A ice cream shop sells 8 different flavors of ice cream with A choice of three different styles of calls how many different ice cream cones are possible if you select one ice cream flavor with one type of ice cream cone

Answers

Answer 1
Answer:   24

Explanation:

There are 8 different flavors and 3 types of cones. This means there are 8*3 = 24 different combos possible.

Imagine a table with 8 rows and 3 columns. Each row is a different flavor and each column is a different cone type. The table formed has 24 inner cells to represent a different combination of flavor + cone type. So that's why we multiplied those values earlier.

Note: This only works if you're only able to select one type of flavor.


Related Questions

Find the volume (in cubic yards) of a cylinder with radius 1.2 yards and height 2.9 yards. (Round your answer to one decimal place.)

Answers

Answer:

11.8 yd³

Step-by-step explanation:

It has a time to failure distribution which is normal with a mean of 35,000 vehicle miles and a standard deviation of 7,000 vehicle miles. Find its designed life if a .97 reliability is desired.

Answers

Answer:

The designed life should be of 21,840 vehicle miles.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 35,000 vehicle miles and a standard deviation of 7,000 vehicle miles.

This means that [tex]\mu = 35000, \sigma = 7000[/tex]

Find its designed life if a .97 reliability is desired.

The designed life should be the 100 - 97 = 3rd percentile(we want only 3% of the vehicles to fail within this time), which is X when Z has a p-value of 0.03, so X when Z = -1.88.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.88 = \frac{X - 35000}{7000}[/tex]

[tex]X - 35000 = -1.88*7000[/tex]

[tex]X = 21840[/tex]

The designed life should be of 21,840 vehicle miles.

2. The prices, in dollars per unit, of the three commodities X, Y and Z are x, y and z,
respectively
Person A purchases 4 units of Z and sells 3 units of X and 3 units of Y.
Person B purchases 3 units of Y and sells 2 units of X and 1 unit of Z.
Person C purchases 1 unit of X and sells 4 units of Y and 6 units of Z.
In the process, A, B and C earn $40, $50, and $130, respectively.

a) Find the prices of the commodities X, Y, and Z by solving a system of linear
equations (note that selling the units is positive earning and buying the units is
negative earning).​

Answers

Answer:

Price of X is $24.81

Price of Y is $3.66

Price of Z is $11.36

Step-by-step explanation:

for person A, we know that earns $40, then we can write the equation:

-4*z + 3*x + 3*y = $40

For person B, we know that earns $50, then:

1*z + 2*x - 3*y = $50

For person C, we know that earns $130, then:

6*z - 1*x + 4*y = $130

Then we have a system of equations:

-4*z + 3*x + 3*y = $40

1*z + 2*x - 3*y = $50

6*z - 1*x + 4*y = $130

To solve the system, we need to isolate one of the variables in one of the equations.

Let's isolate z in the second equation:

z = $50 - 2*x + 3*y

now we can replace this in the other two equations:

-4*z + 3*x + 3*y = $40

6*z - 1*x + 4*y = $130

So we get:

-4*($50 - 2*x + 3*y) + 3*x + 3*y = $40

6*($50 - 2*x + 3*y) - 1*x + 4*y = $130

Now we need to simplify both of these, so we get:

-$200 + 11x - 9y = $40

$350 - 13*x + 28*y = $130

Now again, we need to isolate one of the variables in one of the equations.

Let's isolate x in the first one:

-$200 + 11x - 9y = $40

11x - 9y = $40 + $200 = $240

11x = $240 + 9y

x = ($240 + 9y)/11

Now we can replace this in the other equation:

$350 - 13*x + 28*y = $130

$350 - 13*($240 + 9y)/11 + 28*y = $130

Now we can solve this for y.

- 13*($240 + 9y)/11 + 28*y  = $130 - $350 = -$220

-13*$240  - (13/11)*9y + 28y = - $220

y*(28 - (9*13/1) ) = -$220 + (13/11)*$240

y = ( (13/11)*$240 - $220)/(28 - (9*13/1) ) = $3.66

We know that:

x = ($240 + 9y)/11

Replacing the value of y, we get:

x = ($240 + 9*$3.66)/11  = $24.81

And the equation of z is:

z = $50 - 2*x + 3*y = $50 - 2* $24.81 + 3*$3.66 = $11.36

Then:

Price of X is $24.81

Price of Y is $3.66

Price of Z is $11.36

Which proportion resulted in the equation 3a = 7b?

StartFraction 3 over a EndFraction = StartFraction 7 over b EndFraction
StartFraction 3 over b EndFraction = StartFraction 7 over a EndFraction
StartFraction a over b EndFraction = StartFraction 3 over 7 EndFraction
StartFraction 3 over 7 EndFraction = StartFraction 3 over b EndFraction

Answers

Answer:

The correct one is 3 over b equals 7 over a

Answer:

3/b = 7/a

Step-by-step explanation:

I took it on Edge

Seth and Ted can paint a room in 5 hours if they work together. If Ted were to work by himself, it would take him 2 hours longer than it would take Seth working by himself. How long would it take Seth to paint the room by himself if Ted calls in sick?

Answers

Answer:

9 hours

Step-by-step explanation:

Let

x = number of hours it would take Seth to work by himself

He would paint 1/x in 1 hour

x + 2 = number of hours it would take Ted to work by himself

He would paint 1/(x + 2) in 1 hour

Seth and Ted = 5 hours

They would paint 1/5 in 1 hour

The equation is this:

1/x + 1/(x + 2) = 1/5

(x + 2)+x/x(x+2) = 1/5

x+2+x / x(x+2) = 1/5

2x + 2 / x(x+2) = 1/5

2x + 2 = x(x + 2)1/5

2x + 2 = (x² + 2x)1/5

5(2x + 2) = x² + 2x

10x + 10 = x² + 2x

x² + 2x - 10x - 10 = 0

x² - 8x - 10 = 0

x = -b ± √b² - 4ac/2a

= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)

= 8 ± √64 - (-40) / 2

= 8 ± √64 + 40) / 2

= 8 ± √104 / 2

= 8 ± 2√26 / 2

= 8/2 ± 2√26/2

= 4 ± √26

= 4 ± 5.0990195135927

= 4 + 5.0990195135927 or 4 - 5.0990195135927

= 9.0990195135927 or -1.Answer:

Step-by-step explanation:

Let

x = number of hours it would take Seth to work by himself

He would paint 1/x in 1 hour

x + 2 = number of hours it would take Ted to work by himself

He would paint 1/(x + 2) in 1 hour

Seth and Ted = 5 hours

They would paint 1/5 in 1 hour

The equation is this:

1/x + 1/(x + 2) = 1/5

(x + 2)+x / x(x+2) = 1/5

x+2+x / x(x+2) = 1/5

2x + 2 / x(x+2) = 1/5

Cross product

2x + 2 = x(x + 2)1/5

2x + 2 = (x² + 2x)1/5

Cross product

5(2x + 2) = x² + 2x

10x + 10 = x² + 2x

x² + 2x - 10x - 10 = 0

x² - 8x - 10 = 0

x = -b ± √b² - 4ac/2a

= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)

= 8 ± √64 - (-40) / 2

= 8 ± √64 + 40) / 2

= 8 ± √104 / 2

= 8 ± 2√26 / 2

= 8/2 ± 2√26/2

= 4 ± √26

= 4 ± 5.0990195135927

= 4 + 5.0990195135927 or 4 - 5.0990195135927

= 9.0990195135927 or -1.0990195135927

Approximately,

x = 9 hours or -1 hour

It can't take Seth negative hours to work

Therefore,

x = number of hours it would take Seth to work by himself = 9 hours

Marla scored 70% on her last unit exam in her statistics class. When Marla took the SAT exam, she scored at the 70th percentile in mathematics. Explain the difference in these two scores.

Answers

Answer:

The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.

Step-by-step explanation:

Marla scored 70% on her last unit exam in her statistics class.

This means that in her statistics class, Marla got 70% of her test correct.

When Marla took the SAT exam, she scored at the 70th percentile in mathematics.

This means that on the SAT exam, graded on a curve, Marla scored better than 70% of the students.

Explain the difference in these two scores.

The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.

PLEASE HELP WILL MARK BRAINLIEST!

Answers

9514 1404 393

Answer:

  7.5

Step-by-step explanation:

Corresponding sides are proportional, so ...

  UV/VW = LM/MN

  x/6 = 15/12

  x = 6(15/12) = 15/2

  x = 7.5

Your EZ Pass account begins with $80. It costs you $4/day. Write an equation
for the amount in your account (A) in terms of the number of days (D).

Answers

Answer:

The equation is [tex]A(d) = 80 - 4d[/tex]

Step-by-step explanation:

Linear function:

A linear function for the amount of money in an account after t days is given by:

[tex]A(d) = A(0) - md[/tex]

In which A(0) is the initial value and m is the daily cost.

Your EZ Pass account begins with $80. It costs you $4/day.

This means that [tex]A(0) = 80, m = 4[/tex]

So

[tex]A(d) = A(0) - md[/tex]

[tex]A(d) = 80 - 4d[/tex]

La señora Alcántara realiza una compra en el supermercado fortuna, ella solo tiene 12,400 pesos ,compra varios artículos y su compra es equivalente a 13,600 pesos. ¿Cuánto tiene que pagar si le realizan un descuento de un 15%? ¿Cuántos le quedaron de lo que tenía en efectivo?

Answers

Answer:

She spent = 11560 pesos

Amount left = 840 pesos

Step-by-step explanation:

Mrs. Alcántara makes a purchase at the fortuna supermarket, she only has 12,400 pesos, she buys several items and her purchase is equivalent to 13,600 pesos. How much do you have to pay if they give you a 15% discount? How many was left of what he had in cash?

Amount she has = 12400pesos

Item purchased = 13600 pesos

discount = 15 %

So, the total discount on the item purchased is

= 15 % of 13600

= 0.15 x 13600

= 2040 pesos

So, the amount spent = 13600 - 2040 = 11560 pesos

Amount she left = 12400 - 11560 = 840 pesos

The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y -4 = %(x -8). What is
the slope-intercept form of the equation for this line?
O y = ÷x-12
O y= x-4
O y= =x+2
O y= =x +6

Answers

Answer:

y= x-4

Step-by-step explanation:

what is the range of the funcion y=x^2

Answers

Answer:

Range = [0, infinity)

Step-by-step explanation:

Minimum point of the graph is at (0,0) and it is a u shaped graph. Hence, range is 0 inclusive to infinity

The range of the function y = x2 is all real numbers, y, such that y ≥ 0. In the case of the function y = x2, the domain consists of all real

2.6.58
The lot in the figure shown, except for the house, shed, and driveway, is lawn. One bag of lawn fertilizer
costs $15.00 and covers 3,000 square feet.


Please help :)

Answers

Answer:

50 bags ;

£750

Step-by-step explanation:

The dimension of the rectangular lawn is 500ft by 300 ft

The area of the lawn an e obtained thus :

Area of rectangle = Length * width

Area of rectangle = 500 ft * 300 ft

Area of rectangle = 150000 feets

1 bag of fertilizer covers 3000 feets

The minimum bags of fertilizer required :

Area of rectangle / Area covered by 1 bag of fertilizer

Minimum bags of fertilizer required :

(150,000 / 3000) = 50 bags

50 bags of fertilizer

Cost per bag = 15

Total cost = 15 * 50 = £750

If the current through a circuit is 2 A and the resistance of a light bulb in the circuit is 10 Ohms what is tge voltage difference across the light bulb ​

Answers

Answer:

v = ir

2 times 10 = 20v

Step-by-step explanation:

i think it is the one

A ball is thrown vertically upward with an initial velocity of 19 m/s. Its height, h(t)metres after t seconds, is given by the equation h(t) = -3t2 + 20t + 2.0.

The time taken by the ball to reach the maximum height is ________ seconds. Round your answer to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

There are 2 different ways to do this: calculus and by completing the square. In this particular instance, calculus is WAY easier, and since I don't know for what class you are doing this, I'll do both ways. First the calculus way. We know the position equation, and the first derivative of the position is velocity. We also know that when the velocity is equal to 0 is when the object is at its max height. So we'll find the derivative first, then solve it for t:

If [tex]s(t)=-3t^2+20t+2[/tex] then the first derivative is

v(t) = -6t + 20 Solving for t requires that we set the velocity equal to 0 (again, this is where the object is at its max height), so

0 = -6t + 20 and

-20 = -6t so

t = 3.3 seconds. Now that we know that at 3.3 seconds the object is at its highest point, we sub that time into the position function to see where it is at that time:

s(3.3) = [tex]-3(3.3)^2+20(3.3)+2[/tex] and

s(3.3) = 35.3 meters.

Now onto the more difficult way...completing the square. Begin by setting the position function equal to 0 and then move over the constant to get:

[tex]-3t^2+20t=-2[/tex] Since the leading coefficient is not a 1 (it's a 3), we have to factor out the 3, leaving us with:

[tex]-3(t^2-\frac{20}{3}t)=-2[/tex] Now the rule is to take half the linear term, square it, and add it to both sides. Our linear term is [tex]\frac{20}{3}[/tex] and half of that is [tex]\frac{20}{6}[/tex]. Squaring that:

[tex](\frac{20}{6})^2=\frac{400}{36}=\frac{100}{9}[/tex]. We will add that in to both sides. On the left it's easy, but on the right we have to take into account that we still have that -3 sitting out front, refusing to be ignored. So we have to multiply it in when we add it to the right. Doing that gives us:

[tex]-3(t^2-\frac{20}{3}t+\frac{100}{9})=-2-\frac{100}{3}[/tex] We will clean this up a bit now. The reason we do this is because on the left we have created a perfect square binomial which will give us the time we are looking for to answer this question. Simplifying the right and at the same time writing the perfect square binomial  gives us:

[tex]-3(t-\frac{20}{6})^2=-\frac{106}{3}[/tex] Now the last step is to move the constant back over and set the quadratic back equal to y:

[tex]y=-3(t-\frac{20}{6})^2+\frac{106}{3}[/tex].  The vertex of this quadratic is

[tex](\frac{20}{6},\frac{106}{3})[/tex] where

[tex]\frac{20}{6}=3.3[/tex] as the time it takes for the ball to reach its max height of

[tex]\frac{106}{3}=35.3[/tex] meters.

I'd say if you plan on taking calculus cuz you're not there yet, you'll see that many of these types of problems become much simpler when you know it!

In any triangle ABC,Prove by vector method c^2=a^2+b^2-2abcosC​

Answers

Answer:

Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:

[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]

[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]

[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]

[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]

[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]

Step-by-step explanation:

Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:

[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]

[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]

[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]

[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]

[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]

Determine the value of z in the figure
5z
130°

A.Z = 30°
B.Z = 45°
C.z = 50°
D.Z = 10°

Answers

Hi!

180° - 130° = 50°

5z = 50° || : 5

z = 10°

Answer:

10

Step-by-step explanation:

since 130 and the 5z are complementary angles, by subtracting 130 from 180, you get 50. then you equal in 50 to 5z. 50=5z. to solve, you divide 5 from 50 and your answer is 10.

40 points! Need help finding.

Answers

The cordent plan of the answer is 2

Answer:

The scale factor will just be 2

Step-by-step explanation:

The length of PQ is twice as larger than the length of AB.

so from 12 to 6 or 6 to 12, we multiply 6 by 2 which equals to 12

A Line passes through the .4 -6 and has a slope of -3 and four which is the equation of the line

Answers

Answer:

(in the image)

Step-by-step explanation:

I'm not sure I understood your question completely but I hope this helps.

xp-q+1×xq-r+1×xr-p+1​

Answers

Answer:

Look into the picture

Step-by-step explanation:

Let me know if there's something wrong to my answer

I’m not quite sure but if u can press thanks it would mean a lot because I need help with mine and I don’t know

math help plz
how to divide polynomials, how to understand and step by step with an example provided please

Answers

Answer:

hiiiiiii....!!! how r u

What type of line is PQ⎯⎯⎯⎯⎯⎯⎯⎯?

Answers

Answer:

median

Step-by-step explanation:

Q is at the midpoint of RS and so PQ is a median

A median is a segment from a vertex to the midpoint of the opposite side.

We want to define what type of line is PQ (the line that passes through points P and Q) by looking at the given image, one can easily see that the line PQ is a median, now let's explain why.

First, let's analyze the image:

In the image, we can see that P is one vertex of the triangle, and Q is the midpoint of the segment RS (you can see that RQ = 4 and QS = 4) , where R and S are the other two vertexes of the triangle.

Particularly, we can define a median of a triangle as the line that passes through the midpoint of one side of the triangle and by the vertex that does not belong to that side.

With that definition, we can see that PQ is a median because Q is the midpoint of one side of the triangle and P is the vertex that does not belong to that side.

If you want to learn more, you can read:

https://brainly.com/question/2272632

The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests negative, given that he or she did not have the disease.
The individual actually had the disease
Yes No
Positive 135 11
Negative 99 145

Answers

Answer:

0.9295 = 92.95% probability of getting someone who tests negative, given that he or she did not have the disease.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

11 + 145 = 156 people did not have the disease.

Out of those, 145 tested positive. So

[tex]p = \frac{145}{156} = 0.9295[/tex]

0.9295 = 92.95% probability of getting someone who tests negative, given that he or she did not have the disease.

1. You measure 24 textbooks' weights, and find they have a mean weight of 75 ounces. Assume the population standard deviation is 3.3 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.
2. You measure 37 backpacks' weights, and find they have a mean weight of 45 ounces. Assume the population standard deviation is 10.1 ounces. Based on this, construct a 95% confidence interval for the true population mean backpack weight.
3. You measure 30 watermelons' weights, and find they have a mean weight of 37 ounces. Assume the population standard deviation is 4.1 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight.
4. A student was asked to find a 99% confidence interval for widget width using data from a random sample of size n = 16. Which of the following is a correct interpretation of the interval 11.8 < μ < 20.4?
A. There is a 99% chance that the mean of a sample of 16 widgets will be between 11.8 and 20.4.
B. The mean width of all widgets is between 11.8 and 20.4, 99% of the time. We know this is true because the mean of our sample is between 11.8 and 20.4.
C. With 99% confidence, the mean width of all widgets is between 11.8 and 20.4.
D. With 99% confidence, the mean width of a randomly selected widget will be between 11.8 and 20.4.
E. There is a 99% chance that the mean of the population is between 11.8 and 20.4.
5. For a confidence level of 90% with a sample size of 23, find the critical t value.

Answers

Answer:

(73.845 ; 76.155) ;

(41.633 ; 48.367) ;

1.273 ;

C. With 99% confidence, the mean width of all widgets is between 11.8 and 20.4. ;

1.717

Step-by-step explanation:

1.)

Given :

Mean, xbar = 75

Sample size, n = 24

Sample standard deviation, s = 3.3

α = 90%

Confidence interval = mean ± margin of error

Margin of Error = Tcritical * s/√n

Tcritical at 90% ; df = 24 - 1 = 23

Tcritical = 1.714

Margin of Error = 1.714 * 3.3/√24 = 1.155

Confidence interval = 75 ± 1.155

Confidence interval = (73.845 ; 76.155)

2.)

Given :

Mean, xbar = 45

Sample size, n = 37

Sample standard deviation, s = 10.1

α = 95%

Confidence interval = mean ± margin of error

Margin of Error = Tcritical * s/√n

Tcritical at 95% ; df = 37 - 1 = 36

Tcritical = 2.028

Margin of Error = 2.028 * 10.1/√37 = 3.367

Confidence interval = 45 ± 3.367

Confidence interval = (41.633 ; 48.367)

3.)

Given :

Mean, xbar = 37

Sample size, n = 30

Sample standard deviation, s = 4.1

α = 90%

Margin of Error = Tcritical * s/√n

Tcritical at 90% ; df = 30 - 1 = 29

Tcritical = 1.700

Margin of Error = 1.700 * 4.1/√30 = 1.273

5.)

Sample size, n = 23

Confidence level, = 90%

df = n - 1 ; 23 - 1 = 22

Tcritical(0.05, 22) = 1.717

What is the solution to the system of equations below

Answers

Answer:

A

Step-by-step explanation:

1/2x-4=-2x-9...u vil get the ans

Find the area of the figure

Please help :)

Answers

9514 1404 393

Answer:

  66.5 cm²

Step-by-step explanation:

A horizontal line at the "knee" on the right will divide the figure into a 4 cm by 2 cm rectangle, and a trapezoid with bases 4 cm and 9 cm, and height 11-2 = 9 cm. Then the total area of the figure is ...

  A = LW + 1/2(b1 +b2)h

  A = (4 cm)(2 cm) + (1/2)(4 cm +9 cm)(9 cm) = 8 cm² +58.5 cm²

  A = 66.5 cm² . . . . area of the figure

Determine the mean and variance of the random variable with the following probability mass function. f(x)=(216/43)(1/6)x, x=1,2,3 Round your answers to three decimal places (e.g. 98.765).

Answers

Mean:

E[X] = ∑ x f(x) = 1 × f (1) + 2 × f (2) + 3 × f (3) = 51/43 ≈ 1.186

Variance:

Recall that for a random variable X, its variance is defined as

Var[X] = E[(X - E[X])²] = E[X ²] - E[X

Now,

E[X ²] = ∑ x ² f(x) = 1² × f (1) + 2² × f (2) + 3² × f (3) = 69/43

Then

Var[X] = 69/43 - (51/43)² = 366/1849 ≈ 0.198

(each sum is taken over x in the set {1, 2, 3})

Assume that $4,000 I deposited into an investment account doubled in value over a six year period. What annual interest rate must I have earned over this period? Is the initial amount of the deposit relevant to the calculation of the annual interest rate? Why or why not?

Answers

Answer:

Interest rate is about 12.246%

The initial deposit doesn't matter because when you divide both sides by the initial deposit you're always left with (1+i)ⁿ=2

Step-by-step explanation:

[tex]4000(1+i)^6=8000\\(1+i)^6=2\\1+i=\sqrt[6]{2} \\1+i=1.122462048\\i=.12246[/tex]

In what ratio of line x-y-2=0 divides the line segment joining (3,-1) and (8,9)?​

Answers

Let the given points ( 3 , -1 ) and ( 8 , 9 ) be A and B respectively. Let A ( 3 , - 1 ) be ( x₁ , y₁ ) and B ( 8 , 9 ) be ( x₂ , y₂ ). Let the point P ( x , y ) divides the line segment of joining points A ( 3 , -1 ) and ( 8 , 9 ) in the ratio m : n. Let m be m₁ and n be m₂ We know that :

[tex] \large{ \tt{❁ \: USING \: INTERNAL \: SECTION \: FORMULA: }}[/tex]

[tex] \large{ \bf{✾ \: P(x \:, y \: ) = ( \frac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}} \: ,\: \frac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}}) }}[/tex]

[tex] \large{ \bf{⟹ \: ( \frac{8m + 3n}{m + n} , \: \frac{9m -n}{m + n}) }}[/tex]

Since point P lies on the line x - y - 2 = 0 ,

[tex] \large{ \bf{ ⟼\frac{8m + 3n}{m + n} - \frac{9m - n}{m + n} - 2 = 0 }}[/tex]

[tex] \large{ \bf{⟼ \: \frac{8m + 3n - 9m + n}{m + n} - 2 = 0 }}[/tex]

[tex] \large{ \bf{⟼ \: \frac{4n - m}{ m + n} - 2 = 0 }}[/tex]

[tex] \large{⟼ \: \bf{ \frac{4n - m}{m + n }} = 2} [/tex]

[tex] \large{ \bf{⟼ \: 4n - m = 2m + 2n}}[/tex]

[tex] \large{ \bf{⟼ \: 4n -2 n = 2m + m}}[/tex]

[tex] \large{ \bf{⟼2n = 3m}}[/tex]

[tex] \large{ \bf{⟼ \: 3m = 2n}}[/tex]

[tex] \large{ \bf{⟼ \: \frac{m}{n} = \frac{2}{3} }}[/tex]

[tex] \boxed{ \large{ \bf{⟼ \: m : \: n = 2: \: }3}}[/tex]

Hence , The required ratio is 2 : 3 .

-Hope I helped! Let me know if you have any questions regarding my answer and also notify me , if you need any other help! :)

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find the value of...​

Answers

Answer:

1

Step-by-step explanation:

tan(1)tan(2)....tan(89)=?

Recall tan(90-x)=cot(x) and cot(x)tan(x)=1.

tan(89)=tan(90-1)=cot(1)

tan(88)=tan(90-2)=cot(2)

tan(87)=tan(90-3)=cot(3)

...

tan(46)=tan(90-44)=cot(44)

tan(45)=tan(90-45)=cot(45)

So we can replace the last half of the factors with cotangent of the angles in the first half.

The only one that doesn't get a partner is the exact middle factor which is tan(45).

So this is whar we have:

tan(1)tan(2)tan(3)....tan(45)....cot(3)cot(2)cot(1)

So you should see that cot(1)tan(1)=1 and cot(2)tan(2)=1 and so on....

So the product equals tan(45) and tan(45)=1 using unit circle.

How Do I do this equation

Answers

Answer:

Part A 12 ≤ 6x ≤ 36

Part B 2 ≤ x ≤ 6

Step-by-step explanation:

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