Answer:
9,942 bacteria were there at 10 hours.
Step-by-step explanation:
Equation for population decay:
The equation for population decay, after t hours, is given by:
[tex]P(t) = P(0)(1-r)^t[/tex]
In which P(0) is the initial population and r is the decay rate, as a decimal.
Researchers recorded that a certain bacteria population declined from 200,000 to 900 in 18 hours.
This means that [tex]P(0) = 200000[/tex] and that when [tex]t = 18, P(t) = 900[/tex]. So we use this to find r.
[tex]P(t) = P(0)(1-r)^t[/tex]
[tex]900 = 200000(1-r)^{18}[/tex]
[tex](1-r)^{18} = \frac{900}{200000}[/tex]
[tex]\sqrt[18]{(1-r)^{18}} = \sqrt[18]{\frac{900}{200000}}[/tex]
[tex]1 - r = (\frac{900}{200000})^{\frac{1}{18}}[/tex]
[tex]1 - r = 0.7407[/tex]
So
[tex]P(t) = P(0)(1-r)^t[/tex]
[tex]P(t) = 200000(0.7407)^t[/tex]
At this rate of decay, how many bacteria was there at 10 hours?
This is P(10). So
[tex]P(10) = 200000(0.7407)^{10} = 9941.5[/tex]
Rounding to the nearest whole number:
9,942 bacteria were there at 10 hours.
sam bought 4kg of red apples some yellow apples and 3 kg of green apples she bought a total of 9,000 whats the mass of the yellow apples
John took all his money from his savings account. He spent $108 on a radio and 5/9 of what was left on presents for his friends. Of the money remaining, John put 5/6 into a checking account and the last remaining $80 was left to charity. How much money did John originally have in his savings account?
Answer:
I believe its 313$
Step-by-step explanation:
John originally have $1,118 in his savings account.
Here,
We have to find the original savings account of John.
What is Number system?
A system of writing to express numbers is called Number system.
Now,
Let us assume amount of money John originally have in his savings account = $x
Money spent on a radio = $108
Remaining money = x - 108
Money spent on presents for his friends = Two third of remaining money = 5/9 (x - 108).
(Because 1 - 5/9 = 1/1 - 5/9 = 4/9)
Remaining money = 4/9 (x - 108).
Five sixth of his remaining money into a checking account = 5/6 * 4/9(x - 108)
( because 1 - 5/6 = 1/1 -5/6 = 1/6)
Remaining money = 1/6 *4/9 (x - 108).
Final remaining money = 1/6 *4/9 (x - 108)
And that is equal to the money donated to charity.
We can setup an equation now.
1/6 *4/9 (x - 108) = 80
4(x - 108) = 80 * 9 *6
x - 108 = 20 * 54
x = 1080 + 108
x = 1,188
Therefore, John originally have $1,118 in his savings account.
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Find the exact value of the expression cos-1(1/2)
Answer:
60
Step-by-step explanation:
Plug it into the calculator
Which of the following ratios are equivalent?
O A. 5:7 and 10:12
O B. 2:3 and 12:20
O C. 6:7 and 18:21
O D. 8:9 and 32:27
Answer:
:::::::::
C. 6:7 = 18:21
answer: it is C
Step-by-step explanation:
6 = 18 because 6 times 3 is 18. And 7 times 3 = 21. so they are both equivalent.
hope it helps :)
help pls giving branliest
Answer:
https://youtu.be/TZbTr1oBwKU
A Packaging Company produces boxes out of cardboard and has a specified weight of 16 oz. A random sample of 36 boxes yielded a sample mean of 15.3 oz. Given the standard deviation is 1.7 oz, obtain a 99% confidence interval for the true mean weight of the boxes. Interpret your results in the context of the problem. State the margin of error.
Answer:
The margin of error is of 0.73 oz.
The 99% confidence interval for the true mean weight of the boxes is between 14.57 oz and 16.03 oz. This means that we are 99% sure that the true mean weight of all boxed produced by the Packaging Company is between these two values, and that the specified weight is in this interval.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{1.7}{\sqrt{36}} = 0.73[/tex]
The margin of error is of 0.73 oz.
The lower end of the interval is the sample mean subtracted by M. So it is 15.3 - 0.73 = 14.57 oz.
The upper end of the interval is the sample mean added to M. So it is 15.3 + 0.73 = 16.03 oz.
The 99% confidence interval for the true mean weight of the boxes is between 14.57 oz and 16.03 oz. This means that we are 99% sure that the true mean weight of all boxed produced by the Packaging Company is between these two values, and that the specified weight is in this interval.
Find the compound amount and compound interest on $6000 invested at 6%
compounded continously for 6 years. Use e = 2.71828
(Round value of exponential expression upto 4 decimal places.)
Answer:
$8,511.1147
Step-by-step explanation:
Compound interest formula is expressed as;
A = P(1+r)^n
P is the amount invested = $6000
r is the rate = 6% = 0.06
t is the time = 6yrs
A is the compound amount
A = 6000(1+0.06)^6
A = 6000(1.06)^6
A = 6000(1.4185)
A = 8,511.1147
Hence the compound amount to 4dp is $8,511.1147
need help!! I don't know how to solve theseeeeeeeeeeeeeeeeeeeeeeeeeeee.
1. Solve the inequality. x/8 >4
Answer:
X > 32
Step-by-step explanation:
Brainliest?
Evaluate the six trigonometric functions of the angle 0
7
5
sin =
csc =
cos =
sec 0 =
tan A=
cotA=
Answer:
sin=The sin of an acute angle is defined in the context of a right triangle.
csc= The length of the hypotenuse divided by the length of the side opposite the angle.
cos= The length of the adjacent side divided by the length of the hypotenuse.
sec 0=The ratio of the length of the hypotenuse to the length of the adjacent side is the secant of an angle in a right-angled triangle.
tan A=In any right triangle, the tangent of an angle is the length of the opposite side (O) divided by the length of the adjacent side (A).
cotA= In a right triangle, the cotangent of an angle is the length of the adjacent side divided by the length of the opposite side.
Step-by-step explanation:
someone help me please like mega pleaseee help a girl out
Answer:
B.
Step-by-step explanation:
I need help hurry!!!!
Answer:
none of the above is a pythagorean triple
Charlotte is making 20 flower bouquets 4/5 of the bouquet are daisies and the rest are tulips how many bouquets are tulips
Answer:
4 bouquets
Step-by-step explanation:
5/5 = 20 flower bouquets.
Find out how much flower bouquets there are when it's 1/5.
5/5 = 20
1/5 = 20 ÷ 5 = 4
Since tulips are 1/5 as 5/5 - 4/5 = 1/5, 4 bouquets are tulips.
The origin is a point anywhere along the x-axis. True or False
Answer:
False
Step-by-step explanation:
The origin is at 0 on the x-axis, and 0 on the y-axis. Hence, (0,0) lies on both the axis.
hope this helps and is right. p.s. i really need brainliest :)
if my answer is wrong then i am incredibly sorry!
The statement "The origin is a point anywhere along the x-axis" is False.
What is Origin?Origin is referred to as the first point or the starting point from which we begin our calculations or measurements in mathematics, particularly in the subject of coordinate geometry. The 0 on a ruler is the point at which we begin taking measurements; as a result, it is referred regarded as the scale's origin.
As, The intersection of the x and y axes in a coordinate plane is where the origin is located.
Coordinates can be used to name any point on the coordinate plane.
The coordinates are where the origin is ( 0, 0 ).
So, the x- coordinate is 0 and y- coordinates is 0.
Hence, the given statement is False.
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I NEED HELP ASAP HELP HELP HELP....
According to the line plot, what is the total amount of time spent studying by the students who studied for 1/2 of an hour each?
Answer:
2.5hrs
Step-by-step explanation:
Can someone help me please? I forgot how to do this
Answer:
90°-33°=57°
57=2x+1
-1. -1
56=2x divide both sides by 2
28=x
x =28
Answer:
x = 28
Step-by-step explanation:
Both of these would add up to 90 degrees.
Equation → 2x + 1 + 33 = 90
Add like terms → 2x + 34 = 90
Subtract both sides by 34 → 2x + 34 - 34 = 90 - 34
Divide both sides by 2 → 2x = 56
→ x = 28
hope this helps! :)
Samantha opened a savings account and deposited $200.00. The account earns 10% interest, compounded monthly. If she wants to use the money to buy a new bicycle in 3 years, how much will she be able to spend on the bike?
Answer:
200(1.10^1)
Step-by-step explanation:
Draw a line tangent to the circle at the point (0, 4). Write an equation for this tangent line. Explain your work.PLEASE HELP
Answer:
y = 1/4x + 4
Step-by-step explanation:
An independent-samples t test was conducted to compare high-altitude exercise to exercise at sea-level. Imagine the mean comfort level of participants, rated on a 7-point scale where high values reflect high comfort, at high altitude was 3.5 while the average at sea-level was 5.1. Imagine also that values were calculated for sdifference of 1.1, 2.04 for pooled variance, and 35 for degrees of freedom total. What are the critical cutoffs for this test
Answer:
-2.03, 2.03
Step-by-step explanation:
The degree of freedom (df) ;
Df total for the two samples = 35
Therefore, obtuaking the critical value using a T-test distribution at 95% confidence level.
(1 - 95%) / 2 = (1 - 0.95) / 2 = 0.05 / 2 = 0.025
Using a T critical value calculator or t table distribution ;
Tcritical, 0.025, df = 35 = 2.03
Left tail = - 2.03
Right = 2.03
Hence, critical cutoff :
(-2.03 ; 2.03)
for the function f(x)=4/3x+8, what is the average rate of change over any given interval
a. 4
b. 3
c. 4/3
d. 3/4
Answer:
C i think i hope it helps
have a good night
1/5 x 3/8 x (-5) as a fraction in simplest form
Answer:
-3/8
Step-by-step explanation:
nothing can be simplified further
please help me i really need help please i really need help please
Answer:
(-1,-2)
Step-by-step explanation:
For a point (a,b) rotated 90° counterclockwise about the origin, it's new coordinates are (-b,a).
So since C is originally (-2,1), it's new coordinates are (-1,-2)
PLEASE HELP ITS DUE TODYA PLEASE HELP!!!!!!!
Answer:
AC = 7.8 cm
Step-by-step explanation:
AE² = 6² - 3² = 36 - 9 = 27
AE = √27 = 5.196
EC² = 4²- 3² = 16 - 9 = 7
EC = √7 = 2.646
AC = 5.196 + 2.646 = 7.84 cm
An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the mean daily revenue was $675 with a population standard deviation of $75. A sample of 30 days reveals a daily mean revenue of $625. If you were to test the null hypothesis that the daily mean revenue was $675, which test would you use
Answer:
One sample t test
Step-by-step explanation:
A one proportion sample t test is employed when we intend to test the sample mean of a certain sample against a particular or specified population property . In the scenario above, we could use the information given to obtain the one sample proportion test statistic by using the formular :
Test statistic = (xbar - μ) ÷ (σ/sqrt(n))
Where, xbar = sample mean ;
μ = population mean
σ = population standard deviation
n = sample size
Using the test statistic, we can then obtain the Pvalue and compare to the specified α - level
A grain dealer sold to one customer 5 bushels of wheat, 2 of com, and 3 of ryo, for $228: to another, 2 of wheat, 3 of corn, and 5 of ryo, for $228, and to a third, 3 of wheat, 5 of com, and 2 of rye, for $228. What was the price per bushel for com?
Answer:
2.30 :) hope this helps!!!!!!! :)
Step-by-step explanation:
w = wheat c = corn r = rye
6w + 3c + 6r = 45.90
3w + 6c + 6r = 49.20
6w + 6c + 3r = 41.40
since you want the answer for c, manipulate then add 2 equations that will get rid of 1 variable:
if we multiply the first equation by -1 then add it to the second equation, it will eliminate the r
-6w - 3c - 6r = - 45.90
3w + 6c + 6r = 49.20
------------------------------------
- 3w +3c = 3.30 or w - c = - 1.10
If we multiply the 3rd equation by -2 then add it to the first equation, it will eliminate the r again:
-12w - 12c - 6r = - 82.80
6w + 3c + 6r = 45.90
------------------------------------------
- 6w - 9c = - 36.90 or 2w + 3c = 12.30
now we have 2 equations and 2 variables that we can solve by substitution:
w = c - 1.10
2(c - 1.10) + 3c = 12.30
2c - 2.20 + 3c = 12.30
5c = 14.50
c = 2.90
w = c - 1.10 or 1.80
3r = 41.40 - 6(1.80) - 6(2.90)
3r = 13.20 r = 4.40
I will pick the 2nd equation to check my answers :)!
3(1.80) + 6(2.90) + 6(4.40) = 49.20
5.40 + 17.40 + 26.40 = 49.20
As per linear equation, the price per bushel for corn is $22.8.
What is a linear equation?A linear equation is an equation that has one or multiple variable with the highest power of the variable is 1.
Given, a grain dealer sold to one customer 5 bushels of wheat, 2 of corn, and 3 of rye, for $228.
To another customer, he sold 2 of wheat, 3 of corn, and 5 of rye, for $228.
To a third customer, 3 of wheat, 5 of corn, and 2 of rye, for $228.
Let, per piece of wheat is of $x.
Per piece of corn is of $y.
Per piece of rye is of $z.
Therefore, 5x + 2y + 3z = 228 ....(1)
2x + 3y + 5z = 228 .........................(2)
3x + 5y +2z = 228 ..........................(3)
Multiplying equation(1) by '2' and equation(2) by '5' and substract, we get:
2(5x + 2y + 3z) - 5(2x + 3y + 5z) = 2(228) - 5(228)
⇒ (10x + 4y + 6z) - (10x + 15y + 25z) = - 3(228)
⇒ (- 11y - 19z) = - 684
⇒ 11y + 19z = 684 ......(4)
Multiplying equation(2) by '3' and equation(3) by '2' and substract, we get:
3(2x + 3y + 5z) - 2(3x + 5y +2z) = 3(228) - 2(228)
⇒ (6x + 9y + 15z) - (6x + 10y + 4z) = 228
⇒ - y + 11z = 228 .......(5)
Now, multiplying equation(5) by '11' and then add with equation (4), we get:
11y + 19z + 11(- y + 11z) = 684 + 11(228)
⇒ 140z = 3192
⇒ z = 22.8
Putting the value of 'z' in equation (5) we get:
- y + 11(22.8) = 228
⇒ y = 22.8
Now, putting the values of 'y' and 'z' in equation (1), we get:
5x + 2(22.8) + 3(22.8) = 228
⇒ 5x = 114
⇒ x = 22.8
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An airplane takes 3 hours to travel a distance of 1560 miles with the wind. The return trip takes 4 hours against the wind. Find the speed of the plane in still air and the speed of the wind.
Answer:
it takes 3 hour
Step-by-step explanation:
ypir welcome
find the volume of a box whose length breadth and height are 28 CM 18 cm and 10cm respectively
I will mark them as brainlists all the best
Which best describes an angle?
A. Two distinct rays that originate from a common point
B. Two parallel lines on a plane
C. The set of all points equidistant from a particular point
D. A line with a starting point that extends to infinity
Will give to the brainliest!!
Rani takes a 40-question test. She answers 5% of the questions incorrectly
How many questions does she answer incorrectly? Show your work.
Answer:
2 Questions.
Step-by-step explanation:
To calculate a how much a percentage is of a number, you multiply the number by the percent.
So, we have the equation:
40 x 0.05 = 2
So, Rani got 2 questions incorrect.
Hope this helps!
Somone PLEASE answer this thanks!
A movie complex is showing the same movie in three theaters. In theater A, 44 of the 80 seats are taken. In theater B, 42 seats are taken and 28 seats are empty. In theater C, 27 of the 90 seats are empty. Which theater has the greatest percent of its seats taken? Which theater has the greatest of its seats taken ?
Answer:
Theater C
Step-by-step explanation:
Theater A has 80 seats, 44 of which are taken. 44/80 can be simplified to 11/20, which is 0.55 in decimal form, and 55% in percent form.
Theater B has 70 seats, because 42+28 = 70. 42 of those 70 seats are taken. 42/70 is 60%
Theater C has 90 seats, and because 27 are empty, we can subtract 27 from 90, which leaves us at 63 seats are taken. 63/70 is 70%
70% is the biggest percentage, so Theater C has the greatest seats taken.
I hope this helps! :))