Three draws are made at random with replacement from a box with 10 tickets numbered 1 through 10. The chance the 3rd number is bigger than twice the first is:
A. None of these choices
B. 1
C. 3
D. 2

Answer:

Step-by-step explanation:

Let X denote the life span of a car battery and it follows and exponential distribution with average of 6 years.

Thus , the parameter of the exponential distribution is calculated as,

μ = 6

\(\frac{1}{\lambda} =6\)

\(\lambda = \frac{1}{6}\)

a) The required probability is

\(P(X>4)=1-P(X\leq 4)\\\\=1-F(4)\\\\1-(1-e^{- \lambda x})\\\\=e^{-\frac{4}{6}\)

= 0.513

Hence, the probability that a randomly selected car battery will last more than four years is 0.513

b) The variance of the battery span is calculated as

\(\sigma ^2=\frac{1}{(\frac{1}{\lambda})^2 }\\\\\sigma ^2=\frac{1}{(\frac{1}{6})^2 } \\\\=6^2=36\)

The 95% percentile \(x_{a=0.05}\) (α = 5%) of the battery span is calculated

\(x_{0.05}=-\frac{log(\alpha) }{\lambda} \\\\=-\frac{log(0.05)}{1/6} \\\\=-6log(0.05)\\\\=17.97 \ years\)

c)  

Let \(X_r\) denote the remaining life time of a car battery

i)the probability the battery will last an additional five years is calculated below

\(P(X_r>5)=e^{-5\lambda}\\\\=e^{-\frac{5}{6} }\\\\=0.4346\)

ii) The average time that the battery is expected to last is calculated

\(E(X_r)=\frac{1}{\lambda} \\\\=6\)

Answer:

x = 14

Step-by-step explanation:

Please note, the word trapezium is a synonym for the word trapezoid.

This problem gives one the area of the trapezoid, a well as one of the measurements of a base and the height of the figure. One is asked to find the length of the other base. This can be done by using the formula to find the area of a trapezoid. This formula is the following,

\(A=(h)(\frac{b_1+b_2}{2})\)

Where (A) represents the area of a trapezoid, (\(b_1\)) and (\(b_2\)) represents the bases and (h) represents the height. Substitute in the given values and solve for the unknown base.

\(b_1=7\\h=6\\A=84\)

\(A=(h)(\frac{b_1+b_2}{2})\\\)

Substitute,

\(84=6(\frac{7+b_2}{2})\\\)

Inverse operations,

\(84=6(\frac{7+b_2}{2})\)

\(14=\frac{7+b_2}{2}\)

\(28=7+b_2\)

\(14=b_2\)

Answer:

Decimal Representation: 0.67

Percent Representation: 67%

Answer:

decimal = 0.67

percentage =67%

Answer:

b

Step-by-step explanation:

grocery

2.80÷8=0.35

0.35×16=5.6

farmers

4.20÷14=0.3

0.3×16=4.8

5.6-4.8=0.8

A formula that describes the average revenue per person is:

average revenue per person = 1.4w

Average revenue per person is the ratio of the total revenue received to the number of people. It is calculated by dividing total revenue by the number of people.

We have:

Total revenue formula, M = 350w⁴

Total number of people formula, T = 250w³

Thus,

Average revenue per person = M/T

Average revenue per person = 350w⁴/250w³

Average revenue per person = 1.4w

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Solve;

Answer:

the answer is A

I followed the point slope formula and added in the x and y values

Answer:

25/9

Step-by-step explanation:

3 1/3 ÷ 1 1/5

3 1/3 = 10/3

1 1/5 = 6/5

10/3 ÷ 6/5 = 10/3 x 5/6 = 50/18 = 25/9

So, the answer is 25/9

Answer:

n = 120

Step-by-step explanation:

Given that,

Side length the cube = 3 inches = 0.25 feet

We need to find the number of games can be packed inside of a box whose dimensions are 5 foot by 3 foot by 2 feet.

Let there are n games.

\(n=\dfrac{\text{Volume of box}}{\text{Volume of the game}}\\\\=\dfrac{5\times 3\times 2}{0.25}\\\\n = 120\)

Hence, there are 120 games packed inside the box.

Answer:

- Substitute $410 for C in the equation and solve.

- 9 people could go on the trip with $410

Step-by-step explanation:

B) We are told the bus company is charging them using the formula;

C = 50 + 40n

Where;

C is the total cost

n is the number of people

Now, we are told that a parent group is willing to give the club $410. Thus, we will substitute $410 for C in the equation and solve.

410 = 50 + 40n

Subtract 50 from both sides to get;

410 - 50 = 40n

360 = 40n

n = 360/40

n = 9

The inequality expression on the graph is \(\frac{4}{5}x-2y\ge3\)

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

The graph

On the graph, we can see that

The line is a shaded line and the down is shaded

This means that the expression must be ≥

Testing the options (c) and (d) on a graph, we have the match expression to be \(\frac{4}{5}x-2y\ge3\)

hence, the inequality is \(\frac{4}{5}x-2y\ge3\)

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Answer: To calculate the total, we need to first calculate the discount and then the tip.

First, calculate the discount: $21.50 x 10% = $2.15

Then, subtract the discount from the subtotal: $21.50 - $2.15 = $19.35

Next, calculate the tip: $19.35 x 20% = $3.87

Finally, add the tip to the subtotal after the discount to find the total: $19.35 + $3.87 = $23.22

Therefore, Abdiel's total would be $23.22 if he uses a coupon for 10% off the subtotal and leaves a 20% tip before the discount.

Step-by-step explanation:

Tom is blind and can claim a standard deduction amount of C. $21,150.

An additional tax-free stipend is known as the Blind Person's Allowance.

That implies that you can make more money before having to start paying income tax.

Tom's 13-year-old nephew, Frank, resided with him the entire time.

Tom gave all of his assistance and paid for more than half of the home's maintenance costs.

Tom is blind and unable to be claimed as a dependent by another taxpayer. He made $44,000 in salary.

Tom and Frank are both citizens of the United States, have active Social Security numbers, and spent the entire calendar year here.

Tom can take the standard deduction for $21,150 for the entire year as a blind taxpayer.

Q. Tom is 36 years old and has never been married.

Frank, age 13, is Tom's nephew who lived with him all year. Tom provided all of his support

and provided over half the cost of keeping up the home.

Tom earned $44,000 in wages.

Tom is blind and cannot be claimed as a dependent by another taxpayer.

Tom and Frank are U.S. citizens, have valid Social Security numbers, and lived in the U.S. the

entire year.

2. Tom is blind and can claim a standard deduction amount of: A. $12,950 B. $19,400 C. $21,150 D. $25,900

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Bruce and Felicia would have a unique solution to the given equation. The value of x that satisfies the equation is 15.

To determine if the equation 6x + 2 = 5x + 17 has a unique solution, we need to check if the variable x has a consistent value that satisfies the equation.

By simplifying the equation, we can see that the equation becomes:

6x - 5x = 17 - 2

Simplifying further, we have:

x = 15

Since the variable x has a specific value, in this case, x = 15, the equation does have a unique solution. When x is substituted with 15 in the equation, both sides are equal.

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Answer:

7500

Step-by-step explanation:

1 year= 2500

3 years= x

So we got

2500 × 3 = 7500

The population after another three years will be 15,625.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

Assume a populace becomes as per a strategic model with starting populace of 1,000 and conveying limit of 10,000.

If the population grows to 2500 after one year. Then the increasing factor is given as,

b = 2,500 / 1,000

b = 2.5

Then the equation is given as,

y = 1,000 × (2.5)ˣ

Then the population after another three years will be given as,

y = 1,000 × (2.5)³

y = 1,000 × 15.625

y = 15,625

The population after another three years will be 15,625.

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The graph of this function will behave as (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

The demand function is given by d = 100 - 10p. This means that the quantity demanded (d) decreases as the price (p) increases.

The slope of the demand function is the rate of change of the quantity demanded with respect to the price. In this case, the slope is -10, which is negative. This indicates that as the price increases, the quantity demanded decreases.

The initial value of the demand function is 100, which represents the quantity demanded when the price is zero. This means that the demand function intersects the y-axis at (0, 100).

Therefore, the correct answer is (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

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Answer:

Sorry If I'm wrong but I'm pretty sure you would use theoretical

Step-by-step explanation:

Because Theoretical is used to make predictions and when doing this you would have to make lots of predictions on what you would get.

(Hope It's Right!)

Answer:

Step-by-step explanation:

The cost of 2 orders of fries and 4 drinks is $5.68 and the cost to get f orders of fries and d drinks is $0.92f+0.96d

When something is calculated on its one unit, then it is called its unit rate. for example: If 5 mangoes is of $50 then cost of 1 mango is 50/5 = 10 here $10 is unit rate for mangoes.

Given that, At the fast food restaurant, an order of fries costs $0.92 and a drink costs $0.96.

We have here unit rates of fries and drinks,

So, when 1 pack of fries costs $0.92, then cost of 2 pack of fries = 2×0.92 = $1.84

Similarly, when 1 drink costs $0.96, then the cost of 4 drinks = 4×0.96 = $3.84

Total cost = $5.68

Similarly, the cost to get f orders of fries = $0.92f

And, the cost of d drinks = $0.96d

Total cost =  $0.92f+0.96d

Hence, we get the answer as = a) $5.68 and b) $0.92f+0.96d

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Answer:

Total cost of covering the pedestal is $12.54.

Step-by-step explanation:

The pedestal is a square prism so top and bottom are of square shape.

Hence, we have here length = width

We know that the Total Surface Area of a Prism is:

\(\text{Total Surface Area = } 2 (l\times w+ w \times h+ h \times l)\)

Where l is length,

w is width and

h is height of prism

We know that here w = l = 3 feet

and h = 4 feet

Also, underside of pedestal is not to be covered.

The underside of pedestal is square type.

So,

\(\text{Required Total Surface Area = } l\times w+ 2\times w \times h+2\times h \times l\)

\(\Rightarrow 3 \times 3 + 2 \times 3 \times 4 + 2 \times 3 \times 4\\\Rightarrow 9 + 24 + 24\\\Rightarrow 57\ ft^{2}\)

Cost of cover per square foot = $ 0.22

Total cost of \(57\ ft^{2}\)  \(\Rightarrow 0.22 \times 0.57 = \$12.54\)

Answer:

To add fractions, find the LCD (Least Common Denominator) or any common denominator of the fractions. For example, if you wanted to add 1/3+2/7, you find the LCD, which is 21, because 3x7=21, and 3 and 7 are both prime numbers. Now each fraction will have denominators of 21, so we will get 7/21+6/21. To add them together, add the numerators to get 13/21. Find the least common denominator of two fractions and then add the numerators. Hope it helps!

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

8 * 3 + 4 = 28

Answer:

6 m

Step-by-step explanation:

27m^3 /8m^3= 20 m / X

8m^3 × 20 m = 27m^3 × X

160 /27 = X

X = 5.9

= 6

Answer:

V = a cubed

Step-by-step explanation:

Hope this helps

Answer:

Flip over y axis.

Step-by-step explanation:

rule of transformation

Answer:

A, Reflected

B, Rotated

C, Translated

Step-by-step explanation:

The simplified polynomial for the area and perimeter of the rectangles are:

13). Area = 5x² + 40, Perimeter = 12x + 16

14). Area = x² + 10x + 12, Perimeter = 4x + 20

Area of rectangle = Length × Width

Perimeter of rectangle = 2(Length + Width)

13). Area of the rectangle = 5x × (x + 8)

Area of the rectangle = 5x² + 40

Perimeter of the rectangle = 2[5x + (x + 8)]

Perimeter of the rectangle = 2(6x + 8)

Perimeter of the rectangle = 12x + 16

12). Area of the rectangle = (x + 3)(x + 7)

Area of the rectangle = x² + 7x + 3x + 21

Area of the rectangle = x² + 10x + 21

Perimeter of the rectangle = 2[(x + 3) + (x + 7)]

Perimeter of the rectangle = 2(2x + 10)

Perimeter of the rectangle = 4x + 20.

Therefore, the simplified polynomial for the area and perimeter of the rectangles are:

13). Area = 5x² + 40, Perimeter = 12x + 16

14). Area = x² + 10x + 12, Perimeter = 4x + 20

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Step-by-step explanation:

70 ÷ 3 = 23  1/3