Answers
Answer:
7) x= 8[tex]\sqrt{3}[/tex] y= 8
8) x= 10[tex]\sqrt{3}[/tex] y= 15
9) x= 22 y= 11[tex]\sqrt{3}[/tex]
10) x= 4 y= 4[tex]\sqrt{3}[/tex]
11) x= 6[tex]\sqrt{3}[/tex] y= 12[tex]\sqrt{3}[/tex]
12) x= 13 y= 26
Step-by-step explanation:
Just use your 30, 60, 90 triangle rules:
hypotenuse= 2x the shortest leg (the one opposite the angle measuring 30 degrees)
longer leg= the shortest leg times [tex]\sqrt{3}[/tex]
to find shortest leg, substitute the variables
Related Questions
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.
Answers
A 3D modeling software can be useful for creating plans for the space station because it allows for the creation of detailed 3D models that can be easily manipulated and viewed from different angles. This can make it easier to visualize different configurations of the modules and to experiment with different shapes and sizes for the space station.
In addition, many 3D modeling software options have built-in tools for creating and manipulating shapes, which can be useful for designing the space station. For example, software such as SketchUp offers a wide range of tools for creating different shapes, including extruding, curving, and stretching. This can make it easier to create complex shapes for the space station that incorporate the 24 modules.
Another tool that could be used is graph paper and pencil. While this method may be less precise and less visually appealing than 3D modeling software, it is a low-tech option that can be useful for quickly sketching out different ideas and configurations. Graph paper can be useful for ensuring that the modules are lined up correctly and are the s
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.
Answers
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 with this math question!
Answers
Answer:
[tex]2000 {(1 + \frac{.07}{12}) }^{5 \times 12} = 2835.25[/tex]
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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.
Answers
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.
Find the measure or 3
Answers
The measure of angle 3 is 48°
How to find the measure of angle 3?We can see that both horizontal lines are parallel, then the measure of angle 3 and the angle below it (the 132° one) must add up to 180°.
Then we can write:
∠3 + 132° = 180°
And solve this equation for the measure of angle 3.
∠3 = 180° - 132° = 48°
That is the measure.
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What is the value of x?
Answers
Answer:
55°
Step-by-step explanation:
the total sum of a triangle is 180.
75+50= 125
180-125= 55
& since x is an acute angle we know x is less than 90.
How could expanded land acreage and pricing be viewed as some to be a bad thing
for the recovering Great Plains?
Answers
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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Justin says that x^-2and -x² are equivalent. Is he
correct? Justify your answer.
Answers
[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]
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.
Answers
Answer:
i think its 11.2
Step-by-step explanation:
Plsss help!!! I can’t figure this out
Answers
The volume of the solid figure is 1795.5 metres squared. Therefore, the answer is d.
How to find the volume of a figure?The volume of the figure is the area of the base multiplied by the height of the figure.
Therefore, let's find the volume of the figure as follows:
volume of the figure = area of the base × height of the figure
area of the base =1 / 2 (a + b)h
where
a and b are the basesh = heightTherefore,
area of the base =1 / 2 (a + b)h
area of the base = 1 / 2 (11 + 16)9.5
area of the base = 128.25
Therefore,
volume of the figure = area × height
volume of the figure = 128.25 × 14
volume of the figure = 1795.5 metres squared
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Which expression is equivalent to 2.5+3a - 20-9.5?
A: 5.5a - 29.5
B: 3a - 32
C: 3a - 27
D: 5.5a - 10.5
Answers
Answer: C - 3a - 27
Step-by-step explanation:
We start with 2.5 + 3a - 20 - 9.5, and first solve for variables:
3a
Then we solve for constants:
2.5 - 20 - 9.5 = 2.5 - 29.5 = -27
Add the two together:
3a - 27
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.
Answers
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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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.
Answers
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:
Evaluate the expression.
20.4 0.2
Write your answer as an integer or a decimal. Do not round.
Answers
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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PLEASE HELP I NEED THIS SO I DONT GET KICKED :,)
Determine the Direction and Degree of Rotation used to create the image
90° Counterclockwise
270° Clockwise
90° clockwise
180° Clockwise
Answers
Answer:
270 counter clockwise I think I'm not sure though
A car was valued at $38,000 in the year 1994. The value depreciated to $14,000 by the year 2004.
A) What was the annual rate of change between 1994 and 2004?
r =
Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r= %.
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2007 ?
value = $
Round to the nearest 50 dollars.
Answers
r = (V2/V1)^(1/n) - 1
where V1 is the initial value, V2 is the final value, n is the number of years, and r is the annual rate of change (expressed as a decimal).
Plugging in the given values, we get:
r = (14000/38000)^(1/10) - 1
r ≈ -0.1102
So the annual rate of change between 1994 and 2004 is approximately -0.1102.
B) To convert the rate to a percentage, we can multiply by 100:
r ≈ -11.02%
So the correct answer to part A written in percentage form is approximately -11.02%.
C) To find the value of the car in 2007, we can use the formula:
V = V0*(1+r)^n
where V0 is the initial value, r is the annual rate of change (expressed as a decimal), n is the number of years, and V is the final value.
We want to find the value in 2007, which is 3 years after 2004. So we plug in:
V0 = 14000 (since that was the value in 2004)
r = -0.1102 (the annual rate of change)
n = 3 (the number of years since 2004)
V = 14000*(1-0.1102)^3
V ≈ $9,679.65
Rounding to the nearest 50 dollars, we get:
value ≈ $9,700
Therefore, the value of the car in the year 2007 is approximately $9,700.
What are the domain and range of the function?
f(x) = -3√x
Answers
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
The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.
What was the initial mass (in mg) of the sample? --------------
What is the mass 7 weeks after the start?-------------
Answers
the initial mass of the sample was 32 mg. the mass of the sample 7 weeks after the start is approximately 0.8384 mg.
What is a half-life?
the amount of time it takes for half of a radioactive substance to decay the amount of time it takes for all of a radioactive substance to decay half the time it takes for a radioactive substance to break down the reactive half of a radioactive substance
We can use the half-life formula to solve this problem. The formula is:
[tex]mass = initial mass * (1/2)^{\frac{time}{half-life} }\\[/tex]
where:
mass: the final mass of the sample
initial mass: the initial mass of the sample
time: the time that has elapsed since the start
half-life: the half-life of the substance
Let's use the formula to find the initial mass of the sample:
[tex]2 \ mg = initial mass * (1/2)^(16/4)\\\\2 = initial mass * (1/2)^4\\\\2 = initial mass * 1/16\\\\initial mass = 2 * 16 = 32 mg[/tex]
Therefore, the initial mass of the sample was 32 mg.
7 weeks × 7 days/week = 49 days
Then we can use the half-life formula again:
[tex]mass = initial mass * (1/2)^{(time/half-life)}[/tex]
[tex]mass = 32 \ mg * (1/2)^{(49/4)}[/tex]
mass = 32 mg × 0.0262
mass ≈ 0.8384 mg
Therefore, the mass of the sample 7 weeks after the start is approximately 0.8384 mg.
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If a man was born in 1898 how old was he in 1945
Answers
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]
If the sum of a number and eight is tripled, the result is four less than twice the number. Find the number.
Answers
x = −26
Explanation screen shot inserted below:
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.
Answers
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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What is the third quartile of this data set? 14, 18, 20, 21, 25, 32, 42, 46, 48
Answers
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?
Answers
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:
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
Answers
Answer:
C) 4
Step-by-step explanation:
Can someone help me with as many as possible (even one is ok) please
Answers
Answer:
7.30
Step-by-step explanation:
number 13 is simple subtraction.
Order each amount from least to greatest
1 pint, 2 gallons, 3 quarts, 3 cups
Answers
what number is 1/2% of 96? round the answer to the nearest hundredth if necessary.
Answers
1/2% is read as 1.2 out of one hundred
so divide 100/1.2 which the answer would be 83.33333333 or 83.3
please help me in this question is math,solve just d, e&f
Answers
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
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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
Answers
Answer:
0.077
Step-by-step explanation:
The manager of a company wants to find out how many hours the employees worked in the previous month. Which of the following is a statistical question that the manager can ask?
Answers
It only seeks a single value and does not involve collecting data to draw general conclusions.
Which of the following is a statistical question that the manager can ask?"Which employee worked the most hours in the previous month?" is not a statistical question because it only seeks a single value and does not involve collecting data to draw general conclusions.
On the other hand, "What is the average number of hours worked by employees in the previous month?" is a statistical question because it involves collecting data on all employees and using it to draw general conclusions about the entire workforce.
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