Match each relationship on the right with the correct description on the
left.
Direct
variation
Indirect
variation
Joint
variation
The amount of time it takes to
drive some place depends on
the distance.
The volume of a can depends
on its radius and on its height.
The time it takes to shingle a
roof depends on how many
workers are helping shingle the
roof.
Each relationship should be matched with the correct description as follows:
Direct variation: the amount of time it takes to drive some place depends on the distance.Joint variation: the volume of a can depends on its radius and on its height.Indirect variation: the time it takes to shingle a roof depends on how many workers are helping shingle the roof.What is direct variation?Direct variation can be defined as a type of proportional relationship in which a variable is directly proportional to another variable.
What is an indirect variation?An indirect variation can be defined as a type of proportional relationship in which a variable is inversely proportional to another variable. This ultimately implies that, an indirect variation represents two variables that are inversely proportional to each other.
In conclusion, a joint variation describes a situation in which a variable depends on two other variables which share a directly proportional relationship.
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What is the contrapositive of the following statement?
"If it does not have four legs, then it is a fish."
If it is a fish, then it does not have four legs.
If it has four legs, then it is not a fish.
If it is not a fish, then it has four legs.
If it does not have four legs, then it is not a fish.
The contrapositive statement of "If it does not have four legs, then it is a fish." is "If it is not a fish, then it has four legs" .Option C
What is a contrapositive statement?A contrapositive statement is simply defined as a law or rule obtained by contradicting the conclusion and hypothesis of a statement.
It includes the exchange of both the hypothesis and conclusion of a particular conditional statement before negating both the hypothesis and conclusion.
It is also known for the combination of a converse and an inverse statement.
The hypothesis and conclusion are switched or interchanged
A contrapositive statement is represented as;
x y is equivalent to y ~x
Given the statement:
"If it does not have four legs, then it is a fish."
The contrapositive statement would be;
If it is not a fish, then it has four legs.
We can see that the hypothesis and conclusion were interchanged accordingly.
Hence, the statement is "If it is not a fish, then it has four legs"
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Answer: C: If it is not a fish, then it has four legs.
Step-by-step explanation: Hope that helped!
HELP i forgot how to do probability omg
The tree diagram of the outcomes and the number of possibilities is added as an attachment
How to make the tree diagram for the probability?The given parameters are:
Red balls = 6
Blue balls = 4
This means that the total number of balls is
Total number of balls = Red balls + Blue balls
Substitute the known values in the above equation
So, we have the following equation
Total number of balls = 6 + 4
Evaluate the sum in the above equation
So, we have the following equation
Total number of balls = 10
From the question, we understand that the selection is without replacement, and the number of selections is 2
This means that the sample space in total selections is
{RR, RB, BR, BB}
Where
B represents blue and R represents red
Next, we use the sample space {RR, RB, BR, BB} to make the required tree diagram
See attachment for the tree diagram
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a container is in the shape of a square based prism with base measurement of 3m and the height is 5m. The top and bottom are made of steel and the sides are made of aluminum. If steel costs $2.95/m^ and aluminum costs $1.57/m^, how much would it cost to make the container?
The cost for making the container is $28. 27
How to determine the cost of the containerFrom the information given, we have that;
The base of the square prism is 3mThe height of the square prism is 5mWe also have the following deductions;
The top and bottom are made of steelThe sides of the square prism are made of aluminumThe properties of a square prism are;
It has 8 vertices, 6 faces and 12 edgesOpposite sides are parallel to each otherOpposite sides are equal to each otherOpposite angles are equal each otherThe diagonals of the prism bisect each otherThe cost for aluminum = 10($1.57)
expand the bracket
The cost for aluminum = $10. 57
The cost for steel = 6($2.95)
The cost for steel = $17. 7
Total cost for the container = $10. 57 + $17. 7
Total cost for the container = $28. 27
Hence, the cost is $28. 27
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the switchboard in a minneapolis law office gets an average of 5.5 incoming phone calls during the noon hour on mondays. experience shows that the existing staff can handle up to six calls in an hour. let x
On Mondays at noon, the switchboard in a Minneapolis legal firm receives an average of 5.5 incoming calls. Consequently, X's standard deviation is 2.35 calls.
The current personnel can handle up to six calls in an hour, according to experience.
A Poisson distribution with an average number of calls of 5.5 on Mondays around lunchtime can be used to model the scenario that is being given.
Thus, the following equation represents the standard deviation for the number of calls received, X:
2.35 calls make up the standard deviation of X.
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Write the numbers below (expressed in expanded form) in standard form.
500,000 +90,000+ 6000+600 + 80 + 1
900,000+ 50,000+6000+800+ 10 +6
90,000+ 6,000+0+0+1
60,000,000+ 9.000,000+ 500,000+ 90,000+ 6.000 + 100+60 + 8
1,000+ 900+50 +8
90 000,000+ 5.000.000 + 500,000+ 90,000+ 6.000+600 + 10 + 8
Answer:
1. 596,681
2. 956,816
3. 96,001
4. 69,596,168
5. 1958
6. 95,596,618
Step-by-step explanation:
1. 500,000 + 90,000 + 6000 + 600 + 80 + 1 = 596,681
2. 900,000 + 50,000 + 6000 + 800 + 10 + 6 = 956,816
3. 90,000 + 6,000 + 0 + 0 + 1 = 96,001
4. 60,000,000 + 9,000,000 + 500,000 + 90,000 + 6.000 + 100 + 60 + 8 = 69,596,168
5. 1,000 + 900 + 50 + 8 = 1958
6. 90,000,000 + 5,000,000 + 500,000 + 90,000 + 6,000 + 600 + 10 + 8 = 95,596,618
I hope this helps!
Does the function f of x equals 3 times the quantity 1 over 2 end quantity to the x power represent growth or decay? what is the y-intercept of f(x)? growth; 0 comma one-half growth; (0, 3) decay; 0 comma one-half decay; (0, 3)
For the exponential function f(x) = 3(0.5)^x, we have that:
The function represents exponential decay.The y-intercept of the function is given by point (0,3).What is an exponential function?An exponential function is modeled according to the rule given below:
[tex]y = ab^x[/tex]
In which the parameters are described as follows:
a is the initial value of the function, hence the y-intercept is of (0,3).b is the rate of change of the function, determining if it represents exponential growth (|r| > 1) or exponential decay (|r| < 1).For this problem, the rule of the exponential function is given by:
y = 3(0.5)^x.
Hence the parameters are:
a = 3, b = 0.5.
Then:
The function represents exponential decay, as |b| = 0.5 < 1.The y-intercept of the function is given by point (0,3), as the coefficient a has a value of a = 3.More can be learned about exponential functions at https://brainly.com/question/25537936
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Answer:
decay; (0,3)
Step-by-step explanation:
Lily is behind on her homework. The ritualistic teacher assigned exactly 5 homework assignments every day for the past 9 learning days. Here is the amount of homework assignments Lily has been able to get done each night (if she didn’t finish some of the 5 assignments from the night before, she would start work on them the next day): 3, 6, 2, 4, 3, 7, 1, 3, 2. If Lily doesn’t finish all her assignments, she won’t be able to go on a fun field trip next month. Lily can’t do more than 10 assignments in one night. There is one more homework night, with 5 more assignments. Can Lily still make it to the field trip?
Answer:
she cannot go on the field trip.
Step-by-step explanation:
Day 1 = 5, done = 3, remaining = 2.
Day 2 = 2 + 5, done = 6, remaining = 1
Day 3 = 1 + 5, done = 2, remaining = 4
Day 4 = 4 + 5, done = 4, remaining = 5
Day 5 = 5 + 5, done = 3, remaining = 2 + 5
Day 6 = 2 + 5 + 5, done = 7, remaining = 5
Day 7 = 5 + 5, done = 1, remaining = 4 + 5
Day 8 = 4 + 5 + 5, done = 3, remaining = 1 + 5 + 5
Day 9 = 1+ 5+ 5+ 5, done = 2, remaining = 4+5+5
Day 10 = 4+5+5+5, done = 10(maximum assignment done assumed), remaining = 4 + 5
At the end of day 10, she had 9 remaining assignments, so she cannot go on the field trip.
A tablet data provider offers different plans for data usage. The plan Raul chose has a monthly fee of $29.99 per month for 5 GB of data with an additional cost of $10 for each gigabyte over 5
The minimum number is 9 GB to make the unlimited cheaper.
What is a gigabyte?A gigabyte is a specific unit of data that's equal to about 1 billion bytes of data. The term gigabyte is typically used to describe the amount of stored data or the capacity of a storage device. For example, an HDD might offer 500 GB of raw capacity but is currently storing only 200 GB of data.
Given that,
A tablet data provider offers different plans for data usage
The plan Raul chose has a monthly fee of $29.99 per month for 5 GB of data with an additional cost of $10 for each gigabyte over 5.
Assume that he will use n gigabyte per month
The monthly fee is $29.99 for 5 GB
∵ The cost per GB after the first 5 GB is $10
∵ The number of GB whose cost is $10 is (n - 5)
∴ His monthly fees = 29.99 + 10 (n - 5) ⇒ current plan
The fees of the unlimited is $59.99 per month
∵ We need the unlimited cheaper than current plane
Let the current plan greater than the unlimited plan
∴ 29.99 + 10 (n - 5) > 59.99
Subtract both sides by 29.99
∴ 10 (n - 5) > 30
Divide both sides by 30
∴ n - 5 > 3
Add both sides by 5
∴ n > 8
Hence, The minimum number is 9 GB to make the unlimited cheaper.
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What is the distance between (8,-3) and (4, -7)?
Choose 1 answer:
6
9
√32
√42
Answer:
C. 32Step-by-step explanation:
Use the distance formula.
Distance:
[tex]\Rightarrow \sf{\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}}[/tex]
y₂=(-7)
y₁=(-3)
x₂=4
x₁=8
[tex]\sf{\sqrt{\left(4-8\right)^2+\left(-7-\left(-3\right)\right)^2}}[/tex]
Solve.
Use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtractDo parentheses first.
(4-8)=-4
[tex]\sf{\left(-4\right)^2+\left(-7-\left(-3\right)\right)^2}[/tex]
-7-(-3)=-7+3
-7+3=-4
[tex]\sf{\left(-4\right)^2+\left(-4\right)^2}[/tex]
Do exponents.
[tex]\sf{(-4)^2=4^2=4*4=16}[/tex]
Then, you add.
16+16
[tex]\Rightarrow \boxed{\sf{32}}[/tex]
Therefore, the correct answer is C. 32.
Write the quadratic equation that has roots [tex]\frac{(-1-\sqrt{2})}{3}[/tex] and [tex]\frac{(-1+\sqrt{2})}{3}[/tex] if its coefficient with [tex]x^{2}[/tex] is equal to -3/5.
The quadratic equation is [tex]-3/5x^2-2/3x-\frac{1+2\sqrt{2}}{3}[/tex]
Quadratic Equation:
A quadratic function is a function of degree two.
The general form of the quadratic equation is
x² + (sum of roots)x + Product of roots.
Given,
Here we have the roots,
[tex]\frac{-1-\sqrt{2} }{3} ,\frac{-1+\sqrt{2} }{3}[/tex]
And the coefficient with x² is equal to -3/5.
Through the given details we have to find the quadratic equation.
To find the equation we have to identify the sum of roots and the product of roots.
So, the sum of roots is,
[tex]= > \frac{-1-\sqrt{2} }{3} +\frac{-1+\sqrt{2} }{3}[/tex]
[tex]= > \frac{-1 }{3} +\frac{-1 }{3}\\= > \frac{-2}{3}[/tex]
Now the product of roots is,
[tex]= > \frac{-1-\sqrt{2} }{3} \times\frac{-1+\sqrt{2} }{3}[/tex]
[tex]= > \frac{1-\sqrt{2}-\sqrt{2}-2 }{3}=\frac{-1-2\sqrt{2} }{3}[/tex]
So, the quadratic equation is,
[tex]= > -3/5x^2-2/3x-\frac{1+2\sqrt{2}}{3}[/tex]
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Reuters reports that 15 percent of australians smoke. by introducing tough laws banning brand labels on cigarette packages, australia hopes to ultimately reduce the percentage of people smoking to 10%. answer the following questions based on a sample of 240 australians..
The mean of the sampling distribution of proportion is 0.15
The probability the sample proportion will be within 0.04 of the population proportion is 0.9182
The probability the sample proportion that will be within 0.02 of the population proportion is 0.6157
P(Smokers) in Australia= 15/100=0.15
Sample, n =240
Part a, The mean of the sampling distribution of proportion:
μ₂ = P(Smokers)
= 0.15
The mean of the sampling distribution of proportion is 0.15
The standard deviation of the sampling distribution of proportion is,
δ [tex]=\sqrt{p\frac{(1-p)}{n} }[/tex]
[tex]=\sqrt{0.15\frac{(1-0.15)}{240} }[/tex]
[tex]=0.0230[/tex]
The standard deviation of the sampling distribution of proportion is 0.0230
Part b, The probability the sample proportion will be within +/-0.04 of the population proportion:
To find this, we first, compute the z score then find probability based on standard normal table.
For 0.15-0.04, p=0.11 and converts to:
[tex]z=\frac{p-u_{p} }{standard deviation} \\[/tex]
[tex]=\frac{0.11-0.15}{0.0230}[/tex]
= -1.74
For 0.15+0.04, p=0.19, and converts to:
[tex]z=\frac{0.19-0.15}{0.0230}[/tex]
= 1.74
From the standard normal distribution table, the associated probability for z values and subtracts the probability is,
[tex]=p(-1.74\leq z\leq 1.74)[/tex]
[tex]=0.9591-0.0409[/tex]
[tex]=0.9182[/tex]
Hence, the probability the sample proportion will be within 0.04 of the population proportion is 0.9182
Part c, the probability the sample proportion will be within 0.02 of the population proportion:
First, compute the z score then find probability based on standard normal table.
For 0.15-0.02, p=0.13, and converts to:
[tex]=\frac{0.13-0.15}{0.0230}[/tex]
=-0.87
For 0.15+0.02, p=0.17, this converts to:
[tex]=\frac{0.17-0.15}{0.0230}[/tex]
=0.87
From the standard normal distribution table, the associated probability for z values and subtracts the probability is,
[tex]=p(-0.87\leq z\leq 0.87)[/tex]
[tex]=0.8079-0.1922[/tex]
[tex]=0.6187[/tex]
Hence, the probability the sample proportion will be within 0.02 of the population proportion is 0.6157
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I need serious help with this one.
Whoever helps me thank you god bless
Answer:
Try 20.
Step-by-step explanation:
To round 19.5 to the nearest whole number consider the tenths’ value of 19.5, which is 5 and equal or more than 5. Therefore, we have to round up: the whole number part of 19.5, 19, increases by 1 to 20, and the decimal point and all digits (.5) are removed.
19.5 rounded to the nearest whole number = 20
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = - [tex]\frac{1}{5}[/tex] x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (50, - 10) ← 2 points on the line
m = [tex]\frac{-10-0}{50-0}[/tex] = [tex]\frac{-10}{50}[/tex] = - [tex]\frac{1}{5}[/tex]
the line crosses the y- axis at (0, 0 ) ⇒ c = 0
y = - [tex]\frac{1}{5}[/tex] x + 0 , that is
y = - [tex]\frac{1}{5}[/tex] x ← equation of line
help pls
I would use 2 for this right
Step-by-step explanation:
yeah
Please help, random thing that was assigned
Answer:
I think options BCDE. There is an angle presented in the picture. There are parallel lines. Also skew lines and line segments.
Step-by-step explanation:
Hope it helps! =D
Solve the system of equations by substitutión.
y =-4x+5
y = 3x - 16
Answer:
y = - 4x + 5 ---1
y = 3x - 16 ---2
Substitute 1 into 2:
- 4x + 5 = 3x - 16
7x = 21
x = 3
Substitute x into 1:
y = - 4(3) + 5
= - 7
Here is the histogram of a data distribution.
Which best describes the shape of this distribution?
A. Bimodal skewed
B. Bimodal symmetric
C. Unimodal symmetric
D. Unimodal skewed
E. Uniform
The given distribution is (A) Bimodal skewed as the distribution has 2 humps.
What is Bimodal skewed?If a histogram has one hump, it is unimodal; if it has two humps, it is bimodal; and if it has many humps, it is multimodal. If a histogram is not symmetric, it is referred to as skewed. It is positively skewed if the upper tail is longer than the lower tail. They can have multiple peaks or be bimodal (two peaks) (or many peaks). But a single distribution with two peaks characterizes a bimodal distribution. Typically, it appears as two separate bell curve shapes contained within two normal distributions on a graph that is displayed side by side.As the given graph has 2 humps, we can conclude that the given distribution is an (A) Bimodal skewed.
Therefore, the given distribution is (A) Bimodal skewed as the distribution has 2 humps.
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20) Flud LM if Pelut M is between Points L and N.
LM = 12x - 8, MN = 14, aud LU = 6x + 30
The value of the distance LM in which M is the midpoint between L and N is 64 units.
What is midpoint?
In mathematics. the term midpoint states the middle line of the line segment joining the two sides of the triangle make the third side parallel to the line segment and it also bisect the third side.
According to the question, the point M is the midpoint between L and N. The given parameters are: LM = 12x-8; MN = 14; and LN = 6x + 30
Using standard midpoint property, the distance LN can be written as:
LN = LM + MN ⇒ 6x + 30 = 12x-8 + 14
Taking variables terms one side, we get
6x = 36 ⇒ x = 6
Therefore,
LM = 12x-8 ⇒ 12(6) - 8 = 72 - 8 = 64
Hence, the value of the distance LM in which M is the midpoint between L and N is 64 units.
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A video game arcade offers a yearly membership with reduced rates for game play. a single membership costs $60 per year. game tokens can be purchased by members at the reduced rate of $1.00 per 10 tokens
The function's y-intercept is $60.
The equation y = 1/10x+60 can be used to express the function.
y| y 60 is the range.
The equation for the annual cost in dollars, y, based on x, the quantity of game tokens purchased for an arcade member, is represented by the following statements:
A) The function's y-intercept is $60.
B) The equation y = (1/10)x + 60 can be used to express the function.
C) y ≥ 60 is the range.
Typically, the slope-intercept form of the equation of a line is expressed as;
y = mx + c
Where;
the slope is m.
C is the y-intercept.
The input variable or domain is called x.
The output variable or range is called y.
As of right now, we're informed that a single membership costs $60 annually. This is the cost before any input, in this case, the purchase of game tokens.
It follows that the y-value intercept is $60.
According to what we've been told, members can purchase Game tokens for a discounted price of $1 for every 10 tokens. This implies;
y/x = 1/10
Thus, slope = 1/10
Putting this function's equation in slope intercept form now yields
y = (1/10)x + 60
The quantity of game tokens purchased is now limited to a minimum of 0. Thus;
Therefore, Domain; x ≤ 0
The price cannot be less than $60 since x ≤ 0.
Therefore, Range; y ≥ 60
Complete Question: A video game arcade offers a yearly membership with reduced rates for gameplay. A single membership costs $60 per year. Game tokens can be purchased by members at the reduced rate of $1.00 per 10 tokens. Which statements represent the function of the yearly cost in dollars, y, based on x, the number of game tokens purchased for a member of the arcade? Select three answers. The slope of the function is $1.00. The y-intercept of the function is $60. The function can be represented by the equation y = y equals StartFraction 1 Over 10 EndFraction x plus 60.X + 60. The domain is all real numbers. The range is {y| y ≥ 60}.
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8. In the Aribic system , the value of a digit is based on what?
Answer
In the Arabic system, the value of a digit is based on the position of the specific digit.
What is the value of the Arabic numbers?The ten numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 serve as the basic building blocks for the decimal, or base ten, a place-value number system that makes up Hindu-Arabic numerals. According to its position, every digit in a number has a place value. The figure zero is theirs. Arabic uses a base-ten system, where each number must be placed in a specified order to represent a particular value. Egyptian, Indian, and Arab contributions were used to construct the Arabic numeral system over millennia.To learn more about Arabic system visit:
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Given the area of a square window is 36 ft2, what is the measure of one side? Show your work.
Answer:
The length is 6 ft
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
36 = s^2
Take the square root of each side
sqrt(36) = sqrt(s^2)
6 =s
The length is 6 ft
Answer:
6 ft
Step-by-step explanation:
We know that the formula to find the area of a square is :
Area = a² ( length × width)
According to the question they've already given the area of the square as 36ft².
So, to find the the measure of a one side, let the in unknown measure of a side be a.
Remember that, all the sides of a square are equal to each other.And now, using the formula let us find the value of a ( length of a one side).
[tex] \sf \: Area = a² \\ \sf 36 = a² \\ \sf \: \sqrt{36} = a \\ \sf6ft = a[/tex]
Find an estimate for the mean time. Please fast !!
Mean time = 142 minutes
What is the mean of data?One of the the most common expression for the mean of a statistical distribution with random variables is the average of all the terms. The mean of any given data can be found out by adding all numbers in the data set and then dividing that by the number of values.
First calculate the mid point of the time interval :
(15+17)/2=16
(17+19)/2 = 18
(19+21)/2= 20
(21+23)/2= 22
Multiply each time mid point with respective frequency :
16*5=80
18*12= 216
20*7= 140
22*6= 132
Adding this and dividing by the total number of times that is 4:
= (80+216+140+132)/4
= 568/4
Mean time =142 minutes
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The height of a ball in feet can be found by the function h(t)=-16t^2+80t+5 where t is the elapsed time in seconds. Find the time or times that the ball is 34 feet high to the nearest tenth of a second
The times that the ball is 34 feet high to the nearest tenth of a second is equal to 4.61 and 0.39 seconds.
How to calculate the times?In order to determine the time or times for this ball at a height of 34 feet, we would simply substitute the value of the height into the function h(t) as follows;
h(t) = -16t² + 80t + 5
34 = -16t² + 80t + 5
Re-arranging the equation, we have:
16t² - 80t + 34 - 5 = 0
16t² - 80t + 29 = 0
Next, we would solve the quadratic equation by using the quadratic formula:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-(-80)\; \pm \;\sqrt{-80^2 - 4(16)(29)}}{2(16)}\\\\x = \frac{80\; \pm \;\sqrt{6400 - 1856}}{32}\\\\x = \frac{80\; \pm \;\sqrt{4544}}{32}[/tex]
x = (80 ± 8√71)/32
x = (80 + 8√71)/32 and x = (80 - 8√71)/32
x = 4.61 and 0.39 seconds.
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Suppose 91% of students chose to study French their sophomore year, and that meant that there were 819 such students. How many students chose not to take French their sophomore year?
Using percentage we can calculate that 81 students did not take French.
In mathematics, a number or ratio that is expressed as a fraction of 100 is referred to as a percentage. Although the abbreviations "pct" and "pc" are also often used, the percent symbol "%" is the one that is most frequently used. A % is a number that has neither established units of measurement nor dimensions.
The percentage can be calculated by taking the value and dividing it by the total value, then multiplying the result by 100. using the formula (Value/Total Value) × 100% to calculate percentages.
Let the total number of students be x.
Now 91% of this students is equal to 819.
Now using the properties of percentages we can write:
91% of x = 819
or, x = 900
Number of students who did not take French = 900 - 819 = 81
Hence using percentages we can say that 9% or 81 students did not take French.
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If you wanted to know which number, when raised to the exponent 3, results in 1,331, which action should you perform?
Find the cube of 1,331.
Find the square root of 1,331.
Find the cube root of 1,331.
Find the square of 1,331.
====================================================
Reason:
The cube root undoes the cubing operation.
It's similar to how the square root undoes squaring.
Your calculator should have a cube root button, or an nth root button. If not, then you can type in 1331^(1/3)
The exponent of 1/3 is the same as a cube root.
The result of 1331^(1/3) is 11
11^3 = 11*11*11 = 1331
Interpretation: You have a box that is 11 cm by 11 cm by 11 cm. The volume is 11^3 = 1331 cubic cm.
As you can see, the cube root is useful if you know the volume and want to work backwards to determine the side length of the cube.
the cube root of 1331 = ∛(11 × 11 × 11) = 11.
The square root of 1331 is 36.48287.
When should you cross multiply with fractions
Answer:
fractions are cross multiplied in two situations:
division:
for e.g what is [tex]\frac{3}{2}[/tex]÷[tex]\frac{7}{5}[/tex]
to solve this expression we cross-multiply fractions:
=15/14
In equation:
for eg [tex]\frac{8x}{7}[/tex] = [tex]\frac{2}{9}[/tex]
to solve this we cross multiply:
8x(9)=2(7)
72x=14
x=14/72
In equation cross multiplication can only be carried out if denominator is same for e.g [tex]\frac{2}{1}[/tex]+ [tex]\frac{8x}{7}[/tex] = [tex]\frac{4}{7}[/tex] cannot be cross multiplied until denominator of 8x and 2 is same
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By cross multiplying, you can simplify the equation and solve for the unknown variable.
Cross multiplication is a technique used when solving equations involving fractions. It is typically used when you have a proportion or an equation with fractions, and you want to eliminate the denominators and solve for the unknown variable.
Cross multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction and vice versa. This technique is useful for simplifying equations and solving for the unknown variable.
You should cross multiply with fractions when you have an equation in the form:
a/b = c/d
To cross multiply, you would multiply ad (product of the numerators) and bc (product of the denominators) and set them equal:
ad = bc
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Point G is on line segment FH. Given G H= 8, F H= 3x +3, and FG=2x, determine the numerical length of FG.
The length of line segment FG is 10 units.
What is a line segment?A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies within those endpoints. The Euclidean distance between two endpoints of a line segment determines its length. In real life, a line segment might be a stick, a pencil, or a ruler. The sun's rays are an illustration of a ray. The sun is where the sun's rays begin, but there is no end to them.So, the length of FG:
FG + GH + FH2x + 8 = 3x + 33x - 2x = 8 - 3x = 5So, insert x = 5 in 2x:
FG = 2xFG = 2(5)FG = 10Therefore, the length of line segment FG is 10 units.
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find the standard form of the equation of the ellipse given the following properties. foci \displaystyle \left(0,\pm3\right)(0,±3) vertices \displaystyle \left(0,\pm13\right)(0,±13).
The standard form of the given equation of the ellipse according to the given properties is [tex]b^{2}[/tex] = ± 4√2.
Here the foci are given which are ( 0,3) and to the eight (0, ±3) and the vertices are (0,13) and (0, ±1), so we have to find the standard form these values to put these values in a formula which is given below
The formula we are using in this is to form an equation :
[tex]\frac{(x-k)^{2} }{a^{2} }[/tex] + [tex]\frac{(y-k)^{2} }{b^{2} }[/tex] = 1
[tex]\frac{x^{2} }{a^{2} }[/tex] + [tex]\frac{y^{2} }{b^{2} }[/tex] = 1
[tex]\frac{x^{2} }{36}[/tex] + [tex]\frac{y^{2} }{32}[/tex] = 1
After solving the equation given above
we get [tex]b^{2}[/tex] + 4 = 36
Subtract - 4 on both sides then we get
[tex]b^{2}[/tex] + 4 - 4 = 36 - 4
[tex]b^{2}[/tex] = 32
[tex]b^{2}[/tex] = ± 4√2
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assume that births are randomly selected and of the births are girls. use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high.
According to the statement the number of girls is significantly high. This was because of 50 birth, 49 are girls.
What are objective statement?Objective judgments are those that are based on or employ facts that can be observed or verified, particularly by scientific methods, and are independent of one's own thoughts, feelings, or preconceptions.
From the information, births are randomly selected and of the 50 births, 49 are girls. This illustrates that the number of girls as significantly high. The have a percentage of (49/50) × 100= 98%.
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Assume that births are randomly selected and of the 50 births, 49 are girls. use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high.
Based on the information provided, the number of girls in the births cannot be categorized as significantly high, significantly low, or neither significantly low nor significantly high, solely through subjective judgment.
The description of "significantly high" or "significantly low" typically requires statistical analysis and comparison to a reference point or expected value. Without knowing the total number of births or having a reference point for the expected proportion of girls in the births, it is not possible to determine whether the number of girls is significantly high or low.
The term "significantly" in statistics usually involves assessing whether an observed value deviates from an expected value by a statistically significant margin.
Subjective judgment alone cannot accurately assess whether the number of girls in the births is significantly high or low. To determine significance, a statistical analysis would involve calculations such as calculating the expected proportion of girls, performing hypothesis testing, and assessing the p-value to make an informed judgment.
Without these quantitative measures, it is not possible to make an accurate subjective determination of the significance of the number of girls in the births.
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