A survey was held to find the time taken by students to reach school from
their homes. Each student was asked to choose from 5, 10, 15, 20, or 25
minutes.
Number of
Minutes 5 10 15 20 25
Number of
Students
11
8
2
3
6
What is the mode for the data set?
A. 5 min b. 10 min c. 20 min d. 25 min

Answer:

the first one

Step-by-step explanation:

Answer:

first row you add 4 to get the next term. look at the difference in numbers.

second row the difference is 3 so you add 3 to get the next one.

3rd row the nth term is 3n so the one above would be 2n and the first /top nth term would just be n on its own - meaning one lot of it

4th row add 5 so 7-5= 2 being the 0th term. so just add 5 each time. so it would be 4n

bottom row the difference is 14 or to get that do 26-12

don't let it trick you out- after the third term it goes to the tenth so it would be best getting a piece of paper and working the whole of it out so u don't get confused

Answer:

[tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative Property [Addition/Subtraction]:                                                            [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Quotient Rule]:                                                                               [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \frac{3x + 5}{\sqrt{x}}[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

Below.

Step-by-step explanation:

log  10  ( 100 )  =  2

Answer:

First one: log_10 (100) = 2 OR log (100) = 2

Second one: 5^-3 = 1/125

Step-by-step explanation:

Let's say the formula for a basic exponent equation is this:

a = b^x

a is the answer when you calculate b^x

b is the base

x is the exponent

Here's the log formula using those variables:

log_b (a) = x

As long as you know how to rearrange the numbers/variables, you are good to go:

100 = 10^2

a = 100

b = 10

x = 2

log_10 (100) = 2

You can also write this one as log (100) = 2 because when you put log by itself, it's assumed that the base thing already equals 10.

log_5 (1/125) = -3

a = 1/125

b = 5

x = -3

5^-3 = 1/125

Hope it helps (●'◡'●)

Answer:

Part 1)

1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.

2) Dylan is perfectly correct.

3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.

Part 2)

Only Skyler's approach was incorrect. When Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.

Step-by-step explanation:

Part 1)

We want to simplify the expression:

[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7}[/tex]

We can divide. Recall that xᵃ / xᵇ = xᵃ ⁻ ᵇ. Hence:

[tex]\displaystyle =0.88\times 10^{-11-7}=0.88\times 10^{-18}[/tex]

In scientific notation, the coefficient is always between 1 or 10.

So, we can multiply 0.88 by 10. To keep the equality, we need to divide 10⁻¹⁸ by 10. Hence:

[tex]\displaystyle =0.88(10)\times \frac{10^{-18}}{10}[/tex]

(You can see that the 10s can cancel out, giving us our original expression.)

Simplify. Thus:

[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7} = 8.8\times 10^{-19}[/tex]

Therefore, as we can see:

1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.

2) Dylan is perfectly correct.

3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.

Part 2)

Reviewing their work, we can see that only Skyler's approach was incorrect.

729 is indeed 3⁶. However, when Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.

Both Robert and Kevin are correct, having set each exponent equal to each other after their bases are equivalent and solving for x.

Answer:

The solution set is: (-1,3)

We want to find the set of the x-values of the points that belong to the given graph and have an y-value larger than zero.

The set is: s = (-1, 3)

To find the set, we need to see the x-values of the points on the graph such that y > 0.

y > 0 means that we only look at the region of the graph that is above the x-axis.

We can see that this region goes from x =-1 to x = 3

Then for all the x-values between x = -1 and x = 3 the points p(x, y) on the graph have an y-value larger than zero.

Notice that because the value must be larger than zero, then the particular x-values:

x = -1 and x = 3 are not in the set.

So the set must be written as:

s = (-1, 3)

This is the set in the interval notation.

If you want to learn more, you can read:

https://brainly.com/question/24600195

Answer:

547737

Step-by-step explanation:

So first when know that the equation for exponentinal growth is f(x)=a(1+r)^x

Then you need to substitue so it would be f(x)=350,000(1+0.0775)^6

So then you would add the 1 and 0.0775 to equal 1.0775

So now its f(x)=350,000(1.0775)^6

So after that following PEMDAS, you would basically do 1.0775 to the power of 6 and get 1.56496155465

After you would do 1.56496155465 times 350,000 and that would be 547736.544129 and since its to the nearest whole number the answer would be 547737

Hopefully, that helped. If I did end up making a mistake then just comment on my answer. :)

Answer:

0.5587 = 55.87% probability that the sample mean would differ from the true mean by less than 1.1 dollars.

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 normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

The cost of 5 gallons of ice cream has a variance of 64 with a mean of 34 dollars during the summer.

This means that [tex]\sigma = \sqrt{64} = 8, \mu = 34[/tex]

Sample of 38

This means that [tex]n = 38, s = \frac{8}{\sqrt{38}}[/tex]

What is the probability that the sample mean would differ from the true mean by less than 1.1 dollars ?

P-value of Z when X = 34 + 1.1 = 35.1 subtracted by the p-value of Z when X = 34 - 1.1 = 32.9. So

X = 35.1

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

By the Central Limit Theorem

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

[tex]Z = \frac{35.1 - 34}{\frac{8}{\sqrt{38}}}[/tex]

[tex]Z = 0.77[/tex]

[tex]Z = 0.77[/tex] has a p-value of 0.77935

X = 32.9

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

[tex]Z = \frac{32.9 - 34}{\frac{8}{\sqrt{38}}}[/tex]

[tex]Z = -0.77[/tex]

[tex]Z = -0.77[/tex] has a p-value of 0.22065

0.77935 - 0.22065 = 0.5587

0.5587 = 55.87% probability that the sample mean would differ from the true mean by less than 1.1 dollars.

Answer:

μ = 6500

μx= 6500

σx= 76

σ= 450

n= 35

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes 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.

The average game is attended by 6,500 fans, with a standard deviation of 450 people.

This means that [tex]\mu = 6500, \sigma = 450[/tex]

35 games:

This means that [tex]n = 35[/tex]

Distribution of the sample mean:

By the Central Limit Theorem, we have [tex]\mu_x = \mu = 6500[/tex] and the standard deviation is:

[tex]\sigma_x = \frac{450}{\sqrt{35}} = 76[/tex]

Answer:

Solution given:

[tex]x_{1},y_{1}=(8,-8)[/tex]

[tex]x_{2},y_{2}=(-1,-5)[/tex]

Now

Distance between them is:

d=[tex]\sqrt{(x_{2}-x_{1})²+(y_{2}-y_{1})²}[/tex]

d=[tex]\sqrt{(-1-8)²+(-5+8)²}=3\sqrt{10}[/tex]

Distance between them is [tex]\bold{3\sqrt{10}}[/tex]

9514 1404 393

Answer:

  you cannot use an equation to pick random numbers

Step-by-step explanation:

"Picked randomly" and "using an equation" are mutually exclusive. A random number cannot be predicted, so an equation cannot be used to generate it.

That being said, many programming languages make use of a "linear congruential generator" for generating random numbers. Such a generator generates a next number (x') from a previous number (x) using the equation ...

  x' = (a·x +c) mod m

Numbers generated in this way are called "pseudo-random numbers." The sequence of generated numbers will repeat at some point, and the statistics of generated numbers may or may not be suitable for any given application. (For example, sequential numbers may tend to be correlated.) The distribution of numbers is inherently uniform, so if you need other distribution, you need to perform some math on what you get from a linear congruential generator. Methods are available for approximating about any kind of distribution you might want.

This is not the only "equation" that can be used, and is certainly not the best.

__

A variety of different values of a, c, m are used in generators of this type. Some are better than others at producing what looks like randomness. Here's a set of numbers you can try: (no claim is made regarding suitability for your purpose)

This will produce numbers in the range 0–16777215. To get numbers in the range of 1-70, you can map these to your range in any suitable fashion. For example, you could add 1 to the integer part of the result from division by 239675.

Below is a graph of the sorted output of 200 values in the range 1–70 from the generator described here. You can see the distribution is approximately linear, and that some values are missing while others show up more often than average. (You expect this with random numbers.) The seed for these numbers (first value of x) is 1337457.

__

There is a web site available that will produce random numbers to your specification, based on the background noise of the universe. They are truly random.

9514 1404 393

Answer:

  B  2/6

Step-by-step explanation:

2 of the 6 possible outcomes are ones that are of interest. A "fair" die means the mutually-exclusive outcomes have equal probability, so ...

  P(4 or 5) = P(4) +P(5) = 1/6 + 1/6 = 2/6

Answer:

52mtrs

Step-by-step explanation:

if length is 56meeters and the width is 4meeters less then 56 -4 = 52 so width is 52mtrs

Answer:

please which level is this

and also is it core maths or elective math

Answer:

option a is correct by using quadratic formula

Answer:

[tex]200oz[/tex]

Step-by-step explanation:

The question says that there are [tex]50[/tex] portions that are [tex]4oz[/tex] each.

Write an equation

[tex](50)4oz[/tex]

Simplify

[tex]200oz[/tex]

Answer:

e=12.5 or e=25/2

Step-by-step explanation:

Answer:

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

Step-by-step explanation:

A manufacturer of nails claims that only 4% of its nails are defective.

At the null hypothesis, we test if the proportion is of 4%, that is:

[tex]H_0: p = 0.04[/tex]

At the alternative hypothesis, we test if the proportion is more than 4%, that is:

[tex]H_a: p > 0.04[/tex]

The test statistic is:

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

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

4% is tested at the null hypothesis

This means that [tex]\mu = 0.04, \sigma = \sqrt{0.04*0.96}[/tex]

A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective.

This means that [tex]n = 20, X = 0.1[/tex]

Value of the test statistic:

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

[tex]z = \frac{0.1 - 0.04}{\frac{\sqrt{0.04*0.96}}{\sqrt{20}}}[/tex]

[tex]z = 1.37[/tex]

P-value of the test and decision:

Considering an standard significance level of 0.05.

The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.

Looking at the z-table, z = 1.37 has a p-value of 0.9147

1 - 0.9147 = 0.0853

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

Answer:

Considering an standard significance level of 0.05.

The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.

Looking at the z-table, z = 1.37 has a p-value of 0.9147

1 - 0.9147 = 0.0853

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

10 - 1/2 x = 12-4/3x

60 - 3x = 72-2x

-12 = - x

Hello,

2 points of the line: (2,0) and (0,3)

[tex]\Delta\ y=3-0=3\\\Delta\ x=0-2=-2\\\dfrac{\Delta\ y}{\Delta\ x} =\dfrac{-3}{2} \\\\y-0=\dfrac{-3}{2}*(x-2)\\\\\boxed{y=-\dfrac{3x}{2}+3}\\[/tex]

Step-by-step explanation:

12/100=30/x

12x=3000

x=250

hiii! !!

Answer:

Chips: 1.25 and Sandwiches: 6.5

Step-by-step explanation:

3s+2c=22

2s+c=14.25

The cost of bag and chips should be 1.25 and 6.5.

3s+2c=22

2s+c=14.25

Here we need to multiply by 2 in equation 2

3s + 2c = 22

2s + 2c = 28.25

s = 6.5

Now

c should be

2(6.5) + c = 14.25

13 +  c = 14.25

c = 1.25

Learn more: brainly.com/question/16911495

Answer:

second option

Step-by-step explanation:

I'm not sure how to explain but if you really need an explanation please message me

The function that represents the absolute function will be y = -|x + 3| + 3. Then the function is represented by graph A.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

If the vertex of the absolute function is at (h, k). Then the absolute function is given as

f(x) = | x - h| + k

The function is given below.

y =    -x,    if x > -3

y = x + 6,  if x ≤ -3

The value of the functions at x = -3 is calculated as,

y = - (-3)

y = 3

y = -3 + 6

y = 3

The capability that addresses the outright capability will be y = - |x + 3| + 3. Then the capability is addressed by diagram A.

The graph is given below.

More about the absolute function link is given below.

https://brainly.com/question/10664936

#SPJ2

Answer:

50.24 or 50.272

Step-by-step explanation:

Square radius and then times by 3.14 or 3.142

4^2*3.14 = 50.24

4^2*3.142 = 50.272

Answer:

1: $1200

2: Food ($6000)

3: $3000

4: $1800

5: $3000

Step-by-step explanation:

1: 10%*12000 = 1200

2: Food 50%*12000 = 6000

3: 25%*12000 = 3000

4: 15%*12000 = 1800

5: Food - Education = 6000 - 3000 = 3000

Answer:

Hence the answer is given as follows,

Step-by-step explanation:

Graph of y = f(x) given,

(a) [tex]\lim_{x\rightarrow 2^{-}}f(x)=3[/tex]

(b) [tex]\lim_{x\rightarrow 2^{+}}f(x)=1[/tex]

(c) [tex]\lim_{x\rightarrow 2}f(x)= DNE \left \{ \therefore \lim_{x\rightarrow 2^{-}} f(x)\neq \lim_{x\rightarrow 2^{+}}f(x) \right.[/tex]

(d) [tex]f(2)=3[/tex]

(e) [tex]\lim_{x\rightarrow 4}f(x) = 4[/tex]

(f) [tex]f(4)= DNE.[/tex]{ Hole in graph}

Hence solved.

Step-by-step explanation:

Answer:

[tex]x<41[/tex]

Step-by-step explanation:

[tex](x)+(x+1)<83[/tex]

simplify both sides

[tex]2x+1<83[/tex]

subtract one from the both sides to isolate the variable

[tex]2x<82[/tex]

divide both sides by 2 to isolate the variable

[tex]x<41[/tex]

Answer:

A: f(t) = t2(4t) - 14

B: It is a maximum because it continues redistributing forever.

C: Assuming you plotted this on a 0/0 grid, your axis of symetry would be at 18/28

Hope this helps, please mark brainliest

Step-by-step explanation:

A: it is simple really, your just redistributing each T to itself, which is what makes a square / vertex.