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A population of bacteria can be modeled by P(t) = 540e0.12r where t is the number of hours since 540 bacteria were recorded.

(a) How many bacteria does the model predict will be present after 5 hours. Round to the nearest whole number.

(b) Algebraically determine how many hours, to the nearest tenth, it will take for the population to reach 2000.

The value of a, b and c are found as 6, 10 and 2 respectively.

Values for exponents, commonly referred to as powers, indicate how many often to multiply a quantity by itself.

The given expression is;

\(4x^{8} y^{c} = \frac{24x^{b}y^{-3} }{ax^{2} y^{-5} }\)

Solving expression using the law of indices.

\(x^{8} y^{c} = \frac{6x^{b-2}y^{-3+5} }{a}\)

\(ax^{8} y^{c} = {6x^{b-2}y^{2} }\)

Comparing powers of both sides:

a = 6

8 = b-2 : b = 10

c = 2

Thus, the value of  a, b and c are found as 6, 10 and 2 respectively.

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Answer:

Step-by-step explanation:

Basically you just multiply everything together

1) 6.842

2) 2524.691522

3) 4321.4

4) 9370.2

5) 0.0999999

Best way to solve these questions is either a calculator or write the questions down and figure it out yourself. It isn't that hard.

Explanation on how to place the decimal places I found on a good website:

Decimals are multiplied as if they were whole numbers, and then the decimal point is placed in the product.

To find out where the decimal point should be placed, count the number of decimal places after the decimal point in each factor.

Multiply 0.7 by 0.352

   0.7      1 decimal place

0.352      3 decimal places

              A total of 4 decimal places

Once you have found the sum of the decimal places in each factor, you know how many decimal places the product will need after its decimal point. Starting at the far right of the number, move the decimal point toward the left that number of decimal places.

0.2464 (4 decimal places after the decimal point)

Dividing decimals

1.  Move the decimal point in the divisor to the right to make the divisor a whole number.  

2.  Move the decimal point in the dividend the same number of places to the right.  

3.  Place the decimal point in the quotient directly over the decimal point in the dividend for the final quotient.

4.  Divide as if working with whole numbers

Answer:

(X-6)(3x^2+5)

Step-by-step explanation:

9514 1404 393

Answer:

  true for all values of d; an infinite number of solutions

Step-by-step explanation:

Most folks find it convenient to eliminate the fractions as a first step. Here, we can do that by multiplying the equation by 12.

  4(2d) +(d +3) = 3(3d +1)

  9d +3 = 9d +3

This is true for all values of d. The equation has an infinite number of solutions.

Answer:

0.16

Step-by-step explanation:

The computation of the minimum no of usual smokers expected to get out of 20 adults is shown below:

Here the standard deviation is

\(= \sqrt{npq} \\\\= \sqrt{20\times 0.18 \times (1 - 0.18)}\\\\= \sqrt{20\times 0.18\times 0.82}\\\\= \sqrt{2.952}\)

= 1.72

Now the minimum no of smokers is

\(= np - 2\times 1.72\\= 20 \times 0.18 - 3.44\\\\= 0.16\)

30 is the lowest common denominator for the fractions 13/15, 1/6, and 8/5.

What is fraction?

A fraction is a mathematical expression that represents a part of a whole or a ratio between two numbers. It is written in the form of a numerator and a denominator, separated by a horizontal line.

To find the lowest common denominator for the fractions 13/15, 1/6, and 8/5, we need to find the least common multiple (LCM) of the denominators.

The denominators are 15, 6, and 5.

The multiples of 15 are: 15, 30, 45, 60, 75, 90, ...

The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...

The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...

From these lists, we can see that the least common multiple of 15, 6, and 5 is 30.

Therefore, the answer is D. 30.

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The domain and the range of the graphed relation are given as follows:

The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, considering the graph of the function, the domain is given by the values of x of the graph.

As the graph contains open circles at both the ends of the domain, the domain is composed by an open interval.

The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, considering the graph of the function, the range is given by the values of y of the graph.

The graph assumes a minimum value of -6, hence the lower bound is closed, however the upper bound at y = 4 is open, as the only point the graph reaches y = 4 is on the open circle.

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Answer:

542, 543, 544, 545.

Step-by-step explanation:

Divide 2174 by 4 = 543.5  

(because there are 4 integers) 543.5 is not an integer.

However, one of the four integers is 543.

Write down four consecutive numbers that include 543 and add them:  

like 541+542+543+544 =. if that is 2174, you have the answer, if it's too low, try moving up one number, like

542+543+544+545 = if it's still too low, move up one number again  

543+544+545+546=  

You only have to do that a max of 3 times to get the answer.

The four consecutive integers are  

542, 543, 544, 545.

good luck, hope this helps :)

Answer:

t=18

Step-by-step explanation:

3=54/t

times both sides by t

3t=54

then divided by 3 on both sides to get t by itself

t=54/3

to simplify this it's

t=18

Answer:

Station 4: EOC Slope | Algebra I Quiz - Quizizz. What is the slope of the line that passes through the points (26,7) and (-39,12)? The slope of the line that passes through the points (-6, w) and (-10,4) is 1/8 .

Step-by-step explanation:

Hope this helps

Answer:

5 1/3 grams per serving

Step-by-step explanation:

To get a unit rate, we want a 1 in the denominator

4 grams

3/4 servings

4 * 4/3  grams per serving

16/3 grams per serving

5 1/3 grams per serving

Answer:  40

Step-by-step explanation:

Answer:

Step-by-step explanation:

Kareem will earn:

$4.90 (1 large necklace) + $4.20 (4 small necklaces)

= $4.90 + $16.80

= $21.70.

Therefore, he will earn $21.70 from selling 1 large necklace and 4 small necklaces.

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

D. A pair of intersecting lines

Step-by-step explanation:

A conic section is a fancy name for a curve that you get when you slice a double cone with a plane. Imagine you have two ice cream cones stuck together at the tips, and you cut them with a knife. Depending on how you cut them, you can get different shapes. These shapes are called conic sections, and they include circles, ellipses, parabolas and hyperbolas. If you cut them right at the tip, you get a point. If you cut them slightly above the tip, you get a line. If you cut them at an angle, you get two lines that cross each other. That's what happened in your question. The plane cut the cone at an angle, so the curve is two intersecting lines. That means the correct answer is D. A pair of intersecting lines.

I hope this helps you ace your math question.

Answer:

The weight that does not round to 2.46 pounds is C 2.454 pounds.

Step-by-step explanation:

Based on the given information, the weights of the four similar packs of tomatoes are as follows:

Malcolm rounds the weights to the nearest hundredth pound. To round to the nearest hundredth pound, we look at the digit in the hundredths place. If it is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is. Therefore, we can obtain the rounded weights as follows:

From the above rounded weights, we see that Pack C rounds to 2.45 pounds and does not round to 2.46 pounds. Therefore, the weight that does not round to 2.46 pounds is C 2.454 pounds.

Answer:

15. A

16. B

17. B

18. C

Step-by-step explanation:

Answer:

55.6 yards

Step-by-step explanation:

Answer:

8 and 3; 56 and 21; 896 and 336 all have the same ratio i.e. 8:3

Answer:

B. 86.6 :))

Step-by-step explanation:

took the test on edge

Answer:

0.4cents

Step-by-step explanation:

The value of distance AB is 187.5 units

Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other.

sine rule can be expressed as;

a/sinA = b/sinB = c/sinC

The opposite side to angle A is BC

the opposite side to angle C is AB

therefore;

A = 180-( 117 +24)

A = 180- 141

A = 39°

290/sin 39 = x/ sin24

xsin39 = 290 × sin24

0.629x = 117.95

x = 117.95/0.629

x = 187.5

therefore the distance AB is 187.5

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ANSWER;

a)Vertically compress by a factor of 2

b) Shift down by 5 units

EXPLANATION;

Here, we want to select the options that correctly transforms the original equation to the new one

Firstly, we deduce the difference between the two functions

Looking at the two, we can see that the differences here are the 1/2 multiplying the x and the -5 subtracted from the equation itself

Now, what we have here is that there is a compression, since the new value is half the old value

This mean there was a vertical compression by 1/2 uinit (this is what the 1/2 multiplying the x mean)

Now, let us talk about the -5

What this simply mean is that -5 is subtracted from the whole of the original function. This mean that there was a shift of 5 units toward the negative y-axis; which simply shows a downward shift by 5 units

Answer:

the percentage of  bearings   that will  not be acceptable = 7.3%

Step-by-step explanation:

Given that:

Mean = 0.499

standard deviation = 0.002

if the true average diameter of the bearings it produces is 0.500 in and bearing is acceptable if its diameter is within 0.004 in.

Then the ball bearing acceptable range = (0.500 - 0.004, 0.500 + 0.004 )

= ( 0.496 , 0.504)

If x represents the diameter of the bearing , then the probability for the  z value for the random variable x with a mean and standard deviation can be computed as follows:

\(P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - \mu}{\sigma} \leq \dfrac{X -\mu}{\sigma} \leq \dfrac{0.504 - \mu}{\sigma})\)

\(P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - 0.499}{0.002} \leq \dfrac{X -0.499}{0.002} \leq \dfrac{0.504 - 0.499}{0.002})\)

\(P(0.496\leq X \leq 0.504) = (\dfrac{-0.003}{0.002} \leq Z \leq \dfrac{0.005}{0.002})\)

\(P(0.496\leq X \leq 0.504) = (-1.5 \leq Z \leq 2.5)\)

\(P(0.496\leq X \leq 0.504) = P (-1.5 \leq Z \leq 2.5)\)

\(P(0.496\leq X \leq 0.504) = P(Z \leq 2.5) - P(Z \leq -1.5)\)

From the standard normal tables

\(P(0.496\leq X \leq 0.504) = 0.9938-0.0668\)

\(P(0.496\leq X \leq 0.504) = 0.927\)

By applying the concept of probability of a  complement , the percentage of bearings will now not be acceptable

P(not be acceptable)  = 1 - P(acceptable)

P(not be acceptable)  = 1 - 0.927

P(not be acceptable)  = 0.073

Thus, the percentage of  bearings   that will  not be acceptable = 7.3%

The best straight line through the data is horizontal.option a.

In other words, a correlation coefficient (r) of 0.0 indicates that there is no linear relationship between the two variables being studied. The absence of correlation means that there is no predictable pattern or trend between the variables.

It does not imply any specific relationship, whether positive or negative.

In more detail, the correlation coefficient (r) measures the strength and direction of the linear relationship between two variables.

It ranges from -1 to +1. A correlation coefficient of 0 indicates no linear relationship.

This means that the points on a scatter plot of the data do not align along any straight line, whether horizontal, vertical, or diagonal.

Even though there is no linear relationship, it is still possible that a non-linear relationship or other types of associations might exist between the variables.

The correlation coefficient only captures linear relationships. Therefore, it is important to consider other statistical analyses or explore the data further to determine if there are other types of relationships present.option a.

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