Answer:
B. They are perpendicular to each other
Step-by-step explanation:
Perpendicular Lines are lines that intersect each other and make a (or multiple) right angles or 90°.
Answer:b
Step-by-step explanation:
A 500-gallon water tank drains at a rate of 50 gallons per minute. The amount of water left in the tank depends on the number of minutes it has been draining. What is the range of this relation?
Answer:0<Y<500
The amount of water Left in the thing depends on the number of minutes it’s been draining so the dependent variable is the amount of water left in the tank.
What's 1 trillion to the 10th power
The result of the number 1 trillion to the 10th power as required to be determined is; 10¹²⁰.
What is the result of 1 trillion to the 10th power?The result of the number 1 trillion to the 10th power is as follows;
Recall; 1 trillion = 1,000,000,000,000 = 10¹²
Hence; 1 trillion to the 10th power is; ( 10¹² )¹⁰.
From the laws of indices; we therefore have that;
= 10¹²⁰
Ultimately, the result is; 10¹²⁰.
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Two identical gardens are to be weeded, each by a two-person team. Team A includes one gardener who could weed the garden in 2 h and another who could weed the garden in 4 h. Team B includes two gardeners, either of whom could weed the garden in 3 h. Which team will finish first? Explain.
Step-by-step explanation:
Team A time is 1 garden / ( 1 garden/ 2 hr + 1 garden/4 hr) = 1 1/3 hr
Team B = 1 / ( 1/3 + 1/3) = 1 1/2 hr
Team A wins !
For an investment of 26,245, a quarterly statement reports that the account is 26,292. The statement reports that for the same quarter, the rate of return of the investment was - 0.02%. Given the information regarding the investment quarterly activity, does the reported rate of return seem reasonable?
No. The reported return rate appears lower than expected.
Rate of returnsTo determine whether the reported rate of return is reasonable or not, we can calculate the expected rate of return based on the investment amount and the ending value of the account.
First, we need to calculate the total number of quarters that have elapsed between the initial investment and the current quarter. Let's assume that the investment has been held for n quarters.
Then, we can use the following formula to calculate the expected rate of return:
Expected rate of return = (Ending value / Initial investment) ^ (1/n) - 1
Plugging in the given values, we get:
n = 1 (since we are only given information for a single quarter)
Initial investment = 26,245
Ending value = 26,292
Expected rate of return = (26,292 / 26,245) ^ (1/1) - 1 = 0.18%
Comparing the expected rate of return of 0.18% with the reported rate of return of -0.02%, we can see that they are quite different. However, it's important to note that a single quarter's rate of return may not be indicative of the overall performance of the investment.
Therefore, while the reported rate of return seems lower than expected, we would need to consider the performance over a longer period of time to make a more informed assessment of the investment's performance.
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(TONS OF POINTS AND BRAINLYEST)
Please answer the question that is stated in the image below. Thank you. It really means a lot to me.
Answer:
Below
Step-by-step explanation:
a) they won 120 games out of 369 played = 40/23=.325
b) they lost 248 out of 369 played = 248/369 = .672
c) Home games are 185 out of 369 = .501
d ) at home they won 72 out of (72+112+1) = 72/ 185 = .389
A survey found that women's heights are normally distributed with mean 63.6 in and standard deviation 2.5 in. A branch of the military requires women's heights to be between 58 in and 80 in.
a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?
b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?
Answer:
(A)
Step-by-step explanation:
The survey follows of women's height a normal distribution.
The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.
The new height requirements would be 57.7 to 68.6 inches
The given parameters are:
\mathbf{\mu = 63.5}μ=63.5 --- mean
\mathbf{\sigma = 2.5}σ=2.5 --- standard deviation
(a) Percentage of women between 58 and 80 inches
This means that: x = 58 and x = 80
When x = 58, the z-score is:
\mathbf{z= \frac{x - \mu}{\sigma}}z=
σ
x−μ
This gives
\mathbf{z_1= \frac{58 - 63.5}{2.5}}z
1
=
2.5
58−63.5
\mathbf{z_1= \frac{-5.5}{2.5}}z
1
=
2.5
−5.5
\mathbf{z_1= -2.2}z
1
=−2.2
When x = 80, the z-score is:
\mathbf{z_2= \frac{80 - 63.5}{2.5}}z
2
=
2.5
80−63.5
\mathbf{z_2= \frac{16.5}{2.5}}z
2
=
2.5
16.5
\mathbf{z_2= 6.6}z
2
=6.6
So, the percentage of women is:
\mathbf{p = P(z < z_2) - P(z < z_1)}p=P(z<z
2
)−P(z<z
1
)
Substitute known values
\mathbf{p = P(z < 6.6) - P(z < -2.2)}p=P(z<6.6)−P(z<−2.2)
Using the p-value table, we have:
\mathbf{p = 0.9999982 - 0.0139034}p=0.9999982−0.0139034
\mathbf{p = 0.9860948}p=0.9860948
Express as percentage
\mathbf{p = 0.9860948 \times 100\%}p=0.9860948×100%
\mathbf{p = 98.60948\%}p=98.60948%
Approximate
\mathbf{p = 98.61\%}p=98.61%
This means that:
The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.
So, many women (outside this range) would be denied the opportunity, because they are either too short or too tall.
(b) Change of requirement
Shortest = 1%
Tallest = 2%
If the tallest is 2%, then the upper end of the shortest range is 98% (i.e. 100% - 2%).
So, we have:
Shortest = 1% to 98%
This means that:
The p values are: 1% to 98%
Using the z-score table
When p = 1%, z = -2.32635
When p = 98%, z = 2.05375
Next, we calculate the x values from \mathbf{z= \frac{x - \mu}{\sigma}}z=
σ
x−μ
Substitute \mathbf{z = -2.32635}z=−2.32635
\mathbf{-2.32635 = \frac{x - 63.5}{2.5}}−2.32635=
2.5
x−63.5
Multiply through by 2.5
\mathbf{-2.32635 \times 2.5= x - 63.5}−2.32635×2.5=x−63.5
Make x the subject
\mathbf{x = -2.32635 \times 2.5 + 63.5}x=−2.32635×2.5+63.5
\mathbf{x = 57.684125}x=57.684125
Approximate
\mathbf{x = 57.7}x=57.7
Similarly, substitute \mathbf{z = 2.05375}z=2.05375 in \mathbf{z= \frac{x - \mu}{\sigma}}z=
σ
x−μ
\mathbf{2.05375= \frac{x - 63.5}{2.5}}2.05375=
2.5
x−63.5
Multiply through by 2.5
\mathbf{2.05375\times 2.5= x - 63.5}2.05375×2.5=x−63.5
Make x the subject
\mathbf{x= 2.05375\times 2.5 + 63.5}x=2.05375×2.5+63.5
\mathbf{x= 68.634375}x=68.634375
Approximate
\mathbf{x= 68.6}x=68.6
Hence, the new height requirements would be 57.7 to 68.6 inches
Insert parts a through E for the functions shown below
Factor x square on the function on the function
\(f(x)=x^2\cdot(6+x)\)then, equal the expression to 0 in order to find the x-intercepts
\(0=x^2\cdot(6+x)\)finally, if the product is equal to 0 it means that at least one of them is equal to 0
\(\begin{gathered} x^2=0 \\ x=0 \\ 6+x=0 \\ x=-6 \end{gathered}\)The graph of the function touches the x-axis and turns around at
x=0,-6.
21% of the animals at an animal shelter are dogs. About what fraction of the animals at the shelter are dogs
About 21% of the animals at an animal shelter are dogs, which can be written as the fraction 21/100 or simplified to 3/14.
To convert the percentage of dogs at the animal shelter to a fraction, we can write 21% as a ratio of 21 dogs for every 100 animals.
This means that for every 100 animals at the shelter, there are 21 dogs. To express this as a fraction, we can write 21/100.
So, about 21/100 of the animals at the shelter are dogs. This fraction can be simplified to 3/14, which means that out of every 14 animals at the shelter, there are 3 dogs.
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Robert's book bag is weighing him down. His bag alone weighs 4 pounds. His library book
weighs 2 pounds. The math book is 4 times the weight of the library book, and his science
book is 2 times the weight of the math book. How much does his book bag weigh with all
these books? What is the heaviest book in his book bag?
Answer:
1) 30 pounds is the weight of the bag all together
2) science book is the heaviest book
Step-by-step explanation:
bag=4 pounds
library book=2 pounds
maths book=2×4=8 pounds
science book=8×2=16 pounds
4+2+8+16=30 pounds all together
heaviest book= science book (16 pounds)
x squared plus 2x factorised
Answer:
x(x+2)
Step-by-step explanation:
Answer x(x+2)
Step-by-step explanation:
simplify this complex fraction 4/3/2/5
Answer:
If the question is (4/3) / (2/5), then the answer is 10/3 or 3 and 1/3
Step-by-step explanation:
a, b, and c are positive real numbers;
a×b= 5742×6368
a×c= 5748×6362
c×b= 5738×6372
?<?<?
And please clarify your answers in a simple language
Given the equations a × b = 5742 × 6368, a × c = 5748 × 6362, and c × b = 5738 × 6372, we need to determine the relationship between the three variables a, b, and c.
By comparing the given equations, we notice that the numbers on the right-hand side of each equation are very close to each other, differing only by small amounts. This suggests that a, b, and c are approximately equal.Since a × b, a × c, and c × b involve the same numbers with slight variations, we can conclude that a, b, and c are all very close in value.
Therefore, the inequality we can infer from this information is a ≈ b ≈ c, indicating that a, b, and c are approximately equal.
In simple terms, based on the given equations, it suggests that the values of a, b, and c are very similar or approximately equal to each other.
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Find a value a > 0 so that the graph of the exponential function f(x) = a^x contains the point
(2,1/16).
a =
I NEED HELP PLEASE ITS FOR MATH!!!
Answer:
5x+3y=-6
Step-by step explanation:
(-3,3) (3,-7)
Slope=(-7-3)/(3-(-3))=-10/6=-5/3
y=mx+c
y=-5/3*x-2[from graph]
y=-5x-6/3
3y=-5x-6
3y+5y=-6
5x+3y=-6
Answer:
Step-by-step explanation:
y = mx + b
slope m = Δy/Δx = (-7 - 3) / (3 - (-3)) = -10/6 = -5/3
y intercept is read directly from the chart at x = 0
b = -2
y = (-5/3)x - 2
X+X+(60% of X)=180
Ez points plus brainliest
Answer:
x = 900/ 10 + 3fo
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
For the rhombus below, find the measures of ∠1, ∠2, ∠3, and ∠4.
Answer:
∠1 = 116 ° , ∠2 = 32° , ∠3 = 116 ° and ∠4 = 32°
Step-by-step explanation:
∠2 = 32° (The diagonals of a rhombus bisect pairs of opposite angles)
Opposite sides of a rhombus are parallel ,so
∠2 = ∠4 (Alternate interior angles )
∠4 = 32°
32° + ∠4 + ∠3 = 180° (angle sum property of a triangle)
64° + ∠3 = 180°
∠3 = 180 - 64
∠3 = 116°
∠3 =∠1 (in a rhombus opposite angles are equal )
∠1 = 116°
Addicted to the Internet?The Ann Arbor public school officials would like to estimate the population mean daily Internet usage time for all Ann Arbor teens. To do so, a large random sample of Ann Arbor teens was selected. Here are the results of their study. The 95% confidence interval for the mean daily internet usage time for the population of all such Ann Arbor teens was found to be (6.7 hours, 9.3 hours).The 99% confidence interval or the mean daily internet usage time for the population of all such Ann Arbor teens was found to be (6.257 hours, 9.743 hours).The Ann Arbor public school officials know that you have some statistical background and would like your opinion. Please read each statement carefully and share with us your opinion.
Answer:
We can assure the Ann Arbor officials that after look the information we conclude that the mean is 8 h
Step-by-step explanation:
From CI ( 95 % ) = ( 6,7 ; 9,3 )
And the information "large random size sample" we conclude that the population has a normal distribution; a normal distribution has a bell shape curve, and data must spread symmetrically with respect to the mean, therefore the mean is:
6,7 + 9,3 = 16
16/2 = 8
If we need t check we can use the other CI
CI ( 99 % ) = (6,257 , 9,743 )
6,257 + 9,743 = 16
16/2 = 8
We are sure the mean is 8 h
Listed below is a table showing the number of employees. 20 years or older by gender in the United states
The total number of workers that were studied can be found to be 139,340,000.
The percent of workers unemployed would be 5. 4 %.
Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.
How to find the employment figures ?Number of employed workers :
= 74,624,000 + 64, 716, 000
= 139,340,000
Percentage unemployed :
= ( 4, 209,000 + 3,314,000 ) / 139,340,000
= 5. 4 %
Percentage of unemployed men :
= 4,209,000 / 74,624,000
= 5.6 %
Percentage of unemployed women:
= 3,314,000 / 64, 716, 000
= 5. 1 %
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The full question is:
a. How many workers were studied?
b. What percent of the workers were unemployed?
c. Compare the percent unemployed for the men and the women.
unit 4: congruency triangles
Answer:
What about congruency triangles i think you need a picture so we can see
Step-by-step explanation:
A fair die with its faces numbered from 1 to 6 will be rolled. Which of the following is the best interpretation of the probability that the number landing face up will be less than 3?
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/3
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/2
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3
For three rolls of the die, a number less than 3 will land face up one time.
It will take three rolls of the die before a number less than 3 lands face up for the first time.
The best interpretation of the probability that the number landing face up will be less than 3 is \(\frac{1}{3}\).
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is \(\frac{1}{3}\).
As per the given question a fair die with its faces numbered from 1 to 6 will be rolled.
Here we have to calculate the probability that the number landing face up will be less than 3.
The event of the number landing face up will be less than 3 is exhaustive, mutually exclusive, and independent face of a die = 6
(1, 2, 3, 4, 5, 6)
Favorable number of faces of a die = 2
(1, 2)
Since the number landing faces up will be less than 3.
Therefore the probability that the number landing face up will be less than 3
\(=\frac{\text { Favourable Number }}{\text { Total Number }}$\)
\(& =\frac{2}{6} \\\)
\(& =\frac{1}{3}\)
Therefore the best interpretation of the probability that the number landing face up will be less than 3 is \(\frac{1}{3}\)
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The long-run relative frequency of a number less than 3 landing face up is 2/3.
The best interpretation of the probability that the number landing face up will be less than 3 is that for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3. This can be expressed mathematically as P(x<3) = 2/3, where P(x) is the probability of the number landing face up being less than 3.
For a single roll of the die, the probability of a number less than 3 landing face up is 1/2. This is because there are three numbers (1,2,3) which are less than 3, and 6 possible outcomes. Therefore, the probability of any one of those three numbers landing face up is 3/6, or 1/2.
For multiple rolls of the die, the probability of a number less than 3 landing face up is the sum of the probabilities of each of those three numbers landing face up. This can be expressed mathematically as P(x<3) = (1/2) + (1/2) + (1/2), or 2/3.
Therefore, for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3.
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Statement True False There are whole numbers that are not integers.
True!
your very welcome
Write an expression, using an exponent, that is equivalent to 8×8×8×8
Answer:
8 to the power of 4
Step-by-step explanation:
since their are four 8, (8x8x8x8) , you have to put that into an exponent
still need proof?
8x8x8x8=4096
8 to the power of 4 = 4096
so to conclude, 8 to the power of 4 is the same thing as saying 8x8x8x8, it is jsut the exponent version
$8 is what percent of $8?
Answer:
100%?
Step-by-step explanation:
What is the volume of a sphere, to the nearest cubic inch, if the radius equals 5 inches? Use π = 3.14.
Answer:
V = 523 in^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
V = 4/3 ( 3.14) * 5^3
V = 523.33333repeating
Rounding to the nearest inch^3
V = 523 in^3
Answer:
\( 523.6 {in}^{3} \)
Step-by-step explanation:
\(v = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \pi \times 5 \times 5 \times 5 \\ = 523.6 {in}^{3} \)
translate then solve:five times the difference of twice and number and three decreased by the sum of the number and 8 equals 13
Answer: x = 4
Step-by-step explanation:
Translating the problem into mathematical terms:
Let's call the number x. Then the problem can be written as:
5 * (2x - 3) - (x + 8) = 13
Expanding the left side of the equation:
5 * 2x - 5 * 3 - x - 8 = 13
Simplifying the left side of the equation:
10x - 23 - x - 8 = 13
Combining like terms:
9x - 31 = 13
Adding 31 to both sides of the equation:
9x = 44
Dividing both sides of the equation by 9:
x = 4.88888...
Since x has to be a whole number, we round down to the nearest whole number:
x = 4
Therefore, the number that satisfies the equation is 4.
please help me with this
Answer:
F
Step-by-step explanation:
64x³ = -1
x³ = -1/64
x = ∛-1/∛64
x = -1/4
Answer:
x = - \(\frac{1}{4}\)
Step-by-step explanation:
64x³+1=0
Add 1 to both sides:
64x³=-1
Divide both sides by 64:
x³=-\(\frac{1}{64}\)
Find cubed root of both sides:
x=-\(\sqrt[3]{\frac{1}{64}}\)
Note that \(\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}\) :
x=-\(\frac{\sqrt[3]{1} }{\sqrt[3]{64} }\)
Evaluate:
x = - \(\frac{1}{4}\)
A family has a combined monthly income of $1590. Their food budget is $260/month. What percentage of their monthly income is budgeted for food? (Round your answer to
Approximately % is budgeted for food.
the nearest whole percent)
In a classroom, 100 plastic fish are in a tub. The tub is hidden from the student view. Some fish are green, and the rest are yellow. The students know that there are 100 fish, but they don’t know how many of each color there are. The students go fishing, each time, picking a random fish from the tub, recording its color, and throwing the fish back in the tub. At the end of the day, 65 fish have been chosen, 12, green and 53 yellow. What is the best estimate you can give for the number of green fish in the number of yellow fish in the tub? Describe how to calculate this best estimate, and explain why your method of calculation makes sense in a way that a seventh grader my understand. Is your best estimate necessarily accurate? Why or why not?
The best estimate for the number of fish is that there are 82 yellow fish and 18 green fish, which you can calculate using the rule of three. This estimate is expected to be accurate.
What is the estimated number of fish of each color?This can be calculated using a rule of three as follows. Let's start with the yellow fish:
53 = 65
x = 100
53 x 100 / 65 = 82 yellow fish
Green fish:
12 = 65
x = 100
12 x 100 / 65= 18 green fish
Is this estimate accurate?This estimate is expected to be accurate; however, there might be small differences in real life such as 80 yellow fish and 20 green fish.
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Someone please help answer !
Choose the number that is closest to the mean of the distribution
The mean of the distribution is 3
What is arithmetic mean?Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean. One of the basic methods used to acquire a result, the term "Mean" is commonly used in the field of statistics.
The formula for the mean of a given set of data is as follows:
Mean = Sum of Observations/Total number of observations
According to the first graph,
Given the bar of observations as :
0, 5, 6, 3, 1, 1, 3, 6, 4, 1
Here the Sum of Observations = 30
And the total number of observations = 10
The mean of the distribution = 30/10
The mean of the distribution = 3
According to the second graph,
Given the bar of observations as :
0, 1, 3, 3, 9, 0, 9, 4, 4, 1
Here the Sum of Observations = 34
And the total number of observations = 10
The mean of the distribution = 34/10
The mean of the distribution = 3.4
The mean of the distribution = 4 (closest)
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if n = 4 then σ(4)=1+2+4=7 and H4 = 1+1/2+1/3+1/4. Solve this equation to either prove or disprove the following inequality n≥1? Does it hold for all n≥1?
Using the method of mathematical induction, we show that the inequality σ(n) > H(n) holds for all n≥1. Thus, the inequality n≥1 is true for all n≥1.
What is mathematical induction?It is a a technique used in mathematics to prove that a statement is true for every positive integer or natural number. It consists of two steps:
Base case: Prove that the statement is true for the first positive integer (usually 1).Inductive step: Assume that the statement is true for some arbitrary positive integer k, and then prove that it must also be true for the next positive integer (k+1).We can calculate like this:
Base case: Show that the inequality holds for n=1.
When n=1, we have σ(1) = 1 and H1 = 1, so the inequality 1 ≤ 2^(σ(1)/H1) becomes 1 ≤ 2^(1/1), which is true.Inductive hypothesis: Assume that the inequality holds for some arbitrary positive integer k, i.e., k ≤ 2^(σ(k)/Hk).
Inductive step: Show that the inequality also holds for k+1. Consider σ(k+1) and H(k+1). We can express them as σ(k+1) = σ(k) + k+1 and H(k+1) = H(k) + 1/(k+1).
Using the inductive hypothesis, we have:
k ≤ 2^(σ(k)/Hk),So, we can raise both sides to the power of (k+1)/(kH(k+1)) to get:
k^(1/(kH(k+1))) ≤ 2^((k+1)/(kH(k+1)) * σ(k)/Hk).By the AM-GM inequality, we know that σ(k+1)/k+1 ≥ H(k+1), so we can replace the denominator (kH(k+1)) with H(k+1) and simplify to get
k^(1/H(k+1)) ≤ 2^(σ(k+1)/H(k+1)).Therefore, we have shown that k+1 ≤ 2^(σ(k+1)/H(k+1)), which means the inequality holds for all positive integers n by mathematical induction.
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