Suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 12 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Charles, Margaret, and Sean are chosen?

Answer:

y=1.5x+9

Step-by-step explanation:

We can first write in 9 as b because the baby already started at 9 pounds, meaning the line showing the weight will also start from 9.

The question tells us that the baby grows 3 pounds every 2 months. In the equation, x represents months. We need to convert the rate of growth into 1 month to write in as the slope.

\(\frac{3pounds}{2 months} = \frac{1.5 pounds}{1 month}\)

Now we know every month, the baby grows 1.5 pounds, which represents the rate of change, or M, in the equation.

Answer:

\( \frac{3( {5}^{8} - 1) }{5 - 1} = 292968\)

Answer:

7 : 5

Step-by-step explanation:

\(\boxed{\begin{minipage}{4 cm}\underline{Area of a semicircle}\\\\$A=\dfrac{1}{2} \pi r^2$\\\\where:\\ \phantom{ww} $\bullet$ $r$ is the radius.\\ \end{minipage}}\)

If the diameter of the outer semicircle is 8 cm, then its radius is 4 cm.

Area of a semicircle with radius 4 cm:

\(\implies A=\dfrac{1}{2} \pi \cdot 4^2\)

\(\implies A=\dfrac{1}{2} \pi \cdot 16\)

\(\implies A=8 \pi \; \sf cm^2\)

Area of a semicircle with radius 3 cm:

\(\implies A=\dfrac{1}{2} \pi \cdot 3^2\)

\(\implies A=\dfrac{1}{2} \pi \cdot 9\)

\(\implies A=\dfrac{9}{2} \pi \; \sf cm^2\)

Area of a semicircle with radius 2 cm:

\(\implies A=\dfrac{1}{2} \pi \cdot 2^2\)

\(\implies A=\dfrac{1}{2} \pi \cdot 4\)

\(\implies A=2\pi \; \sf cm^2\)

Area A

To find the area of section A, subtract the area of a semicircle with radius 3 cm from the area of a semicircle with radius 4 cm:

\(\implies \textsf{Area A}=8 \pi - \dfrac{9}{2} \pi\)

\(\implies \textsf{Area A}= \dfrac{7}{2} \pi \; \sf cm^2\)

Area B

To find the area of section B, subtract the area of a semicircle with radius 2 cm from the area of a semicircle with radius 3 cm:

\(\implies \textsf{Area A}=\dfrac{9}{2} \pi-2 \pi\)

\(\implies \textsf{Area A}=\dfrac{5}{2} \pi\; \sf cm^2\)

Therefore, the ratio of area A to area B is:

\(\implies \dfrac{7}{2} \pi : \dfrac{5}{2} \pi\)

\(\implies \dfrac{7}{2} : \dfrac{5}{2}\)

\(\implies 7:5\)

Answer:

P = 1/4

Step-by-step explanation:

If we select a two-child family, the possibilities are:

boy, boy

boy, girl

girl, boy

girl, girl

We have 4 possible outcomes and in only one outcome the family has two boys.

So, the probability the selected family has two boys is P:

Answer:

a) \( E = \frac{49.2-17.6}{2}= 15.8\)

b) For this case we have 95% of confidence that the true mean would be between \(\pm 15.8\) units respect the true mean.

c) \(n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112\)

So the answer for this case would be n=112

d) \(36.5-2.58\frac{45}{\sqrt{112}}=25.53\)    

\(36.5+2.58\frac{45}{\sqrt{112}}=47.47\)

Step-by-step explanation:

Part a

For this case we know that the cinfidence interval for the true mean is given by:

\( \bar X \pm E\)

Where E represent the margin of error. For this case we have the confidence interval at 95% of confidence and we can estimate the margin of error like this:

\( E = \frac{49.2-17.6}{2}= 15.8\)

Part b

For this case we have 95% of confidence that the true mean would be between \(\pm 15.8\) units respect the true mean.

Part c

The margin of error is given by this formula:

\( ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\)    (a)

And on this case we have that ME =11 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

\(n=(\frac{z_{\alpha/2} \sigma}{ME})^2\)   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The critical value would be \(z_{\alpha/2}=2.58\), replacing into formula (b) we got:

\(n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112\)

So the answer for this case would be n=112

Part d

The confidence interval for the mean is given by the following formula:

\(\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\)   (1)

Replcaing the info given we got:

\(36.5-2.58\frac{45}{\sqrt{112}}=25.53\)    

\(36.5+2.58\frac{45}{\sqrt{112}}=47.47\)

Answer:

\(\frac{dy}{dx}=\frac{8(xsec^2(x)-tan(x)+3)}{(3-tan(x))^2}\)

Step-by-step explanation:

\(y=\frac{8x}{3-tan(x)}\\ \\\frac{dy}{dx}=\frac{(3-tan(x))(\frac{d}{dx}8x)-(\frac{d}{dx}(3-tan(x)))(8x)}{(3-tan(x))^2}\\ \\ \frac{dy}{dx}=\frac{(3-tan(x))(8)-(-sec^2(x))(8x)}{(3-tan(x))^2}\\ \\ \frac{dy}{dx}=\frac{24-8tan(x)+8xsec^2(x)}{(3-tan(x))^2}\\ \\ \frac{dy}{dx}=\frac{8xsec^2(x)-8tan(x)+24}{(3-tan(x))^2}\\\\ \frac{dy}{dx}=\frac{8(xsec^2(x)-tan(x)+3)}{(3-tan(x))^2}\)

Remember to use the Quotient Rule

Answer:

600?

Step-by-step explanation:

you do 2400÷4 which would be 600 for each hour

Step-by-step explanation:

Using the roots given in order given:

y=  ( x+4)(x+2)(x-4)(x-2)     would  fit the bill.....

The simplified boolean expression for F5 is F5 = P OR (NOT R). In this expression, P represents one boolean variable, and (NOT R) represents the negation of another boolean variable R. The OR operator combines the two variables, resulting in the final boolean expression F5.

To simplify the boolean expression F5 = (P AND Q) OR (R AND NOT P), we can apply Boolean algebra rules to reduce it to its simplest form.

Step 1: Apply De Morgan's laws

NOT (R AND NOT P) can be simplified as (NOT R) OR P.

Step 2: Distributive property

F5 = (P AND Q) OR ((NOT R) OR P)

Step 3: Apply associative property

F5 = (P AND Q) OR (P OR (NOT R))

Step 4: Apply absorption law

F5 = P OR (P OR (NOT R))

Step 5: Apply idempotent law

F5 = P OR (NOT R)

By simplifying the expression, we have reduced it to its simplest form while preserving its logical meaning. The simplified expression can be used to analyze and evaluate logical circuits or systems where the variables P and R are used.

Remember, boolean algebra allows us to manipulate and simplify complex logical expressions by applying various rules and properties. These simplifications help in understanding and analyzing logical operations in digital systems and circuits.

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The question probable may be:

Consider the boolean variables P, Q, and R. Determine the boolean expression for the variable F5 using the given variables:

F5 = (P AND Q) OR (R AND NOT P)

Using the boolean variables P, Q, and R, can you simplify the expression F5 to its simplest form by applying Boolean algebra rules?

Answer: 10

Step-by-step explanation:

Step-by-step explanation:

10x-8y = 40 (1)

5x-2y= 40  (2)

multiply (2) by -2 then add to (1) to get rid of x

-10x+4y+10x-8y = 40+ (-80)

-4y = -40

4y = 40

y= 40/4

y = 10

the answer is 10

Answer:

Response variable is the hats because it is the variable that is being predicted.

Step-by-step explanation:

A response variable is the subject/variable that responds to the various changes being made in an experiment. For example, if we are testing the effect of some drugs on people's emotions. The response variable here will be "emotions" because it is the subject that responds to the substance of the experiment.

Now, applying that to our question, the size of the hats will be the response variable because it is the variable in the experiment that the company is trying to predict from the circumference.

See the attachment  for the graphed inequalities.

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

The system of equations x - 4y = - 5 and - x + ay = 10, will have

exactly one solution when, a. a= 3, c. a = 5 and d. a = 1.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

We know, A system of linear equations has a unique solution when,

a₁/a₂ ≠ b₁/b₂.

Given, x - 4y = - 5 and - x + ay = 10.

Therefore, a₁/a₂ = b₁/b₂ ⇒ 1/(-1) = - 4/a.

- 1 = - 4/a.

a = 4.

But to have a unique solution a ≠ 4.

Q. Select all of the values for "a" that result in the system of equations having exactly 1 solution, x - 4y = - 5 and - x + ay = 10.

a. a = 3

b. a = 4.

c. a = 5.

d. a = 1

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The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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The graph of the function y = 5|x - 4| is added as an attachment

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

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

Money of the cycle=$280

Money saved =80%=(80/100)×280=$224

Money to be saved= (280-224)=$56

Answer:

She has saved 224 dollars

Step-by-step explanation:

She has saves 80% of the money required

280 * 80%

Change to decimal form

280 *.80

224

Probability is simply how likely something is to happen. There can be many probability of the same thing to occur in future. the probability that a box of cereal will be:

A. The probability that a box of cereal will be more than one ounce underweight is equivalent to the probability of getting a weight less than 15 ounces. Using a standard normal distribution table or calculator, we can find that this probability is approximately 0.0228 or 2.28%.

B. The probability that a box of cereal will not be underweight is equivalent to the probability of getting a weight greater than or equal to 16 ounces. Using a standard normal distribution table or calculator, we can find that this probability is approximately 0.5 or 50%.

C. The likelihood that a package of cereal will weigh less than or equal to 17 ounces is the same as the likelihood that it won't be more than 1 ounce overweight. This chance can be calculated using a typical normal distribution chart or calculator as 0.9772 or 97.72%.

D. Because weight is a continuous variable with an infinitesimally tiny chance of attaining any precise value, the likelihood of receiving exactly 16 ounces is very low. The area under the normal distribution curve between 15.5 and 16.5 ounces, or roughly 0.3829 or 38.29%, can be used to determine the chance.

Possibility or probability is all game of occurrence of the thing.

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(p ² q ⁵) ⁻⁴ (p ⁻⁴ q ⁵) ⁻²

= (p ⁻⁸ q ⁻¹⁰) (p ⁻⁸ q ⁻¹⁰)

= p ⁻¹⁶ q ⁻²⁰

Answer:

-15.5

Step-by-step explanation:

1/3 (32.48-14.0.2)

1/3(-46.5)

Answer = -15.5

Answer:

Step-by-step explanation:

total interest paid is given as $4,643.46.

total payments = $429.95 x 36 months = $15,478.20

total lease payments = total payments - total interest

total lease payments = $15,478.20 - $4,643.46 = $10,834.74

Remaining balance = Total cost of the lease - Total lease payments

$23,495 - $10,834.74 = $12,660.26

The value of the equation (1 - x)/2x² + x²/(2x - 2) is 0 if x² + x - 1 = 0

From the question, the equation is given as

x² + x - 1 = 0

Make x² the subject of the above equation

So, we have the following equation

x²  = 1 - x

The equation to calculate is given as

(1 - x)/2x² + x²/(2x - 2) = ?

Substitute x²  = 1 - x

(1 - x)/2x² + x²/(2x - 2) = x²/2x² + x²/(2x - 2)

Evaluate the quotient

So, we have the following equation

(1 - x)/2x² + x²/(2x - 2) = 1/2 + x²/(2x - 2)

Factor out -2

(1 - x)/2x² + x²/(2x - 2) = 1/2 - x²/2(1 - x)

Substitute x²  = 1 - x

Factor out -2

(1 - x)/2x² + x²/(2x - 2) = 1/2 - x²/2x²

Evaluate the quotient

(1 - x)/2x² + x²/(2x - 2) = 1/2 - 1/2

Evaluate the difference

(1 - x)/2x² + x²/(2x - 2) = 0

Hence, the solution to the equation is 0

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Answer:

Step-by-step explanation:

Well, since the length of a month can vary in the number of days, this answer can also vary.

For example, February is only 28 days long, while December is 31 days long.

That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back   July 19th of July 20th.

I hope this helps!

Answer:

c. number shows the proportional relationship between x and y...

Answer:

me I would guess

Step-by-step explanation:

like break it down step by step or just buy answers

By HL congruence,  triangle ABC congruent to triangle DEF. Therefore, option D is the correct answer.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Consider the given triangles as ABC and DEF.

From the given triangles,

AC=DF=14 in.

BC=EF=20 in.

∠A=∠D=90°

The Hypotenuse-Leg (HL) Triangle Congruence Theorem is a special case that allows you to show that two right triangles are congruent. If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

By HL congruence, ΔABC ≅ ΔDEF

Therefore, option D is the correct answer.

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the profit for winning should be $140 for the game to be fair.

What is polynomials?

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

Let's call the profit for winning "p". Then the expected value of the game can be expressed as:

E = (1/36) * p + (35/36) * (-4)

For the game to be fair, the expected value should be zero:

0 = (1/36) * p + (35/36) * (-4)

Solving for p:

(1/36) * p = 35/36 * 4

p = (35/36 * 4) / (1/36)

p = 140

So the profit for winning should be $140 for the game to be fair.

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