When engaging in weight-control (fitness/fat burning) types of exercise, a person is expected to attain approximately 60% of his or her maximum heart rate. For 20-year-olds, this rate is approximately 120 bpm. A simple random sample of thirty 20-year-olds was taken, and the sample mean was found to be 107 bpm, with a standard deviation of 45 bpm. Researchers wonder if this is evidence to conclude that the expected level is actually lower than 120 bpm. Report a 95% confidence region for the mean level of heart rate for this group. the mean level of heart rate is greater than 117.67 the mean level of heart rate is lower than 120.96 the mean level of heart rate is lower than 114.47 the mean level of heart rate is greater than 114.47

Answer:

0.8

Step-by-step explanation:

the opposite of a negative is the positive version of the number

Answer:

the opposite of -0.8 is 0.8

Step-by-step explanation:

opposite of a negative number is the same number but positive or vice verse

Answer:

40 bricks

Step-by-step explanation:

3 1/2×8

=28

56×20

=1,120

1,120÷28

=40 bricks

Answer:

The mean of the the random variable X is 1200.

The standard deviation of the random variable X is 21.91.

Step-by-step explanation:

The random variable X is defined as the number of city residents in the sample who support the proposal.

The random variable X follows a Binomial distribution with parameters n = 2000 and p = 0.60.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

Check the conditions as follows:

[tex]np=2000\times 0.60=1200>10\\\\n(1-p)=2000\times (1-0.60)=800>10[/tex]  

Thus, a Normal approximation to binomial can be applied.

So,  the random variable X can be approximate by the Normal distribution .

Compute the mean of X as follows:

[tex]\mu=np[/tex]

  [tex]=2000\times 0.60\\=1200[/tex]

The mean of the the random variable X is 1200.

Compute the standard deviation of X as follows:

[tex]\sigma=\sqrt{np(1-p)}[/tex]

  [tex]=\sqrt{2000\times 0.60\times (1-0.60)}\\=\sqrt{480}\\=21.9089\\\approx 21.91[/tex]

The standard deviation of the random variable X is 21.91.

Answer:

61/495

Step-by-step explanation:

Answer:

that is the solution to the question

Answer:

16 cakes

Step-by-step explanation:

If you do 6 divided by 3/8, you would get 16, which is the amount of cakes that Kevin will be able to make.

Answer:

because I said one is the best number

Step-by-step explanation:

[tex](2x^2-6x^3+4)+(2x^3+3x^2+4)[/tex]

Since this is addition, you can just easily combine the terms.

[tex](2x^2+3x^2)+(-6x^3+2x^3)+(4+4)[/tex]

[tex]5x^2 -4x^3+8[/tex]

Now, all we have to do is put it in standard form meaning the exponents have to go in descending order. Largest exponent to smallest exponent.

[tex]-4x^3+5x^2+8[/tex]

So, this is your answer in standard form.

Answer:

(a)Yes, it is an exponential function.

(b)[tex]P(t)=200\cdot 2^{t/20}[/tex]

Step-by-step explanation:

(a)A population grows exponentially if it increases by a common ratio(called the growth ratio). We can see from the given information that the population of E.coli doubles every 20 minutes, therefore it is an exponential growth with a growth ratio of 2.

(b)The population, P(t) at any time t of an initial population, [tex]P_o[/tex]  with a growth ratio of r over a period k can be modeled using the function:

[tex]P(t)=P_o\cdot r^{t/k}[/tex]

In this Case:

[tex]P_o[/tex]=200

Growth rate,r=2

Growth Period,k=20 minutes

Therefore, the equation that models the function is:

[tex]P(t)=200\cdot 2^{t/20}[/tex] , t is in minutes

Jenny is correct that E. coli growth can be modeled with an exponential function, characterized by doubling in population size at regular time intervals. An equation representing this growth is N(t) = N0 x 2^(t/20), where N0 is the initial amount of E. coli and t is time in minutes.

I agree with Jenny, the E. coli growth can indeed be modeled with an exponential function. This is supported by the fact that the E. coli population doubles after each consistent time period (20 minutes). In an exponential growth model, the rate of increase of a population is proportional to the current population size, which means as the population gets larger, it grows at an even faster rate.

Part B: Equation of Exponential Growth:

The exponential growth model for a population starting with N0 individuals and a growth rate r can be described by the equation N(t) = N0ert, where N(t) is the population at time t, N0 is the initial population size, e is the base of the natural logarithm, and r is the growth rate per unit time. For E. coli, with a doubling time of 20 minutes, the growth rate can be calculated using the doubling formula: Td = ln(2)/r, solving for r gives r = ln(2) / 20 minutes. The continuous exponential growth equation can be simplified to a discrete model for this case: N(t) = N0 * 2(t/20), where t is given in minutes.

Answer:

-6

Step-by-step explanation:

simplify

Answer:

Step-by-step explanation:

Let the cost of a bag of popcorn=p

Let the cost of a drink=d

Mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks.

Christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks.

The required system of equations is:

Multiply the first equation by 2 to eliminate p

6p+12d=91.5

6p+4d=71.50

Subtract

8d=20

d=20/8=$2.5

Substitute d=2.5 into any of the equations to obtain p.

6p+12d=91.5

6p+12(2.5)=91.5

6p=91.5-12(2.5)

6p=91.5-30

6p=61.5

Divide both sides by 6

p=$10.25

Therefore:

Answer:

The answers below ._.

Step-by-step explanation:

A secant is a line that intersects a circle in exactly two points. When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

The formation of secant lines that intersect within a circle is related when a secant and a tangent or two tangents intersect each other outside a circle.

A secant line is a straight line that connects two points on a curve. The secant line approaches a tangent line when the two points are drawn together.

So, If a tangent and a secant, or two tangents intersect at the exterior side of a circle, the angle created has a measure equal to one-half the positive difference between the intercepted arcs' measures.

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Answer:

Respuesta D

Step-by-step explanation:

Paola afirma: Todo número compuesto par, se puede escribir como la multiplicación de factores primos.

Esta afirmación es cierta, pues es un caso  de la afirmación de que todo número natural mayor que uno se puede escribir como multiplicación de números primos. A este proceso se le llama descomposición en factores primos.

Edwin afirma: Todo número compuesto impar se puede escribir como la suma de dos números primos.

Esta afirmación es falsa. Note que al sumar dos números impares de la forma 2k+1 y 2m+1 para k distinto de m, se obtiene

[tex] 2k+1+2m+1 = 2(km+1)[/tex]

Es decir, la suma de dos números impares es siempre par.

Note que a excepción de 2, todo número primo es impar. Para que esta afirmación fuera cierta, necesariamente tendría que pasar que cualquier número impar k se escriba de la forma p+2 donde p es un número primo. Esto es equivalente que para cualquier número impar k, el número k-2 sea primo.

Basta con dar un ejemplo para ver que esto no pasa. Tomemos k=11. En este caso, k-2 = 9, el cuál no es un número primo. Entonces 11 no se puede  descomponer como la suma de dos números primos.

Answer:

b) The margin of error is approximately 3.24

e) The critical value is 1.7921.

Step-by-step explanation:

Step(i):-

Given sample size 'n' =20

Given sample standard deviation 's' = 10

Margin of error

The margin of error is determined by

[tex]M.E = \frac{t_{\alpha } S.D }{\sqrt{n} }[/tex]

The level of significance ∝ =0.95

The degrees of freedom = n-1 = 20-1=19

t₀.₉₅ = 1.729

[tex]M.E = \frac{1.729 X10 }{\sqrt{20} }[/tex]

Margin of error = 3.866

Step(ii):-

Margin of error

The margin of error is determined by

[tex]M.E = \frac{t_{\alpha } S.D }{\sqrt{n} }[/tex]

Given another sample size n =30

The level of significance ∝ =0.95

The degrees of freedom = n-1 = 30-1=29

t₀.₉₅ = 1.70

[tex]M.E = \frac{1.7021 X10 }{\sqrt{30} } =3.24[/tex]

Margin of error = 3.24

To find the values of the two numbers, we can set up a system of equations based on the given information and then solve for x and y. The first number is 16 and the second number is 22.

Let's represent the first number as x and the second number as y.

We can set up two equations based on the given information.

The first equation is: x = y - 6

The second equation is: 6x = 4y + 8

Now we can solve this system of equations to find the values of x and y.

Substituting the first equation into the second equation, we get: 6(y - 6) = 4y + 8

Simplifying, we get: 6y - 36 = 4y + 8

Bringing like terms together, we have: 6y - 4y = 8 + 36

Combining like terms, we get: 2y = 44

Dividing both sides by 2, we have: y = 22

Now substitute y = 22 back into the first equation: x = 22 - 6

Simplifying, we get: x = 16

Therefore, the first number is 16 and the second number is 22.

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Answer:

We conclude that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote.

Step-by-step explanation:

We are given that 513 employed persons and 604 unemployed persons are independently and randomly selected, and that 287 of the employed persons and 280 of the unemployed persons have registered to vote.

Let [tex]p_1[/tex] = percentage of employed workers who have registered to vote.

[tex]p_2[/tex] = percentage of unemployed workers who have registered to vote.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex]      {means that the percentage of employed workers who have registered to vote does not exceeds the percentage of unemployed workers who have registered to vote}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1>p_2[/tex]     {means that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote}

The test statistics that would be used here Two-sample z test for proportions;

                          T.S. =  [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex]  ~ N(0,1)

where, [tex]\hat p_1[/tex] = sample proportion of employed workers who have registered to vote = [tex]\frac{287}{513}[/tex] = 0.56

[tex]\hat p_2[/tex] = sample proportion of unemployed workers who have registered to vote = [tex]\frac{280}{604}[/tex] = 0.46

[tex]n_1[/tex] = sample of employed persons = 513

[tex]n_2[/tex] = sample of unemployed persons = 604

So, the test statistics  =  [tex]\frac{(0.56-0.46)-(0)}{\sqrt{\frac{0.56(1-0.56)}{513}+\frac{0.46(1-0.46)}{604} } }[/tex]

                                       =  3.349

The value of z test statistics is 3.349.

Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.

Since our test statistic is more than the critical value of z as 3.349 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote.

Answer:

The 99% confidence interval for the mean height of all men recruits between the ages 18 and 24 is between 69.44 inches and 69.96 inches.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{2.8}{\sqrt{772}} = 0.26[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 69.7 - 0.26 = 69.44 inches

The upper end of the interval is the sample mean added to M. So it is 69.7 + 0.26 = 69.96 inches

The 99% confidence interval for the mean height of all men recruits between the ages 18 and 24 is between 69.44 inches and 69.96 inches.

Answer:

54

Step-by-step explanation:

because it is

Answer: The volume of the composite solid is about 589.5 cubic feet.

Step-by-step explanation:

Step-by-step explanation:

-13 > x - 43

-13 + 43 > x

30 > x

Answer:

Wat is the question?

Step-by-step explanation:

Answer:

45°-(315°) = 360°

-315°-45°=-360°

Second part: WOULD

Step-by-step explanation:

Trust me I gotchu

Subtracting angles involves accounting for the directions implied by their positive or negative signs. The subtraction of 45°-(-315°) equates to an addition, giving a resultant angle of 360°. Conversely, -315° – 45° provides a resultant angle of -360°.

The question involves the mathematical concept of angles, specifically, subtracting them. Here, we are dealing with angles of 45° and -315°. When subtracting angles, consider the directions indicated by the positive and negative signs. A positive angle is measured counterclockwise from the initial side to the terminal side, while a negative angle is measured clockwise.

So, for 45°-(-315°), you're essentially adding 45 and 315 because subtracting a negative number becomes the addition of the positive equivalent. This gives you a resultant angle of 360°.

And in the case of -315° – 45°, you're subtracting 45 from -315 which gives you a resultant angle of -360°.

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Answer:

Ermm here I graphed it :)

Sorry for dark mode..

Answer:

x = ± 6sqrt(5)

Step-by-step explanation:

x^2 = 180

Take the square root of each side

sqrt(x^2) = ±sqrt(180)

x =±sqrt(36)sqrt(5)

x = ± 6sqrt(5)

Answer:

Edge 2020

A

-13.42, 13.42

Step-by-step explanation:

Answer:

The null hypothesis is represemted as

Null: p ≥ 0.80

The alternative hypothesis is given as

Alternative: p < 0.80

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.

The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.

For this question, the survey that involved comparison was the proportion of US students at the university that owned a smartphone and the proportion of college students in the US that own a smartphone (80%).

Specifically, we want to check if the proportionof smartphone owners at the university is lower than the overall proportion of smartphone owners amongst US college students (80%).

Hence,

The null hypothesis would be that there isn't significant evidence to conclude that the proportion of smartphone owners is lower at this university than the general proportion of smartphone owners amongst college students.

That is, the proportion of smartphone users at this university isn't lower than the proportion of college students in the U.S. that own a smartphone or the proportion of smartphone owners at this university is higher than or equal to the proportion of college students in the U.S. that own a smartphone.

The alternative hypothesis is then that there is significant evidence to conclude that the proportion of smartphone users at this university is lower than the proportion of college students in the U.S. that own a smartphone.

Mathematically,

The null hypothesis is represemted as

Null: p ≥ 0.80

The alternative hypothesis is given as

Alternative: p < 0.80

Hope this Helps!!!

The null hypothesis states that the proportion of smartphone owners at the university is not lower than 80%, while the alternative hypothesis states that the proportion is lower. A hypothesis test can be conducted using the data from the survey to determine if the proportion is significantly lower.

The research question is whether the proportion of smartphone owners at this university is lower than the national average of 80%. We can state the hypotheses as:

Null Hypothesis (H0): The proportion of smartphone owners at this university is not lower than 80%.

Alternative Hypothesis (Ha): The proportion of smartphone owners at this university is lower than 80%.

To test these hypotheses, we need to analyze the data from the survey and perform a hypothesis test. We can use statistical software to calculate the proportion of smartphone owners at the university and conduct the test.

Answer:

Check the explanation

Step-by-step explanation:

Cost of over reserving full cost tickets, Co = $440 ( empty seats as we cannot get even the discounted revenue)

Cost of under reserving Cu = 770-440 = $330 ( because you sell more discounted tickets)

Now critical ratio = Cu / (Cu+Co) = 330/770 = 0.42857

Now for above critical ratio ,z = -0.18 ( refer standard normal distribution table)

Optimal protection level = mean +z*standard deviation = 100-0.18*25 = 95.5 = 96

The possible costs include: all the above. You may need to provide compensation to passenger and make alternative travel arrangements. Also passenger won't be happy by over booking and their will be loss of good will.

Answer:

405

Step-by-step explanation:

To find sample size, use the following equation, where n = sample size, za/2 = the critical value, p = probability of success, q = probability of failure, and E = margin of error.

[tex]n=\frac{(z_{\frac{\alpha }{2} })^{2} *p*q }{E^2}[/tex]

The values that are given are p = 0.84 and E = 0.03.

You can solve for the critical value which is equal to the z-score of  (1 - confidence level)/2.  Use the calculator function of invNorm to find the z-score.  The value will given with a negative sign, but you can ignore that.

(1 - 0.9) = 0.1/2 = 0.05

invNorm(0.05, 0, 1) = 1.645

You can also solve for q which is 1 - p.  For this problem q = 1 - 0.84 = 0.16

Plug the values into the equation and solve for n.

[tex]n =\frac{(1.645)^2*0.84*0.16}{(0.03)^2}\\n= 404.0997333[/tex]

Round up to the next number, giving you 405.

The length of side DE in the right triangle shown is 4.24 units.

We can use the Pythagorean Theorem to solve for the length of DE, since we know the lengths of the other two sides.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The hypotenuse of the triangle is DE, and the other two sides are DF and EF. We know that DF = EF = 3 units. Therefore, we can set up the following equation:

[tex]DE^2 = DF^2 + EF^2[/tex]

Substituting in the known values, we get:

[tex]DE^2 = 3^2 + 3^2[/tex]

[tex]DE^2 = 9 + 9[/tex]

[tex]DE^2 = 18[/tex]

Taking the square root of both sides, we get the length of DE:

DE = √18

DE ≈ 4.24 units

Therefore, the length of side DE in the right triangle shown is 4.24 units.

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Question

Answer:

Step-by-step explanation:

answer 76800

length- 20

width- 12

20x12=240

240x320(people)= 76800

The population of given Rectangleville is 76800.

The area of Rectangle is length times of width.

Given that Rectangleville's limits form a perfectly rectangular shape whose length is 20 kilometers and width is 12 kilometers

length is 20 km

width is 12 km

Area of rectangleville = Length × width

=20x12

=240 square kilometer.

Now  It has a population density of 320 people per square kilometer

We need to find the population.

To find this we need to multiply two hundred forty with three hundred twenty.

240x320

= 76800

Hence, the population of given Rectangleville is 76800.

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Answer:

b

Step-by-step explanation: