.07 MC)
Which of the following is a solution of x2 + 6x = -22?
O-3±1√13
0-3+√√52
O-6±1 13
0-6±i√√52

1. It is not unusual for Joe to roll a four twice in six attempts because a die has 6 sides, so the probability of rolling a four is 1/6 (one in six).

2. If Joe rolled a four three times in six attempts, it would still not be considered unusual because when the probability of rolling a four three times is slightly lower than rolling it twice, it is still not considered a very low probability or unusual occurrence.

It is not unusual for Joe to roll a four twice in six attempts. Here's why:
1. A die has 6 sides, so the probability of rolling a four is 1/6 (one in six).
2. When rolling the die six times, the probability of rolling a four twice can be calculated using the binomial probability

formula:\(P(X=k) = (nCk) * (p^k) * (q^(n-k)),\)

where n is the number of trials,

k is the number of successful outcomes,

p is the probability of success, and q is the probability of failure (1-p).
3. In this case, n=6, k=2, p=1/6, and q=5/6.

So, \(P(X=2) = (6C2) * (1/6)^2 * (5/6)^4\) ≈ 0.2009 or 20.09%.
4. Since 20.09% is not a low probability, it is not unusual for Joe to roll a four twice in six attempts.
If Joe rolled a four three times in six attempts, it would still not be considered unusual. Here's why:
1. Using the same binomial probability formula as before, we now have k=3.
2. \(P(X=3) = (6C3) * (1/6)^3 * (5/6)^3\) ≈ 0.1550 or 15.50%.
3. While the probability of rolling a four three times is slightly lower than rolling it twice, it is still not considered a very low probability or unusual occurrence.

For similar question on unusual.

https://brainly.com/question/13839270

#SPJ11

Use the horizontal number line, the statements which are true include the following:

A. –9 < –7

C. –1 > –3

A number line can be defined as a type of graph with a graduated straight line which is composed of both positive and negative numbers that are placed at equal intervals along its length.

In Mathematics, a number line typically increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In this context, we can reasonably and logically deduce that the following inequalities on a number line are either true or false:

Read more on number line here: https://brainly.com/question/28032137

#SPJ1

Complete Question:

Use the horizontal number line shown to answer the question. Which statements are true?

-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1

Check all that apply.

A. –9 < –7

B. –6 = 6

C. –1 > –3

D. 0 < –3

Answer: A & C

Step-by-step explanation:

Answer:

Step-by-step explanation:

3.75

The height of the right cone is \(7 \ units\).

To find the height of the right cone, we can use the formula for the volume of a cone:

Volume = \(\frac{1}{3} \times \pi \times r^{2} \times h\)

where \(\pi\) is the mathematical constant pi (approximately \(3.14159\)), r is the radius of the base of the cone, and h is the height of the cone.

Given that the volume is \(21 \ \pi\) units and the diameter is \(6\) units, we can find the radius:

Radius (r) =

\(\frac{diameter}{2} \\= \frac{6}{2} \\= 3\)

Substituting the known values into the formula, we have:

\(21 \pi = \frac{1}{3} \times \pi \times 3^{2} \times h\)

Simplifying the equation:

\(21 = (\frac{1}{3}) \times 9 \times h\)

Multiplying both sides by \(3\):

\(63 = 9h\)

Dividing both sides by \(9\\\):

\(h = \frac{63}{9} \\ = 7 units\)

Therefore, the height of the right cone is \(7 \ units\).

For more such questions on height: https://brainly.com/question/28122539

#SPJ11

Answer:

3 and -2

Step-by-step explanation:

xy = -6

x + y = 1

let 'x' = y-1

y(y-1) = -6

y² - y + 6 = 0

(y-3)(y+2) = 0

y = 3 and -2

Answer:

53

Step-by-step explanation:

if x is 13, you would simply do the following:

multiply 5 by 13 which is 65.

then subtract 65 by 12 which is your final answer, 53!

Answer:

(x/4)(x-2)

(x-6)(x-3)

Step-by-step explanation:

Answer:

14 nails

Step-by-step explanation:

The value of P for which the demand is unit elastic can be found by equating the price elasticity of demand to 1. Given the demand function Q = Ye^(0.01P).

The price elasticity of demand (E) is calculated as the derivative of Q with respect to P, multiplied by P divided by Q. Therefore, E = (dQ/dP) * (P/Q). To find the value of P for unit elasticity, we set E = 1 and substitute Y = 800 into the equation.

Solving for P gives the value of P at which the demand is unit elastic.

To find the price elasticity of demand at the current price of 150, we need to calculate the derivative of Q with respect to P and then evaluate it at P = 150. Using the demand function Q = Ye^(0.01P), we differentiate Q with respect to P, substitute Y = 800 and P = 150, and calculate the price elasticity of demand.

To estimate the percentage change in demand when the price increases by 4% from the current level of 150, we can use the concept of elasticity. The percentage change in demand can be approximated by multiplying the price elasticity of demand by the percentage change in price.

We calculate the price elasticity of demand at the current price of 150 (as calculated in part b), and then multiply it by 4% to find the estimated percentage change in demand.

To know more about  lasticity of demand refer here:

https://brainly.com/question/28945373#

#SPJ11

Answer:

A) -20

Step-by-step explanation:

AS it passes through the origin (0,0) and the point (3,5) we can find the slope
(y2-y1) / (x2-x1) =
(5 -0 ) / (3-0)   =

 5/3

Becasue is passes through the origin the equation is :
5/3x = y

For the other point (-12,b)  -12 is "x" and  "b" represent "y" in the equation

  -12 * 5/3 = -60/3 = -20

b = -20

The Answer A) -20 is the one

Answer:

\(y = \frac{2}{3} x\)

Step-by-step explanation:

let's first collect some data from the graph...

1. The line passes through the origin, so the y intercept equals 0

2. we now look for two points where the graph intersects. as established in number one it passes through point (0,0). from there we can go up the y-axis 2 spaces and to the right along the x-axis 3 spaces. this will give us our slope m rise over run or ⅔. That's enough information to write the equation of our line.

\(y = mx + b \\ m = \frac{2}{3} \\ b = 0 \\ y = \frac{2}{3} x + 0 \\ y = \frac{2}{3} x\)

Answer:

x=0

y=7

Step-by-step explanation:

Divide 6x-4y=-28 by -2..... -3x+2y=14

3x+5y=35

-3x+2y=14

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

7y=49

y=7

6x-4*7=-28

x=0

Answer:

The answer would be B !

Step-by-step explanation

Answer:

3 1/2x + 215=495

495-215=280

3 1/2 ÷280

x=80

if this helps

Answer + explanation:

\(3\frac{1}{2} x +215=495\)

Minus 215 on both sides

\(3\frac{1}{2}x = 280\)

Divide both sides by \(3\frac{1}{2}\) to isolate x

280/3.5 = 80

x = 80

Hope this helps :)

Have an awesome day!

The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is: B. 68%.

In Mathematics and Statistics, a frequency table can be used to graphically represent the frequencies or relative frequencies that are associated with a categorical variable.

In Mathematics and Statistics, the cumulative frequency of a data set can be calculated by adding each frequency from a frequency distribution table to the sum of the preceding frequency. Thus, the relative cumulative frequency would be calculated as follows;

Cumulative frequency of students = 4 + 8 + 15 + 7 = 34.

Cumulative frequency of students = 34.

Total frequency = 4 + 8 + 15 + 7 + 7 + 3 + 4 + 2

Total frequency = 50.

Therefore, the relative cumulative frequency can now be determined;

Relative cumulative frequency = 34/50

Relative cumulative frequency = 0.68 or 68%

Read more on cumulative frequency here: https://brainly.com/question/23895074

#SPJ1

Answer:

68%

Step-by-step explanation:

Got it right.

Answer:

im really not to sure on this one. sorry dude

Step-by-step explanation:

The overall sample for the survey consists of 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors, totaling 155 students.

To create an overall sample for the survey, the administrators selected a certain number of students from each class level. They randomly sampled 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors. By combining these individual samples from each class, the administrators obtained an overall sample size of 50 + 40 + 35 + 30 = 155 students. This overall sample represents a portion of the student population from each class level and allows for a representation of students from different academic years in the survey.

To know more about sample,

https://brainly.com/question/31661667

#SPJ11

Answer:

$1,281.00

Step-by-step explanation:

We start by calculating the value $50 added each month after the first month

= $50 × 11

= $550

Calculation:

First, converting R percent to r a decimal

r = R/100 = 5.5%/100 = 0.055 per year.

P = Principal = 500 + 550

= $1050

Calculation:

First, converting R percent to r a decimal

r = R/100 = 5.5%/100 = 0.055 per year.

Solving our equation:

A = 1050(1 + (0.055 × 4)) = 1281

A = $1,281.00

Therefore, there would be $1,281.00 after 4 years.

Answer: The first two

Step-by-step explanation:

Answer:

x=13

Step-by-step explanation:

For a to be parallel to b, 7x-26 + 9x-2 would have to = 180.

If we solve this equation,

16x-28=180

16x=208

x=13

x would have to equal 13 for a || b.

Answer:

x=13

Step-by-step explanation:

7x-26+9x-2=180

16x-28=180

16x=208

208/16=x

13=x

True. The consumer group could have made a type II error. A type II error occurs when the consumer group fails to reject the null hypothesis, which states that the average score increase is equal to 30 points, even though it is actually false.

In this case, if the study program does increase the average score by a different amount, the consumer group may fail to detect this difference and incorrectly conclude that the average score increase is 30 points. This error is possible because no statistical test is perfect, and there is always some level of uncertainty involved in hypothesis testing.

To minimize the risk of a type II error, the consumer group should use an appropriate sample size and consider conducting a power analysis before conducting the study.

To know more about average visit:

https://brainly.com/question/24057012

#SPJ11

Answer:D

Step-by-step explanation:

In the Bertrand Duopoly Competition, choosing a price of $0 is a dominated strategy for each firm because they can always earn a higher profit by setting a positive price. Similarly, setting a price of $6 is also a dominated strategy for both firms. Choosing a price higher than the monopoly price is also a dominated strategy, as it results in lower profits. The rationalizable strategies in this game are setting a positive price between $0 and the monopoly price.

(a) Setting a price of $0 is a dominated strategy for each firm because their rival firm can undercut them by setting a slightly positive price, resulting in zero profits for the firm setting $0. Similarly, setting a price of $6 is dominated because the rival firm can set a slightly lower price and capture the entire market demand, leaving the firm setting $6 with zero profits.

(b) The monopoly price represents the highest price that a firm can set while still maximizing its profits. Any price higher than the monopoly price will result in a decrease in demand and lower profits. Thus, choosing a price higher than the monopoly price is a dominated strategy.

(c) The rationalizable strategies in this game are the set of prices between $0 and the monopoly price. The Nash Equilibrium occurs when both firms set the monopoly price, as neither firm has an incentive to deviate from this strategy.

(d) In the Nash Equilibrium, both firms set the monopoly price, resulting in a quantity sold in the market that corresponds to the demand at the monopoly price. Each firm earns a profit equal to half of the total industry profits, as they split the resulting demand equally between them.

(e) The market outcome in Bertrand competition with the Nash Equilibrium price and quantity is different from the monopoly outcome. In the monopoly outcome, the single firm sets the monopoly price and quantity, earning higher profits compared to the Nash Equilibrium in Bertrand competition. The presence of competition in the Bertrand model drives prices down towards marginal costs, resulting in lower profits for both firms compared to the monopoly outcome.

Learn more about price  here:

https://brainly.com/question/14871199

#SPJ11

Answer:

B? I think itts B

Step-by-step explanation:

Answer:

The slope formula is m=(y2-y1)/(x2-x1).

Step-by-step explanation:

Use the slope formula to find the slope of a line given the coordinates of two points on the line. The coordinates of the first point represent x1 and y1. The coordinates of the second points are x2, y2.

Answer:

a. -2

b. y = -2x + 4

Step-by-step explanation:

using (-9, 10) and (-3, -2)

Slope m = (y2-y1)/(x2-x1)

m = (-2 - 10)/(-3 - -9)

m = -12/6 = -2

Slope-intercept: y = mx + b

using (-3, -2)

-2 = -2(-3) + b

-2 = 6 + b

b = 4

y = -2x + 4

Answer:

This hypothesis test is a two-tailed test.

Step-by-step explanation:

When carrying out a hypothesis test, the null hypothesis and the alternative hypothesis are identified. The null hypothesis is generally the one that is initially assumed to be true, while the alternative hypothesis is the one that is being tested. The following are the hypotheses for the scenario presented in the question:

H0: p = 0.856

H1: p ≠ 0.856

To see if there is enough evidence to conclude that the proportion differs from the national percentage, a hypothesis test will be conducted with alpha = 0.01.

The null hypothesis in this case is that the proportion of undergraduates in the state is equal to the national percentage of 85.6 percent, while the alternative hypothesis is that the proportion differs from the national percentage. Therefore, the correct identification of the claim with the hypothesis is as follows:

H0: p = 0.856

H1: p ≠ 0.856

This hypothesis test is a two-tailed test because the alternative hypothesis is non-directional, indicating that the proportion may differ from the national percentage in either direction.

Learn more about hypothesis test in statistics,

https://brainly.com/question/15980493

#SPJ11

The probability to get a 3 or 4 in the third toss and 6 in the fourth toss is 1/18.

The sample space for a six-sided die is

{1, 2, 3, 4, 5, 6}

Hence the total number of possibilities = 6

The rolling of a die is IID that is Independently and Identically distributed.

Hence,

the result of one toss will not affect the result of the successive tosses.

Probability

= n(E)/n

= no of favorable outcomes for any event /total no. of outcomes

Here,

n = 6

Let A be the event of getting a 3 or 4 in the third toss

Let B be the event of getting 6 on the fourth toss

E(A) = {3,4}

n(A) = 2

Hence,

P(A) = 2/6

= 1/3

B = {6}

n(B) = 1

P(B) = 1/6

Since these are IID,

P(A and B) = P(A) X (B) [Property of independent events]

Hence P(A∩B) = 1/3 X 1/6

= 1/18

To learn more about probability visit

https://brainly.com/question/17142351

#SPJ4

Using the distributive property, the expanded form of (−1/4)(−8x+12y) is c) 2x - 3y.

The distributive property states that when you multiply a number or a variable expression by a sum or a difference, you can distribute the multiplication over each term within the parentheses.

So, to expand the expression (−1/4)(−8x+12y), we can apply the distributive property by multiplying -1/4 to each term inside the parentheses:

(−1/4)(−8x+12y) = (−1/4) × (−8x) + (−1/4) × (12y)

= (1/4) × 8x − (1/3) × 12y

= 2x − 3y

Therefore, the expanded form of (−1/4)(−8x+12y) is 2x − 3y. Hence, the correct answer is (c) 2x-3y.

To learn more about distributive property here:

https://brainly.com/question/29048637

#SPJ1