The formula of a volume of a rectangle prism:
[tex]V=lwh[/tex]
l - length
w - width
h - height
We have
[tex]l=n^2+2;\ w = 10,\ h=n+5[/tex]
Substitute:
[tex]V=(n^2+2)(10)(n+5)=(10n^2+20)(n+5)\\\\=(10n^2)(n)+(10n^2)(5)+(20)(n)+(20)(5)\\\\=10n^3+50n^2+20n+100[/tex]
Answer: V = (10n³ + 50n² + 20n + 100) in³The volume of the aquarium in terms of n is calculated by multiplying its length (n2 +2 inches), width (10 inches), and height (n + 5 inches) giving the formula V = (n2 + 2) imes (n + 5) imes 10, which expands to V = 10n3 + 60n2 + 20n + 100 cubic inches.
We use the formula V = length times width times height, where the volume V is the space inside the aquarium. The question provides the dimensions of the aquarium in terms of n: the length (n2 +2 inches), height (n + 5 inches), and width (10 inches).
To calculate the volume, simply multiply the dimensions together:
Length: n2 + 2 inchesHeight: n + 5 inchesWidth: 10 inchesVolume, V = (n2 + 2) imes (n + 5) imes 10
Expanding the expression gives us the volume V in cubic inches as a function of n:
V = 10n3 + 60n2 + 20n + 100 cubic inches
What is the y-coordinate of point D after a translation of (x, y) ? (x + 6, y – 4)?
Answer:
Y-coordinate = y - 4
Step-by-step explanation:
In the given question point D coordinate is (x, y)
and D after translation
x goes to 6 unit to the right and y goes to 4 unit down.
Hence,
Y-coordinate = y-4
Example:From graph
Let point D coordinate (x , y) = (2 , 3)
After rotation
D coordinates is (x+6 , y-4) = (2+6 , 3_4) = (8 , -1)
Answer:
On edge. the answer is 1
Step-by-step explanation:
i just took it
Mrs.Claus needs to knit socks for all of santa's Reindeer. He has 5 reindeer pens with 13,22,14,24 and 17 reindeer in them. How many socks does she need to knit
Find the slope of the line passing through the points (-7,2) and (9,6)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-7, 2) and (9, 6). Substitute:
[tex]m=\dfrac{6-2}{9-(-7)}=\dfrac{4}{16}=\dfrac{1}{4}[/tex]
Answer: The slope = 1/4The slope of the line passing through the points (-7,2) and (9,6) is 1/4.
Formula of slope
Point-slope formula
[tex]y-y_{1} = m(x-x_{1} )[/tex]
In the slope formula, m stands for slope which is calculated as the
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$[/tex]
= Δy/Δx
where, m = slope
[tex](x_1, y_1)=[/tex] coordinates of the first point in the line
[tex](x_2, y_2)=[/tex] coordinates of the second point in the line
We have the points (-7,2) and (9,6).
Substitute the values [tex]x_{1}}$$[/tex], [tex]{x_{2}[/tex] and [tex]y_{1}}[/tex], [tex]${y_{2}[/tex] in the above equation, we get
[tex]$m=\frac{6-2}{9-(-7)}[/tex]
[tex]$=\frac{4}{16}=\frac{1}{4}$[/tex]
Therefore, the slope m = 1 / 4.
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What is the perimeter of a triangle with the given side lengths? s1 = x + 4 cm s2 = 3x + 1 cm s3 = 7x + 3 cm P = x + cm
Answer:
11x+8 cm = Perimeter
Step-by-step explanation:
A triangle has 3 sides. We add up all three sides to get the perimeter.
s1+s2+s3 = Perimeter
(x+4) +( 3x+1) + (7x+3) = Perimeter
Combine like terms
11x+8 = Perimeter
Please help! Urgent!
Triangle GHJ has the exterior angles shown below.
Answer options:
-2.7
-5.8
-12
-29
Exterior angles of triangles = 360°.
So by definition:
[tex]9x + 6 + 10x - 1 + 10x + 7 = 360\\29x + 12 = 360\\29x = 348\\x = 12[/tex]
The value of x is 12.
Answer: 12
Step-by-step explanation:
We know that the sum exterior angles of a polygons is [tex]360^{\circ}[/tex].
Therefore,according to the given picture , we have
[tex]\angle{GHJ}+\angle{HJG}+\angle{JGH}=360^{\circ}\\\\\Rightarrow\ (9x+6)^{\circ}+(10x-1)^{\circ}+(10x+7)^{\circ}=360\\\\\Rightarrow\ 9x+6+10x-1+10x+7=360\\\\\Rightarrow\ 29x+12=360\\\\\Rightarrow\ 29x=348\\\\\Rightarrow\ x=\dfrac{348}{29}\\\\\Rightarrow\ x =12[/tex]
Hence, the value of x = 12
Marquise has 200 meters of fencing to build a rectangular garden. The gardens area (in square meters) as a function of the gardens width w (in meters) is modeled by:
Answer: 2500 meters²
Step-by-step explanation:
Perimeter: 200 = 4w
⇒ 50 = w
Area = w²
= (50)²
= 2500
The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
The perimeter of the rectangle = 2( length + Width)
200 = 2( length + Width)
100 - w = L
The area of the rectangle = length × Width
= w(100 - w)
= (-w)²+ 100w
So, (-w)²+ 100w where, a = -1 and b = 100
w = -100/2(-1)
w = 50
The area of the rectangle = (-w)²+ 100w
= (-50)²+ 100(50)
= 2500
Thus, The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.
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1.You roll a fair six sided die twice.What is the probability of rolling a 3 and then a 5? A.1/3 B.1/6 C.1/12 D.1/36 2.What is the number of possible outcomes if two marbles are picked out of a bag that contains three red marbles and three blue marbles? [Note: Order does not matter.] A) 2 B) 3 C) 4 D) 6
Answer:
1. The correct answer is D) 1/36
Step-by-step explanation:
WE can tell this because the chance of rolling either is 1/6. To find the total probability we multiply those together.
1/6 * 1/6 = 1/36
Marta's starting annual salary is 24,900. At the beginning of each new year, she receives a $2700 raise. Write a recursive formula to find Marta's salary f(n) after n years. What will Marta's salary be after 4 years? A. f(n)=f(n-1)-2700;35,700 B. f(n)=f(n-1)+2700; 33,000 C. f(n)= 2700f(n-1);33,000 D. f(n)=-2700f(n-1);35,700
The solution is Option B.
The recursive formula to calculate Marta's salary is given by the equation
f ( n ) = f ( n - 1 ) + 2700
The salary of Marta after 4 years will be $ 33,000
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the initial salary of Marta be f ( 0 ) = $ 24,900
The increment in Marta's salary every year = $ 2700
So , the equation will be
f ( n ) = f ( n - 1 ) + 2700
when n = 1
Substitute the value of n = 1 in the equation , we get
f ( 1 ) = f ( 1 - 1 ) + 2700
f ( 1 ) = f ( 0 ) + 2700
f ( 1 ) = 24,900 + 2700
f ( 1 ) = $ 27,600
when n = 2
Substitute the value of n = 2 in the equation , we get
f ( 2 ) = f ( 2 - 1 ) + 2700
f ( 2 ) = f ( 1 ) + 2700
f ( 2 ) = 27,600 + 2700
f ( 2 ) = $ 30,300
when n = 3
Substitute the value of n = 3 in the equation , we get
f ( 3 ) = f ( 3 - 1 ) + 2700
f ( 3 ) = f ( 2 ) + 2700
f ( 3 ) = 30,300 + 2700
f ( 3 ) = $ 33,000
Hence , after 4 years the salary of Marta will be $ 33,000
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Marta's annual salary increases by $2700 each year. Applying the recursive formula: f(n) = f(n-1) + 2700; f(4)=f(3)+2700=f(2)+2700+2700=f(1)+2700+2700+2700=f(0)+2700+2700+2700+2700=24900+4*2700=35500, we determine that Marta's salary in 4 years would be $35,500.
Explanation:The subject of the question involves recursion, or constructing a sequence of numbers in a specific way. In Marta's case, her salary can be calculated using a recursive formula that builds upon her previous salary. This formula relies on the concept of numerical patterns and can be represented as follows: f(n) = f(n-1) + 2700; where f(n) is Marta's salary after n years and f(n-1) is her salary the previous year.
At the start, Marta's salary is 24,900, which serves as the base case for our recursive function. Therefore, her income increases by $2700 each year. To get Marta's salary in 4 years, we would use the recursive formula: f(4) = f(3) + 2700 = f(2) + 2700 + 2700 = f(1) + 2700 + 2700 + 2700 = f(0) + 2700 + 2700 + 2700 + 2700 = 24,900 + 4*2700 = 35,500. So, Marta's salary is $35,500 after 4 years.
Therefore, the correct option among choices provided is none from the given options.
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Four balls are placed in a bowl. one green, one black and two yellow. the bowl is shaken and someone draws two balls from the bowl. he looks at the balls and announces that at least one of them is yellow. what are the chances that the other drawn ball is yellow?
Answer:
1/5 chance
Step-by-step explanation:
well their are 4 balls and 2 chosen
their is 1/2 chance or pulling a yellow
1/4 chance of pulling a black and green
Y1 Y2,Y1 B,Y1 G,Y2 Y1,Y2 B,Y2 G,B Y1,B Y2,B G,G Y1,R Y2,G B
so their is a 1/5 chance of pulling it
There are 20 questions if peter gets a 80% how many questions did he get correct
Answer:
16 correct.
Step-by-step explanation:
We need to change 80% to a decimal
80 % = .8
If there are 20 questions
20 * .80 = 16
He got 16 questions correct
Identify the values of the variables. Give your answers in simplest radical form. Help PLEASE!!
Answer:
x = 5 sqrt(6)/3
y= 10 sqrt(6)/3
Step-by-step explanation:
We know sin 60 = opposite/hypotenuse
sin 60 = 5 sqrt(2) /y
Multiply each side by y
y sin 60 = 5 sqrt(2)
Divide each side by sin 60
y sin 60/ sin 60 = 5 sqrt(2)/ sin 60
y = 5 sqrt(2) / sin 60
y = 5 sqrt(2) / sqrt(3) /2)
y = 10 sqrt(2)/ sqrt(3)
You cannot leave a sqrt in the denominator
y= 10 sqrt(2)/ sqrt(3) * sqrt(3)/sqrt(3)
y= 10 sqrt(6)/3
tan 60 = oppositve/ adjacent
tan 60 = 5 sqrt(2)/ x
Multiply each side by x
x tan 60 = 5 sqrt(2)
Divide by tan 60
x = 5 sqrt(2)/tan 60
x =5 sqrt(2)/sqrt(3)
You cannot leave a sqrt in the denominator
x = 5 sqrt(2)/sqrt(3) * sqrt(3)/sqrt(3)
x = 5 sqrt(6)/3
About 16/20 of a tomato is water what present of a tomato is water?
94.46% Is the amount of water in a tomato
16/20 = 80/100
multiply both top and bottom by 5 to go from 16/20 to 80/100
80/100 = 80% by definition of what "percent" means, which is "per 100" or "for every 100"
So 16/20 = 80% meaning 80% of the tomato is water
Note on a calculator, 16/20 = 0.80 which converts to 80% if you move the decimal point 2 spots to the right.
O is the centroid. Find the value of x. (Sorry if u cant see the photo :/, but this is Geometry btw)
Answer: x = 6
==============================================
Explanation:
The medians of a triangle meet up at the centroid in such a way that they cut each other at a ratio of 2:1, meaning that one part of the median is twice as long as the other. In this case, MO is two times longer than OP, so,
OP = 2*MO
and
MP = MO + OP
MP = MO + 2*MO .... replace OP with 2*MO
MP = 3*MO
9x-24 = 3*(x+4) ... plug in the given expressions
9x-24 = 3x+12
9x-3x = 12+24
6x = 36
x = 36/6
x = 6
Name the property of real numbers illustrated by the equation.
-3(x+4)=-3x-12
A. Distributive Property
B. Associative Property of Addition
C. Associative Property of Multiplication
D. Commutative Property of Addition
Answer:
A. Distributive Property
Step-by-step explanation:
I'm taking the exam right now. :)
What is the remainder R when the polynomial p(x) is divided by (x + 1)? Is (x + 1) a factor of p(x)? p(x) = -3x4 + 2x3 - x2 + 6
Answer:
(x+1) is a factor with remainder 0.
Step-by-step explanation:
We divide (x+1) into the polynomial [tex]-3x^4+2x^3-x^2+6[/tex] through long division or synthetic. We choose long division and look for what will multiply with (x+1) to make the polynomial [tex]-3x^4+2x^3-x^2+6[/tex] .
[tex](x+1)(-3x^3)=-3x^4-3x^3[/tex]
We subtract this from the original [tex]-3x^4-(-3x^4)+2x^3-(-3x^3)-x^2+6[/tex].
This leaves [tex]5x^3-x^2+6[/tex]. We repeat the step above.
[tex](x+1)(5x^2)=5x^3+5x^2[/tex].
We subtract this from [tex]5x^3-(5x^3)-x^2-(5x^2)+6=-6x^2+6[/tex]. We repeat the step above.
[tex](x+1)(-6x)=-6x^2-6x[/tex].
We subtract this from [tex]-6x^2-(-6x^2)+0x-(-6x)+6=6x+6[/tex]. We repeat the step above.
[tex](x+1)(6)=-6x+1[/tex].
We subtract this from [tex]6x-(6x)+6-(6)=0[/tex]. There is no remainder. This means (x+1) is a factor.
Richie the Racoon and his family are all going to a family reunion! At the reunion there is a grandmother, a grandfather, two mothers, two fathers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, a mother-in-law, a father-in-law and a daughter-in-law. How many people came to Richie's family reunion?
Answer:
Seven
Step-by-step explanation:
We have the following list of people coming to the reunion,
A grandmother = 1
A grandfather = 2
Two mothers = 1 and 3
Two fathers = 2 and 4
i.e. Up until here there are total 4 people - Grandmother, Grandfather, Mother, Father ( 1, 2, 3, 4)
Four children = 4, 6, 7, 8
Three grandchildren = 6, 7, 8
One brother = 6
Two sisters = 7, 8
Two sons = 4, 6
Two daughters = 7, 8
Therefore, in addition to the four people above, one of the child will be the father and so there are 3 grandchildren.
So, number of people added in this step is 3 and total number of people up until here becomes 7.
A mother-in-law = 1
A father-in-law = 2
A daughter-in-law = 3
So, no new family member is added in this step.
Hence, total number of family members coming to reunion are 7 namely Grandmother, Grandfather, Mother, Father, Three children.
On a standardized test, a score of 82 falls exactly 1 standard deviation below the mean. If the standard deviation for the test is 4, what is the mean score for the test?
Answer:
The correct answer is 86.
Step-by-step explanation:
Because 82 is only one standard deviation below the mean, then to find the mean, only add 82 + 4 = 86
The mean score for the test is 86.
What do you mean by standard deviation?In statistics, Standard deviation is a measure of the variation of a set of values.
σ = standard deviation of population
N = number of observation of population
X = mean
μ = population mean
We are given that;
Score=82
Number of tests=4
Now,
We can substitute σ=4 and xi=82 into the formula. We also know that there is only one data point that satisfies this condition, so we can use N=1.
[tex]\mu = \frac{\sum_{i=1}^{N}(x_i - \mu)^2}{N\sigma^2} + \mu[/tex]
We get:
μ=(82−μ)^2/4^2 +μ
Simplifying and solving for μ, we get:
μ=86
Therefore, by standard deviation the answer will be 86.
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Sophie Ruth is eating a 50-gram chocolate bar with contains 30% cocoa. How many grams of cocoa are in the chocolate bar?
A farmhouse 75 acres of wheat. The farmer can harvest the wheat from 12 acres per day. In how many days will all the Field be harvested?
Answer:
6.25
Step-by-step explanation:
Because to know the answer we have to divide 75 by 12 which is 6.25
PLEASE HELP ASAP 30 POINTS ):
Answer:
c (0,-4)
Step-by-step explanation:
-5x+y = -4
4x - 4y =16
Solve the first equation for y since we are using substitution.
-5x+y = -4
Add 5x to each side
-5x+5x+y = -4+5x
y = 5x-4
Substitute this equation y = 5x-4 into the second equation.
4x -4(5x-4) = 16
Distribute the -4
4x - 4(5x) -4(-4) = 16
4x-20x +16 = 16
Combine like terms
-16x +16 =16
Subtract 16 from each side
-16x+16-16 = 16-16
-16x =0
Divide by -16
x=0
But we still need to find y
y = 5x-4
y = 5(0) -4
y = -4
PLEASE HELP ASAP 25 POINTS
Answer:
Your answer is B!
Step-by-step explanation:
How to solve this 25 points!!!
[tex]\mathsf{Given : \dfrac{(3x^2y^-^3)^3}{27(xy)^-^9}}[/tex]
[tex]\mathsf{\implies \dfrac{(3)^3(x^2)^3(y^-^3)^3}{27(x)^-^9(y)^-^9}}[/tex]
[tex]\mathsf{\implies \dfrac{27(x)^6(y)^-^9}{27(x)^-^9(y)^-^9}}[/tex]
[tex]\mathsf{\implies \dfrac{(x)^6}{(x)^-^9}}[/tex]
[tex]\mathsf{\implies x^6^+^9}[/tex]
[tex]\mathsf{\implies x^1^5}[/tex]
Alex buys 24 cans of vegtables. 80 cents for a can of tomatoes. 40 cents for a can of corn. His total is $12.80. How many cans of corn does he buy?
Answer:
16 cans of corn
Step-by-step explanation:
Which statement about parallel lines is true
A new truck that sells for 28,000 decreases in value 13% each year. What is the decay factor , b?
40 (pts)
show work and answer(not multiple choice)
Quadrilateral OPQR is inscribed inside a circle as shown below. What is the measure of angle Q? You must show all work and calculations to receive credit.
Circle N is shown with an inscribed quadrilateral labeled OPQR. O is labeled 2x degrees. P is labeled y degrees. Q is labeled 2x plus 4 degrees. R is labeled 3y plus 8 degrees.
Answer:
m<Q = 92 degrees
Step-by-step explanation:
Opposite angles of a quadrilateral inscribed in a circle are supplementary.
Angles O and Q are opposite angles, so they are supplementary, so their measures add up to 180 degrees.
m<O + m<Q = 180
2x + 2x + 4 = 180
4x + 4 = 180
4x = 176
x = 44
m<Q = 2x + 4 = 2(44) + 4 = 92
Answer:
Q =92
Step-by-step explanation:
Since the quadrilateral is inscribed in a circle, the opposite angles add to 180 degrees.
<O + <Q = 180
2x+ 2x+4 = 180
4x+4 =180
Subtract 4 from each side
4x= 180-4
4x= 176
Divide by 4
x = 44
Q = 2x+4
Q = 2(44)+4
Q = 88+4
Q = 92
The table shows the input and output of a function Table(input:3,4,6,11. Output:5,7,11,21)
(a) Explain what makes this set of data a function.
(B) what could cause this set of data to not be a function? Provide a specific example to support your statement and explain throughly.
(c) write an equation, in function nation, that would fit in the inputs and outputs in the table. Show your work that proves your equation is true for the given data.
Answer:
(A)This set of data is a function because every input has an output.
(B) This set of data would not be a function if two inputs had the same output, for example, if the inputs were 3,4,4,11 and the outputs were 5,7,11,21 then the data set would not be a function because for input 4 it has two different outputs.
Step-by-step explanation:
Evaluate the expression described below if the variable given is 9. Two times the difference of one-third of a number and three. A. –9 B. –3 C. 0 D. 12
Answer:
Option C is correct.
The answer for the given expression is 0.
Step-by-step explanation:
Given the statement: Two times the difference of one-third of a number and three. and also variable given is 9.
Let x be the variable or number.
"One-third of a number" means [tex]\frac{1}{3}x[/tex]
Also, "difference of one third of a number and three " means [tex]\frac{1}{3}x-3[/tex]
Now, "Two times the difference of one-third of a number and three" means [tex]2 \times (\frac{1}{3} x -3)[/tex]
Then, the expression for the given statement : [tex]2 \times (\frac{1}{3} x -3)[/tex]
Substitute the value of x =9 in above expression we have;
[tex]2 \times (\frac{1}{3}(9) -3)[/tex] = [tex]2 \times (3 -3)[/tex] = [tex]2 \times (0)[/tex] = 0
therefore, the answer for the given expression is, 0
Tank A has a capacity of 9.5 gallons. 6 1\3 gallons of the tank"s water are poured out. How many gallons of water are left in the tank
Answer: Since 1/3 can't be turned into a decimal, change .5 into 1/2. In order to subtract, the fractions need a common denominator. The least common denominator is 6. So 1/3 turns into 2/6, and 1/2 turns into 3/6. Now you need to take 9 3/6 minus 6 2/6. The answer is 3 1/6 gallons of water.
Step-by-step explanation:
Final answer:
To find the remaining water in Tank A after pouring out 6 1/3 gallons, subtract 6.333 from the tank's total capacity of 9.5 gallons, which leaves 3.167 gallons remaining in the tank.
Explanation:
The question involves determining the remaining quantity of water in a tank after a certain volume has been removed, which is a basic subtraction problem in mathematics. To solve it, subtract the volume of water that was poured out from the total capacity of the tank.
Tank A capacity: 9.5 gallons
Volume of water poured out: 6 1/3 gallons
To perform the subtraction, we first need to convert 1/3 of a gallon into a decimal. A third of a gallon is approximately 0.333 gallons. Adding this to 6 gallons gives us 6.333 gallons.
Now, subtract the volume poured out from the tank's capacity:
9.5 gallons (capacity) - 6.333 gallons (poured out) = 3.167 gallons (remaining in the tank)
Therefore, 3.167 gallons of water are left in the tank.
Given a standard deck of playing cards, what is the probability of randomly selecting a card that is either red or a face card or both? (a standard deck of playing cards has 52 cards, divided equally between red cards and black cards. there are twelve face cards among these 52, which are also divided equally between red cards and black cards. no card may be both red and black.)
Answer: [tex]\bold{\dfrac{8}{13}}[/tex]
Step-by-step explanation:
Red or Face - duplicates (both red & face)
[tex]\dfrac{26}{52}[/tex] + [tex]\dfrac{12}{52}[/tex] - [tex]\dfrac{6}{52}[/tex]
= [tex]\dfrac{32}{52}[/tex]
= [tex]\dfrac{8}{13}[/tex] simplified
Final answer:
The probability of selecting a red or face card from a standard deck of cards is 8/13. This outcome is more likely than selecting a heart suit face card specifically, which has a probability of 3/52.
Explanation:
The problem can be solved by understanding that the deck has 26 red cards (hearts and diamonds) and 12 face cards (jacks, queens, and kings), with 6 face cards being red. The total number of unique choices that are either red cards or face cards is the number of red cards plus the number of black face cards. This avoids double-counting red face cards.
There are 26 red cards, but we need to exclude the 6 red face cards already counted, and add the 6 black face cards (from clubs and spades), giving us 26 + 6 = 32 unique cards that are either red or face cards. The probability, P, is then 32/52, which simplifies to 8/13.
To compare, the probability of drawing specifically a heart suit face card is 3/52 as there are only 3 face cards (jack, queen, and king) in the heart suit. Comparing probabilities, 8/13 is greater than 3/52, so it is more likely to draw a red or face card than a heart suit face card.