Use the given information to find the unknown value. y varies inversely with the cube of x . When x=4 , then y=1 . Find y when x=1 .

The probability that a student chosen randomly from the class plays both basketball and baseball is 39%.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

In a certain Algebra 2 class of 23 students, 11 of them play basketball and 13 of them play baseball.

There are 8 students who play neither sport.

Either (or both) sports = (23 - 8) = 15 students play

Both = [11 basketball and 13 baseball) - 15] = 9 must play both

Probability=9/23

Probability=0.39 or 39%

Hence, the probability that a student chosen randomly from the class plays both basketball and baseball is 39%.

To know more about probability, click on the link

https://brainly.com/question/24756209

#SPJ1

The total amount that will ba paid altogether is $710.

From the information, the person borrow 500 for 6 years at an annual interest rate of 7%.

It should be noted that interest is calculated as:

= Principal × Rate × Time

= 500 × 7% × 6

= $210

The total amount will be:

= Principal + Interest

= $500 + $210

= $710

The total amount is $710

Learn more about interest on:

brainly.com/question/25793394

#SPJ1

Using the formula of test statistic, the value of the test statistic is 2.6961.

The mean of the public accountant is

Mean x(p) =50.2+59.8+57.3+59.2+53.2+56.0+49.9+58.5+56.0+51.9/10

x(p) = 55.2

Now the standard deviation of public accountant is

SD(p) = √{∑(x-x(p))^2/n-1}

SD(p) = √(50.2-55.2)^2+(59.8-55.2)^2+..................+(51.9-55.2)^2/n-1

After solving;

SD(p) = 3.34

The mean of the financial planner is

Mean x(F) =48.0+49.2+53.1+55.9+51.9+53.6+49.7+53.9+52.8+48.9/10

x(F) = 51.6

Now the standard deviation of financial planner is

SD(F) = √{∑(x-x(p))^2/n-1}

SD(F) = √(48.0-51.6)^2+(49.2-51.6)^2+..................+(48.9-51.6)^2/n-1

After solving;

SD(F) = 2.57

Test Statistic (t) = [tex]\frac{x(P)-x(f)}{\sqrt{\left(\frac{(n(p)-1)s(p)^2+(n(f)-1)s(f)^2}{n(p)+n(f)-2}\left(\frac{1}{n(p)}+\frac{1}{n(f)}\right)\right)}}[/tex]

t = [tex]\frac{55.2-51.61}{\sqrt{\left(\frac{(10-1)(3.34))^2+(10-1)(2.57)^2}{10+10-2}\left(\frac{1}{10}+\frac{1}{10}\right)\right)}}[/tex]

After solving

t = 2.6961

Hence, the value of the test statistic is 2.6961.

To learn more about test statistic link is here

brainly.com/question/14128303

#SPJ4

The right question is

public accountant  50.2  59.8  57.3  59.2  53.2  56.0  49.9  58.5  56.0  51.9

financial planner   48.0  49.2  53.1   55.9  51.9   53.6  49.7  53.9 52.8  48.9

Use a 0.05 level of significance and test the hypothesis that there is no difference between the starting annual salaries of public accountants and financial planner

Find the value of the test statistic.

Considering the image, we can say that (B) DO and (D) OA represents the radius of the circle.

A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of such line segments.

The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."

The phrase may refer to an object's circumradius, circumscribed circle radius, or circumscribed sphere radius if it lacks a center.

The radius, which is typically defined as the greatest distance between any two points of the figure, may in either case be greater than half the diameter.

So, according to the given figure, we can simply tell that:

DO and OA represents the radius of the given circle.

Therefore, considering the image, we can say that (B) DO and (D) OA represents the radius of the circle.

Know more about the radius here:

https://brainly.com/question/24375372

#SPJ1

Correct question:
Which item on the diagram below of a circle, with center 0, represents the radius of the circle?

Grape flavor has the smallest ratio of mix to water.

What is ratio proportion?

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent. A ratio compares two numbers by division.

Here, we have

The ratios of punch mix to water for several fruit drinks as Grape mix (1 Grape flavor has the smallest ratio of mix to water.

cup to 3 cups), Cherry mix (5 cups to 12 cups), Lemon mix (7 cups to 12 cups), and Orange mix (2 cups to 3 cups).

We have to find which flavor has the smallest ratio of mix to water.

So, we compare all the given proportions by having a common base.  

Proportions of grape, cherry, lemon, and orange mixed in water = 1/3, 5/12, 7/12, 2/3

Now let us have a common denominator 12 as LCM of 3 and 12 is 12.  

Proportions of grape, cherry, lemon, and orange mixed with water = 1×4/3×4, 5/12, 7/12, 2×4/3×4

Proportions of grape, cherry, lemon, and orange mixed with water = 4/12, 5/12, 7/12, 8/12

Hence, the Grape flavor has the smallest ratio of mix to water.

To learn more about the ratio proportion from the given link

https://brainly.com/question/19994681

#SPJ1

Answer: 3 pieces

Step-by-step explanation:

This problem can be solved by modeling the problem using equivalent fractions.

We know Stephanie put icing on 9 of her 15 pieces, this gives us a fraction of [tex]\frac{9}{15}[/tex].

Tammy cut her cake in 5 pieces, but we do not know how many were iced, the pieces of iced cake will be our variable, x, so her fraction is [tex]\frac{x}{5}[/tex].

Both of the fractions need to be equivalent so [tex]\frac{9}{15} =\frac{x}{5}[/tex], which can be solved for x = 3 pieces.

At tα/2= -1.66, we reject H0.

What is the Null hypothesis?

The null hypothesis is a standard statistical theory that contends there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

Data provided

sample size is 100, and

sample mean, 52.0 for x

The standard deviation of the sample, s= 22.0

Average population, = 60.0

Level of significance, = 0.05

Theorem testing

The alternate and the null hypothesis is

H0: u = 60

Ha: u < 60

Crucial component:

value crucial at 0.05

tα/2= -1.66

Region of rejection:

To know more about the Null hypothesis

https://brainly.com/question/28920252

#SPJ4

a) The Turing machine that accepts a string containing even number of b's is (see in attachments).

b) The Turing machine that accepts a string containing  equal number of a’s and b’s is (see in attachments).

Turing machine:

The Turing machine is an abstract machine that manipulates symbols on a strip of tape in accordance with a set of rules. It is a mathematical model of computation. The paradigm is straightforward, but it can implement any computer algorithm. The machine runs on a never-ending tape of memory that is divided into distinct cells, each of which can store a single symbol selected from a limited range of symbols known as the machine's alphabet. It has a "head" that is always placed over one of these cells during operation, and it has a "state" chosen from a limited number of states. Turing machines demonstrated that mechanical computation's power has some fundamental limitations.

To learn more about Turing machine visit: https://brainly.com/question/29570188

#SPJ4

The rate of change of y with respect to x for a given line is 4/5.

What is the rate of change?

The rate of change is measured by a line's slope. It is frequently used when discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.

The rate of change of y with respect to x for a given linear function is simply the slope expressed as:

dy/dx = (y2 - y1)/(x2 - x1)

Let us take the first 2 coordinates from the graph which are:

(0, 3) and (5, 7)

Thus;

dy/dx = (7 - 3)/(5 - 0)

dy/dx = 4/5

Hence, the rate of change of y with respect to x for a given line is 4/5.

To learn more about the rate of change visit,

https://brainly.com/question/8728504

#SPJ1

Answer:

[tex]\boxed{26.74}.[/tex]

Step-by-step explanation:

John spends $2.75 on donuts for his office employees every weekday, so he spends 5 * $2.75 = $<<5*2.75=13.75>>13.75 on donuts for his office employees throughout the week.

He also spends $12.99 on donuts on Sunday mornings, so in total he spends $13.75 + $12.99 = $<<13.75+12.99=26.74>>26.74 on donuts throughout the week. Answer: \boxed{26.74}.

The speed of the boat in still water is 3 miles per hour

Given that,

A boat travels 40 miles upstream in 4 hours and 48 miles downstream in 3 hours.

To find : The speed of the boat in still water

We use the distance formula. D = r * t

48/3 = 16 mph | Trip 1 |

40/4= 10mph | Trip 2 |

16-10 = 6 mph difference traveling upstream or downstream. Thus the speed of the current is 3 miles per hour.

Therefore, The speed of the boat in still water is 3 miles per hour.

To learn more about distance click here:

brainly.com/question/15172156

#SPJ4

The prime number that cannot be in the set is A . 2.

Prime number:

In math, prime number is a natural number greater than 1 that is not a product of two smaller natural numbers

Given,

Here we need to find the prime number that is not in the set, if if the sum of a set of ten different positive prime numbers is an even number.

Here we know that, all prime numbers except the first prime number are odd except 2.

And here we assume that the two prime numbers are different,

So, if one of the prime number is 2 which is even, the other prime number would be odd and hence sum of the prime numbers would be odd as sum of an even and an odd number is always odd.

Where as if none of the prime numbers are odd, then both the prime numbers would be odd and hence sum of the prime numbers would be even as sum of two odd numbers is always even.

There the correct option is A. 2.

To know more about Prime number here.

https://brainly.com/question/9315685

#SPJ4

The equation of the transformed function is g(x) = 2√x - 12

From the question, we have the following function that can be used in our computation:

f(x) = √x -- parent root function

g(x) = horizontally compress of f(x) by a factor 4 and a downward shift of 12 units.

Mathematically, this can be represented as

g(x) = f(4x) - 12

Substitute the known values in the above equation, so, we have the following representation

g(x) = (√4x) - 12

So, we have

g(x) = 2√x - 12

Hence, the transformed function is g(x) = 2√x - 12

Read more about transformation at

brainly.com/question/27224272

#SPJ1

Answer:

somone in my class is literally a new York rat

Step-by-step explanation:

Answer:

∠ x ≈ 8°

Step-by-step explanation:

the tangent of the angle x is equal to the slope m , that is

tanx = m = [tex]\frac{7}{50}[/tex] , then

x = [tex]tan^{-1}[/tex] ( [tex]\frac{7}{50}[/tex] ) ≈ 8° ( to the nearest degree )

The types of angles include the supplementary, complementary, adjacent and vertical angles.

An angle is defined as the common point that is being formed when two straight lines meet at a common endpoint.

There are various types of angles that include the following:

Learn more about angles here:

https://brainly.com/question/25770607

#SPJ1

The different ways for him to taste all dishes in order (assuming he will taste all salads, meat, desserts and soup) is 720.

i) John Smith and his wife Mary Smith}   ⇒ 3 different salads

     and his daughter Judy Smith         }                 dishes.

ii) John right side neighbor  → 2 desserts.

iii) John left side neighbor   →  1 meat dish.

iv) John cross street neighbor   → 1 soup.

Total dishes = 3+2+1+1

= 6

# First time John has 6 choices to taste a dish ,

then 5 choices, then 4 choices , then 3 choices  then 2 choices and finally one dish will left.

therefore, total different ways for him to taste :

= 6×5×4×3×2×1

= 720 ways.

Hence we get the required answer.

Learn more about Permutations here:

brainly.com/question/4658834

#SPJ4

Yes, if fₙ and gₙ are sequences of Real numbers such that converge uniformly to f and g, on A⊂ R respectively, then (fₙ gₙ) isconverges uniformly to (f g).

Suppose fn → f uniformly and gn → g uniformly

on A ⊆ R and that both f and g are bounded. Then (fₙ.gₙ) converges uniformly to (fg) on A.

Proof. Let ε > 0. Suppose M₁ > 0 is an upper bound for f (meaning |f(x)| ≤ M₁ for all x ∈ A) and that M₂ is an upper bound for g.

Since fn → f uniformly, there exists N₁ ∈ N such

that n ≥ N₁ implies |fn(x) − f(x)| < 1 for all x ∈ A. Equivalently, |fn(x)| < |f(x)| + 1 ≤ M₁ + 1 for all

x ∈ A.

In turn, since gn → g uniformly, there exists N₂ ∈ N such that n ≥ N₂ implies

|gn(x) − g(x)| < 2(M₂ + 1).

Finally, since fn → f uniformly, there exists N₃∈ N such that n ≥ N3 implies |fn(x) − f(x)| < 2M₂ .

Now, if N = max{N₁, N₂, N₃} and n ≥ N, we have

|fn(x)gn(x) − f(x)g(x)| = |fn(x)gn(x) − fn(x)g(x) + fn(x)g(x) − f(x)g(x)|

≤ |fn(x)gn(x) − fn(x)g(x)| + |fn(x)g(x) − f(x)g(x)|

= |fn(x)||gn(x) − g(x)| + |g(x)||fn(x) − f(x)|

≤ (M₁ + 1)|gn(x) − g(x)| + M₂|fn(x) − f(x)|

< (M₁ + 1) ε/2(M₁ + 1) + εM₂/2M₂

= ε for all x ∈ A So, we see that, indeed, (fngn) → (fg) uniformly on A. Hence proved.

To learn more about Uniform convergence of sequence, refer:

https://brainly.com/question/16294413

#SPJ4

The cumulative distribution function, for

a > 0 is  F((x - b)/a) and for  a < 0 is 1 -  F((x - b)/a).

What is cumulative distribution function?

The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x in probability theory and statistics.

We have to find the c.d.f  of ax + b for a > 0 and a < 0.

F(x) = P(X < x)

a>0:

P(aX + b < x) = P(aX < (x - b)) = P(X < (x - b)/a) = F((x - b)/a)

a < 0 :

P(aX + b < x) = P(aX < (x - b)) = P(X > (x - b)/a) = 1 - P(X < (x - b)/a) =

1 -  F((x - b)/a).

Hence, the cumulative distribution function, for

a > 0 is  F((x - b)/a) and for  a < 0 is 1 -  F((x - b)/a).

To know more about cumulative distribution function, click on the link

https://brainly.com/question/15244608

#SPJ4

In January the Net cash flow: ($35,200) , In February Net cash flow: $6,400 and In march Net cash flow: $21,900.

A cash receipt is an official document that is issued to a customer or client when they make a payment in cash. It serves as proof of the payment, and is an important record for both the buyer and the seller. A cash receipt typically contains the date and time of the transaction, the amount of cash received, and a description of the goods or services that were purchased. It is usually signed by both the seller and the buyer.

January
Cash receipts:
Cash sales: $400,000 x 60% = $240,000
Credit sales from November: $260,000 x 20% = $52,000
Credit sales from December: $340,000 x 20% = $68,000
Total cash receipts: $360,000

Cash payments:
Materials: $400,000 x 20% = $80,000
Labor: $400,000 x 50% = $200,000
Selling and administrative: $400,000 x 15% = $60,000
Overhead: $31,000
Depreciation: $10,600
Taxes: $8,600
Dividends: $5,000
Total cash payments: $395,200
Net cash flow: ($35,200)

February
Cash receipts:
Cash sales: $440,000 x 60% = $264,000
Credit sales from December: $340,000 x 20% = $68,000
Credit sales from January: $400,000 x 20% = $80,000
Total cash receipts: $412,000

Cash payments:
Materials: $440,000 x 20% = $88,000
Labor: $440,000 x 50% = $220,000
Selling and administrative: $440,000 x 15% = $66,000
Overhead: $31,000
Depreciation: $10,600
Total cash payments: $405,600
Net cash flow: $6,400

March
Cash receipts:
Cash sales: $410,000 x 60% = $246,000
Credit sales from January: $400,000 x 20% = $80,000
Credit sales from February: $440,000 x 20% = $88,000
Total cash receipts: $414,000

Cash payments:
Materials: $400,000 x 20% = $80,000
Labor: $410,000 x 50% = $205,000
Selling and administrative: $410,000 x 15% = $61,500
Overhead: $31,000
Depreciation: $10,600
Dividends: $5,000
Total cash payments: $392,100
Net cash flow: $21,900

To learn more about Cash receipt
https://brainly.com/question/2851549
#SPJ1

Debit Common Dividends Payable $ 234,850 ; credit Cash $ 234,850.

What is arithmetic?

Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addi - tion, subtraction, multiplication, division, exponents, and root extraction. The Peano axioms, developed by the Italian mathematician Giuseppe Peano in the 19th century and still vital to the modern study of mathematical logic, formalised arithmetic. There are only a few ancient artefacts that can be used to date the invention of addition and subtraction. The best-known of these is the disputedly interpreted Ishango bone from africa, which dates to between 20,000 and 18,000 BC.

Main Body:

Debit Common Dividends Payable $100,100; credit Cash $100,100.

= $0.55 * (456,000 shares - 19,000 shares)

= $0.55 *427,000 shares

= $ 234,850

Hence ,debit Common Dividends Payable $ 234,850 ; credit Cash

$ 234,850.

To know more related to arithmetic , click on the link below:

brainly.com/question/13378503

#SPJ1

The angles in order from the smallest to the largest are ∠E < ∠D < ∠F.

Option D is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

∠D is opposite to the side length 15.

∠E is opposite to the side length 14.

∠E is the smallest angle.

∠F is opposite to the side length 23.

∠F is the largest angle.

Thus,

∠E < ∠D < ∠F

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

The percent change is -25% that is decreased.

What is percent change ?

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent , half of it is 50 percent , none of something is 0 percent.

Percent change equals the change in value divided by absolute value of original value and multiplied by 100.

Negative precent change :

When the change goes on decreasing, i.e. final value is less than original.

Positive percent change :

When the change goes on increasing i.e. final value is more than original.

In given que,

initial value = 8

final value = 6

change in value = 6-8

                           = -2

So, percent change = -2/8 *100 = -25%

Learn more about percent change using link :

https://brainly.com/question/809966

#SPJ1

The number of hours to operate the mines to minimize cost are Mine 1 hour = 30 hours and Mine 2 hour = 10 hours

The given parameters can be represented using the following table of values

                             Mine 1 (x)              Mine 2 (y)   Available

Regular grade          5                            20             350

Low grade               17                             10              610

Operating cost      7000                     29000

Time                        54                              27

From the table, we understand that we are to minimize cost

This means that:

Objective function: C = 7000x + 29000y

Subject to:

5x + 20y ≥ 350

17x + 10y ≥ 610

Next, we plot the constraints on a graph (see attachment)

From the graph, we have

(x, y) = (30, 10)

This means that

Mine 1 hour = 30 hours

Mine 2 hour = 10 hours

Hence, the number of hours are 30 and 10 hours

Read more about minimizing cost at

brainly.com/question/1592715

#SPJ1

The equation of the volume of the cylinder is V = A× h where a is base area and h is height.

Given that,

We have to find the equation of the volume of the cylinder.

We know that,

Given that a cylinder and a prism have similar shapes, but a cylinder differs from a prism in that it has a curved side face, we can determine a cylinder's volume using the same formula. We are aware that the formula, which is used to determine a prism's area,

Where V = A× h

A = the base's area

height is h.

Using the formula above, the volume (V) of a right circular cylinder is,

V = πr²h

To learn more about volume visit: https://brainly.com/question/13338592

#SPJ4

1) Initial value of the linear equation is 0. and 2) Rate of change is equal to -3.

The initial value of a linear equation is the value of the y-intercept, which is the point where the equation intersects the y-axis. It is the constant term in the equation and is represented by the letter "b" in the form y=mx+b. Therefore, the initial value of a linear equation is the value of the constant "b".

The initial value of a linear equation is the y-intercept of the line.

The given linear equation is y=-3x
1) Initial value of the linear equation is the y-intercept.  
   the y-intercept of y=-3x is 0.
   Therefore the initial value of the given equation is 0.

2) Rate of change of y=-3x is the derivative of y.
    [tex]\frac{dy}{dx}=-3\frac{dx}{dx}[/tex]
    ⇒[tex]\frac{dy}{dx}=-3[/tex]
   Therefore the rate of change is -3.

To learn more about linear equations refer to the link below:

https://brainly.com/question/12788590
#SPJ1

If On December 31, a corporation determines that they have income taxes expense of $20,000, with $15,000 currently due. the journal entry is Debit Income taxes expense $20,000, Credit income taxes payable $15,000 Credit Deferred income tax liability $5,000.

Based on the given information the appropriate journal entry to record the transaction is"

Journal entry

Debit Income taxes expense $20,000

Credit income taxes payable $15,000

Credit Deferred income tax liability $5,000

($20,000 -$5,000)

(To record income taxes)

Therefore the entry is Debit Income taxes expense ,Credit income taxes payable and Credit Deferred income tax liability.

Learn more about journal entry here:https://brainly.com/question/28390337

#SPJ1

For the  given  quadratic function, the  highest  point  that the object  reaches is  (5, 768).

Since we are given with the quadratic function of h(t)=−16t2+160t+368, where  Let a = -16, b = 160, and c = 368, so the vertex for the equation will be  :t = -b/2a = -(160)/2(-16) = -160/(-32) = 5, so substituting this value  in the equation for the value of t is

h(5) = -16(5)2 + 160(5) + 368 = -400 + 800 + 368 = 768

Here the highest point that the object reaches is (5, 768), which means that  at a time of 5 seconds, the object reaches the building after being launched at the height of  768 feet  

To know more about quadratic equations refer to the link  brainly.com/question/19030778

#SPJ4

We are standing on the top of a 368 feet tall building and launching a small object upward. The object's vertical position, measured in feet, after t seconds is

We are standing on the top of a 1200 feet tall building and launch a small object upward. The object's vertical position, measured in feet, after t seconds is  What is the highest point that the object reaches?

The amount deposited at each rate is 7,700 if the total annual interest income is $2030

What is annual interest income?

The compensation received by an entity for lending its money or allowing another organization to utilize it is known as interest income. The amount that an investor's money invested in a project or venture earns is referred to as interest income on a bigger scale.

Here, we

Let x = the amount invested at 4.5%.

let y = the amount invested at 5.0%.

Total interest is $2030

Equation becomes:

.045*x + .05*y = 2030.....(1)

y = 2 x,

so we can replace y with 2x and your equation becomes:

.045*x + .05*2*x = 2030

factor out the x to get x * (.045 + .05*2) = 2030

simplify and combine like terms to get

.145 * x = 2030

solve for x to get x = 14,000

2x is therefore equal to 28,000.

she has 14,000 invested at 4.5% and

28,000 invested at 5%.

Now, put the value of x and y in equation (1), and we get

.045*14,000 + .05*28,000 = 7,700

Hence, the amount deposited at each rate is 7,700 if the total annual interest income is $2030.

To learn more about the annual interest income from the given link

https://brainly.com/question/18156459

#SPJ1