459 randomly selected lightbulbs were tested in a laboratory 291 lasted more than 500 hours find a point estimate of the true proportion of all lightbulbs in that last more than 500 hours

Answer:

The value of [tex]k(x)=\frac{5^{2x}-1}{5^x}[/tex]

Step-by-step explanation:

We have given two function [tex]g(x)=5^x\text{and}h(x)=5^{-x}[/tex]

We have to find k(x)=(g-h)(x)

[tex]k(x)=g(x)-h(x)[/tex]           (1)

We will substitute the values in equation (1) we will get

[tex]k(x)=5^x-(5^{-x})[/tex]

Now, open the parenthesis on right hand side of equation we will get

[tex]k(x)=5^x-5^{-x}[/tex]

Using [tex]x^{-a}=\frac{1}{x^a}[/tex]

[tex]k(x)=5^x-\frac{1}{5^x}[/tex]

Now, taking LCM which is [tex]5^x[/tex] we will get after simplification

[tex]k(x)=\frac{5^{2x}-1}{5^x}[/tex]

Hence, the value of [tex]k(x)=\frac{5^{2x}-1}{5^x}[/tex]

Answer:

0.604 on a p e x

volume = (1/3)*PI*(r1^2+r1*r2+r2^2)*h

 h=10

r1=5

r2=2

= 408.41 cubic inches

 round off answer as needed.

The equation of line passing through points (-2,7) and (3,2) is y = -x + 5. The slope, m, is -1. The y-intercept, b, is 5.

The subject matter here is finding the equation of a line in slope-intercept form, which is expressed as y = mx + b. Here, 'm' is the slope of the line and 'b' is the y-intercept. The slope, m, can be found using the formula: m = (y2 - y1)/(x2 - x1). Applying the coordinates given, (-2,7) and (3,2), we find the slope, m = (2 - 7) / (3 - (-2)) = -5 / 5 = -1.

Then, substituting m, x, and y into the equation, we get the y-intercept. Using the point (-2,7), we have: 7 = -1*-2 + b -> 7 = 2 + b -> b = 7 - 2 = 5. So the y-intercept, b, is 5. Therefore, the equation of the line in slope-intercept form is y = -x + 5.

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Answer:

4 of the 20 radio contest winners selected to try for the grand prize : C

5 friends waiting in line at the movies: C

6 students selected at random to attend a presentation: P

Final answer:

The scenarios illustrate combination when order does not matter (selecting contest winners and student attendees) and permutation when order matters (friends in line). The correct sequence is combination, permutation, combination.

Explanation:

In the context of the scenarios provided, we need to differentiate whether the situations are examples of combinations or permutations. A permutation is an arrangement of objects where order matters, while a combination is a selection of objects where order does not matter.

Thus, the correct answer to the sequence of scenarios is: combination, permutation, combination, which correlates with option c.

Final answer:

The first consecutive term of the arithmetic sequence that sums to 303 is 150. The second consecutive term is 153. We found this by setting up an equation for the sum of two consecutive terms and solving for the first term.

Explanation:

To find the two consecutive terms in the arithmetic sequence 3, 6, 9, 12, ... that sum up to 303, we first need to understand the properties of an arithmetic sequence. The given sequence has a common difference of 3 (that is, each term is 3 more than the previous term). Let's denote the first of these two consecutive terms as a. Therefore, the next term would be a + 3 (since the common difference is 3).

We are given that the sum of these two terms is 303, so we can write an equation:

a + (a + 3) = 303

Combining like terms, we get:

2a + 3 = 303

Subtracting 3 from both sides gives:

2a = 300

Dividing both sides by 2 gives:

a = 150

So, the first term is 150 and the second term, being a + 3, is 153.

Answer:

119 hundreths

Step-by-step explanation:

To Find: What is the product of 119 thousandths times 10?

Solution:

Thousandths can be represented in the fraction form as[tex]\frac{1}{1000}[/tex]

So, 119 thousandths = [tex]\frac{119}{1000}[/tex]

Now to find the product of 119 thousandths times 10

[tex]\Rightarrow \frac{119}{1000} \times 10[/tex]

[tex]\Rightarrow \frac{119}{100} [/tex]

Now hundreths  can be represented in the fraction form as[tex]\frac{1}{100}[/tex]

So, [tex]\Rightarrow \frac{119}{100} [/tex]  = 119 hundreths.

Hence the product of 119 thousandths times 10 is 119 hundreths.

Thus Option A is True.

Answer: P(S\cup T)=72%

Step-by-step explanation:

We are given that S and T are mutually exclusive events.

Therefore, the intersection of both the events must be 0.

i.e. [tex]p(S\cap T)=0[/tex]

P (S) = 65% and P(T) = 7%

We know that P(S or T)=[tex]P(S\cup T)=P(S)+P(T)-P(S\cap T)[/tex]

[tex]\Rightarrow P(S\cup T)=65\%+7\%=72\%[/tex]

Hence, P(S\cup T)=72%

To find the number of 2n-digit integers where odd position digits are odd, and even position digits are even and positive, we calculate based on the choices for each position, giving us a result of (5^n) * (4^n).

We encounter a combinatory problem in working out how many 2n-digit positive integers can be formed if the digits in odd positions must be odd and the digits in even positions must be even. Before proceeding, it's important to grasp the concept of positional numbering, where the rightmost digit is considered at position 1, and the counting proceeds from right to left.

For a 2n-digit positive integer, i.e., an integer with an even number of digits, there will be n digits at odd positions and n digits at even positions. For the odd positions, the digits can be any one of the five odd integers (1, 3, 5, 7, 9) and for the even positions, the digits can be any one of the four even positive integers (2, 4, 6, 8) because 0 is excluded as the question mentions they should be positive.

Therefore, for each position, we have a choice of five odd integers or four even integers. Since there are n odd positions and n even positions, we end up with (5^n) * (4^n) total possibilities or combinations.

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The total number of valid 2n-digit positive integers, where digits in odd positions must be odd and digits in even positions must be even, is calculated using the formula 5ⁿ * 4ⁿ.

To solve this problem, we need to consider the constraints given: digits in odd positions must be odd and digits in even positions must be even. Let's break down the problem step-by-step:

Total combinations = (Number of choices for odd positions) n * (Number of choices for even positions) n = 5ⁿ * 4ⁿ

This is the formula to calculate the number of valid 2n-digit integers under the given constraints.

To answer this item, we let x be the speed of the boat in still water. The speed of the current, we represent as y.

When the boat travels upstream or against the current, the speed is equal to x – y and x + y if it travels downstream or along with the current.

The time it takes for the an object to travel a certain distance is calculated by dividing the distance by the speed.

First Travel:    35 / (x – y)   + 55 / (x + y) = 12

Second travel: 30 / (x – y)   + 44 / (x + y) = 10

Let us multiply the two equations with the (x-y)(x+y)

This will give us,

              35(x + y) + 55(x – y) = 12(x-y)(x+y)

              30(x + y) + 44(x – y) = 10(x-y)(x+y)

Using dummy variables:

Let a = x + y and b be x – y

                35a + 55b = 12ab

                30a + 44b = 10ab

From the first equation,

                     b = 35a/(12a – 55)

Substituting to the second equation,

                30a + 44(35a/(12a – 55)) = 10a(35a/(12a-55))

The value of a is 11.

              b = 35(11)/(12(11) – 55))

              b = 5

Putting back the equations,

        x + y = 11

       x – y = 5

Adding up the equations give us,

  2x = 16

    x = 8 km/hr

The value of x, the speed of the boat in still water, is 8 km/hr. 

speed of the stream = 3 km/hr

and speed of boat in still water= 8 km/hr

Let s be the speed of the boat upstream

and s' be the speed of the boat downstream.

We know that:

[tex]Time=\dfrac{distance}{speed}[/tex]

Hence, we get:

  [tex]\dfrac{35}{s}+\dfrac{55}{s'}=12[/tex]

and

[tex]\dfrac{30}{s}+\dfrac{44}{s'}=10[/tex]

Now, let

[tex]\dfrac{1}{s}=a\ and\ \dfrac{1}{s'}=b[/tex]

Hence, we have:

[tex]35a+55b=12--------------(1)\\\\\\and\\\\\\30a+44b=10--------------(2)[/tex]

on multiplying equation (1) by 4 and equation (2) by 5 and subtract equation (1) from (2) we get:

[tex]a=\dfrac{1}{5}[/tex]

and by putting value of a in (2) we get:

[tex]b=\dfrac{1}{11}[/tex]

Hence, speed of boat in upstream= 5 km/hr

and speed of boat in downstream= 11 km/hr

and we know that:

speed of boat in upstream=speed of boat in still water(x)-speed of stream(y)

and speed of boat in downstream=speed of boat in still water(x)+speed of stream(y)

Hence, we get:

[tex]x-y=5\\\\\\and\\\\\\x+y=11[/tex]

Hence, on solving the equation we get:

[tex]x=8[/tex]

and y=3

Hence, we get:

speed of the stream = 3 km/hr

and speed of boat in still water= 8 km/hr

John's net pay is calculated by subtracting deductions for Medicare, Social Security, state and federal taxes, and insurance from his gross pay of $500. The total deductions amount to $168.25, resulting in a net pay of $331.75.

Calculation of John's Net Pay

To calculate John's net pay, we need to subtract all the deductions from his gross pay. Since his gross pay is $500, we will apply the following deductions:

Medicare tax: 1.45% of $500 = $7.25

Social Security tax: 6.2% of $500 = $31.00

State tax: 2% of $500 = $10.00

Federal income tax: 20% of $500 = $100.00

Insurance deduction: $20.00

Add up all deductions: $7.25 (Medicare) + $31.00 (Social Security) + $10.00 (State Tax) + $100.00 (Federal Tax) + $20.00 (Insurance) = $168.25

John's net pay is therefore calculated by subtracting the total deductions from his gross pay: $500.00 - $168.25 = $331.75.

The linear equation formed is C = 5250 + 175S, where C is the total cost and S is the amount of sugar in tons. This expresses the cost for Sugar Sweet Company to transport its sugar to the market, beginning from a fixed cost of $5250 with an additional $175 charged per ton of sugar transported.

The question involves the creation of a linear equation that represents the total cost, C, of transporting sugar. We are told the initial cost of renting trucks is $5250 and there's an additional cost of $175 for each ton of sugar, S.

Therefore, we can write the equation as: C = 5250 + 175S.

To graph this equation, start at the point (0, 5250) on the y-axis which represents the initial cost. The slope of the line is 175, which means for each ton of sugar transported, the cost increases by $175. From the starting point, you can plot other points moving up vertically 175 units for each unit moved to the right horizontally.

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Answer:

Option A The graph in the attached figure

Step-by-step explanation:

Let

x-----> the number of ream of paper

y-----> the number of ink cartridge

we know that    

[tex]6x+18y\leq 252[/tex] ----> inequality that represent the possible combinations of paper and ink cartridges that Adam may buy

using a graphing tool

the solution is the triangular shaded area

see the attached figure

The next value in the sequence is 16, following an increment of 3 in each step.

The next value in the sequence is 16.

The sequence increments by 3 starting from 4 (4, 7, 10, 13, ...)

Therefore, the next value after 13 would be 13 + 3 = 16.

Final answer:

Each friend ate approximately 0.3636 of a pizza when the four pizzas were divided evenly among 11 friends.

Explanation:

The student's question involves dividing four pizzas evenly among 11 friends, so each person gets the same proportion of pizza. We need to convert this proportion into decimal form to answer the question.

To find the proportion of a pizza that each friend ate, we calculate 4 pizzas ÷ 11 friends. So, each friend ate ≈ 0.3636 of a pizza. We arrived at this by dividing 4 by 11, which yields a repeating decimal, so we round it to four decimal places to express it accurately.

This value represents the proportion of pizza each person ate when the pizzas were divided equally.

The value of s is greater or equal to 22.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

2s + 5 greater than or equal to 49.

This can be written as,

(2s + 5) ≥ 49

Solve for s.

2s + 5 ≥ 49

2s ≥ 49 - 5

2s ≥ 44

s ≥ 22

Thus,

s is greater than or equal to 22.

Learn more about inequalities here:

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