The growth in the mouse population at a certain county dump can be modeled by the exponential function A(t)= 906e0.012t, where t is the number of months since the population was first recorded. Estimate the population after 36 months.

Answer:

[tex]t=\frac{(4-3.5)-0}{\sqrt{\frac{1.5^2}{11}+\frac{1^2}{9}}}}=0.890[/tex]  

The p value for this case would be:

[tex]p_v =P(t_{18}>0.890)=0.193[/tex]  

The p value is higher than the significance level so then we can conclude that we can FAIL to reject the null hypothesis and then the true mean for group A is not significantly higher than the mean for B

Step-by-step explanation:

Information given

[tex]\bar X_{1}=4[/tex] represent the mean for sample A

[tex]\bar X_{2}=3.5[/tex] represent the mean for sample B

[tex]s_{1}=1.5[/tex] represent the sample standard deviation for A

[tex]s_{2}=1[/tex] represent the sample standard deviation for B  

[tex]n_{1}=11[/tex] sample size for the group A

[tex]n_{2}=9[/tex] sample size for the group B  

[tex]\alpha=0.1[/tex] Significance level provided

t would represent the statistic

Hypothesis to test

We want to verify if the student who graduates from college A has taken more math classes, on the average, the system of hypothesis would be:  

Null hypothesis:[tex]\mu_{1}-\mu_{2} \leq 0[/tex]  

Alternative hypothesis:[tex]\mu_{1} - \mu_{2}> 0[/tex]  

The statistic is given by:

[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}[/tex] (1)  

And the degrees of freedom are given by [tex]df=n_1 +n_2 -2=11+9-2=18[/tex]  

Replacing we got:

[tex]t=\frac{(4-3.5)-0}{\sqrt{\frac{1.5^2}{11}+\frac{1^2}{9}}}}=0.890[/tex]  

The p value for this case would be:

[tex]p_v =P(t_{18}>0.890)=0.193[/tex]  

The p value is higher than the significance level so then we can conclude that we can FAIL to reject the null hypothesis and then the true mean for group A is not significantly higher than the mean for B

Answer:

between 3 and 4

Step-by-step explanation:

type sqrt(10) into your calculator

The requried, square root 10 lies between integers 3 and  4.

Integers are a set of whole numbers and their negative counterparts. They include positive numbers, negative numbers, and zero.

Examples of integers include -3, -2, -1, 0, 1, 2, 3, and so on.

The integer squares nearest to 10 are 9 and 16, which are the perfect squares of 3 and 4, respectively.

Since [tex]$\sqrt{9}=3$[/tex] and [tex]$\sqrt{16}=4$[/tex], we know that [tex]$\sqrt{10}$[/tex]  is between these two integers, we can say that [tex]$3 < \sqrt{10} < 4$[/tex].

Learn more about integers here:

https://brainly.com/question/15276410

#SPJ3

Answer:

719/47 is 15.29787234

Answer:

2 litre = 200 ml

so 200/50 = 4 glasses

Answer:

It's 40 of 50ml glass

Step-by-step explanation:

It's basically 2 litre/50ml

But 1000ml = 1 litres ;

Meaning 2 litres = 1000 × 2 = 2000ml

Therefore 2 litre/50ml = 2000/50

= 40

Answer:

7.5 feet

Step-by-step explanation:

Scale of the Model =5 in: 25 ft.

If we divide both sides by 5

[tex]\dfrac{5 in.}{5} : \dfrac{25 ft.}{5}\\\\$1 inch: 5 feet[/tex]

If a window on the model is 1.5 inch wide, from the unit ratio derived above we then have that:

1 Inch X 1.5 : 5 feet X 1.5 feet

1.5 Inch : 7.5 feet

Therefore, if a window in the model is 1.5 in. wide, the actual window is  7.5 feet wide.

Answer:

450 bacteria.

Step-by-step explanation:

To find this, we can set up an exponential equation as shown:

[tex]28800 = a (2)^{\frac{120}{20} }[/tex]

**'a' being the initial value

** '2' representing the culture doubling

Simplify the equation down:

[tex]28800 = a (2)^{6}[/tex]

[tex]28800 = 64a\\a = 450.[/tex]

Therefore, the initial amount of bacteria was 450.

Answer:

[tex] z = \frac{216-222}{\frac{15}{\sqrt{26}}}= -2.040[/tex]

And we can find this probability on this way:

[tex]P(z<-2.040)=0.0207[/tex]

Step-by-step explanation:

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

[tex]X \sim N(222,15)[/tex]  

Where [tex]\mu=222[/tex] and [tex]\sigma=15[/tex]

We are interested on this probability

[tex]P(\bar X<216)[/tex]

The z score formula is given by:

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

And if we find the z score we got:

[tex] z = \frac{216-222}{\frac{15}{\sqrt{26}}}= -2.040[/tex]

And we can find this probability on this way:

[tex]P(z<-2.040)=0.0207[/tex]

Answer:

  [tex]\dfrac{x^3-5x^2 +4x}{2x+8}[/tex]

Step-by-step explanation:

The basic idea is to factor each expression and cancel common factors from numerator and denominator.

  [tex]\dfrac{x^2-16}{2x+8}\cdot\dfrac{x^3-2x^2 +x}{x^2+3x-4}=\dfrac{(x-4)(x+4)}{2(x+4)}\cdot\dfrac{x(x-1)^2}{(x+4)(x-1)}\\\\=\dfrac{(x-4)x(x-1)}{2(x+4)}\cdot\dfrac{(x+4)(x-1)}{(x+4)(x-1)}\\\\=\boxed{\dfrac{x^3-5x^2 +4x}{2x+8}}[/tex]

Hey there! I'm happy to help!

It appears that we are trying to figure out which triangles are similar, which means that their side lengths have the same ratio. In ΔABC, we see that two sides have a length of 10 and the shorter has a length of 5. This means that the ratio between the long sides and the short sides must be 2:1 to be similar to this triangle.

Let's look at ΔJKL. Our long side has to be double our short side. If we double 2.5, it will be 5, not six, so JKL is not similar with ABC.

Now, let's look at ΔDEF. We see that it's long sides are double the short sides because 6 is double three. This means that the triangles ABC and DEF are similar.

The answer is A) ΔABC ~ ΔDEF.

I hope that this helps! Have a wonderful day!

Answer:

Step-by-step explanation:

Consider a sample with data values of 10, 20, 12, 17, and 16. (a) Compute the mean and median. Mean = Median = (b) Consider a sample with data values 10, 20, 12, 17, 16, and 12.

Mean = Total of values/ Total number of observations

Total of values = 10+20+12+17+16 = 75

Total number of observations = 5

Mean = 75/5 = 15

Median:

Arrange in ascending order = 10, 12,16,17,20

Median = [n+1] / 2

N = number of observation = 5

Median = [5+1]/2 = 3rd observation

Median = 16

Answer:

P(A∣D) = 0.667

Step-by-step explanation:

We are given;

P(A) = 3P(B)

P(D|A) = 0.03

P(D|B) = 0.045

Now, we want to find P(A∣D) which is the posterior probability that a computer comes from factory A when given that it is defective.

Using Bayes' Rule and Law of Total Probability, we will get;

P(A∣D) = [P(A) * P(D|A)]/[(P(A) * P(D|A)) + (P(B) * P(D|B))]

Plugging in the relevant values, we have;

P(A∣D) = [3P(B) * 0.03]/[(3P(B) * 0.03) + (P(B) * 0.045)]

P(A∣D) = [P(B)/P(B)] [0.09]/[0.09 + 0.045]

P(B) will cancel out to give;

P(A∣D) = 0.09/0.135

P(A∣D) = 0.667

Step-by-step explanation:

21

may be, I am not sure about this answer. But it can be

Answer:

x = 30

Step-by-step explanation:

4x + 2x = 180

6x = 180  

x = 30

3x² + 2x - 4 = 0

Δ = b² - 4.a.c

Δ = 2² - 4 . 3 . -4

Δ = 4 - 4. 3 . -4

Δ = 52

x = (-b +- √Δ)/2a

x' = (-2 + √52)/2.3    

x'' = (-2 - √52)/2.3

x' = 0,8685170918213297    

x'' = -1,5351837584879966

2 Decimal places

x' = 0,87

x'' = -1,54

Answer: .8685

Step-by-step explanation:

Answer: 18.48

Step-by-step explanation:

To solve this problem, you would use the order of operations. You would solve the parenthesis first and then solve the rest.

(5.6-2.3)(5.4+0.2)

3.3(5.6)

18.48

Answer:

Step-by-step explanation:

18.48

Answer:

total surface area Stot = 753.9816 m2

lateral surface area Slat = 351.85808 m2

top surface area Stop = 201.06176 m2

bottom surface area Sbot = 201.06176 m2

Answer:

Lateral area = 352 Square m

Surface area = 756. 3 square m

Volume = 1408 cubic m

Step-by-step explanation:

[tex]lateral \: area = 2\pi \: rh \\ = 2 \times \frac{22}{7} \times \frac{16}{2} \times 7 \\ = 22 \times 16 \\ = 352 \: {m}^{2} \\ \\ surface \: area = 2\pi \: r(h + r) \\ = 2 \times 3.14 \times 8(7 + 8) \\ = 6.28 \times 8 \times 15 \\ = 6.28 \times 120 \\ = 756.3 \: {m}^{2} \\ \\ volume = \pi {r}^{2} h \\ = \frac{22}{7} \times {8}^{2} \times 7 \\ = 22 \times 64 \\ = 1408 \: {m}^{3} \\ [/tex]

Answer:

180 ways

Step-by-step explanation:

U just multiply the number of sauce, noodle, vegetable, and meat

So 3 times 3 times 4 times 5

Correct me if this is wrong

Answer:

180

Step-by-step explanation:

you multiply 3X3X4X5 thus it equals 180

Answer:

a) The null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]

b) Sample proportion (p) = 0.6

Sample size (n) = 200

P-value = 0.0029

c) Conclusion: there is enough evidence to support the claim that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.

Step-by-step explanation:

The question is incomplete: there is no attached file with the data.

a) We want to test if more than half of the physiscians over the age of 55 have been sued at least once.

Then, the claim that will be stated in the alternative hypothesis should be that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.

The null hypothesis should state that this proportion is not signficantly different from 0.5.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]

b) As we do not have the file, we will work with a sample with size n=200 and sample proportion of 0.6.

This sample proportion can be calculated from the data as

[tex]p=x/n=120/200=0.6[/tex]

where x is the number of subjects in the sample that have been sued at least once.

The claim is that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]

The significance level is 0.01.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{200}}\\\\\\ \sigma_p=\sqrt{0.00125}=0.035[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.6-0.5-0.5/200}{0.035}=\dfrac{0.098}{0.035}=2.758[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>2.758)=0.0029[/tex]

As the P-value (0.0029) is smaller than the significance level (0.01), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.

Answer:

5

Step-by-step explanation:

The right answer is 5.

look at the attached picture

Hope it helps...

Good luck on your assignment

Answer:

[tex]z=\frac{0.462 -0.35}{\sqrt{\frac{0.35(1-0.35)}{78}}}=2.074[/tex]  

Now we can calculate the p value with this probability:

[tex]p_v =P(z>2.074)=0.019[/tex]  

If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.

Step-by-step explanation:

Information given

n=78 represent the random sample taken

X=36 represent the students with jobs

[tex]\hat p=\frac{36}{78}=0.462[/tex] estimated proportion of students with jobs

[tex]p_o=0.35[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to test if the proportion of students with jobs is higher than 0.35, the system of hypothesis are:  

Null hypothesis:[tex]p \leq 0.35[/tex]  

Alternative hypothesis:[tex]p > 0.35[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info we got:

[tex]z=\frac{0.462 -0.35}{\sqrt{\frac{0.35(1-0.35)}{78}}}=2.074[/tex]  

Now we can calculate the p value with this probability:

[tex]p_v =P(z>2.074)=0.019[/tex]  

If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.

[tex]g(x) = \sqrt{x - 4}[/tex]

[tex]h(x) = 2x - 8[/tex]

g x h = [tex]\sqrt{x-4}.(2x-8)[/tex]

Looking at the equation we know that there's no way to have a negative root, so we need x - 4 to be greater than or equal to 0

[tex] x - 4 \geq 0[/tex]

[tex]x \geq 4[/tex]

Answer:

It's 6

Step-by-step explanation:

Answer:

55.95 ft²

Step-by-step explanation:

Circumference formula:  C = 2πr  =>  r = C / (2π)

Area formula:  A = πr²

Substituting C / (2π) for r in the above equation, we get:

               C                        47 ft

A = π( ----------- )²  =  π ( -------------- )²

              2π                       (2π)

or ...

          π(47 ft)²                   2209 ft²

A = ----------------------  =  --------------------  =  55.95 ft²

               4π²                   4(3.14159)²

Answer: Three have a right angle. These are the green rectangle, the pinkish square, and the orange trapezoid.

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = -[tex]\frac{3}{4}[/tex]x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.

Answer: L = 1; W = 9/4; A = 2.25;

Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:

A = x.y

A = x(-[tex]\frac{3}{4}.x + 3[/tex])

A = -[tex]\frac{3}{4}.x^{2} + 3x[/tex]

To maximize, we have to differentiate the equation:

[tex]\frac{dA}{dx}[/tex] = [tex]\frac{d}{dx}[/tex](-[tex]\frac{3}{4}.x^{2} + 3x[/tex])

[tex]\frac{dA}{dx}[/tex] = -3x + 3

The critical point is:

[tex]\frac{dA}{dx}[/tex] = 0

-3x + 3 = 0

x = 1

Substituing:

y = -[tex]\frac{3}{4}[/tex]x + 3

y = -[tex]\frac{3}{4}[/tex].1 + 3

y = 9/4

So, the measurements are x = L = 1 and y = W = 9/4

The maximum area is:

A = 1 . 9/4

A = 9/4

A = 2.25

Answer & Step-by-step explanation:

We are given two equations...

a + b = 7

a - b = 3

We are asked to find 3a ÷ 3b. In order to find the value of a and b, we have to rearrange one of the equations so it will be easier to find the values of the variables. Let's rearrange the second equation.

a - b = 3 → a = 3 + b

Now that we have an equation that shows the value of a, we can use this equation and plug it into the first equation.

a + b = 7

a = 3 + b

(3 + b) + b = 7

3 + 2b = 7

2b = 4

b = 2

We have the value of b. Now, we have to find the value of a by plugging b into the second equation.

a - b = 3

b = 2

a - 2 = 3

a = 5

Now that we have the values of both variables, we can plug them into (3a÷3b)

3a ÷ 3b

3(5) ÷ 3(2)

15 ÷ 6

5/2 or 2.5

So, 3a ÷ 3b equals 5/2 or 2.5

Use the law of cosines to find the missing length, which we'll call [tex]d:[/tex]

[tex]d^2=100^2+120^2-2(100)(120)\cos 45^\circ[/tex]

[tex]d^2=24400-12000\sqrt{2}[/tex]

[tex]\boxed{d\approx 86\text{ cm}}.[/tex]

Answer:

a) Null hypothesis:[tex]\mu \geq 3[/tex]  

Alternative hypothesis:[tex]\mu < 3[/tex]  

This hypothesis test is a left tailed test.

b) [tex]t=\frac{2.8-3}{\frac{2.6}{\sqrt{1310}}}=-2.784[/tex]  

The p value for this case can be calculated with this probability:  

[tex]p_v =P(z<-2.784)=0.0027[/tex]  

We can conduct the test with the Ti84 using the following steps:

STAT>TESTS>T-test>Stats

We input the value [tex]\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310[/tex] and for the alternative we select [tex]< \mu_o[/tex]. Then press Calculate.

And we got the same results.  

Step-by-step explanation:

Information given

[tex]\bar X=2.8[/tex] represent the sample mean

[tex]s=2.6[/tex] represent the population standard deviation  

[tex]n=1310[/tex] sample size  

[tex]\mu_o =3[/tex] represent the value to test

[tex]\alpha=0.5[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic

[tex]p_v[/tex] represent the p value for the test

Part a) System of hypothesis

We want to test if the true mean is less than 3, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 3[/tex]  

Alternative hypothesis:[tex]\mu < 3[/tex]  

This hypothesis test is a left tailed test.

Part b

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]t=\frac{2.8-3}{\frac{2.6}{\sqrt{1310}}}=-2.784[/tex]  

The p value for this case can be calculated with this probability:  

[tex]p_v =P(z<-2.784)=0.0027[/tex]  

We can conduct the test with the Ti84 using the following steps:

STAT>TESTS>T-test>Stats

We input the value [tex]\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310[/tex] and for the alternative we select [tex]< \mu_o[/tex]. Then press Calculate.

And we got the same results.  

Answer:

False

Step-by-step explanation:

4 cos^4 (4x)-3 = 0

Substitute into the equation

4 cos^4 (4pi/24)-3 = 0

4 cos^4 (pi/6)-3 = 0

Take the cos pi/6

4 ( sqrt(3)/2) ^4 -3 =0

Take it to the 4th power

4 ( 9/16) -3 =0

9/4 -3 =0

9/4 - 12/4 = 0

-3/4 =0

False

Answer:

THE ANSWER IS TRUE.

Step-by-step explanation:

I did this on my homework.