Answer:
1,495,672
Step-by-step explanation:
Build a table to track the number of adult rats, 3-week old rats (let's call them teens), and baby rats.
[tex]\left[\begin{array}{ccccc}Week&Adult&Teen&Baby\\1&2&0&0\\3&2&0&10\\6&2&10&10\\9&12&10&10\\12&22&10&60\\15&32&60&110\\18&92&110&160\end{array}\right][/tex]
The pattern is this: every 3 weeks, the number of adults becomes the previous number of adults + the number of teens. The number of teens becomes the previous number of babies. And the number of babies becomes the previous number of adults × 5.
Continuing:
[tex]\left[\begin{array}{ccccc}Week&Adult&Teen&Baby\\1&2&0&0\\3&2&0&10\\6&2&10&10\\9&12&10&10\\12&22&10&60\\15&32&60&110\\18&92&110&160\\21&202&160&460\\24&362&460&1010\\27&822&1010&1810\\30&1832&1810&4110\\33&3642&4110&9160\\36&7752&9160&18210\\39&16912&18210&38760\\42&35122&38760&84560\\45&73882&84560&175610\\48&158442&175610&369410\\51&334052&369410&792210\end{array}\right][/tex]
So at the end of the year, there are a total of 1,495,672 rats.
Question # 4
1) Brett is 18 years younger than Mark. Carl is 10 years younger
than Mark. The sum of the ages of Brett, Mark, and Carl is 212
How old are each of the 3 men? EXPLAIN:
Answer:
Brett is 62 years old, Mark is 80 years old and Carl is 70 years old
Step-by-step explanation:
First; we let Brett age to be = x
let Mark age to be = y
let Carl age to be = z
From the question;
since Brett is 18 years younger than Mark, then Brett age is ;
x = y - 18
Also, since Carl is 10 years older younger than Mark, then Carl age is:
z = y-10
Also, from the question says the sum of the ages of Brett, Mark and Carl is 212
This means when you add all their ages together, you will have 212
so; x + y + z = 212
From the equation above, we can substitute x with y-18 and then substitute z with y-10
y-18 + y + y-10 = 212
3y - 28 = 212
add 28 to both-side of the equation
3y - 28 + 28 = 212 + 28
3y = 240
Divide both-side of the equation by 3
3y/3 = 240/3
y = 80
But x = y -18 = 80 -18 = 62
Also; z = y - 10 = 80 -10 = 70
Since x represent Brett age, then Brett's is 62 years old
Also, y represent Mark's age, therefore Mark is 80 years old
Finally z represent Carl's age, therefore Carl is 70 years old.
According to this information, what was the percentage of carbon-14 remaining in an object after 55 years?
Answer:
Option A that is [tex]99.34[/tex] is the correct choice.
Step-by-step explanation:
To find what percentage of carbon-14 is still remaining after [tex]55[/tex] years.
We have to pull the equation and instead of [tex]t[/tex] we will put the years in numbers that is [tex]t=55[/tex]
Lets see the equation.
[tex]C(t)=100.e^{-0.000121(t)}[/tex]
Now to find the carbon-14 percentage.
Putting the value of [tex]t[/tex] in years.
So
[tex]C(t)=100.e^{-0.000121(t)}[/tex] and [tex]e^{-0.000121(55)}=0.9934[/tex]
[tex]C(t)=100\times 0.9934 =99.34[/tex]
As mentioned that the function is already framed to find the percentage we need not to convert it or multiply with [tex]100[/tex].
So the percentage of C-14 remaining after [tex]55[/tex] years is [tex]99.34[/tex]
Option A is the correct choice.
The angle measures of equilateral triangle ABC can be represented by (2x+10)degrees. Find the value of x.
A.) 60
B.) 35
C.) 55
D.) 25
A manufacturer of window frames knows from past experience that 15 per cent of the production will have some type of minor defect that will require adjustment. Suppose 20 windows are selected at random: How many window frames would you expect to have minor defects?
Answer: 3
Step-by-step explanation:
Given : A manufacturer of window frames knows from past experience that 15 per cent of the production will have some type of minor defect that will require adjustment.
i.e. the proportion of production will have some type of minor defect that will require adjustment. : p=0.15
If n=20 windows are selected at random , then the expected number of window frames have minor defects = np
[tex]=20\times0.15=3[/tex]
Hence, the expected number of window frames have minor defects =3
W=3C - 4D, Solve C in terms of W and D
The solution for C in terms of D and W is:
[tex]C = \frac{W+4D}{3}[/tex]
Step-by-step explanation:
Solving a formula for a given variable means to isolate the variable on one side of the equation
Given equation is:
[tex]W = 3C-4D[/tex]
We have to solve for C in terms of W and D
Adding 4D on both sides
[tex]W+4D = 3C-4D+4D\\W+4D=3C[/tex]
Dividing both sides by 3
[tex]\frac{W+4D}{3}=\frac{3C}{3}\\C = \frac{W+4D}{3}[/tex]
So,
The solution for C in terms of D and W is:
[tex]C = \frac{W+4D}{3}[/tex]
Keywords: Formula, Variables
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Danielle and Tracy are building a rectangular sandbox. Danielle has two boards that are equal in length, and Tracy has two boards that are each 5 feet longer than Danielle’s. They use the four boards as the four sides of their sandbox. Use the variable x to write an algebraic expression to relate the perimeter of the sandbox to the length of one of Danielle’s boards.
Answer:
[tex]P=4x+10[/tex]
Step-by-step explanation:
Let
x -----> the length of Danielle's board in feet
y ----> the length of Tracy's board in feet
we know that
[tex]y=x+5[/tex] ----> equation A
The perimeter of the sandbox is equal to
[tex]P=2(x+y)[/tex] ----> equation B
substitute equation A in equation B
[tex]P=2(x+x+5)[/tex]
[tex]P=2(2x+5)[/tex]
[tex]P=4x+10[/tex]
What Passes through (6,-3) parallel to y= -2x-5?
Answer:
y+2x=9 is the line passing through (6,-3) parallel to y=-2x-5
Step-by-step explanation:
In the question we are given with a point (6,-3) and a line [tex]y=-2x-5[/tex]. we have to find the line passing through given point and parallel to given line.\
formula used: equation of a line passing through a point(a,b) with slope m is given by [tex](y-b) = m(x-a)[/tex].
here we have (a,b)=(6,-3) and the slope of the line is slope of [tex]y=-2x-5[/tex]
i.e, -2( coefficient of x).
therefore, substituting point and slope in formula we get [tex]y+3 = -2(x-6)[/tex]
which simplifies to [tex]y+3= -2x+12\\ y+2x=9[/tex] is asked line equation
Round 8.795 to the nearest cent
Answer:
8.80
Step-by-step explanation:
Final answer:
To round 8.795 to the nearest cent, look at the third decimal place. Since it's 5 or greater, round up the second decimal place to get 8.80.
Explanation:
When rounding 8.795 to the nearest cent, the focus is on the hundredth's place, since a cent is one hundredth of a dollar. You look at the digit in the thousandth's place to decide whether to round up or down. The digit in the thousandth's place is a 5, which means we follow the rule to round up since it is greater than 5. Thus, rounding 8.795 to the nearest cent gives us 8.80.
Three groups of a number plus two
Answer:
Step-by-step explanation:
This can be modelled with the variable x to represent the "groups"
3x + 2
Multiplifcation means groups of.
3x is 3 times x, which is 3 groups of x.
The question 'Three groups of a number plus two' translates to the algebraic expression 3x + 2 in mathematics. Here, x represents the unknown number.
Explanation:The question 'Three groups of a number plus two' pertains to algebraic expressions and equations. When you interpret the question as a mathematical equation, it represents the formula 3x + 2, where 'x' is a variable representing an unknown number. In this formula, 'Three groups of a number' corresponds to the component '3x', and 'plus two' is the mathematical operation adding 2 to this number. This is the fundamental concept behind forming algebraic expressions and equations.
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A box has dimensions of 14inches long,1.5 feet wide,and 7inches high. What is the volume of the box?
Step-by-step explanation: In this problem, we are asked to find the volume of a box which means we use the formula for finding the volume of a rectangular prism.
To find the volume of a rectangular prism or a prism whose base is a rectangle, we use the following formula.
Volume = length × width × height
Before plugging any numbers into our length, width, or height, first notice that we have dimensions in inches and feet. To make this easier, let's first convert the width which is 1.5 feet into inches. 1.5 feet is equal to 18 inches so now we are all set.
Since the rectangular prism has a length of 14 inches, a width of 18 inches, and a height of 7 inches, we can plug this information into the formula.
Volume = (14 in.) (18 in.) (7 in.)
Volume = 1,764 in.³
Therefore, the volume of the box is 1,764 in.³.
help
step for step please
Answer:
x + y ≥ 35 and 15x + 8y ≥ 350
Step-by-step explanation:
Mitch is packing books into boxes.
Each box can hold either 15 small books or 8 large books.
Now, given that Mitch needs to pack at least 35 boxes and at least 350 books.
Now, if x is the number of small book-boxes and y is the number of large book-boxes,
Then, we can write from the above conditions that
x + y ≥ 35.......... (1) and
{Since total number of boxes must be at least 35}
15x + 8y ≥ 350 .......... (2)
{Since the total number of books must be at least 350 and each large book-boxes contain 8 large books and each small book-boxes contain 15 small books}
Therefore, the equations (1) and (2) are the required inequality equations that model the situation. (Answer)
36.00 divided by 54
PLEASE MARK BRAINLIEST!
Answer:
36.00 ÷ 54 = 36 ÷ 54
Step-by-step explanation:
Decimal Form:
0.66666666...
Fraction Form:
2/3
Percent form:
66.6...%
I hope this helps!
Answer:
66%, 2/3 or 0.66666...7
Step-by-step explanation:
Dividing 36.00 by 54 is the same as "36 ÷ 54". Now to solve:
36 ÷ 54 = 0.66666...7
There are different ways to show this such as:
66%, 2/3 and 0.66666...7
Hope this helps,
♥A.W.E.S.W.A.N.♥
P.S. The "..." in 0.66666...7 just mean there are more 6s.
You can give 5accsdeletedalready Brainliest!
A toy car costing $50 is reduced by 10% in the sale. how much money is it reduced by?
Answer:
$5
Step-by-step explanation:
10% = 10/100 = 1/10.
1/10 of 50 = 5
How many zeros does the function f(x)=3x^12 -17x^8+11x^4-6x+23 have
Answer:
12.
Step-by-step explanation:
The number of zeros to an equation is the highest power of the polynomial.
A quadratic equation whose highest degree is 2, has two solutions.
The equation f(x) = [tex]$ 3x^{12} - 17x^{8} + 11x^{4} - 6x + 23 $[/tex] will have 12 solutions (or zeroes) since the highest degree is 12.
Twice a number added to a smaller number is 5. The difference of 5 times the smaller number and the larger number is 3. Let
x represent the smaller number and y represent the larger number. Which equations represent the situation?
2y+x25
5x-y-3
2x+y = 5
5y-x-3
2y+x=5
y- 5x-3
2x+y=5
x-5y-3
Answer:
The equations that represent the situation are:
2y+x=5
5x-y=3
Answer:
2y+x=5
5x-y-3
Step-by-step explanation:
Two times of the larger number which is y is 2y added to the smaller number x is equal to 5 . Which is 2y+x=5
The difference of five times the smaller number and larger number is 5x-y
And the resulting answer is 3
ie..5x-y=3 , when the 3 crosses to the other side it becomes 5x-y-3=0
hence,the equation 5x-y-3
km
Two buses leave a station at the same time and travel in opposite directions. One bus travels 10 - - slower than the other. If the two buses are 1442
kilometers apart after 7 hours, what is the rate of each bus?
Rate of the slower bus:
X
5
?
Rate of the faster bus:
Answer:
The speed of faster bus is 108 kmph and The speed of slower bus is 98 kmph .
Step-by-step explanation:
Given as :
The two buses apart 1442 km
The time taken for apart = 7 hours
Let The speed of faster bus = x kmph
The speed of slower bus = ( x - 10 ) kmph
Now Speed = [tex]\dfrac{\textrm distance}{\textrm time}[/tex]
∵ Both the buses traveling in opposite direction
So, The speed of faster bus + the speed of slower bus = [tex]\dfrac{\textrm distance cover}{\textrm time}[/tex]
Or, x + x - 10 = [tex]\frac{1442}{7}[/tex]
or, 2 x = 206 + 10
or, 2 x = 216
∴ x = [tex]\frac{216}{2}[/tex]
I.e x = 108 kmph
So, The speed of faster bus = x = 108 kmph
And The speed of slower bus = ( x - 10 ) = 108 - 10 = 98 kmph
Hence The speed of faster bus is 108 kmph and The speed of slower bus is 98 kmph . Answer
How many solutions does this system have?
Answer:
One solution since x=0
3x +10 < 3 or 2x -5 > 5
For this case we must find the solution set of the given inequalities:
Inequality 1:
[tex]3x + 10 <3[/tex]
Subtracting 10 from both sides of the inequality:
[tex]3x <3-10[/tex]
Different signs are subtracted and the major sign is placed.
[tex]3x <-7[/tex]
We divide between 3 on both sides of the inequality:
[tex]x <- \frac {7} {3}[/tex]
The solution is given by all values of x less than[tex]- \frac {7} {3}[/tex]
Inequality 2:
[tex]2x-5> 5[/tex]
Adding 5 to both sides of the inequality:
[tex]2x> 5 + 5\\2x> 10[/tex]
Dividing by 2 to both sides of the inequality:
[tex]x> \frac {10} {2}\\x> 5[/tex]
The solution is given by all values of x greater than 5.
Thus, the solution set is given by:
(-∞, [tex]- \frac {7} {3}[/tex]) U (5,∞)
ANswer:
(-∞, [tex]- \frac {7} {3}[/tex]) U (5,∞)
You want lose an average of 4 pounds per month on a new weight loss program. In the first 3 months, you lost 3 pounds, 7 pounds and 4 pounds. How much weight must you lose during the fourth month to maintain an average weight loss to 4 pounds per month
Answer:
Add all pounds lost during 3 months. 3+7+4= 14. 4 lbsx4 months =16. 16-14=2. 2 lbs must be lost during the 4 month to stay consistent with the 4 lbs weight loss per month.
Step-by-step explanation:
To maintain an average weight loss of 4 pounds per month, you must lose 2 pounds in the fourth month. This calculation is obtained by subtracting the total weight already lost (14 pounds in three months) from the target total weight loss (16 pounds in four months).
Explanation:The question is asking how much weight you need to lose in the fourth month to maintain an average weight loss of 4 pounds per month, given that you've lost 3, 7 and 4 pounds in the first three months respectively.
First, let's calculate the total weight you've lost so far: 3 pounds + 7 pounds + 4 pounds = 14 pounds lost in the first three months.
Next, calculate how much weight you would need to lose in total over four months to maintain an average loss of 4 pounds per month: 4 months * 4 pounds per month = 16 pounds.
Now, subtract the total weight you've already lost from the target total weight to find out how much weight you need to lose in the fourth month: 16 pounds - 14 pounds = 2 pounds. Therefore, you need to lose 2 pounds in the fourth month to maintain an average monthly weight loss of 4 pounds.
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In parallelogram ABCD,m
Answer:
After that????? Please ask me the full question please.
Thank you
kyle made a pot of chili with 48 ounces of ground beef and two tablespoons of chili powder he made another pot of chili with the same amount of ground beef but he used three times as much chili powder howmany pounds of ground beef per tablespoons of chili powder did he use in the second pot
Answer:
8 pounds per tablespoon
Step-by-step explanation:
2 (3) = 6
48 (1/6) = 8
Answer:
8 pounds per tablespoon
Step-by-step explanation:
2 (3) = 6
Step-by-step explanation:
Prove that congruent triangles have congruent corresponding medians.
Answer:
Proved
Step-by-step explanation:
Figure two triangles which are congruent to each other has been attached
Proof :
1)BC= CD ( given )
2) AC= CE ( Given)
3) ∠ACB= ∠ECD ( vertically opposite to each other)
therefore, ΔABC≅ΔDCE ( By SSA postulate)
Now, CF and CG be medians on the sides Ab and DE of the Δ's ABC and DCE respectively
⇒CF= CG because of CPCTC that is corresponding parts of congruent triangles are congruent.
Therefore, congruent triangles have congruent corresponding medians.
Becky buys 3 books and the total cost is $24.18. What is the constant of proportionality that relates the cost in dollars, y, to the number of books, x?
Answer: 1x = $8.06y
Step-by-step explanation:
thats honestly all i know..
This composite figure is made of two identical pyramids attached at their bases. Each pyramid has a height of 2 units.
2 identical pyramids with rectangular bases are connected at their base. The height of the pyramid is 2. The lengths of the sides of the rectangle are 5 and 0.25 units.
Answer:
The total volume of the solid is 1.67 cubic units.
Step-by-step explanation:
Each pyramid with a height of 2 units and a rectangular base with dimensions of 5 units × 0.25 units.
Therefore, the volume of each pyramid will be [tex]\frac{1}{3} \times \textrm {(Area of base rectangle)} \times \textrm {Height}[/tex]
= [tex]\frac{1}{3} \times (5 \times 0.25) \times 2 = 0.833[/tex] cubic units.
So, the total volume of the solid is (2 × 0.833) = 1.67 cubic units. (Answer)
Final answer:
To calculate the volume of the composite figure made from two identical pyramids with rectangular bases, we first find the volume of one pyramid using the formula for the volume of a pyramid and then multiply by two, resulting in a total volume of 1.666 cubic units.
Explanation:
The question involves calculating the volume of a composite figure made of two identical pyramids attached at their bases, with each pyramid having a rectangular base. The dimensions provided are a height of 2 units for each pyramid, and the rectangle's sides are 5 and 0.25 units. To find the volume of one pyramid, we use the formula for the volume of a pyramid, V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. The area of the rectangular base, B, is calculated as length × width = 5 × 0.25 = 1.25 square units. Substituting the values into the volume formula gives us V = (1/3)×1.25×2 = (1/3)×2.5 = 0.833 cubic units for one pyramid. Since the composite figure is made up of two such pyramids, the total volume is 2 × 0.833 = 1.666 cubic units.
The first term of an arithmetic sequence is -3 and the fifteenth term is 53. What is the common difference of the sequence?
A: 14/13
B: 25/7
C: 4
C: 4 is the right answer
Step-by-step explanation:
Given
a1 = -3
a15 = 53
We know that explicit formula for the arithmetic sequence is:
[tex]a_n=a_1+(n-1)d[/tex]
For the 15th, term it will be
[tex]a_{15}=-3+(15-1)d\\53=-3+14d[/tex]
Adding 3 on both sides
[tex]53+3 = -3+3 + 14d\\56 = 14d[/tex]
Dividing both sides by 14
[tex]\frac{56}{14}=\frac{14d}{14}\\d=4[/tex]
Hence,
C: 4 is the right answer
Keywords: Arithmetic sequence, Common Difference
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Answer:
C) 4 is the correct answer
On the middle school baseball team, 8 players are sixth graders. Of the players, 40% are sixth graders. How many
players are on the team? Explain your answer.
There are 20 players are on the team.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
On the middle school baseball team, 8 players are sixth graders.
And, Of the players, 40% are sixth graders.
Now,
Let number of players on the team = x
So, We can formulate;
⇒ 40% of x = 8
⇒ 40/100 × x = 8
⇒ 40x = 800
⇒ x = 800/40
⇒ x= 20
Thus, Number of players on the team = 20
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Final answer:
There are 20 players on the middle school baseball team in total, calculated by dividing the number of sixth graders (8) by the percentage that represents sixth graders (40%).
Explanation:
Based on the information given, if 40% of the players on the middle school baseball team are sixth graders, and there are 8 sixth graders on the team, we can calculate the total number of players on the team. We know that 40% is equal to 0.40 when expressed as a decimal. Thus, the equation to find the total number of players (T) is 0.40 * T = 8.
To find T, divide both sides of the equation by 0.40:
T = 8 / 0.40
T = 20
Therefore, there are 20 players on the team in total.
The sum of four consecutive whole numbers is 94.what is the largest numbers?
Answer: 25
Step-by-step explanation: This problem states that the sum of four consecutive whole numbers is 94 and it asks us to find the largest number.
Three consecutive whole numbers can be represented as followed.
X ⇒ first number
X + 1 ⇒ second number
X + 2 ⇒ third number
X + 3 ⇒ fourth number
Since the sum of our four consecutive whole numbers is 94, we can set up an equation to represent this.
X + X + 1 + X + 2 + X + 3 = 94
We can combine the x's on the left side of the equation and combine the numbers as well.
4x + 6 = 94
-6 -6 ← subtract 6 from both sides of the equation
4x = 88
÷4 ÷4
X = 22
X ⇒ first number = 22
X + 1 ⇒ second number = 23
X + 2 ⇒ third number = 24
X + 3 ⇒ fourth number = 25
Therefore, the largest number would be 25.
How do I solve this?
5x + 3x + 7x = 180
15x = 180
x = 12
I = 5(12) = 60
M = 3(12) = 36
S = 7(12) = 84
Check: 60 + 36 + 84 = 180
Answer:
∠I=75° , ∠M=45° ,∠S=105°, ∠E=173.5°
Step-by-step explanation:
given ∠I=5X,∠M=3X,∠S=7X, ∠E=128.5+3X
IN TRIANGLE IMS
∠I+∠M+∠S=180°
5X+3X+7X=180°
12X=180°
X=15°
HENCE ∠I=5X=[tex]5\times15°[/tex]
∠I=75°
∠M=3X=[tex]3\times15°[/tex]
∠M=45°
∠S=7X=∠[tex]7\times15°[/tex]
∠s=105°
∠E=128.5+3X=128.5+45=173.5°
∠E=173.5°
Beth bought 20 tickets to a movie, where adult tickets cost $8.00 and senior citizen tickets cost $4.00. She spent a total of $140. Which system of equations will determine the number of adult tickets, a, and the number of senior citizen tickets, s, Beth purchased?
Answer:
The Total number of adults ticket's is 15
The Total number of Senior citizen ticket's is 5
Step-by-step explanation:
Given as :
The total number of movies tickets were bought = 20
The cost of adults tickets = $ 8.00
The cost of senior citizen tickets = $ 4.00
The total money spent on movie tickets = $ 140
Let The total number of adults tickets = A
And The total number of senior citizen tickets = S
Now, According to question
The total number of movies tickets were bought = 20
I.e The total number of adults tickets + The total number of senior citizen tickets = 20
Or, A + S = 20
And $ 8 A + $ 4 S = $ 140 .........1
I.e 8 × ( A + S ) = 8 × 20
Or, 8 A + 8 S = 160 .......2
Solving the equation 1 and 2
Or, ( 8 A + 8 S ) - ( 8 A + 4 S ) = 160 - 140
Or, ( 8 A - 8 A ) + ( 8 S - 4 S ) = 20
or, 0 + 4 S = 20
∴ S = [tex]\frac{20}{4}[/tex]
I.e S = 5
So, The number of Senior citizen ticket's = 5
Put The value of S in eq 1
So, 8 A + 4 × 5 = 140
Or, 8 A = 140 - 20
Or, 8 A = 120
∴ A = [tex]\frac{120}{8}[/tex]
I.e A = 15
So, The number of adult's tickets = 15
Hence The Total number of adults ticket's is 15
And The Total number of Senior citizen ticket's is 5 Answer
a rectangular plot of land has an area of 52/96 square kilometers and a length of 4/12 kilometers what is the width of plot of land
The width of plot of land is 13/8 kilometers.
Step-by-step explanation:
Area of rectangular plot = 52/96 square kilometers
Length of plot = 4/12 kilometers
Width of plot = w
Area of rectangle = length * width
[tex]\frac{52}{96}=\frac{4}{12}*w\\[/tex]
Multiplying both sides by [tex]\frac{12}{4}\\[/tex]
[tex]\frac{52}{96}*\frac{12}{4}=\frac{12}{4}*\frac{4}{12}w\\\\\frac{624}{384}=w\\\\\frac{13}{8}=w\\\\w=\frac{13}{8}[/tex]
The width of plot of land is 13/8 kilometers.
Keywords: rectangle, area
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