The population of the bacteria after 7 hours is 230 bacteria.
An exponential function is given by:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let y represent the population of bacteria after x hours.
Given that he starts his experiment with 200 bacteria, hence
a = 200
The bacteria grow at a rate of 2% per hour, hence:
b = 100% + 2% = 1.02
The exponential equation becomes:
y = 200(1.02)ˣ
After 7 hours:
y = 200(1.02)⁷ = 230
The population of the bacteria after 7 hours is 230 bacteria.
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Evaluate the expression 3 x ; for x = 7
This would become 3(7) because of x = 7 in the original equation of 3x and the answer would be 21.
Answer:
3(7)= 21
Step-by-step explanation:
3 x
This means you are multiplying.
x = 7
3(7)= 21
Question
For every 3 kg of a child's weight, pediatricians prescribe 8 mg of fever reducer. If Nidhi weighs 15 kg, how many milligrams
of the fever reducer will the pediatrician prescribe?
Answer: 40 mg
Unitary method:
For 3kg --> 8mg
For 1kg --> 8/3 mg
For 15kg--> (8/3) * 15
--> 40 mg
The number of milligrams of the fever reducer the pediatrician will prescribe is 40 mg.
Given that, for every 3 kg of a child's weight, pediatricians prescribe 8 mg of fever reducer.
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here, for 1 kg of child's weight pediatricians prescribe [tex]\frac{8}{3}[/tex] mg of fever reducer.
If Nidhi weighs 15 kg, then the fever reducer = [tex]\frac{8}{3}\times15[/tex]
[tex]=8\times5[/tex]
[tex]=40[/tex] mg
Therefore, the number of milligrams of the fever reducer the pediatrician will prescribe is 40 mg.
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What do we call these types of fractions?
1/2 and 5/10
Answer:
Proper Fractions.
Step-by-step explanation:
These are Proper Fractions because the numerator (1 and 5) is lower than the denominator (5 and 10).
pls help im being timed
Answer:
He needs 8 health packs
Step-by-step explanation:
3x + 5 [tex]\geq[/tex] 29
3x [tex]\geq[/tex] 24
x [tex]\geq[/tex] 8
If it took 8 hours to mow 10 lawn, then at that rate how many lawns could be mowed in 24 hours
if 24 bags of sugar with equal weight weigh 21 kg, how many bags of sugar would weigh 122kg?
Answer:
24 bags = 21 kg
1.142 bag = 1 kg
About 139 bags = 122 kg
You start off with 24 bags that equal the same amount as 21 kg. You need to find out how many bags of sugar equal the same amount as 122 kg. The first line is a ratio and to find your answer you need to figure out what is 1 kilogram equal to in the amount of bags. You divide both sides by 21 leaving 1.142 bag equal to 1 kilogram. In order to find 122 kilograms, you have to multiply both sides by 122 kilograms which would give you about 139 bags = 122 kilograms.
Your final answer: 139 bags
I hope this helped!
A sample of one-year-old girls had a mean weight of pounds with a standard deviation of pounds. Assume that the population of weights is normally distributed. A pediatrician claims that the standard deviation of the weights of one-year-old girls is less than pounds. Do the data provide convincing evidence that the pediatrician's claim is true
Answer:
cool and cool and cool and cool
11/2 ___ 55%? PLS I NEED A AWNSER
Answer:
The answer is >
Step-by-step explanation:
11/2 as a percentage is equal to 550% which is greater than (>) 55%
A restaurant is making hamburgers. The cooks use 2/3 pounds of beef for each hamburger. If the cooks have 44 and 2/3 pounds of beef,how many hamburgers can they make?
Answer:
67 hamburgers
Step-by-step explanation:
In order to find the answer to this question, you must do the following equation:
44÷2/3. The answer to this is 66.
Then, you add 1 to 66, because 2/3 divided by 2/3 = 1!
So, the cook can make 67 hamburgers.
The sum of three consecutive terms of an arithmetic sequence is 27, and the sum of their squares is 293. What is the absolute difference between the greatest and the least of these three numbers in the arithmetic sequence?
The answer is 10 but I don’t know how to get it
The absolute difference between the greatest and the least of these three numbers in the arithmetic sequence is 10.
The sequence is an arithmetic sequence. Therefore,
d = common difference
let
a = centre term
Therefore, the 3 consecutive term will be as follows
a - d, a, a + d
a - d + a + a + d = 27
3a = 27
a = 27 / 3
a = 9
Therefore,
(a-d)² + (a)² + (a + d)² = 293
(a²-2ad+d²) + 9² + (a² + 2ad + d²) = 293
(81 - 18d + d²) + 81 + (81 + 18d + d²) = 293
243 + 2d² = 293
2d² = 50
d² = 50 / 2
d = √25
d = 5
common difference = 5
Therefore, the 3 numbers are as follows
9 - 5 , 9, 9 + 5 = 4, 9, 14
The difference between the greatest and the least of these 3 numbers are as follows:
14 - 4 = 10
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Between which two integers does - 1 3/4 lie?
A) -2 and -1
B) -1 and 0
C) 0 and 1
D) 1 and 2
HALLPPP its worth 50 points
Rewrite the innermost expressions with negative exponents:
[tex]\displaystyle \left[\left(\frac{a^6}{5b^{-1}}\right)^2 \cdot \left(\frac{b}{9a^{-11}}\right)^{-1}\right]^{-3}[/tex]
[tex]\displaystyle \implies \left[\left(\frac{a^6b^1}{5}\right)^2 \cdot \left(\frac{ba^{11}}{9}\right)^{-1}\right]^{-3}[/tex]
[tex]\displaystyle \implies \left[\left(\frac{a^6b^1}{5}\right)^2 \cdot \left(\frac9{ba^{11}}\right)^1\right]^{-3}[/tex]
Simplify the product:
[tex]\displaystyle \implies \left[\left(\frac{a^6b}{5}\right)^2 \cdot \frac9{ba^{11}}\right]^{-3}[/tex]
[tex]\displaystyle \implies \left[\frac{\left(a^6b\right)^2}{5^2} \cdot \frac9{ba^{11}}\right]^{-3}[/tex]
[tex]\displaystyle \implies \left[\frac{\left(a^6\right)^2b^2}{25} \cdot \frac9{ba^{11}}\right]^{-3}[/tex]
[tex]\displaystyle \implies \left[\frac{a^{12}b^2}{25} \cdot \frac9{ba^{11}}\right]^{-3}[/tex]
[tex]\displaystyle \implies \left[\frac{9ab}{25}\right]^{-3}[/tex]
Rewrite the last negative exponent:
[tex]\implies \boxed{\left(\frac{25}{9ab}\right)^3}[/tex]
Factor each product-
0.7√300
-0.125√192
Answer:
1. 7 to the square root of 3
2. negative square root of 3
Step-by-step explanation:
1. simplify 0.7 x 10 square of 3
2. Calculate: you get 7 to the square root of 3
1. simplify -0.125 x 8 to the square root of 3
2. Calcaute: you get negative square root of 3
The factors of the expression 0.7√300 and -0.125√192 will be 7 x √3 and - 1 x √3, respectively.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expressions are given below.
0.7√300 and -0.125√192
Simplify the expressions, then we have
0.7√300 and -0.125√192
7√3 and - √3
Factorize the expression, then we have
7 x √3 and - 1 x √3
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Solve the PROPORTIONS!
Answer:
q = 39Step-by-step explanation:
91 : 14 = q : 6
q = 91 * 6 : 14
q = 39
----------------------
check
91 : 14 = 39 : 6
6.5 = 6.5
the answer is good
Help help math math please pelsss
Answer:
116°
Step-by-step explanation:
together both angles equal 180 because they are on a straight line and are opposite of each other.
180 - 64 = 116
I hope this helps!!
PLEASE HELP ME NOW!!! I WILL MARK U AS BRAINLIEST
[tex]\huge \bf •Answer •\\ [/tex]
1188 g
[tex]\huge \bf •Solution •\\ [/tex]
We know,
[tex]\sf \dfrac{mass \: \: of \: \: solute}{mass \: \: of \: \: solution} \times 100= concentration \: \: of \: \: solution \\ = > \sf \dfrac{mass \: \: of \: \: solute}{mass \: \: of \: \: solute + mass \: \: of \: \: solvent} \times 100= concentration \: \: of \: \: solution[/tex]
Given, concentration of solution = 1%
Mass of sugar (solute) = 12 g
Let the mass of water (solvent) be x.
Therefore,
[tex]\sf \dfrac{12g}{12g + x} \times 100= 1 \\ \sf = > 1200g= 12g + x \\ \sf= > (1200 - 12)g = x \\ \sf = > x = 1188g[/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Round 4.789443 to the nearest whole number
Answer:
5
Step-by-step explanation:
I don't think I should have to explain this but if it's in between 4.5 and 5 it will be 5 and if it's 4.5-4 it would be 4
Let f(x) =
=(x^2-16x+39
Divide by X-3
a,if x #3
if x = 3
Answer:
Step-by-step explanation:
x² - 16x + 39 = ( x - 3 )( x - 13 )
name a ray with endpoint u
i don't know hindi ko po alam
a and b
alam ko
Select the range of the following relation { (20, 2), (30, 4), (40, 1), (50, 2)} A {1, 2, 3) B {1,2,4} C {1, 2, 3, 4) D {2, 3, 4)
Answer:
B {1,2,4}
Step-by-step explanation:
I took the test
what ratio is equivelant to 5 : 4
Answer:
1.25 to 1
Step-by-step explanation:
5/4 = 1.25 4/4 = 1 So the ratio is 1.25 to 1
What’s the Question? Selena ran farther than
Manny.
If Selena ran x miles and manny ran y miles, who ran more miles
x=any number
y=any number smaller than x
help me on my 7th grade math homework
Answer:
Step-by-step explanation:
divide the money or degrees by the hours or form of time they give. for the first one you divide 585/52 to get $11.25 an hour.
I can write an equation
Answer:
Step-by-step explanation:
y = mx + b
slope m is found as the change in y over the change in x
as y decreases 3 units for a 3 unit increase in x, the slope is -3/3 = -1
The y intercept b is where the plot crosses the y axis, 4 units above the x axis
y = -1x + 4
or
y = 4 - x
22. A baker is planning to make a batch of sugar cookies for his bakery. For one large batch of cookies, the recipe calls for 6 eggs and 4 cups of sugar. The ratio for this 1 batch is 6 to 4 6:4 or The baker has to make 5 batches of cookies. How many eggs and cups of sugar she 4 will need to make these 5 batches. 6 22. eggs 23. cups of sugar 24. The Ratio in word form for the 5 batches of cookies:
Answer:
22. 30
23. 20
25. Thirty to twenty, or 30:20
Step-by-step explanation:
22.6*5
23.4*5
Simplify.
(2a2−3ab+5b2)−(a2−2ab+3b2)
A.a4−a2b2+2b4
B.3a2−5ab+8b2
C.a2−5ab+2b2
D.a2−ab+2b2
Simplify. (6x−3)−(2x−2)
A.4x2−1
B.4x−1
C.4x−5
D.4x2−5
Answer:
DBStep-by-step explanation:
You may find this easier if you distribute the minus sign first.
1)2a^2 -3ab +5b^2 -a^2 +2ab -3b^2
= (2 -1)a^2 +(-3+2)ab +(5 -3)b^2
= a^2 -ab +2b^2 . . . . . matches choice D
__
2)6x -3 -2x +2
= (6 -2)x +(-3 +2)
= 4x -1 . . . . . matches choice B
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Answer:
C or the third option.
Step-by-step explanation:
The equation is y = 4x - 4
Hope this helps! Pls give brainliest!
jamie uses 54 buttons to make shirts. jamie uses 6 buttons to make each shirt. how many shirts did she make?
Answer: 9 shirts I think
Step-by-step explanation: 54/6=9
When rolling a die what is probability of rolling a one
Answer:
1/6
Step-by-step explanation:
6 sides. 1 face with number 1. 1/6
patrick had 144 coins in his collection of nickels and quarters. If the coins have a total value of $20, how many are nickels and how many are quarters?
Answer:
30
Step-by-step explanation: