Three pairs of siblings from different families can be seated in two rows of three chairs so that siblings may not sit next to each other in the same row, and no child may sit directly in front of their sibling in 96 ways.
There are 3 pairs of siblings. We can name them as a₁, a₂, b₁, b₂, c₁ and c₂, a total of 6 children.
There are 2 rows of 3 seats each.
We will try to find the number of ways each seat can be filled.
So considering the first seat in first row, it can be filled in 6 different ways. Because any one from 6 children, say a₁, can be seated.
Now for the second seat in first row can only be filled by one of b₁, b₂, c₁ or c₂ because the first seated child a₁ along with the sibling a₂ of the same cannot be seated in the second seat. So in 4 different ways.
For the third seat remaining in the first row, one out of the remaining pair of siblings c₁ or c₂ can be seated. This can be done in 2 ways.
Now after filling the first row in this manner, the second row can be filled in only 2 ways.
So total number of ways the children can be seated = 6 x 4 x 2 x 2 = 96 ways
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For f(x) = 2x² - 1, what is (f. f)(−2)?
(See image below)
f is 7. The process of composing small units into larger units that solve larger problems is known as composition.
What is Composition function?A function composition is an operation that produces a new function, h, by combining two functions, f and g, in such a way that h(x) = g(f(x)). That is, function g is being applied to function x.In essence, one function is applied to the output of another. A composite function is one that is reliant on another.A composite function is created when one function is substituted for another. For example, f(g(x)) is the composite function formed by replacing x in f with g(x) (x). The expression f(g(x)) is pronounced "f of g of x."Therefore,
f = 2 (-2)² - 1 : f = 7
Steps
f = 2 (-2)² - 1
2 (-2)² =2³
f = 2³-1
2³ = 8
f = 8-1
Subtract the numbers:
8 - 1 = 7
f = 7
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A line contains the points (-21,-94) and
(-34,-172).
What is the slope of the line in simplified form?
Find the area of circle b 1.5 yd in terms of pi
In terms of π, the area of the circle is 2.25π yd².
What is the area of the circle?A circle is a sphere with no edges or bounds.The point from which all of the distances to the other points on the circle are equal is the center of the circle.The measurement in question is the circle's radius.A radius is a section of a line with one end in the circle's center and the other outside.So, the radius of circle(r) = 1.5 yd
The area of the circle is given by:
A = π r²A = π * 1.5²A = 2.25π yd²Therefore, in terms of π, the area of the circle is 2.25π yd².
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round your answer to the nearest tenth.
The next place value on the right should be used to round a number to the closest tenth (the hundredths). Simply take away all the digits to the right if it's 4 or fewer. Remove all the digits to the right after adding 1 to the digit in the tenths position if the number is five or above.
To what decimal place do you round?
Examine the hundredth number to determine the decimal number's nearest tenth. Add one to the tenth value if the number is more than 5. Remove all the numbers that are present after the tenth place if the value is less than 5, but keep the tenth place value in place otherwise. As an illustration, if you want to round up to the nearest.
Triangle Area Solver
A=hbb
2
b Base
Enter value
hb Height
Enter value
γ
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(middle school question) hey can someone please answer this with shown work please I have been stuck on it for like an hour
Answer:
1.95 hours or 1 hour and 57 minutes.
Step-by-step explanation:
You can read the problem as 13% of the battery. "Of" is a keyword that means to multiply.
The battery lasts 15 hours, so multiply by 13%. You need to change 13% to a decimal first by dividing it by 100, or moving the decimal left two places.
13% = 0.13
Now solve.
0.13 × 15 = 1.95
If you need to convert the 0.95 to minutes, multiply it by 60 since there are 60 minutes in an hour.
0.95 x 60 = 57 minutes.
Divide $180 in the ratio of 2 : 3 : 4
Answer:
40,60,80
Step-by-step explanation:
let 2x 3x and 4x
9x=180
x=20
2x=40
3x=60
4x= 80
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What are some organizations in the college Edward waters university?
Organizations in College Edward Waters University include
Accounting ClubEconomics ClubDelta Sigma Pi, Theta Omega ChapterGraduate Business Student Association (GBSA)Hilltop American Marketing AssociationWhere is the college Edward waters university?College Edward waters university was the first independent higher institution and black college located in Florida state of the United States of America.
The institution was found in 1866 in Jacksonville, Florida. It is owned by African Methodist Episcopal Church which is a Christian denomination.
Organizations refers to arrangement where people come together for a defined purpose. Organizations so exist in this high institution of learning
Delta Sigma Pi, Theta Omega Chapter is one of the organizations in this institution. The purpose of this organization is aid students in studying business in several ways and financial aids is one of them.
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a computer is rendering two scenes. the computer has already rendered 540 thousand pixels of a kitchen scene and renders another 90 kpx each minute.
the computer has rendered 960 kpx of a garden scene and renders 60 kpx more pixels each minute
after how many more minutes will the scenes have the same amounts rendered?
A computer is rendering two scenes then after 14 minutes of the scenes have the same amounts rendered.
As given in the question,
As per condition:
Computer rendered 540 thousands pixels of a kitchen scene and renders another 90kpx each minute:
The expression for the kitchen is illustrated as 540 + 90t
Computer rendered 960kpx of a garden scene and renders 60kpx more pixels each minute
The expression for the garden is illustrated as 960 + 60t
For the scenes have the same amounts rendered is given by :
540 + 90t = 960 + 60t
Collect like terms
90t - 60t = 960 - 540
⇒30t = 420
⇒t = 420/30
⇒t = 14
Therefore, a computer is rendering two scenes then after 14 minutes of the scenes have the same amounts rendered.
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Please help i need an explanation i have no idea how to do this.
Answer:
f(2)=3
f(1)=2
f(-1)=0
f(0)=1
Step-by-step explanation:
f(x)=y
when finding what f(x)=? you would see whats in the () and find that number on the x-axis. Find where the line hits on the x-axis and find the number on the y-axis that correlates with it. The y-axis number is what goes the the ().
when finding whats in the () you find what number it equal to on the y-axis and what is in the () would be the number that the line is on on the x-axis
Ple help me with Problems 2 & 3 ASAP
2) w = 16.5 mis the equation represents the relationship shown in the table.
3) The number of minutes is proportional to the number of pages, with a unit rate of 2.25 minutes per page is the best statement describes the relationship in the table.
How is a proportion determined?When determining if two ratios or fractions are equivalent, the proportion formula is utilized. We can calculate the missing value by dividing the given values. One way to express the percentage formula is as a: Whereas a and d are the extreme terms and b and c are the mean terms, a:b::c: d = a/b = c/d.
2) Divide the number of gallons of water with number of minutes
66/4 = 16.5
So, the equation represents the relationship shown in the table is
w = 16.5 m
3) Divide number of minutes by number of pages, we get
9/4 = 2.25
13.5/6 = 2.25
So, option (B) best describes the relationship in the table.
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deltamath i need answers fast
Answer:
To stay within budget, she must use 3.9 gigabytes.
Caroline can use approximately 3.9 gigabytes of data while staying within her budget of $74 per month.
Let's assume the number of gigabytes of data Caroline can use while staying within her budget is represented by the variable "x."
The flat cost per month is $54.50, and Caroline pays an additional $5 per gigabyte.
If she wants to keep her bill at $74 per month, the equation can be set up as follows:
54.50 + 5x = 74
To solve for "x," we can isolate the variable on one side of the equation. First, subtract 54.50 from both sides:
5x = 74 - 54.50
5x = 19.50
Finally, divide both sides by 5:
x = 19.50 / 5
Simplifying the division gives us:
x = 3.9
Therefore, Caroline can use approximately 3.9 gigabytes of data while staying within her budget of $74 per month.
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If F, G, and H are the midpoints of the sides of triangle JKL, FG=37, KL=48, and GH=30, find each measure. FH=, JL=, KJ=, FJ=
DCM, this is the solution:
According to the midpoint theorem, the line connecting the midpoints of two sides is parallel to the third and its length is half of the third side.
Therefore,
KJ = 2 * GH
KJ = 2 * 30
KJ = 60 and FJ = 30
JL = 2 * FG
JL = 2 * 37
JL = 74
solve for w: x=7w-8z-4
Answer:
W=x/7+ 8z/7 + 4/7
Step-by-step explanation:
Let the roots of the polynomial x^2 + 7x - 2 be a and b Evaluate a^2 + b^2.
First gets brainliest, ty!
Answer:
53
Step-by-step explanation:
You want the value of a^2 +b^2, given that 'a' and 'b' are roots of the polynomial x^2 +7x -2.
FactorsIf the roots are 'a' and 'b', then the factored form is ...
(x -a)(x -b) = x^2 -(a+b)x +ab
Comparing this to the given polynomial, we see that ...
-(a+b) = 7
ab = -2
Desired expressionThe expression a^2 +b^2 can be written as the sum ...
a^2 +b^2 = a^2 +2ab +b^2 -2ab = (a+b)^2 -2ab
Using the values of (a+b) and ab from above, we see that ...
a^2 +b^2 = (-7)^2 -2(-2) = 49 +4 = 53
The given expression has a value of 53.
the quality control manager at a computer manufacturing company believes that the mean life of a computer is 99 months, with a standard deviation of 8 months. if he is correct, what is the probability that the mean of a sample of 69 computers would be less than 97.94 months? round your answer to four decimal places.
The probability that the mean of a sample of 78 computers would be less than 97.94 months exists 0.883.
What is meant by probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place.
Let the given values be
[tex]\mu[/tex] = 99, [tex]$\sigma[/tex] = 8
Let x be the random variable that represents the life of a computer.
Sample size: n = 69
Then, the z-score corresponds to x = 97.94 will be :-
[tex]$z=\frac{97.94-99}{\frac{8}{\sqrt{69}} \quad[\because} \quad z=\frac{x-\mu}{\left.\frac{\sigma}{\sqrt{n}}\right]}$[/tex]
z = -1.10062
Required probability ( using standard z-value table ) :-
P(x < 97.94) = P(z < -1.10) = 1 - P(z < 1.10)
= 1 - 0.1170 = 0.883
Therefore, the probability that the mean of a sample of 78 computers would be less than 97.94 months exists 0.883.
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Kamala is reading about her favorite superhero, Captain Marvel. She would like to read at least 235 pages in one week. She has already read 25 pages. How many pages does Kamala need to read each day?
The number of pages that Kamala needs to reach each day is p ≥ 30.
What is the number of pages that Kamala needs to read?Here are inequality signs and what they mean:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toThe inequality sign that would be used is ≥. This is because the pages Kamala needs to read each day can be equal to 235 or greater than 235
25 + 7p ≥ 235
Combine similar terms: 7p ≥ 235 - 25
Add similar terms: 7p ≥ 210
Divide both sides of the equation by 7: p ≥ 210 / 7
p ≥ 30
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what is (9x10^4) (6x10^-7)
The simplified form of the expression ( 9 × 10⁴ ) × ( 6 × 10⁻⁷ ) in scientific notation form is 5.4 × 10⁻²
How to multiply numbers in scientific form?The scientific notation form is simply a method of presenting larger or smaller numbers in a more simple way.
Given the data in the question;
( 9 × 10⁴ ) × ( 6 × 10⁻⁷ )
First, multiply 9 and 6
( 9 × 10⁴ ) × ( 6 × 10⁻⁷ )
9 × 6 ( 10⁴ × 10⁻⁷ )
54( 10⁴ × 10⁻⁷ )
Next, multiply 10⁴ × 10⁻⁷ by adding the exponents.
Using power rule mᵃ × mᵇ = mᵃ ⁺ ᵇ
54( 10⁴ × 10⁻⁷ )
54( 10⁴ ⁺ ⁻⁷ )
54( 10⁴ ⁻⁷ )
Subtract 7 from 4
54 × 10⁻³
Move the decimal point in 54 to the left by place and increase the power of 10⁻³ by 1
5.4 × 10⁻³ ⁺ ¹
5.4 × 10⁻²
Therefore, the simplified form is 5.4 × 10⁻².
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please help me answer this question
Answer:
Step-by-step explanation:
130 decrease
help me please I suck at math because it's confusing
A reciprocal parent function represents a simple rational function, that is, a function that has the variable x as the denominator.
Hence, the answer is B.What is the relationship between the two highlighted angles?
Angles 1 and 2 are remote interior angles while angle 3 exists as a remote exterior angle. The required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.
What is meant by triangle?The triangle exists a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.
A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.
Angles 1 and 2 are remote interior angles while angle 3 exists as a remote exterior angle. So there exists a property of a triangle in that the sum of the remote interior angles exists equivalent to the remote exterior angle.
∠1 +∠2 = ∠3.
Therefore, the required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.
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Write an exponential function in the form y and (2,171). ab that goes through points (0,19)
The exponential function has the following form:
[tex]y=a\cdot b^x[/tex]The function goes through the points ( 0, 19) and ( 2, 171 )
We will use the points to find the values of a and b
[tex]\begin{gathered} x=0\rightarrow y=19 \\ \\ 19=a\cdot b^0 \\ b^0=1 \\ a=19 \end{gathered}[/tex]Substitute with the point ( 2, 171 ) and the value of a to find b
[tex]\begin{gathered} x=2\rightarrow y=171 \\ a=19 \\ \\ 171=19\cdot b^2 \\ \\ b^2=\frac{171}{19}=9 \\ \\ b=\sqrt[]{9}=3 \end{gathered}[/tex]So, the answer will be:
[tex]y=19\cdot3^x[/tex]6x+1y=44 find the slope
Answer:
answer would be -6 since you are just subtracting -6 to move to the other side
Step-by-step explanation:
Which of the following are solutions to the equation below?Check all that apply.x-5x+ 1 = 0A. x =5+29B. x = 5 - 292.C. x= 5+ V212D. x= -1 - 212E. x = =*+,x21F. x =5 - 2152
It is calculated using the quadratic formula
[tex]x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In the equation
[tex]x^2-5x+1=0[/tex]a = 1, b = -5 and c = 1
Substitute the given to the quadratic formula
[tex]\begin{gathered} x\text{ = }\frac{5+\sqrt[]{21}}{2} \\ x\text{ = }\frac{5-\sqrt[]{21}}{2} \end{gathered}[/tex]please help!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
I believe the answer is D!
Write an expression to represent the perimeter of the figure below: Do NOT use spaces in your answer.
The expression that represents the perimeter of the figure is 6x - 2
How to find the perimeter of a figure?The figure above is a rectangle. A rectangle is a quadrilateral that has opposite sides equal to each other. Opposite sides are also parallel to each other.
Therefore, the perimeter of a rectangle is the sum of the sides of the rectangle.
Hence,
perimeter of the rectangle = 2(l + w)
where
l = lengthw = widthTherefore,
l = 2x - 3
w = x + 2
Hence,
perimeter of the rectangle = 2(2x - 3 + x + 2)
perimeter of the rectangle = 2(2x + x - 3 + 2)
perimeter of the rectangle = 2(3x - 1)
Therefore,
perimeter of the rectangle = 6x - 2
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The perimeter of a rectangle is 48 centimeters, The relationship
between the length, the width, and the perimeter of the rectangle
can be described with the equation 2 • length + 2 • width = 48.
Find the length, in centimeters, if the width is:
1. 10 centimeters
2. 3.6 centimeters
3. w centimeters
Please help me it is due today!
Answer: B
Step-by-step explanation:
The range of values for F(x) would be on the y - axis, so go up on the y - axis to find the points, and since it is not a line it has no inequality symbols, and how sideways it is doesn't matter, it is only how tall it is that matters because it is on the y - axis.
mary walked to school at an average speed of 2 miles per hour and jogged back along the same route at an average speed of 6 miles per hour. if her total traveling time was 1 hour, what was the total number of miles in the round trip?
As a result, the total distance traveled by Mary in her round trip is 3/2 mile + 3/2 mile = 6/2 mile = 3 mile
How to calculate total distance?We can calculate the total distance traveled by a body with position function s (t) if it moves along a coordinate line without changing direction from t = a to t = b. If the body changes direction during the journey, we must integrate the body's speed |v (t)| to find the total distance traveled.
Therefore,
We know Mary spent only a third of the time coming from school as she did going because she traveled three times as fast coming from school as she did going to school (6 miles per hour versus 2 miles per hour). If x represents the time it took her to get to school, then x/3 represents the time it took her to return.
Knowing that the total trip took 1 hour, we have:
x + x/3 = 1
3x/3 + 1x/3 = 1
4x/3 = 1
x = 3/4
So we know it took Mary 3/4 of an hour to get to school (and 1/4 of an hour to get home).
Remembering that distance = rate × time, Mary's commute to school was (2 miles per hour) × (3/4 of an hour) = 3/2 mile. Furthermore, because she returned via the same route, she must have traveled 3/2 of a mile.
As a result, the total distance traveled by Mary in her round trip is 3/2 mile + 3/2 mile = 6/2 mile = 3 mile.
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is housework hazardous to your health? a study in public health report compares the life expectancies of 25-year-old white women in the labor force with those who are housewives. how large a sample would have to be taken from each group in order for you to be 95% con dent that the estimate of the difference in mean life expectancies for the two group is within 1 year of the true difference? assume that equal sample sizes will be selected from the two groups and that the standard deviation for both groups is approximately 15 years.
the difference in mean life expectancies for the two groups is within 1 year of the true difference is 1729
Health issues can arise from substances other than chemicals like bleach. The way you clean your house and the environment in which you live both matters. Scientists caution that performing these tasks could have a detrimental effect on your health.
A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score.
Given data:
σ₁ = σ₂ = 15
n₁ = n₂ = n
Margin of error = 1
Confidence level = 95% = α = 1 - 0.95 = 0.05
z score of α / 2 = 0.05 / 2 = 1.96 , n₁ = n₂ = ?
For the difference of mean test, the margin of error will be:
E = z score α / 2 [tex]\sqrt \frac{(SD1)^{2} }{n1}+\sqrt \frac{(SD2)^{2} }{n2}[/tex]
[tex]1 = 1.96 \sqrt\frac{(15)^{2} }{n} + \sqrt \frac{(15)^{2} }{n}[/tex] [∵ n₁ = n₂ = n]
[tex]1 = 1.96 * 15 \sqrt \frac{2}{n}[/tex]
1 = 41.58 / √n
√n = 41.58 / 1 = 41.58
On squaring both sides:
n = 1728.90 ≈ 1729
∴ n₁ = n₂ = 1729
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Which fraction is equivalent to3-3? - 1 27 1 1 27