathrm{For\:a\:line\:equation\:for\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is\:}\mathbf{m}\\m=6[/tex]

If there is $15 off on the dress and the original price of the dress was $96 the sale price of the dress will be $81.

In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.

Given that Sophie discovered a dress she liked that was $15 off. The dress cost $96.

The sale price of the dress is obtained by subtracting the original price from the price discount on the dress,

= $96 - $15

=$  $81

Thus, if there is $15 off on the dress and the original price of the dress was $96 the sale price of the dress will be $81.

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Answer:

C

Step-by-step explanation:

According to SohCahToa, cosine is adjacent over the hypotenuse.

The adjacent when looking from angle b, is 21.

The hypotenuse of this triangle is 29.

So Cos B=21/29

Answer:

R'(- 2, 4 )

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , thus

R(4, - 2 ) → R'(- 2, 4 )

Answer:

R'(- 2, 4 )

Step-by-step explanation:

I got it right on edg

Answer:

a. The first six terms are:

-7, -4, -1, 2, 5, 8

b. The first six terms are:

0, 2, 0, 2, 0, 2.

c. The first six terms are:

4, 8, 24, 96, 480, 2880

Step-by-step explanation:

a. an - 3n - 10

For n = 1

a1 = 3(1) - 10

= -7

For n = 2

a2 = 3(2) - 10

= -4

For n = 3

a3 = 3(3) - 10

= -1

For n = 4

a4 = 3(4) - 10

= 2

For n = 5

a5 = 3(5) - 10

= 5

For n = 6

a6 = 3(6) - 10

= 8

The first six terms are:

-7, -4, -1, 2, 5, 8

b. an= (1+(-1)^n)^n

For n = 1

a1 = (1+(-1)^1)^1

= 0

For n = 2

a2 = (1+(-1)^2)^1

= 2

For n = 3

a3 = (1+(-1)^3)^1

= 0

For n = 4

a4 = (1+(-1)^4)^1

= 2

For n = 5

a5 = (1+(-1)^5)^1

= 0

For n = 6

a6 = (1+(-1)^6)^1

= 2

The first six terms are:

0, 2, 0, 2, 0, 2.

c. an= 2n! (2)

For n = 1

a1 = 2(1!)(2)

= 4

For n = 2

a2 = 2(2!)(2)

= 8

For n = 3

a3 = 2(3!)(2)

= 24

For n = 4

a4 = 2(4!)(2)

= 96

For n = 5

a5 = 2(5!)(2)

= 480

For n = 6

a6 = 2(6!)(2)

= 2880

The first six terms are:

4, 8, 24, 96, 480, 2880

Answer:

Step-by-step explanation:

To find the height h we use tan

tan ∅ = opposite / adjacent

From the question

The adjacent is 2000 ft

The opposite is h

So we have

tan 15° = h / 2000

h = 2000 tan 15

h = 535.89 ft

h = 536 ft to the nearest foot

Hope this helps you