The random variable X, representing the number of cherries in a cherry puff, has the following probability distribution:x: 4 - 5 - 6 - 7 P(X=x): 0.2 - 0.4 - 0.3 - 0.1 (a) Find the mean μ and the variance σ² of X.(b) Find the mean [tex]\mu_{\bar X}[/tex] and the variance [tex]\sigma^2_{\bar X}[/tex] of the mean [tex]\bar X[/tex] for random samples of 36 cherry puffs.(c) Find the probability that the average number of cherries in 36 cherry puffs will be less than 5.5.

Answers

Answer 1

Answer:

Step-by-step explanation:

Given is the probability distribution of a random variable X

X 4 5 6 7 Total

P 0.2 0.4 0.3 0.1 1

x*p 0.8 2 1.8 0.7 5.3

x^2*p 3.2 10 10.8 4.9 28.9

a) E(X) = Mean of X = sum of xp = 5.3

[tex]Var(x) = 28.9-5.3^2=0.81[/tex]

Std dev = square root of variance = 0.9

------------------------------------

b) For sample mean we have

Mean = 5.3

Variance = var(x)/n = [tex]\frac{0.81}{{36} } \\=0.0225[/tex]

c) [tex]P(\bar X <5.5)\\= P(Z<\frac{5.5-5.3}{\sqrt{0.0225} } \\= P(Z<1.33)\\=0.908[/tex]

Answer 2

The mean and the variance from the data about the cherries will be 5.3 and 0.81.

How to calculate the mean and variance?

The required mean from the information given will be:

= (4 × 0.2) + (5 × 0.4) + (6 × 0.3) + (7 × 0.1)

= 0.8 + 2.0 + 1.8 + 0.7

= 5.3

The variance will be calculated thus:

= (4² × 0.2) + (5² × 0.4) + (6² × 0.3) + (7² × 0.1) - (5.3)²

= 3.2 + 10 + 10.8 + 4.9 - (5.3)²

= 0.81

The variance is 0.81.

The probability that the average number of cherries in 36 cherry puffs will be less than 5.5 will be:

= P(x = 4( + P(x = 5)

= 0.2 + 0.4

= 0.6

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Related Questions

Sammy is making a bacon wrapped pizza for dinner. She is wrapping 47.1 inches of bacon around the outside edge of the pizza. What is the area of the pizza?

Answers

Answer:

Approx. 1.8 in.²

Step-by-step explanation:

Circumference of a circle (the pizza) = 2πr

Area of a circle = πr²

Set 2πr = 4.71 (because that's the length of bacon around the pizza) and solve for the radius "r". Then plug that "r" into the area equation πr² to find the area. You should get 1.8 square inches if I plugged them in correctly.

HELPPPPP


(Attaching the pic now)





Answers

Explanation:

1. BF bisects ∠CBA. Given

2. ∠CBF ≅ ∠ABF. Definition of angle bisector

3. BF ≅ BF. Reflexive property

4. ∠CFB ≅ ∠AFB. Given

5. ΔCBF ≅ ∆ABF. ASA congruence postulate

6. CF ≅ FA. Corresponding parts of congruent triangles are congruent (CPCTC)

_____

Comment on the problem

It appears as though all of the congruence symbols have gone missing.

Which of the following is the simple interest paid on a loan of $354 at 6% for six months?


$10.62


$10.26


$12.47


$12.74

Answers

Answer: interest at the end of 6 months is $10.62

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T = 6 months = 6/12 = 0.5 years

P = $354

R = 6%

Therefore

I = (354 × 6 × 0.5)/100

I = 1062/100

I = 10.62

Three pounds of dried cherries cost $15.90, 5 pounds of dried cherries cost $26.50, and 9 pounds of dried cherries cost $47.70. Which equation gives the total cost y of x pounds of dried cherries?

Answers

Final answer:

The equation that gives the total cost of x pounds of dried cherries is y = (10.60/2)x.

Explanation:

Let's create a table to represent the given information:

Pounds of Dried Cherries (x)Total Cost (y)315.90526.50947.70

To find an equation that gives the total cost of x pounds of dried cherries, we need to find a pattern in the data. From the table, we can see that as the pounds of dried cherries increase, the total cost also increases. This suggests a linear relationship between pounds and cost.

Now, let's analyze the changes in cost for each additional pound of dried cherries:

From 3 to 5 pounds: The cost increased by $26.50 - $15.90 = $10.60.From 5 to 9 pounds: The cost increased by $47.70 - $26.50 = $21.20.

Based on these changes, the cost increased by $10.60 for every 2 additional pounds of dried cherries. Therefore, the equation that gives the total cost y of x pounds of dried cherries is:

y = (10.60/2)x

Calculate the simple interest paid on a loan of $544 at 3% for three months.


$48.96


$4.80


$4.90


$4.08

Answers

Answer:

4.08

Step-by-step explanation:

Interest I =Pnr

3 months =3/12 year = n

r = 3%

and, P = 544$

Therefore,

[tex]i = 544 \times (3 \div 100) \times (3 \div 12) \\ \: \: \: = 4.08[/tex]

an agent of a broker-dealer wishes to create a website to solicit securities business from customers. based on each customer's reponses to questions asked, appropriate investment recommendations will be made. which statement are true?

Answers

Answer:

The following statements are true:

The broker-dealer must review and approve the content of the website The broker-dealer must be registered in each State where a customer responds to the website The agent must be registered in each State where a customer responds to the website

Step-by-step explanation:

An agent of a broker-dealer wishes to create a website to solicit securities business from customers based on each customer's response to questions asked, appropriate investment recommendation will be made. The statement which is not true under the given conditions is: "The Administrator must review and approve the content of the website." because the broker-dealer has to approve the content of the website.These recommendations which are discussed above are for the benefit and will ensure the safety and prevent the damage.

2. Jenna Ford purchased a compact stereo that regularly sells for $229.99 at a markdown rate of 53%. In California, where Jenna lives, the sales tax rate on this item is 7%. Find the final price of the item.

Answers

Answer:

$115.67

Step-by-step explanation:

given that the markdown rate is 53%, that means that the markdown is 53% of the original price, or,

markdown = 53% of $229.99 = 0.53 x 229.99 = $121.89

sale price before tax = Original Price - Markdown

= 229.99 - 121.89

= $108.10

sales tax = 7% of sale price before tax

= 0.07 x 108.10

= $7.57

Final price =  price before tax + tax

= 108.1 + 7.57

= $115.67

If you have a lowest score of 21 and a range of 47, your highest score will be:________

Answers

Answer: 68

Step-by-step explanation:

range=47 lowest score = 21 let highest score =x

Range=highest score - lowest score

47 = x - 21

x = 47 + 21

x = 68

Therefore the highest score is 68

The highest score is 68.

Range = Highest Score - Lowest Score

In this case,

the lowest score is 21 and

the range is 47.

So, we can rearrange the formula to solve for the highest score:

Highest Score = Range + Lowest Score

Substituting in the given values:

Highest Score = 47 + 21

Thus, the highest score will be 68.

Your grandmother always has a jar of cookies on her counter. One day while you are visiting, you eat 555 cookies from the jar. In the equation below, ccc is the number of cookies remaining in the jar and bbb is the number of cookies in the jar before your visit.

Answers

Answer:

For 1 How does grandma have so many cookies??? For 2 if i eat 555 cookies then imma have diabetes. and for 3 there really is no way to find this out. The only way to find out how many cookies there is now it to see how much cookies there were before and you cant do that without seeing how much is in there now. Its a catch 22.

Step-by-step explanation:

Jake, a varsity swimmer, is training for his upcoming season and needs to accelerate his post-exercise recovery rates. He trains intensely for 2 hours, 5 days a week. If he weighs 155-lb (70.45 kg), which of the following nutritional strategies would BEST replenish his glycogen stores?

Answers

Answer:

high glycemic carb with some protein

Step-by-step explanation:

Food like white bread made from dextrose supplement and chocolate milk that contains some protein for muscle repair.

Due to the spongelike characteristic of the muscle would make it soak up glucose from high glycemic carb.

Can someone please write the equation of hyperbola with vertices (0, -5) and (0, 5) and co-vertices (-2, 0) and (2, 0)?

Thank you so much!

Answers

Answer:

  y^2/25 -x^2/4 = 1

Step-by-step explanation:

The equation can be written as ...

  y^2/a^2 -x^2/b^2 = 1

where the vertices are at (0, ±a) and the co-vertices are at (±b, 0). Filling in the given values (a=5, b=2) gives the equation shown above.

7600 people were surveyed about their favorite type of milkshake what percentage of the people like vanilla how many of the people like chocolate how many of the total people like vanilla or strawberry

Answers

Answer:

Lack of information

Step-by-step explanation:

I can't find what percent or whatever information about the flavour,so I guess you need to give more information. If you give me more information, I will try to reply in the comments.

Hope this helps!!! ;)

A 20 kg sphere is at the origin and a 10 kg sphere is at x = 20 cm. At what position on the x-axis could you place a small mass such that the net gravitational force on it due to the spheres is zero?

Answers

The small mass should be placed at x = 11.72 cm or x = 68.28 cm

Step-by-step explanation:

Let the small mass be m and position on x axis be y.

A 20 kg sphere is at the origin.

Distance to 20 kg mass = y

A 10 kg sphere is at x = 20 cm

Distance to 10 kg sphere = 20 - y

We have forces between them are equal

We have gravitational force   

                    [tex]F=\frac{GMm}{r^2}[/tex]              

          Where G =  6.67 x 10⁻¹¹ N m²/kg²

                      M = Mass of body 1

                      M = Mass of body 2

                      r = Distance between them

Here we have

            [tex]\frac{G\times 20\times m}{y^2}=\frac{G\times 10\times m}{(20-y)^2}\\\\800-80y+2y^2=y^2\\\\y^2-80y+800=0\\\\y=68.28cm\texttt{ or }y=11.72cm[/tex]

So the small mass should be placed at x = 11.72 cm or x = 68.28 cm

The positions on the x-axis obtained using quadratic equation such that net gravitational force is zero are 68.28 and 11.72 cm respectively.

Recall the force of universal gravitational attraction :

[tex] \frac{Gm_{1}m_{2}}{r^{2}}[/tex]

Sphere 1 :

Mass = 20 kg Distance of 20kg sphere = d

Sphere 2 :

Mass = 10kgDistance of 10kg sphere = 20 - d

Gravitational force ; sphere 1 :

[tex] \frac{G \times 20 \times m_{2}}{d^{2}}[/tex] --(1)

Gravitational force ; sphere 2 :

[tex] \frac{G \times 10 \times m_{2}}{(20 - d)^{2}}[/tex] - - (2)

Equate (1) and (2)

[tex] \frac{G \times 20 \times m_{2}}{d^{2}} = \frac{G \times 10 \times m_{2}}{(20 - d)^{2}} [/tex]

[tex] 20(20 - d)^{2} = 10 \times d^{2} [tex]

20(400 - 40d + d²) = 10d²

8000 - 800d + 20d² = 10d²

10d² - 800d + 8000 = 0

Divide through by 10

d² - 80d + 800 = 0

Using a quadratic equation solver :

d = 68.28 cm or d = 11.72 cm

The possible positions are 68.28 cm and 11.72 cm

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Keys went to the grocery store on Monday and bought 5 apples and 2 oranges for a total of 3.45. On Thursday she bought 3 oranges and 7 apples for a total of $4.90

Answers

Answer:

Keys would have to spend $6.60 on apples for both days.

Step-by-step explanation:

Keys went to buy 5 apples and 2 oranges for $3.45 and 7 apples and 3 oranges for $4.90 .

We have to find how much money she spends on apples on both the days.

Let price of apples be x and oranges be y.

We have to make equations and solve them to find the price of oranges and apples.

5x + 2y = 3.45

7x + 3y = 4.90

Solve both these equations to find x and y.

We get x= $0.55 and y = $0.35

Key has bought 12 apples and it would cost = 12 [tex]\times[/tex] 0.55

                                           = $6.60

Twenty different video games showing alcohol use were observed. The duration times of alcohol use ​(in seconds) were recorded.
1. When using this sample for a t-test of the claim that the population mean is greater than 89 ​sec, what does df​ denote?

A. The sample standard deviation
B. The number of degrees of freedom
C. The sample size
D. The test statistic
2. What is its​ value?

Answers

Answer:

Degree of freedom = 19

Step-by-step explanation:

We are given the following information in the question:

Sample size, n = 20

For a t-test hypothesis it was claimed that the population mean is greater than 89 ​second.

1) df

Df denotes the degree of freedom.

The Degrees of Freedom refers to the number of values involved in the calculations that have the freedom to vary.

2) Degree of freedom  = n - 1

where n is the sample size

Degree of freedom = 20 - 1 = 19

Judy bought her tent on sale .The same price was $70 off the original price . Judy also used a coupon for an extra $15 off if Judy paid $125 for the tent , what was it's original price

Answers

Answer:210

Step-by-step explanation:

175+70+15=210

Answer:the original price is $210

Step-by-step explanation:

Let x represent the original price of the tent. She bought it at price that is $70 off the original price. This means that $70 was taken off the original price.The amount after the discount has been removed would be

x - 70

Judy also used a coupon for an extra $15 off. This means that the amount the Judy finally paid for the tent would be

x - 70 - 15

if Judy paid $125 for the tent, it means that

x - 70 - 15 = 125

x = 125 + 70 + 15

x = $210

please answer soon Which expression is equivalent to − 7 x + 6 ( x − 8 2 ) − 2 ( x + 3 ) + 10 ? A. − 3 x + 40 B. − 15 x − 20 C. − 3 x − 20 D. 15 x + 40

Answers

Multiply the parenthesis by 6:

-7x+6x-492-2(x+3)+10

Multiply the parenthesis by -2:

-7x+6x-492-2x-6+10

Calculate the sum of similar terms:

-3x-492-6+10

Calculate the sum or difference:

-3x-488

At Delia’s company, the purchases are recorded at net amounts. On August 5, $40,000 worth of merchandise was purchased on account for terms of 2/10, n/30. $3,000 of this merchandise was returned, and the account was credited. As of August 31, the balance still had not been paid. What amount will be recorded as the purchase return?

Answers

Answer:

$2,940

Step-by-step explanation:

Data provided in the question:

Cost of merchandise purchased = $40,000

Cost of merchandise returned = $3,000

Terms = 2/10, n/30

Now,

The amount that will be recorded as the purchase return

= Cost of merchandise returned - Discount on cost of merchandise

= $3,000 - ( 2% of $3,000 )

= $3,000 - ( 0.02 × $3,000 )

= $3,000 - $60

= $2,940

21. What is the exact volume of a sphere whose diameter is 14 cm? Show your work.

Answers

Answer:

The exact volume of a sphere is [tex]V=1437cm^3[/tex]

Step-by-step explanation:

Given that the diameter of a sphere is 14cm.

That is d=14

First find the radius of the sphere with diameter

[tex]r=\frac{d}{2}[/tex]

[tex]r=\frac{14}{2}[/tex]

Therefore r=7cm

Now to find the volume of the sphere:

[tex]V=\frac{4}{3}\pi r^3cm^3[/tex]

[tex]V=\frac{4}{3}\frac{22}{7}(7)^3[/tex]  (here[tex]\pi=\frac{22}{7}[/tex] and r=7)

[tex]V=\frac{4}{3}(22)(7)^2[/tex]

[tex]V=\frac{4}{3}(22)(49)[/tex]

[tex]V=\frac{4}{3}(1078)[/tex]

[tex]V=\frac{4312}{3}[/tex]

[tex]V=1437.33cm^3[/tex]

Therefore the volume of the given sphere is [tex]V=1437.33cm^3[/tex]

The exact volume of a sphere is [tex]V=1437cm^3[/tex]

Susan has 5 more pennies than dimes, three times more nickels than dimes and 4 less quarters than pennies. If Susan has 7 dimes, what is the total value of her money?

Answers

Answer: $3.35

To solve this, let’s first write equations for each of the coins listed. Let’s start with pennies.

We know that Susan has 3 more pennies than dimes. This means that pennies is equal to dimes, plus three. This would turn into this equation:

Pennies: d+3

Now let’s move onto nickels. The question says that Susan has three times more nickels than dimes. This means that nickels is equal to dimes, times three. This would be our equation:

Nickels: n=3d

Finally, let’s write the equation for quarters. It says that Susan has four less quarters than pennies. This means that quarters are equal to pennies minus three. This would be the equation:

Quarters: q=p-4



Now time to solve. We need to solve the amount of...

Pennies: ?
Nickels: ?
Dimes: ?
Quarters: ?

The question tells us that Susan has 7 dimes, so let’s fill that in now.

Pennies: ?
Nickels: ?
Dimes: 7
Quarters: ?

We can use the dime information to solve for the other coins, using our equation. Let’s go in order and start with pennies.

Our equation for pennies is: p=d+3. We know that d is 7, so let’s fill this in and solve.

p=d+3
p=7+3
p=10

Susan has 10 pennies. Let’s fill this into the information we have.

Pennies: 10
Nickels: ?
Dimes: 7
Quarters: ?

Now let’s do nickels. Our equation says n=3d. Let’s substitute the value for d and solve

n=3d
n=3(7)
n=21

Susan has 21 nickels. Let’s fill that into the information we have.

Pennies: 10
Nickels: 21
Dimes: 7
Quarters: ?

Let’s finally do quarters. The equation we have written for quarters is: q=p-4. Let’s fill in the value of p and solve

q=p-4
q=10-4
q=6

Susan has 6 quarters. This is our final information on the coins:

Pennies: 10
Nickels: 21
Dimes: 7
Quarters: 6

Let’s now calculate how much money she has altogether. We will do this by multiplying how many coins she has by the value of each coin.

Pennies: 10 • .01= .10
Nickels: 21•.05=1.05
Dimes: 7•.10=.70
Quarters: 6•.25=1.5

Now that we know that, let’s add these all together. This will tell us the final answer of how much is the value of her money.

.10+1.05+.70+1.5= $3.35

That’s your answer! Hope this helps comment below for more questions :)

Prove that if f is one-to-one, then f(X) ∩ f(Y ) = f(X ∩ Y ) for all X, Y ⊆ A. Is the converse true?

Answers

Answer:

See proof below, the converse is true

Step-by-step explanation:

Let f be a function whose domain is the set A, and X,Y be arbitrary subsets of A. One way to prove the equality of sets f(X)∩f(Y)=f(X∩Y) is, by definition, to prove the inclusions f(X)∩f(Y) ⊆ f(X∩Y)  and f(X)∩f(Y )⊇f(X∩Y).

First, let a∈f(X)∩f(Y). Then a∈f(X) and a∈f(Y) by definition of intersection. Thus, a=f(t) for some t∈X (because a is an element of the direct image of X) and a=f(s) for some s∈Y. Then a=f(t)=f(s). We know that f is 1-1, so the previous equality implies that t=s. Now, t∈X and t=s∈Y, thus t∈X∩Y. Therefore, a=f(t) for some t∈X∩Y, which means that a is an element of the direct image of X∩Y, that is, a∈f(X∩Y). This holds for all a, thus f(X)∩f(Y) ⊆ f(X∩Y).

For the second inclusion, let b∈f(X∩Y), then there exists some z∈X∩Y such that b=f(z). Since z∈X∩Y, we have that z∈X and z∈Y. Thus, b=f(z) for some z∈X, that is, b∈f(X). Similarly, b∈f(Y) because b=f(z) and z∈Y. Therefore b∈f(X)∩f(Y) for all  b∈f(X∩Y), then f(X)∩f(Y )⊇f(X∩Y). Note that this holds for any function f, as we did not use that f is 1-1.

To prove the converse, suppose that f(X)∩f(Y)=f(X∩Y)  for all  X, Y⊆ A. We will prove that f is 1-1, that is, for all a,b∈A if f(a)=f(b) then a=b.

Define the sets X:={a} and Y:={b}. Then f(X)={f(a)} and f(Y)={f(b)}. Assuming that f(a)=f(b), we obtain f(X)=f(Y). We know that f(X)∩f(Y)=f(X∩Y), which means {f(a)}=f(X∩Y). Then, there exists some s∈X∩Y such that f(s)=f(a), thus X∩Y is a non-empty set, which implies that a∈Y. But Y has only one element, b, therefore a=b which shows that f is 1-1.

Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.

Answers

Rich will accrue approximately $1,518.45 in interest during the 4.5-year nonpayment period on his federal unsubsidized student loan.

To calculate the interest that Rich will accrue during the 4.5-year nonpayment period on his federal unsubsidized student loan, we can use the formula for simple interest:

Interest = Principal (loan amount) x Rate x Time

Where:

Principal (loan amount) = $7,900

Rate = 4.29% (0.0429 as a decimal)

Time = 4.5 years

Now, plug these values into the formula:

Interest = $7,900 x 0.0429 x 4.5

Interest = $7,900 x 0.19205

Interest ≈ $1,518.45

So, Rich will accrue approximately $1,518.45 in interest during the 4.5-year nonpayment period on his federal unsubsidized student loan.

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Final answer:

Rich has been approved for a federal unsubsidized student loan and wants to know the interest that will accrue during his 4.5 years as a freshman in college. Calculating the interest using the formula, the total accrued interest is $1,146.75.

Explanation:

Rich is attending a 4-year college and has been approved for a 10-year federal unsubsidized student loan of $7,900 at an interest rate of 4.29%. During his 4 years as a freshman, he has the option to start repaying the loan after 4.5 years. However, interest will continue to accrue at a rate of 4.29% during this non-payment period.

To calculate the interest that will accrue during the 4.5 years, we can use the formula:

Interest Accrued = Principal x Interest Rate x Time

Substituting the values, we get:

Interest Accrued = $7,900 x 0.0429 x 4.5 = $1,146.75

Therefore, the interest that will accrue during the non-payment time is $1,146.75.

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In an arcade game, a 0.13 kg disk is shot across a frictionless horizontal surface by being compressed against a spring and then released. The spring has a spring constant of 242 N/m and is compressed from its equilibrium position by 5.2 cm. What is the magnitude of the spring force on the disk at the moment it is released?

Answers

Answer:

12.584 N

Step-by-step explanation:

To solve this problem you need to use Hokke's law, this is a physics lar which states the force (F) you need to compress a spring for some distance (x) can be easily calculated with the equation F=kx. The constant k (the stiffness of the spring) is the value of 242 N/m and x is the distance 5.2 cm = 0.052 m. So if you multiply 242 N/m by 0.052 m you will obtain 12.584 N, which is the necessary force to compress the spring 5.2 cm. The mass of the spring is a nonrelevant data in this problem.

math question in the attached text

Answers

Answer:

A 1.44 cm cubed

Step-by-step explanation:

Just multiply all the numbers to get the area of the block

Answer:

A 1.44 cm cubed

Step-by-step explanation:

Match the key aspect of a function's graph with its meaning.
f(x) > 0
intervals of the domain where the
graph is above the x-axis
f(x) < 0
location on graph where input is zero
x-intercept
location on graph where output is
zero
y-intercept
intervals of the domain where the
graph is below the x-axis

Answers

Answer:

Part 1) Intervals of the domain where the  graph is above the x-axis (f(x) > 0)

Part 2) location on graph where input is zero  (y-intercept)

Part 3) location on graph where output is zero  (x-intercept)

Part 4) Intervals of the domain where the  graph is below the x-axis (f(x) < 0)

Step-by-step explanation:

Verify each case

Part 1) we have

Intervals of the domain where the  graph is above the x-axis

we know that

If the graph is above the x-axis, then the value of f(x) is positive

therefore

f(x) > 0

Part 2) we have

location on graph where input is zero  

Let

x ---> the independent variable or input value

f(x) ---> the dependent variable or output value

we know that

The y-intercept is the value of f(x) (output value) when the value of x (input value) is zero

therefore

y-intercept

Part 3) we have

location on graph where output is zero  

Let

x ---> the independent variable or input value

f(x) ---> the dependent variable or output value

we know that

The x-intercept is the value of x (input value) when the value of the function f(x) (output value) is zero

therefore

x-intercept

Part 4) we have

Intervals of the domain where the  graph is below the x-axis

we know that

If the graph is below the x-axis, then the value of f(x) is negative

therefore

f(x) < 0

Answer:

Intervals of the domain where the  graph is above the x-axis (f(x) > 0)

location on graph where input is zero  (y-intercept)

location on graph where output is zero  (x-intercept)

Intervals of the domain where the  graph is below the x-axis (f(x) < 0)

Step-by-step explanation:

answer edge 2020

If an integer n is to be selected at random from the integers 1 to 100, inclusive, what is the probability that n(n 1) will be divisible by 4

Answers

Answer:

Step-by-step explanation:

total integers=100 (1,2,3,...,98,99,100)

numbers divisible by 4 =25 (4,8,12,...,96,100)

P=25/100=1/4

Sketch the graph of the given function. Then state the function’s domain and range. f(x)= 1/2(5)^x+3

Answers

Answer:

Graph of the following function is attached with the answer.

Domain : ( - ∞ , + ∞ )

Range : ( 3 , + ∞ )

Step-by-step explanation:

[tex]f(x)=\frac{1}{2}x^{2}+3[/tex]

Domain of any quadratic equation is from negative infinity to positive infinity under no restrictions.

So, Domain : ( - ∞ , + ∞ )

The Range of any function can be calculated easily if there is just one term with variable. The method to find Range by that method is explained with the example as follows:

Range of x : ( - ∞ , + ∞ )Range of [tex]\textrm{x}^{2}[/tex] : [ 0 , + ∞ ) as every square number is more than or equal to zero.Range of [tex]\frac{1}{2}\textrm{x}^{2}[/tex] : [ 0 , + ∞ ) as 0/2 = 0 and ∞/2 = ∞.Range of [tex]\frac{1}{2}\textrm{x}^{2}+3[/tex] : [ 3 , + ∞ ) as 0 + 3 = 3 and ∞ + 3 = ∞.

Therefore the Range of [tex]\mathbf{f(x)\boldsymbol=\frac{1}{2}x^{2}\boldsymbol+3}[/tex] is [ 3 , + ∞ )

(NOTE : [a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.

(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.

(a,b] means all the numbers between 'a' and 'b' including only 'b' not 'a'.

[a,b) means all the numbers between 'a' and 'b' including only 'a' not 'b'.

{a,b} means only 'a' and 'b'.

{a,b] or (a,b} doesn't mean anything. )

The measures of one acute angle in a right triangle is four times the measure of the other acute
angle. Write and solve a system of equations to find the measures of the acute angles.

Help with this exercise

Answers

Answer:

[tex]A_2[/tex] = 18°

[tex]A_3[/tex] = 4(18°) = 72°

Step-by-step explanation:

Given:

One angle in the triangle is 90°One angle that isn't 90° is 4 times larger than another angle that isn't 90°

Angles:

[tex]A_1[/tex] = 90°

[tex]A_2[/tex] = x

[tex]A_3[/tex] = 4x

Solution Pathway:

Under the rules for any triangle, a triangle's interior angles must add up to 180°. Using this, we can set up the equation:

sum of the interior angles = 180°90° + x + 4x = 180°

Now let's solve for x.

90 +x + 4x = 18090 + 5x = 1805x = 90x = 18°

Now that we know x is 18°, lets plug this value into the two unknown acute angles.

[tex]A_2[/tex] = 18°[tex]A_3[/tex] = 4(18°) = 72°

Answer:

72 degrees and 18 degrees.

Step-by-step explanation:

If the 2 angles are x and y, we have the system:

x + y = 90           (as it is a right triangle)

x = 4y                  (given).

Substitute x =- 4y in the first equation:

4y + y = 90

5y = 90

y = 18.

So  x + 18 = 90

x = 90 - 18

x = 72.

Find f(2) if f(x) = 2x + 1.
A) 3
B) 5
C) 7
D) 9

Answers

Answer:

The answer to your question is letter B

Step-by-step explanation:

Process

1.- Write the equation

                                   f(x) = 2x + 1

find f(2)

2.- Substitute x for 2

                                  f(2) = 2(2) + 1

3.- Simplify

                                 f(2) = 4 + 1

                                 f(2) = 5

Answer:

5

Step-by-step explanation:

2(2) + 1 = 5

1/4 + 1/8= I know it should be easy but my teacher told me that we can't add fractions if they have different denominators. Now if you are going to explain the to me I am in 5th grade so please don't make it to complicated.Thank you.

Answers

1/4 + 1/8= 3/8
Remember you need a common denominator so 4*2 is 8 and you multiply the numerator by 2 to get 2/8. Which makes the problem 2/8+1/8=3/8
Alright, this is my first question I’ve answered so excuse me.

When adding fractions, it’s easier to ask yourself how you can get the denominators to be the same. In this case, 1/4 can also be 2/8, if we multiply 1/4 by 2/2. 1x2 is 2 and 4x2 is 8. 1/4 and 2/8 are the same because 2/2 can also be written as 1, and 1 times anything gives the same answer.

Now we have 1/8 + 2/8, which would be 3/8.

I hope this answer helps! :)
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