You roll a fair six-sided die twice. Find the probability of rolling a 3 the first time and a number greater than 4 the second time.

There are 9 numbers from 10 to 99 in which the difference between the largest digit and the smallest digit equals 4

The difference can be represented as

Largest - Smallest = 4

Also, we have two instances to be

15 and 51

And the range is given as

Range = 10 to 99

In a range of 10, there is only one number whose difference between the digits is 4

There are 9 ranges of 10 from 10 to 99

So, the count of the range is

Count = 9 range * one number

Rewrite as

Count = 9 * 1

Evaluate

Count = 9

Hence, there are 9 of such numbers from 10 to 99

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Answer:

3x  + 12

Step-by-step explanation:

3(x+1)+9

= 3x  + 3 + 9

= 3x  + 12

Earned income is said to be $35,000, Base tax amount at that level is $4386, The amount over $31850 is  $3150, Line 3 is multiplied by 25% is $787.50, The sum of lines 2 and 4 is $5173.50 and This amount divided by 12 is $431.13.

Two or more expressions with an Equal sign is called as Equation.

Given,

The given Federal Income Tax Table Single: Over But not over The tax is $0 $7,825 10% of the amount over $0 $7,825 $31,850 $788 + 15% of the amount over $7,825 $31,850 $77,100 $4,386 + 25% of the amount over $31,850 $77,100 $160,850 $15,699 + 28% of the amount over $77,100 $160,850 $349,700 $39,149 + 33% of the amount over $160,850 $349,700 And Over $101,469 + 35% of the amount over $349,700

Earned income is said to be $35,000.

Base tax amount at that level is $4386.

The amount over $31850 is $35000-31850 = $3150

Line 3 is multiplied by 25%: $3150×0.25 = $787.50

The sum of lines 2 and 4 is $4386 +787.50 = $5173.50

This amount divided by 12 is ... $5173.50/12 ≈ $431.13

Hence, Earned income is said to be $35,000, Base tax amount at that level is $4386, The amount over $31850 is  $3150, Line 3 is multiplied by 25% is $787.50, The sum of lines 2 and 4 is $5173.50 and This amount divided by 12 is $431.13.

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The number of quarts in 12 L is 12.684 qt.

Given that, 12 L to qt.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

Here,

There are 1.057 quarts in a liter, and there are 0.946 liters in a quart.

Now, 12 L=12×1.057

= 12.684 qt

Therefore, the number of quarts in 12 L is 12.684 qt.

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Two times or Twice the sum of a number and 3 is 8. The value of the number will be 1.

Let the value of the unknown number or variable be c.

Given,

"Two times the sum of a number and 3 is equal to 8", which means when you add the unknown number with 3 and then multiply it by 2, then the final answer will come as 8.

If we form the statement into an equation, then finding the value of the unknown variable will be a lot easier.

The equation will be:

    2(c + 3) = 8

=> 2c + 6 = 8

=> 2c = 8- 6

=> 2c = 2

=> c = 2/2

=> c = 1.

Hence, the value of the unknown number c will be 1.

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Answer:

Any Integer less than 20 ( ex. 19 , 18 , 17 , 16 , ........)

Step-by-step explanation:

Solve the Inequality to find the Integers that satisfy the Inequality

x - 4 < 16

add 4 for both terms

x - 4 + 4 < 16 + 4

x < 20

So any Integer less than 20 will make the Inequality True

The probability that 3 of the 6 children of this parents has the genes would be 0.1318

The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

The total number of children from the family is n = 6

and the probability of those with the cystic fibrosis is x = 3,

Probability of the disease = 0.25

We have the formula as

[tex]^{6} C_{x} *P^{x} *(1-p)^{n-x}[/tex]

The probability is 1/4 = 0.25

This is then written as

6C3 x 0.25³ x (1 - 0.25)⁶⁻³

= 20 x 0.015625  0.421875

= 0.1318

The probability that 3 out of the 6 children would have this gene is 13.18%

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(A) and (E) are the true statement.

Given,

In the question:

Jake and Liana make and sell wooden birdhouses. Jake spent $150 buying supplies. He sells each birdhouse for $15. The equation P = 12x - 120 represents the profit, P, Liana earns for selling x birdhouses. Jake and Llana each made 50 birdhouses.

To find the which statement is true?

Now, According to the question:

Jake's Profit: J = 15x - 150

Liana's Profit : P = 12x - 120

(A) when x = 0, P = -120, J = -150

then, 150 - 120 = $30

So, Jake spent $30 more than Liana

So, A is true, B is wrong.

(C) when x = 50 , J = 15 x 50 - 150 = $600

P = 12 x 50 - 120 =$480

Since, 600> 480

(D) when J = P

then, 15x - 150 = 12x = 120

3x = 30

x = 10

x = 10 not equal to 20

So, D is wrong

(E)  when P> -0 , and J > 0

then, 12x -120 > 0 and 15x - 150 > 0

=> x > 10

So, the minimum is 11, E is true .

Hence, Above the solution (A) and (E) are the true statement.

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-4 2/3 ,-3 2/3, -1 2/3 2/3

Answer:

1.3% decrease

Step-by-step explanation:

% change = (9.69 - 9.56) / 9.69) x 100 = 1.3% decrease

9.69-9.56 = 0.13

0.13/0.69= 0.0134158972

Multiply by 100 and you get 1.34158927

Round to nearest tenth and you get = 1.3%

Therefore, the percentage decrease is 1.3

Answer:

2/20

Step-by-step explanation:

Only 7 and 17 contain the number 7

The best interpretation of the function v(2) = 8 is that the volume of a cube with side length of 2 units is 8 cubic units

Function notations are the representation of a function using expressions such as g(x), f(x), etc

From the question, we have the following function notation that can be used in our computation:

v(2) = 8

From the question, we have the following representation

v(s)

This means that the volume of a cube of side length s is v(s)

When the above function is compared to v(2) = 8, we have the following comparison

s = 2 and v(s) = 8

This means that a cube of side length 2 has a volume of 8

The above represents the best interpretation of v(2) = 8

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Answer:

1

Step-by-step explanation:

Perpendicuar lines have slopes that are opposite reciprocals: 6 ==> -1/6

y=mx+b

y=-x/6 + b ==> plug in slope -1/6 into slope equation

1 = -6/6 + b ==> plug in x and y values into slope equation

1 = -1 + b

1 + 1 = -1 + 1 + b

b = 2 ==> solve for b

y = -x/6 + 2 ==> plug in the value of b into the equation

y - 1 = -x/6 + 2 - 1

y - 1 = -x/6 + 1

y - 1 = -(x/6-1) ==> answer: 1

Answer:

Step-by-step explanation:

I think the slope and the y is not 1/x because 2 is not part of the slope, im not sure

Answer:

100.86

Step-by-step explanation:

8.2*8.2+0.5(8.2)*8.2

Answer:

Step-by-step explanation:

We know that:

Then 6 gallons is:

Add 3 quarts to get total:

Answer:

27 quarts

Step-by-step explanation:

Now we have to,

→ find how many quarts does 6 gallons 3 quarts of paint measure.

Formula we use,

→ 1 gallon = 4 quarts

Now the required solution will be,

→ (6 × 4) + 3

→ 24 + 3

→ 27 quarts

Hence, the answer is 27 quarts.

Answer:

B. 10

Step-by-step explanation:

[tex]\rm \implies 28 \div 7 + 2 \times 3 \\ \\ \rm \implies 4 + 2 \times 3 \\ \\ \rm \implies 4 + 6 \\ \\ \rm \implies 10[/tex]

Answer:

m=3.7

Step-by-step explanation:

m²=14

m=√14

m=3.7416573868

m=3.7(2 d.p)

The probability that the sample proportion of the number of people using the courier will differ from the population proportion by greater than 0.03 is 0.0504

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ  = p = 0.05

sample size, n = 202

standard deviation, σ

= √{(p(1 - p)) / n}

= √{(0.05(1 - 0.05)) / 202}

= √{(0.05 * 0.95) / 202}

= 0.01533

The probability

differ from the population proportion by less than 3%

|X - 0.05| > 0.03

X < 0.02 OR X > 0.08

P(z < 0.02) + P(z > 0.08 )

z score for z < 0.02

z = (0.02 - 0.05) / 0.01533

= -1.9569

p value for z < -1.9569 = 0.02518

z score for z > 0.08

z = (0.08 - 0.05) / 0.02196

= 1.9569

p value for z > 1.9569 = 1 - 0.9748 = 0.02518

The probability required = 0.02518 + 0.02518 = 0.0504 = 5.04%

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a) $149911.84 can be afforded

b) $39600 is the total money you will pay the loan company

c) $246088.16 is the interested amount

Calculation

Given,

d=$1100

N= 30 years

r = 8% or 0.08

a) Loan amount that can be afforded

[tex]=\frac{d[1- (1+\frac{r}{k})^{-Nk} }{\frac{0.08}{12} }[/tex]

[tex]=\frac{1100[1- (1+\frac{0.08}{12})^{-30*12} }{\frac{0.08}{12} }[/tex]

= $149911.84

b) Total money you pay = d×N×k

=1100×30×12

=$39600

c) Interest paid = Total money paid – loan amount

⇒39600–14911.84 = $246088.16

Hence,

a) $149911.84 can be afforded

b) $39600 is the total money you will pay the loan company

c) $246088.16 is the interested amount

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The winner of the race among the friends would be Leslie.

The person who has the highest average speed will win the race. Average speed is the total distance travelled per time.

Average speed = total distance / total time

Carolina's average speed = 7/8 ÷ 1/2

7/8 x 2 = 7/4 = 1 3/4 miles per hour

Leslie's average speed = 1 ÷ 1/3

1 x 3 = 3 miles per hour

Bryan's average speed = 3/4 ÷ 3/4

3/4 x 4/3 = 1 mile per hour

Javier's average speed = 1 ÷ 2/3

1 x 3/2 = 1 1/2 miles per hour

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The terms which are equivalent to the slope in a proportional relationship include:

Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."

The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope formula is the rise over run formula, where the fraction consists of a rise, whether the line is going up or down, divided by the run.

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Complete question

Select all the terms which are equivalent to the slope in a proportional relationship.

Constant of proportionality

Origin

Inverse

Rise over run

Unit rate

The vertex is (-2, 11), then the vertex form of the quadratic is:

f(x) = 5*(x + 2)^2 - 11

A quadratic equation with a leading coefficient a and a vertex (h, k) can be written in vertex form as:

y = a*(x - h)^2 + k

And for a quadratic equation of the form:

y = a*x^2 + b*x + c

The vertex is at:

h = -b/2a

In this case, our equation is:

f(x) =5x^2 + 20x + 9

Then:

h = -20/2*5 = -2

Evaluating in x = -2 we get:

f(-2) = 5*(-2)^2 + 20*-2 + 9

f(-2) = 5*4 - 40 + 9

f(-2) = 20 - 40 + 9 = -20 + 9 = -11

The vertex is (-2, -11), and the leadin coefficient is a = 5, then the vertex form is:

f(x) = 5*(x + 2)^2 - 11

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They should charge for its premium in order to have an expectation of $0 for the policy is $85.

Given that, the probability that a 50-year-old male in the U.S. will die within one year is about 0.00142.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Here, probability of alive 100-0.00142

= 0.99858

P(A)=0.99858A+0.00142(A+60000)

Put A=0, in the obtained function, we get

P(0)=0.99858(0)+0.00142(0+60000)

=0.00142×(60000)

=$85.2

= $85

Therefore, they should charge for its premium in order to have an expectation of $0 for the policy is $85.

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Answer:

        2813

m = ----------

         932

Step-by-step explanation:

619m + 313m = 2813

932m = 2813

÷932      ÷932

        2813

m = ----------

         932

I hope this helps!

Answer:

[tex]m=\frac{2813}{932}[/tex]

Step-by-step explanation:

Combine like terms:

[tex]{619m}+{313m}=2813{932m}=2813[/tex]

Divide both sides by the same factor:

932m=2813

[tex]\frac{932m}{932}}=\frac{2813}{932}}\\[/tex]

Simplify

Cancel terms that are in both the numerator and denominator

[tex]m=\frac{2813}{932}[/tex]

The dimensions of the rectangular window that gives a maximum area are as follows;

Width = [tex]\dfrac{12}{2+\pi }[/tex] feet and length = 3 feet

The maximum value of a function is given by the point at which the graph of the function has the highest value.

The parameters of the window are;

Length of the framing material available = 12 ft.

The shape of the window = A semicircle on top of a regular rectangular window

Required; The dimension of the rectangular part of the Norman window that allows the most light

Solution;

Diameter of the semicircular part of the window = The width of the rectangular part

Let x represent the width of the window, we have;

Perimeter of the semicircle = π·x/2

Side length of the rectangular window = (12 - π·x/2 - x)/2

Area of the rectangular part of the window, A = x × (12 - π·x/2 - x)/2

Area of the semicircle = π·x²÷4

Area of the window, is therefore;

[tex]A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} +\dfrac{ \pi \cdot x^2}{4}[/tex]

At the maximum area, of the rectangular part, we have;

[tex]A_r' =\dfrac{d}{dx}\left( A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} \right) = -\dfrac{x\cdot \pi +2\cdot x-12}{2} = 0[/tex]

x·π + 2·x - 12 = 0

The width, x = [tex]\dfrac{12}{2+\pi }[/tex] feet

The length of the rectangle is therefore;

[tex](12 - \pi \cdot \dfrac{6}{2+\pi } - \dfrac{12}{2+\pi })/2 = 6 - \pi \cdot \dfrac{3}{2+\pi } - \dfrac{6}{2+\pi } = 3[/tex]

The length of the rectangular window = 3 feet

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Answer:

1/3

Explanation:

Imagine you repeat the experiment 100 times.

It is expected that half of the times (50) you take the fair coin and half of the times (50) the trick coin.

When you take the fair coin, half of the times you get heads, that is 25 times from 100 you “get the fair coin AND you get heads with the fair coin”.

When you take the trick coin, all the times you get heads, that is 50 times from the original 100 you “get the trick coin AND you get heads with the trick coin”.

In total, it is expected you get heads 75 times. And from those, 50 times will be with the trick coin and 25 times with the fair coin.

Now, if you get one of those at random, what’s the likelihood it was the fair coin?

Well, you have 25 cases it was the first coin and 50 cases it wasn’t, so it is 25 from a total of 75 and that is 25/75 = 1/3. That is, about 33.33%

Also, with probability theory:

Bayes’ Theorem:

P(B|A) = P(A ∩ B) / P(A)

P(A|B) = P(A ∩ B) / P(B)

So: with just the definitions I prove Bayes:

P(B|A) = P(A|B) * P(B) / P(A)

In our case:

P(Fair| Heads) = P(Heads|Fair) * P(Fair) / P(Heads)

p = P(Fair | Heads) = 0.5 * 0.5 / P(Heads)

What is P(Heads) ??

We can apply this:

Heads = (Heads ∩ Fair) U (Heads ∩ Trick)

And those in the union are disjoint (mutually exclusive), so:

P(Heads) = P(Heads ∩ Fair) + P(Heads ∩ Trick) =

= P(Heads|Fair) * P(Fair) + P(Heads|Trick) * P(Trick) =

= 0.5 * 0.5 + 1.0 * 0.5 = 1/4 + 1/2 = 3/4

Then:

p = P(Fair | Heads) = 0.5 * 0.5 / P(Heads) = 1/4 / (3/4) = 1/3

Answer:

Kieran shaded the multiples of 9 instead of the multiples of 3

Step-by-step explanation: