The perimeter of a rectangle can be found using the expression 2ℓ + 2w, where ℓ represents the length and w represents the width. Determine the perimeter if ℓ = 6 units and w = 3 units.

Then it will take approximately 6.3 hours for the culture to grow to 80,000 bacteria

The given formula for the number of bacteria in a culture after t hours is:y = 5000(3)^tWe are required to find the number of hours it will take the culture to grow to 80,000.

This can be done by setting y equal to 80,000 and then solving for t.5000(3)^t = 80,000

Divide both sides by 5000:3^t = 16Now, we need to solve for t by taking the logarithm of both sides.

However, it is easier to use logarithmic properties to simplify the equation first.3^t = 2^4

Raise both sides to the power of (1/log3):log3(3^t) = log3(2^4)t = 4/log3(2)Using a calculator, log3(2) ≈ 0.631, so:t ≈ 4/0.631 ≈ 6.3.

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Answer: A

Step-by-step explanation:

The polynomial has roots at \(x=-4, -2, 4\).

So, the equation should have factors of \((x+4), (x-2), (x-4)\).

This eliminates everything except for A.

The graph of g(x) = 4x, is the translation of f(x) by subtracting 3.5 units, 2 of 3.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The cost can be modeled by the function f(x)=4x+3.5, where x represents the number of games bowled.

As per the given question, the required solution would be as:

g(x) = 4x , is the translation of f(x) by subtracting 3.5 units, 2 of 3.

The graph of g(x) would be identical to the graph of f(x), but shifted 3.5 units downward, 3 of 3.

This is because the flat fee for the rental of bowling shoes is not present in the function g(x), so the y-intercept of the graph would be at (0,-3.5) instead of (0,0) in f(x) function.

The slope and the shape of the function will remain the same.

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Answer: x=3

Step-by-step explanation:

3(4)^x=192

4^x=192/3

4^x=64

4^3=64

x=3

Hope this helped!

Answer:

Question 32

Question 33

Step-by-step explanation:

Scale Factor: A number used as a multiplier when scaling an object.

Perimeter: The total distance around the outside of a 2D shape.

Area: The space occupied by a flat shape, measured in two dimensions.

Scale Factor

To find the scale factor from the shaded figure to the unshaded figure, divide the given side length of the unshaded figure by the given side length of the shaded figure:

\(\implies \sf \dfrac{unshaded}{shaded}=\dfrac{9}{24}=\dfrac{3}{8}\)

Ratio of Perimeters

Perimeters are measured in one dimension (length).  To find the ratio of the perimeters, divide the given side length of one figure by the given side length of the other:

\(\sf \implies\dfrac{shaded}{unshaded}=\dfrac{24}{9}=\dfrac{8}{3}\)

Therefore:

\(\sf \implies shaded:unshaded=8:3\)

Ratio of Areas

Area is measured in two dimensions. To find the ratio of the areas, divide the square of the given side length of one figure by the square of the given side length of the other:

\(\sf \implies\dfrac{shaded}{unshaded}=\dfrac{24^2}{9^2}=\dfrac{64}{9}\)

Therefore:

\(\sf \implies shaded:unshaded=64:9\)

Area of the smaller figure (unshaded)

Area of shaded figure = 1024 mm²

Let x = area of unshaded figure

Use the ratio found above:

\(\begin{aligned}\implies \sf \dfrac{shaded\:area}{unshaded\:area} & =\sf \dfrac{64}{9}\\\\\sf \dfrac{1024}{x} & =\sf \dfrac{64}{9}\\\\\sf 1024 \cdot 9 & = \sf 64x\\\\\sf x & = \sf \dfrac{1024 \cdot 9}{64}\\\\\implies \sf x & = \sf 144\:\:mm^2\end{aligned}\)

Scale Factor

To find the scale factor from the shaded figure to the unshaded figure, divide the given side length of the unshaded figure by the given side length of the shaded figure:

\(\implies \sf \dfrac{ushaded}{shaded}=\dfrac{20}{14}=\dfrac{10}{7}\)

Ratio of Perimeters

Perimeters are measured in one dimension (length).  To find the ratio of the perimeters, divide the given side length of one figure by the given side length of the other:

\(\sf \implies\dfrac{shaded}{unshaded}=\dfrac{14}{20}=\dfrac{7}{10}\)

Therefore:

\(\sf \implies shaded:unshaded=7:10\)

Ratio of Areas

Area is measured in two dimensions. To find the ratio of the areas, divide the square of the given side length of one figure by the square of the given side length of the other:

\(\sf \implies\dfrac{shaded}{unshaded}=\dfrac{14^2}{20^2}=\dfrac{49}{100}\)

Therefore:

\(\sf \implies shaded:unshaded=49:100\)

Area of the smaller figure (shaded)

Area of unshaded figure = 400 in²

Let x = area of shaded figure

Use the ratio found above:

\(\begin{aligned}\implies \sf \dfrac{shaded\:area}{unshaded\:area} & =\sf \dfrac{49}{100}\\\\\sf \dfrac{x}{400} & =\sf \dfrac{49}{100}\\\\\sf x& = \sf \dfrac{400 \cdot 49}{100}\\\\\implies \sf x & = \sf 196\:\:in^2\end{aligned}\)

The set of factors used to factor the given trinomial are -4 and -4. Therefore, option C is the correct answer.

The given trinomial is x²-8x+16.

Factors of 16           Sum of factors

-1 and -16               -1+(-16)=-17

-2 and -8                  -2+(-8)=-10

-4 and -4                  -4+(-4)=-8

The set of factors would used to factor the trinomial are -4 and -4.

Therefore, option C is the correct answer.

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Answer:

The Answer Is 8 five dollar bills

Step-by-step explanation:

First you Multiply 5 by 8 Then divide the answer by 5

For the given median, there are 50 students who scored greater than 72.

What is median?

The median is a measure of central tendency in a set of numerical data. It is the value that separates the higher half of the data from the lower half when the data is arranged in order from least to greatest or greatest to least.

We are given that 99 6th graders took a test and the median score was 72. We want to find out how many students scored greater than 72.

Let the scores be denoted by S1, S2, ..., S99. We can sort these scores in order from least to greatest:

S1 ≤ S2 ≤ ... ≤ S99

Since the median score is 72, exactly half of the scores are above 72 and half are below 72. Thus, the 50th score in the sorted list is 72.

Since there are 99 scores in total, we can approximate the number of students who scored above 72 by dividing the total number of students by 2:

\($\frac{99}{2} = 49.5$$\)

This means that approximately 49.5 students scored above 72.

Since 0.5 rounds up to 1, we round 49.5 up to 50. Therefore, approximately 50 students scored greater than 72.

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The points does the graph of the function below intersect the x-axis equation is= y = 4x²-9x+9 is  C) - 0

because this equation does not have any x intercept

Y = 4x² -9x +9 is a quadratic equation

To know at what point this equation intersect x axis we have to put the value of y= 0

Y = 4x²2 -9x +9

0 = 4x² -9x + 9

4x²-9x+9=0

This equation can be solved using quadratic formula

We need to find the value of discriminant

D= √(b²-4ac)

D=√((-9)²-4(4)(9))

D= √(81-144)

D=√(-63)

As the value of discriminate is not a real number so reel roots does not exit and hence this equation does not have any x intercept

Hence, option c is correct because this equation does not have any x intercept

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Answer:

2/5

Step-by-step explanation:

4 raspberry / 10 total

4/10

2/5

It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  \(9 \frac{1}{10}\)   to a decimal number:

⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)

⇒ \(\frac{91}{10}\)  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

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Answer:

n=189

Step-by-step explanation:

\(n-63=126\\n=126+63\\n=189\)

I hope this helps! :)

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An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The current price of the item is 97.06

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Original price of an item = 99.15

The price has been reduced by 2.09.

The current price.

= 99.15 - 2.09

= 97.06

Thus,

The current price of the item is 97.06

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Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

Yes, based on the 99% confidence interval (0.297, 0.503), there is convincing evidence of a difference in the proportion of "big" bank customers who bank with more than one bank compared to the "small" customers who bank with more than one bank.

The confidence interval (0.297, 0.503) represents the range of values within which the true difference in proportions between the two customer groups is likely to fall with 99% confidence. Since the interval does not include zero (0), we can conclude that there is a statistically significant difference between the proportions.

To further explain, the confidence interval was constructed using the sample proportions and the standard error. The sample proportion for the "big" customers who bank with other banks is 160/200 = 0.8, and for the "small" customers, it is 120/300 = 0.4. The standard error takes into account the sample sizes and proportions, and it measures the uncertainty in the estimation.

Since the confidence interval does not include zero, it indicates that the true difference in proportions is unlikely to be zero. In other words, there is strong evidence that the proportion of "big" bank customers who bank with more than one bank is higher than the proportion of "small" customers who do the same.

Therefore, based on the provided data and the confidence interval, we can conclude that there is convincing evidence of a difference in the proportion of "big" bank customers who bank with more than one bank compared to the "small" customers who bank with more than one bank.

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The required distance between the foot of the ladder to the wall is 14.14 feet.

Using trigonometry, we can find that the distance from the wall (x) is given by:
x = 20sin(45°)
  = 20(√2/2)
  = 10√2 feet.

This is approximately equal to 14.14 feet when rounded to two decimal places.

The correct answer is C. 14.14 feet.

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28 to 42 means 28/42

We now reduce 28/42 to lowest terms.

28 ÷ 7 = 4

42 ÷ 7 = 6

We now have 4/6.

We now reduce 4/6.

4 ÷ 2 = 2

6 ÷ 2 = 3

Final answer: 2/3

Answer:

use cymath it really helps with finding slopes

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

Two formulas come into play here. One is the future value of a series of payments. The other is the payment amount available from an ordinary annuity.

  FV = An/r((1 +r/n)^(nt) -1) . . . . future value of payments of A made n times per year for t years

  A = P(r/n)/(1 -(1 +r/n)^(-nt)) . . . . payment from principal P at invested at rate r for t years, compounded n times per year.

__

Problem 1

You want FV = $350,000, A = $400, r = 0.057, n = 12, and we want to find t. We can solve the FV equation for t to get ...

  log(FV·r/(An) +1)/log(1 +r/n) = nt . . . . . number of months

  log(350000·0.057/(400·12) +1)/log(1 +0.057/12) = nt ≈ 346.1

The retirement account can be funded by 346.1 monthly payments. That will take 28.8 years.

__

Problem 2

Again, solving for t, we get ...

  log(1 -Pr/(An))/(-n·log(1 +r/n)) = t

The parameters for this are P = 700,000, A = 5000, n = 12, r = 0.054, so the account can be expected to last for ...

  log(1 -700000·0.054/(5000·12))/(-12·log(1 +0.054/12)) ≈ 18.5 . . . years

Changing the withdrawal to $3000 per month makes the account last forever.  It earns $3150 in interest each month, so the account balance continues to increase.

The account will support withdrawals of $5000 per month for 18.5 years.

The account will support withdrawals of $3000 per month forever.

No, the relationship on the table is not proportional

From the question, we have the following parameters that can be used in our computation:

x   y

____ ____

6 -2

7 -1

8 0

9  1

On the table of values, we can see that:

Using the above as a guide, we have the following:

The relationship is not a proportional relationship

This is so because it does not have a constant rate (addition of 1 to x and y does not represent proportional relationship)

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Answer:

Domain = (-∞, ∞) Range = (-∞, ∞)

End Behavior: As X -> -∞, Y -> -∞ | As X -> ∞, Y -> ∞

Inflection Point: (2,0)

Step-by-step explanation:

Answer:

1; 31.2 2; 12.4 3; 30.8 4; 118.4 5; 16.53 (i ran out of time or else i wouldve finished, just use google for answers! ^_^)

done the rest, just Step-by-step explanation:

Answer:

point A

Step-by-step explanation:

The value of x is 4.

What are vertical angles?

The opposing angles formed when two lines cross. They are constantly on par. In this illustration, the angles a° and b° are vertical. The term "vertical" refers to the vertex, not up or down, where they cross.

Here, we have

Given the following parameters

m∠A= (6x +29)° and

m∠B = (7x+25)°

Now, we equate both angles to find the value of x and we get

6x+29 = 7x + 25

6x-7x = 25 - 29

-x = -4

x = 4

Hence,  the value of x is 4.

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Answer:

Step-by-step explanation:

148 people

Answer:

a. 60km/2hours =30km per hour. 12/30=0.4 hours. 24 minutes

Step-by-step explanation:

The graph below is an example of graph function is cubic.

We must identify the kind of the graph after receiving it.

A parabola represents the graph of a quadratic function. As a result, the presented graph is not a quadratic function graph.

A straight line is represented by a linear function. The presented graph is not a graph of a linear function as a result.

A square root function's graph resembles a half parabola. Therefore, it can't be the square root function graph.

A cubic function's final behaviour is "opposite at both ends." We can see that the provided graph satisfies this requirement.

As a result, the shown graph illustrates a cubic function.

The right graph is C.

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The new dimension of the rectangular field are 45 ft by 120ft.

If the field has originally dimensions length L and width W, and we apply a scale factor K, then the new dimensions of the rectangle are:

lenght = K*L

width = K*W

In this case the original dimensions are:

L = 30ft

W = 80ft

And the scale factor is K = 1.5, then the new dimensions are:

L' = 1.5*30ft = 45ft

W' = 1.5*80ft = 120ft

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Answer:

bc it dose

Step-by-step explanation: