3. A scientist starts an experiment with 5 bacteria. The number triples every 30
minutes. How many bacteria are in the culture after 2 hours and 30 minutes?

Answer:

B. -1.

Step-by-step explanation:

Note: 10 = 10^1 so:

10^-3 x 10 x 10^k = 10^(-3 + 1 + k) = 10^(k - 2).

So 10^(k - 2) = 10 ^(-3)

and k - 2 = -3

k = 2 - 3 = -1.

Answer: -1

Step-by-step explanation:

Answer:

Less

Step-by-step explanation:

5 divided by 6 is less than 1.

Answer: 0.83...

Answer:

Each student get less than 1 cup of broth.

Step-by-step explanation:

We have been given that a  teacher divides the 5 cups of broth among 6 students. We are asked to determine the amount that each student will get would be more than or less than 1 cup of broth.

Since there are 5 cups of broth, so we can distribute them to 5 students each having one cup of broth.

As the teacher divides the 5 cups of broth among 6 students, therefore each student will get less than one cup that is [tex]\frac{5}{6}[/tex] of cup.

Answer:

Step-by-step explanation:

[tex]\dfrac{3x}{x+1}+\dfrac{2x}{x-2}=\dfrac{4x^2-4}{x^2-x-2}\\\\Domain:\\\\x+1\neq0\ \wedge\ x-2\neq0\ \wedge\ x^2-x-2\neq0\\\\(1)\ x+1\neq0\qquad\text{subtract 1 from both sides}\\x\neq-1\\\\(2)\ x-2\neq0\qquad\text{add 2 to both sides}\\x\neq2\\\\(3)\ x^2-x-2\neq0\\x^2+x-2x-2\neq0\\x(x+1)-2(x+1)\neq0\\(x+1)(x-2)\neq0\to\ x+1\neq0\ \wedge\ x-2\neq0\\\\\bold{DOMAIN:}\ x\in\mathbb{R}-\{-1,\ 2\}[/tex]

[tex]\dfrac{3x}{x+1}+\dfrac{2x}{x-2}=\dfrac{4x^2-4}{x^2-x-2}\\\\\dfrac{(3x)(x-2)}{(x+1)(x-2)}+\dfrac{(2x)(x+1)}{(x+1)(x-2)}=\dfrac{4x^2-4}{(x+1)(x-2)}\\\\\dfrac{(3x)(x-2)+(2x)(x+1)}{(x+1)(x-2)}=\dfrac{4x^2-4}{(x+1)(x-2)}\\\\\text{therefore}\\\\(3x)(x-2)+(2x)(x+1)=4x^2-4\qquad\text{use the distributive property}\\\\(3x)(x)+(3x)(-2)+(2x)(x)+(2x)(1)=4x^2-4\\\\3x^2-6x+2x^2+2x=4x^2-4\qquad\text{combine like terms}\\\\(3x^2+2x^2)+(-6x+2x)=4x^2-4[/tex]

[tex]5x^2-4x=4x^2-4\qquad\text{subtract}\ 4x^2\ \text{from both sides}\\\\x^2-4x=-4\qquad\text{add 4 to both sides}\\\\x^2-4x+4=0\\\\x^2-2x-2x+4=0\\\\x(x-2)-2(x-2)=0\\\\(x-2)(x-2)=0\\\\(x-2)^2=0\iff x-2=0\qquad\text{add 2 to both sides}\\\\x=2\notin\bold{D}[/tex]

Answer:

4x^3 + 5

Step-by-step explanation:

(6x^3 - 4) + (-2x^3 + 9)

You can get rid of the parentheses

6x^3 - 4 + -2x^3 + 9

Combine like terms

6x^3 + -2x^3 = 4x^3

-4 + 9 = 5

4x^3 + 5

Answer:

2.2360679775 or simply put 2.2

Step-by-step explanation:

The square root of 5 will not be a perfect square.

Answer:24

Step-by-step explanation:

The ratio of 6 to 4 is the same as the ratio of 36 to 24. This is found by setting up the ratios as fractions, setting them equal to each other, and then solving for the unknown.

The question is asking for an equivalent ratio to that of 6 to 4, using 36 as the first term. To do this, you need to determine what number 36 is in the same ratio. A ratio is a relationship between two numbers indicating how many times the first number contains the second. In our case, 6 is to 4 as 36 is to what?

To find the answer, you can set up the ratios as fractions and solve for the unknown. For example, the ratio of 6 to 4 is expressed as 6/4. Because we want a ratio that's equivalent, we say 6/4 = 36/x, where x is the unknown number, we need to find.

Solving for x involves arranging the equation to isolate x and then performing the algebraic operation that gives the value of x. This would be: 6/4 = 36/x -> 6x = 36×4 -> 6x = 144 -> x = 144/6 -> x = 24.

Therefore, the ratio of 6 to 4 is equal to the ratio of 36 to 24 in math.

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Answer:

y = -2x - 18

Step-by-step explanation:

-4 = -2[-7] + b

14

-18 = b

y = -2x - 18

↑

rate of change [slope]

* Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES]:

½ → -2

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The answer would be "320 jokes."

[tex]\frac{5}{100}[/tex]

[tex]\frac{5}{100} of320[/tex]

[tex]\frac{5}{100} \times320=16[/tex]

[tex]=16[/tex]

Therefore Mr. Larios made 320 jokes this year and only 16 of them were funny.

Hope this helps

Answer:

he makes 320 jokes a year

Step-by-step explanation:

Answer:

A. -7 - 7 = -14

B. 7 - 7 = 0

C. -7 - (-7) = 0

D. 7 - (-7) = 14

Answer:

-7 - 7 = -14  ; Two negatives equal a positive

7 - 7 = 0  ;

-7 - (-7) = 0

7 - (-7) = 14 two negatives equal a positive

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4p-2

Replace the P with the 8

4(8)-2

4*8=32

32-2=30

your answer would be 30 cause 4 times 8 is 32 then 32 - 2 = 30

Answer:

Step-by-step explanation:

Answer:

negative

Step-by-step explanation:

that would be a negative corrolation

Answer:

m=8

Step-by-step explanation:

-88=-3(4m+5)-(1-3m)

-88=-12m-15-(1-3m)   <- Distributive Property

-88=-12m-15-1+3m  <- Open () if there is a negative negative the symbol equals positive

-88=-9m-16    <- Simplify

0=-9m+72   <- Add 88 to both sides

9m = 72 <- Add 9m to both sides

9m = 72

/9      /9

m=8

Final answer:

To find the width of a rectangular poster with a perimeter of 124 inches and a length that is 10 inches longer than the width, set up the perimeter equation, solve for the width, and find that the width is 26 inches.

Explanation:

The student asks to find the width of a rectangular poster where the length is 10 inches longer than the width, and the perimeter is 124 inches.

Firstly, let's denote the width of the poster as w inches. Therefore, the length is w + 10 inches. The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

We can set up the equation for the given perimeter:

2(w + 10) + 2w = 124

Simplifying the equation:

2w + 20 + 2w = 124

4w + 20 = 124

4w = 104

w = 26

The width of the poster is 26 inches.

Absolute values are always non-negative, so |-2.24| equals 2.24.

The absolute value of a number is its distance from zero on the number line, ignoring its sign. For -2.24, the distance from zero is 2.24 units.

This concept is useful in various mathematical calculations, such as finding the magnitude of a vector in physics or determining the error in measurements. In practical terms, it allows us to express distances, differences, or deviations without regard to direction. For example, if you are comparing temperatures, the absolute difference between -5°C and 8°C is 13°C, regardless of whether you are measuring an increase or decrease in temperature. This property makes absolute values valuable in many areas of mathematics, science, and everyday life.

Complete question: What is |-2.24|?

Answer:

Ana will have to multiply the amount of each item on the recipe by .25

For the 1/2 cup amount of coconut oil to be used instead of butter will be .125 or 1 and 5/8 amount of coconut oil to be used instead of butter.

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Answer:

-10 * 3/2= -30/2 = -15 is the solution

Answer:

-15

Step-by-step explanation:

-10/ 2/3

-10/1 / 2/3

-10/1 x 3/2

-30/2

=-15

Answer:

49 million if I'm not mistaken.

Step-by-step explanation:

Answer:

Part A) The proportional equation is [tex]c=55h[/tex]

Part B) 8 hours of training

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

Let

c -----> the cost to hire a dog

h ----> the amount of time in hours

The linear equation is equal to

[tex]c=kh[/tex]

Sue spent $660 on 12 hours of obedience training for her dog Muffin

Find the value of k (constant of proportionality)

[tex]k=y/x[/tex]

substitute the values

[tex]k=660/12=55[/tex]

therefore

The linear equation is

[tex]c=55h[/tex]

For [tex]c=\$440[/tex]

Find the value of h

substitute in the equation and solve for h

[tex]440=55h[/tex]

[tex]h=440/55=8\ hours[/tex]

Answer:

400 + 5x = 582 - 8x

14 weeks

Step-by-step explanation:

Set them both up in an equation ---> x = weeks

400 + 5x = 582 - 8x

Solve

13x = 182

x = 14

To determine how many weeks it will take for Chris and Ben to have the same amount in their bank accounts, we can set up and solve an equation based on their weekly deposits and withdrawals. After setting their equations equal to each other and solving for 'x', we find that it will take 14 weeks.

To determine how many weeks it will take for Chris and Ben to have the same amount in their bank accounts, we can set up an equation based on their weekly deposits and withdrawals. Let's represent the number of weeks as 'x'.

Chris's bank account balance can be represented by the equation: 400 + 5x

Ben's bank account balance can be represented by the equation: 582 - 8x

To find the number of weeks it takes for their balances to be equal, we can set their equations equal to each other and solve for 'x':

400 + 5x = 582 - 8x

Combining like terms and isolating 'x', we get:

13x = 182

Dividing both sides by 13, we find that x = 14.

Thus, it will take 14 weeks for Chris and Ben to have the same amount in their bank accounts.

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Answer:

20x - 4

Step-by-step explanation:

4 less than 20 times some number

Let's break it up.

4 less than = -4

20 times some number = 20x (x is representing "some number")

So, let's put that together.

4 less than 20 times some number

20x - 4

Answer:

[tex]6 = f(4) \\ \\ 0 = f(-2)[/tex]

Step-by-step explanation:

Think of f(x). Those numbers in parentheses next to the f are x-coordinates, all you have to do is look in the chart and see what y-coordinate they gave you with respect to the given x-coordinates.

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Answer:

y = (Cm)/4 + (Cn)/4

Answer:

Step-by-step explanation:

C= 4y/m+n

4y = c(m+n)

y =  c(m+n)/4

Answer:

C.  Reflect triangle J across the y-axis, then across the x-axis.

Answer:

I think the answer is B but i might be wrong

Answer:

[tex]x\le 400-23\\ \\x\le 377\ pounds[/tex]

Step-by-step explanation:

The winner of a weight-lifting competition bench-pressed weight 400 pounds.

All other competitors bench-pressed at least 23 pounds less. So, the maximum weight that all other competitors bench-pressed is

[tex]400-23=977\ pounds[/tex]

If x pounds is the weight that the other competitors bench-pressed, then

[tex]x\le 400-23\\ \\x\le 377\ pounds[/tex]

that sounds as the other competitors bench-pressed at most 377 pounds weight.

Answer:

18 batches of pancakes

Step-by-step explanation:

22.5/1.25=18

Answer:

17 batches

Step-by-step explanation:

Divide (1 1/4 cup per batch) into 22 1/2 cups:

  22 1/5 cups

---------------------- = 22.2/1.25 batches = 17.76 batches

   1 1/4 cup

   --------------

     1 batch

One bag of flour will make 17 batches with about 3/4 batch unfinished.

Answer:

y

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3, thus

y = 3x + c ← is the partial equation of the line

To find c substitute ( [tex]\frac{2}{3}[/tex], 4) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = 3x + 2 → A

Answer:

Step-by-step explanation:

[tex]\left(\dfrac{2}{3};\ 4\right)\to x=\dfrac{2}{3},\ y=4\\\\\text{Put to the each equation:}\\\\A.\ y=3x+2\\\\4=3\left(\dfrac{2}{3}\right)+2\\4=2+2\\4=4\qquad\bold{CORRECT}[/tex]

We do not check other equations because all the lines have the same slope. Therefore, they are parallel lines. If one of the lines passes through a given point, then another cannot pass through that point.

Carlo will attend art class in 4 weeks,

fencing lessons in 3 weeks,

and chess club in 2 weeks.