colby and jaquan are growing bacteria in an experiment in a laboratory. Colby starts with 50 bacteria in his culture and the number of bacteria doubles every 2 hours. Jaquan starts with 80 of a different type of bacteria that doubles every 3 hours.

Let x equal number of days.

Colby’s experiment follows the model:
1) y=50*2^x
2) y=50*2^8x
3) y=50*2^12x

Jaquan’s experiment follows the model:
1) y=80*2x
2) y=80*2^8x
3) y=80*2^12x


20 POINTS*****

Answer:

Changing value of "a" changes the amplitude of the sine graph.

Step-by-step explanation:

Question says to find about how does the a value affect your sine graph.

General equation of sine function can be given as:

[tex]y=a\cdot\sin\left(b\left(x-h\right)\right)+k[/tex]

There value of "a" gives amplitude.

So changing value of "a" changes the amplitude of the sine graph.

[tex]\bf ~~~~~~~~~~~~\textit{angle between two vectors } \\\\ cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\stackrel{\textit{magnitude product}}{||u||~||v||}} \implies \measuredangle \theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||~||v||}\right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} u=i+\sqrt{7}j\implies &<1,\sqrt{7}>\\\\ v=-i+9j\implies &<-1,9> \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf u\cdot v\implies (1)(-1)~+~(\sqrt{7})(9)\implies -1+9\sqrt{7}\implies 9\sqrt{7}-1~\hfill dot~product \\\\[-0.35em] ~\dotfill\\\\ ||u||\implies \sqrt{1^2+(\sqrt{7})^2}\implies \sqrt{1+7}\implies \sqrt{8}~\hfill magnitudes \\\\\\ ||v||\implies \sqrt{(-1)^2+9^2}\implies \sqrt{1+81}\implies \sqrt{82} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \theta =cos^{-1}\left( \cfrac{9\sqrt{7}-1}{\sqrt{8}\cdot \sqrt{82}} \right)\implies \theta =cos^{-1}\left( \cfrac{9\sqrt{7}-1}{\sqrt{656}} \right) \\\\\\ \theta \approx cos^{-1}(0.8906496638868531)\implies \theta \approx 27.05[/tex]

make sure your calculator is in Degree mode.

Answer: [tex]GCF=h^4[/tex]

Step-by-step explanation:

You need to remember that:

1) The definition of Greatest common factor (GCF): This is the greatest factor that divides two numbers.

2) The Product of powers property states that:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

3) To find the Greatest common factor between two numbers, for example, you can descompose them into their prime factors and then choose the commons with the lowest exponent.

In this case, you have [tex]h^4[/tex] and [tex]h^8[/tex]

You can observe that the common base is "h", then you only need to choose the one with the lowest exponent. This is:

[tex]GCF=h^4[/tex]

4) You can also rewrite  [tex]h^4[/tex] and [tex]h^8[/tex] as:

[tex]h^4=h*h*h*h\\*h^8=h*h*h*h*h*h*h*h[/tex]

You can observe that the common factor between  [tex]h^4[/tex] and [tex]h^8[/tex] is: [tex]h*h*h*h=h^4[/tex]

Then:

[tex]GCF=h*h*h*h=h^4[/tex]

Each time, you are subtracting 6 to get to the next term. The 8th term would be 12.

165,000, since 90,000÷1200=75. So 75×2200=165,000.

The assessed value of a property, given a tax amount of $2200, using the proportional ratio obtained from a known property value and tax amount pairing, is $165,000.

The subject of your question relates to a simple form of proportionality or ratio. The scenario provided allows us to set up a ratio problem. If the tax on a property valuing $90,000 is $1,200, we can write this ratio as 1200/90000. Now, using that ratio, you want to find the property value for a tax amount of $2,200. Therefore, we can set up the equation 1200/90000 = 2200/x, with x being the property value we're trying to find. Solving for x, we find that x = (90000*2200)/1200 which equals $165,000. Therefore, the assessed value of a property if the tax amounts to $2,200 is $165,000.

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Answer:

Markup= 1.81

Sale price =9.06

Step-by-step explanation:

The markup is the original prices times the markup rate

markup = 7.25 * 25%

            = 7.25 * .25

             =1.8125

We round this to the nearest cent

           =1.81

The new sale price will be the original price + the markup

7.25+1.81

9.06

Answer:

9.06, or real explanation.

Step-by-step explanation:

"Marco buys a certain brand of shampoo for a supplier $7.25 per bottle he sells it to his customers at a makeup 25% what would the makeup be"

I am going to assume makeup is supposed to be markup, but I will answer all there is.

To find how much higher he charges people for the shampoo, we can multiply the original cost by the percent of increase, so in our case 7.25*.25

7.25*.25=1.8125, or $1.81

1.8125 is the total extra he charges people for the soap.

NOW FOR THE TOTAL COST-------------------

For the total cost we take the original + the added cost

1.8125+7.25=9.0625, or 9.06

Answer:

pi/4 and 7pi/4.

Step-by-step explanation:

Sin 3pi/4 is in the second quadrant and is positive and has the same value as sin pi/4.

Sin (3pi/4) = sin (pi/4) = cos pi/4.

Also as cos x is positive in the 4th quadrant  cos (2pi - pi/4)

= cos 7pi/4 is also equal to sin 3pi/4.

Answer:

[tex]\frac{\pi}{4}\,,\,\frac{7\pi}{4}[/tex]

Step-by-step explanation:

Angle [tex]\frac{3\pi}{4}[/tex] lies in second quadrant in which [tex]\sin[/tex] is positive .

[tex]\sin \left ( \frac{3\pi}{4} \right )\\=\sin \left ( \pi-\frac{\pi}{4} \right )\\=\sin \left ( \frac{\pi}{4} \right )\\=\frac{1}{\sqrt{2}}[/tex]

We know that [tex]\cos[/tex] is positive in first and fourth quadrant .

In first quadrant :

We know that angle [tex]\frac{\pi}{4}[/tex] lies in first quadrant .

[tex]\cos \left ( \frac{\pi}{4} \right )=\frac{1}{\sqrt{2}}[/tex]

In fourth quadrant :

We know that angle [tex]\frac{3\pi}{4}[/tex] lies in fourth quadrant.

[tex]\cos \left ( \frac{7\pi}{4} \right )\\=\cos \left ( 2\pi-\frac{\pi}{4} \right )\\=\cos \left ( \frac{\pi}{4} \right )\\=\frac{1}{\sqrt{2}}[/tex]

So, for angles [tex]\frac{\pi}{4}\,,\,\frac{7\pi}{4}[/tex] , [tex]\cos x[/tex] has the same value as [tex]\sin \left ( \frac{3\pi}{4} \right )[/tex]

It is undefined, meaning it will not pass the vertical line test

Answer: x=4

Step-by-step explanation: isolate variable using division

=9a-4a=6+14

=5a=20

a=20/5

a=4

A. Truck A , because of every mile the truck uses 19 gallons.

Once put into the quadratic formula the numbers in the square root of they are negative no solutions if it is 0 then 1 solution if more then more than one solution

Answer:

Step-by-step explanation:

The worker will have approximately $8,296.00 in their retirement account after a year.

Calculate the interest earned: Multiply the principal amount ($8,000) by the annual interest rate (3.7%): $8,000 * 0.037 = $296.00.

Add the interest earned to the principal: $8,000 + $296.00 = $8,296.00.

Therefore, the worker will have approximately $8,296.00 in their retirement account after one year due to the accrued interest.

Answer:

10.5 ft.

Step-by-step explanation:

1. Find the radius of the larger circle

4/7 = 3/r --> the ratio should be constant

cross-multiplication: 21 = 4r

Divide: r = 5.25 ft.

2. Find the circumference

Equation: C = 2πr

C = 2π*5.25

C = 10.5π ft.

For this case we have the following functions:

[tex]f (x) = x ^ 2-6x + 8\\g (x) = x-2[/tex]

We must subtract the functions:

[tex]f (x) -g (x) = x ^ 2-6x + 8- (x-2)\\f (x) -g (x) = x ^ 2-6x + 8-x + 2\\f (x) -g (x) = x ^ 2-7x + 10[/tex]

We build a table of values for [tex]x = 0,1,2,3.[/tex]

[tex]x = 0, f (x) -g (x) = 0 ^ 2-7 (0) + 10 = 10\\x = 1, f (x) -g (x) = 1 ^ 2-7 (1) + 10 = 1-7 + 10 = 4\\x = 2, f (x) -g (x) = 2 ^ 2-7 (2) + 10 = 4-14 + 10 = 0\\x = 3, f (x) -g (x) = 3 ^ 2-7 (3) + 10 = 9-21 + 10 = -2[/tex]

Answer:

[tex]f (x) -g (x) = x ^ 2-7x + 10[/tex]

Answer:

Step-by-step explanation:

To solve divide the number of events by the number of possible outcomes.So in this case 60 is the event and 3 is the possible outcome because there is only 3 even numbers out of the 6. So the answer would be 20. Hope the is right. Good luck

Answer:

(1, 2)

Step-by-step explanation:

Remember that the final shape and position of a figure after a transformation is called the image, and the original shape and position of the figure is the pre-image.

In our case, our figure is just a point. We know that after the transformation T : (x, y) → (x + 3, y + 1), our image has coordinates (4, 3).

The transformation rule T : (x, y) → (x + 3, y + 1) means that we add 3 to the x-coordinate and add 1 to the y-coordinate of our pre-image. Now to find the pre-image of our point, we just need to reverse those operations; in other words, we will subtract 3 from the x-coordinate and subtract 1 from the y-coordinate.

So, our rule to find the pre-image of the point (4, 3) is:

T : (x, y) → (x - 3, y - 1)

We know that the x-coordinate of our image is 4 and its y-coordinate is 3.

Replacing values:

                (4 - 3, 3 - 1)

                (1, 2)

We can conclude that our pre-image is the point (1, 2).

Final answer:

The preimage of the point (4, 3) under the transformation T : (x, y) → (x + 3, y + 1) is (1, 2), found by reversing the transformation.

Explanation:

The transformation T : (x, y) → (x + 3, y + 1) maps each point in the plane to a new point that is 3 units to the right and 1 unit up from the original point. Finding the preimage of the point (4, 3) means determining which original point would be mapped to (4, 3) by this transformation. To do this, we set up the equations x + 3 = 4 and y + 1 = 3 and solve for x and y. Solving these equations gives us the preimage (1, 2).

Here's the step-by-step math:

Set up the equations based on the transformation T:
x + 3 = 4
y + 1 = 3

Solve for x:
x = 4 - 3 = 1

Solve for y:
y = 3 - 1 = 2

Therefore, the preimage of the point (4, 3) under the given transformation is (1, 2).

8•9+12\4-(5+3)

We are gonna use the method PEMDAS (Parenthesis, Exponents, Multiplication/Division, Addition/ Subtraction) to help us solve this equation.

8•9+12/4-8

72+12/4-8

72+3-8

75-8

67

To solve the equation 8 × 9 + 12 ÷ 4 - (5 + 3), apply the order of operations (BIDMAS/PEMDAS): Brackets, Indices, Division/Multiplication (left to right), Addition/Subtraction (left to right). The final answer is 67.

The subject of this question is Mathematics and it pertains to the correct order of operations. To solve the provided equation, 8 × 9 + 12 ÷ 4 - (5 + 3), we must follow the order of operations which is popularly known as BIDMAS or PEMDAS. This acronym stands for:

Here, we proceed by doing the operations within the brackets. (5+3) equals 8. Now, substitute 8 in the expression and we get 8 × 9 + 12 ÷ 4 - 8. Now according to BIDMAS/PEMDAS, the next step is to do multiplication and division from left to right. The expression now becomes 72 + 3 - 8. Finally, we do addition and subtraction from left to right, so the final result is 67.

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Answer: Option C.

Step-by-step explanation:

The equation of the line in slope-intercept form is:

[tex]y=mx+b[/tex]

Where the slope is "m" and the intersection of the line with the y-axis is "b".

Given the function f(x) in the form [tex]f(x)=x[/tex], you can identify that:

[tex]m=1\\b=0[/tex]

This means that the line passes through the origin (0,0)

And from the function g(x) in the form [tex]g(x)=x-16[/tex], , you can identify that:

[tex]m=1\\b=-16[/tex]

This means that the line of the function g(x) and the line of the function f(x) have the same slope, but the line of g(x) passes through the point (0,-16)

Therefore, the graph of f(x) must be shifted 16 units down to produce the graph of g(x)

I'm pretty sure quadrant II (2,2)

Answer:

(1,1)

Step-by-step explanation:

the point (1,1) lies on the graph of the function!

Answer:

a) 2

Step-by-step explanation:

9x - 7 = 6x - 4

3x = 3

x = 1

when x = 1

y = 9x - 7 = 9(1) - 7 = 2

or

y =  6x - 4 = 6(1) - 4 = 2

Answer

a) 2

Answer:

The answer is b) 1

Step-by-step explanation:

If you plug in y=9(1)-7= 2

same goes for y=6(1)-4=2

both the same answer

A: (x-2)(3+y)

3x - 6 + xy - 2y

(3x - 6) + (xy - 2y)

3(x - 2) + y(x - 2)

Your two terms are: (3 + y) and (x - 2)

Answer:  The correct option is (A). [tex](x-2)(3+y).[/tex]

Step-by-step explanation:  We are given to factor the following expression by grouping :

[tex]E=3x-6+xy-2y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Since we are given to factorize the expression (i) by grouping, so we will take 3 common from first two terms and y common from last two terms.

The factorization of expression (i) is as follows :

[tex]E\\\\=3x-6+xy-2y\\\\=3(x-2)+y(x-2)\\\\=(x-2)(3+y).[/tex]

Thus, the required factored form of the given expression is [tex](x-2)(3+y).[/tex]

Option (A) is CORRECT.

Answer:

D

Step-by-step explanation:

The percentage of students surveyed whi didn't take bus to school is 48%.

From the table:

The percentage value can be computed thus :

Now we have :

(12 / 25) × 100%

0.48 × 100%

= 48%

Complete Question:

Hector surveyed students in his homeroom about how they got to school last Monday and noted whether they arrive on time or late. The data he gathered is shown in the two-way table below.

According to the data in the table, what percentage of students in Hector’s homeroom did not take the bus to school last Monday?

Answer:

Option A) 2 square root 3

Step-by-step explanation:

we know that

The equilateral triangle has three equal sides and three equal angles (60 degrees each)

The triangle BOD is a right triangle

we have

<OBD=(60°/2)=30°

BD=12/2=6 units

tan(<OBD)=DO/BD

tan(30°)=DO/6

DO=6*tan(30°)

DO=2√3 units

Answer:

The correct answer is A. 2√3

Step-by-step explanation:

Answer:

0.34

Step-by-step explanation:

Do the inverse operation so;

0.034 / 1/10 = 0.34

Now go back and subsitute,

0.34 * 1/10 = 0.034

In the equation □ x 1/10 = 0.034, the missing value is 0.34 as obtained by isolating □ on one side, i.e., □ = 0.34.

The equation presented in the question is □ x 1/10 = 0.034. The missing value is the number that should be multiplied by 1/10 to result in 0.034. To solve for this missing value, we can rearrange the equation using the basic algebraic method. We isolate the missing value (□) on one side by dividing both sides of the equation by 1/10. This results in □ = 0.034 / (1/10), which simplifies further to □ = 0.34. Therefore, the missing value in the equation □ x 1/10 = 0.034 is 0.34.

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24 times 2 which will be 48

Answer:

d = sqrt(101)

Step-by-step explanation:

To find the distance between two points, we use the formula

d =sqrt ((x2-x1)^2 + (y2-y1)^2)  where (x1,y1) and (x2,x2) are the points

d = sqrt ((-13--3)^2 + (-23--22)^2)

d = sqrt ((-13+3)^2 + (-23+22)^2)

d = sqrt((-10)^2 + (-1)^2)

d = sqrt(100)+1)

d = sqrt(101)

To make the inequality 8 + y ≥ 11 true, y could be any value equal to or greater than 3. Examples of such numbers are 3, 4, and 5.

The inequality 8 + y ≥ 11 is asking for all the values of 'y' that, when added to 8, will give a number that is greater than or equal to 11. First, we can solve for the smallest possible 'y' by subtracting 8 from both sides of the inequality: y ≥ 11 - 8 simplifies to y ≥ 3. Therefore, any number greater than or equal to 3 will make the inequality true. Three examples of such numbers are 3, 4, and 5.

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A.certain because everybody can do that

Answer:

unlikely just took a test

Answer: real numbers?

Step-by-step explanation:

Answer:

The number line is graph of the or can be graph of any of the following set of numbers.

  1. Natural numbers

  2. Whole numbers

  3. Integers

  4.Rational Numbers

   5.Irrational numbers

   6. Real numbers

We can represent all this set of numbers on the graph of number line.