MAJOORRRR HELPPPP!!!
A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find how long it takes for the bacteria cells to increase to 300. Use the formula , where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number.

It takes hours for the number of bacteria to increase to 300.

Answer:

Step-by-step explanation:

The length AC is 3, but the corresponding length FD is 1, so the dilation factor is FD/AC = 1/3.

The reflection is a left/right reflection, so it is across a vertical line. We suspect the only vertical line you are interested in is the y-axis. (It could be reflected across x=1/2, and then the only translation would be downward.)

The above transformations will put C' at (1, 0). Since the corresponding point D is at (2, -2), we know it is C' is translated by (1, -2) to get to D.

  C' + translation = D

  (1, 0) +(1, -2) = (2, -2)

Answer: 66.50 inches

Step-by-step explanation:

Given : The distribution of heights of women for a certain country is approximately​ Normal with ,

[tex]\mu=\text{63.6 inches }\\\\\sigma=\text{2.8 inches}[/tex]

To find the height of the shortest 15​% of all women, first we need to find the z-score corresponding to the p-value 0.15 from the standard normal distribution table, we get 1.0364.

Let x be the random variable that represents the height of the randomly selected woman.

Then[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

[tex]1.0364=\dfrac{x-63.6}{2.8}\\\\\Rightarrow\ x=2.8\times1.0364+63.6\\\\\Rightarrow\ x=66.50192\approx66.50[/tex]

Hence, the height of the shortest 15​% of all women in this​ country =66.50 inches.

Answer:

1 1/3

Step-by-step explanation:

Absolute values are how far away it is from 0, so it is always positive. It is always the positive number of itself, so absolute values of negative numbers are the opposite, and the absolute value of positive numbers and just the same numbers.

Answer:

Step-by-step explanation:

/ -1 1/3​/ = -(-11/3) = 11/3

Answer:

Second Option (10° Celsius)

Step-by-step explanation:

There is a formula to convert the temperature which is in degree Celsius into degree Fahrenheit and vice versa. The formula to convert the temperature in degree Fahrenheit into degree Celsius is:

C° = (F° - 32) * 5/9.

It is given that the temperature is 50° Fahrenheit. Therefore, F° = 50°. Substituting F° = 50° in the formula gives:

C° = (50° - 32) * 5/9.

Further simplification results in:

C° = 18 * 5/9. Therefore, C° = 10°.

So the correct answer is 10° Celsius!!!

Answer:

  No, the triangles are not similar

Step-by-step explanation:

The (reduced) side length ratios, shortest to longest, are ...

  12 : 18 : 20 = 6 : 9 : 10

and

  5 : 12 : 13

These are not the same, so the triangles are not similar.

Answer:

The last answer is correct.

Also known as E

Step-by-step explanation:

Answer:

168.75π cm^3 is your answer.

Volume of a cone is 1/3 πr^2h.

Here, radius is given 7.5cm and height is given 9cm. So by using the formula we get the above answer.

For this case we have that by definition, the volume of a cone is given by:

[tex]V = \frac {\pi * r ^ 2 * h} {3}[/tex]

Where:

h: It's the height

r: It is the cone radius

According to the data we have:

[tex]h = 9cm\\r = 7.5cm[/tex]

Substituting:

[tex]V = \frac {\pi * (7.5) ^ 2 * 9} {3}\\V = \frac {\pi * 56.25 * 9} {3}\\V = 168.75\pi[/tex]

Thus, the volume of the cone is [tex]168.75 \pi \ cm ^ 3[/tex]

Answer:

Option C

Answer:

Step-by-step explanation:

Horizontal lines have the form " y = " where vertical lines have the form " x = ".

Horizontal lines run parallel to the y = 0 line, the x-axis, so horizontal lines are found in the y coordinate of the point.  Therefore, the horizontal line at that point is y = 7.

The vertical lines run parallel to the y-axis, which is the line x = 0.  The vertical lines are found then in the x coordinate of the point.  Therefore, the vertical line at that point is x = -10

Answer:

0.614

Step-by-step explanation:

Let the time be given by  = t

and P(S )  = probability that a person is sick

      P(s)    = probability that a person is not sick

P(s) = [tex](\frac{17}{23})^{23}* (1-\frac{17}{23})\\[/tex]

Then the probability for that there are at least 3 weeks of no sick students before the 2nd week of at least one sick student is given by:

[tex](\frac{17}{23})(\frac{17}{23})(\frac{17}{23})(\frac{17}{23}) + \frac{6}{23} + 3(\frac{17}{23})^{3}\\ = 0.614[/tex]

Answer:

Step-by-step explanation:

A. Points A, B, and D are on both planes.

  -- true. These points are on the line of intersection of the planes, so are in both planes.

B. Point H is not on plane R.

  -- true. Point H is not shown as being on either of the identified planes.

C. Plane P contains point F.

  -- false. Point F is shown as being in plane R, not P.

D. Points C, D, and A are noncollinear.

  -- true. Point C is not on the line containing points A and D.

E. The line containing points F and G is on plane R.

  -- true. F and G are both in plane R, so the line containing them will also be in that plane.

F. The line containing points F and H is on plane R.

  -- false. Point H is not in plane R, so will not be on any line in plane R.

The answer to this is a, b, d, e

Answer:

0.2

Step-by-step explanation:

we have given sample space = {1,2,3,4,5,6,7,8,9,10}

favorable outcomes E={2,4}

we know that probability is defined as the ratio of favorable otcomes to the sample space

probability [tex]P=\frac{favorable\ outcomes}{ sample\ space }[/tex]

we have  favorable outcomes E={2,4} that is  favorable outcomes=2

and sample sapce =  {1,2,3,4,5,6,7,8,9,10}

so the probability [tex]p=\frac{2}{10}=0.2[/tex]

The probability of event E={2,4} from the sample space S={1,2,3,4,5,6,7,8,9,10} is 1/5 or 20%, calculated by dividing the number of favorable outcomes (2) by the total number of outcomes (10).

The student asked to compute the probability of event E={2,4} from a sample space S={1,2,3,4,5,6,7,8,9,10}. Since the outcomes are equally likely, we use the formula for theoretical probability, which is the number of favorable outcomes divided by the total number of possible outcomes in the sample space.

To find P(E), first count the number of outcomes in event E, which includes just 2 and 4. There are two favorable outcomes. The total number of outcomes in the sample space S is 10. Therefore, P(E) equals 2/10 or 1/5 when simplified. This means the probability of event E occurring is 0.20 or 20%.

Answer:

C. The mean is 111.9F and the median is 114.5F.

Step-by-step explanation:

The mean is 111.9 given that (105 + 113 + 122 + 121 + 116 + 118 + 107 + 93)/8 = 111.875 which can be rounded to 111.9 F.

Organizing the values we have:

[93, 105, 107, 113, 116, 118, 121, 122]

We find that the median is going to be between 113 and 116. Therefore:

(113 + 116) / 2 = 114,5

Therefore, the correct answer is option C.

The answer would be "C"

mean = 111.9F

median = 114.5F

For the mean, we would add up all the numbers in the data. In this case, we would add...

105 + 113 + 122 + 121 + 116 + 118 + 107 + 93 = 895

Next, we would divide the sum by the number of bars we have in the graph. There are 8 bars in the graph with 8 different temperatures so we would divide 895 by 8 and we will get a quotient of 111.875. 111.875 rounded to the nearest tenths place is 111.9F

For the median, we would first place all the numbers in order from least to greatest.

least to greatest- 93,105,107,113,116,118,121,122

next, we need to find the two middle numbers because there is no middle number in an even set of data.

The two middle numbers in the data set are 113 and 116. The halfway point between 113 and 116 is 114.5 so our median would be 114.5

Answer:

-14/9

Step-by-step explanation:

Combine -2, -3, x, 2x, 4, 8.  We get -5 + 3x + 12.  This sum is -7.

Solve this equation for x:  3x + 7 = -7, so 3x = -14/3.

Then x is -14/9.

Answer:

-4.7

Step-by-step explanation:

-2 + (-3) + x + 2x + 4 + 8 =  -7

                    -5 + 3x +12 =  -7

                            3x + 7 =  -7

                                  3x = -14

                                    x = -14/3 = -4.7 °F

The value of x is -4.7.

Check:

-2 + (-3) + (-4.7) + 2(-4.7) + 4 + 8 = -7

                      -5 - 4.7 - 9.3 + 12 = -7

                                               -7 = -7

OK

Answer:

The area of triangle DEF is [tex]101\ cm^{2}[/tex]

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its heights is proportional and this ratio is called the scale factor and the ratio of its areas is equal to the scale factor squared

step 1

Find the scale factor

Let

z ----> the scale factor

[tex]z=\frac{13}{5}[/tex] ----> ratio of its heights

step 2

Find the area of triangle DEF

Let

z ----> the scale factor

x ----> the area of triangle DEF

y ----> the area of triangle ABC

so

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{13}{5}[/tex]

[tex]y=15\ cm^{2}[/tex]

substitute and solve for x

[tex](\frac{13}{5})^{2}=\frac{x}{15}[/tex]

[tex]x=(\frac{169}{25})(15)[/tex]

[tex]x=101\ cm^{2}[/tex]

Answer:

  see below

Step-by-step explanation:

Oddly enough, it is the one that with f(x) reflected over the y-axis. All points on the graph are mirrored across that axis (x is changed to -x, y is left alone).

When a graph gets reflected over y-axis it means that a horizontal reflection reflects a graph horizontally over the y-axis.

The graph of [tex]f(x) = 2^x[/tex] is shown on the grid.

The graph of [tex]g(x) = (\dfrac{1}{2})^x[/tex]  is the graph of f(x) reflected over the y-axis.

For x= 0 , [tex]g(x) = (\dfrac{1}{2})^0=1[/tex]

For x= 1 , [tex]g(x) = (\dfrac{1}{2})^1=\dfrac{1}{2}=0.5[/tex]

For x= 2 , [tex]g(x) = (\dfrac{1}{2})^2=\dfrac{1}{4}=0.25[/tex]

i.e. graph of g(x) passes through (-1,2) , (0,1) , (1,0.5) , (2,0.25)

From all the given graph , the correct graph is shown below .

It is showing the exact mirror-image of the given graph across y-axis and it is passing through the(-1,2) , (0,1) , (1,0.5) , (2,0.25) .

Answer:

x^3+9x^2+14x-24 has roots of -6,-4 and 1

Option D is correct

Step-by-step explanation:

If the polynomial has roots of -6 -4 and 1

then x=-6, x=-4, x=1

Which can be written as:

(x+6)(x+4)(x-1)

Multiplying we get,

(x+6)(x(x-1)+4(x-1))

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

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

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

x^3+3x^2-4x+6x^2+18x-24

x^3+3x^2+6x^2-4x+18x-24

x^3+9x^2+14x-24

So, x^3+9x^2+14x-24 has roots of -6,-4 and 1

Option D is correct

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[9-0]^2+[6-(-6)]^2}\implies d=\sqrt{(9-0)^2+(6+6)^2} \\\\\\ d=\sqrt{9^2+12^2}\implies d=\sqrt{225}\implies d=15[/tex]

From the information below the games is over in 3 sets. For Gina to win the match there are 3 possibilities.

1) Gina wins the first 2 sets with probability

2)Gina wins the first set. Looses the next set. Wins the third set.

3)Gina looses the first set. Wins the next 2 sets.

The required probability that Gina wins is the sum of the above 3 probabilities . That is the probability that Gina wins the match is

Answer:[tex] P=\frac{9+4}{25}=\frac{13}{25}[/tex]

Step-by-step explanation:

Given

Fred has a chance of 3/5 to win

and Gina has a chance of 2/5 to win

Probability(P) that the match is decided in only two sets is when

Either Fred or Gina win both matches continuously

P=P(Fred win both match)+P(Gina win both match)

[tex]P=\frac{3\times 3}{5\times 5}+\frac{2\times 2}{5\times 5}[/tex]

[tex] P=\frac{9+4}{25}=\frac{13}{25}[/tex]

Answer:

The solution of the equation is [tex]x=\frac{(ln4)-5}{2}[/tex] ⇒ 3rd answer

Step-by-step explanation:

* Lets explain how to solve this problem

- The function f(x) = e^x is called the (natural) exponential function

- The natural logarithm (㏑), or logarithm to base e, is the inverse

 function to the natural exponential function

∵ [tex]e^{2x+5}=4[/tex] is an exponential function

∴ We can solve it by using the inverse of e (㏑)

- Remember:

# [tex]ln(e)=1[/tex]

# [tex]ln(e^{m})=m(ln(e))=m[/tex]

- Insert ln in both sides

∴ [tex]ln(e^{2x+5})=ln(4)[/tex]

∵ [tex]ln(e^{2x+5})=(2x+5)ln(e)=2x+5[/tex]

∴ 2x + 5 = ㏑(4)

- Subtract 5 from both sides

∴ 2x = ㏑(4) - 5

- Divide both sides by 2 to find x

∴ [tex]x=\frac{ln(4)-5}{2}[/tex]

* The solution of the equation is [tex]x=\frac{(ln4)-5}{2}[/tex]

Answer:

Answer is C on edge

Step-by-step explanation:

x= (ln 4)- 5/2

Answer:

The total momentum of the system remains the same.Momentum before collision is equal to momentum after collision

Step-by-step explanation:

Momentum is defined as the product of mass and velocity of the bodies.According to the law of conservation of momentum, a collision that occurs in an isolated system, the momentum before collision equals that after collision.After collision, the bodies can move in the same direction thus their momentum is combined.

Answer:

According to the law of conservation of momentum, in a system where particles collide, the momentum loss on one particles is gained by the other one. This is what create an reaction during the collision, for example, if two bodies collide, one will decrease its speed while the other will increase its speed, that's why the momentum is conserved.

So, basically, after the train cars collide, the momentum must be conserved, remaining the same.

Answer:

x = 16.49

Step-by-step explanation:

By Pythagorean Formula

8.34² + 14.22² = x²

x² = 69.556 + 202.208

x² = 271.764.

x = √271.764

x = 16.4852

x = 16.49 (rounded to 2 dec. pl)

Answer:

A regional soccer tournament has 64 participating teams.

In the first round of the tournament, 32 games are played.

In each successive round, the number of games played decreases by 1/2.

Part A:

We know;

[tex]a_n=a_1\times r^{n-1}[/tex]

[tex]a_1=32[/tex]

[tex]r=\frac{-1}{2}[/tex]

So, we get;

The rule for the number of games played in the nth round is given by:

[tex]a_n=32(\frac{1}{2})^{n-1}[/tex]

where [tex]1\leq n\leq 6[/tex]

Part B:

As in each successive round the rounds are decreasing by 1/2 we have.

round 1 = 32

round 2 = 16

round 3 = 8

round 4 = 4

round 5 = 2

round 6 = 1

So, the total number of games played in the regional soccer tournament are: [tex]32+16+8+4+2+1=63[/tex]

Answer:

63 games total

Step-by-step explanation:

edge 2021

The given expression evaluates to 1/(1000x^3).

Option (C) is correct.

The exponent of a number of says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number.

As per the given data:

The given expression is (10x)^(–3)?

We can write the expression as:

= [tex]\frac{1}{(10x)^3}[/tex]

= [tex]\frac{1}{10^3x^3}[/tex]

= [tex]\frac{1}{1000x^3}[/tex]

= 1/(1000x^3)

Hence, the given expression evaluates to 1/(1000x^3).

To learn more about Exponents, click:

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(The given question is incomplete, the complete question is given below)

Which expression is equivalent to (10x)^-3?

a. 10/x^3

b. 1000/x^3

c. 1/(1000x^3)

d. 1/10x^3

Answer:

69.7 ft

Step-by-step explanation:

we know that

The function sine of angle of 35 degrees is equal to divide the opposite side to the angle of 35 degrees (the height of the vulture in a tree) by the hypotenuse ( the distance from the vulture to the roadkill)

Let

z -----> the distance from the vulture to the roadkill

sin(35°)=40/z

z=40/sin(35°)=69.7 ft

Answer:

69.7 feet.

Step-by-step explanation:

Let x represent the distance between vulture and roadkill.

We have been given that a vulture is perched 40 ft up in a tree and looks down at an angle of depression of a 35 and spots roadkill.

We can see from the attachment that vulture, roadkill and angle of depression  forms a right triangle with respect to ground, where, x is hypotenuse and 40 ft is opposite side.

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\text{sin}(35^{\circ})=\frac{40}{x}[/tex]

[tex]x=\frac{40}{\text{sin}(35^{\circ})}[/tex]

[tex]x=\frac{40}{0.573576436351}[/tex]

[tex]x=69.7378718[/tex]  

[tex]x\approx 69.7[/tex]  

Therefore, the roadkill is 69.7 feet away from the vulture.

Answer: The answer would be choice C because there is a constant rate of change of 3 :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

If x and y are proportional then the ratio y/x is constant.

[tex]A.\\\\\dfrac{4}{2}=2,\ \dfrac{6}{3}=2,\ \dfrac{9}{4}\neq2\\\\B.\\\\\dfrac{4}{3},\ \dfrac{16}{9}\neq\dfrac{4}{3}\\\\C.\\\\\dfrac{12}{4}=3,\ \dfrac{15}{5}=3,\ \dfrac{18}{6}=3\ \qquad\bold{CORRECT}\\\\D.\\\\\dfrac{4}{1}=4,\ \dfrac{8}{2}=4,\ \dfrac{15}{3}=5\neq4[/tex]

Answer:

[tex]r=\sqrt[3]{\dfrac{T^2GM}{4\pi^2}}[/tex]

Step-by-step explanation:

Divide by the coefficient of the r factor, then take the cube root.

[tex]T^2=\dfrac{4\pi^2}{GM}r^3 \qquad\text{given formula}\\\\\dfrac{T^2GM}{4\pi^2}=r^3 \qquad\text{divide by the coefficient of the r factor}\\\\r=\sqrt[3]{\dfrac{T^2GM}{4\pi^2}} \qquad\text{cube root}[/tex]

Answer:

The formula to solve r is [tex]r=\sqrt[3]{\frac{GMT^{2}}{4\pi^{2}}}[/tex].

Step-by-step explanation:

Consider the provided formula:

[tex]T^{2}=\frac{4\pi^{2}r^{3}}{GM}[/tex]

Where r is the orbit’s mean radius, M is the mass of the planet, and G is the universal gravitational constant.

Multiply both side by GM.

[tex]T^{2}GM=4\pi^{2}r^{3}[/tex]

Further solve the above equation.

[tex]\frac{T^{2}GM}{4\pi^{2}}=r^{3}[/tex]

[tex]\sqrt[3]{\frac{GMT^{2}}{4\pi^{2}}}=r[/tex]

Hence, the formula to solve r is [tex]r=\sqrt[3]{\frac{GMT^{2}}{4\pi^{2}}}[/tex].

Answer:

Step-by-step explanation:

Let f and p represent the costs of a file and a pen, respectively. The two purchases are ...

  f +3p = 32.85

  2f +8p = 83.50

Subtracting twice the first equation from the second gives an equation for the cost of pens:

  (2f +8p) -2(f +3p) = (83.50) -2(32.85)

  2p = 17.80 . . . . simplify

  p = 8.90 . . . . . . divide by 2

The cost of one pen is $8.90.

_____

Comment on "how do you do it?"

You are given two purchases related to the costs of two items. Write equations that describe the purchases. (The total cost is sum of the costs of each of the items, which will be the product of the number of items and the cost of each. You have been shopping, so you know this.)

Once you have a "system of equations", there are many ways they can be solved. You are usually instructed on "elimination" and "substitution" as methods of solution. Above, we used "elimination" to eliminate the "f" variable and give an equation only in "p".

Answer:

[tex]4032x^4[/tex]

Step-by-step explanation:

Use the 10th row of Pascal's Triangle to get you where you need to be.  You need 10 rows because any polynomial raised to the 9th power has 10 terms.  Those 10 terms are, in order:

1, 9, 36, 84, 126, 126, 84, 36, 9, 1

Setting up for the first 6 terms:

[tex]1(x^9)(2^0)+9(x^8)(2^1)+36(x^7)(2^2)+84(x^6)(2^3)+126(x^5)(2^4)+126(x^4)(2^5)+...[/tex]

The 6th term is the last one.  It goes on from there, but I stopped at the 6th term, since that is what you need.

Simplifying gives us:

[tex]126(x^4)(32)[/tex]

and multiplying gives us:

[tex]4032x^4[/tex]

The 6th term in the expansion of (x + 2)^9 is calculated using the binomial theorem, with the result being 4032x^4.

The 6th term in the expansion of the binomial expression (x + 2)9 is found using Binomial Theorem. The general formula for any term in the expansion of (a + b)^n, where n is a positive integer, is C(n, k) * (a^(n-k)) * (b^k), where C(n, k) is the combination of n items taken k at a time, and k is the term number minus 1.

For the 6th term, k equals 5 (since k = term number -1). By substituting these values into formula, you get: C(9, 5) * (x^(9-5)) * (2^5), which equals 126 * x^4 * 32, or 4032x^4.

So, the 6th term in the expansion of (x + 2)9 is 4032x^4.

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Step-by-step explanation:

10.

First, convert 1+i from Cartesian to polar.

r = √(1² + 1²)

r = √2

θ = atan(1/1), θ in first quadrant

θ = 45°

Therefore:

(1+i)²⁰ = (√2 (cos 45° + i sin 45°))²⁰

(1+i)²⁰ = 1024 (cos 45° + i sin 45°)²⁰

Now applying the De Moivre theorem:

1024 (cos (20×45°) + i sin (20×45°))

1024 (cos (900°) + i sin (900°))

1024 (-1 + 0)

-1024

11.

Repeat the same steps from Question 10.  First, convert to polar:

r = √(1² + (-1)²)

r = √2

θ = atan(-1/1), θ in fourth quadrant

θ = 315°

Therefore:

(1−i)¹⁰ = (√2 (cos 315° + i sin 315°))¹⁰

(1−i)¹⁰ = 32 (cos 315° + i sin 315°)¹⁰

Now applying the De Moivre theorem:

32 (cos (10×315°) + i sin (10×315°))

32 (cos (3150°) + i sin (3150°))

32 (0 − i)

-32i