I select two cards from a deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which of the following is the most appropriate sample space S for the possible outcomes?

a. S={red, black}
b. S={(red, red), (red, black), (black, red), (black, black)} where, for example, (red, red) stands for the event "the first card is red and the second card is red."
c. S={0,1, 2}
d. All of the above

Answer:

[a] y=x^2+3,  vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

[d] y= (1/2)x^2 - 5, vertex, V(0,-5)

Step-by-step explanation:

The vertex, V, of a quadratic can be found as follows:

1. find the x-coordinate, x0,  by completing the square

2. find the y-coordinate, y0, by substituting the x-value of the vertex.

[a] y=x^2+3,  vertex, V(0,3)

y=(x-0)^2 + 3

x0=0, y0=0^2+3=3

vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

y=2(x-0)^2+0

x0 = 0, y0=0^2 + 0 = 0

vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

y=-(x^2-0)^2 + 4

x0 = 0, y0 = 0^2 + 4 = 4

vertex, V(0,4)

y = (1/2)(x-0)^2 -5

x0 = 0, y0=(1/2)0^2 -5 = -5

vertex, V(0,-5)

Conclusion:

When the linear term (term in x) is absent, the vertex is at (0,k)

where k is the constant term.

Answer:

The integers are 7 and 14.

Step-by-step explanation:

y = 2x

1/y + 1/x = 3/14

1/(2x) + 1/x 3/14

1/(2x) + 2/(2x) = 3/14

3/(2x) = 3/14

1/2x = 1/14

2x = 14

x = 7

y = 2x = 2(7) = 14

Answer: The integers are 7 and 14.

The required two integers are 7 and 14

This is a question on word problems leading to the simultaneous equation:

Let the two unknown integers be x and y. If a positive integer is twice another, then x = 2y .......... 1

Also, if the sum of the reciprocals of the two positive integers is 3/14, then:

[tex]\frac{1}{x}+ \frac{1}{y} =\frac{3}{14}[/tex] ..........2

Substitute equation 1 into 2

[tex]\frac{1}{2y} +\frac{1}{y} =\frac{3}{14} \\[/tex]

Find the LCM of 2y and y

[tex]\frac{1+2}{2y} =\frac{3}{14} \\\frac{3}{2y} =\frac{3}{14} \\\\cross \ multiply\\2y \times 3=3 \times 14\\6y=42\\y=\frac{42}{6}\\y=7[/tex]

Substitute y = 7 into equation 1:

Recall that x = 2y

[tex]x = 2(7)\\x = 14[/tex]

Hence the required two integers are 7 and 14.

Learn more here: https://brainly.com/question/17671977

Given:

An equilateral triangle JKL inscribed in circle M.

Solution:

To draw an equilateral triangle inscribed in circle follow the steps:

1: Draw a circle with any radius.

2. Take any point A, anywhere on the circumference of the circle.

3.  Place the compass on point A, and swing a small arc crossing the circumference of the circle.

Remember the span of the compass should be the same as the radius of the circle.

4. Place the compass at the intersection of the previous arc and the circumference and draw another arc but don't change the span of the compass.

5. Repeat this process until you return to point A.

6. Join the intersecting points on the circle to form the equilateral triangle.

So the correct option is A. The width must be equal to the radius of circle M.

Answer:

488p-244

Step-by-step explanation:

=> (50+11)*(8p-4)

=> 61(8p-4)

Expanding by distributive property.

=> 488p-244

Answer:

The 95% confidence interval for the population mean rating is (5.73, 6.95).

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=50-1=49[/tex]

The t-value for a 95% confidence interval and 49 degrees of freedom is t=2.01.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.01 \cdot 0.305=0.61[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 6.34-0.61=5.73\\\\UL=M+t \cdot s_M = 6.34+0.61=6.95[/tex]

The 95% confidence interval for the mean is (5.73, 6.95).

Answer:

20°

Step-by-step explanation:

A complementary angle adds up to 90°. If the other angle is already 70°, then the missing angle that adds up would have to be 20°

Answer:

20

Step-by-step explanation:

Complementary angles add up to 90°.

90 - 70 = 20

The measure of the complementary angle is 20°.

Answer:

The first first five terms of this sequence are

Step-by-step explanation:

[tex]a(n) = 27(0.1)^{n - 1} [/tex]

where n is the number of term

For the first term

n = 1

[tex]a(1) = 27(0.1)^{1 - 1} = 27(0.1) ^{0} [/tex]

= 27(1)

Second term

n = 2

[tex]a(2) = 27(0.1)^{2 - 1} = 27(0.1)^{1} [/tex]

= 27(0.1)

Third term

n = 3

[tex]a(3) = 27(0.1)^{3 - 1} = 27(0.1)^{2} [/tex]

Fourth term

n = 4

[tex]a(4) = 27(0.1)^{4 - 1} = 27(0.1)^{3} [/tex]

Fifth term

n = 5

[tex]a(5) = 27(0.1)^{5 - 1} = 27(0.1)^{4} [/tex]

Hope this helps you

Answer:

x=11

Step-by-step explanation:

Since the lines in the middle are parallel, we know that both sides are proportional to each other.

6:48 can be simplified to 1:8

Since we know the left side ratio is 1:8, we need to match the right side with the same ratio

We can multiply the ratio by 5 to match 5:3x+7

5:40

5:3x+7

Now we can set up the equation: 40=3x+7

Subtract 7 from both sides

3x=33

x=11

Start by making a table for the ordered pairs with the x-values

in the left column and the y-values in the right column.

            --x--|--y--

             -2  |  -5

              1   |  -3

                  |

                  |

Now remember that the slope is equal to the rate of change

or the change in y over the change in x.

We can see that the y-values go from -5 to -3 so the change in y is 2.

The x-values go from -2 to 1 so the change in x is 3.

So the change in y over the change in x is 2/3.

This means that the slope is also equal to 2/3.

Answer:

d. There is a 98% chance that the true proportion of customers who click on ads on their smartphones is between 0.56 and 0.62.

Step-by-step explanation:

Confidence interval:

x% confidence

Of a sample

Between a and b.

Interpretation: We are x% sure(or there is a x% probability/chance) that the population mean is between a and b.

In this question:

I suppose(due to the options) there was a small typing mistake, and we have a 98% confidence interval between 0.56 and 0.62.

Interpreation: We are 98% sure, or there is a 98% chance, that the true population proportion of customers who click on ads on their smartphones is between 0.56 and 0.62. Option d.

Answer:

1. y² - 3x - 18

2. 4x² - 33x + 35

3. 12x² - 11x + 2

Step-by-step explanation:

All we do with these questions are expanding the factored binomials. Use FOIL:

1. y² + 3y - 6y - 18

y² - 3y - 18

2. 4x² - 28x - 5x + 35

4x² - 33x + 35

3. 12x² - 3x - 8x + 2

12x² - 11x + 2

Answer:

1) (y-6) (y+3)

=> [tex]y^2+3y-6y-18[/tex]

=> [tex]y^2-3y-18[/tex]

2) (4x-5) (x-7)

=> [tex]4x^2-28x-5x+35[/tex]

=> [tex]4x^2-33x+35[/tex]

3) (3x - 2) ( 4x - 1)

=> [tex]12x^2-3x-8x+3[/tex]

=> [tex]12x^2-11x+3[/tex]

Answer:

a. 1/13

b. 1/52

c. 2/13

d. 1/2

e. 15/26

f. 17/52

g. 1/2

Step-by-step explanation:

a. In a deck of cards, there are 4 suits and each of them has a 7. Therefore, the probability of drawing a 7 is:

P(7) = 4/52 = 1/13

b. There is only one 6 of clubs, therefore, the probability of drawing a 6 of clubs is:

P(6 of clubs) = 1/52

c. There 4 fives (one for each suit) and 4 queens in a deck of cards. Therefore, the probability of drawing a five or a queen​​​​​​​​​​​ is:

P(5 or Q) = P(5) + P(Q)

= 4/52 + 4/52

= 1/13 + 1/13

P(5 or Q) = 2/13

d. There are 2 suits that are black. Each suit has 13 cards. Therefore, there are 26 black cards. The probability of drawing a black card is:

P(B) = 26/52 = 1/2

e. There are 2 suits that are red. Each suit has 13 cards. Therefore, there are 26 red cards. There are 4 jacks. Therefore:

P(R or J) = P(R) + P(J)

= 26/52 + 4/52

= 30/52

P(R or J) = 15/26

f. There are 13 cards in clubs suit and there are 4 aces, therefore:

P(C or A) = P(C) + P(A)

= 13/52 + 4/52

P(C or A) = 17/52

g. There are 13 cards in the diamonds suit and there are 13 in the spades suit, therefore:

P(D or S) = P(D) + P(S)

= 13/52 + 13/52

= 26/52

P(D or S) = 1/2

Answer:

(0.6231 , 0.6749)

Step-by-step explanation:

With the information we have, it is impossible to solve the exercise, therefore I was looking for information to complete it and we have to:

the sample proportion is 64.9%, or 0.649 plus the sample size is 1300 (n)

Now, we have that the standard error is given by:

SE = (p * (1 - p) / n) ^ (1/2)

replacing

SE = (0.649 * (1 - 0.649) / 1300) ^ (1/2)

SE = 0.0132

Now we have that confidence level is 95%, hence α = 1 - 0.95 = 0.05

α / 2 = 0.05 / 2 = 0.025, Zc = Z (α / 2) = 1.96

With this we can calculate margin of error like so:

ME = z * SE

ME = 1.96 * 0.0132

ME = 0.0259

Finally the interval would be:

CI = (p - ME, p + ME)

CI = (0.649 - 0.0259, 0.649 + 0.0259)

CI = (0.6231, 0.6749)

Answer:

x = 15

y = 90

Step-by-step explanation:

Step 1: Find x

We use Definition of Supplementary Angles

9x + 3x = 180

12x = 180

x = 15

Step 2: Find y

All angles in a triangle add up to 180°

3(15) + 3(15) + y = 180

45 + 45 + y = 180

90 + y = 180

y = 90°

Answer:

(f o g) = x, then, g(x) is the inverse of f(x).

Step-by-step explanation:

You have the following functions:

[tex]f(x)=-\frac{2}{x}-1\\\\g(x)=-\frac{2}{x+1}[/tex]

In order to know if f and g are inverse functions you calculate (f o g) and (g o f):

[tex]f\ o\ g=f(g(x))=-\frac{2}{-\frac{2}{x+1}}-1=x+1-1=x[/tex]

[tex]g\ o\ f=g(f(x))=-\frac{2}{-\frac{2}{x}+1}=-\frac{2}{\frac{-2+x}{x}}=\frac{2x}{2-x}[/tex]

(f o g) = x, then, g(x) is the inverse of f(x).

Answer:

8.96 seconds

Step-by-step explanation:

Answer:

(a) X ~ N([tex]\mu=63, \sigma^{2} = 13^{2}[/tex]).

    [tex]\bar X[/tex] ~ N([tex]\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}[/tex]).

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

Step-by-step explanation:

We are given that the amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and a standard deviation of 13 mL.

Suppose that 43 randomly selected people are observed pouring syrup on their pancakes.

(a) Let X = amount of syrup that people put on their pancakes

The z-score probability distribution for the normal distribution is given by;

                      Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean amount of syrup = 63 mL

            [tex]\sigma[/tex] = standard deviation = 13 mL

So, the distribution of X ~ N([tex]\mu=63, \sigma^{2} = 13^{2}[/tex]).

Let [tex]\bar X[/tex] = sample mean amount of syrup that people put on their pancakes

The z-score probability distribution for the sample mean is given by;

                      Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean amount of syrup = 63 mL

            [tex]\sigma[/tex] = standard deviation = 13 mL

            n = sample of people = 43

So, the distribution of [tex]\bar X[/tex] ~ N([tex]\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}[/tex]).

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < X < 62.8 mL)

   P(61.4 mL < X < 62.8 mL) = P(X < 62.8 mL) - P(X [tex]\leq[/tex] 61.4 mL)

  P(X < 62.8 mL) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{62.8-63}{13}[/tex] ) = P(Z < -0.02) = 1 - P(Z [tex]\leq[/tex] 0.02)

                                                           = 1 - 0.50798 = 0.49202

  P(X [tex]\leq[/tex] 61.4 mL) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{61.4-63}{13}[/tex] ) = P(Z [tex]\leq[/tex] -0.12) = 1 - P(Z < 0.12)

                                                           = 1 - 0.54776 = 0.45224

Therefore, P(61.4 mL < X < 62.8 mL) = 0.49202 - 0.45224 = 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < [tex]\bar X[/tex] < 62.8 mL)

   P(61.4 mL < [tex]\bar X[/tex] < 62.8 mL) = P([tex]\bar X[/tex] < 62.8 mL) - P([tex]\bar X[/tex] [tex]\leq[/tex] 61.4 mL)

  P([tex]\bar X[/tex] < 62.8 mL) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{62.8-63}{\frac{13}{\sqrt{43} } }[/tex] ) = P(Z < -0.10) = 1 - P(Z [tex]\leq[/tex] 0.10)

                                                           = 1 - 0.53983 = 0.46017

  P([tex]\bar X[/tex] [tex]\leq[/tex] 61.4 mL) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{61.4-63}{\frac{13}{\sqrt{43} } }[/tex] ) = P(Z [tex]\leq[/tex] -0.81) = 1 - P(Z < 0.81)

                                                           = 1 - 0.79103 = 0.20897

Therefore, P(61.4 mL < X < 62.8 mL) = 0.46017 - 0.20897 = 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

Answer:

A velocity of 120km/h is needed to cover the distance in one hour

Step-by-step explanation:

The velocity formula is:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance and t is the time.

A car travelling from Ibadan to Lagos at 90 km/hr takes 1 hour 20 min.

This means that [tex]v = 90, t = 1 + \frac{20}{60} = 1.3333[/tex]

We use this to find d.

[tex]v = \frac{d}{t}[/tex]

[tex]90 = \frac{d}{1.3333}[/tex]

[tex]d = 90*1.3333[/tex]

[tex]d = 120[/tex]

The distance is 120 km.

How fast must one travel to cover the distance in one hour?

Velocity for a distance of 120 km(d = 120) in 1 hour(t = 1). So

[tex]v = \frac{d}{t}[/tex]

[tex]v = \frac{120}{1}[/tex]

[tex]v = 120[/tex]

A velocity of 120km/h is needed to cover the distance in one hour

Answer:

6.68% probability that a diode selected at random would have a length less than 20.01mm​

Step-by-step explanation:

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.

In this question:

[tex]\mu = 20.04, \sigma = 0.02[/tex]

Find the probability that a diode selected at random would have a length less than 20.01mm​

This is the pvalue of Z when X = 20.01. So

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

[tex]Z = \frac{20.01 - 20.04}{0.02}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

6.68% probability that a diode selected at random would have a length less than 20.01mm​

Answer:

24

Step-by-step explanation:

Using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction), we get:

[tex]32+3(6-22)/6=\\32+3(-16)/6=\\32-48/6=\\32-8=\\24[/tex]

Answer:

24

Step-by-step explanation:

32 + 3(6 − 22) ÷ 6

PEMDAS

Parentheses first

32 + 3(-16) ÷ 6

Multiply and divide from left to right

32+ -48÷ 6

32+ -8

Then add and subtract from left to right

24

Answer:

Hello There!

Your best choice is B. Both the mean and median will decrease, But the mean will decrease by more than the median. Because, A. wouldn't make sense at all. Well, C. The mean will decrease but also the median aswell too. And, D. They both will decrease aswell but the mean will drop down more than the median. So, Your best answer is B. Hope This Example help your homework!!~

Answer:

Hey!

I definitely think that B is the answer!

Step-by-step explanation:

(a, c and dont work with The Question!!)

HOPE THIS HELPS!!

:>

Answer:

the 3rd option is the answer

Step-by-step explanation:

I hope the attached file is self-explanatory

Step-by-step explanation:

Option D is the correct answer because 3.544 is greater than 3.455

Option D is true in given comparison.

Here,

We have to find the correct comparison.

What is Decimal expansion?

The decimal expansion terminates or ends after finite numbers of steps. Such types of decimal expansion are called terminating decimals.

Now,

In option D;

The one tenth of 3.544 is 5 and place value of one tenth number in 3.455 is 4.

Clearly, 5 > 4

So, 3.544 > 3.455

Hence, option D; 3.544 > 3.455 is true.

Learn more about the Decimal expansion visit:

https://brainly.com/question/26301999

#SPJ2

Answer:

Yes based on the numbers .

Step-by-step explanation:

Answer:Yes

Step-by-step explanation:Based on the number given, it shows that there is a hypotenuse (The longest side of a right triangle, in this case being 12), And opposite (Another part of the right triangle, that could be either 9 or 7), and the adjacent (The line next to the opposite, which could be 9 or 7)

Answer:

286.60

Please tell me if I'm wrong.

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Suppose you are forming a committee from a group of 15 biology student, 12 math students, and 9 physics students. How many possibilities are there if your committee needs to have at most 2 biology students, exactly 3 math students, and exactly 2 physics students?

To tackle this question, we will use the concept of combination since it deals with selection. Generally, selecting 'r' objects out of 'n' pools of object can be done using the formula;

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

If we are to form a committee of at most 2 biology students, exactly 3 math students and exactly 2 physics students from a group of 15 biology student, 12 math students, and 9 physics students, this can be done in the following ways;

For Physics students:

Selecting exactly 2 physics students from a group of 9 students will be:

9C2 = [tex]\frac{9!}{(9-2)!2!}\\[/tex]

= [tex]\frac{9!}{(7)!2!}\\[/tex]

[tex]= \frac{9*8*7!!}{(7)!2!}\\= 9*4\\= 36ways[/tex]

for Mathematics students:

Selecting exactly 3 math students from a group of 12 students will be:

[tex]12C3 = \frac{12!}{12-3)!3!}\\= \frac{12!}{9!3!}\\= \frac{12*11*10*9!}{9!*6}\\= 220 ways[/tex]

For Biology Students:

Selecting at most 2 biology students from a group of 15biology student will be:

15C1 * 15C2 (at most 2 students)

= [tex]\frac{15!}{14!1!} * \frac{15!}{13!2!}\\\\[/tex]

= 15*105

= 1,575 ways

The total number of possibilities will be = 36*220*1,575 = 12,474,000 possibilities

Answer:

y = 5x - 4

Step-by-step explanation:

Step 1: Write known variables

m = 5

y = 5x + b

Step 2: Find b

6 = 5(2) + b

6 = 10 + b

b = -4

Step 3: Rewrite equation

y = 5x - 4