Answer:
The answer is 9 hours
Step-by-step explanation:
From the initial population of 180 cells, the number grows by 8% every hour for the first 9 hours.
This represents a increased population of 108% the previous population.
108% = 108/100 = 1.08
So the new population after n hours is
180 x 1.08^n
When population is 360
360 = 180 x 1.08^n
1.08^n = 2
Take log of both sides
n x Log1.08 = Log 2
n = Log 2/Log 1.08
n = 9
h(x) = 3x + 2; Find h(-5)
Answer:
h(-5) = -13
Step-by-step explanation:
h(x) = 3x + 2
Let x = -5
h(-5) = 3(-5) +2
= -15 +2
= -13
Answer:
H(-5)= -13
Step-by-step explanation:
1) Plug in -5 for the variable X
2) Then Solve
h(-5)= 3(-5) + 2
h(-5)= -15 + 2
H(-5)= -13
Hope this Help!
Find the area of a circle with a radius of 3
Either enter an exact answer in terms of π or use 3.143.143.143, point, 14 for π\piπpi and enter your answer as a decimal.
The area of the circle with a radius of 3 is approximately 28.26 square units using the approximation [tex]\( \pi \approx 3.14 \).[/tex]
The area [tex]\(A\)[/tex] of a circle with radius [tex]\(r\)[/tex] is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]
Given that the radius [tex]\(r\)[/tex] is 3, we can substitute this value into the formula:
[tex]\[ A = \pi \times (3)^2 \][/tex]
[tex]\[ A = \pi \times 9 \][/tex]
Using the approximation [tex]\( \pi \approx 3.14 \),[/tex] we can calculate:
[tex]\[ A \approx 3.14 \times 9 \][/tex]
[tex]\[ A \approx 28.26 \][/tex]
Therefore, the area of the circle with a radius of 3 is approximately [tex]\(28.26\).[/tex]
Nick wants to build a rectangular enclosure for his animals. one side of the pen will be against the barn, so he needs no fence on that side. the other three sides will be enclosed with wire fencing. if nick has 700 feet of fencing, you can find the dimensions that maximize the area of the enclosure.
Answer:
350 ft long facing the barn and 175 ft wide
Step-by-step explanation:
Let a and b be the length and width of his rectangular fence. Since he has 700 feet of fencing and one side does not need fencing. We have the following constraint equation:
a + 2b = 700
a = 700 - 2b
We want to maximize the following area formula
A = ab
We can substitute a = 700 - 2b
[tex]A = (700 - 2b)b = 700b - 2b^2[/tex]
To find the maximum value of this, simply take the 1st derivative, and set it to 0
A' = 700 - 4b = 0
b = 700 / 4 = 175 ft
a = 700 - 2b = 700 - 350 = 350 ft
What is the shortest distance between points (-2, 1) and (2,-2)?
Select the appropriate response:
A) 1
B) 2
C) 3
D) 5
Distance = SQRT((X2 -x1)^2 + (y2-y1)^2)
Distance = sqrt((2 - (-2)^2) + (-2 - 1)^2))
Distance = sqrt(4^2 + -3^2)
Distance = sqrt(16 + 9)
Distance = sqrt(25)
Distance = 5
Answer is D. (5)
Answer:
D) 5
Step-by-step explanation:
sqrt[(-2 - 2)² + (1 - -2)²]
sqrt(25)
5
Cylindrical tank A has 9/10 of the radius and 9/10 of the height of cylindrical tank B. If tank A can hold 20 gallons, approximately how many gallons can tank B hold?
Answer: Tank B can hold 27.4 gallons
Step-by-step explanation:
Volume of a cylinder = πr^2h
Given that Cylindrical tank A has 9/10 of the radius and 9/10 of the height of cylindrical tank B
Let the radius of A = r
Radius of B = R
Height of A = h
Height of B = H
r = 0.9R and h = 0.9H
Volume of A = πr^2h
= π(0.9R)^2(0.9H)
= 2.29R^2H
Given that tank A can hold 20 gallons, approximately
20 = 2.29R^2H
R^2H = 20/2.29 = 8.73 ..... (1)
Volume of B = πR^2H
Substitutes R^2H in equation (1) into Volume of B
Volume of B = 3.143 × 8.73
Volume of B = 27.4 gallons
Answer: Tank B can hold 27.43 gallons
Step-by-step explanation: Please see the attachments below
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly and at a constant rate. After 8 88 months, he weighed 138 138138 kilograms. He started at 90 9090 kilograms. Let y yy represent the sumo wrestler's weight (in kilograms) after x xx months. Complete the equation for the relationship between the weight and number of months.
Final answer:
The equation representing the sumo wrestler's weight gain over time is y = 6x + 90, where y is the weight after x months, starting at 90 kilograms and increasing by 6 kilograms each month.
Explanation:
The student has provided the initial and final weights of the sumo wrestler, as well as the duration in months over which the weight gain occurred. We can use this information to calculate the rate of weight gain per month and create an equation to represent this relationship. The sumo wrestler started at 90 kilograms and reached 138 kilograms after 8 months. The equation will be in the form of y = mx + b, where m is the slope (rate of weight gain) and b is the y-intercept (initial weight).
To calculate the slope, m, we use the formula:
m = (Final weight - Initial weight) / (Final time - Initial time)
In this case, m = (138 kg - 90 kg) / (8 months - 0 months) = 48 kg / 8 months = 6 kg/month.
The y-intercept, b, is the initial weight of the sumo wrestler, which is 90 kilograms.
Therefore, the complete equation is y = 6x + 90, where y represents the sumo wrestler's weight after x months.
Help please will give brainly! What is the relationship between addition and subtraction, multiplication, and division?
Answer: PEMDAS
Step-by-step explanation:
A cow walks 1/2 mile in 1/4 of an hour. How many miles will the cow walk in 1 hour?
the cow will walk 2 miles
Step-by-step explanation:
half a mile - 0.5 miles
1/4 of an hour = 0.5 miles
2/4 of an hour = 1 Miles
3/4 of an hour = 1.5 miles
4/4 of an hour (one hour) = 2 miles
0.5 × 4 = 2
The population of a particular country was 22 million in 1985; in 1993, it was 31 million. The exponential growth function A=22e^kt describes the population of this country t years after 1985. Use the fact that 8 years after 1985 the population increased by 9 million to find k to three decimal places.
Answer:
0.043
Step-by-step explanation:
We are given that
Initially when t=0
Then, A=22 million
The population of a country after t years is given by
[tex]A=22e^{kt}[/tex]
When t=8 then A=31 million
Substitute the values
[tex]31=22e^{8k}[/tex]
[tex]\frac{31}{22}=e^{8k}[/tex]
[tex]1.409=e^{8k}[/tex]
[tex]8k=ln(1.409)=0.343[/tex]
[tex]k=\frac{0.343}{8}=0.043[/tex]
Rearrange the equation so r is the independent variable.
10q-5r=30
Independent variable is the variable that you change.
Dependent variable is the variable you measure that results from or depends on the independent variable.
Since you want "r" to be the independent variable, you isolate/get the variable "q" by itself in the equation: [this is because "r" would be the variable that changes, and "q" would be the variable you find/measure that depends on "r"]
10q - 5r = 30 Add 5r on both sides
10q = 5r + 20 Divide 10 on both sides to get "q" by itself
[tex]q=\frac{5r+30}{10}[/tex]
[tex]q=\frac{5r}{10} +3[/tex]
[tex]q=\frac{1}{2} r+3[/tex]
The value of r is the independent variable is [tex]\rm \dfrac{10q-30}{5}[/tex].
Given that,
Equation; [tex]\rm 10q-5r = 30[/tex]
We have to determine,
The value of r is the independent variable.
According to the question,
A variable whose values do not change is known as independent changes. They have their own value, which is not changed with the equation.
To determine the value of r is the independent variable following all the steps given below.
Therefore,
The value of r is the independent variable is,
[tex]\rm 10q-5r = 30\\\\10q=30+5r\\\\q = \dfrac{30+5r}{10}\\\\q = \dfrac{5}{5} \times \dfrac{6+r}{2}\\\\ q = \dfrac{1}{2}r + \dfrac{6}{2}\\\\ q = \dfrac{1}{2}r + 3\\\\[/tex]
Hence, The value of r is the independent variable is [tex]\rm \dfrac{1}{2}r + 3[/tex].
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GEOMETRY! PLEASE SHOW YOUR WORK. (updated picture)
Given:
The base of the given triangle has two part:
Left( left side of the hypotenuse) = 25
Right ( right side of the hypotenuse) = x
The altitude (h) = 60
To find the value of x.
Formula:
By Altitude rule we know that, the altitude of a triangle is mean proportional between the right and left part of the hypotenuse,
[tex]\frac{left}{altitude} =\frac{altitude}{right}[/tex]
Now,
Putting,
left = 25, altitude = 60 and right = x we get,
[tex]\frac{25}{60} =\frac{60}{x}[/tex]
or, [tex](25)(x )=(60)(60)[/tex] [ by cross multiplication]
or, [tex]x = \frac{3600}{25}[/tex]
or, [tex]x = 144[/tex]
Hence,
The value of x is 144.
Answer:
x = 144
Step-by-step explanation:
Height Theorem
60² = 25·x
3600 = 25x
x = 3600 : 25
x = 144
A local theater sells out their show. They sell all 500 tickets for a total of $8,070. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children’s tickets, how many of each type was sold?
Answer:
The number tickets sold was 120 student tickets, 95 children tickets and 285 adult tickets.
Step-by-step explanation:
Given:
A local theater sell all 500 tickets for a total of $8,070.
The price of tickets were $15 for students, $12 for children, and $18 for adults.
The adult tickets sold were three times as many as children’s tickets.
Now, to find the number of student tickets, children tickets and adult tickets sold.
Let the number of students ticket be [tex]x.[/tex]
Let the number of children ticket be [tex]y.[/tex]
So, the number of adults ticket be [tex]3y.[/tex]
Now, the total number of tickets sold:
[tex]x+y+3y=500\\\\x+4y=500\\\\x=500-4y\ \ \ ...(1)[/tex]
Now, the total cost of tickets:
[tex]x(15)+y(12)+3y(18)=8070\\\\15x+12y+54y=8070\\\\15x+66y=8070\\\\Substituting\ the\ value\ of\ x\ from\ equation\ (1):\\\\15(500-4y)+66y=8070\\\\7500-60y+66y=8070\\\\7500+6y=8070\\\\Subtracting\ both\ sides\ by\ 7500\ we\ get:\\\\6y=570\\\\Dividing\ both\ sides\ by\ 6\ we\ get:\\\\y=95.[/tex]
Thus, the number of children ticket is 95.
According the adult tickets sold were three times as many as children’s tickets.
Therefore, the number of adult tickets = 95 × 3 = 285.
Now, substituting the value of [tex]x[/tex] in equation (1) to get the number of student tickets:
[tex]x=500-4y\\\\x=500-4(95)\\\\x=500-380\\\\x=120.[/tex]
Hence, the number of student tickets is 120.
Therefore, the number tickets sold was 120 student tickets, 95 children tickets and 285 adult tickets.
The problem can be solved by creating a system of equations representing each type of ticket sales and their respective prices. Three equations are formed from the information provided and are then solved to find the numbers of each type of ticket sold.
Explanation:This problem can be solved using a system of equations, representing each type of ticket sales and their prices. Let's define the variables. Let's let x represent the number of student tickets, y represent the number of children's tickets, and z represent the number of adult tickets.
We know that the total number of tickets sold is 500, so we can form the equation:
x + y + z = 500.
Moreover, we know that the total amount of money made from the tickets is $8070, so we can form the equation:
15x + 12y + 18z = 8070.
Lastly, we know that the theater sold three times as many adult tickets as children's tickets, forming the equation:
z = 3y.
Using these three equations, we can substitute and simplify to find the values of x, y, and z, representing the numbers of student, children, and adult tickets sold respectively.
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Kenyl covers the front of a circular bulletin board with fabric that costs 1.48 per square foot. The bulletin board has a radius of 2.5 feet. Kenyl will count only the cost the exact amount of fabric he uses What is the cost of the fabric. Round to the nearest cent.
Answer:
29
Step-by-step explanation:
In this question we are trying to calculate the cost of exact amount of fabric used given the cost per area of the fabric.
To answer this question mathematically, we need to know the area of the bulletin board. To do this , we employ a mathematical approach. We know that the bulletin board is circular in shape from the question and thus we calculate the area of this shape.
Mathematically, the area of the circular bulletin board is pi * r^2 where r refers to the radius. From the question, we can identify that this radius is 2.5 feet. let’s insert this into the equation we have.
mathematically A = 2.5^2 * pi = 19.63 sq. feet
The cost of the fabric per square feet is 1.48.
now the cost for this area that we have will be 1.48 * 19.63 = 29.0524
This is nearest to 29
Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function f(x) = -16t2 + 96t gives the height, in feet, of the soccer ball after t seconds. This function is shown in the graph below.
How long will it take for the ball to hit the ground? Write your answer as an integer.
The ball will come to ground after 6 seconds.
We have a function of time given by -
f(x) = [tex]-16t^{2} +96t[/tex]
that gives the height of the ball in feet at ' t ' second.
We have to find out after how much time the ball will hit the ground.
In the question given to us above, the type of motion discussed is called ?The type of motion discussed in the above question is a two - dimensional projectile motion.
We have - h(t) = f(x) = [tex]-16t^{2} +96t[/tex]
Now, in order to find out the time at which the ball will hit the ground again, we will equate h(t) = f(x) = 0
[tex]-16t^{2} +96t=0\\-16t(t - 6)=0\\-16t =0\;\;\;\;\;\;t -6 = 0[/tex]
Now, time can never be 0.
Hence -
t - 6 = 0
t = 6 seconds.
Hence, the ball will come to ground after 6 seconds.
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3x-7x=12x how would u solve this?
Answer:
Because theres nothing to solve for x is all real numbers
Step-by-step explanation:
There is no way to solve it as theres nothing to solve for. You just plug in the x's with any number you want and it still will be there
find the ending balance $35,600 at 9% for 2 years
Answer:
42,008
Step-by-step explanation:
The ending balance after 2 years will be equal to $42008.
What is a simple interest?The amount of interest calculated on the principal amount over a whole year of the loan amount is called simple interest.
In finance and economics, interest is the payment of an amount over repayment of the original sum by a borrower or deposit-taking financial institution to a lender or depositor at a specific rate by a borrower or depositor. It differs from a fee that the borrower may pay to the lender or a third party.
Given that the amount is $35600 at 9% interest for 2 years. The total balance after 2 years will be,
SI = ( P x R x T ) /100
SI = ( 35600 x 9 x 2 ) / 100
SI = 6408
Ending amount = 6408 + 35600
Ending amount = $42008
Therefore, the ending balance after 2 years will be equal to $42008.
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Write 0.000000123 as a power of 10.
Answer:
1.23 x 10^-7
Step-by-step explanation:
you went back 7 so its negative
Answer:
123 x 10^(-9)
Step-by-step explanation:
just put it in scientific notations and you will get 123 x 10^(-9)
b/4 =7.25. What is b?
A triangle has a 40 degree angle and a 35 degree angle. What is the measure of the third triangle?
Answer:
105
Step-by-step explanation:
The sum of the angles of a triangle add to 180 degrees
<1 + <2 + <3 = 180
40 + 35 + <3 = 180
Combine like terms
75+ <3 = 180
Subtract 75 from each side
75-75 + <3 = 180-75
<3 = 105
Answer:
105 degrees
Step-by-step explanation:
In a triangle, the three interior angles always add to 180°
40 + 35 = 75
180-75 = 105 degrees
A small swimming pool has a circumference of 3π feet. Select the true statement about the pool.
a The radius is 3 ft.
b The diameter is 3 ft.
c The diameter is 1.5 ft.
d The radius is 6 ft.
Answer:
d dfghjkl
Step-by-step explanation:
i just knowvghnm,.
Simplify 6xy - 20y + 7z - 8x + 25y - 11z
Answer:
6xy - 8x + 5y - 4z
Step-by-step explanation:
6xy - 20y + 7z - 8x + 25y - 11z
Group the ones with the variable first to make an equation:
6xy - 8x - 20y + 25y + 7z - 11z
Solve the equation
6xy - 8x +5y - 4z
What is the surface area of the cylinder with height 5 in and radius 3 in? Round
answer to the nearest thousandth
The surface area of the cylinder with a height of 5 inches and a radius of 3 inches is calculated using the formula A = 2πrh + 2πr² and comes out to approximately 150.796 in² when rounded to the nearest thousandth.
Explanation:To calculate the surface area of a cylinder, we use the formula A = 2πrh + 2πr², where 'r' is the radius and 'h' is the height of the cylinder. Given the height 'h' is 5 inches and the radius 'r' is 3 inches, we substitute these values into the formula.
Calculating the lateral surface area (the area of the side):
A_lateral = 2πrh = 2π(3 in)(5 in) = 30π in².
Calculating the area of the two bases:
A_bases = 2πr² = 2π(3 in)² = 18π in².
Now, add the lateral area and the area of the bases to find the total surface area:
A_total = A_lateral + A_bases = 30π in² + 18π in² = 48π in².
Using π ≈ 3.14159, the total surface area is: A_total ≈ 48(3.14159) = 150.796 in². Rounded to the nearest thousandth, the surface area of the cylinder is 150.796 in².
What does it mean to say there is an association between characteristics in a two-way frequency table?
Answer:
An "association" exists between two categorical variables if the row (or column) conditional relative frequencies are different for the rows (or columns) of the table. ... If the conditional relative frequencies are nearly equal for all categories, there may be no association between the variables.
Step-by-step explanation:
Ben is 20 years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was 3 times as old as Daniel. How old is Daniel now?
The first thing to do is identify the unnecessary information (that they met 2 years ago).
From there, let's go back three years ago. We'll call Daniel's age x, and Ben's age will be 3x. Ben's age is also equal to x + 20.
3x = x+ 20
2x = 20
x = 10
Daniel was 10 three years ago, and Ben was 30. Now, Ben is 33.
5x + 7 < -3 or 3x - 4 > 11
Answer:
x < -2; x > 5
Step-by-step explanation:
5x + 7 < - 3 3x - 4 > 11
-7 -7 +4 +4
5x < - 10 3x > 15
/ 5 /5 /3 /3
x < -2 x > 5
To solve two inequalities: 5x + 7 < -3 and 3x - 4 > 11. The solutions are x < -2 and x > 5, respectively.
1. 5x + 7 < -3
2. 3x - 4 > 11
Let's solve each inequality one by one.
For the first inequality, 5x + 7 < -3, subtract 7 from both sides to get 5x < -10, then divide both sides by 5 to find that x < -2.
For the second inequality, 3x - 4 > 11, add 4 to both sides to obtain 3x > 15, then divide by 3 yielding x > 5.
The solution to the system of inequalities is that x can be any number less than -2 or any number greater than 5.
The second hand on a clock is 8 \text{ cm}8 cm8, space, c, m long. What is the distance the tip of the second hand travels in 101010 minutes? Round your answer to the nearest \text{cm}cmc, m. \text{cm}cm
Answer:
The distance the tip of the second hand travels in 10 minutes is 502 cm.
Step-by-step explanation:
Given : The second hand on a clock is 8 cm long.
To find : What is the distance the tip of the second hand travels in 10 minutes?
Solution :
The circumference of clock is [tex]C=2\pi r[/tex]
The radius is r=8 cm
[tex]C=2\times 8\times \pi[/tex]
[tex]C=16\pi[/tex]
i.e. in 1 minute it cover [tex]16\pi[/tex]
In 10 minutes it cover [tex]16\pi\times 10[/tex]
In 10 minutes it cover [tex]160\times 3.14[/tex]
In 10 minutes it cover [tex]502.4[/tex]
Therefore, the distance the tip of the second hand travels in 10 minutes is 502 cm.
What are the coordinates of Z?
A: (a – c, 0)
B: (c – 2a, 0)
C: (a, 0)
D: (0, b)
Solve for x.
Geometry
Answer:
x =17
Step-by-step explanation:
Given shape is of a irregular hexagon.
Sum of all angles of an irregular hexagon
[tex]=(6 - 2) \times 180 \degree = 4 \times 180 \degree = 720 \degree \\ \\ \therefore \: (6x - 2)\degree + (7x + 19)\degree + 116 \degree \\ \: \: \: + (5x + 36)\degree + (8x - 1)\degree + 110 \degree \\ \: \: \: = 720 \degree \\ \\ \therefore \:(26x + 52)\degree + 226\degree = 720 \degree \\ \\ \therefore \:26x\degree + 278\degree = 720 \degree \\ \\ \therefore \:26x\degree = 720 \degree - 278\degree \\ \\ \therefore \:26x\degree = 442 \degree \\ \\ \therefore \:x = \frac{442\degree}{26\degree} \\ \\ \huge \red{ \boxed{\therefore \:x = 17}}[/tex]
While walking by a classroom, Linda sees two perfect squares written on a blackboard. She notices that their difference is her favorite number, 99. She also notices that there are exactly two other perfect squares between them. What is the sum of the two perfect squares on the blackboard
Answer:
15^2
18^2
Step-by-step explanation:
Answer:
549
Step-by-step explanation:
considering 'n²' to express first square on board.
Remember 'n' is an integer
Now expressing second square with (n+3)² on the board.
(Therefore, The other two perfect squares in between are (n+1)² and (n+2)².
If asking for the difference that is 99:
(n+3)² - n² = 99
Solving for n:
n² + 6n + 9 - n² = 99
6n + 9 = 99
6n = 90
n = 90/6
n = 15
So the perfect squares on the board are:
n² => 15² = 225
(n+3)²=> 18² = 324
The difference between the above is 99
and exactly two other perfect squares (16² = 256 and 17² = 289) are in between.
Thus, the sum of the two perfect squares on the blackboard is,
225 + 324 = 549
The national touring company Spice on Ice visited Seattle, Washington, last year. THe producers held a special promotional ticket sale for one hour. During this time, adult tickets sold for $5, junior tickets (ages 9-17) sold for $2, and children’s tickets (ages 0-8) sold for the ridiculously low price of 10 cents. During this sale, 120 tickets sold for exactly $119. How many of each kind of ticket were sold during the sale?
Answer: Adult 84
Children 34
Junior 2
Step-by-step explanation:
Adults tickets = $5
Children tickets = $.10
Junior tickets = $2
Total ticket sold = 120 at $119
Total tickets price
= Adults + junior + children
= 5 + 2 + 0.10 = 7.1
No of tickets sold for adults
= 5 / 7.1 × 119
= 84
No of tickets sold for children
= 2/7.1 × 119
= 34
No of tickets sold for junior
= 0.10/7.1 × 119
= 2
Total ticket sold
= 84 + 34 + 2
= 120
Final answer:
During the sale, 22 adult tickets, 67 junior tickets, and 31 children's tickets were sold.
Explanation:
Let's assume that the number of adult tickets sold is x, the number of junior tickets sold is y, and the number of children's tickets sold is z.
According to the information given, the cost of an adult ticket is $5, the cost of a junior ticket is $2, and the cost of a children's ticket is $0.10 (10 cents).
The total number of tickets sold is 120, so we can write the equation:
x + y + z = 120
Additionally, the total amount collected from the ticket sales is $119, so we can write the equation:
5x + 2y + 0.10z = 119
We now have a system of equations that we can solve to find the values of x, y, and z.
By using substitution or elimination methods, we can find that x = 22, y = 67, and z = 31.
Therefore, during the sale, 22 adult tickets, 67 junior tickets, and 31 children's tickets were sold.