The initial number of bacteria in the dish was 1,150. The amount of bacteria doubles at the end of each hour. Write a function b(t) that would represent this relationship after t hours. Use this function to determine how many bacteria would be in the dish after 10 hours and write it only as a number without units.
Answer:
[tex]B(t) = 1150*(2)^{t}[/tex]
After 10 hours: 1,177,600
Step-by-step explanation:
The number of bacteria after b hours is given by the following equation:
[tex]B(t) = B(0)(1+r)^{t}[/tex]
In which B(0) is the initial number of bacteria and r is the rate that it increases.
The initial number of bacteria in the dish was 1,150. The amount of bacteria doubles at the end of each hour.
This means that [tex]B(0) = 1150, B(1) = 2*1150[/tex]
So
[tex]B(t) = B(0)(1+r)^{t}[/tex]
[tex]2*1150 = 1150(1+r)^{1}[/tex]
[tex]1 + r = 2[/tex]
[tex]r = 1[/tex]
So
[tex]B(t) = 1150*(2)^{t}[/tex]
After 10 hours:
[tex]B(10) = 1150*(2)^{10} = 1177600[/tex]
1,177,600 bacteria after 10 hours.
A slot machine has 3 dials each dial has 30 positions one of which is jackpot. To win jackpot all three dials must be in jackpot position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot
Answer:
3/90
Step-by-step explanation:
1 slot is 1/30
2 slot is 1/30
3 slot is 1/30
this gives you that 3/90 when you had them
Answer:
D) 1/(30×30×30) = 1/27000 = 0.00003 or 0.003%
Step-by-step explanation:
Solve (x + 6)2 = 64.
Answer:
x=26
Step-by-step explanation:
(x+6)2=64
x+6=32
x=26
Answer:
Here is the solution. Mark as brainlist please.
The number 65 is decreased to 62. What is the percentage by which the number was decreased, to the nearest tenth of a percent?
Answer:4.6
Step-by-step explanation:
Percentage decrease=(65-62)/65 x 100
Percentage decrease=3/65 x 100
Percentage decrease=(3x100)/65
Percentage decrease=300/65
percentage decrease=4.6
A recent survey showed 3 out of 65 Happy Meals contained a “special” prize. How many “special” prizes should a person expect to win if 130 Happy Meals were purchased?
Answer:
6
Step-by-step explanation:
The ratio would be 3:65, so to get it to ?:130 you would multiply by 2 (65•2=130). So all you have to do is do 3•2=6 to get the correct ratio which is 6:130. So that answer would be 6.
Suppose you had to
guess on a four-choice
multiple-choice test and
were given four questions.
Find the binomial
probability distribution.
( + ) ℎ =
4 = 0.25
Answer:
For 0 correct answer [tex]^4c_0p^0q^{4-0}[/tex]
For 1 correct answer [tex]^4c_1p^1q^{4-1}[/tex]
For 2 correct answer [tex]^4c_2p^0q^{4-2}[/tex]
For 3 correct answer [tex]^4c_3p^1q^{4-3}[/tex]
For 4 correct answer [tex]^4c_4p^1q^{4-4}[/tex]
Step-by-step explanation:
It is given that there are 4 questions n = 4
Number of choices is 4
So probability of getting correct answer [tex]=\frac{1}{4}[/tex]
Probability of getting incorrect answer [tex]=1-\frac{1}{4}=\frac{3}{4}[/tex]
Probability distribution is given by [tex]^nc_rp^rq^{n-r}[/tex]
Therefore probability distribution of 0 correct answer
[tex]^4c_0p^0q^{4-0}[/tex]
Therefore probability distribution of 1 correct answer
[tex]^4c_1p^1q^{4-1}[/tex]
Therefore probability distribution of 2 correct answer
[tex]^4c_2p^0q^{4-2}[/tex]
Therefore probability distribution of 3 correct answer.
[tex]^4c_3p^1q^{4-3}[/tex]
Therefore probability distribution of 4 correct answer.
[tex]^4c_4p^1q^{4-4}[/tex]
Fie triunghiul ABC isoscel cu AB=AC=3 cm daca mediatoarea laturi AC intersectat cu latura BC in M si perimetrul thriunghiului AMC=12 cm.Calculati MC
Answer:
MC = 4.5cm
Step-by-step explanation:
Question:
Let the isosceles triangle ABC with AB = AC = 3 cm. if the mediator of the sides AC intersects with the side BC in M and the perimeter of the triangle AMC = 12 cm. Calculate MC.
Solution:
Find attached the diagram used in solving the question.
Given:
∆ABC is an isosceles triangle (two sides and angles are equal)
AB = BC = 3cm
Perimeter of ∆AMC = 12cm
From the diagram, M cuts AC at the the middle.
AD = CD = AC/2 = 3/2
Perimeter of Right angled ∆AMD = AM + AD + MD
= 3/2 + AM +MD
Perimeter of Right angled ∆CMD =CM + CD + MD
= 3/2 + CM +MD
Right angled ∆AMD = Right angled ∆CMD
CM = AM
Therefore ∆AMC is an isosceles triangle
CM = AM (two sides of an isosceles triangle are equal)
Let CM = AM = x
Perimeter of ∆AMC = AM + CM + AC
12 = x + x + 3
12 = 2x + 3
2x = 12-3
2x = 9
x = 9/2 = 4.5
CM = AM = 4.5cm
MC = CM = 4.5cm
e is 5 more than d.
fis 7 less than d.
a) Write an expression for e in terms of d.
Answer:
C
Step-by-step explanation:
Answer:
e = d + 5
Step-by-step explanation:
e = d + 5
f = d - 7
Solve for e means write as e = ...d
and this is already there...
You can not write it more compact then this.
If you try, you will notice you finally end with the initial equation which you started with, or you endup with something which is obviously very true like
e = e or d = d.
The median and mode of this set of data (23,13,17,11,11)
Answer:
Mode: 11
Median: 13
Answer:
(23, 13, 17, 11, 11):
Median: 13
Arithmetic mean: 15
Geometric mean: 14.380735416546
Harmonic mean: 13.848764056076
Mode: 11
Standard deviation: 4.5607017003966
Variance: 20.8
Mean Absolute Deviation: 4
Range: 12
Interquartile range: 9
Lower quartile: 11
Upper quartile: 20
Quartile deviation: 4.5
Population size:5
In ΔXYZ, the measure of ∠Z=90°, the measure of ∠X=57°, and XY = 8 feet. Find the length of YZ to the nearest tenth of a foot.
Answer:
21
Step-by-step explanation:
Answer:
6.7
Step-by-step explanation:
what is the cube root of 1
Answer:
1.
Step-by-step explanation:
∛1= 1.
It can also be seen as:
1×1×1= 1.
100 POINTS
PLEASE PROVIDE STEPS.
THANK YOU!!!
Answer:
⅓ m/s
Step-by-step explanation:
Area of a square is:
A = s²
Take derivative of both sides with respect to time:
dA/dt = 2s ds/dt
Given that dA/dt = 6 m²/s and s = 9 m:
6 m²/s = 2 (9 m) ds/dt
ds/dt = ⅓ m/s
The Formula of the area of a square: A = bh or A = s^2
Solution:
~Take derivative of both sides
da/dt = 2s * ds/dt
~Use given values (6m^2/s and 9m)
6 = 2(9) * ds/dt
~Simplify
1/3m/s = ds/dt
Best of Luck!
Sam conducted a survey to determine your favorite flavor of ice cream is his hometown. 15 of the 50 people he surveyed liked strawberry best. How many of the 3,500 residents in the town would you expect to like strawberry best
Answer: 1050 people.
Step-by-step explanation: It's a rule of three question.
15/50 as x/3500
Then you have that 50x = 52500
x = 1050
There you have it.
Sally wants to fill ten 8-inch tea glasses. How much tea does she need?
A) 80 ounces
B) 40 ounces
C) 80 cubic inches
D) Not enough information to answer
Answer
I believe C considering cubic mass
Answer:
D
Step-by-step explanation:
10 X 5/11=
just multiplication get it right and get brainlyest
60pts or whatever it narrows it down to
The answer is 4.55
When you divide 5 by 11 you will get 0.45454545454 than when you multiply these numbers by 10 you will get 4.54545454545 and then the rounded answer is 4.55.
Answer: 4.54
Step-by-step explanation:
If the base-ten blocks shown are to be divided into 5 equal groups, what should be done first?
Answer:
2 divided
Step-by-step explanation:
Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Stacy spins the pointer 120 times and records the results. The pointer lands 30 times on a section numbered 2, 19 times on 3, 25 times on 4, 29 times on 5, and 17 times on 6.
Write a probability model for this experiment, and use the probability model to predict how many times Stacy would spin a 6 if she spun 50 times. Give the probabilities as decimals, rounded to 2 decimal places
Answer:
Hence, Stacy will spin 6, 8.33 times out of her n = 50 attempts.
Step-by-step explanation:
Let us consider a success to get a 6. In this case, note that the probability of having a 6 in one spin is 1/6. We can consider the number of 6's in 50 spins to be a binomial random variable. Then, let X to be the number of trials we get a 6 out of 50 trials. Then, we have the following model.
We will estimate the number of times that she spins a 6 as the expected value of this random variable.
Recall that if we have X as a binomial random variable of n trials with a probability of success of p, then it's expected value is np.
Then , in this case, with n=50 and p=1/6 we expect to have number of times of having a 6, which is 8.33.
perform the following operations on matrices (1 8 0 7) (7 6 7 4) = ( )
Answer:
[tex]\left[\begin{array}{cc}63&38\\49&28\end{array}\right][/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{cc}1&8\\0&7\end{array}\right]\left[\begin{array}{cc}7&6\\7&4\end{array}\right]=\left[\begin{array}{cc}(1)(7)+(8)(7)&(1)(6)+(8)(4)\\(0)(7)+(7)(7)&(0)(6)+(7)(4)\end{array}\right]\\\\=\left[\begin{array}{cc}63&38\\49&28\end{array}\right][/tex]
Each element of the product matrix is the dot product of the corresponding row in the left matrix and the corresponding column in the right matrix.
For example, the element at row 2, column 1 of the product is [0 7]·[7, 7], the dot product of row 2 of the left matrix with column 1 of the right matrix.
_____
Many calculators, spreadsheets, and web sites can do this tedious math for you.
Help ! I don’t know if I have it correct. Can somebody check it out. I got 81/65536 which I know has to be incorrect.
Work Shown:
In the numerator, we have 2^2*x^2, which is really just 4x^2. Replace x with 3 and we get 4*x^2 = 4*3^2 = 36.
For the denominator, xy^2, we get
x*y^2 = 3*2^2 = 12
So far we have,
[tex]\frac{2^2x^2}{xy^2} = \frac{4x^2}{xy^2} = \frac{36}{12} = 3\\\\\text{ or simply} \\\\\frac{2^2x^2}{xy^2} = 3[/tex]
when x = 3 and y = 2.
Square both sides to end up with...
[tex]\frac{2^2x^2}{xy^2} = 3\\\\\left(\frac{2^2x^2}{xy^2}\right)^2 = 3^2\\\\\left(\frac{2^2x^2}{xy^2}\right)^2 = 9[/tex]
5×60=5×___tens
=_____tens
=______
Answer:
300
Step-by-step explanation:
5x60=5x6 tens it equal to 30 tens. 30 tens equals 300
Answer:
see below
Step-by-step explanation:
there are 6 tens in 60!
5x60 = 5 x 6 tens
= 30 tens
= 300
Please help ASAP! I will mark BRAINLIEST! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY
Answer:
D. 96
F. 32
Step-by-step explanation:
The inequality 3x ≥ 96, means that x and 3 must be multiplied to get a product that is greater than 96. So to figure this out, you must plug in the numbers given for x, like so:
3x ≥ 96
A. 3(31) ≥ 96
93 ≥ 96 This is incorrect since 93 is not greater than 96
A tip that makes this easier is that, you can see that 31 multiplied by 3 is 93, which is only a couple numbers off 96, so all numbers after 31 will result in a product greater than 96. For example:
D. 3(96) ≥ 96
288 ≥ 96 This inequality is correct
F. 3(32) ≥ 96
96 ≥ 96
The inequality sign states that the number must be either greater or equal to 96, which it is.
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY
Answer:
E 39
Step-by-step explanation:
x+6 = 45
Subtract 6 from each side
x+6-6 = 45-6
x = 39
will mark the branliest to first one who answers
Answer:
3 1/4
Step-by-step explanation:
3/4 + (1/3 ÷1/6) - (-1/2)
Subtracting a negative is adding
3/4 + (1/3 ÷1/6) +1/2
Parentheses first
Copy dot flip
3/4 + (1/3 * 6/1) +1/2
3/4 + 2 + 1/2
Get a common denominator
3/4 + 2 + 2/4
2 + 5/4
2 + 4/4 +1/4
2+1 + 1/4
3 1/4
The base of a parallelogram measures 14 cm, and the height is unknown. The area of the parallelogram is more than 42 square cm. Which graph represents all possible values for the height of the parallelogram?
A number line going from negative 1 to positive 7. An open circle is at 3. Everything to the right of the circle is shaded.
A number line going from negative 1 to positive 7. An open circle is at 3. Everything to the left of the circle is shaded.
A number line going from 24 to 32. An open circle is at 28. Everything to the right of the circle is shaded.
A number line going from 24 to 32. An open circle is at 28. Everything to the left of the circle is shaded.
Answer:
A number line going from negative 1 to positive 7. An open circle is at 3. Everything to the right of the circle is shaded.
Step-by-step explanation:
The area of a parallelogram is given by the formula ...
A = bh
So, we have the condition that ...
A > 42
bh > 42 . . . . . substitute the expression for area
14h > 42 . . . . fill in the given base
h > 3 . . . . . . . divide by 14
Numbers greater than 3 are to the right of 3 on the number line.
_____
The relation is > rather than ≥, so the "or equal to" case is not included. That is why the circle is open, rather than solid.
Answer:
a).
Step-by-step explanation:
please ASAP , giving BRAINLIEST if correct.
Answer:
B. -3(4x + 1) (x - 4)
Step-by-step explanation:
Out of the other answer choices, "B," is the only that factorizes correctly and ends up with the correct factorization (It already gives you the break-down of the trinomial).
However, if you're unsure about the answer, you can always take the end result: -3(4x + 1) (x - 4), and multiply it together to see if you can end up with the original trinomial: [tex]-12x^2 + 45x + 12[/tex]
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
A. X=6 only
Step-by-step explanation:
Solve 20x = 10 for x. A. x = 1/2 B. x = 1.5 C. x = 2 D. x = 10
Answer:
A. 1/2
Step-by-step explanation:
20x=10
Divide 20 on both sides of the equation to get x by itself
20x=10
___. __
20. 20
x =1/2
Answer:
A) x= 1/2
Step-by-step explanation:
20x= 10 we then divide 10 by 20 to get x= 10/20 or if we simplify x= 1/2. Thus answer choice A) is correct!
The average mark of c
andidates in an aptitude test was 128.5 with a standard deviation of
8.2. Three scores extracted from the test are; 148, 102, 152. What is the average of the
extracted scores that are extreme values (outliers)?
Answer:
The average of the extracted scores that are extreme values (outliers) = 102
Step-by-step explanation:
With the logical assumption that the population size is large enough, for a normal distribution,
68% of the data lies within 1 standard deviation of the mean.
95% of the data lies between 2 standard deviations of the mean.
99.7% of the data lies within 3 standard deviations of the mean.
So, the outliers for a normal distribution are usually beyond 3 standard deviations of the mean.
The mean = 128.5
Standard deviation = 8.2
The range of scores within 3 standard deviations of the mean is obtainable thus
(Mean ± 3standard deviations)
3 × standard deviations = 3 × 8.2 = 24.6
(128.5 ± 24.6) = (103.9, 153.1)
The 3 extracted scores are 148, 102 and 152. The only extreme value of these 3 extracted scores is 102. The two other scores are within the range of 3 standard deviations of the mean.
Hence, the average of the extracted scores that are extreme values (outliers) = 102
Hope this Helps!!!
what is the sum of this arithmetic series? 586+564+542+...+212
Answer:
Basically it's asking for the sum of 212 + 216 + 220 + ..... 586
Each number is 22 more than the previous one.
Therefore the sum will be 212 + (212+22) + (212+22*2) + (212+22*3)
the amount of numbers from 212 through 586 is 18.
Therefore we will need 212 plus 212 * 17 = 3,816 *******************
We will also need all those 22's.
We must add 22 *1 plus 22*2 plus 22*3 ..... plus 22*17
Which equals 22 + 44 + 66 + 88 ... 374
Which totals 3,366 *****************
So, we total 3,816 + 3,366 which equals 7,182
Step-by-step explanation:
[tex]\displaystyle\bf\\Sum=586+564+542+...+212\\\\Sum=212+234+256+...+586\\\\\textbf{We calculate the number of terms (n):}\\\\n=\frac{586-212}{22}+1=\frac{374}{22}+1=17+1=18\\\\\boxed{\bf~n=18~terms}\\\\Sum=\frac{n(586+212)}{2}\\\\Sum=\frac{18\times 798}{2}\\\\Sum=9\times798\\\\\boxed{\bf~Sum=7182}[/tex]
9x-3=87 what is the anwser
Answer:
x=10
Step-by-step explanation:
9x-3=87
add 3 to both sides
9x=90
divide by 9 on both sides
x=10
Answer:
x=10
Step-by-step explanation:
9x-3=87
you add 3 to both sides
9x-3(+3)=87(+3)
which equals
9x=90
90/9= 10
answer:
x =10
I hope this helped!
