Select the correct answer.
Find the value of g(7) for the function below.

OA.
60
7
OB.
45
8
O C.
58
O D.
49
8

The answers are:

a) The z-score for a light bulb that lasts 500 hours is -10.

b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.

c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.

d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.

a) The z-score is calculated as:

z = (X - μ) / σ

Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,

z = (500 - 1000) / 50 = -10.

The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.

b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is

50/√20

≈ 11.18 hours.

z = (980 - 1000) / 11.18 ≈ -1.79.

The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.

c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:

z = (400 - 1000) / 50 = -12.

The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.

d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.

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The variables are evaluated to give;

1. 2

2. 6

An algebraic expression can be defined as an expression that is made up of terms, variables, coefficients, factors and constants.

These expressions are also thought to consist of mathematical or arithmetic operations such as;

From the information given, we have that;

A=1 b=2 c=3 x=3 y=2 z=1

1. ab

Let's substitute the values into the formula

1(2)

Multiply the values

2

2. Abc

Substitute the values

(1)(2)(3)

multiply the values

6

Hence, the values are 2 and 6

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Answer:

9(8d + 9)

Step-by-step explanation:

Since 72 and 81 are both divisible by 9, we can factor out a 9 from the expression:

72d + 81

9(8d + 9)

So, the factored expression is 9(8d + 9)

Note that the above is a complex 2 dimensional geometrical shape. To begin solving this you must deconstruct it into more regular shapes as shown in the attached.

In the simplified version, it is clear that the complex shape is made up of

In a case where the dimensions were given, we could solve for the area of the individual parts then sum all the areas up to get the Total Area of the complex shape.

Recall that the Area of a Rectangle is given by:

L x W

Where L = Length

W = Width

Triangle:

(b x h) /2

Where

B = Base

H = Height

Semi circle

1/2(πr2 )

Where

r = radius

π = 3.14


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Answer:

9:30am

Step-by-step explanation:

To find what time simply add all of the minutes together and subtract. All of the steps take 100 minutes to do. 11.10 am is 670 minutes. So 670 - 100 = 570 then divide by 60 to get the time ie 9:30 am

An equation for Windy Kite's total cost, y, in terms of the number of kites purchased, x, is y = 2x + 20.

An equation for Kites-R-Fun's total cost, y, in terms of the number of kites purchased, x, is y = 4x + 8.

Based on the table, if the Alaskan customer wants to buy 4 kites, Kites-R-Fun charges the least.

If the Alaskan customer wants to buy 10 kites, Windy kites charges the least.

The solution to the system of equations is (6, 32)

In order to write a linear equation to describe this situation, we would a assign variable to the number of kites purchased and the total cost respectively, and then translate the word problem into a linear equation as follows:

Since Wendy charges $2 per kite and a flat rate of $20 for shipping, a linear equation that models the total cost is given by:

y = 2x + 20

When x = 4, the total cost for Windy kites is given by:

y = 2(4) + 20

y = $28.

When x = 7, the total cost for Windy kites is given by:

y = 2(7) + 20

y = $34.

When x = 10, the total cost for Windy kites is given by:

y = 2(10) + 20

y = $40.

For Kites-R-Fun, a linear equation that models the total cost is given by:

y = 4x + 8

When x = 4, the total cost for Kites-R-Fun is given by:

y = 4(4) + 8

y = $24.

When x = 7, the total cost for Kites-R-Fun is given by:

y = 4(7) + 8

y = $36.

When x = 10, the total cost for Kites-R-Fun is given by:

y = 4(10) + 8

y = $48.

Lastly, we would use an online graphing calculator to plot the system of linear equations as shown in the graph attached below.

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Answer:

There are no solutions.

Step-by-step explanation:

im assuming that the equation is x^2+20=2x, but if not, x=10.

quadratic formula is

(-b+-√(b^2-4ac))/2a, and a=1, b=-2, and c=20. plug these values in and you will find that you are asked to square root a negative number. There are no solutions.

Answer:

4th one (One to very right)

Step-by-step explanation:

y-intercept = 2 so that means 2 must be on y axis,  you don't even need to look at anything else because there are no other 2. Also it is the prettiest line and I chose  that by default

Answer:

D

Step-by-step explanation:

log(x^4*sqrt(x^3-2)/(x+1)^5)=log(x^4)+log(sqrt(x^3-2))-log((x+1)^5)

=> 4log(x)+(1/2)*log(x^3-2)-5log(x+1)

Yes, it is possible for a plot of a partial expansion of f[x] to share ink with the plot of f[x] all the way from -[infinity] to + [infinity].

Explanation:

We can approximate f(x) as a Fourier series, as follows:

\($$f(x) = \sum_{n=0}^{\infty}a_n\cos\left(\frac{n\pi x}{L}\right)+\sum_{n=1}^{\infty}b_n\sin\left(\frac{n\pi x}{L}\right)$$\)

If f(x) is an odd function, the cosine terms are gone, and if f(x) is an even function, the sine terms are gone.

We can create an approximation for f(x) using only the first n terms of the Fourier series, as follows:

\($$f_n(x) = a_0 + \sum_{n=1}^{n}\left[a_n\cos\left(\frac{n\pi x}{L}\right)+b_n\sin\left(\frac{n\pi x}{L}\right)\right]$$\)

For any continuous function f(x), the Fourier series converges uniformly to f(x) on any finite interval, as given by the Weierstrass approximation theorem.

However, if f(x) is discontinuous, the Fourier series approximation does not converge uniformly.

Instead, it converges in the mean sense or the L2 sense. The L2 norm is defined as follows:

\($$\|f\|^2 = \int_{-L}^{L} |f(x)|^2 dx$$\)

Hence, it is possible for a plot of a partial expansion of f(x) to share ink with the plot of f(x) all the way from -[infinity] to + [infinity].

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(a) The differential equation that is satisfied by y is:

\(\frac{dy}{dt} = ky(1-y)\)

(b) To solve the differential equation, we separate the variables and integrate both sides:

\(\frac{dy}{y*(1-y)} = k*dt\)

Integrating both sides, we get:

\(\frac{lnly}{1-y} = k*t +c1\)

where C1 is an arbitrary constant of integration.

We can rewrite the equation in terms of y:

\(\frac{y}{1-y} = e^{(k*t+c1)}\)

Multiplying both sides by (1-y), we get:

\({y} = e^{(k*t+c1)} *(1-y)\)

\(y= \frac{C}{(1+(c-1)e^{-kt} }\)

where C = y(0) is the initial fraction of the population who have heard the rumor.

(c) In this case, the initial fraction of the population who have heard the rumor is y(0) = \(\frac{100}{1300}\) = 0.077. At noon, half the town has heard the rumor, so y(4) = 0.5.

Substituting these values into the equation from part (b), we get:

\(0.5= \frac{0.077}{1+(0.777-1) e^{-k4} }\)

Solving for k, we get:

\(k= ln(\frac{12.857}{4} )\)

Substituting this value of k into the equation from part (b), and setting y = 0.9 (since we want to find the time at which 90% of the population has heard the rumor), we get:

\(0.9= \frac{0.077}{1+(0.777-1) e^{-ln(12.857}*\frac{t}{4} }\))

Solving for t, we get:

t = 8.7 hours after the beginning (rounded to one decimal place)

A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).

Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.

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In geometry, the ray, line, or segment that splits a given angle into two equal pieces is known as the angle bisector. ,m∠2 = 40°.

An unending, one-dimensional figure with no breadth is a straight line. It consists of an infinite number of points connected on either side of a point. A straight line has a 180° measurement.

In geometry, the ray, line, or segment that splits a given angle into two equal pieces is known as the angle bisector. For instance, a 60-degree angle will be split into two angles of 30 degrees each by an angle bisector. Alternatively said, it divides two smaller congruent angles. Given below is an image of an angle bisector of ∠AOB.

The graphic XYQ is the straight line, m∠3 = 40°, and m∠4 = 25°. YZ is the angle bisector of ∠s.

m∠2 =  40°  the reason is YZ is the angle bisector of ∠s

∠s = m∠2  + m∠3  

m∠2  = m∠3

therefore m∠2 =  40°

m∠1  + m∠2 +  m∠3  + m∠4 = 180° the reason is XYQ is the straight line.

substitution of all values

m∠1  + 40° +  25° + 40° = 180°

m∠1  + 105° = 180°

m∠1 =  75°  (straight line, substitution of all values )

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hi <3

i'm not sure of which method you will have been taught but i'll try to explain the method i was shown.

so, you need to multiply the coefficient of x^2 by the last value

3 x -12 = -36

now, you need to find two values that multiply to make -36 but add to make 5.

9 and 4 would work. it would have to be positive 9 and negative 4, as these would subtract to give the 5 that you need

now we have:

(x - 4)(x + 9)

however, we need to achieve the 3 from somewhere so it needs to be divided somewhere

9 is divisible by 3 so you can divide it there. as 4 cannot divide by 3, you would move the 3 up to be the coefficient.

thus, your final answer would be:

(3x - 4)(x + 3)

hope this helps :)

Answer:

it's gonna be 3(X*2 + 4X - 4)

Step-by-step explanation:

Just factor out 3 from the expression

Answer:

answer is 0

..................3rd option

Answer:

x=1,y=-1

x3+y3=(1)3+(-1)3=1-1=0

so, answer is (c) 0

Answer:

182i2j3jdii32i3i38839393838383383 yan yung sagot pasalamat ka nalang mamaya

Step-by-step explanation:

hakdog ses dog

Answer:

72 members of the class voted

Step-by-step explanation:

0.60*120=72

just turn the percent into a decimal and multiply it by the other value.

hope this helps <3

Answer:

72

Step-by-step explanation:

60/100 = 0.6

0.6 x 120 = 72

P(7) is 1/3

The 5, 7, and 6 are the numbers on the spinner. If so there is 1 (one) even option out of 3. We are assuming the spinner isn't rigged, so the chance that it will land on an even number is 1/3.

Hence P(7) is 1/3.

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Answer:

G

Step-by-step explanation: The dice will always land on a number between 1 and 6 because as long as it lands on a number this will come true so there is a 100% chance that a number is landed on.  G

The confidence interval for the population mean difference is between -33.2 and + 33.2

You have a 5% probability of being incorrect with such a 95% confidence interval. You have such a 10% probability of becoming incorrect with a 90% confidence interval. In contrast to a 95 % confidence interval, a 99 per cent confidence interval would be larger (plus or minus 4.5 per cent as opposed to 3 per cent, for example).

The answer in this situation would be +/-(2 * 16.6) from the mean, or -33.2 and +33.2 points from the sample mean because the 95% confidence interval is equal to two standard deviations on either side of the mean. This would result in an answer of A.

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Your question is incomplete, but probably the full question was:

A teacher wants to compare the mean geology scores of two different classes. She is testing the null hypothesis that there is no difference in the population mean scores of the two classes. The difference of the sample means is 51.4. If the standard deviation of the distribution of the difference of sample means is 16.66, what is the 95% confidence interval for the population mean difference?

A)between -33.2 and + 33.2

B)between -49.9 and +49.9

C)between -102.8 and +102.8

D)between -154.2 and +154.2

Answer:

63/5

Step-by-step explanation:

I have no explanation

Answer:

A

Step-by-step explanation:

Answer:

\((9y^2-4x)\,(9y^2+4x)=81y^4-16x^2\)

and it is the special factor product that leads to a difference of squares

Step-by-step explanation:

The product: \((9y^2-4x)\,(9y^2+4x)\)

is a product of the form:

\((a-b)\,(a+b) = a^2-b^2\)

which leads as shown to a difference of squares. So they binomials \((a-b)\) and \((a+b)\)  are the factors of the difference of squares \(a^2-b^2\).

In our case, the product:

\((9y^2-4x)\,(9y^2+4x)= (9y^2)^2-(4x)^2=81y^4-16x^2\)

Answer:

B

Step-by-step explanation:

To estimate the cost of a new 3000-ft² heat exchange system for a plant retrofit, we can use the price index and the information about the cost of a previous heat exchanger. Given that the price index 7 years ago was 1360 and is now 1478, and assuming a power-sizing exponent of 0.55, rough estimate for the cost of the new heat exchanger system is $77,700.

To estimate the cost, we need to account for the change in the price index over the years. The price index ratio is calculated as (new price index)/(old price index), which in this case is 1478/1360 = 1.085. Since the power-sizing exponent is 0.55, we raise the price index ratio to the power of 0.55, resulting in \(1.085^{0.55 {\)≈ 1.036.

Next, we multiply the cost of the previous heat exchanger by this factor to estimate the cost of the new system. The cost of the previous heat exchanger was $75,000, so the rough estimate for the cost of the new heat exchanger system is approximately $75,000 × 1.036 ≈ $77,700.

It's important to note that this estimate is a rough approximation and does not account for other factors such as inflation or changes in technology. It serves as a starting point for estimating the cost of the new heat exchanger system based on the given information and assumptions.

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Answer:

If AR = 26, find AD = 13

If BD = 9, find BQ = 18

If MQ = 35, find LQ = 17.5

If LP = 13.25, find NP = 26.50

Step-by-step explanation:

For the first question which is finding AD, is basically half the line of AR. So it's half of AR.

26 ÷ 2 = 13

For the second question which is finding BQ, the line is just 2x the line of BD. So it's 2 times of BD.

9 x 2 = 18

For the third question which is finding LQ, it's half the line of MQ. So it's half of MQ.

35 ÷ 2 = 17.5

For the fourth question which is finding NP, it's 2 times of LP. So it's 2 times of LP.

13.25 x 2 = 26.50

The total number of games the team played last year was 80 (option C). In the first half of the year, the team won 60 percent of their games, indicating that they won 6 out of every 10 games played.

In the second half of the year, the team played 20 games and won 3 of them. This means that in the second half, they won only 3 out of 20 games, which is equivalent to winning 15 percent of their games.

To find the overall percentage of games won, we can calculate the weighted average of the two percentages. Since the team won 50 percent of their games overall, we can assign equal weights to the first and second halves of the year. Therefore, the average winning percentage for the team would be the midpoint between 60 percent and 15 percent, which is (60% + 15%) / 2 = 37.5%.

Let's assume the total number of games played last year was x. Since the team won 37.5% of the games, they won 0.375x games. We can set up an equation based on the information given:

0.375x = 50% of x

0.375x = 0.5x

0.5x - 0.375x = 0

0.125x = 0

x = 0 / 0.125

x = 0

However, we have arrived at an invalid result. It seems there is an error in the information provided or the calculations made.

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Answer:

c=2

Step-by-step explanation:

To make it a little simpler, use the distributive proptery on both sides of the equations first.

For the left side, it's asking 24 -(3c+4). We can multiply the (-) sign by (3c+4).

This leaves us with 24-3c-4. Combine Like Terms: 20-3c.

For the right side of the equation its asking 2(c+4) +c. First, distribute 2 to c+4. This leaves you with 2c+8+c (because 2 times c=2c and 2 times 4= 8). Combine Like Terms: 3c+8.

The final equation is 20-3c=3c+8. Solve from there.

20-3c+3c=3c+3c+8     Add 3c to both sides

20=6c+8                

20-8=6c-8                 Subtract 8 from both sides.

12=6c                              Divide by 2

2=c

Please correct me if I'm wrong:)

A. The result of the iterated integral by converting to polar coordinates is 0.

To evaluate this iterated integral, we will convert it to polar coordinates. First, we need to make the substitution x = rcos(θ) and y = rsin(θ). Then, we will need to find the limits of integration for r and θ. The region of integration is the area between the circles with radii a and 2 and between the x-axis and y-axis.

In polar coordinates, the integral becomes ∫∫r dr dθ from r = a to r = 2, and θ = 0 to θ = π/2.

We can now solve the integral by multiplying the integral of r by the integral of θ.

∫2^2 r dr dθ = ∫π/2^0 (-1/2)r^3 dθ = -1/2 * [(r^2)/2] from r = 2 to r = a = -1/2*(2^2 - a^2) = -1/2*(4-a^2) = -2+a^2/2

So the result of the integral is -2+a^2/2 = -2+4/2 = -2+2 = 0

Note that this is not a common way to solve iterated integrals, but rather a way to check the correctness of the solution. The common way is to find the limits of integration by solving the inequality and graphing the area of integration.

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The parcel occupies the area of 3/32 of a section, which is equal to 60 acres. The parcel is located in the NW 1/4 of the SE 1/4 and the S 1/2 of the SW 1/4 of the NE 1/4.

To solve this problem, we need identify the location of the parcel. The section is a square, divided into four quarters (NE, NW, SE, SW), each of which is further divided into four quarters.

The parcel occupies, the NW 1/4 of the SE 1/4, which is 1/16 of the section, and the S 1/2 of the SW 1/4 of the NE 1/4, which is 1/2 * 1/4 * 1/4 = 1/32 of the section.

Adding these fractions together, we get:

1/16 + 1/32 = 3/32

Therefore, the parcel occupies 3/32 of the section.

To find the area of the parcel in acres, we need to know the total area of the section. A section contains 640 acres.

So, the area of the parcel is:

3/32 * 640 = 60 acres

Therefore, the parcel is 60 acres in size.

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The area of the given rectangle with a height of \(4x^4\)and a width of \(3x^13 + x + 1\)can be expressed as the product of the height and width. To calculate the area, we multiply the height by the width:

To find the area of a rectangle, we multiply its length by its width. In this case, the height is given as \(4x^4\) and the width is \(3x^13 + x + 1.\)

Area = Height * Width

\(= (4x^4) * (3x^13 + x + 1)\)

Using the distributive property, we can expand the expression:

\(= 12x^4 * x^13 + 4x^4 * x + 4x^4\)

Simplifying further, we add the exponents when multiplying like terms:

\(= 12x^(4+13) + 4x^(4+1) + 4x^4= 12x^17 + 4x^5 + 4x^4\)

Therefore, the area of the given rectangle is expressed as\(12x^17 + 4x^5 + 4x^4.\)

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