Okay, here we have this:
Considering the provided information we obtain the following:
Let us take the diameter of the earth as d, so the diameter of the moon is d/4
Thus, the earth radius is d/2, and the moon radius is d/4/2=d/8.
Now, let's find the volume of the the earth and the moon separately to finally compare them:
\(\begin{gathered} \text{Volume of earth=}\frac{4}{3}\pi r^3 \\ =\frac{4}{3}\pi(\frac{d}{2})^3 \\ =\frac{1}{8}\cdot\frac{4}{3}\pi d^3 \\ =\frac{1}{6}\pi d^2 \end{gathered}\)\(\begin{gathered} \text{Volume of moon=}\frac{4}{3}\pi r^3 \\ =\frac{4}{3}\pi(\frac{d}{8})^3 \\ =\frac{1}{512}\cdot\frac{4}{3}\pi d^3 \\ =\frac{1}{384}\pi d^3 \end{gathered}\)Finally let's compare its volumes:
\(\begin{gathered} \frac{Volume\text{ of moon}}{Volume\text{ of earth}}=\frac{\frac{1}{384}\pi d^3}{\frac{1}{6}\pi d^3} \\ =\frac{1}{64} \end{gathered}\)Finally we obtain that the volume of the moon is 1/64 of the volume of the earth.
Cameron spent 32 minutes on Instagram on Friday. The next day
he spent 30% of that on Instagram. In total, how much time did
Cameron spend on Instagram?
Answer:
41.6
Step-by-step explanation:
32 x 0.3 = 9.6
9.6 + 32 = 41.6
41.6
i had the same question
Write the prime factorization of 38.
Mr. Roper has eight teams of students in his debate class. Their grades on the last debate assignment are denoted by the set {99, 72, 86, 80, 96, 87, 79, 87). Which 5-number
summary represents the data set? (2 points)
A {72, 79, 86, 96, 99)
b {72, 79.5, 86.5, 91.5, 99}
c {72, 79, 83, 87, 96)
d {72, 79, 86, 87, 96)
Answer:
{72, 79.5, 86.5, 91.5, 99}
Step-by-step explanation:
I took the quiz and got it correct.
Minimum is 72
Maximum is 99
Q1 is 79.5
Q3 is 91.5
Median is 86.5
So the 5-number summary is {72, 79.5, 86.5, 91.5, 99}
How would i graph the solution set for 1/3x (greater than or equal to) y+2?
When Louis Brandeis graduated from Harvard Law School, he immediately established a
reputation in Boston as an attorney who would accept cases
Later appointed
This is a question on me homework and me need help so plz help
Find the value of angle W
Answer:
w = 73°
Step-by-step explanation:
The relations involved in solving this figure are ...
linear pairs are supplementarythe angle sum for the quadrilateral is 360°__
The linear pair at lower left gives us a relation we can solve for x:
x +(3x -24) = 180
4x = 204
x = 51
Then the sum of angles inside the quadrilateral is ...
w +(x +15) +(2x -10) +(3x -24) = 360
w +(51 +15) +(2(51) -10) +(3(51) -24) = 360
w +66 +92 +129 = 360
w = 360 -287 = 73
Angle W is 73°.
_____
Additional comment
The remaining angles are supplementary to those inside the quadrilateral:
v = 180° -w = 107°
y = 180° -92° = 88°
z = 180° -66° = 114°
x = 51°
A company that sells paper has a tiered pricing model based on how much paper you buy. If you buy less than 10 reams, they charge you $7 per ream and a shipping cost of $8. If you buy 10 or more reams but less than 20 reams, they charge you $6 per ream and a shipping cost of $16. If you buy 20 or more reams, they charge you $6 per ream and shipping is free.
a. Write a function that models the price in terms of the number of reams bought.
b. What is the domain of the function?
c. What is the range of the function?
d. How much will it cost to buy 25 reams of paper?
f. How much paper can you buy for $60?
The function can be defined as price = 6x
It will cost $150 to buy 25 reams of paper.
How to explain the functionThe domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.
The range of the function is all non-negative real numbers, since the price cannot be negative.
Fir 25 items, price = 6(25) = $150
It will cost $150 to buy 25 reams of paper.
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PLEASE HELP WILL MARK BRAINLIEST!!TY!!
Answer:AB = 5/2 and CD = 2/-5, perpendicperpendicular
Step-by-step explanation:
0+5 = 5
2+2=4
1+2=3
8-5=3
The function family that best describes f(x) isA. linear B. Absolute Value C. Exponential D. Quadratic Write the equation of the horizontal asymptote below.y=?A. -10B. -8C. 0D. 4
By the form of the graph, you can notice that the famili function that best describes the function is
C. Exponential
An equation of the horizontal asymptote is given by y = c, where c is the value of y at which the curve approximates where x approcahes to infinity. This value of y is y = -8
B. -8
1. Out of 318 seventh and eighth grade CAVA students there were 48 students that chose Music as their elective
course and the rest chose World Language. There were a total of 124 eighth grade students and 108 of them
chose World Language as their elective.
Use this information to complete the two-way table completely.
Enter your answer by filling in the boxes to complete the table (5 pts)
Answer:
8th Grade
7th Grade
Totals
Music
48
World Language
108
Totals
124
318
The students in 8th class who choose music are 16 in number,
The students in 7th class who choose music are 32 in number
The total who choose world language is 270
The totals who are in 7th grade be 194
The number of students who choose world language in 7th class are 162
Let x be the students in 8th class who choose music
x+108=124
x=124-108
x=16 students
Now y be the students in 7th class who choose music
16+y=48
y=48-16
y=32
Let z be the total who choose world language
48+z=318
z=318-48
z=270
Now the totals who are in 7th grade be A
124+A=318
A=318-124
A=194
B be the number of students who choose world language in 7th class
Now 32+B=194
B=194-32
B=162
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There are 24 marbles in a jar. 3 marbles are added to the jar when the class is good. How many times can the class be rewarded to get 100 marbles
Which point is located at (3, 7)?
Answer:
B
Step-by-step explanation:
A three dimensional figure is formed by a rectangular prism and an isosceles triangular prism as shown in the diagram below
Use the information given in the image to find the surface area of the composite figure
The surface area of the composite figure is 4364 sq. m.
What is a composite figure?A composite figure that consists of more than one shape. Thereby it is formed by joining two or more shapes.
In the given composite figure, we have;
i. area of one triangular surface = 1/2 x base x height
= 1/2 x 25x13
= 162.5
area of one of its triangular surfaces is 162.5 sq. m.
ii. area of rectangular surface 1 = length x width
= 27 x 18
= 486 sq. m.
iii. area of rectangular surface 2 = length x width
= 27 x 23
= 621 sq. m.
iv. area of rectangular surface 3 = length x width
= 25 x 23
= 575 sq. m.
v. area of its base = length x width
= 27 x 25
= 675 sq. m.
surface area of the composite figure = (2*162.5) + (2*486) + (2*621) + (2*575) + 675
= 4364
The surface area of the composite figure is 4364 sq. m.
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GIVING EXTRA POINTS PLS HELP
Answer:
4 and 6
Step-by-step explanation:
I have learned this in my own Algebra class and I've done this exact problem today and when I saw you needed help this is what the answer is.
for item 6 which pair of words is the odd one out
Answer:
A odd # is 3.5.7 and etc such that you have odd numbers
Find the slope of the line. Describe how one variable changes in relation to the other. A. 2; distance increases by 2 miles per hour B. 2; distance decreases by 2 miles per hour C. 1/2; distance increases by 1 mile every 2 hours D. 1/2; distance decreases by 1 mile every 2 hours
The line's slope is \(\frac{1}{2}\) and the distance increases by 1 mile every 2 hours.
What is a good example of a line's slope?
The proportion of the increase in the y-value to the increase in the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) & Q = (4,1) on the line.
A. Since the line's slope is 2, it follows that the y-variable, which is most likely distance, grows by 2 units for every increment in the x-variable, which is most likely time. The accurate statement is thus: speed is increased by Two miles per hour.
B. Since the line's slope is 2, it follows that the y-variable will drop by 2 units for every unit rise in the x-variable, which is most likely time. The accurate description is thus: speed drops by Two miles per hour.
C. If the line's slope is 1/2, the y-variable will rise by 1/2 unit for every increment in the x-variable, which is probably time. The precise description is that the distance grows by a mile every two hours.
D. If indeed the line's slope is 1/2, the y-variable will drop by 1/2 unit for every unit rise in the x-variable, which is probably time. The precise description is: distance shrinks by a mile every two hours.
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Who is life insurance best suited for?
A. College students
B. Children
C. People with debt
D. Doctors
SUBMIT
Answer:
People with dependents
Step-by-step explanation:
AP3X
Solve the inequality for the missing variable
24 -1t
1/5
Answer:
−t+24
Step-by-step explanation:
connie poured 200 milliliters of juice into a glass from a juice carton. She then poured 225 milliliters into a second glass. What is the final change in the volume of the carton?
Answer:
425 ml
Step-by-step explanation:
200+225= 425 ml
Which expressions are equivalent to 24-7? Choose all the correct answers. Show your work.
The equivalent expressions to \(24^{-7}\) are given as follows:
C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)
F. \((24^3 \times 24^4)^{-1}\)
What are are equivalent expressions?Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.
The exponent in the denominator can be moved to the numerator with the changed signal, hence:
\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)
Applying the power of power rule, we multiply the powers, hence:
\((24^7)^{-1} = 24^{-7}\)
When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:
\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)
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Mia hired a moving company. The company charged $500 or its services, and Mia gives the movers a 16% tip.
Answer:
The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580
Step-by-step explanation:
Which statement best describes discretionary government spending?
Back
A. A fixed amount of money spent on the same categories every year
B. The money used to pay for Social Security and Medicare
C. A changing amount of money spent on different categories each year
D. Money that you determine how it is spent by the government when you submit your taxes
Select an answer
C. A changing amount of money spent on different categories each year
What is amount?Amount is a term used to describe a quantity of something, typically money. It is often used to refer to the total value of a financial transaction or the sum of multiple payments. Amount can also refer to any other quantifiable measure, such as a number of items, units of time, or a volume or quantity of something.
Discretionary government spending is a type of government spending that is determined each year by the Congress, and typically includes funds for defense, education, infrastructure, and other government programs. The amount of money spent on each category can vary from year to year, making it a type of changing, or discretionary, spending.
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may someone please help me? I’m having trouble finding G and H. It would be okay if you only found G for me. I will give the first answer a brainliest if it is reasonable or correct! Thanks you
g would be 125 degrees
h would be 62 degrees
Answer:
g = 118°
Step-by-step explanation:
b = 180 - 62 = 118 because b is supplementary to the 62° angle
g = 118 because b and g are alternate interior angles
PLS HELP I WILL BE SO HAPPY. IF YOU CAN HELP ME DROP YOUR PAYPAL IN TOO
Answer:
I recommend to do your note
Step-by-step explanation:
The table below shows the value of two different antiques over a period of five years.
Value of Two Antiques Over Five Years
Year 1 2 3 4 5
Antique 1 $100 $108 $116 $124 $132
Antique 2 $70 $77 $84 $89 $97
Which of the antiques has a value that has been increasing at a constant rate? What is that rate? Explain your reasoning.
Answer:
As we can see the first antique is increasing by 8$, while the second one is increasing by 7$. The answer would logically be the first antique since it has a higher rate and has higher amount paid to get for. So the answer is the first Antique.
relationship between the two number
b 70.908
7.908
Which one is greater
Answer:
70.908 is greater than 7.908 .
I hope your day goes nice
Answer:
70.9 0 8 is Greaterboth are different because of different placement of point.
Write the English phrase that represents the number 522,043,009
Hello User,
Answer: five hundred and twenty-two million and forty-three thousand and nine
one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!! Part 2.
2. What is a determinant and what role does it play with matrices (Hint: What does a determinant of 0 mean)? How can this be used when solving systems of equations?
9514 1404 393
Explanation:
Definition
The determinant of a square matrix is a single number that is computed (recursively) as the sum of products of the elements of a row or column and the determinants of their cofactors. The determinant of a single element is the value of that element.
The cofactor of an element in an n by n matrix is the (n-1) by (n-1) matrix that results when the row and column of that element are deleted. The "appropriate sign" of the element is applied to the cofactor matrix. The "appropriate sign" of an element is positive if the sum of its row and column numbers is even, negative otherwise. (Rows and columns are considered to be numbered 1 to n in an n by n matrix.)
Uses
The inverse of a square matrix is the transpose of the cofactor matrix, divided by the determinant. Hence if the determinant is zero, the inverse matrix is undefined. This means any system of equations the matrix might represent will have no distinct solution. (There may be zero solutions, or there may be an infinite number of solutions. The determinant by itself cannot tell you which.)
Cramer's Rule for the solution of linear systems of equations specifies that the value of any given variable is the ratio of the determinants of two matrices. The numerator matrix is the original matrix with the coefficients of the variable replaced by the constants in the standard-form equations; the denominator matrix is the original coefficient matrix. This rule lets you solve a system of 3 equations in 3 variables by computing 3+1 = 4 determinants, for example.
Let's look at an example.
If we wanted to solve this system of equations
\(\begin{cases}2x-y = 2\\x+y = 7\end{cases}\)
Then it's equivalent to solving this matrix equation
\(\begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}2\\7\end{bmatrix}\)
We can then further condense that into the form
\(Aw = B\)
Where,
\(A = \begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\\\\w = \begin{bmatrix}x\\y\end{bmatrix}\\\\B = \begin{bmatrix}2\\7\end{bmatrix}\)
------------------------------------------
To solve the matrix equation Aw = B, we could compute the inverse matrix \(A^{-1}\) and left-multiply both sides by this to isolate w.
So we'd go from \(Aw=B\) to \(w = A^{-1}*B\). The order of multiplication is important.
For any 2x2 matrix of the form
\(P = \begin{bmatrix}a & b\\c & d\end{bmatrix}\)
its inverse is
\(P^{-1} = \frac{1}{ad-bc}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}\)
Notice the expression ad-bc in the denominator of that fractional term outside. This \(ad-bc\) expression represents the determinant of matrix P. Some books may use the notation "det" to mean "determinant"
\(P^{-1} = \frac{1}{\det(P)}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}\)
or you may see it written as
\(P^{-1} = \frac{1}{|P|}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}\)
Those aren't absolute value bars, even if they may look like it.
Based on that, we can see that the determinant must be nonzero in order to compute the inverse of the matrix. Consequently, the determinant must be nonzero in order for Aw = B to have one solution.
If the determinant is 0, then we have two possibilities:
There are infinitely many solutions (aka the system is dependent)There are no solutions (the system is inconsistent)So a zero determinant would have to be investigated further as to which outcome would occur.
------------------------------------------
Let's return to the example and compute the inverse (if possible).
\(A = \begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\\\\A^{-1} = \frac{1}{2*1 - (-1)*1}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}\\\\A^{-1} = \frac{1}{3}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}\\\\\)
In this case, the inverse does exist.
This further leads to
\(w = A^{-1}*B\\\\w = \frac{1}{3}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}*\begin{bmatrix}2\\7\end{bmatrix}\\\\w = \frac{1}{3}\begin{bmatrix}1*2+1*7\\-1*2+2*7\end{bmatrix}\\\\w = \frac{1}{3}\begin{bmatrix}9\\12\end{bmatrix}\\\\w = \begin{bmatrix}(1/3)*9\\(1/3)*12\end{bmatrix}\\\\w = \begin{bmatrix}3\\4\end{bmatrix}\\\\\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}3\\4\end{bmatrix}\\\\\)
This shows that the solution is (x,y) = (3,4).
As the other person pointed out, you could use Cramer's Rule to solve this system. Cramer's Rule will involve using determinants and you'll be dividing over determinants. So this is another reason why we cannot have a zero determinant.