Answer: The square of the orbital period, T, of a planet is equal to the cube of the average distance, A, of the planet from the Sun.
Step-by-step explanation:
In mathematics, A number or variable 'a' to its second power is said to be square of 'a' i.e. [tex]\ a^2[/tex] is the square of a.
A number or variable 'b' to its third power is said to be cube of 'b' i.e. [tex]\ b^3[/tex] is the cube of b.
In the given equation: [tex]T^2 = A^3[/tex]
Here, [tex]T^2 [/tex] is square of T.
And [tex]A^3[/tex] is cube of A.
Therefore, The square of the orbital period, T, of a planet is equal to the cube of the average distance, A, of the planet from the Sun.
The area of a circle is 225 pie square inches. Find the area of the sector whose central angle is 45°.
The area of the sector of the circle is 28.125π inches²
What is a Circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the centre for every angle
The total internal angle is 360° about the centre
The area of the sector of the circle = ( θ / 360° )πr²
The perimeter of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
Given data ,
Let the area of the circle be = A
The value of A = 225 inches²
Now , the area of the sector whose central angle is 45° is calculated by
The area of the sector of the circle = ( θ / 360° )πr²
Substituting the value for θ = 45° , we get
Area of the sector of the circle = ( 45/360 ) x 225
= ( 1/8 ) x 225
= 28.125 inches²
Therefore , the area of the sector is 28.125 inches²
Hence , The area of the sector of the circle is 28.125π inches²
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Please help me with question 26
The length of time that an auditor spends reviewing an invoice is approximately normally distributed with a mean of 600 seconds and a standard deviation of 100 seconds. what is the probability that an auditor will spend more than 12 minutes on an invoice?
The probability that an auditor will spend more than 12 minutes on an invoice is approximately 88.49%.
Calculate the probability an auditor will spend more than 12 minutes on an invoice using the Z-score formula for a normal distribution.
The probability that an auditor will spend more than 12 minutes on an invoice can be calculated using the Z-score formula for a normal distribution.
Calculate the Z-score: Z = (12*60 - 600) / 100 = -1.2.Find the probability corresponding to this Z-score using a standard normal distribution table. P(Z > -1.2) = 0.8849.Therefore, the probability that an auditor will spend more than 12 minutes on an invoice is approximately 88.49%.how to discriminant of each quadratic equation then state the number and type of solutions. yall fr help me
Final answer:
The discriminant of a quadratic equation determines the number and type of solutions.
Explanation:
The discriminant of a quadratic equation can help determine the number and type of solutions.
If the discriminant is greater than zero, there are two real solutions.
If the discriminant is zero, there is one real solution.
If the discriminant is negative, there are no real solutions.
Which type of deposit is paid in advance to protect landlords against nonpayment?
a.security deposit
b.special deposit
c.surity deposit
20 POINTS!! pleasee help!
Katherine practices skiing for 1 1/2 hours every day except Saturday and Sunday. She practices for four hours on Saturday and three hours on Sunday. How many hours does she practice in a week?
1 1/2 hours x 5 days = 7 1/2 hours
4+3 +7 1/2 = 14 1/2 hours per week
A student is raising money for a homeless shelter. A local business agrees to donate an additional 20% of what the student raises, while a local politician also agrees to donate an additional 10% of what the student raises. If the student raises $600.00, how much will be donated?
Answer: the answer is $780.00
Step-by-step explanation:
$600.00 x .20 = $120.00
$600.00 x .10 = $60.00
Total:
$600.00 + $120.00 + $60.00 = $780.00
Answer:
780
Step-by-step explanation:
Factor each expression: 5a-25
Efetue as divisões X ao cubo+10x+29x+20:x ao quadrado+5x+4
Rhoads earned $324.65 delivering newspapers. She promised her sister 0.2 of her earnings for helping her.How much does Rhoads owe her sister?
Do I have to subtract?? if not help me solve plz
a total of 324 tickets were sold for the school play they were either adult tickets or student tickets the number of student tickets sold was three times the number of adults tickets sold how many adult tickets were sold?
The correct answer is 81
Final answer:
To find the number of adult tickets sold when a total of 324 tickets were sold for a school play and student tickets were three times the number of adult tickets, we set up the equation x + 3x = 324, solved for x, and found out that 81 adult tickets were sold.
Explanation:
The question is asking us to find out how many adult tickets were sold when a total of 324 tickets were sold for a school play, with the number of student tickets being three times the number of adult tickets sold. To solve this, we let x represent the number of adult tickets. Therefore, 3x will represent the number of student tickets since there are three times as many student tickets as adult tickets.
The equation representing the total number of tickets sold would be: x (adult tickets) + 3x (student tickets) = 324. Simplifying, we have 4x = 324. Dividing both sides by 4 gives us x = 81.
Therefore, the number of adult tickets sold is 81.
Jennifer made 5 liters of punch for her party. Her brother made another 750 mL. If they combine the two batches, how many 180mL servings would they have? Would there be any punch left over? If so how much? Please respond with the answer of how much of the two batches combined and how many 180mL there are
On the surface of the moon, the value of g is 1.67 m/s2. What is the horizontal distance traveled during a 2.00-meter high jump if the jumper runs as at 20 miles per hour?
the value of the building owned by two veterinarians went from 125000 to 117500. What is the percent decrease
A grandmother deposited $4,000 in an account that pays 5% per year compounded annually when her granddaughter was born. What will the value of the account be when the granddaughter reaches her 13th birthday?
The value of the account is $7542.59.
What is interest?It is computed by adding the annual interest rate raised to the number of compound periods and subtracting one after multiplying the initial principal amount by one. The resulting value is subsequently deducted from the loan's entire original amount.
Given:
P=4000
r = 5%
t = 13 years
Now, using the formula
[tex]A = P( 1 + r/n)^{nt}[/tex]
A = 4000[tex](1 + 0.05/1)^{(13)(1)[/tex]
A= 4000[tex](1.05)^{13[/tex]
A = 4000 x 1.8856
A = $7542.59
Hence, The value of the account is $7542.59.
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Ms Cohen gave a riddle: A string is 2 meters longer than a rod. Half of the rod is 1 meter shorter than half of the string. Is this true or false?
the price of a tablet was reduced from $250 to $200. By what percentage was the price of the tablet reduced? Please help me solve this.
identify the roots of -3x^3-21x^2+72x+540=0. State the multiplicity of each root.
Could someone help me with this?
(Multiple Choice Worth 4 points) (05.01)A flower bed is in the shape of a triangle, with a base of 13 feet and a height of 5 feet. What is the area of the flower bed?
A 18 square feet
B 32.5 square feet
C 65 square feet
D 130.5 square feet
Answer:
b
Step-by-step explanation:
what is the slope of the line represented by the equation below? y=-2/3x+3
Answer:
-2/3
Step-by-step explanation:
The slope is the coefficient of x: -2/3.
___
This tells you how much y changes when x changes by 1 unit. The slope is the change in y divided by the change in x.
A population of 1200 leopards decreases by 12% per year. How many leopards will there be in the population after 6 years? Round your answer to the nearest whole number
Where a is determined by the conditions x2 + y2 ≤ 1 and x + y ≥ 1?
Mr. jones has two children. the older child is a girl. what is the probability that both children are girls?
Final answer:
Given that the older child is already a girl, the probability that both children of Mr. Jones are girls is 50%, assuming an equal chance of having a boy or a girl.
Explanation:
The question is asking about the probability that both children of Mr. Jones are girls, knowing that the older child is already a girl. Since the older child is a girl, we only need to consider the probability that the second child is a girl. In a typical scenario where the probability of having a boy or a girl is equal (assuming a 50% chance for each), the probability that the second child is a girl, given that the family already has one girl, is simply 0.5 or 50%. Therefore, in this case, the probability that both children are girls is 50%.
The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the cone to the volume of the prism?
Answer:
B. 1/3
I had this question on Plato this is the answer.
Last year, 120 new houses were built in a neighborhood. So far this year, 56 of them have been sold. How many new houses have been sold this year?
Finally, 43 is 5% of what number?
Use the simplified ratio to find the equivalent ratio with a numerator of 43.
Enter your answer in the box.
43 is 5% of __?
Final answer:
43 is 5% of 860.
Explanation:
To find out what number 43 is 5% of, we can set up a proportion where 5% (or 0.05 when written as a decimal) is equal to 43 over an unknown total number X.
The formula to calculate this is part = percentage imes total, which in this case turns into 43 = 0.05 * X.
To solve for X, divide 43 by 0.05, giving us X = 43 / 0.05 which equals 860.
Therefore, 43 is 5% of 860.
What has an infinite number of points extending in opposite directions that has only one dimension
Describe how to solve problems for the area of a reduced or enlarged figure when the scale factor and dimensions of the original figure are given.
To solve problems for the area of a reduced or enlarged figure, determine the scale factor, find the corresponding dimensions, and calculate the area using the appropriate formula.
Explanation:To solve problems for the area of a reduced or enlarged figure when the scale factor and dimensions of the original figure are given, follow these steps:
1. Determine the scale factor by comparing the dimensions of the original figure to the dimensions of the reduced or enlarged figure.
2. Use the scale factor to find the corresponding dimensions of the reduced or enlarged figure.
3. Calculate the area of the reduced or enlarged figure using the appropriate formula for the shape (e.g., length * width for a rectangle).
For example, if the original figure is a rectangle with dimensions of 4 inches by 6 inches, and the scale factor is 2, the corresponding dimensions of the reduced or enlarged figure would be 8 inches by 12 inches. The area of the reduced or enlarged figure would then be calculated as 8 inches * 12 inches = 96 square inches.
Sample Response: To solve problems for the area of a reduced or enlarged figure, first square the scale factor. Then use the given dimensions to find the area of the original figure. Multiply the square of the scale factor by the area of the original to get the reduced or enlarged figure.
Henry sells rings for $8 each. His expenses are $1.50 per ring, plus $91 for supplies. How many rings does he need to sell for his revenue to equal his expenses?
Answer:
14 rings.
Step-by-step explanation:
in order to calculate how many rings does he have to sell to break even we first have to calculate the profit that he has on the sell of every ring from which he can take money to pay per supplies, so that would be the selling price minues expenses:
8-1.5=6.5
Now we have to divide the 91 in supplies by the profit:
91/6.5=14
So he has to sell 14 rings in order to break even between expenses and supplies.
Henry needs to sell approximately 14 rings to cover his expenses, which include $1.50 per ring and $91 for supplies, with each ring priced at $8.
To find out how many rings Henry needs to sell for his revenue to equal his expenses, you can set up an equation.
Let's denote the number of rings he needs to sell as "x."
Revenue from selling x rings = Expenses
Revenue is calculated as the price per ring multiplied by the number of rings sold, which is $8x.
Expenses consist of the cost per ring and the supplies cost, which is $1.50x + $91.
So, the equation becomes:
$8x = $1.50x + $91
Now, let's solve for x:
Subtract $1.50x from both sides of the equation:
$8x - $1.50x = $1.50x + $91 - $1.50x
$6.50x = $91
Now, divide both sides by $6.50 to find the value of x:
x = $91 / $6.50
≈ 14
Therefore, Henry needs to sell approximately 14 rings for his revenue to equal his expenses.
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