in a laboratory under favorable conditions, a bacteria population grows at an exponential rate. the number of cells C in the population is modeled by the function C(t)=ab^t. where a and b are constants and t is measured in hours. which function can be used to find the number of cells in the population at the time?


t: 0,1

C(t): 8,24

Answer:

The measure of angle LJC is [tex]m\angle LJC=43\°[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of arc LC

we know that

[tex]arc\ LC+arc\ JC=180\°[/tex] ----> because the diameter divide the circle into two equal parts

substitute the given values

[tex]arc\ LC+94\°=180\°[/tex]

[tex]arc\ LC=180\°-94\°=86\°[/tex]

step 2

we know that

The inscribed angle measures half that of the arc comprising

so  

[tex]m\angle LJC=\frac{1}{2}[arc\ LC][/tex]

substitute

[tex]m\angle LJC=\frac{1}{2}[86\°]=43\°[/tex]

Answer:

$6

Step-by-step explanation:

$15.50 is $3.50 more than $12. And $12 is twice $6. The cost of the screwdriver is $6.

Answer:

The tall of the tree is about 109.85 feet

Step-by-step explanation:

* Lets study the situation in the problem

- The tree and its shadow formed a right angle triangle with legs

  x the tall of the tree and 125 feet the shadow of the tree

- Ellie and her shadow formed a right triangle with legs 4 feet and

 10 inches the tall of Ellie and 5.5 feet the shadow of Ellie

- The two triangles are similar

- There is an equal ratio between the corresponding sides of the

 similar triangles

# Ex: If triangles ABC and XYZ are similar

∴ AB/XY = BC/YZ = AC/XZ

* Lets use this rule to solve the problem

∵ The tall of the tree is x

∵ The tall of Ellie is 4 feet and 10 inches

- Lets change the tall of Ellie to feet only

∵ 1 foot = 12 inches

∴ 10 inches = 10/12 = 5/6 foot

∴ The tall of Ellie is 4 feet and 5/6 foot = 4 + 5/6 = 29/6 feet

∵ The shadow of the tree is 125 feet

∵ The shadow of Ellie is 5.5 feet

- By using similarity ratio

∴ Tall of tree/tall of Ellie = shadow of tree/shadow of Ellie

∴ x/(29/6) = 125/5.5 ⇒ using cross multiplication

∴ 5.5(x) = 125(29/6) ⇒ divide both sides by 5.5

∴ x ≅ 109.85 feet

* The tall of the tree is about 109.85 feet

Answer:

The tall tree is about 109.85

Step-by-step explanation:

Hope this helps!

Answer:

48 ft³

Step-by-step explanation:

The volume (V) of the pyramid is

V = [tex]\frac{1}{3}[/tex] area of base × perpendicular height (h)

Calculate h using the right triangle formed by a segment from the vertex to the midpoint of the base and across to the slant face ( the hypotenuse )

Using Pythagoras' identity on the right triangle then

h² + 3² = 5²

h² + 9 = 25 ( subtract 9 from both sides )

h² = 16 ( take the square root of both sides )

h = [tex]\sqrt{16}[/tex] = 4

area of square base = 6² = 36, hence

V = [tex]\frac{1}{3}[/tex] × 36 × 4 = 12 × 4 = 48 ft³

Answer: OPTION A.

Step-by-step explanation:

We know that a circle measures 360 degrees. Then, to determine the size of a section, we need to multiply the percent of the category by 360 degrees.

First, we need to write 65 out of a hundred in decimal form:

[tex]\frac{65}{100}=0.65[/tex]

Now, let be "x" the degrees of the section representing 65 out of a hundred. We need to multiply 360 degrees by 0.65. Therefore, we get this result:

[tex]x=360\°*0.65\\x=234\°[/tex]

This matches with the option A.

The degree measurement for a section representing 65 out of 100 on a circle graph is 234 degrees. This is obtained by forming a ratio of the data point to the total data and multiplying by 360 (the total degrees in a circle).

To determine the degree measurement for a section on a circle graph, we must understand that a full circle consists of 360 degrees. The proportion that every bit of data takes in that circle is found by making a ratio of the data point to the total data multiplied by 360 degrees. Therefore, to find the proportion of 65 out of 100, we would make a ratio of 65 to 100 and multiply that by 360. Which comes out to: (65/100) * 360 = 234 degrees. So the correct answer would be 234 degrees (Option A).

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Answer:THE ANSWER IS D

Step-by-step explanation:

Mean increases and median is unchanged. Therefore, option D is the correct answer.

A dot plot, also known as a strip plot or dot chart, is a simple form of data visualization that consists of data points plotted as dots on a graph with an x- and y-axis. These types of charts are used to graphically depict certain data trends or groupings.

From the given dot plot A

The data is, 12, 12, 13, 13, 13, 13, 13, 14, 14

Data of plot B is 12, 12, 13, 13, 13, 13, 13, 14, 14, 20

Here, median of plot A and plot B is same.

Mean of plot B is greater than the mean of plot A.

Therefore, option D is the correct answer.

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Answer:

A. 196 m²

Step-by-step explanation:

The two similar solids have volumes 1728 m³ and 343 m³.

The ratio of their side lengths is :

[tex]\sqrt[3]{1728}:\sqrt[3]{343}[/tex]

This simplifies to:

[tex]12:7[/tex]

If the surface area of the larger solid is  576 m², then the surface area of the smaller solid is given by:

[tex]\frac{7^2}{12^2}\times 576=196[/tex]

The correct answer is A

Answer:

slope = 5

Step-by-step explanation:

To calculate the slope m use the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 3) and (x₂, y₂ ) = (2, 8) ← ordered pairs from the table

m = [tex]\frac{8-3}{2-1}[/tex] = 5

The slope of a line can be calculated using the formula (y2-y1) / (x2-x1) using any two points on the line. The result you get from this calculation is the slope of the line.

To find the slope of a line from a set of coordinates, you need two points from the line. Let's consider these two points as (x1, y1) and (x2, y2). The formula for the slope is (y2-y1) / (x2-x1). This formula shows the change in y-values divided by the change in x-values, often referred to as 'rise over run'.

If, for instance, from your table the two points are (3,4) and (5,8), substitute these values into the formula: Slope = (8-4) / (5-3) = 4/2 = 2. So the slope of the line is 2.

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Answer:

It would look like this basically..

Step-by-step explanation:

If a function, f(x) is shifted to the left four units, the

function that represents the transformation would be f(x+4). Adding it would make it go right..

*If you ever need help graphing, use desmos!

Answer:

  10 and 1

Step-by-step explanation:

Let x and y represent the two numbers. The problem statement lets us write two equations describing their relationships:

  x + y = 11

  x - y = 9

Adding these equations together, we have ...

  (x +y) +(x -y) = (11) +(9)

  2x = 20

  x = 10 . . . . . . . . . you will notice this is the average of the two given numbers

Then ...

  10 + y = 11 . . . . substitute for x in the first equation

  y = 1 . . . . . . . subtract 10

The two numbers are 10 and 1.

The data set is likely to be Normally distributed is given as:

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

As per the definition,

The Data that is significantly concentrated around the mean, with progressively fewer data points for values far away from the mean in both directions, is likely to be normally distributed.

and,  Insufficient Data can cause a normal distribution to look completely scattered.

So, The first statement is comes under normal distribution.

The second statement does not comes under normal distribution.

The third statement does not comes under normal distribution.

The fourth statement is comes under normal distribution.

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The answers for the statements to check whether normally distributed or not are 1.Yes,2.No,3.No,4.Yes

[tex]

\sin(\beta)=\frac{y}{h} \\

\sin(27)=\frac{y}{350} \\

y=350\sin(27)\approx\boxed{158.9}

[/tex]

Step-by-step explanation:

0 = x² - 6x - 27

a = 1, b = -6, c = -27  Factor using AC method.

ac = (1)(-27) = -27

Factors of -27 that add up to -6 are -9 and 3.

Therefore:

0 = (x - 9) (x + 3)

x = -3, x = 9

The x-intercepts are (-3, 0) and (9, 0).

Answer:

117

Step-by-step explanation:

182/14=13

13x9=117

ANSWER

Step 2

EXPLANATION

The system of equations are:

Equation A:

[tex]y = 4 - 2z[/tex]

Equation B:

[tex]4y=2 - 4z[/tex]Step 1: Multiply equation A by -4.

Equation A:

[tex] - 4(y) = - 4(4 - 2z)[/tex]

Equation B:

[tex]4y=2 - 4z[/tex]

Step 2: Simplify equation A in step 1,

Equation A:

[tex] - 4y= - 16 + 8z[/tex]

This is where the student made the first error.

He didn't expand the second parenthesis correctly.

Answer:

The student made the first mistake in step 2.

Step-by-step explanation:

Answer:

$7.15/hour

Step-by-step explanation:

Find Janie's unit rate of pay:  Amount per Hour:

$35.75 / (5 hours) = $7.15/hour

In each hour of working on Saturday morning, Janie earns $7.15.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Each Saturday morning Janie works five hours and earned $35.75.

So, To obtain the amount of money she earns each hour can be obtained by dividing the total amount she earned by the total number of hours she worked which is,

= $(35.75/5).

= $7.15.

So, Each hour Janie earns $7.15 by working in Saturday morning.

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Answer:

The exact value of [tex]\sin(60\degree)[/tex] is [tex]\frac{\sqrt{3} }{2}[/tex].

Step-by-step explanation:

Recall that   [tex]\sin(60\degree)[/tex]  is a special angle that can be obtained using an equilateral triangle.

The right triangle obtained using one of the lines symmetry was used to find the exact value of  [tex]\sin(60\degree)[/tex]  using SOH-CAH-TOA

The exact value of [tex]\sin(60\degree)[/tex] is [tex]\frac{\sqrt{3} }{2}[/tex].

Step-by-step explanation:

[tex] { \sin(x) }^{2} + { \cos(x) }^{2} = 1 \\ { \cos(theta) }^{2} = \frac{9}{16} \\ \: { \sin(theta) }^{2} = \frac{6}{16} = \frac{3}{8} \\ \: \sin(theta) = \frac{ \sqrt{3} }{ \sqrt{8} } \\ \sin(theta ) = \frac{ \sqrt{24} }{8}

= \frac{ 2\sqrt{6} }{8} = \frac{ \sqrt{6} }{4}

[/tex]

Answer:

[tex]\frac{\sqrt{7} }{4}[/tex]

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1, then

sinx = [tex]\sqrt{1-cos^2x}[/tex]

sinΘ = [tex]\sqrt{1-(3/4)^2}[/tex]

        = [tex]\sqrt{1-\frac{9}{16} }[/tex] = [tex]\sqrt{\frac{7}{16} }[/tex] = [tex]\frac{\sqrt{7} }{4}[/tex]

Let X = the number.

You have 21 more than 3 times the number which is:

3x +21 = -15

Subtract 21 from both sides:

3x = -36

Divide both sides by 3:

x = -36 /3

x = -12

The answer is B.

Answer:

-13

Explanation:

Rewrite Equation:

(3 · x) + 21 = -15

Subtract 21 From Both Sides:

(3 · x) + 21 - 21 = -15 - 21

Simplify:

3x = -36

Divide Both Sides By 3:

[tex]\bold{\frac{3x}{3} \ = \ \frac{-36}{3} }[/tex]

Simplify:

x = -12

Mordancy.

Answer:

[tex]r=\frac{1}{3+2cos\theta}[/tex]

Step-by-step explanation:

Let us write the equations in standard form:

[tex]r=\frac{1}{3+2cos\theta} \implies r=\frac{\frac{1}{3} }{1+\frac{2}{3}\cos \theta }[/tex]

We have

[tex]e=\frac{2}{3}\:<\:1[/tex] and

 [tex]ep=\frac{1}{3}[/tex]

Since the eccentricity  of this conic is less than 1, the conic represents an ellipse.

The second equation is [tex]r=\frac{3}{2+3\sin \theta}[/tex].

This is a hyperbola, because eccentricity is more than 1.

The third equation is [tex]r=\frac{5}{2+2\sin \theta}[/tex].

This is a parabola, because eccentricity is  1.

The fourth equation is [tex]r=\frac{2}{2-3\sin \theta}[/tex].

This is also a hyperbola, because eccentricity is more than 1.

(X+5)^2+(y+6)^2=61 and then to find the radius take the square root of both sides

Answer:

A. 7.07 units

Step-by-step explanation:

Use the distance formula for coordinates:

[tex]d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2   }[/tex]

Fill in the coordinates accordingly:

[tex]d=\sqrt{(1-(-4))^2+(-3-2)^2}[/tex]

which simplifies down to

[tex]d=\sqrt{25+25}[/tex]

which is of course

[tex]d=\sqrt{50}[/tex]

Plug that into your calculator and you'll get the answer

Answer:

288 ft.

Step-by-step explanation:

Find the perimeter. 50+50+94+94 = 288

Answer:

1.75 miles

Step-by-step explanation:

If he rides around his block 3 times it is 1.5 miles and if he only rides around his block half-way not a time it is a quarter of a mile added on instead of a half.

Answer:

1 3/4

Step-by-step explanation:

3 1/2*1/2=1 3/4. Hope this helps.

Answer:

1 hour (60 minutes)

Step-by-step explanation:

If his speed remains the same, that means that this is a linear relationship.  y increases at the same rate as x increases.  Direct variation and all of that.  Because this is a linear relationship, it can be solved using proportions.  Set up the given info in a ratio with miles on the top and minutes on the bottom:

[tex]\frac{miles}{minutes}:\frac{4}{20}[/tex]

Now we want to know how long (unknown number of minutes) it will take him to go 12 miles.  Keep miles with miles and minutes with minutes:

[tex]\frac{miles}{minutes}:\frac{4}{20}[/tex]=[tex]\frac{12}{x}[/tex]

We can cross multiply now to get 4x = 12(20) and 4x = 240.  That means that x=60.  It will take him 60 minutes (1 hour) to go 12 miles.

Answer: 60 minuites

Step-by-step explanation: actully the dude thats on top of me its only 60 mins not 1hr and 60 mins

Answer:

6 pairs of supplementary (when perpendicular)

a pair of complementary(0 for perpendicular)

4 pairs of adjacent

4 pairs of linear

2 pairs of vertical

Answer:

  D)  x² + (y − 2)² = 52

Step-by-step explanation:

The center of the circle is the midpoint of the diameter, so is the average of the end points:

  (h, k) = ((-6, 6) +(6, -2))/2 = (0, 4)/2 = (0, 2)

Then the distance between the center and an end point is the radius. It is found using the distance formula:

  r = √((x2 -x1)² +(y2 -y1)²) = √((-6 -0)² +(6 -2)²) = √(36 +16) = √52

Putting these values into the standard form equation for a circle ...

  (x -h)² +(y -k)² = r²

gives ...

  (x -0)² +(y -2)² = (√52)²

  x² +(y -2)² = 52 . . . . . matches choice D

Answer:

3.00p ≥ 135; p ≥ 45

Step-by-step explanation:

You sell each for $3 so 3(pastries sold or p).

You want to make AT LEAST 135 (you could make more but not less.)

so 3.00p ≥ 135.

To solve: divide 135 by 3.

p ≥ 45

Answer: [tex]3p\geq135[/tex]  ; [tex]p\geq45[/tex]

Step-by-step explanation:

Given : The French club is sponsoring a bake sale. If their goal is to raise at least $135 (greater than of equal to $135).

Let p be the number of pastries they sell.

If  they sell at $3.00 each in order to meet that goal, then the total price of p pastries will be : 3p

Then, the inequality for the given statement will become:-

[tex]3p\geq135[/tex]

Divide both sides by 3 , we get

[tex]p\geq45[/tex]

Hence, they must sell 45 or more pastries to raise at least $135.

Answer:

375

Step-by-step explanation:

So first you would want to divide 1,500 by 4 because the ratio is 4:7. The answer you get if you divide 1,500 by 4 is 375. This is your answer because if you divide 1,500 by 4 you are seeing out of how many 'dentist' would recomend this product.

1500/4

375

Use a calculator

Very helpful

Answer: (v - 9)^2 - 81

Step-by-step explanation: Use the formula (b/2)^2 in order to create a new term to complete the square.

Hope this helps! :) ~Zane