Identifying Characteristics of the Exponential Function y = bx (b > 1)
The domain of an exponential function is . The range of an exponential function is .

On a coordinate plane, the graph of y = 2 Superscript x is shown. The curve approaches the x-axis in quadrant 2 and then increases quickly into quadrant 1.

Answer:

[tex]z=\frac{704-732}{\frac{65}{\sqrt{28}}}=-2.279[/tex]      

[tex]p_v =P(z<-2.279)=0.0113[/tex]  

If we compare the p value and the significance level given for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we can reject the null hypothesis, and the the true mean is significantly lower than 732 hours so we have enough evidence to reject the claim

Step-by-step explanation:

Data given and notation      

[tex]\bar X=704[/tex] represent the sample mean

[tex]\sigma=65[/tex] represent the standard deviation for the population      

[tex]n=28[/tex] sample size      

[tex]\mu_o =732[/tex] represent the value that we want to test    

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

t would represent the statistic (variable of interest)      

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.      

We need to conduct a hypothesis in order to determine if the true mean is at least 732 or no, the system of hypothesis would be:      

Null hypothesis:[tex]\mu \geq 732[/tex]      

Alternative hypothesis:[tex]\mu < 732[/tex]      

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:      

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

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic      

We can replace in formula (1) the info given like this:      

[tex]z=\frac{704-732}{\frac{65}{\sqrt{28}}}=-2.279[/tex]      

Calculate the P-value      

Since is a one-side lower test the p value would be:      

[tex]p_v =P(z<-2.279)=0.0113[/tex]  

Conclusion      

If we compare the p value and the significance level given for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we can reject the null hypothesis, and the the true mean is significantly lower than 732 hours so we have enough evidence to reject the claim

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ ≥ 732

For the alternative hypothesis,

µ < 732

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = lifetime of the bulb

µ = mean lifetime

σ = standard deviation

n = number of samples

From the information given,

µ = 732

x = 704 hours

σ = 65 hours

n = 28

z = (704 - 732)/(65/√28) = - 2.28

Looking at the normal distribution table, the probability corresponding to the z score is 0.011

Since alpha, 0.05 > than the p value, 0.011, then we would reject the null hypothesis. Therefore, At a 5% level of significance, there is enough evidence to reject the​ manufacturer's claim

Answer:

5 : 20 = 1 : 4

Step-by-step explanation:

Common multiple is 5 so divide each number bu five.

Answer: 75% or .75

Step-by-step explanation:

Answer:

0.75%

Step-by-step explanation:

Start off by laying it out

                  3

            ------------

                  4

        --------------------

                100

Now that we have a visual representation of it:

Multiply 3/4 by its opposite reciprocal.

This means multiply 3/4 by 1/100 which

when you flip and multiply like that, you are technically dividing

So now lets look at it like this

3                   1

----     x     ------------

4                 100

Here we'll multiply straight across which goes as follows

In the numerator our answer will be 3*1

In the denominator is 4*100

The final fraction.

3/400

Now lets turn that into a decimal

0.0075

Then multiply it by 100 and add a % on the end and done

0.75%

Answer:

7.1 yds

Step-by-step explanation:

i just answered it

Answer:

7.1

Step-by-step explanation:

answer:

yeah i dont knoww....

Answer:

G.P.A.=2.5

The Student did not make the Dean's List

Step-by-step explanation:

The Students Grade and Subject Weight are listed below.

[TeX]\left|\begin{array}{c|c|c|c}------&-------&------&------\\ Grade&Credit Hour& Grade Weight & Product \\------&-------&------&------\\ A & 3 & 4 & 12 \\ C & 4 & 2 & 8\\A & 3 & 4 & 12\\C & 2 & 2 & 4\\D & 4 & 1 & 4\\------&-------&------&------\\Total& &16 &40 \end{array} \right| [/TeX]

Grade Point Average=Total Credit Hour÷Total Number of Hours

=40÷16

G.P.A.=2.5

Since the Dean's list requires a GPA of 3.0 or greater, the student does not make the Dean's list.

Answer:

Step-by-step explanation:

According to the question, a slide is 7 feet due west of a tire swing and 7 feet due right of the monkey bars and we were asked the calculated the distance between them.

If you look at it carefully, since the slide is due west of the tire swing and 7 feet due south of the monkey bars, you'll notice a shaped form, the shape formed is an inverted right-angled triangle.

Right-angled Triangles can be solved using pythagoras' theorem which says [tex]a^{2} + b^{2} = c^{2}[/tex].

a= 7, b=7, c=??

[tex]c^{2} = 7^{2} + 7^{2}[/tex]

[tex]c =\sqrt{98}[/tex]

c = 9.9 feet

Final answer:

The distance between the tire swing and the monkey bars is found using the Pythagorean theorem, which gives approximately 9.90 feet.

Explanation:

To find the distance between the tire swing and the monkey bars, we can model the situation using a right triangle. The slide being 7 feet due west of the tire swing and 7 feet due south of the monkey bars forms a right-angled triangle with the slide as the vertex where the right angle is, the tire swing and monkey bars forming the other two vertices.

Using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b), we can find the distance (hypotenuse) between the tire swing and the monkey bars.

In other words, we have:

a² + b² = c²

Given:

a = 7 feet (distance from slide to tire swing)

b = 7 feet (distance from slide to monkey bars)

We can calculate:

c² = 72 + 72 = 49 + 49 = 98

The distance (c) is the square root of 98, which is approximately 9.90 feet.

Therefore, the distance between the tire swing and the monkey bars is approximately 9.90 feet.

Answer:

The percent change is 16.67

Step-by-step explanation:

Answer:

16.7%

Step-by-step explanation:

Her weight decreased by 30 lb.

Expressed as a fraction:  (-30 lb)/(180 lb) = (-1/6)

As a percentage, her weight loss came to (-1/6)(100%) = 16.7%

Answer:

D

Step-by-step explanation:

If you plug it into desmos, this is the answer.

Answer:

this is right!

Step-by-step explanation:

i got it right on edge

The functions that have the given properties are the sine and cosine functions. The sine function is odd, with x-intercepts at integer multiples of pi and a minimum value of -1 at x=3pi/2. The cosine function is also odd, with x-intercepts at odd multiples of pi/2 and a minimum value of -1 at x=pi.

The functions that have the given properties are the sine and cosine functions.

Therefore, the functions that satisfy all the given properties are the sine and cosine functions.

Answer:

x = 3

The number of games lost if 27 games are won = 3

Step-by-step explanation:

Complete question

Will records the wins and losses for his high school basketball team each year. He notices that the ratio of wins to losses has been consistent each year.

W | L

18 | 2

45 | 5

36 | 4

27 | x

Using the information in the table, how many losses should he predict for next year if the number of games won is 27?

1 3 6 9

The ratio of wins to losses each year has been consistent, in other words, the same. Hence, we can use this ratio to find x.

Ratio of wins to losses

18 : 2 = 9 : 1

45 : 5 = 9 : 1

36 : 4 = 9 : 1

Hence, 27 : x = 9 : 1

(27/x) = (9/1)

27 = 9x

x = (27/9) = 3

x = 3

Hope this Helps!!!

Answer: what there trying to say is x=3 and that's ur answer :)

Step-by-step explanation:

Answer:

(C) The first is a premise supporting the argument's main conclusion; so is the second.

Step-by-step explanation:

The two sections in boldface are "Supplies in local freshwater reservoirs have been declining for years" and "few users have bothered to adopt even easy conservation measures"

In the economist's argument, both highlighted sections are premises giving the reason why the price of tap water should be drastically raised.

The conclusion of the argument is that the supply of water be drastically raised, the two boldfaced sections are just premises on which the conclusion is based.

We want to find word problems that gives rise to the following systems of algebraic equations.

a)

x+y=13

x-y=1.

Answer: The sum of the ages of two students is 13. The difference between their ages is 1. Find the ages of the two students.

b)

3x-30y=15

2x+10y=40

Answer:

The difference between 3 times Dan's age and 30 times Mark's age is 15. If the sum of 2 times Dan's age and 10 times Mark's age is 40. Find the ages of Dan and Mark.

c)

8x+3y=37

8x-3y=50

Answer:

The sum of 8 times an eagle's distance above sea level in feet and a herring's distance below sea level is 37 feet. The difference between 8 times an eagle's distance in feet above sea level and 3 times the herring's distance below sea level is 50. Find the distance of the eagle and the herring relative to the surface of the sea.

d) x-5y=4

3x+5y=32

The difference between a pig's age and 5 times the age of a piglet is 4 years. If the sum of 3 times pigs and 5 times the piglet's age is 32 years, find the ages of the pig and its piglet.

Answer:

8i - 7j - 9k

Step-by-step explanation:

We have three points:

A (1,0,3)

B (2,5,0)

C (3,1,4)

First of all, we write the following two vectors:

[tex]AB=(2-1,5-0,0-3)=(1,5,-3)[/tex]

[tex]BC=(3-2,1-5,4-0)=(1,-4,4)[/tex]

These two vectors connect A with B and B with C, and since these 3 points lie on the plane, the two vectors also lie on the plane.

Therefore, the cross product of these two vectors must be a vector perpendicular to the plane.

The cross product of the two vectors is:

[tex]AB \times BC = i(5\cdot 4 -(-3\cdot-4))+j(-3\cdot 1 -1\cdot 4)+k(1\cdot -4-5\cdot 1)=\\=8i-7j-9k[/tex]

And the equation of the plane can be found as:

[tex]8(x-a_x)-7(y-a_y)-9(z-a_z)=0\\8(x-1)-7(y-0)-9(z-3)=0\\8x-7y-9z=-19[/tex]

Answer:

A on Edge 2020

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

hi.

Jerry spent 4/5 hour riding on the bus.

First, let's find the total time Jerry spent walking and riding the train:

Walking time = 2/5 hour

Train ride time = 1 4/5 hours

To find the total time spent, add these two:

2/5 + 1 4/5 = (2/5) + (1 + 4/5) = (2/5) + (1 + 4/5) = (2/5) + (5/5 + 4/5) = (2/5) + (9/5) = (2 + 9)/5 = 11/5 hours

Now, since Jerry spent a total of 11/5 hours walking and riding the train, to find out how much time he spent on the bus, we subtract this from the total time it took him to get to his grandmother's house:

Total time = 3 4/5 hours

Bus ride time = Total time - (Walking time + Train ride time)

              = 3 4/5 - 11/5

              = (15/5) - (11/5)

              = 4/5 hours

Answer: a=-1

Step-by-step explanation: -3+1=-2 and 1-3also equals -2

Answer:

A unit rate is something over a unit of something else.

Such as:  (50 miles) / hour

If you have (150 miles) / 3 hours

This is not a unit rate, therefore you have to divide the top and bottom by 3 to get the unit rate

(150/3 miles) / (3/3 hours)

(50 miles) / hour

Hope this helps :)

Answer:

likely

Step-by-step explanation:

Answer:

The conditions that are not necessary to use the odd´s ratio to estimate the relative risk are a. Cases are representative of all cases and c. The exposure in question is rare in the population.

Step-by-step explanation:

Case-control studies are an example of observational studies. In this kind of studies, people are selected because of the presence or absence of a sisease, searching for the previous presence of the suspected cause (exposure).  The idea is to select a group of people that has a particular condition or disease (the group of cases) and compare it with a group of persons that does not have this disease (the control group). Reasearchers analyse both groups and compare them in order to find some information related with the presence of previous or present exposure to factors that are considered as the cause of the disease. The variable used to estimate the relationship between the exposure and the development of the disease is called odd ratio and it is an aproximation of another variable "relative risk".

The odd ratio is aproximately equal to the relative risk (it means it is a good estimator) when the disease is not frequent on the population (in other words, the event under study is rare in the population) and when controls are representative of the population that give rise to the cases.

The point a. Cases are representative of all cases is a dessirable condition but could it not be present.

Finally c. The exposure in question is rare in the population is not necessary, the only factor that must be rare in the population is the disease.

Summarizing, points b and d are strictly necessary, c. is a dessirable condition and a. is not necessary.  

Dan will have £25783.21 after 7 years by investing £18790 at a simple interest rate of 5.3% per year.

The question concerns how much money Dan will have after 7 years with an investment of \£18790\ at a \simple interest rate\ of 5.3% per year. We can calculate the total amount in Dan's bank account using the formula for simple interest:

Total amount = Principal + (Principal × rate × time)

Where:

Principal (P) is the initial amount invested, which is £18790.

Rate (r) is the annual interest rate, which is 0.053 (5.3% expressed as a decimal).

Time (t) is the number of years the money is invested, which is 7 years.

Now, let's do the calculation:

Total amount = £18790 + (\£18790 * 0.053 * 7\)

Total amount = £18790 + £6993.21

Total amount = £25783.21

Thus, Dan will have \£25783.21\ in his bank account after 7 years.

Complete Question:

Lenny asked 125 randomly chosen seventh grade students at his school to name their favorite beverage there are 1500 seventh grade students in the school predict the number of seventh grade students in his schoolwhose favorite food is pizza. 58 of the 125 students likes pizza.

Answer:

n = 696

Step-by-step explanation:

Sample size = 125

number of students out of the 125 that like Pizza = 58

Probability that a student will like pizza, P = 58/125

P = 0.464

Since there are 1500 seventh grade students in the school, based on the probability that a student likes pizza = 0.464, number of seventh grade students in the school that like pizza will be:

n = 100 * P

n = 1500 * 0.464

n = 696

Answer:

The value of r to have maximum profit is 3/25 ft

Step-by-step explanation:

To find:

The size of the sphere so that the profit can be maximized.

Manufacturing cost of the solid sphere = $500/ ft^3

Selling price of sphere (on surface area) = $30 / ft^2

We see that the manufacturing cost dealt with he volume of the sphere where as the selling price dealt with the surface area.

So,

To maximize the profit (P) .

We can say that:

⇒ [tex]P(r)=(unit\ cost)\ (SA) - (unit\ cost)\ (Volume)[/tex]

⇒ [tex]P(r)=(30)\ (4 \pi r^2) - (500)\ (\frac{4\pi r^3}{3} )[/tex]

⇒ [tex]P(r)=(120)\ (2\pi r^2) - (\frac{500\times 4}{3} )\ \pi r^3[/tex]

⇒ [tex]P(r)=(120)\ (\pi r^2) - (\frac{2000}{3} )\ \pi r^3[/tex]

Differentiate "[tex]P[/tex]" and find the "[tex]r[/tex]" value then double differentiate "[tex]P[/tex]", plug the "[tex]r[/tex]" values from [tex]P'[/tex] to find the minimum and maximum values.

⇒ [tex]P(r)'=(120)\ 2\pi r - (\frac{2000}{3} )\ 3\pi r^2[/tex]

⇒ [tex]P(r)'=(240)\ \pi r - (2000)\ \pi r^2[/tex]

Finding r values :

⇒ [tex](240)\ \pi r - (2000)\ \pi r^2 =0[/tex]  

Dividing both sides with 240π .

⇒ [tex]r-\frac{25}{3} r^2 =0[/tex]    ⇒ [tex]r(1-\frac{25}{3} r) =0[/tex]

⇒ [tex]r=0[/tex] and [tex]r=\frac{3}{25}[/tex]  

To find maxima value the double differentiation is :

⇒ [tex]P(r)'=(240)\ \pi r - (2000)\ \pi r^2[/tex]     ...first derivative

Double differentiating :

⇒ [tex]P(r)''=(240\pi) - (2000\pi)\ 2(r)[/tex]    ...second derivative

⇒ [tex]P(r)''=(240\pi) - (4000\pi)\ (r)[/tex]

Test the value r = 3/25 dividing both sides with 240π

⇒  [tex]1 - \frac{50\pi r}{3}[/tex]

⇒ [tex]1 - \frac{50\times \pi\times 3 }{3\times 25}[/tex]

⇒ [tex]-5.28 < 0[/tex]

It passed the double differentiation test.

Extra work :

Thus:

⇒ [tex]P(r)=(120)\ (\pi r^2) - (\frac{2000}{3} )\ \pi r^3[/tex]

⇒ [tex]P(r)=(120)\times (\pi (\frac{3}{25} )^2) - (\frac{2000}{3} )\times \pi (\frac{3}{25} )^3[/tex]

⇒ [tex]P(r) =1.8095[/tex]

Finally r =3/25 ft that will maximize the profit of the manufacturing company.

Answer:

Type of coffee

Step-by-step explanation:

First, that is, it is the independent variable.

It is the variable that does not depend on another value or other circumstance, it is the variable that generally would be the options to choose from and depending on what is chosen, different results are obtained.

In this case, the variable that has this behavior is the type of coffee that will be taken, whether it is caffeinated or decaffeinated coffee.

Answer:

Step-by-step explanation:

a) Consider the sequence [tex]a_n =1 [/tex] if n is odd, and [tex] a_n= -1[/tex] if n is even. So, the sequence diverges (since as n tends to infinity the sequence doesn't approach any particular number), but the subsequence of the even integers is convergent to -1 since it is constant.

b) consider the sequence [tex] a_n = -e^{-n}[/tex]. The function f(x) = [tex] e^{-x}[/tex] when x is real is a monotolically decreasing function and tends to 0. Then, when multiplying by a minus sign, it becomes a monotonically increasing function that tends to 0. Hence, the given sequence is monotonically increasing and converges to 0.

c) Suppose that the sequence [tex]a_n[/tex] converges to a. So, from an specific n and on, the values of [tex]a_n[/tex] are really close to a. So, for almost all the value of the sequence, they are less than a+1 and greater than a-1. Hence it must be bounded.

d) It is a theorem that a monotonically decreasing/increasing sequence that is bounded must converge, so such a sequence can't exist.

In mathematics, various types of sequences can be studied. Examples of sequences satisfying certain conditions are presented in this solution.

(a) An example of a divergent sequence {an} such that {a2n} converges is the sequence {1, -1, 1, -1, ...}. The terms of the sequence alternate between positive and negative 1, so the sequence does not converge. However, the subsequence {a2n} consists of only positive 1's, which converges to 1.

(b) An example of a monotonically increasing sequence that converges to 0 is the sequence {1/n} for n = 1, 2, 3, ... Each term of the sequence is smaller than the previous term, and as n approaches infinity, the terms get closer and closer to 0.

(c) It is not possible for a convergent sequence to be unbounded. By definition, a convergent sequence approaches a specific limit, which means it cannot go beyond a certain value. If a sequence is not bounded, it cannot converge.

(d) An example of a monotonically decreasing bounded sequence that diverges is the sequence {(-1)^n/n} for n = 1, 2, 3, ... The terms of the sequence alternate between positive and negative values, but as n approaches infinity, the terms get smaller and smaller, converging towards 0. Therefore, the sequence is bounded. However, the sequence does not converge to a specific value, so it diverges.

https://brainly.com/question/30262438

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Answer:

21 kids

Step-by-step explanation:

Let's get started!

Ok, let's relay some information!

Boys: 18

Girls: 24

18 + 24

= 30 + 12

= 42

42 kids total

If we divide by two we get an even number also since it is divisible by two that means we can have the greatest amount of kids there.

42 ÷ 2

= 21

21 kids

A 36 year old male will pay $4.55 per $1,000 for a 10 year policy,

He bought a $150,000 policy:

150,000 / 1000 = 150

Multiply the rate per 1000 by 150:

4.55 x 150 = 682.50

His annual premium is $682.50

Answer:

His annual premium is $682.50

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

x + 6 = 18/2

x+6=9

x=9-6

x=3

Answer:

12$

Step-by-step explanation:

Answer:

$375

Step-by-step explanation:

Sale price = original price - (markdown percentage)(original price), or

Sale price = (1 - markdown percentage)(original price

That 32% discount is equivalent to multiplying the original price by 0.32.

Here, $255 = (1 - 0.32)(original price), or

          $255 = 0.68(original price)

Then (original price) = $255/0.68 = $375

Answer:

90

Step-by-step explanation:

If we have total around 281 items, and we can divide them into groups of 3.

We can make around 281/3 groups which is about 90