2d +9= 19
The solution is d =

Answer:

a) P(0) = 80

b) [tex]P(t) = 80(2.2361)^t[/tex]

c) 22,363 cells.

d) The rate of growth after 7 hours is of 18,000 bacteria per hour.

e) 9.7 hours.

Step-by-step explanation:

A bacteria culture grows with a constant relative growth rate.

This means that the population is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

In which P(0) is the initial population and r is the growth rate, as a decimal.

After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.

This means that in 6 hours, the population went from 400 bacteria to 50,000 bacteria. We use this to find r. So

[tex]50000 = 400(1+r)^6[/tex]

[tex](1+r)^6 = \frac{50000}{400}[/tex]

[tex](1+r)^6 = 125[/tex]

[tex]\sqrt[6]{(1+r)^6} = \sqrt[6]{125}[/tex]

[tex]1 + r = 125^{\frac{1}{6}}[/tex]

[tex]1 + r = 2.2361[/tex]

So

[tex]P(t) = P(0)(2.2361)^t[/tex]

(a) Find the initial population. P(0)

We have that P(2) = 400. We use this to find P(0). So

[tex]P(t) = P(0)(2.2361)^t[/tex]

[tex]400 = P(0)(2.2361)^2[/tex]

[tex]P(0) = \frac{400}{(2.2361)^2}[/tex]

[tex]P(0) = 80[/tex]

So

[tex]P(t) = 80(2.2361)^t[/tex]

(b) Find an expression for the population after t hours.

[tex]P(t) = 80(2.2361)^t[/tex]

(c) Find the number of cells after 7 hours.

This is P(7). So

[tex]P(7) = 80(2.2361)^7 = 22363[/tex]

22,363 cells.

(d) Find the rate of growth after 7 hours.

We have to find the derivative when t = 7. So

[tex]P(t) = 80(2.2361)^t[/tex]

[tex]P^{\prime}(t) = 80\ln{2.2361}(2.2361)^t[/tex]

[tex]P^{\prime}(7) = 80\ln{2.2361}(2.2361)^7 = 18000[/tex]

The rate of growth after 7 hours is of 18,000 bacteria per hour.

(e) When will the population reach 200,000?

This is t for which [tex]P(t) = 200000[/tex]. So

[tex]P(t) = 80(2.2361)^t[/tex]

[tex]200000 = 80(2.2361)^t[/tex]

[tex](2.2361)^t = \frac{200000}{80}[/tex]

[tex](2.2361)^t = 2500[/tex]

[tex]\log{(2.2361)^t} = \log{2500}[/tex]

[tex]t\log{2.2361} = \log{2500}[/tex]

[tex]t = \frac{\log{2500}}{\log{2.2361}}[/tex]

[tex]t = 9.7[/tex]

So 9.7 hours.

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Answer:

  (c)  A = 38.13 square inches; P = 23.42 inches

Step-by-step explanation:

The radius of the circle is half the diameter, so is 3 inches. This means the entire figure will fit in a rectangle 6 inches wide and 4+3 = 7 inches high. The perimeter of such a rectangle is ...

  P = 2(L+W) = 2(7+6) = 26 inches

The area of that rectangle is ...

  A = LW = (7)(6) = 42 square inches

Then area of the given figure is less than 42 square inches, and the perimeter is less than 26 inches. The only answer choice that matches these bounds is ...

  A = 38.13 square inches; P = 23.42 inches

Answer:

Step-by-step explanation:

(D+R) = 80:2 = 40

D = 40-R

(D+8) * R = 72X

Thay D=40-R

(40-R+8)*R = 72X

R=1.55, D=38.45

Answer:

1130

Step-by-step explanation:

1109+7 = 1116

1116+7 = 1123

Adding 7 each time

1123+7 = 1130

Answer:

r3jehejn wbbwbwbbwmwkwkwjwjwhhejehehehhe

on 220 acres

66 ⅔% is just ⅔ of 100%

330 * 2 / 3 = 220

Answer:

x=2

Step-by-step explanation:

you first have to make the bases the same

3^2x+1=9^2x-1

3^2x+1=3^2(2x-1) if you make the bases the same you will use 3^2 because it's equal to 9

3^2x+1=3^4x-2

2x+1=4x-2

2x-4x=-2-1

-2x/-2=-4/-2

x=2

I hope this helps

Answer:

A. H0: p = 0.67; H1: p < 0.67

A. The standard normal, since np > 5 and nq > 5.;

Test statistic = - 0.397 ;

Pvalue = 0.3457;

D. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

B. There is insufficient evidence at the 0.05 level to conclude that the true proportion of women athletes who graduate is less than 0.67.

Step-by-step explanation:

p = 0.67 ; q = 1 - p = 1 - 0.67

Sample size, n = 36

x = 23

Test for normality :

(36*0.67) = 24.12

(36 * (1-0.67)) = 11.88

For a normal distribution :

np ≥ 5 and n(1 - p) ≥ 5

The hypothesis :

H0 : p = 0.67

H1 : p < 0.67

The Test statistic :

Z = (phat - p) / √[(p(1 -p))/n]

Phat = x / n = 23 / 36

Z = ((24/36) - 0.67)) / √[(0.67(1 -0.67))/36]

Z = - 0.031 / 0.0783687

Z = - 0.396983

Z = - 0.397

Usong the Pvalue from Z calculator ;

Pvalue of Z = 0.3457

If Pvalue < α ; Reject H0 ; If otherwise, Fail to reject H0

Answer:

When time is short and you just want a rough estimate of the standard deviation, turn to the range rule to quickly estimate the standard deviation value. The standard deviation is approximately equal to the range of the data divided by 4. That's it, simple.

Answer:

18m squared

Step-by-step explanation:

4m x 4.5m = ?

Step-by-step explanation:

3x-1=4

3x=4+1

3x=5

x=5/3

Answer:

x = 5/3                       x = -1

Step-by-step explanation:

|3x-1| = 4

There are two solutions, one positive and one negative

3x-1 =4    and 3x-1 = -4

Add 1 to each side

3x-1+1 = 4+1     3x-1+1 = -4+1

3x = 5                  3x = -3

Divide by 3

3x/3 = 5/3             3x/3 = -3/3

x = 5/3                       x = -1

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Answer:

  (a)  M = 0.25n +100

Step-by-step explanation:

The distance between the dots on the graph is a rise of 1 grid square and a run of 2 grid squares. If we extend the sequence of dots to the left, we expect to place one at (0, 100). That is, the y-intercept of this function is 100 (eliminates choices C and D).

The rise of 1 grid square represents 25 kg, and the run of 2 grid squares represents 100 CDs. Then the slope of the function (rate of change) is ...

  slope = rise/run = 25/100 kg/CD = 0.25

Then the equation describing the points on the graph will be ...

  M = 0.25n +100

Answer:

0.0079 = 0.79% probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The trees are arranged, so, to find the number of outcomes, the arrangements formula is used.

Arrangements formula:

The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

Desired outcomes:

5 sycamores(5! possible ways) and then the 5 palm trees(5! possible ways)

5 palm trees(5! possible ways) then the 5 sycamores(5! possible ways).

[tex]D = 2*5!*5![/tex]

Total outcomes:

Arrangements of 10 plants, so:

[tex]T = 10![/tex]

What is the probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other?

[tex]p = \frac{D}{T} = \frac{2*5!*5!}{10!} = 0.0079[/tex]

0.0079 = 0.79% probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other.

Answer:

D.) y = 2x + 2

Step-by-step explanation:

First, we need to find the slope.

Lets use the points (0, 2) and (-2, -2).

Using the formula for calculating slope, we get 2 as our slope.

Since the equation should be in slope-intercept form, we use this formula.

y = mx + b

We'll use our first point (0, 2) to substitute for x and y and use 2 to substitute for m (slope):

2 = 2(0) + b

2 x 0 = 0

2 = 0 + b

-0 = -0

= 2 = b

Now, substitute b for 2 for 2 for m.

= y = 2x + 2.

Hope this helps!

If there is something wrong, please let me know.

1099.56m² is the surface area of a cylinder that has a radius of 7 m and a height of 18 m.

Answer:

C

Step-by-step explanation:

It is 8.6 because we are finding the difference and using subtraction.  

So I did 68.8-59.9 and I got 8.6

can u plz check if the question is right

Answer:

12/40 or simplified it would be 3/10

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A function is a relation in which each input, x, has only one output, y.

There are two ways to determine if a relation is a function:

1. If each x-input has only one, unique y-output, then it's a function. If some x-inputs share the same y-outputs, it's not a function.

2. Vertical Line Test on Graphs:

To determine whether y is a function of x, when given a graph of relation, use the  following criterion: if every vertical line you can draw goes though only 1 point, the relation can be a function. If you can draw a vertical line that goes though more than 1 point, the relation cannot be a function.

Since we're given a graph relation, let's test both of the answers out.

If I were to draw a vertical line in a specific place on the first graph, I'd be hitting more than one point in the coordinate plane.

If I were to draw a vertical line in a specific place on the second graph, I'd only be hitting one point in the coordinate plane.

Therefore, choice B is a function.

Answer:

just fill in 40 squres

Step-by-step explanation:

Answer:

Step-by-step explanation:

For each game played the chance of winning is 0.05 and losing is 0.95.

If the student wins, they get $5 -$1 = $4, but they lose $1.

Expected value is:

It means you will make $0.75 per average game.

Answer:

21.8

Step-by-step explanation:

Step 1

This is a problem on finding the mean of continuous grouped data. We first find the midpoint of each interval. For example, the first interval or class is 0 - 10. The mid-point of this class will be (0 + 10)/2 = 5.

fullscreen

Step 2

We now calculate the product of mid-point and frequency for each class. Here, the number of athletes in each class is the frequency of that class. For example, for the first class 0 – 10, its frequency is 3.

fullscreen

Step 3

We can now use the formula to calculate mean. Note that t...

Answer:

A

Step-by-step explanation:

I guess that is the answer

Answer:

First Choice: As the number of hours spent on homework increases, the tests scores increase.

Step-by-step explanation:

The definition of a positive correlation  is a relationship between two given variables, in which both variables are moving in the same direction. This can mean when one variable increases and the other variable increases, too, or one variable decreases and the other decreases as well.

The first choice is a positive correlation because both variables are changing (increasing) in the same direction. As you spend more time on homework, you're likely to get a higher test score.

The second choice cannot be a positive correlation because only one variable is having some kind of change (increasing). The doctor visits amount remains the same, so we can call this a zero-correlation relationship because the number of apples eaten yearly doesn't affect the amount of doctor visits. An apple a day keeps the doctor a way is just a proverb, not to be taken literally.

The third choice cannot be a positive correlation because the two variables are going different directions. Even though the number of times going to bed early is increasing, the number of times waking up late decreases, which is not moving in the same direction as the other variable.

The fourth choice cannot be a positive correlation because, similarly to the third choice, the two variables are going different directions. One variable is increasing, which is the amount of practice time. Meanwhile, the other variable is decreasing (going in the opposite direction), which is the number of games lost in a season.

Answer:

-0.54

Step-by-step explanation:

Hope it helped.

• • •

Answer:

Step-by-step explanation:

area of top face = π15² = 225π in²

volume = 225π × 40 = 9000π ≅28,260 in³

Answer:

Following are the solution to the given question:

Step-by-step explanation:

The population std. dev of the dog weight=8

[tex]\sigma=8\\\\P(\text{guess with in 16 lbs}) = P(|X-\mu|\leq 16)\\\\=P(-2 \leq Z \leq 2) = 0.9544\\\\[/tex]

Calculating the payout w s.t:

[tex]E[netpay]=0=(-5) \times 0.9544+w\times (1-0.9544)\\\\ w =(5 \times \frac{0.9544}{1-0.9544}) =\$ 104.65[/tex]

therefore, we assume that the weight of the dog is a normal distribution with std. deviation that is 8.

Answer:

D. y - 7 = 11(x - 5)

Step-by-step explanation:

Use point slope form, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Plug in the given slope and point:

y - y1 = m(x - x1)

y - 7 = 11(x - 5)

So, the correct answer is D. y - 7 = 11(x - 5)

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Answer:

  x = 100°

  y = 95°

Step-by-step explanation:

It is probably easier to find y first. Opposite angles of an inscribed quadrilateral are supplementary, so ...

  y = 180° -85° = 95°

The measure of an arc is double the measure of the inscribed angle subtending it. The arc subtended by angle y is ...

  90° +x = 2y

  x = 190° -90° = 100°

_____

Additional comment

The rule cited above regarding opposite angles of an inscribed quadrilateral comes from the theorem regarding inscribed angles. In the given diagram, the diagonal from the bottom vertex to the top one is a chord that divides the circle into two arcs. Their sum is 360°. The inscribed angle theorem tells you ...

  2y +2(85°) = 360°

  y + 85° = 180° . . . . . . . divide by 2; opposite angles are supplementary

Find the difference between each number:

-11 to -3 is +8

-3 to 5 is +8

The difference is 8

Use the following formula:

Bn = b1 + d(b -1)

Answer: bn = -11 + 8( b-1)