Lucky Lumen light bulbs have an expected life that is exponentially distributed with a mean of 20,000 hours. Determine the probability that one of these light bulbs will last

a. At least 24,000 hours.
b. No longer than 4,000 hours.
c. Between 4,000 hours and 24,000 hours.

9514 1404 393

Answer:

  c. 11

Step-by-step explanation:

The sum of all 6 numbers is ...

  6 × average of 6 = total of 6

  6 × 6 = 36 = total of 6

Then the remaining number is ...

  total of 5 + sixth number = total of 6

  25 + sixth number = 36

  sixth number = 36 -25 = 11

A: The differential equation can be expressed in the form f(x ,y) = g(x)h(y) = 0, indicating that it is homogeneous. Divide both sides of the equation by y to observe this, which results in  dy/dx + sin^2(x) = cos^2(x)

B: Since there is just one function y and its derivative dy/dx involved in the equation, it is an ODE.

D: Because there is only one function y and its derivative  dy/dx involved in the equation, first-order differential equations are what it is.

G: The formula for the equation is a(x)y' + b(x)y = c(x), where a(x)=1, b(x) = sin^2(x), c(x) = cos^2(x) . Given that x and the coefficients of y and dy/dx are constants, the equation is linear.

H: The equation may be written as dy / y =  (cos^2(x))dx/(1+sin^2(x)),and it is a candidate for integrating factors because we can multiply both sides by (1+sin^2(x))dx .

I: The variables x and y can be separated by integrating both sides of the equation, which can be represented as  (dy/y) = (cos^2(x))dx/(1+sin^2(x)) + (sin^2(x))dx .

J: The equation is self-sufficient; it is not dependent on any explicit function of t.

       Therefore, the differential equation  dy/dx+sin^2(x)y=cos^2(x)y .A candidate for integrating factors exists in the first-order linear, homogeneous, separable, and autonomous ODE known as y.

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Being a girl and playing a sport are C. No, they are not independent events, because P(girl) 0.49 and P(girl plays a sport) ~ 0.62.

Let's consider the probabilities:

P(girl) = (number of girls) / (total number of students) = 135 / 275 ≈ 0.49

P(girl plays a sport) = (number of girls playing a sport) / (total number of students) = 76 / 275 ≈ 0.276

If being a girl and playing a sport were independent events, the joint probability would be the product of the individual probabilities:

P(girl) × P(girl plays a sport) ≈ 0.49 × 0.276 ≈ 0.13524

However, the actual joint probability is different from the expected value:

P(girl, plays a sport) ≈ 76 / 275 ≈ 0.276

Since the joint probability does not match the product of the individual probabilities, we can conclude that being a girl and playing a sport are not independent events based on the given data.

Therefore, option C. No, they are not independent, because P(girl) 0.49 and P(girl plays a sport) ~ 0.62. is the correct answer.

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Answer:

the answer is 16000

because 4 × 3848 is the best estimate for 16000 its nearby 15 k

hopefully its correct

Answer:

In an hour the factory makes 3848 pencils

In four hours the factory will make four times as much

=4×3848=15392 pencils

the best estimate is 16000 pencils

The class of the equation and the cross section equation are;

The equation is a hyperboloid of two sheets

The cross sections are;

Equation at z = 0 is; y²/8 - x²/8 = 1

Equation at y = -4 is; x²/8 + z² = 1

Equation at y = 0 is; x²/8 + z² = -1

Equation at y = 4 is; x²/8 + z² = 1

Equation at x = 0 is; y²/8 - z² = 1

An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.

The equation can be presented as follows;

y² = x² + 8·z² + 8

y² - x² - 8·z² = 8

y²/8 - x²/8 - z² = 1

The above equation is the equation of an hyperboloid of two sheets, where;

a² = 8, b² = 1, and c² = 8

Please find attached the diagram of the surface, created with an online 3D graphing tool.

The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;

y²/8 - x²/8 - 0 = 1

y²/8 - x²/8 = 1

The above equation is the equation of an hyperbola in the xy plane

The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 4²/8 = -1

- x²/8 - z² = -1

x²/8 + z² = 1

The above is an equation of an ellipse in the xz plane

The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;

0²/8 - x²/8 - z² = 1

- x²/8 - z² = 1

Therefore; x²/8 + z² = -1

The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 2 = -1

x²/8 + z² = 1

The above equation is the equation of an ellipse in the xz plane

The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;

y²/8 - 0²/8 - z² = 1

y²/8 - z² = 1

The equation is the equation of an hyperbola in the yz plane

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if you have a 90 th you get in

The measure οf the supplementary angle οf x = 61.33° is fοund tο be 118.67°.

An angle is a figure in plane geοmetry that is created by twο rays οr lines that have a shared endpοint. The twο rays are termed the sides οf an angle, and the cοmmοn terminatiοn is called the vertex. Angles are typically expressed as degrees. A "prοtractοr" is a crucial geοmetrical instrument that aids in measuring angles in degrees. Twο sets οf numbers οn a prοtractοr are οriented in οppοsitiοn tο οne anοther. On the οutside rim, οne set gοes frοm 0 tο 180 degrees, while οn the inner rim, the οther set gοes frοm 180 tο 0 degrees.

Let the angle be x.

Twο angles are cοmplementary when their sum is 90°.

Tοw angles are supplementary when their sum is 180°

If x is οne angle, then its cοmplementary angle is (90-x)°

Given x is 4 mοre than twice its cοmplement.

We can write the equatiοn as:

x = 4 + 2*(90-x)

Sοlving,

x = 4 + 180 - 2x

3x = 184

x = 61.33°

Nοw we are asked tο find the supplementary angle οf x.

Supplementary angle = 180 - x = 180 - 61.33 = 118.67°

Therefοre the measure οf the supplementary angle οf x = 61.33° is fοund tο be 118.67°.

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...1...1...1...1...1...

Answer:

  4

Step-by-step explanation:

You are given a table of function values in which x increases by 2, and you want to know the factor by which f(x) increases when x increases by 1.

Let k represent the factor by which f(x) increases when x increases by 1. This means ...

  f(2) = k·f(1)

  f(3) = k·f(2) = k·(k·f(1)) = k²·f(1)

  64 = k²·4

  k² = 64/4 = 16

  k = √16 = 4

The output value increases by a factor of 4 as the input value increases by 1.

__

Additional comment

The table values would also be obtained if the factor of increase were -4. That is, f(x) = -(-4)^x would give the same table. In that case, f(x) would not be a continuous function.

Answer:

You can spend all of the money by getting 1 sandwich and 2 things of chips

Step-by-step explanation:

1 sandwich =4$

1 bag of chips =3$

4 + 3 =7

7+ 3= 10

Answer:

2π(x+y+z)

is the factorization

Considering the given graph, the profit during the period was of -2 dollars.

We add all the negative numbers, all the positive numbers, then keep the signal of the higher absolute value, and subtract the values.

From the graph, we have that:

8 > 6, hence the profit is negative given by:

-(8 - 6) = -2 dollars.

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Answer:

26 weeks

Step-by-step explanation:

$5.50-one week ☞︎ $5.50 x 5 = $27.50

+ $27.50

$55.00 (20 weeks)

$5.50 x6=$33.00 + $33.00

$88.00(26 weeks)

Answer:

Ummmm.... Whats your qustion???? Im confused...

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I’ve attached my work

hope it helps!

Based on the data recorded by Anna on Saturday, we can estimate the number of people expected to visit The Youth Wing on Sunday.

Let's calculate the proportion of visitors to The Youth Wing compared to the total number of visitors on Saturday:

\(\displaystyle \text{Proportion} = \frac{\text{Visitors to The Youth Wing on Saturday}}{\text{Total visitors on Saturday}} = \frac{382}{382 + 461 + 355}\)

Next, we'll apply this proportion to the total number of visitors on Sunday to estimate the number of people expected to go to The Youth Wing:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times \text{Total visitors on Sunday}\)

Now, let's substitute the values into the equation and calculate the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355}\)

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times 800\)

Calculating the proportion:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355} = \frac{382}{1198}\)

Calculating the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \frac{382}{1198} \times 800\)

Simplifying the equation:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx \frac{382 \times 800}{1198}\)

Now, let's calculate the approximate number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx 254\)

Therefore, based on the data recorded on Saturday, we can estimate that around 254 people should be expected to go to The Youth Wing on Sunday.

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The type of bias best described by the survey is Response bias and the Bias can be remedied through C. The interviewer should survey people by phone and in person.

Now, According to the question:

He conducts a nationwide survey of 1160 randomly selected adults 18 years and older

Response bias refers to several factors that can lead someone to respond falsely or inaccurately to a question. Self-report questions, such as those asked on surveys or in structured interviews, are particularly prone to this type of bias.

Another example of response bias is when a person selects an answer to a question that they are aware is incorrect, but they make this choice because they are uncomfortable reporting their honest answer.

Response bias is the best describes the bias in the survey.

The bias be remedied can :

The interviewer should reword the question.

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Answer:

Step-by-step explanation:

Girl: "what I am not a freakin gold diggerrr I just like moneyyy"

Girl: "what I am not a freakin gold diggerrr I just like moneyyy" Hooman: Say "ChEeZe"

Girl: "what I am not a freakin gold diggerrr I just like moneyyy" Hooman: Say "ChEeZe" Girl: dances on lambo showing too much..

Girl: "what I am not a freakin gold diggerrr I just like moneyyy" Hooman: Say "ChEeZe" Girl: dances on lambo showing too much.. Hooman: Good Good You're a perfect picture of a gold digger.

Girl: "what I am not a freakin gold diggerrr I just like moneyyy" Hooman: Say "ChEeZe" Girl: dances on lambo showing too much.. Hooman: Good Good You're a perfect picture of a gold digger. Girl: "my outfit matches your carr"

Girl: "what I am not a freakin gold diggerrr I just like moneyyy" Hooman: Say "ChEeZe" Girl: dances on lambo showing too much.. Hooman: Good Good You're a perfect picture of a gold digger. Girl: "my outfit matches your carr"Hooman: it does

Girl: "what I am not a freakin gold diggerrr I just like moneyyy" Hooman: Say "ChEeZe" Girl: dances on lambo showing too much.. Hooman: Good Good You're a perfect picture of a gold digger. Girl: "my outfit matches your carr"Hooman: it doesHooman: too bad you're a gold digger and digging to much for gold.

Answer:

It is not a integer, it is a rational number

Answer: No, this isn't. An integer is any whole number, positive or negative. Having extraneous digits to the right of the decimal other than zero, radicals or any fractions are excluded from being considered an integer. Integers, for example, are 2, 85, -923, etc. Hope this helps!

Step-by-step explanation:

Answer:

100.72

Step-by-step explanation:

\(Given,\)

event requires each runner to jump 10 hurdles that are spaced 8.5 meters apart.

If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line,

Solution:

runner to jump 10 hurdles that are spaced 8.5 meters apart.

Distance between 10 hurdles

=(10-1)* 8.5

=9*8.5

=76.5

If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line,

Hence length of race = 13.72+76.5+10.5

=100.72

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Answer:

100.72 meters

Step-by-step explanation:

To find the total length of the race, we need to sum:

The distance from the starting line to the first hurdle is 13.72 meters.

The distance between each of the 10 hurdles is 8.5 meters.

There are 9 spaces between hurdles 1 and 10, so the distance between the hurdles is 9 × 8.5 = 76.5 meters.

The distance from the last hurdle to the finish line is 10.5 meters.

To find the total length of the race, add these distances together:

\(\begin{aligned}\textsf{Total length of the race} &=\sf 13.72\; meters + 76.5\; meters + 10.5 \;meters\\\\&=\sf 100.72\; meters\end{aligned}\)

Therefore, the race is 100.72 meters long.

Answer:

WW1

Step-by-step explanation:

what is it for?

Answer:

Bridget has $5.55.

Step-by-step explanation:

First let's find how much money Bridget needs to buy 5 vases. To do this, multiply the cost per vase by the amount of vases she wants to buy:

2 * 5 = 10

It would cost $10 to buy 5 vases.

Bridget needs $4.45 in order to buy 5 vases. So, to find how much money she already has, subtract the amount of money she needs from the total cost of the 5 vases:

10 - 4.45 = 5.55

Bridget has $5.55.

Answer:

$ 5.55

Step-by-step explanation:

Find the price of 5 vases

Cost of 5 vases = 5 * 2 = $ 10

She needs $4.45 to buy 5 vases. If we subtract this 4.45 from $10, the result will be the money she has already with her

Money Bridget has = 10 - 4.45

                               = $ 5.55

Answer:

c. all accounts fewer than 31 or more than 60 days past due.

Step-by-step explanation:

The Universal Set is the set of all past due accounts.

Event A = the event that the account is between 31 and 60 days past due.

Event B = the event that the account is that of a new customer.

Therefore, the complement of A will be the event of all the accounts fewer than 31 or more than 60 days past due.

The correct option is C.

Answer:

The third options

Step-by-step explanation:

Counting we can see that 10 students went to two or less states, and 10 went to three or more

Answer:

  see attached for a sketch

  area = 5 1/3 square units

Step-by-step explanation:

You want the area under the square root curve, above y=0, from x=0 to x=4.

The area is found by integrating a differential of area over appropriate limits. A vertical slice will have hight √x and width dx, so we have ...

  dA = (√x)dx

  A = ∫(√x)dx

The power rule can be used for the integration:

  \(\displaystyle A=\int_0^4{x^{\frac{1}{2}}}\,dx=\left[\dfrac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]^4_0=\dfrac{2}{3}(4^\frac{3}{2})=\dfrac{16}{3}=\boxed{5\dfrac{1}{3}}\)

The area of the region is 5 1/3 square units.

__

Additional comment

You will notice that the area is bounded by a rectangle 4 units wide and 2 units high, for an area of 4·2 = 8. The area under the parabolic curve is 2/3 of that: 2/3·8 = 16/3 = 5 1/3 square units.

This fraction will be true for any area bounded by a parabola where the vertex is one of the corners of the rectangle.

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The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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Answer: \(2\sqrt{6}\)

Step-by-step explanation:

Find the perfect square root(1,4,9,16.....) of 24 which is 4.

\(\sqrt{4 x 6}\)=\(\sqrt{24}\)

sqr root of 4 is 2 so that becomes

\(2\sqrt{6}\)

Answer:

The simplified version of this equation is -3x - 12.

Step-by-step explanation:

To simplify this equation, distribute -3 to both x and 4.

-3(x+4) = -3x -12

Answer:

-3x-12 as an expression

Step-by-step explanation:

To solve this problem, we need to distribute!

Multiply -3 by both the x and the 4

When we do this, we get:

-3x and -12

Note: when you multiply a positive by a negative, you get a negative so it turns into a negative number

Note 2: When you see an x without a number in front of it, it becomes 1x. In this problem, that is why it is a -3x because -3 x 1 is -3

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Multiples of 3

: 3, 6, 9, 12, 15, 18, 21, 24, ...

Multiples of 4

: 4, 8, 12, 16, 20, 24, ...

Multiples of 8

: 8, 16, 24, ..

2

Find the smallest number that is shared by all rows above. This is the LCM.

LCM = 2424

Method 2: By Prime Factors

1

List the prime factors of each number.

Prime Factors of 3

: 3

Prime Factors of 4

: 2, 2

Prime Factors of 8

: 2, 2, 2

2

Find the union of these primes.

2,2,2,32,2,2,3

3

Multiply these numbers: 2\times 2\times 2\times 3=242×2×2×3=24. This is the LCM.

LCM = 2424