A number is selected at
random from each of the sets
£2,3,4} and {1, 3, 5}. Find the
Probability that the sum of the two numbers is greater than 3 but less than 7?
​

Given:

The enrollment increases by approximately the same percentage between 2000 and 2010 as it decreased between 1950 and 1960.

To find:

The expected enrollment in 2010.

Solution:

Percentage decrease formula:

[tex]\%\text{ decrease}=\dfrac{\text{Initial value - New value}}{\text{Initial value}}\times 100[/tex]

The percentage decrease in between 1950 and 1960 is:

[tex]\%\text{ decrease}=\dfrac{4-3.5}{4}\times 100[/tex]

[tex]\%\text{ decrease}=\dfrac{0.5}{4}\times 100[/tex]

[tex]\%\text{ decrease}=\dfrac{50}{4}[/tex]

[tex]\%\text{ decrease}=12.5[/tex]

The enrollment decreased by 12.5% between 1950 and 1960. So, the enrollment increases by 12.5% between 2000 and 2010.

The expected enrollment in 2010 is:

[tex]\text{Expected enrollment}=7+\dfrac{12.5}{100}\times 7[/tex]

[tex]\text{Expected enrollment}=7+0.875[/tex]

[tex]\text{Expected enrollment}=7.875[/tex]

Therefore, the expected enrollment in 2010 is 7.875 thousands.

Hello!

[tex]\large\boxed{y = 13(2)^x}}[/tex]

y = abˣ

We know that at x = 0, b = 1 because any number to the power of 0 = 1.

Therefore:

13 = a(1)

13 = a

Now, plug in this value to solve for b:

y = 13bˣ

Substitute in the next point:

416 = 13(b)⁵

Divide both sides by 13:

32 = b⁵

Take the 5th root of both sides:

2 = b

Rewrite:

y = 13(2)ˣ

(C)

Step-by-step explanation:

The sum of angles a and b is 180°, which make the two supplementary angles.

Answer:

4

Problem:

If m and n are positive integers and m^2 - n^2 = 9, which of the following could be the value of

n?

A) 1

B) 16

C) 9

D) 4

Step-by-step explanation:

One approach would be to plug in the choices and see.

If n=1, then we have m^2-1=9.

This would give m^2=10 after adding 1 on both sides. There is no integer m when squared would give us 10. ( Square root of 9 is a decimal )

If n=16, then we would have m^2-256=9.

This would give m^2=265 after adding 256 on both sides. There is no integer m when squared would give us 265. ( Square root of 265 is a decimal )

If n=9, then we would have m^2-81=9.

This would give m^2=90 after adding 81 on both sides. There is no integer m when squared would give us 90. ( Square root of 90 is a decimal )

If n=4, then we would have m^2-16=9.

This would give m^2=25 after adding 16 on both sides. There is an integer m when squared would give us 25. ( Square root of 25 is a 5)

Answer:

[tex]\displaystyle y' = 20x^3 + 6x^2 + 70x + 9[/tex]

General Formulas and Concepts:

Pre-Algebra

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative Property [Multiplied Constant]:                                                              [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

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 [Product Rule]:                                                                                [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = (x^3 + 7x - 1)(5x + 2)[/tex]

Step 2: Differentiate

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

Unit: Derivatives

Book: College Calculus 10e

Incurring a budget surplus and allowing that surplus to accumulate as idle Treasury balances. Then the correct option is B.

A span of transitory negative growth marked by a drop in Income in four quarters.

The negative effects of a recession would be reduced by the fiscal policy decision will be

Incurring a budget surplus and allowing that surplus to accumulate as idle Treasury balances

Then the correct option is B.

More about the Recession link is given below.

https://brainly.com/question/18075358

#SPJ1

Step-by-step explanation:

90*8.25=742 rounds to 675 because its the closest. 85-95=10 divided by 2=5+85=90. 9-7.5=1.5 divided by 2=0.75+7.5=8.25. thats how i got those numbers. THE ANSWER IS C

Your answer is July.

From least to greastest:

January: $50

February: $80

September: $80

May: $95

April: $100

March: $110

June: $250

August: $300

July: $320

I hope this helps!

The month that had the largest deposit is the month of; July

How do you Interpret a Histogram?

From the given histogram with savings account on the x-axis and amount deposited on the y-axis, we can see the following amounts deposited for each month as follows;

The month with the largest deposit is clearly July

Read more about Histograms at; https://brainly.com/question/25983327

Answer:

t = [tex]\frac{75}{n}[/tex]

Step-by-step explanation:

Use the inverse variation equation, y = [tex]\frac{k}{x}[/tex]

Replace y with t, and replace x with n, since those are the variables in this situation:

t = [tex]\frac{k}{n}[/tex]

Plug in 3 as t and 25 as n, and solve for k:

3 = [tex]\frac{k}{25}[/tex]

75 = k

Create the equation by plugging in 75 as k:

t = [tex]\frac{75}{n}[/tex]

So, the equation is t = [tex]\frac{75}{n}[/tex]

Answer:

Yes it is very good for establishing identities.

Step-by-step explanation:

Since its a very preferable start it is a very good way to establish identity.

The largest rate of change occurs in the same direction as the gradient of f at the point.

∇f(x, y, z) = (∂f/∂x, ∂f/∂y, ∂f/∂z) = (y, x, -1/z)

==>   ∇f (1, 1, 1) = (1, 1, -1)

In other words, f changes at the highest rate in the direction of the vector (1, 1, -1).

9514 1404 393

Answer:

 10x +9y = 60

Step-by-step explanation:

The equation for the tangent line at a point is ...

  y -f(a) = f'(a)(x -a)

For the given function,

  f(x) = 10/x

The derivative is ...

  f'(x) = -10/x^2

Then the equation of the tangent line is ...

  y -10/3 = -10/9(x -3) . . . . equation of the tangent line (point-slope form)

Clearing fractions, we have ...

  9y -30 = -10(x -3) = -10x +30

  10x +9y = 60 . . . . . equation in standard form

Answer:

their sizes vary

Step-by-step explanation:

their sizes vary

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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.

Answer:

No unless x is being used to define only elements of an integer set.

Step-by-step explanation:

No, not in general unless x is defined as a integer or a subset of the integers like the naturals, whole numbers....

Usually 6<=x<=10 means all real numbers between 6 and 10, inclusive. This means example that 6.6 or 2pi are in this set with infinitely other numbers that I can't name.

{6,7,8,9,10} just means the set containing the numbers 6,7,8,9,10 and that's only those 5 numbers.

Answer:

55.75 cents per ounce

Step-by-step explanation:

Take the cost and divide by the number of ounces

We want cents per ounce so change dollars to cents

446 / 8

55.75 cents per ounce

Answer:

<A ≈ 45 degrees

<B ≈ 57 degrees

<C ≈ 78 degrees

Step-by-step explanation:

Hi there!

1) Find <C with the law of cosines

Typically, we want to solve for the angle opposite the largest side first.

Law of cosines: [tex]cosC=\frac{a^2+b^2-c^2}{2(a)(b)}[/tex]

Plug in given values

[tex]cosC=\frac{5^2+6^2-7^2}{2(5)(6)}\\cosC=\frac{1}{5}\\C=cos^-^1(\frac{1}{5} )\\C=78[/tex]

Therefore, <C is approximately 78 degrees.

2) Find <B with the law of cosines

[tex]cosB=\frac{a^2+c^2-b^2}{2(a)(c)}[/tex]

Plug in given values

[tex]cosB=\frac{5^2+7^2-6^2}{2(5)(7)}\\cosB=\frac{19}{35}\\B=cos^-^1(\frac{19}{35})\\B=57[/tex]

Therefore, <B is approximately 57 degrees.

3) Find <A

The sum of the interior angles of a triangle is 180 degrees. To solve for <A, subtract <B and <C from 180:

180-57-78

= 45

Therefore, <A is 45 degrees.

I hope this helps!

Answer:

A

Step-by-step explanation: just divide 71 into 2 which gives you 35.5 making a your answer.

Answer:

Step-by-step explanation:

Set this up as a proportion with the ratios being

[tex]\frac{vinegar}{oil}[/tex]  If there is a 2:5 ratio of vinegar to oil, that ratio looks like this:

[tex]\frac{v}{o}:\frac{2}{5}[/tex] and if we are looking for how much oil, x, is needed for 20 ml of vinegar, then that ratio completes the proportion:

[tex]\frac{v}{o}:\frac{2}{5}=\frac{20}{x}[/tex] and cross multiply.

2x = 100 so

x = 50 ml of oil

Answer:

HOPE IT HELPS PLZ MARK ME BRAINLIEST

Step-by-step explanation:

A={1,2,3,4,5,6}

R={(x,y):y is divisible by x}

We know that any number (x) is divisible by itself.

(x,x)∈R

∴R is reflexive.

Now,(2,4)∈R [as 4 is divisible by 2]

But,(4,2)∈ /

R. [as 2 is not divisible by 4]

∴R is not symmetric.

Let (x,y),(y,z)∈R. Then, y is divisible by x and z is divisible by y.

∴z is divisible by x.

⇒(x,z)∈R

∴R is transitive.

Hence, R is reflexive and transitive but not symmetric.

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Answer:

  -∞ < y ≤ 12

Step-by-step explanation:

The range is the vertical extent of the graph of the function. Here the function values range from -∞ to a maximum of about 12. An appropriate description is ...

  -∞ < y ≤ 12

1. Volume of pyramid= One third× volume of rectangular prism, V= l×w×h

So for pyramid, V= 1/3 (l×w×h) = (l×w×h) ÷ 3.

2. The volume of the cylinder is three times the volume of the cone or the volume of the cone is one third that of the cylinder.

3. Volume of the cone = One third of volume of the cylinder.

4. Sphere's volume is 2/3 of the Cylinder's volume.

Answered by GAUTHMATH

Answer:

C

Step-by-step explanation:

For this, you want to treat i like any other variable, and combine like terms. However you need to keep in mind that there is a negative sign before the second set of parentheses. This means everything inside it should have a negative before it. So we can write it like this:

(7 + 3i) - (3 - 9i)

7 + 3i -3 +9i

4 + 12i

Hope that helps!

Answer:

The answer is A

Step-by-step explanation:

Hope this helps

Answer:

a) 68%

b) 95%.

c) 2.5%

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 100,000, standard deviation of 10,000.

a. Approximately what percentage of the salaries fall between $90,000 and $110,000?

90,000 = 100,000 - 10,000

110,000 = 100,000 + 10,000

Within 1 standard deviation of the mean, so approximately 68%.

b. Approximately what percentage of the salaries fall between $80,000 and $120,000?

80,000 = 100,000 - 2*10,000

120,000 = 100,000 + 2*10,000

Within 2 standard deviations of the mean, so approximately 95%.

c. Approximately what percentage of the salaries are greater than $120,000?

More than 2 standard deviations above the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean, so approximately 5% are more than 2 standard deviations from the mean.

The normal distribution is symmetric, which means that 2.5% are more then 2 standard deviations below the mean, and 2.5% are more than 2 standard deviations above the mean, which means that 2.5% of the salaries are greater than $120,000.

Answer:

m = 60

Step-by-step explanation:

The context is very important, the 'm' represents the minutes late the parents are and from this we can eliminate some options :

- The last one because then a parent would drop their child off earlier

- The first one and the third one because it is too long

Answer:

Class interval ____, Frequency _ C/frequency

1 - 10 ____________ 1 _________ 1

11 - 20 ___________ 4 _________ 5

20 - 30 __________ 6 _________ 11

31 - 40 ___________3 _________ 14

41 - 50 ___________ 1 _________ 15

51 - 60 ___________ 1 _________ 16

Step-by-step explanation:

Given the data :

35, 26, 31, 17, 46, 30, 28, 21, 26, 34, 15, 27, 7, 18, 16, 57

Class interval ____, Frequency _ C/frequency

1 - 10 ____________ 1 _________ 1

11 - 20 ___________ 4 _________ 5

20 - 30 __________ 6 _________ 11

31 - 40 ___________3 _________ 14

41 - 50 ___________ 1 _________ 15

51 - 60 ___________ 1 _________ 16

The next to highest frequency group has a frequency of 4 and the highest frequency of 6

Total frequency, n = (1 + 4 + 6 + 3 + 1 + 1) = 16