(02.07A HC)


Part A: The Sun produces 3.9 ⋅ 1033 ergs of radiant energy per second. How many ergs of radiant energy does the Sun produce in 2.45 ⋅ 105 seconds? Express your answer in scientific notation and show your work. (5 points)


Part B: Which is the more reasonable measurement of the distance between the tracks on a DVD:

7.4 ⋅ 10−4 mm or 7.4 ⋅ 104 mm? Justify your answer. (5 points)

The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



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Answer:Can you explain this better

Step-by-step explanation:

Answer:

A sample of 675 office workers would be needed to estimate the proportion of workers who respond to emails within 0.05 hours with 90% confidence.

Step-by-step explanation:

To determine the sample size needed, we need to use the following formula:

n = (Z^2 * p * q) / E^2

Where:

n is the sample size needed

Z is the Z-score corresponding to the desired level of confidence (in this case, 90% confidence corresponds to a Z-score of 1.645)

p is the estimated proportion of office workers who respond to e-mail within the desired time frame (we don't have an estimate, so we will assume a conservative estimate of 0.5)

q is the complement of p (q = 1 - p)

E is the margin of error we want to achieve (in this case, 0.05)

Plugging in the values, we get:

n = (1.645^2 * 0.5 * 0.5) / 0.05^2

n = 674.52

Rounding up to the nearest whole number, we get a sample size of 675. Therefore, we would need to sample 675 office workers in order to estimate the proportion of workers who respond to e-mails within 0.05 hours with 90% confidence.

The linear equation of line is d = 115t , where d is the distance in feet and t is the time in seconds

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the distance traveled by the car be represented as d = 920 feet

Let the time taken by the car be represented as t

Now , the speed of the car will be the slope of the line

Now , when t = 0 , the value of d = 0

So , the first point is P ( 0 , 0 )

Let the second point be at t = 8 , Q ( 8 , 920 )

So , the slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 920 - 0 ) / ( 8 - 0 )

Slope m = 115

And , the equation of line is y - y₁ = m ( x - x₁ )

y = 115x

On simplifying the equation , we get

d = 115t   be equation (1)

Hence , the equation is d = 115t

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Sarah found three shark teeth and decided to share the opportunity with her friend John. She can find shark teeth twice as fast as John and can earn even more money with his help.

Sarah can earn $5 for every shark tooth she finds on the beach. She can use the expression 5(2j + 3 + j) to represent the amount of money she can earn.
Part 1:
Sarah's expression is 5(2j + 3 + j). If we replace the coefficients with 4, the expression becomes 4(2j + 3 + j), which is not equivalent to Sarah's expression.
The algebraic expression we created is 4(2j + 3 + j), which translates to "Sarah can earn $4 for every shark tooth she finds on the beach, and she can find shark teeth twice as fast as John."
Part 2:
We can use the distributive property to create an equivalent algebraic expression for the expression our partner sent us. Let's assume our partner sent us the expression 3(4j + 2 + 2j).
Step 1: Distribute the coefficient 3 to the terms inside the parentheses.
3(4j) + 3(2) + 3(2j)
Step 2: Combine like terms.
12j + 6 + 6j
Step 3: Rearrange the terms.
18j + 6
The equivalent algebraic expression is 18j + 6, and we used the distributive property to arrive at this expression.
Part 3:
Sarah found three shark teeth, and John found 1.5 shark teeth. Since Sarah can find shark teeth twice as fast as John, she earned $45 (9 shark teeth x $5 per shark tooth), and John earned $22.50 (4.5 shark teeth x $5 per shark tooth). In total, Sarah earned $67.50.

Thus, Sarah found three shark teeth and decided to share the opportunity with her friend John. She can find shark teeth twice as fast as John and can earn even more money with his help.

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The predicted value of y is 436.6 when x1 equals 15 and x2 equals 33 in this multiple regression model.

To predict y using the given sample regression equation, you need to plug in the given values of x1 and x2 into the equation and then solve for y.

1. Write down the sample regression equation: yˆ = 157 + 12.7x1 - 2.7x2
To predict y when x1 equals 15 and x2 equals 33, we plug those values into the sample regression equation:
yˆ = 157 + 12.7(15) + 2.7(33)
yˆ = 157 + 190.5 + 89.1
yˆ = 436.6
2. Substitute the given values of x1 (15) and x2 (33) into the equation:

yˆ = 157 + 12.7(15) - 2.7(33)

3. Calculate the values within the parentheses:

yˆ = 157 + 190.5 - 89.1

4. Perform the addition and subtraction:

yˆ = 436.6

So, when x1 equals 15 and x2 equals 33, the predicted value of y (rounded to one decimal place) is 258.4.

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Answer: yes I will help you the answer is 10

Step-by-step explanation:

you do 9 times X = 9x then do 9 x -8 = -72 then do 18 + 72 = 90 then do 9x/9 = 90/9 then 90/9 = 10 so then 10 is your answer

As shown in the graph above, the point G is in the interior of the right angled triangle. Angle ABG measures (x^2 + 3x) while angle CBG measures 40x.

Angles ABG and CBG add up to 90 and that gives you;

Knowing that we are dealing with a positive angle measure, we shall take x = 2 (and not x = -45)

Therefore, x = 2, and angle ABG measures

Also angle CBG measures;

Answer:

It looks like you are trying to find the retail price for a given quantity of pairs. To write an equation that could be used to find the retail price for each range of quantities, you will need to know the following information:

The retail price for the first range (0-20 pairs)

The retail price for the second range (21-40 pairs)

The retail price for the third range (41-60 pairs)

The retail price for the fourth range (61-80 pairs)

The retail price for the fifth range (81 or more pairs)

Once you have this information, you can use an if-then statement to create an equation that will work consistently for each range. The equation might look something like this:

if (quantity >= 0 and quantity <= 20):

retail_price = price for 0-20 pairs

elif (quantity >= 21 and quantity <= 40):

retail_price = price for 21-40 pairs

elif (quantity >= 41 and quantity <= 60):

retail_price = price for 41-60 pairs

elif (quantity >= 61 and quantity <= 80):

retail_price = price for 61-80 pairs

else:

retail_price = price for 81 or more pairs

This equation will work consistently for each range because it uses a series of conditions to determine which retail price to use based on the quantity of pairs.

EDIT:

To find the retail price for a given quantity of pairs based on the wholesale prices you provided, you can use the following equation:

if (quantity >= 0 and quantity <= 20):

retail_price = 25.00

elif (quantity >= 21 and quantity <= 40):

retail_price = 23.00

elif (quantity >= 41 and quantity <= 60):

retail_price = 21.00

elif (quantity >= 61 and quantity <= 80):

retail_price = 19.00

else:

retail_price = 17.00

This equation will work consistently for each range because it uses a series of conditions to determine the retail price based on the quantity of pairs. The retail price will be 25.00 for quantities in the first range (0-20 pairs), 23.00 for quantities in the second range (21-40 pairs), 21.00 for quantities in the third range (41-60 pairs), 19.00 for quantities in the fourth range (61-80 pairs), and 17.00 for quantities in the fifth range (81 or more pairs).

Step-by-step explanation:

The 99% confidence interval estimating the proportion of all Ford Fusion drivers who are women is (0.40685, 0.67007). The closest option to this interval is option 2) (0.40385, 0.67307).

The answer is option 1) (0.41689, 0.66003). To design a new advertising campaign, Ford Motor Company conducted a sample survey of 91 Fusion owners and found that 49 of them were women. To estimate the proportion of all drivers who are women, a confidence interval is calculated. The formula for calculating the confidence interval is:

sample proportion ± z*(standard error)

where z is the critical value for the desired confidence level and the standard error is calculated as:

sqrt((sample proportion*(1 - sample proportion))/sample size)

For a 99% confidence interval, the critical value is 2.576. Plugging in the values from the sample, we get:

sample proportion = 49/91 = 0.5385
sample size = 91

Using the formula above, we can calculate the standard error as:

sqrt((0.5385*(1 - 0.5385))/91) = 0.0625

Finally, we can plug in the values into the confidence interval formula:

0.5385 ± 2.576*0.0625

which gives us the interval (0.41689, 0.66003). Therefore, option 1) is the correct answer.

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Answer:

y=x-2

Step-by-step explanation:

Answer:

y=x-2

Step-by-step explanation:

The answer is the first one since y is -2

Answer:

A) Complementary, is your answer.

The amount of money paid for the rope in dollars per inch is 0.025 $/in.

Based on the information provided above, we can logically deduce that the store bought 300 feet of nylon rope.

Conversion:

1 feet = 12 inches.

300 feet × 12 inches/feet = 3600 inches.

Therefore, we now know that this store bought 3600 inches of nylon rope.

Furthermore, this store sold 40 inches of nylon rope for $1.60. Thus, we can calculate the selling unit price of nylon rope in dollars per inch as follows;

Selling unit price = $1.60/(40 in.)

Selling unit price = $0.04/in.

At a price of $0.04 per inch, we have:

Selling Price =3600 inches × $0.04/in.

Selling Price = $144

Therefore, since the profit was $54 for selling all of the nylon rope;

Cost price = Selling price - profit

Cost price = $144 - $54

Cost price = $90

The cost in dollars per inch is given by;

Cost in dollars per inch = ($90)/(3600 in.)

Cost in dollars per inch = 0.025 $/in.

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Answer:

Step-by-step explanation:

0.0154, I think, I apologize if this is wrong.

Step-by-step explanation:

let's call the top of the pole T, and the ground point of the pole G.

so, the situation gives us 2 right-angled triangles:

PTG and QTB.

from both triangles we know one leg (TG, the pole = 9 m), the inner angles at G (90° in both cases), and actually the inner angles at T, because we know the angles of depression there.

the inner triangle angles at T are just the complementary angles of the angles of depression (that means they add up together to 90°).

the inner angle at PTG = 90 - 4 = 86°

the inner angle at QTG = 90 - 7 = 83°

and because the sum of all angles in a triangle is always 180°, we even know the third angles at P and Q :

angle P = 180 - 90 - 86 = 4°

angle Q = 180 - 90 - 83 = 7°

yes, they are the same as the angles of depression (must be the same).

so, we know from both triangles 1 side and all 3 angles.

with the law of sine we can get every missing side.

particularly we need the second legs (sides in the ground) to get the distance between both points.

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c being the sides always opposite of their related angles.

TG/sin(4) = PG/sin(86)

PG = 9×sin(86)/sin(4) = 128.7059963... m

TG/sin(7) = QG/sin(83)

QG = 9×sin(83)/sin(7) = 73.29911785... m

the distance between P and Q can have now 2 solutions :

if P and Q are on different sides of the pole, then

PQ = 128.7059963... + 73.29911785... = 202.0051142... m

but if they are on the same side of the pole, then their distance is

PQ = 128.7059963... - 73.29911785... = 55.40687846... m

due to the phrasing of the first sentence I suspect the first solution to be right.

but just in case, I gave you also the second possible solution.

We know that the cyclicity power (a^n) of 17 is 4.

\(\sf \longmapsto\bigg( \dfrac{17}{4}\bigg) = 1\)

\(\sf \longmapsto17^{(17/4)}\)

\(\sf \longmapsto17 {}^{} \)

\(\sf \longmapsto7(last \: digit )\)

Rewriting the ratio as an equivalent ratio of 1 : m ; n is 1 : 12/7 : 17/7

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

The height of three Russian dolls are in the ratio 7:12:17.

So, we have

Ratio = 7:12:17

The form is given as 1:m:n.

So, we divide through the ratio by 7

So, we have

Ratio = 1 : 12/7 : 17/7

Hence, the equivalent form is 1 : 12/7 : 17/7

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Answer:

2

Step-by-step explanation:

range is your y value and you don't keep typing the same number when u are looking for your domain and range

The metric system of measurement is based on the number 10.

This system is also known as the International System of Units (SI) and is used in most countries around the world. In the metric system, various units of measurement are defined as multiples or fractions of a base unit, which is defined for each quantity being measured. For example, the base unit for length is the meter, and the base unit for mass is the kilogram. Prefixes such as kilo-, centi-, and milli- are used to indicate multiples or fractions of the base unit, based on factors of 10. For example, a kilometer is 1000 meters, a centimeter is 1/100 of a meter, and a milligram is 1/1000 of a gram. This makes the metric system easy to use and convert between units, as well as consistent and universally recognized.

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Answer:

587877.5383m^2

Step-by-step explanation:

First off, we need to find the 3 sides of the triangle. To do this, we need to know that all the sides add up to 3600m. So 5 + 6 + 7 = 3600m. Since we don't know what 5, 6 and 7 are, we have to find out what is 1 worth. So adding them all up equals to 18, so 18 = 3600m. To find 1, simply divide 3600m by 18 which = 200m. Now to find all the sides, multiply each side by 200.

5*200 = 1000m

6*200 = 1200m

7*200 = 1400m

Then to find the area, we will need to use the formula 1/2abSinC.

However to do this, we need an angle. So to find that angle we will use the cosine rule A = cos-1(b^2 + c^2 -a^2/2bc). This will lead to A = 44.4153086º.

Then we can use the area formula to find the area of the land. This will give an area of 587877.5383m which you can round up to whichever extent you want. I have attached a photo with the working out for everything.

The projective geometry in Z3 is a mathematical concept that involves extending the Euclidean geometry over a finite field with three elements, denoted as Z3. In projective geometry, parallel lines intersect at a point at infinity, which allows for a more complete and consistent geometric system than Euclidean geometry.

In Z3, there are three points and three lines passing through each pair of distinct points. Therefore, the total number of lines in the projective geometry in Z3 is nine. These nine lines are:

Each of these nine lines is unique and distinct in the projective geometry in Z3.

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Stephen makes the mistake in the expression as he uses the 4 in the root and the 3 in the power and the expression actually is: ∛(16)/e

We start with the expression:

exp( (4/3)*ln(2) - 1)

Here we can use that:

exp(ln(x)) = x.

and e^(a + b) = e^a*e^b.

the first step here is:

e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)

So the first step of Stephen is correct, but the first step of Helen is not, you can not simplify the expression in that way.

now, we have that:

a*ln(x) = ln(x^a)

then we can write:

(4/3)*ln(2) = ln(2^(4/3))

and e^(ln(2^(4/3)) = 2^(4/3)

then we have:

e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e

now we can write this as:

∛(2^4)/e

Here is where Stephen makes the mistake, he uses the 4 in the root and the 3 in the power.

The expression actually is: ∛(16)/e

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Domain are the x values where the line starts and stops.

A bracket is used for a solid circle and a parentheses is used for open circles

The answer would be the second choice: (1,2)

Rounding to the nearest tenth, the largest possible area of the garden is 625 square feet.

What is area of rectangle?

The area of a rectangle is a measure of the region enclosed by its four sides. It represents the amount of space or surface covered by the rectangle. The formula to calculate the area of a rectangle is:

Area = Length × Width

To find the largest possible area of the garden given a limited amount of chicken wire fence, we need to determine the dimensions of the rectangular garden that would maximize its area.

Let's assume the length of the rectangular garden is L and the width is W. The perimeter of the garden, which is the length of the chicken wire fence required, can be expressed as:

Perimeter = 2L + 2W

Given that the perimeter is 100 running feet, we have:

2L + 2W = 100

Simplifying the equation, we get:

L + W = 50

To maximize the area, we need to maximize the product of the length and width, which represents the area of the garden:

Area = L * W

We can rewrite the equation for the area in terms of one variable using the constraint L + W = 50:

Area = (50 - W) * W

To find the maximum area, we can take the derivative of the area equation with respect to W, set it equal to zero, and solve for W:

d(Area)/dW = 50 - 2W = 0

2W = 50

W = 25

Substituting the value of W back into the equation L + W = 50:

L + 25 = 50

L = 25

Therefore, the largest possible area of the garden is obtained when the length and width are both 25 feet. The maximum area is:

Area = L * W = 25 * 25 = 625 square feet.

Rounding to the nearest tenth, the largest possible area of the garden is 625 square feet.

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Answer:

C. 114

Step-by-step explanation:

bikes have 2 wheels

skateboards have 4 wheels

incline skates have 8 wheels in total

7*2 = 14

9*4 = 36

8*8 = 64

if you add all of these up you get 114 wheels in total. 8*8 was from 24-7-9 = 8

Answer:

58.25n+30p-2

Step-by-step explanation:

Given the expression as;

1 + 4.25n + 32p – 3 + (–2p) + 54n

collect like terms

1-3+4.25n+54n+32p-2p

-2+58.25n+30p

58.25n+30p-2

I have copied one brainly user's answer, sorry for that...

However, hope it helps you!!!

Answer:

20

Step-by-step explanation:

\(20^{2} = 400\)

\(\sqrt{400} = 20\)

Answer: The square root of 400 is 20.

Step-by-step explanation:

The square root of a number is the value that, when multiplied by itself, gives the original number. To find the square root of 400, you can use the long division method or an electronic calculator.

Alternatively, you can approximate the square root of 400 by finding the nearest perfect square (a number whose square root is a whole number). In this case, the perfect squares closest to 400 are 361 and 441. Since the square root of 361 is 19 and the square root of 441 is 21, you can estimate that the square root of 400 is between 19 and 21. Since 20 is halfway between 19 and 21, you can approximate the square root of 400 to be 20.

Hey there! I'm happy to help!

We see that the ladder reaches a height of 6m from the ground while being 2.4 m from the wall. The ratio of the height to the length from the wall is 6:2.4 which can actually just simplify to 2.5 because 6m to is 2.4*2.5.

This person is 80 cm from the ladder's base. We just saw that you can take the distance from the wall (in this case, our wall is the human as the human is touching the height) and multiply it by 2.5 to find the height of the ladder at that specific point. So let's do that.

80*2.5= 200

We are looking for meters though. Since there are 100 centimeters in a meter, this is just going to be 2 meters.

Have a wonderful day! :D