Answer:
A. 86.64%
B. 80
C. y(t)= 80[tex]e^{0.8664t}[/tex]
D. y(5.5) = 9388
E. y(t) = 8134 bacteria for every hour
F. 8.28 hours
Step-by-step explanation:
a. The bacteria count after 4 hours y(4) = 2560
The bacteria count after 12 hours y(12) = 2621440
equation 1: ye^4k = 2560
equation 2: ye^12k= 2621440
divide (2) by (1),
e^8k = 1024
Taking ln both sides:
ln(e8k ) = ln(1024)
8k = 6.931
k=0.8664 // after dividing both sides by 8
rate of growth k% = 0.8664*100 = 86.64%
b. substituting for k in equation 2:
ye^4*0.8664 = 2560
Initial bacteria count y(4) = 80
c. y(t)= 80e^0.8664t
d. the number of bacteria after 5.5 hours => y(5.5) = 80[tex]e^{0.8664(5.5)}[/tex] ≈ 9388
e. y'(5.5) = 80*0.8664e^0.8664(5.5) = 69.31e^0.8664(5.5) = 8134
f. for bacteria population = 104000
where ye^0.8664t = 104000
y = 80
80e^0.8664t = 104000 //divide both sides by 80
e^0.8664t = 1300
ln(e^0.8664t = ln(1300)
t = 7.17 / 0.8664 = 8.28 hours
WILL MARK BRAINLIEST!!
Answer:
only p(x)
Step-by-step explanation:
The others have a restricter domain
Find the value of x.
(8x+19)(9x+9)
Please give step by step
SOLUTION STEPS
(8x+19)(9x+9)
Apply the distributive property by multiplying each term of 8x+19 by each term of 9x+9.
72x 2 +72x+171x+171
Combine 72x and 171x to get 243x.
72x 2 +243x+171
hopefully my weird explanation helped
x
y
-3
6
-1
4.
0
3
1
3
3
4
3
6
What is the distance between the points (2, 1) and (14, 6) on a coordinate
plane?
9514 1404 393
Answer:
13 units
Step-by-step explanation:
The distance is found using the distance formula:
d = √((x2 -x1)² +(y2 -y1)²)
d = √((14 -2)² +(6 -1)²) = √(144 +25) = 13
The distance between the two points is 13 units.
find the factorization of the polynomial below 49x2+70+25
Answer:
(7x + 5) (7x+5)
Step-by-step explanation:
Hope this helps
A flagpole casts a shadow that is 24 ft long at the same time you cast a shadow that is
4.5 ft long. If you are 6 ft tall, how tall is the flagpole?
Answer:
32 ft tall
Step-by-step explanation:
24 divided by 4.5 is 5.3 repeating. 6 times 5.3 is around 32
The deer population is estimated to be 17,600 in northern Illinois, but an actual count was 21,300. What is the percent error? 1 point 82.6% 21% 20% 17.4% Last week, you finished Hurry
Answer:67
Step-by-step explanation: 82.6% is over 49
A deposit of $225 as an integer
Answer:
225
Step-by-step explanation:
A deposit is positive, so a deposit of $225 as an integer (number) would be 225I hope this helps!
Please answer ASAP I have 15 min help
Answer:
32
Step-by-step explanation:
she was supposed to divide and multiply first and then add those answers
6+6+20=32
Jace and his children went into a bakery and he bought $9 worth of cookies and brownies. Each cookie costs $0.75 and each brownie costs $3. He bought twice as many cookies as brownies. Graphically solve a system of equations in order to determine the number of cookies, x,x, and the number of brownies, y,y, that Jace bought.
Answer:
(9, 18) (3, 6) Plz correct me if wrong
Step-by-step explanation:
Jace bought 4 cookies and 2 brownies from the bakery.
Let x represent the number of cookies and y represent the number of brownies.
Since he bought $9 worth of cookies and brownies. Each cookie costs $0.75 and each brownie costs $3. hence:
0.75x + 3y = 9 (1)
Also, he bought twice as many cookies as brownies, hence:
x = 2y
x - 2y = 0 (2)
Solving equation 1 and 2 simultaneously gives x = 4, y = 2
Hence Jace bought 4 cookies and 2 brownies from the bakery.
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Select two ratios that are equivalent to 2:9
Choose 2 correct answers
Answer:
4:18 and 6:27
Step-by-step explanation:
Larry ordered 5 1/2 subs. He wants to share the subs with 4 friends and himself. Larry thinks they will each
receive 1 1/4 subs. Is Larry correct? Why or why not?
given the function f(x)= 3^ - 2 what is the value of f (3)
I need to know the answer lol
Answer:
5/12
Step-by-step explanation:
A transformation is given by the rule (x,y) → (x +3, y - 8). Which of the following describes the effect of this transformation on an object
A a translation by 8 units left and 3 units up
B a rotation by 90 counterclockwise about the origin
C a translation by 3 units right and 8 units down
D a reflection across the line 2 = 3
Answer:
3
Step-by-step explanation:
Answer:
C a translation by 3 units right and 8 units down
Step-by-step explanation: This answers the Unit 3 summative assessment N-gen Math
1/2^-2 2^-3 -4^5
What is the value of
for x = 2 and y=-4?
value of x=2 is-8 and y=-4 is -1024
While printing material from the Internet, Greg used 10 pages of paper from a package of 500 sheets of paper. What percent of the paper did he use?
Answer:
2%
Step-by-step explanation:
The percentage of paper used is 2%
three orders are placed at a pizza shop.
two small pizzas, a liter of soda, and a salad costs $14.
one small pizza, a liter of soda, and three salads costs $15.
three small pizzas, a liter of soda, and two salads costs $22.
how much does each item cost?
Given:
Two small pizzas, a liter of soda, and a salad costs $14.
One small pizza, a liter of soda, and three salads costs $15.
Three small pizzas, a liter of soda, and two salads costs $22.
To find:
The cost of each item.
Solution:
Let x be the cost of a small pizza.
y be the cost of a liter of soda
z be the cost of a salad.
According to the question, two small pizzas, a liter of soda, and a salad costs $14.
[tex]2x+y+z=14[/tex] ...(i)
One small pizza, a liter of soda, and three salads costs $15.
[tex]x+y+3z=15[/tex] ...(ii)
Three small pizzas, a liter of soda, and two salads costs $22.
[tex]3x+y+2z=22[/tex] ...(iii)
From (i), we get
[tex]z=14-2x-y[/tex] ...(iv)
Putting [tex]z=14-2x-y[/tex] in (ii), we get
[tex]x+y+3(14-2x-y)=15[/tex]
[tex]x+y+42-6x-3y=15[/tex]
[tex]-5x-2y=15-42[/tex]
[tex]-(5x+2y)=-27[/tex]
[tex]5x+2y=27[/tex] ...(v)
Putting [tex]z=14-2x-y[/tex] in (iii), we get
[tex]3x+y+2(14-2x-y)=22[/tex]
[tex]3x+y+28-4x-2y=22[/tex]
[tex]-x-y=22-28[/tex]
[tex]-(x+y)=-6[/tex]
[tex]x+y=6[/tex]
Multiply both sides by 2.
[tex]2x+2y=12[/tex] ..(vi)
Subtracting (vi) from (v), we get
[tex]5x+2y-2x-2y=27-12[/tex]
[tex]3x=15[/tex]
[tex]x=5[/tex]
Putting x=5 in (vi), we get
[tex]2(5)+2y=12[/tex]
[tex]10+2y=12[/tex]
[tex]2y=12-10[/tex]
[tex]2y=2[/tex]
[tex]y=1[/tex]
Putting x=5 and y=1 in (iv), we get
[tex]z=14-2(5)-(1)[/tex]
[tex]z=14-10-1[/tex]
[tex]z=3[/tex]
So, [tex]x=5,y=1,z=3[/tex].
Therefore, the cost of a pizza is $5, cost of a liter of soda is $1 and cost of salad is $3.
Solve the following system of equations. x + y + 8z = 16
2x + 7z = 19
4x - 4y + 4z = 4
a. x = 1,y = 2,z = 2
b. x= 2,y = 2,z = 1
c. x = 6,y = 2,z = 1
d. x = 13,y = 11,z = -1
By substitution, we will see that the solution of the system is:
x = 13, y = 11, z = -1
The correct option is D.
How to solve the system of equations?
Here we have a system of 3 equations:
x + y + 8z = 16
2x + 7z = 19
4x - 4y + 4z = 4
I will solve it by substitution, first, let's simplify the equations. Here we can divide the third equation by 4 so we remove all the common factors, then the system becomes:
x + y + 8z = 16
2x + 7z = 19
x - y + z = 1
Now, I will isolate x on the second equation:
x = (19 - 7z)/2 = (19/2) - (7/2)*z = 9.5 - 3.5*z
Now we can replace that on the other two equations:
(9.5 - 3.5*z) + y + 8z = 16
(9.5 - 3.5*z) - y + z = 1
Rewriting the system we get:
y + 4.5z = 6.5
-y - 2.5z = -8.5
Now we can isolate y on the first equation:
y = 6.5 - 4.5z
Replacing that on the other equation we get:
-( 6.5 - 4.5z) - 2.5z = -8.5
-6.5 + 4.5z - 2.5z = -8.5
2z = -8.5 + 6.5 = -2
z = -2/2 = -1
Then the value of y is:
y = 6.5 - 4.5z = 6.5 - 4.5*(-1) = 11
And the value of x is:
x = 9.5 - 3.5*z = 9.5 - 3.5*(-1) = 13
So the solution of the system is:
x = 13, y = 11, z = -1
The correct option is D.
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The rabbit population in a certain area is 200% of last years population there are 1,100 rabbits this year, how many were there last year?
Answer:
550
Step-by-step explanation:
1100/2=550
(can I get brainliest please)
NEED HELP! GIVING BRAINLIEST!
Question 2
1 pts
Seven friends compared vacation plans. All are planning to drive to their destinations.
Find the median distance for the seven travelers.
Distance in
Friend
km
1
435
2
158
3
254
450
4
5
192
219
6
7
457
192 km
If you have 2 pieces of spaghetti that have lengths 4 cm and 10 cm, what could be the possible length of a third piece of spaghetti to complete the triangle? cm < x < cm
Answer:
6 < third side < 14
Third side must be greater than 6 and less than 14
Step-by-step explanation:
A triangle can be formed from 2 sides of any length.
The third side must be longer than the difference of the other 2 sides and
the third side must be less than the sum of the other 2 sides.
(if this question is from k12 lesson check)
Marion and Stefan played a game called "Go." Marion won five times the difference between the number of games Stefan won and the number four. If Marion won fifteen games, then how many games did Stefan win?
Answer:
1 game
15/5=3
4-3=1
Hope it helps
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Using a system of equations, it is found that Stefan won 7 games.
In our system, we have that:
x is the number of games Marion won.y is the number of games Stefan won.Marion won five times the difference between the number of games Stefan won and the number four, hence:
[tex]x = 5(y - 4)[/tex]
Marion won 15 games, hence [tex]x = 15[/tex], and:
[tex]15 = 5(y - 4)[/tex]
[tex]y - 4 = 3[/tex]
[tex]y = 7[/tex]
Stefan won 7 games.
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Find the volume of this right rectangular prism. [Type your answer as a number.]
Answer:
200m
Step-by-step explanation:
To find volume you multiply each side, length, width, and height. 5 times 4 is 20, and 20 times 10 is 200
Solve the equation Only enter the amount. Round to the nearest cent. Twenty tickets cost 182.50 What is the average cost of each ticket?
Answer:
$9.13
Step-by-step explanation:
Jana ran the first 312 miles of a 5-mile race in 13 hours. What was her average rate, in miles per hour, for this first part of the race? Explain how you solved the problem.
Answer:
speed = distance / time
Jana's speed is
speed = (3.5 mi)/(1/3 h) = 3*3.5 mi/h = 10.5 mi/h
Bart read 3,432 pages of books last year! That's 1,544 fewer pages than he read the year before. How many pages did Bart read in the two years combined?
Answer:
5,320 pages
Step-by-step explanation:
Last year: 3,432 pages
Last year: 3,432-1,544= 1,888
3,432+1,888= 5,320
True or False: The Commutative Property of Addition states that for all expressions a and b , ab = ba.
According to the Commutative Property of Addition, ab = ba for all expressions a and b: FALSE
What is the Commutative Property of Addition?According to the commutative property of addition, altering the order of addends has no impact on the sum. Here's an illustration: 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+4. The addition and multiplication arithmetic operations are covered by the commutative property. This implies that the outcome of adding or multiplying two numbers remains unchanged if the order or position of the numbers is changed. For instance, 4 + 5 equals 9, and 5 + 4 equals 9.According to the Commutative Property of Addition, rearranging the addends has no impact on the sum.
a+b=b+aTherefore, the statement "according to the Commutative Property of Addition, ab = ba for all expressions a and b" is FALSE
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Find X HELP ME please!!
Answer:
The answer is A) 3 Hope this helped