The radius of this exoplanet's orbit is equal to 4.71 × 10¹¹ meters.
How to calculate the radius of the exoplanet's orbit?In order to calculate the radius of the exoplanet's orbit, we would apply Kepler's Third Law of planetary motion.
Mathematically, Kepler's third law of planetary motion can be calculated by using this formula:
T² = 2π√(r³/GM)
Where:
T represents the orbital period.M represents the mass.G represents the universal gravitational constant.r represents the radius.Making radius (r) the subject of formula, we have:
Radius, r = ∛(GMT²/2π)
Note: Universal gravitational constant is equal to 6.67 × 10⁻¹¹ m³kg⁻¹s⁻².
Orbital period, T = 3.95 × 365 × 24 × 60 × 60 = 341,280 seconds
Substituting the given parameters into the formula, we have;
Radius, r = ∛(6.67 × 10⁻¹¹ × 3.97×10³⁰ × (341,280)²/2 × 3.142)
Radius, r = 4.71 × 10¹¹ meters.
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The field inside a running track is made up of a rectangle 84.39 m long and 73 m wide, together with a half-circle at each end. The running lanes are 9.76 m Wide all the way around.What is the area of the running track that goes around the field? Round to the nearest square meter.
To find the area of the running track that goes around the field, we need to follow the formula:
area of running track = outside area - inside area
1. Outside Area:
outside area = area of rectangle + 2× area of the semi- circle
= 92.52× 84.39 + π × 46.26² = 14527.32m²
2. Inside Area:
inside area = area of rectangle + 2× area of the semi- circle
= 73 × 84.39 + π × 36.5² = 10343.74m²
So, area of running track = 14527.32 m² - 10343.74m² = 4183.58m² ≈ 4184m²
Converting between fractions, decimals, and percentsUse the definition of the word percent to write each percent as a fraction and then as a decimal.
Answer:
See below for the completed table
Explanation:
A percentage is a number or ratio written as a fraction of 100. It is usually denoted using the symbol %.
To convert from percentage to fraction, divide the percentage by 100.
[tex]25\%=\frac{25}{100}[/tex]You can then convert the fraction to a decimal where:
[tex]\frac{25}{100}=0.25\text{ (In decimal form)}[/tex]Using the method described above, we calculate for the other values on the table:
[tex]\begin{gathered} 50\%=\frac{50}{100}=0.5 \\ 100\%=\frac{100}{100}=1 \\ 1\%=\frac{1}{100}=0.01 \\ 37.5\%=\frac{37.5}{100}=0.375 \\ 110\%=\frac{110}{100}=1.1 \\ \frac{1}{2}\%=\frac{0.5}{100}=0.005 \end{gathered}[/tex]The completed table is attached below.
In order to earn extra money during the summer, Trevor is working as a house painter. The
amount of money he earns depends on the number of houses he paints.
m = the amount of money Trevor earns
h = the number of houses Trevor paints
Which of the variables is independent and which is dependent?
h is the independent variable and m is the
dependent variable
m is the independent variable and h is the
dependent variable
Submit
The correct answer to this question is that m is the dependent variable and h is the independent variable.
The amount of money Trevor earns can be formulated in the form of linear equation. A Linear equation is the one which can be expressed in the form of y = ax + b where y is dependent, and x is independent variable whereas a, b are coefficients. According to question amount of money Trevor earns will depend on the number of houses he paints. If m is the amount of money Trevor earns and h is the number of houses Trevor paints. This can be formulated as
m = hx + b and in this expression, m is dependent variable and h is independent variable as his earning will depend on the number of houses he paints.
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The temperature in the morning was –2º F. The temperature in the evening was 9º F higher than it was in the morning. What was the temperature in the evening?
Answer:
Step-by-step explanation:
-2f
David has a coin collection. He keeps 9 of the coins in his box, which is 2% of the collection. How many total coins are in his collection?
Work Shown:
x = total number of coins
2% of x = 0.02x = 9 coins in the box
0.02x = 9
x = 9/0.02
x = 450 coins total
what is the reciprocal for the fraction 5/7 ?
we know that
The reciprocal of a number is: 1 divided by the number
If you multiply a number by the reciprocal, the result is 1
so
we have
5/7
so
the reciprocal is 7/5
Verify
(5/7)(7/5)=1 -----> is ok
Calculate the distance between the points L=(1, -8) and C=(9, -3) in the coordinate plane.
Round your answer to the nearest hundredth.
kintett. 41
Distance:
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ L(\stackrel{x_1}{1}~,~\stackrel{y_1}{-8})\qquad C(\stackrel{x_2}{9}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ LC=\sqrt{(~~9 - 1~~)^2 + (~~-3 - (-8)~~)^2} \implies LC=\sqrt{(9 -1)^2 + (-3 +8)^2} \\\\\\ LC=\sqrt{( 8 )^2 + ( 5 )^2} \implies LC=\sqrt{ 64 + 25 } \implies LC=\sqrt{ 89 }\implies LC\approx 9.43[/tex]
the probability of a 4 child family having 4 girls is 0.5. is it true or false
Consider the phase space that consists of elements of the form (boy, boy, boy, boy), (girl, boy, boy, boy),...,(girl, girl, girl, girl).
There is a total of 2*2*2*2=2^4=16 possible combinations and each of them has the same probability to happen. Only one element is the case we are interested in (girl, girl, girl, girl).
Therefore, the probability of a family having 4 girls is
[tex]P(girl,girl,girl,girl)=\frac{1}{16}=0.0625[/tex]
The answer is false, the probability is 0.0625
The measure of two complementary angles are in ratio 2:3. What is the measure of the smaller angle
ANSWER
36°
EXPLANATION
Let a and b be the measures of the two angles. We know that they are complementary, so their measures add up to 90°. Also, we know that the quotient between their measures is 2/3,
[tex]\begin{gathered} a+b=90 \\ \frac{a}{b}=\frac{2}{3} \end{gathered}[/tex]Solve the second equation for a,
[tex]a=\frac{2}{3}b[/tex]Replace a with this expression in the first equation,
[tex]\frac{2}{3}b+b=90[/tex]Add like terms,
[tex]\frac{5}{3}b=90[/tex]Solving for b,
[tex]b=90\cdot\frac{3}{5}=54[/tex]So the other angle is,
[tex]a=\frac{2}{3}b=\frac{2}{3}\cdot54=36[/tex]Hence, the measure of the smaller angle is 36°.
1/2 ^1/2 please show the steps
The value of [tex](\frac{1}{2} )^{\frac{1}{2} }[/tex] is 0.707.
1÷2 = 0.5
Given, [tex](\frac{1}{2} )^{\frac{1}{2} }[/tex]
Could be written like, [tex](0.5)^{0.5}[/tex] or √(1 ÷ 2) or √(0.5)
So the value of √(0.5) is 0.707.
Another way is to factorize each integer as the product of its primes using the square root prime factorization method. Follow these methods to find the square root of a certain number using prime factorization:
Step 1: Divide the supplied integer by its decimal equivalent.
Step 2: If the connected components are identical, a pair is generated.
Step 3: Choose one of the pair members for her.
Step 4: Multiply the prime numbers you got by picking one from each pair.
Step 5: This product is the square root of the specified number.
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Given that Kelsey has already made 10 pendants how many additional pendants must she make and sell to make a profit of 50 dollars?
Part a: Kelsey should make 36 pendants
Part b: Kelsey needs to make 26 more pendants
Rent of the booth at the craft fair = $200
The material cost of each pendant = is $7.80
The selling cost of each pendant = is $13.50
Let Kelsey make x number of pendants
Formulating the inequality equation we get:
Selling cost of each pendant*Number of pendants >= Rent of the booth + Material cost of each pendant*Number of pendants
= 13.50x >= 200 + 7.80x
Solving the inequality we get:
13.50x >=200+7.80x
5.70x >= 200
x >= 35.08
So, she should make a total of 36 pendants
Considering that she has already made 10 pendants. She needs 26 more pendants.
Although a part of your question is missing, you might refer to this full question: Kelsey makes pendants that she would like to sell at an upcoming craft fair. She must pay $200 to rent a booth at the craft fair. The materials for each pendant cost $7.80, and she plans to sell each pendant for $13.50. To make a profit, she must make more money than she spends. Kelsey has already made 10 pendants. Part A: Write and solve an inequality to show how many pendants Kelsey should make. Show the steps of your solutions. Part B: Given that Kelsey has already made 10 pendants, how many additional pendants must she make and sell to make a profit?
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Can you please help? I think it is ODD. Do you agree?
Given,
The function is:
[tex]f(x)=x+\frac{12}{x}[/tex]Taking x = -x then,
[tex]\begin{gathered} f(-x)=-x+\frac{12}{-x} \\ =-x-\frac{12}{x} \\ =-(x+\frac{12}{x}) \\ =-f(x) \end{gathered}[/tex]The function is odd.
8 - 5(3 + 2x)I need help
8 - 5(3 + 2x)
open the parenthesis
8 - 15 - 10x
-7 -10x
Question Solve for d. d³ = 27
Answer:
d = 3
Step-by-step explanation:
I took different numbers, like 1 and 2, and multiplied them to themselves 3 times, for example, 2 x 2 x 2, but since that answer was wrong, I decided to try a different number, which was 3 and that was correct.
Write an equation to represent , the balance in an account after years, with an initial investment of $1,000 with an interest rate of 3%, compounded each year.
The balance in the account after years of compound interest arrangement can be represented by the equation; Balance = 1,000 (1.03)^n.
Which equation represents the balance in the account after years of compound interest?It follows from the task content that the equation which represents the balance in the account after years is required to be determined.
It follows that the principal amount is; $1,000 while the interest rate is; 3%.
This indicates that after each year, the new balance is 103% of the preceding balance.
Hence, the exponential equation which correctly represents the balance at any point in time is;
Balance = 1,000 (1.03)^n.
Where n = number of years after.
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Complete the vertical algorithm to evaluate the product.Please see image below
Solution
Complete the vertical algorithm to evaluate the product:
Therefore the product of the expression is
[tex]4.09656[/tex]Divide using synthetic division. Write down the answer as a polynomial.x^3-5x^2-2x+24=0; (x+2)
we are given the following polynomial:
[tex]x^3-5x^2-2x+24=0[/tex]we are asked to use synthetic division by:
[tex]x+2[/tex]first we need to find the root of "x + 2":
[tex]\begin{gathered} x+2=0 \\ x=-2 \end{gathered}[/tex]Now we do the synthetic division using the following array:
[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {\square} & {\square} \\ {\square} & {\square} & {\square}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {\square} & {} & {} \\ {\square} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]Now we lower the first coefficient and multiply it by -2 and add that to the second coefficient:
[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {-2} & {\square} \\ {1} & {-7} & {\square}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {\square} & {} & {} \\ {\square} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]Now we repeat the previous step. We multiply -7 by -2 and add that to the next coefficient:
[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {-2} & {14} \\ {1} & {-7} & {12}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {\square} & {} & {} \\ {\square} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]Now we repeat the previous step. we multiply 12 by -2 and add that to the next coefficient:
[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {-2} & {14} \\ {1} & {-7} & {12}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {-24} & {} & {} \\ {0} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]The last number we got is the residue of the division, in this case, it is 0. Now we rewrite the polynomial but we subtract 1 to the order of the polynomial:
[tex]\frac{x^3-5x^2-2x+24}{x+2}=x^2-7x+12[/tex]Premises:
If I'm a student, then I go to school. If I go to school, then I learn.
Conclusion:
If I'm a student, then I learn.
This is an example of the Law of
?
Answer:
it's wh question I think
solve for the following right triangle upper a and h
we have that
[tex]undefined[/tex]A and B are sets of real numbers defined as follows.A = {x|x≤ 2}XB = {x|x < 7}Write A UB and An B using interval notation.If the set is empty, write 0.
The given sets are
[tex]\begin{gathered} A=\lbrace x:x,x\leq2\rbrace \\ \\ B=\lbrace x:x,x<7\rbrace \end{gathered}[/tex]That means A is all real numbers from 2 to negative infinity, and B is all real numbers between 7 and positive infinity
[tex]\begin{gathered} A=(-\infty,2] \\ \\ B=(7,\infty) \end{gathered}[/tex]Then we can find the union and intersection
[tex]\begin{gathered} A\cup B=(-\infty,2]\cup(7,\infty) \\ OR \\ A\cup B=(-\infty,\infty)-(2,7] \end{gathered}[/tex]I will draw a sketch to show you the intersection
We can see that there is NO intersection between A and B, then
[tex]\begin{gathered} A\cap B=\lbrace\rbrace \\ A\cap B=0 \end{gathered}[/tex]Bob's Golf Palace had a set of 10 golf clubs that were marked on sale for $840. This was a discount of 10% off the original selling price.Step 2 of 4: If the golf clubs cost Bob's Golf Palace $390, what was their profit? Follow the problem-solving process and round youranswer to the nearest cent, if necessary.
Consider that the Bob's Golf Palace bought the set of golf clubs by $390.
Moreover, take into account that the golf clubs were markes on sale for $840.
The profit is only the difference between the marked on sale and the money Bob's Golf Palace payed:
$840 - $390 = $450
Hence, the profit was $450
I really need help with number 5
Given:
Required:
To find the distance from point B to line AC.
Explanation:
The point B touches the line AC at P.
And it is perpendicular.
The length of BP is 4.3.
Therefore, the distance from point B to line AC is 4.3.
Final Answer:
The distance from point B to line AC is 4.3.
A flower garden is shaped like a circle. Its diameter is . A ring-shaped path goes around the garden. The width of the path is .The gardener is going to cover the path with sand. If one bag of sand can cover , how many bags of sand does the gardener need? Note that sand comes only by the bag, so the number of bags must be a whole number. (Use the value for .)
The number sand bags required are 84 approximately.
Given, we have:
Diameter of garden = 38 yd
Width of path = 5 yd
Diameter of garden with path = 38 + 2 x 5 = 48 yd
We need to find area of path.
Area of path = Area of garden with path - area of garden
Area of path = π × 48²/4 - π × 38²/4
Area of path = 7234.56/4 - 4534.16/4
Area of path = 1808.64 - 1133.54
Area of path = 675.1 yd²
Area covered by one sand bag = 8 yd²
Number of sand bags required = Area of path/Area covered by one sand bag
=675.1/8
= 84.38 ≈ 84
Number of sand bags needed = 84
Therefore, number of sand bags required are 84.
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A population doubles every 27 years. Assuming exponential growth find the following:help find continuous growth rate (a) The annual growth rate: 2.6(b) The continuous growth rate is____% per year help (numbers)
Given,
A population doubles every 27 years.
a. Let initial population be 1 and after 27 years it becomes 2.
Considering r as the rate of annuall growth we have,
[tex]\begin{gathered} 1(1+r)^{27}=2 \\ \Rightarrow27\ln (1+r)=\ln 2 \\ \Rightarrow\ln (1+r_{})=\frac{0.693}{27} \\ \Rightarrow1+r=1.0257 \\ \Rightarrow r=0.026 \end{gathered}[/tex]Thus annual growth rate is 2.6%
b. For continuous growth,
[tex]\begin{gathered} 1(e^{27x})=2 \\ \Rightarrow27x=0.693 \\ \Rightarrow x=0.025 \end{gathered}[/tex]The continuous growth rate is _2.5___% per year
which situation can be represented by this inequality1.25x -6.50 > 50 A. Caleb has a balance of 6.50$ in his savings account and deposits 1.25$ each week. What is X the number of weeks must deposit 1.25$ in order to have a balance of more than 50$ in his savings account?B. Caleb earns 1.25% interest on the balance in his checking account and has to pay a monthly charge of 6.50$. What is X the balance that Caleb must have in his checking account in order to have an ending balance greater than 50$ after interest and fees.C. Caleb charges 1.25$ for gasoline plus 6.50$ per hour for mowing lawns. What is X the number of hours he has to mow lawns to earn more than 50$D. Caleb spends 6.50$ on supplies for a lemonade stand and sells each cup of lemonade for 1.25$. what is X the number of cups of lemonade Caleb must sell to earn profit of more than 50$
We need to find a situation that can be represented by the inequality below:
[tex]1.25\cdot x-6.5>50[/tex]This means that there must be a variable for which each unit has a value of 1.25. There must be a fixed cost of 6.5, because we are subtracting that value and the end goal must be to have more than 50.
The only option for which this applies is the option D.
Caleb spent a fixed amount of 6.5, he earns 1.25 for each lemonade he sells and he wants to have a profit of more than 50.
27 is The same as the product of four and a number
Answer:
6.75
Step-by-step explanation:
6.75x4 = 27 so if this is what was meant by this then heres your answer
hope this helped
have a good day ^^
Need help please with this
Answer: It would be Answer D
Step-by-step explanation: He Subtracted from both sides in an incorrect order
1) Consider the ratio table below that compare hours worked to money earned for an employee at a pizza restaurant. Hours Worked 4 12 16 ? Money Earned 36 ? 76 108 144 270 a. How much money would an employee earn for working 8 hours? b. How many hours did a person work if they earned $270? c. Find the ratio associated with the table above (in simplest form). d. If you extend the ratio table, how much money will be earned if an employee works 24 hours? dollars they can amount of time
The ratio table can be used to find the amount earned and the number of hours worked based on the ratio of the values as follows;
a. A person that works for 8 hours earns $72
b. A person that earns $270 worked for 30 hours
c. The ratio is 9 : 1
d. The earnings of a person that works for 24 hours is $216
What is a ratio table?A ratio table is one that shows the constant relationship between the value pairs on the table.
The given ratio table is presented as follows;
Hours Worked; 4, 12, 16, ?
Money Earned; 36, 108, 144,
Required;
a. The amount a person will earn if he or she works for 8 hours
Solution;
Let x represent the hours worked, and let y represent the money earned
y = k•x
Therefore;
k = y/x
From the ratio table, we have;
k = 36/4 = 108/12 = 144/16 = 9
k = 9
y = 9•x
The amount earned, y for working 8 hours, x is therefore;
y = 9 × 8 = 72
The amount earned for working 8 hours is $72
b. The number of hours worked if a person earns $270
If a person earned $270, we have;
270 = 9 × x
x = 270/9 = 30
The number of hours worked if a person earned $270 is 30 hours
c. The ratio associated with the table in the simplest form is 36 : 4 = 9 : 1
d. The amount earned if a person worked 24 hours
Solution;
y = 9•x
Which gives;
y = 9 × 24 = 216
The amount earned if a person worked 24 hours is $216
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Can Some one please help me match the congruence statements below!
Write two numbers that multiply to the value on top and add to the value on bottom.
The values are -3 and -26
What is Multiplication?
A product is an expression that identifies the object to be multiplied, called the result of a multiplication, or coefficient. For example, 30 is the product of 6 and 5, and x\cdot is the product of x.
We have to find the number which is multiply to give the upper value and sum up to give the bottom value
So, the value of these numbers will be
-3 x -23 = 69
-3 + (-23) = -26
Hence the values are -3 and -23
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