When two six-sided dice are rolled what is the probability that the product of their scores will be greater than six?

The statistical technique applicable here is simple random sampling and binomial distribution. The formula for a binomial distribution is used to estimate the probabilities of a specific number of satisfactions among the randomly selected 15 adults. The average number and variability can also be calculated for this binomial distribution.

This question is about statistics, particularly a technique called simple random sampling. In the given scenario, it's reported that 66% of adults are satisfied with the major airlines' job. We're asked to conjecture about a scenario where 15 adults are chosen at random and the number who are satisfied is observed.

First, this scenario is modeled with a binomial distribution. A binomial distribution is appropriate here because you're considering a certain number of 'trials' (15 adults), and for each trial, there are two possible outcomes - the adult is either satisfied or not satisfied with the airlines. The 'success' probability (satisfaction) remains constant (66%).

A. If we want to know the probability of exactly x adults satisfied, the formula for a binomial distribution is used: P(X = k) = C(n, k) * (p^k) * ((1 - p)^(n - k)), where C(n, k) is combinations of n things taken k at a time, n is number of trials (15), p is the probability of success (66% or 0.66), and k is the number of successes we want exact probability for.

B. If we want to know the expected value or the average number of adults satisfied, it's simply n*p, in this case 15*0.66 = 9.9, meaning, on average, about 10 adults out of 15 should be satisfied according to the poll report.

C. If we want to compute the variability, we can calculate the standard deviation. For a binomial distribution, the standard deviation, sigma, is square root of [ n*p*q ], where q = 1-p is the probability of 'failure', or an adult not satisfied.

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Answer:

  [tex]r=\dfrac{I}{Pt}[/tex]

Step-by-step explanation:

Solve this the way you do any "solve for" problem. Locate the variable of interest and identify what has been done to it. Undo that.

Here, the variable of interest is "r". It has been multiplied by Pt. We undo that multiplication by dividing by that product:

  [tex]I=Prt\\\\\dfrac{I}{Pt}=\dfrac{Prt}{Pt}\\\\\dfrac{I}{Pt}=r \quad\text{simplify}[/tex]

Answer:

7.75 F

Step-by-step explanation:

you will do 7/2 *

convert 2.25 to imporper fraction

multiply the denomintor

Answer:

7.75

Step-by-step explanation:

Answer:

a:  1003 < µ < 1023

b:  See attached photo for answers

c:  see below

d and e:  See second attached photo

f:  See below

Step-by-step explanation:

a.  to find a confidence interval, first find the error with the formula,

E = Z(σ/√n)  where Z is the value of the z-score that relates to the confidence level, σ is the standard deviation of the population (or of the sample if the population standard deviation isn't given), and n is the sample size

For this problem, E = 1.96(108/√453) = 9.95 = 10

Now add and subtract that value form the sample average...

x - E < µ < x + E      becomes    1013 - 10 < µ 1013 + 10

simplifies to 1003 < µ < 1023

b.  See attached photo for hypothesis test results...

c.  H0:  µ = 1013  

    Ha:  µ > 1013 (claim)

They want to test if it's greater than their first attempt,  so this claim becomes the alternate hypothesis.  We're testing against their first attempt, that's why µ = 1013, not 1000

d and e.  See second attached photo for hypothesis test results...

f.  There is enough evidence to support the claim that the students second attempt was an improvement from their first attempt.  They happened to take a 2 hour tutoring course between tests.  This doesn't prove that the tutoring was effective thought.  It very well might have been effective, but also, the students taking the test again means they've already seen the test and know what to expect, which could have also boosted their scores.  

ANSWER

Explicit formula:

[tex]a_n= 8n - 23[/tex]

Recursive

[tex]a_{n}= a_{n - 1} + 8,a_1=-15[/tex]

EXPLANATION

The first term of the sequence is

[tex]a_1=-15[/tex]

The common difference is

[tex]d = - 7 - - 15[/tex]

[tex]d = 8[/tex]

The nth term is given by the formula,

[tex]a_n=a_1 + d(n - 1)[/tex]

[tex]a_n= - 15+ 8(n - 1)[/tex]

[tex]a_n= - 15+ 8n -8[/tex]

The explicit formula is;

[tex]a_n= 8n - 23[/tex]

The recursive definition is

[tex]a_{n}= a_{n - 1} + 8,a_1=-15[/tex]

Answer:

Centimeter

Step-by-step explanation:

Erasers are pretty small so I would say it was about 5 cm.

The coefficient of q in the sum of the two expressions is 17/24.

We have,

The given expression is:

(2/3q - 3/4(-1/6q - r))

Let's simplify this expression step by step:

Step 1: Distribute -3/4 to (-1/6q - r):

(2/3q - 3/4 * -1/6q + 3/4 * r)

Step 2: Simplify the multiplication of fractions:

(2/3q + 1/8q + 3/4 * r)

Step 3: Combine like terms:

(17/24q + 3/4 * r)

Thus,

The coefficient of q in the sum of the two expressions is 17/24.

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The coefficient of q in the sum of the expressions is found by simplifying the terms individually and then combining them. After finding a common denominator and adding the terms, the coefficient of q is 19/24.

To find the coefficient of q in the sum of the given expressions (2/3q - 3/4*(-1/6q - r)), we first need to simplify the expression step by step. Starting with the second term, we distribute the -3/4 across the parentheses:

Now adding this to the first term:

To add the q terms, they need to have a common denominator. The common denominator for 3 and 8 is 24. We convert both fractions:

Now we can add them:

The coefficient of q in the sum of the given expressions is 19/24.

ANSWER

[tex] P(G)= \frac{1}{3}[/tex]

EXPLANATION

The number of green marbles in the bag is

[tex]n(G) = 2[/tex]

The total number of marbles in the bag is

[tex]n(S)=1+2+3 = 6[/tex]

The probability of selecting a green marble from the bag without looking is

[tex]P(G)= \frac{n(G)}{n(S)} [/tex]

Substitute the values to get,

[tex]P(G)= \frac{2}{6} [/tex]

[tex]P(G)= \frac{1}{3} [/tex]

Answer:

The probability of drawing a green marble out of the bag without looking = 1/3

Step-by-step explanation:

It is given that, a bag contains 1 blue, 2 green, and 3 red marbles

Therefore total number of marble in the  bag = 1 + 2 + 3 = 6

To find the probability

Total number of marble = 6

Number of green marble  = 2

The probability of drawing a green marble = 2/6 = 1/3

Answer:

[tex]\large\boxed{Q\#1.\ A)\ \dfrac{8}{3}x+6}\\\boxed{Q\#2.\ A)\ \dfrac{1}{3}(p+45)}[/tex]

Step-by-step explanation:

[tex]Q\#1:\\\\\dfrac{2}{3}(4x+9)\qquad\text{use the distributive property}\\\\=\left(\dfrac{2}{3}\right)(4x)+\left(\dfrac{2}{3}\right)(9)=\dfrac{8}{3}x+(2)(3)=\dfrac{8}{3}x+6\\\\Q\#2:\\\\\dfrac{1}{3}p+15=\dfrac{1}{3}p+\dfrac{1}{3}\cdot(3)(15)=\dfrac{1}{3}p+\dfrac{1}{3}\cdot45=\dfrac{1}{3}(p+45)[/tex]

Answer:

C) 120 degrees

Step-by-step explanation:

m<A + m<B + m<C = 180

45 + m<B + 15 = 180

m<B + 60 = 180

m<B = 120

The answer is C) 120

Answer:

[tex]m<1=26.4\°[/tex]

[tex]m<2=153.6\°[/tex]

Step-by-step explanation:

we know that

If m<1 and m<2 form a linear pair

then

[tex]m<1+m<2=180\°[/tex] -----> by supplementary angles

substitute the values and solve for x

[tex](2x+20)+48x=180\°[/tex]

[tex]50x=180\°-20\°[/tex]

[tex]50x=160\°[/tex]

[tex]x=3.2\°[/tex]

Find the measure of each angle

[tex]m<1=(2x+20)=2(3.2\°)+20\°=26.4\°[/tex]

[tex]m<2=48x=48(3.2\°)=153.6\°[/tex]

Answer: First option and last option.

Step-by-step explanation:

By definition, an equation of direct proportion has the following form:

[tex]y=kx[/tex]

Where k is the constant of proportionality.

The equation of the line [tex]y=mx+b[/tex], where m is the slope and b the y-intercept.

When b=0, means that the line passes through the origin. Therefore, it would be:

[tex]y=mx[/tex]

(which is similar to  [tex]y=kx[/tex])

Then, the slope of the line would be the constant of proportionality.

By definition, the slope can be positive or negative.

Keeping on mind the information above, you can see that the equation that have that form are:

[tex]y=-2x\\\\y=4x[/tex]

Answer:

y=−2x

Step-by-step explanation:

I got it right on Imagine math.

Answer:

The times were Lily 9.5 hours and Andrea 6.5 hours.

Equation "D" is correct using those numbers.

Step-by-step explanation:

Answer:

999

 530

+469

----------

 999

Divide the area into 6 portions and find the sum of each one to find the value of the final integral:

f(x)dx = 2(8+4)/2 + 1 (8+6)/2 + 2 (6+10)/2 + 1(10+10)/2 + 2 (10+12)/2 + 1 (12+16)/2

= 12 + 7 + 16 + 10 + 22 + 14 = 81 sq units

Answer:

Step-by-step explanation:

Given is a table of x, f(x) as below

x             1   3   4   6   7  9  10

f(x)         4   8  6  10  10  12  16

Mid pt      6   7   8  10   11  14

width of

interval    2   1     2   1    2    1

dA1         12   7   16  10  22  14

area = area of all rectangles= 81 sq units.

Answer:

300°

Step-by-step explanation:

This may seem really strange and counterintuitive to you, but when you turn 1° 300 times, you have turned 300°.

_____

If you don't want to add it up ...

1° + 1° + 1° ... + 1° . . . . . 300 times

you can use multiplication. It was invented as a shortcut to repeated addition:

1° × 300 = 300°

The gear has turned a total of 300 degrees.

To solve this problem, we need to consider the information given and apply basic multiplication. The gear turns in 1° sections, and it does so a total of 300 times. Since each section is 1°, we can simply multiply the number of sections by the size of each section to find the total degrees turned.

So, the calculation is as follows:

Number of sections = 300

Size of each section = 1°

Total degrees turned = Number of sections × Size of each section

Total degrees turned = 300 × 1°

Total degrees turned = 300°

Therefore, the gear has turned 300 degrees in total.

Answer:

Option C. [tex]65[/tex]

Step-by-step explanation:

we know that

The discriminant of a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]D=b^{2}-4ac[/tex]

in this problem we have

[tex]2x^{2} +3x-7[/tex]  

so

[tex]a=2\\b=3\\c=-7[/tex]

substitute

[tex]D=3^{2}-4(2)*(-7)[/tex]

[tex]D=9+56[/tex]

[tex]D=65[/tex]

The discriminant of the giving polynomial is 65. The correct option is C. 65

From the question, we are to determine the discriminant of the given polynomial

The given polynomial is

2x²+3x-7

This is a quadratic function

The discriminant of a quadratic function is simply the value in the square root of the quadratic formula

That is,

Discriminant, D = b² - 4ac

In the given quadratic function, 2x²+3x-7

a = 2, b = 3 and c = -7

∴ D = 3² -4(2)(-7)

D = 9 +56

D = 65

Hence, the discriminant of the giving polynomial is 65. The correct option is C. 65

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Answer:

2

Step-by-step explanation:

3(2x + 4)=?

6x + 12

6x/6=x

12/6=2

x=2

This would be D cause these are 30,60, 90 angles. 30 (X) 60(X square root of 3 and 90 2x).

Answer:

C

Step-by-step explanation:

Using the sine ratio on the right triangle on the right side

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{8}[/tex]

Multiply both sides by 8 × sin30° = y

⇒ y = 8 × [tex]\frac{1}{2}[/tex] = 4 → C

Answer:

C

Step-by-step explanation:

If the parent function is function [tex]y=f(x)[/tex] and [tex]a>0,[/tex] then

In your case, the grapgh of the function [tex]y=2^x+2[/tex] is translated 2 units up the graph of the function [tex]y=2^x.[/tex]

Answer:

[tex]f(x)=2^{x} +2[/tex] relative to [tex]f(x)=2^{x}[/tex]

This is called translation of functions, and it refers to the movement of a specific function, either upwards, downwards, leftwards or rightwards. To be able to translate a function, we have to use the next rules.

In this case, the problem is saying that we have to move the function upwards by two units, because [tex]f(x)=2^{x} +2[/tex] is the same function as    [tex]f(x)=2^{x}[/tex], but moved 2 units upwards.

In addition, the graph is attached, there you can see the difference between those two functions, you will se that they are the same, but one is moved two units upwards.

Answer:

  yes, and no

Step-by-step explanation:

There are a few trig functions that are "simple" and can be memorized. Usually, these are the ones for angles of 0°, 30°, 45°, 60°, 90°. See below for a table.

To solve an equation like this for DE, you multiply both sides of the equation by 4 (cancelling the denominator).

  4·tan(90°) = DE

The tangent of 90° is "infinity." So, the length of DE will be infinite for an angle of 90°.

_____

Trig functions of multiple angles and half angles can be derived from those in the table using the appropriate formulas. The math can get messy fast.

Of course, SOH CAH TOA reminds you of the relationships between trig function values and right triangle side measures. You may not know the angle measure (and it may be irrelevant), but you can find the trig function value.

Answer:

See below.

Step-by-step explanation:

You can find them by constructing a right angled triangle with the given angle and measuring the sides  giving sin = opposite / hypotenuse , cos = adjacent / hypotenuse and tan = opposite / adjacent ( SOH-CAH-TOA).

For  tan 90 degrees you think of an 'imaginary' triangle where opposite side = hypotenuse and the adjacent side = 0 ( in fact a vertical line!) .Now tan  x = opposite / adjacent  =  opposite / 0 which is indeterminate. There is no value for the tan of 90 degrees and so there is no solution to your problem.

Answer:

[tex]\large\boxed{Q4.\ C.\ \text{Infinitely Many Solutions}}\\\boxed{Q5.\ D.\ \text{No Solution}}[/tex]

Step-by-step explanation:

[tex]Q4.\\\\\left\{\begin{array}{ccc}-4y+4=x&(1)\\2x+8y=8&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\2(-4y+4)+8y=8\qquad\text{divide both sides by 2}\\-4y+4+4y=4\qquad\text{combine like terms}\\4=4\qquad\bold{TRUE}\\\\\text{Infinitely Many Solutions}[/tex]

[tex]Q5.\\\\\left\{\begin{array}{ccc}6x+2=y&(1)\\3y-18x=12&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\3(6x+2)-18x=12\qquad\text{divide both sides by 3}\\6x+2-6x=4\qquad\text{combine like terms}\\2=4\qquad\bold{FALSE}\\\\\text{No Solution}[/tex]

48 students in group 2

43 students in group 1

So in total there are 91 students

7 students play the trump

And 20 play the trombone

Therefore it is known that 27 students play those two instruments in total

Because of this, Subtract 27 from 91 to get the num of students who doesn't play those instruments.

Answer:

10 quarts

Step-by-step explanation:

There are 4 quarts to a gallon, and she bought 2 1/2 gallons, or 2.5 gallons, so she bought 4(2.5) = 10 quarts

Answer:

$42

Step-by-step explanation:

Divide $18 by 3 to get a unit rate of $6 per hour. Then, multiply by 7 hours to get $42.

Answer:

70

Step-by-step explanation:

50+20 = 70

ANSWER

70

EXPLANATION

We want to increase 50 by 40%

Method 1

New amount =50+40% of 50

[tex] = 50 + \frac{40}{100} \times 50[/tex]

[tex] = 50 + \frac{40}{2} [/tex]

[tex] = 50 + 20[/tex]

[tex] = 70[/tex]

Method 2.

50 corresponds to 100%.

New amount corresponds to (100+40=140)%

This implies that, New amount

[tex] = 140\% \times 50[/tex]

[tex] = \frac{140}{100} \times 50[/tex]

[tex] = \frac{140}{2} [/tex]

[tex] = 70[/tex]

Answer: The temperature would be -2 degrees at midnight.

Step-by-step explanation:

If you take 8 and minus 10 then you get -2!

Answer:

-2

Step-by-step explanation:

hope it will help youu!!!

Answer:

  3.9

Step-by-step explanation:

A calculator is useful for this.