Answer:
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius. Since we know that the circular region has an area of 90π square feet, we can set this equal to the area formula and solve for r:
A = πr^2
90π = πr^2
90 = r^2
Taking the square root of both sides, we get:
r = √90
r = √(9 x 10)
r = 3√10
The diameter of the circle is equal to twice the radius, so we have:
d = 2r
d = 2(3√10)
d = 6√10
Therefore, the diameter of the circle is 6√10 feet.
Order each amount from least to greatest
1 pint, 2 gallons, 3 quarts, 3 cups
Need help on this one.
The following recursive function computes the number of comparisons used in the worst case of merge sort.
M (1) = 0
M (2k) = 2M (2k−1) + 2k for all k > 0
Use mathematical induction to prove that M (2k) = k · 2k for all k ∈ N.
By the principle of mathematical induction, we have shown that
M(2k) = k 2k for all k ∈ N.
The Principle of Mathematical Induction:The principle of mathematical induction is a proof technique used to prove a statement that holds for all positive integers.
It consists of two steps:
Base case: Show that the statement is true for the smallest possible value of the positive integer, usually n = 1.
Inductive step: Assume that the statement is true for an arbitrary positive integer k, and then use this assumption to show that the statement must also be true for k + 1.
Here we have
The following recursive function computes the number of comparisons used in the worst case of merge sort.
M (1) = 0
M (2k) = 2M (2k−1) + 2k for all k > 0
To prove that M(2k) = k × 2k for all k ∈ N using mathematical induction, we will first show that the base case holds:
Base case: When k = 1,
we have M(2) = 2M(1) + 2¹ = 2(0) + 2 = 2, and k × 2k = 1 × 2¹ = 2.
Therefore, the base case holds.
Inductive hypothesis:
Assume that M(2k) = k × 2k holds for some positive integer k.
Inductive step:
We need to show that M(2k+1) = (k+1) × 2k+1.
Using the recursive definition of M, we have:
M(2k+1) = 2M(2k) + 2(2k+1)
= 2(k × 2k) + 2(2k+1) (using the inductive hypothesis)
= 2k(2k+2) + 2(2k+1)
= 2k(2(k+1)) + 2(2k+1)
= 2(k+1) × 2k + 2(2k+1)
= (k+1) × 2(2k+1)
Therefore, the inductive step holds.
Hence,
By the principle of mathematical induction, we have shown that
M(2k) = k 2k for all k ∈ N.
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A bag contains 3 red marbles, 6 blue marbles and 4 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that all three marbles drawn will be blue?
please help
Answer:
0.077
Step-by-step explanation:
Help with math problems
1. The solution to the system of equations is v = -3 and w = 4.
2. The solution to the system of equations is y = 6 and z = -2.
How to solve for -v + w = 7; v + w = 1?To eliminate v, we can add the two equations:
(-v + w) + (v + w) = 7 + 1
2w = 8
w = 4
Substitute w = 4 into one of the equations to solve for v:
v + 4 = 1
v = -3
How to solve for y + z = 4; y - z = 8?To eliminate z, we can add the two equations:
(y + z) + (y - z) = 4 + 8
2y = 12
y = 6
Substitute y = 6 into one of the equations to solve for z:
6 + z = 4
z = -2.
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Francisco invested $5,000 into an account that earns 3% compounded
quarterly. How many times will Francisco earn interest after keeping the money in
the account for 5 years?
What will be the value of his account in 5 years if he does not make any
additional deposits or withdrawals?
Answer: To calculate how many times Francisco will earn interest after keeping the money in the account for 5 years, we need to determine the number of quarters in 5 years.
Since there are 4 quarters in a year, the total number of quarters in 5 years is:
4 quarters/year x 5 years = 20 quarters
Therefore, Francisco will earn interest 20 times over the 5-year period.
To calculate the value of his account in 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time the money is invested (in years)
In this case, P = $5,000, r = 0.03, n = 4 (since the interest is compounded quarterly), and t = 5. Substituting these values into the formula, we get:
A = $5,000(1 + 0.03/4)^(4x5)
A = $5,000(1.0075)^20
A = $5,866.02
Therefore, the value of Francisco's account in 5 years, if he does not make any additional deposits or withdrawals, will be $5,866.02.
Step-by-step explanation:
What is the value of u?
since its on a straight line we instantly know that u+100=180 since a straight line is 180 degrees. From thay we can easily find out that u=180-100=80. So u is 80 degrees. Also pls mark as brainliest answer thx.
Answer:
u=180
Step-by-step explanation:
The two angles add together to form a straight line, so they add to 180
100+u = 180
u = 180-100
u= 80
Evaluate the expression.
20.4 0.2
Write your answer as an integer or a decimal. Do not round.
After solving the given expression 2 - 0.4 ÷ 0.2 the resultant answer is an integer which is 0.
What is an integer?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers.
The inverse additives of the equivalent positive numbers are the negative numbers.
The boldface Z is a common mathematical symbol for the set of integers.
Numbers that are negative: -1, -2, -3, -4, -5, and so on indefinitely.
Non-negative integers include 0 and all whole numbers that are positive, such as 6, 7, 8, 9, 10, and so forth.
Positive integers include 1, 2, 3, 4, 5, and on indefinitely.
So, we have the expression:
= 2 - 0.4 ÷ 0.2
Now, evaluate using the BODMAS rule as follows:
= 2 - 0.4 ÷ 0.2
= 2 - 2
= 0
Therefore, after solving the given expression 2 - 0.4 ÷ 0.2 the resultant answer is an integer which is 0.
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The salaries of six bank employees are $37,000, $38,500, $35,000, $37,000, $45,000, $40,000, and $75,000.
Which statement is true?
Question 1 options:
Both the median and mode are appropriate measures of center.
The mean, median, and mode are all appropriate measures of center.
Both the mean and median are appropriate measures of center.
The median is the only appropriate measure of center.
The correct answer is: Both the mean and median are appropriate measures of center.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and computational tools to summarize and analyze large sets of data, with the goal of extracting meaningful insights and identifying patterns or trends.
Here,
The mean is the sum of all salaries divided by the number of salaries. In this case, the sum is:
37,000 + 38,500 + 35,000 + 37,000 + 45,000 + 40,000 + 75,000 = 307,500
And there are seven salaries. Therefore, the mean is:
307,500 / 7 = 43,928.57
The median is the middle value when the salaries are arranged in order from lowest to highest. First, we need to arrange the salaries in order:
35,000, 37,000, 37,000, 38,500, 40,000, 45,000, 75,000
The median is the middle value, which is 40,000.
The mode is the value that appears most frequently in the set of salaries. In this case, both 37,000 and 40,000 appear twice, so there is no unique mode.
Since the salaries are not symmetrically distributed, the mean is not a perfect measure of central tendency. However, it can still provide useful information about the "average" salary. On the other hand, the median is resistant to extreme values and may be a better measure of central tendency for this dataset. Therefore, both the mean and median are appropriate measures of center for this dataset.
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please help me in this question is math,solve just d, e&f
Step-by-step explanation:
a) factorize A
A = (2x-1)²+2(3-6x)(4x-7)-4x²+1
expand the terms
(2x-1)²-52x²+108x-41
factorize
(2x-1)²-(26x-41)(2x-1)
factor out the common factor 2x-1
-(2x-1)(24x-40)
A = -8(2x-1)(3x-5)
b) show that B = (3x-11)(2x-1)
6x²-25x+11
6x²-3x-22x+11
3x(2x-1)-11(2x-1)
(2x-1)(3x-11)
c) Expand and reduce A
(2x-1)²+2(3-6x)(4x-7)-4x²+1
-48x²+108x-40
d) Calculate A for x=0 and x=-1
when x=0 -48(0)²+108(0)-40
A=0
x=-1 -48(-1)²+108(-1)-40
A=-196
e) Reduce 2A-3B
A=-48x²+108x-40 B=6x²-25x+11
2(-48x²+108x-40)-3(6x²-25x+11)
-96x²+216x-80-18x²+75x-33
-144x²+291x-113
f) Factorize 2A-B
A=-48x²+108x-40 B=6x²-25x+11
2(-48x²+108x-40)-(6x²-25x+11)
-96x²+216x-80-6x²+25x-11
-102x²+241x-91
x=(241 + sqrt(20953))/204
x=(241 - sqrt(20953))/204
Please Mark Me Brainliest!
Please help with this math question!
Answer:
[tex]2000 {(1 + \frac{.07}{12}) }^{5 \times 12} = 2835.25[/tex]
What is the length of side AB?
The length of side AB is given as follows:
[tex]AB = \frac{6}{\sqrt{3}}[/tex]
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For the angle of 30º, we have that:
AB is the opposite side.AC is the adjacent side.Hence the length of side AB is obtained as follows:
tan(30º) = AB/6
AB = 6 x tan(30º)
[tex]AB = 6 \times \frac{1}{\sqrt{3}}[/tex]
[tex]AB = \frac{6}{\sqrt{3}}[/tex]
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The value of the side AB is calculated as: AB = 6/√3
How to use trigonometric ratios?There are different trigonometric ratios used in right angle triangles which are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Looking at the given triangle, the value of AB can be gotten via the trigonometric ratio tan x. Thus:
AB = 6 * tan 30
AB = 6 * 1/√3
AB = 6/√3
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Please help
A space station is being built from 24 cubic modules. The space station can be any shape but the modules must be placed together so that entire faces match up with each other. Choose a tool to create two different plans for the space station. Explain why you chose the tool you selected.
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The brain volumes (cm³) of 20 brains have a mean of 1128.4 cm³ and a standard deviation of 125.9 cm³. Use the
given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or
significantly high. For such data, would a brain volume of 1360.2 cm³ be significantly high?
Significantly low values are cm³ or lower.
Step-by-step explanation:
The range rule of thumb states that for data with a roughly bell-shaped distribution, about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.
Given that the standard deviation is 125.9 cm³, one standard deviation above the mean would be 1128.4 + 125.9 = 1254.3 cm³, and one standard deviation below the mean would be 1128.4 - 125.9 = 1002.5 cm³.
Thus, significantly low values would be 1002.5 cm³ or lower, and significantly high values would be 1254.3 cm³ or higher.
Since 1360.2 cm³ is higher than 1254.3 cm³, it would fall outside the range of one standard deviation above the mean and can be considered significantly high based on the range rule of thumb.
How could expanded land acreage and pricing be viewed as some to be a bad thing
for the recovering Great Plains?
Increased land prices and acreage on the Great Plains could be seen as negative owing to potential ecological impact, as a disruption for Traditional communities and unsustainable resource use.
Why expanded land acreage and pricing in Great plains is considered negative?Ecological impact: Increased land acreage and price may cause habitat loss, biodiversity loss, soil erosion, and water pollution, all of which might be detrimental to the area's natural ecosystem.Disruption of traditional farming and ranching communities: Increasing land prices and greater parcel sizes may make it harder for small-scale farmers and ranchers to compete, which might result in the consolidation of land ownership and the eradication of traditional farming and ranching communities.Unsustainable resource use: Increasing land area might result in more water being used for irrigation, thereby worsening the Great Plains' water shortage problems.Loss of grasslands: The Great Plains are renowned for their distinctive grassland ecosystems, which are essential for biodiversity and carbon sequestration. More land being used for construction or agriculture might lead to the extinction of grasslands, which would have detrimental ecological effects.Degradation of the soil: Intensive agricultural techniques, such as monoculture and extensive chemical usage, may result in the loss of fertility and accelerated erosion of the soil. Long-term, this can have a negative effect on the sustainability and production of agricultural areas.Increased use of chemical inputs: Increasing land area may result in higher usage of chemical pesticides and fertilisers, which might impact regional ecosystems and contribute to environmental degradation.Danger of overproduction: Increased land acreage and pricing may lead to overproduction of agricultural products, which might lead to unstable prices, unstable farmer livelihoods, and potential market saturation.Potential for land speculation: Increasing land prices may encourage speculative investment, which might result in land being bought and retained for financial gain rather than for productive use. This could push up land prices even more and restrict access to land for local farmers and ranchers.Risks to wildlife and biodiversity: Include habitat fragmentation, the loss of wildlife corridors, and the displacement of native species, all of which might have an effect on the biodiversity and animal populations of the area.Learn more about land acreage and pricing here:
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What are the domain and range of the function?
f(x) = -3√x
Answer:
Domain: [tex]x\geq 0[/tex]
Range: [tex]y\leq 0[/tex]
Step-by-step explanation:
Recall that the domain of a function is the values that x can be, while the range of a function is the values that y can be.
Let's take a look at one part of the function: [tex]\sqrt{x}[/tex].
The square root of any positive number does exist. It may not be rational, but it exists. The square root of zero also exists -- it's zero.
However, the square root of a negative number will never exist - it's imaginary. So, x cannot be negative as long as it is under the radical.
The domain is: [tex]x\geq 0[/tex]
Now, to find the range, let's look at the coefficient: -3.
A negative number times a negative number is positive. A negative number times a positive number is negative.
However, x can never be negative, so no matter what real value you plug in for x, you will always be multiplying -3 by a positive number (or zero).
Since zero times any number is zero, and a positive number times a negative number is a negative number, y will always be either equal to zero or negative.
So, the range is: [tex]y\leq 0[/tex]
HELP GIVING BRAINLY AND 20 POINTS CORRECTIONS DUE LATER
Answer:
Step-by-step explanation:
cos47=80/x
x=80/0.6820
x=117.3020 feet
Triangle D has been dilated to create triangle D'. Use the image to answer the question.
112
02
24
3
D
Determine the scale factor used.
2.1
3.8
4.8
D
4.2
Since triangle D has been dilated to create triangle D', the scale factor used include the following: A. 1/2.
What is scale factor?In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image (original figure)
By substituting the given parameters into the formula for scale factor, we have the following;
Scale factor = Dimension of image/Dimension of pre-image
Scale factor = 2.4/4.8
Scale factor = 1/2.
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Find the unknown side length. Simplify radicals to simplest radical form.
Answer: q1. 12 i think q2. 39 i think
Step-by-step explanation
Use the drop-down menus to complete the statements.
When electrons are lost, a
ion is formed.
When electrons are gained, a
ion is formed.
When electrons are lost, a cation is formed.
When electrons are gained, an anion is formed.
An atom can lose or gain electrons to form ions. An ion is an atom or molecule that has an unequal number of protons and electrons, which gives it a net electrical charge.
When an atom loses one or more electrons, it becomes positively charged because the number of protons in the nucleus is greater than the number of electrons. This type of ion is called a cation. Cations are formed when metals lose electrons because they have relatively low electronegativity, which means they don't hold onto their valence electrons as tightly.
On the other hand, when an atom gains one or more electrons, it becomes negatively charged because the number of electrons is greater than the number of protons. This type of ion is called an anion. Anions are formed when nonmetals gain electrons because they have relatively high electronegativity, which means they attract electrons more strongly.
Therefore, When electrons are lost, a cation is formed and When electrons are gained, an anion is formed.
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Answer:
When electrons are lost, a
✔ positive
ion is formed.
When electrons are gained, a
✔ negative
ion is formed.
Step-by-step explanation:
Graph the function.
f(x)=√x-4
Plot four points on the graph of the function: the leftmost point and three additional points. Then click on the graph-a-function button.
The four points on the graph of f(x) = √x-4 including the left most point are: (4,0), (5,1), (8,2), and (20,4).
Finding four points on the graph of the functionTo find points on the graph of f(x) = √x-4, we can choose values of x and find the corresponding values of y.
The leftmost point on the graph is when x is the smallest possible value, which is x = 4 (since we can't take the square root of a negative number). At x = 4, f(x) = √0 = 0, so the leftmost point is (4,0).
To find three additional points, we can choose values of x that are greater than 4 and find the corresponding values of y:
When x = 5: f(5) = √1 = 1, so the point is (5,1)
When x = 8: f(8) = √4 = 2, so the point is (8,2)
When x = 20: f(20) = √16 = 4, so the point is approximately (20.4)
So, four points on the graph of f(x) = √x-4 are: (4,0), (5,1), (8,2), and (20,4).
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Justin says that x^-2and -x² are equivalent. Is he
correct? Justify your answer.
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^{-2}\implies \cfrac{1}{x^2}\hspace{5em} {\Large \begin{array}{llll} \ne \end{array}}\hspace{5em}-x^2[/tex]
Without solving, circle the problem that would have the greatest product and tell how you know.
Step-by-step explanation:
you are in college, and need help with that ?
remember,
a > b
then also
a × c > b × c
c × a > c × b
and that is what we have here
a = 20, b = 30, c = 1/2
so, 30×1/2 is larger.
because 30 > 20.
a = 2/3, b = 2, c = 15
15×2 is, of course, larger.
because 2 > 2/3.
A bolynomial function has zeros √2, 4, and 6i. What is the minimum degree of the
polynomial function?
A. 6
B. 5
C. 4
D. 3
Answer:
C) 4
Step-by-step explanation:
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 155 grams of a radioactive isotope, how much will be left after 5 half-lives?
Use the calculator provided and round your answer to the nearest gram.
Answer:
i think its 11.2
Step-by-step explanation:
If a man was born in 1898 how old was he in 1945
Answer: He could be 47 or 46
Step-by-step explanation: I need the exact date of the time he was born (just the month and the day) to tell you how old he really is, but with the information given, he could be 47 or 46.
He would be 47 years [tex]1945\\-\\1898\\=\\47\\[/tex]
Select the correct answer from each drop-down menu.
Chris purchased a new mattress for $1,399. He will need to pay $78 each month on his interest-free loan to pay off the total price of the mattress in 18
months. Separately, Chris sets aside $50 each month in a savings account, which currently shows a balance of $250.
Create an augmented matrix from a system of equations to help Chris determine when he can use monthly payments and savings to pay off the total
purchase price of the mattress,
Row 1
Row 2
Column 1
Column 2
>
Reset
Column 3
Next
>
>
Rewriting the equations in matrix form, we get:
[1 78/1399 | 1]
[50 1 | 1149/1399]
What is square matrix?
A square matrix is a matrix that has the same number of rows and columns. That is, a matrix A is square if A has dimensions n x n, where n is a positive integer.
To create an augmented matrix, we need to represent the system of equations in matrix form. Let x be the number of months it will take Chris to pay off the total purchase price of the mattress using monthly payments and savings. Then the system of equations is:
1399/18 + 78x = 1399
50x + 250 = 1399
The first equation represents the fact that the total price of the mattress must be paid off in 18 months using monthly payments, and the second equation represents the fact that Chris sets aside $50 each month in savings to put towards the purchase.
Rewriting the equations in matrix form, we get:
[1 78/1399 | 1]
[50 1 | 1149/1399]
This is the augmented matrix for the system of equations, where the leftmost columns represent the coefficients of the variables (1 for x in the first equation, 50 for x in the second equation, and 78/1399 for the monthly payment in the first equation), and the rightmost column represents the constants on the right-hand side of each equation.
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Column 1 Column 2 Column 3
Row 1-- 50 -1 -250
Row 2-- 78 1 1,399
I got it right on my test.
Your Welcome:)
A bag contains 9 green marbles, 6 purple marbles, 4 red marbles, 10 blue marbles, and 7 orange marbles. One marble is randomly selected from the bag.
What is the probability that the marble selected is blue or purple?
Answer as a Fraction, not simplified.
So, the answer as a fraction is 16/36.
What is fraction?A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. It is written as one number (the numerator) placed above another number (the denominator) and separated by a horizontal line. For example, 3/4 is a fraction where 3 is the numerator and 4 is the denominator. The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts that make up the whole. Fractions can also be written in decimal or percentage form. Fractions are commonly used in everyday life, such as in cooking recipes, measurements, and financial calculations.
There are 6 purple marbles and 10 blue marbles, so there are 6 + 10 = 16 marbles that are either blue or purple.
The total number of marbles in the bag is 9 + 6 + 4 + 10 + 7 = 36.
Therefore, the probability of selecting a blue or purple marble is 16/36.
So, the answer as a fraction is 16/36
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Show that by the uniqueness theorem the linear transformation,
Y = aX + b, is also a normal random variable.
We can show by the uniqueness theorem that the linear transformation, Y = aX + b, is also a normal random variable because the resultant probaility density fnction of Y equals: f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)).
How to prove a normal random variableTo show that the linear transformation, Y = aX + b is a normal random variable, we need to demonstrate that it satisfies the properties of a normal distribution. This means that it should have a bell-shaped probability density function, mean, and variance.
We can prove that it meets the mean condition this way:
E(Y) = E(aX + b) = aE(X) + b = aμX + b
Next, we can prove that it meets the variance condition thus:
Var(Y) = Var(aX + b) = a^2Var(X) = a^2σX^2
Lastly, the probability density function is given as f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)). This proves that the conditions for a normal random variable is met.
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A private high school advertised that last year their freshman students, on average, had a score of 80 on the high school entrance exam. Assuming that average refers to the mean, which of the following claims must be true based on this information?
Note: More than one statement could be true. If none of the statements is true, mark the appropriate box.
A. All of the freshman students scored 80 or higher on the exam.
B. Most of the freshman students scored 80 or higher on the exam.
C. None of the freshman students scored 80 or higher on the exam.
A. All of the freshman students scored 80 or higher on the exam.
B. Most of the freshman students scored 80 or higher on the exam.
What is the third quartile of this data set? 14, 18, 20, 21, 25, 32, 42, 46, 48