A population of protozoa develops with a constant relative growth rate of 0.7781 per member per day. On day zero the population consists of six members. Find the population size after four days. (Round your answer to the nearest whole number.) P(4)

Answer:

1, 3, 5, 6

Step-by-step explanation:

Your solution has to be less than the number they are giving you for example if you have -3 one solution could be -16

The numbers that are solutions to the inequality are as follows: 20%, 17%, 29.5%, 1.5%.

The solution of an inequality is the set of all possible values that could serve as the result of the expression. So, for the given problem, the set of values that would correspond to the likelihood of snow is 20%, 17%, 29.5%, and 1.5%.

In other words, these percentages are less than 30% and can be rightly represented by the variable s.

Learn more about inequality here:

https://brainly.com/question/24372553

#SPJ2

Answer:

The number of possible outcomes in each trial of this game is 12

Step-by-step explanation:

Given

Rolling of a 6 sided die followed by tossing of a fair coin

Required

Number of possible outcomes

The first step is to list out the possible outcomes of rolling a die and tossing a coin

Rolling a fair die = {1,2,3,4,5,6}

Tossing a coin = {Head, Tail}

Let Head be represented by H and Tail be represented by T;

So,

Rolling a fair die = {1,2,3,4,5,6}

Tossing a coin = {H, T}

The question states that a roll of a 6 sided die is followed by a toss of a fair coin

This means that each trial is {A roll of die and A toss of coin}

So, the sample space is as follows

Sample Space = {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}

Number of outcomes in the sample space is 12.

Hence, the number of possible outcomes in each trial of this game is 12

Answer:

the total number of possible outcomes in each trial of this game is 12

Step-by-step explanation:

uhhhhhh none :) kk bye <3

Answer:

  8 full turns

Step-by-step explanation:

80 cm is 8 times 10 cm, so is 8 times around the spool.

Alex must unwind 8 full turns of thread from the spool.

__

He must unwind it once.

Answer:

8 in total turns

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

625^x = 5

x = 1/4

Answer:

for the 9th it is 39 for the 150th it is 607

Answer:

16.25%

=0.163 (correct to 3 decimal places)

Step-by-step explanation:

The child dependency ratio of a population is defined as the number of children (Under 15 years) divided by the working-age population (15–64 years old).

[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{{\mathrm{ Population}\,\left( \text{Under 15} \right)}}{{\mathrm{ Population}\,\left( {15-64} \right)}}\times 100[/tex]

From the given table:

Population Under 15 years = 2600

Population of the working class (between 15-64) = 16000

Therefore:

[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{2600}{16000}\times 100\\\\=16.25\%[/tex]

=0.163 (correct to 3 decimal places)

Answer:

yes the above is a function.

Answer:

(a)r=15-b

11.9 Inches

(b)See attached

Step-by-step explanation:

Length of the candle =15 inch

Let b represent the burned length of the candle (in inches)

Let r represent the remaining length of the candle (in inches).

Therefore:

(a) r+b=15

r=15-b

When b=3,1 Inches

Remaining Length, r=15-3.1=11.9 Inches

(b)The graph showing te relationship between r and b is shown below.

r is plotted on the y-axis while b is plotted on the x-axis as labelled.

Formula that express r in terms of b is

[tex]r=15-b[/tex]

Remaining length of candle is 11.9 inches

Given :

A 15-inch candle is lit and steadily burns until it is burned out

Let b represent the burned length   and let r represent the remaining length  

We need to write the formula

remaining length = initial length - burned length

[tex]r=15-b[/tex]

When 3.1 inches have burned from the candle, the remaining length of the candle is inches.

b is 3.1

remaining length [tex]r=15-3.1=11.9[/tex] inches

now we graph the relationship

Graph is attached below.

Learn more :  brainly.com/question/13844802

Answer:

[tex]y=300(1+0.16)^x[/tex]

Step-by-step explanation:

 [tex]A= P(1+r )^t[/tex]

Where

A =final amount  = y

P=initial principal balance = $300

r=interest rate  = 16%= 0.16

t=number of time periods elapsed= x

Hence the equation to model his account balance/ final amount A (y) after time (x) years is

[tex]y=300(1+0.16)^x[/tex]

Answer:

The 80% confidence interval for the average net change is (8.596, 12.904).

Critical value t=1.638.

Step-by-step explanation:

First, we calculate the mean and standard deviation of the sample:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{4}(12+7+13+11)\\\\\\M=\dfrac{43}{4}\\\\\\M=10.75\\\\\\s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{3}((12-10.75)^2+(7-10.75)^2+(13-10.75)^2+(11-10.75)^2)\\\\\\s=\dfrac{20.75}{3}\\\\\\s=6.92\\\\\\[/tex]

We have to calculate a 80% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=10.75.

The sample size is N=4.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.63}{\sqrt{4}}=\dfrac{2.63}{2}=1.315[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=4-1=3[/tex]

The t-value for a 80% confidence interval and 3 degrees of freedom is t=1.638.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.638 \cdot 1.315=2.154[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 10.75-2.154=8.596\\\\UL=M+t \cdot s_M = 10.75+2.154=12.904[/tex]

The 80% confidence interval for the average net change is (8.596, 12.904).

Answer:

1. B

Step-by-step explanation:

1. We are testing against the null hypothesis which is a single mean that sauce the average load is 0.8A

2. The level of significance is 1% (99% confidence interval)

3. The null hypothesis: u = 0.8

Alternative hypothesis: u =/ 0.8

4. a. The Student's t, since we assume that x has a normal distribution with known σ

5. Using the formula t = (x - u) / σ√n

Where x = 1.22 u = 0.8 σ = 0.44 n = 9

t = (1.22-0.8) / 0.44√9

t = 0.42/(0.44x3)

t = 0.42/1.32

t = 0.318

P value for 0.318 at 1% level of significance at 8 degree of freedom is 0.7586. Since our p value here is greater than 0.01, we can convince that there is not enough statistical evidence that indicate that the Toylot claim of 0.8 A is too low.

Answer:

0.288

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 17.48, \sigma = 3.25, n = 10, s = \frac{3.25}{\sqrt{10}} = 1.027740[/tex]

Find the probability that the mean printing speed of the sample is greater than 18.06 ppm.

This is 1 subtracted by the pvalue of Z when X = 18.06. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{18.06 - 17.48}{1.027740}[/tex]

[tex]Z = 0.56[/tex]

[tex]Z = 0.56[/tex] has a pvalue of 0.712

1 - 0.712 = 0.288

The answer is 0.288

Answer:

They have two sets of equal answers...

Step-by-step explanation:

-2 * 2 * 4 = -16

0 - 4 * -2 * -2 = -16

0 * -2 * -2 * 4 = 0

0 * 4 * 4 = 0

Answer:

1, 3, 5.

Step-by-step explanation:

The members of the set are {1, 3, 5}.

Note 0 is an even integer so is not included in the set.

Also 0 is neither negative or positive.

Answer:

Step-by-step explanation:

Hello!

The statistical model predicts the appraised value of houses in a section of the county East Meadow (Y) in relationship with the number of rooms of the house (X)

For a sample of n=64 houses the simple linear regression was estimated:

^Y= 74.80 + 24.93X

Range of X: 5 - 11

Range of Y: 160 - 300 ($ thousands of dollars)

Interpretation of the estimates of the y-intercept and the slope

y-intercept:

74.80 thousand dollars is the estimated average value of a house in a section of the county East Meadow when the house has zero rooms.

Slope:

24.93 [tex]\frac{thousand dollars}{rooms}[/tex] is the modification of the estimated average value of a house in a section of the county East Meadow when the number of rooms increases on one.

I hope this helps!

Since our first equation reads y = 2x + 3, we can substitute a 2x + 3

in for y in our second equation and then solve from there.

So we have 2x + 3 = x + 2.

Now subtract x from both sides to get x + 3 = 2.

Now subtract 3 from both sides to get x = -1.

To find y, plug -1 back into either equation.

I have chosen to plug it into the second.

So we have y = (-1) + 2 which simplifies to 1.

So our solution to this system is (-1, 1).

_______________________________

Hey!!

Answer:{2,4,5}

Explanation:

Let R be relation from A to B.The set of second components or the set of elements of B are called range.

Hope it helps..

_______________________________

Answer:

The critical values of F at 95% confidence are 0.359 and 2.788.

Step-by-step explanation:

We are given that a sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the following:

Store A                     Store B    

nA = 21                      nB = 16

SA = 28.284              SB = 20

And we are interested in determining whether or not the variances of the sales at two small grocery stores are equal.

AS we know that when we are interested in variances of two samples, we use F-test for doing hypothesis testing.

The test statistics for F-test is =  [tex]\frac{S_A^{2} }{S_B^{2} } \times \frac{\sigma_B^{2} }{\sigma_A^{2} }[/tex]  ~ [tex]F__n_A_-_1,_ n_B_-_1[/tex]

where, [tex]S_A[/tex] and [tex]S_B[/tex] are sample standard deviations.

Now, the critical values of F at 2.5% (because two-tailed test) level of significance from F-table at degrees of freedom (21 - 1, 16 - 1) = (20, 15) are given as;

2.788 for right-part and 0.359 for the left-part.

Answer:

They charge an equal amount of money each hour.

Answer:

Gym B and Gym A charge the same hourly rate for childcare.

Step-by-step explanation:

answer on edge

Answer:

a) Probability the fatality resulted from a fall = 0.1422

b) Probability the fatality resulted from a transportation incident = 0.3958

c(i) The cause of fatality that is least likely to occur is fatality due to fires and explosions with the lowest number of fatalities, 113.

c(ii) Probability that the fatality resulted from fires and explosions = 0.0249

Step-by-step explanation:

Data on U.S, Work-Related fatalities by cause follow (The World Almanac, 2012)

Cause of Fatality | Number of Fatalities Transportation Incidents | 1795

Assaults and violent acts | 837

Contacts with objects and equipment | 741

Falls | 645

Exposure to harmful substances | 404

Fires and explosions | 113

Total number of fatalities = 1795+837+741+645+404+113 = 4,535

Assume that a fatality will be randomly chosen from this population.

a. What is the probability the fatality resulted from a fall?

The probabilty of an event is given mathematically as the number of elements in that event divided by the Total number of elements in the sample space.

P(E) = n(E) ÷ n(S)

Probability the fatality resulted from a fall = (645/4535) = 0.14223 = 0.1422

b. What is the probability the fatality resulted from a transportation incident?

Probability the fatality resulted from a transportation incident = (1795/4535) = 0.39581 = 0.3958

c(i) What cause of fatality is least likely to occur?

The cause of fatality that is least likely to occur is the cause of fatality with the lowest frequency or number of fatalities. And this is fatality due to fires and explosions with the lowest fatalities of 113

c(ii). What is the probability the fatality resulted from this cause?

This is the probability that the fatality resulted from fires and explosions.

Probability that the fatality resulted from fires and explosions = (113/4535) = 0.02492 = 0.0249

Hope this Helps!!!

Answer:

[tex]P(X>1600)=P(\frac{X-\mu}{\sigma}>\frac{1600-\mu}{\sigma})=P(Z>\frac{1600-1518}{325})=P(z>0.252)[/tex]

And we can find this probability using the z score formula and the complement rule and we got:

[tex]P(z>0.252)=1-P(z<0.252) =1-0.599= 0.401 [/tex]

[tex] z =\frac{1600-1518}{\frac{325}{\sqrt{81}}}= 2.27[/tex]

And we can find this probability using the z score formula and the complement rule and we got:

[tex]P(z>2.27)=1-P(z<2.27) =1-0.988=0.012[/tex]

Step-by-step explanation:

Let X the random variable that represent the SAT scores of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(1518,325)[/tex]  

Where [tex]\mu=1518[/tex] and [tex]\sigma=325[/tex]

We want to find this probability:

[tex]P(X>1600)[/tex]

And we can use the z score formula given by:

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

Using this formula we got:

[tex]P(X>1600)=P(\frac{X-\mu}{\sigma}>\frac{1600-\mu}{\sigma})=P(Z>\frac{1600-1518}{325})=P(z>0.252)[/tex]

And we can find this probability using the z score formula and the complement rule and we got:

[tex]P(z>0.252)=1-P(z<0.252) =1-0.599= 0.401 [/tex]

For the other part we need to take in count that the distribution for the sampel mean if the sample size is large (n>30) is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

And we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\frac{sigma}{\sqrt{n}}}[/tex]

And replacing we got:

[tex] z =\frac{1600-1518}{\frac{325}{\sqrt{81}}}= 2.27[/tex]

And we can find this probability using the z score formula and the complement rule and we got:

[tex]P(z>2.27)=1-P(z<2.27) =1-0.988=0.012[/tex]

Answer:

X=0,X=-3/7

Step-by-step explanation:

7x^2+3x=0

x(7x+3)=0

x=0

7x+3=0

7x=-3

x=-3/7.

Answer:-3/7

Step-by-step explanation:

Firstly add -3x to both sides of equation. 7x^2+3x-3x=0+-3x

7x^2=-3x

Divid both sides by X

7x^2/X=-3/X

7x=-3

Divid both sides by 7

7x/7=-3/7

X=-3/7

Answer:

-8x - 8

Step-by-step explanation:

You have to combine like term.

So you add 16x + -24x = -8x

And you add -12 + 4 = -8

Your answer would be -8x - 8

I hope this helps!

Answer:

(a) 17/20 b.5/18/25 c. 1.255

Answer:

A=12 feet²

Step-by-step explanation:

1/2*base*height=area

(1/2)*4*6=12

75km convert to m 75x1000=75000m

converted I hour to seconds that is 3600seconds

If 75000m=3600seconds

? =5seconds

that id 75000x5=375000/3600

=104.26…metres

The distance will be 104.16 meters if the car is driving at 75 kilometers per hour.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

A car is driving at 75 kilometers per hour.

Let x be the distance.

As we know from the distance time relation:

Distance = speed×time

Speed = 75 km/h

Speed = 75 km/(3600)seconds

Speed = 0.0208 km/s

x = 0.0208×5

x = 0.10416 km

in meters

x  = 0.104x1000

x = 104.16 meters

Thus, the distance will be 104.16 meters if the car is driving at 75 kilometers per hour.

Learn more about the distance here:

brainly.com/question/26711747

#SPJ2

Answer:

6

Step-by-step explanation:

When the cube is folded, 6 is the opposite of 1.

2 is the opposite of 4 and 5 is the opposite of 3.

When the given net is folded into a cube, the number that we will find opposite 1 is 6.

When the net is folded, two will be folded left and up with 3 being the base. 4 will be folded right with 5 being the top of the cube.

We will then observe the following pairs opposite each other:

This means that the number that we will see opposite 1 will be the number 6.

Find out more on folding nets at https://brainly.com/question/16670460.

#SPJ9

Answer:

[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]

And replacing we got:

[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=2, p=1-0.16=0.84)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

And we can find this probability:

[tex] P(X \geq 1)[/tex]

And we can solve this probability like this:

[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)[/tex]

And if we use the probability mass function we got:

[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]

And replacing we got:

[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]

Answer:

1130

Step-by-step explanation:

since radius of the circle was given and the formula of the area is pie r square