In certain Algebra 2 class of 29 students, 13 of them play basketball and 7 of them play baseball. There are 4 students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?

Answer:

The explicit formula

[tex]a_n = 3 +0.25 (n-1)[/tex]

The recursive formula

[tex]a_1 = 3[/tex]                            for [tex]n=1[/tex]

[tex]a_n = a_ {(n-1)} +0.25[/tex]     if [tex]n>1[/tex]

Step-by-step explanation:

If a sequence is arithmetical then the difference between any of its consecutive terms will be constant

3, 3.25, 3.5, 3.75,

[tex]3.25-3 = 0.25\\\\3.5-3.25 = 0.25\\\\3.75 -3.5 = 0.25[/tex]

The difference between the consecutive terms remains constant so the sequence is arithmetic.

The explicit formula for an arithmetic sequence is:

[tex]a_n = a_1 + d (n-1)[/tex]

Where d is the constant difference between the terms.

[tex]d = 0.25[/tex]

[tex]a_1[/tex] is the first term of the sequence.

[tex]a_1 = 3[/tex]

So

[tex]a_n = 3 +0.25 (n-1)[/tex]

Finally, the recursive formula is:

[tex]a_1 = 3\\\\a_n = a_ {(n-1)} +0.25[/tex]

The value of the given expression i.e. [tex]Log_864[/tex] is 2.

Given that,

Based on the above information, the calculation is as follows:

Let us assume [tex]Log_864[/tex] be n

So,

[tex]64= 8^n\\\\8^2 = 8^n[/tex]

n = 2

Therefore we can conclude that the value of the given expression i.e. [tex]Log_864[/tex] is 2.

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After the above expression has been evaluated, Log8 64 = 2.

To evaluate the expression "Log8 64," we need to determine the exponent to which the base 8 must be raised to obtain 64.

In this case, we are looking for the value of x in the equation 8ˣ = 64.

By observing that 8 is equal to 2³, we can rewrite the equation as (2³)ˣ = 64.

Using the property of exponentiation, we can simplify further: 2³ˣ = 64.

Since 64 is equal to 2⁶, we can equate the exponents - 3x = 6.

Solving for x, we find x = 2.

Therefore, Log8 64 = 2.

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Answer:

The domain is  -∞ < x < ∞ ⇒ answer B

Step-by-step explanation:

* lets revise the meaning of the domain

- The domain is the values of x

- The domain is all the values of x which make the function is defined

- If there are some values of x make the function undefined, we

 exclude these values from the domain

* Now lets look to the figure

- It is a straight line because its ends are arrow, that means the line

 is a straight line no starting point or ending point

- That means x can be any real number

- There is no value of x make the function undefined

∴ The domain of this function is all real numbers

∴ The domain is (-∞ , ∞)

OR

∴ The domain is {x I x all real numbers}

OR

∴ The domain is  -∞ < x < ∞

Answer:

it is b

Step-by-step explanation:

Answer:

m∠A=40°, m∠C=80°, m∠E=140°, m∠D=100°.

Step-by-step explanation:

Quadrilateral ACED is inscribed into the circle (see attached diagram).

Inscribed Quadrilateral Theorem: A quadrilateral can be inscribed in a circle if and only if the opposite angles are supplementary (add up to 180°).

Since angle CAB has the measure of 40°, then opposite quadrilateral's angle CED has the measure of

180°-40°=140°.

Since angle ABC has the measure of 60°, then the third triangle's angle BCA has the measure

180°-40°-60°=80°.

Since angle BCA has the measure of 80°, then opposite quadrilateral's angle ADE has the measure of

180°-80°=100°.

So, in quadrilateral ACED,

m∠A=40°, m∠C=80°, m∠E=140°, m∠D=100°.

Answer:

[tex]3b(2n-5)(5n-2)[/tex]

Step-by-step explanation:

First we can factor out a 3b from each of the terms.

[tex]30n^2b-87nb+30b \\ \\ 3b(10n^2-29n+10)[/tex]

Then, we can factor this out.

[tex]3b(10n^2-29n+10) \\ \\ 3b(2n-5)(5n-2)[/tex]

And you'll get your answer!

Answer:

3b(2n-5)(5n-2)

Step-by-step explanation:

to solve 30n²b - 87nb +30b, we would need to factor out a common term among them

the entire expression has the number 3 in common, as they are all factors of 3. each term has the letter b included as well, so we can factor out 3b from the expression

3b(10n² - 29n + 10)

now we can factor the expression 10n² - 29n + 10. there are many ways we can factor this. i am choosing to factor by grouping, which means breaking down the expression into 4 terms and factoring each term.

to break this down, we can write -29n as a difference. the expression looks as follows:

3b(10n² - 4n - 25n + 10)

now we seperate the new expression into 2 groups with 10n² - 4n being their own group, and -25n + 10 being another

we will now factor 10n² - 4n. both have 2n in common, so we will factor that out:

2n(5n - 2)

next is -25n + 10, both have 5 in common, but we want the factorization of -25n + 10 to be equal to 5n - 2. to do this, we would factor out a -5 to get a -2 out of 10

-5(5n - 2)

the expression looks like the following:

3b(2n(5n-2) -5 (5n-2)) < we can drop a 5n - 2 since there are 2 of them and combine 2n - 5 as another factor of the expression. the fully simplified expression looks like the following:

3b(2n-5)(5n-2) is our answer

Answer:

heres the graph

Step-by-step explanation:

Answer:

13 by using pythagorean theorem

Step-by-step explanation:

Solutions just means the amount of times the lines intersect, so there are no solutions. Since the lines are parallel, they’re going the exact same direction forever and ever, never intersecting. Hope this helps!

Answer:

There is Zero solution to the system of equation.  

Step-by-step explanation:

Consider the provided graph.

The solutions for the system of equations are the values of the variables that simultaneously make both equations true.

Parallel lines are the lines on a plane that never meet. They are always apart from the same distance.

Now consider the provided graph.

From the above definition, it is clear that the parallel lines never intersect. Also, the line has no solution or we can say Zero solution because there are no such variables that simultaneously make both equations true.

Also, the lines never intersect each other. Thus there is zero solution.

Hence, there is Zero solution to the system of equation.

Answer:

600

Step-by-step explanation:

200*3=600

Answer:

600 cocoa beans

Step-by-step explanation:

1×3=3, 200×3= 600

Answer:

Brown.

Step-by-step explanation:

Theoretical probability for each:

 625

   5

= 125

122 is closest to 125. Therefore Brown has the closest experimental probability to it's theoretical probability.

For brown, the experimental probability is closest to the theoretical probability.

We assume that in the ideal case, all the 5 colors have the same probability of being the outcome. Then the probability for each color will be:

P = 1/5 = 0.20

We need to see for which color the experimental probability is closest to 0.20.

The experimental probability will be given by the quotient between the number of times that each color appears and the total number of spins, so we have:

As you can see, the closest one to 0.2 is Brown, so for Brown, the experimental probability is closest to the theoretical probability.

If you want to learn more about probability, you can read:

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Answer:

8

Step-by-step explanation:

if you substitute 3 for x the equation becomes y=2(3) + 2

using order of operations you multiply 3 by 2 and then add 2 which will give you 8

One way to find the least common multiple of two numbers is to first list the prime factors of each number.

8 = 2 x 2 x 2

Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

2: three occurrences

3: one occurrence

So, our LCM should be

2 x 2 x 2 x 3 = 24.

So, Marco can buy, at the very least, 24 beads of each color to have equal colors of beads.

Answer:

10+4x=26

Step-by-step explanation:

Answer:

Step-by-step explanation:

26-10 ÷ 4 = X

   ∨

  16 ÷ 4 = X

     x= 4

you can only rent the bike for 4 hours.

your down payment is $10 so you subtract it form the money you have now you are left with $16 dollars you divide it by four becuase 4 x 4 is 16 there for you know you can only go for 4 hours

Answer:

zero (0)

when the exponent 0 is applied to a nonzero base, the result is always 1

Step-by-step explanation:

Acoording to the zero power rule, a non zero number raised to the power 0 is always 1:

[tex]a^{0} =1[/tex] whit [tex]a=0[/tex]

Let's check this property using an example:

We know that a quantity over itself is always 1:  [tex]\frac{2}{2} =1[/tex]

We also know that a base without exponent is always raised to the power 1: [tex]2=2^{1}[/tex]

Now, according to the division power rule [tex]\frac{a^{m} }{a^{n}} =a^{m-n}[/tex], so [tex]\frac{2}{2} =\frac{2^{1} }{2^{1} } =2^{1-1} =2^{0} =1[/tex]

Answer:

C. The events are independent of one another

Step-by-step explanation:

If the probability remains the same whether or not hardcover or paperback is bought, then the probability is not reliant on this variable, and is independent.

The events are independent of one another since the probability of choosing fiction or nonfiction is unaffected by the book format (hardcover or paperback).

The question deals with the concept of probability in the context of buying books, i.e., whether purchasing a fiction or nonfiction book is affected by the format of the book (hardcover or paperback). It is given that the probability of buying fiction versus nonfiction is the same whether or not the person buys a hardcover or paperback.

This implies that the events (buying fiction or nonfiction) are independent of the format. According to the principles of probability, independent events have no impact on each other's occurrence.

The formula for independent events states that P(A AND B) = P(A)P(B), and P(B|A) = P(B).

mean is the answer nnnnnnnnn

Answer: choice a, the mean

Step-by-step explanation:

Final answer:

The correct statement about the conditions for performing a one-sample z test for the population is that we can't determine if the conditions have been met until we have the sample proportion, p hat.

Explanation:

The correct statement about the conditions for performing a one-sample z test for the population is:

a. We can’t determine if the conditions have been met until we have the sample proportion, p hat.

When performing a hypothesis test of a single population proportion, the conditions for a binomial distribution need to be met. These conditions include a certain number of independent trials, success or failure outcomes, and each trial having the same probability of success. In addition, the shape of the binomial distribution should be similar to the shape of a normal distribution, which is ensured when np and nq are both greater than five. Therefore, the conditions cannot be definitively determined until the sample proportion, p hat, is known.

The Large Counts condition is met (np >= 10, n(1-p) >= 10), allowing the z-test. Other conditions are satisfied, validating the test.

Therefore, the correct answer is: **d. The test cannot be performed because the Large Counts condition has not been met.**

To perform a one-sample z-test for the population proportion, we need to check certain conditions:

1. **Random Sample**: The sample should be chosen randomly from the population to ensure that it is representative.

2. **Normality of Population**: There are two criteria for this condition:

  - If the population distribution is approximately normal, we can proceed.

  - If the population distribution is not normal, the sample size should be large enough (n x p >= 10 and n x (1-p) >= 10) to ensure that the sampling distribution of the sample proportion is approximately normal by the Central Limit Theorem.

3. **Independence**: Each observation in the sample should be independent of the others.

Given:

- Sample size (n) = 30

- Population proportion (p) = 0.04

We need to check if these conditions are met.

a. **We can’t determine if the conditions have been met until we have the sample proportion, p hat.**

  - This statement is incorrect because we can still check the conditions without knowing the sample proportion.

b. **The test cannot be performed because the Random condition has not been met.**

  - This statement is incorrect because the problem states that the buyer took a random sample of 30 apples, so the Random condition has been met.

c. **All conditions for performing the test have been met.**

  - This statement is incorrect because we haven't checked the Large Counts condition yet.

d. **The test cannot be performed because the Large Counts condition has not been met.**

  - To check the Large Counts condition, we need to verify whether the sample size is large enough to ensure that the sampling distribution of the sample proportion is approximately normal.

  - The Large Counts condition is met if both np >= 10 and n(1-p) >= 10.

  - Here, n = 30 and p = 0.04

  - np = 30 x 0.04 = 1.2

  - n(1-p) = 30 x (1 - 0.04) = 28.8

  - Both np and n(1-p) are greater than or equal to 10.

  - So, the Large Counts condition is met.

Therefore, the correct answer is: **d. The test cannot be performed because the Large Counts condition has not been met.**

Answer:

false.

Step-by-step explanation:

Given the function g(x) = f(x − k), can be sketched f(x) shifted k units horizontally. if k is negative, the function is shifted k units to the left.

Given the function g(x) = f(x) + k, we can say that the function is translated vertically upwards k times. If k is negative, the function is translated vertically downwards k times.

In this case, the function is translated two units to the right and 3 units down because the number "-3" is negative.

So it's false. The graph is translated three units downwards and 2 units to the right.

The given statement is a false statement.

We know that the transformation of the type:

f(x) to f(x+k)

is a horizontal shift of the graph.

The graph is shifted k units to the right if k is negative and if k is positive then the graph is shifted k units to the left.

Here we have the graph as:

                [tex]y=6\cos (x)-3[/tex]

and the translated graph is given by:

       [tex]y=6\cos (x-2)-3[/tex]

This means that:

f(x) → f(x-2)

i.e. the graph is shifted horizontally 2 units to the right ( since k=2 is positive )

Answer: x = 2 • ± √2 = ± 2.8284

Step-by-step explanation:

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =  

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.  

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 8 is not a square !!  

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step  1  :

 x2 - 8  = 0  

Step  2  :

Solving a Single Variable Equation :

2.1      Solve  :    x2-8 = 0  

Add  8  to both sides of the equation :  

                     x2 = 8  

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     x  =  ± √ 8  

Can  √ 8 be simplified ?

Yes!   The prime factorization of  8   is

  2•2•2  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 8   =  √ 2•2•2   =

               ±  2 • √ 2  

The equation has two real solutions  

These solutions are  x = 2 • ± √2 = ± 2.8284  

Two solutions were found :

                  x = 2 • ± √2 = ± 2.8284

Not sure what you need help with, but I hope I helped you somehow.

Answer:

option d

{ 4, 8 , 16 , 32 }

Step-by-step explanation:

Given in the question a function

f(x) = 2x

initial value[tex]x_{0}[/tex]=2

First iteration

f(2) = 2(2)

     = 4

[tex]x_{1}=4[/tex]

Second iteration

f(4) = 2(4)

     = 8

[tex]x_{2)=8[/tex]

Third iteration

f(8) = 2(8)

     = 16

[tex]x_{3)=16[/tex]

fourth iteration

f(8) = 2(16)

     = 32

[tex]x_{4}=32[/tex]

Answer:

Step-by-step explanation:

The coordinates of the midpoint M are the average of the coordinates of the two endpoints:

[tex]M_x = \dfrac{2+x}{2},\quad M_y = \dfrac{3+y}{2}[/tex]

Plug the known coordinates of the midpoint:

[tex]-2 = \dfrac{2+x}{2},\quad 6 = \dfrac{3+y}{2}[/tex]

Solve for x and y:

[tex]-4 = 2+x,\quad 12 = 3+y[/tex]

[tex]x=-6,\quad y = 9[/tex]

hence it forms a straight line

Answer: you line is a straight line, is a positive line.

Step-by-step explanation: you rise/run which mean that you have to use (x,y) in the coordinate plane you plug in p)-4 down &  2 up, then you plug in Q) which is 0 is in your original in you go up 4 in you y-axis & then you plug in R) you run 2 & go up 5

Answer:

8 metres long

Step-by-step explanation:

28 = 2l + 12

2[6]

16 = 2l

8 = l

I am joyous to assist you anytime.

Answer:

14

Step-by-step explanation:

a = -2

b = 4

a - ab + b

= (-2) - (-2)(4) + (4)

= -2 - (-8) + 4

= -2 + 8 + 4

= 14

Answer:

10

Step-by-step explanation:

[tex]a=-2 \\ \\ b=4 \\ \\ a-ab+b \\ \\ -2-(-2)(4)+4 \\ \\ -2-(-8)+4 \\ \\ -2+8+4 \\ \\ -2+12 \\ \\ 10[/tex]

X-20 because x is the width and the length is x-20

Answer:

see below

Step-by-step explanation:

In clock arithmetics, your answer has to be in the range 0-N where N is the number of hours in your given clock.

If the initial answer < 0, you add N until you get >=0

If the initial answer >= N, subtract N until you get < N.

a) 8 - 11 (12 clock ) = -3, then -3 + 12 = 9

(a) 9 + 10 (18-clock)  = 19, then 19 - 18 = 1

B) 4 Divide 9 ( 12 clock ) , 4/9

(B) 2 Divide 5 (13-clock)  , 2/5

C) 7 - 6 ( 12 clock ) = 1, fine.

(C) 1 - 5 ( 37 - clock )  = -4, then -4 + 37 = 33

D) 8 Divide 5 ( 12 clock )  = 8/5, fine

( D ) 3 * 9 ( 18 clock ) =27, then 27 - 18 = 9

[tex]\bf (~~\stackrel{\stackrel{x}{\downarrow }}{-3}~~,~~ y~~)\qquad \qquad y=\left( \cfrac{1}{4} \right)^x\implies y=\left( \cfrac{1}{4} \right)^{-3}\implies y=\left( \cfrac{4}{1} \right)^{3} \\\\\\ y=4^3\implies y=64[/tex]

Final answer:

To find the value of y for the point (-3, y) on the function y = (1/4)^x, you substitute x with -3 and calculate y = (1/4)^(-3) = 1/64.

Explanation:

To find the value of y when the point (-3, y) lies on the graph of the function y = (1/4)^x, we need to substitute x with -3 in the given function.

So, we have y = (1/4)^(-3).

Now we find the value of y by calculating the inverse of 4 cubed, which will be:

y = 1/(4^3) = 1/64.

Therefore, y = 1/64.

Answer:1:15 P.M

Step-by-step explanation:just substract it 230-115 and you get your time

If she rode for 1.5 hours and caught a flat @ 2:30 pm she had to have started at 1:15

Answer:

x = 128

Step-by-step explanation:

x and 128 are vertical angles

Vertical angles are equal

x = 128

Hi your answer is 128

Answer:

The answer is $960

Step-by-step explanation:

A = P(1 + rt)

[A] is Answer

[600] is P

[6%] is r

[10] is time