Lauren drinks a variety of soft drinks. Over the past​ month, she has had 19 diet​ colas, 4 cans of​ lemonade, and 5 cans of root beer. a. Given this​ history, what is the probability that her next drink will be a diet​ cola? Lemonade? Root​ beer? b. What definition of probability should be used to answer this​ question?

Answer:

Value of Henley Inc.'s share is $16.76

Step-by-step explanation:

The present value of the dividends over for the three years and the terminal value of the dividends would give us a fair share price that an investor would pay

Year 1 PV of dividends=$1.10/(1+11%)^1=$0.99  

Year 2 PV of dividends=$1.10/(1+11%)^2=$0.89  

Year 3 PV of dividends=$1.10/(1+11%)^3=$0.80  

The terminal value formula=dividend*(1+g)/(r-g)

g is the dividend growth rate of 5%

r is the investor's required rate of return which is 11%

terminal value=$1.10*(1+5%)/(11%-5%)=$19.25

The terminal is discounted to present value using the discount factor of year 3

PV of terminal value =$19.25 /(1+11%)^3=$ 14.08  

Total present values=$0.99+$0.89+$0.80+$14.08 =$16.76

Answer:

Total distance traveled is 100 miles

Step-by-step explanation:

The man will drive half of the trip on the first day, therefore, distance that will be traveled on the first day = 0.5x

where x is the total distance of the trip.

On the second day, he will drive half of the remaining half of the distance, i.e he will drive 0.5 x 0.5x = 0.25x

This implies that the total distance that will be traveled traveled in the final two days of the journey will also be 0.5 x 0.5x = 0.25x.

0.5x + 0.25x + 0.25x = x, which is the total distance traveled.

on the third day he will drive 4 times the distance of the fourth day, therefore, distance that will be traveled on the third day = 4 x 5 = 20 miles

on the fourth day, he will drive 5 mile.

total of the last two days = 5 + 20 = 25 miles.

this 25 miles is equal to 0.25 of the whole trip. Equating these values, we have

0.25x = 25 miles

x = 25/0.25 = 100 miles

Answer:

[tex]1-7i[/tex]

Step-by-step explanation:

[tex]\left(1+i\right)\left(-3-4i\right)[/tex]

[tex]=\left(1\cdot \left(-3\right)-1\cdot \left(-4\right)\right)+\left(1\cdot \left(-4\right)+1\cdot \left(-3\right)\right)i[/tex]

[tex]1\cdot \left(-3\right)-1\cdot \left(-4\right)[/tex]

[tex]=-3+4[/tex]

[tex]=1[/tex]

[tex]1\cdot \left(-4\right)+1\cdot \left(-3\right)[/tex]

[tex]=-4-3[/tex]

[tex]=-7[/tex]

[tex]=1-7i[/tex]

Answer:

-18root7

Step-by-step explanation:

-3root 84*3

-3root4*7*3*3

-3(2*3)root7

-18root7

Answer:

A symmetric bell shape

Step-by-step explanation:

A normal curve has a symmetrical bell shaped curve, this can be seen when a histogram is constructed with values that are normally distributed, the resulting shape is symmetrical and has a bell shape.

Answer:

x=25[tex]\sqrt{2}[/tex]

Step-by-step explanation:

the hypotenuse is equal to a leg times the square root of 2. which means to find the leg with the hyp given. you take [tex]\frac{50}{\sqrt{2} }[/tex] which then translates to 50 root 2/2=x  therefore 25[tex]\sqrt{2}[/tex]

Answer:

[tex]10.71 yd[/tex]

Step-by-step explanation:

First let's find the radius of the quarter circle.

[tex]area =\frac{1}{4} \pi {r}^{2} \\ 7.065 = \frac{1}{4} *3.14 {r}^{2} \\ \frac{7.065}{3.14} = \frac{1}{4} * \frac{3.14 {r}^{2} }{3.14} \\ 9 = {r}^{2} \\ \sqrt{9} = r \\ 3 yd= r[/tex]

Now let's find the arc length of this quarter circle.

[tex] \frac{90}{360} \times 2\pi \: r \\ \frac{1}{4} \times 2 \times 3.14 \times 3 \\ = \frac{9.42}{4} \\ = 4.71yd \\ [/tex]

Now let's find the perimeter[tex]perimeter \\ = arc \: \: length + radius + radius \\ = 4.71 + 3 + 3 \\ = 10.71yd[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Step-by-step explanation:

The formula of an area of a circle:

[tex]A=\pi r^2[/tex]

r - radius

The formula of an area of a quarter circle:

[tex]A=\dfrac{1}{4}\pi r^2[/tex]

We have the area of a quarter circle:

[tex]A=7.065\ yd^2[/tex]

Substitute to the formula and solve for r :

[tex]\dfrac{1}{4}\pi r^2=7.065[/tex]     multiply both sides by 4

[tex]4\cdot\dfrac{1}{4}\pi r^2=7.065\cdot4\\\\\pi r^2=28.26[/tex]

Use 3.14 for π

[tex]3.14r^2=28.26[/tex]            divide both sides by 3.14

[tex]\dfrac{3.14r^2}{3.14}=\dfrac{28.26}{3.14}\\\\r^2=9\to r=\sqrt9\\\\\boxed{r=3\ yd}[/tex]

The circumference of this figure consists of an arc (quarter of a cirumference of a circle) and two radiuses.

The formula of a circumference of a circle:

[tex]C=2\pi r[/tex]

The formula of a quarter of a cicrumference of a circle:

[tex]L=\dfrac{1}{4}\cdot2\pi r[/tex]

Substitute

[tex]L=\dfrac{1}{4}\cdot2\pi\cdot3=1.5\pi[/tex]

Use 3.14 for π

[tex]L=1.5(3.14)=4.71\ yd[/tex]

The perimeter of a quarter circle:

[tex]P=4.71+2(3)=4.71+6=10.71\ yd[/tex]

Answer:

620

Step-by-step explanation:

The formula to find the sum of the first n terms of an arithmetic sequence is n(a1 + aN)/2, where n is the number of terms,  aN is the last term and a1 is the first term. We do not know the last term, though, so we must find it. The equation for this is an=a1+(n−1)d, where d is the common difference and a1 is the first term, and n is the number of terms. Therefore, the last term, an is, -7+(19)4 = 69.

Finally, we plug it into the first formula, the formula to find the sum, and we get 20*(-7+69)/2, which gives us 620 as our final answer.

Answer:

Step-by-step explanation:

(a) Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent

(b) The required [tex]\lambda[/tex] = 1.7 * 10/5 = 3.4

(c) P(r ≥ 4 | r ≥ 2)

= P(r ≥ 4)/P(r ≥ 2)

= {1 - P(r < 4)}/{1 - P(r < 2)}

For Poisson distribution, P(X = x)

[tex]= \frac{e^{- \lambda} \lambda ^x}{x !}[/tex]

Thus, P(r < 4) = P(r = 0) + P(r = 1) + P(r = 2) + P(r = 3)

= 0.5584

and P(r < 2) = P(r = 0) + P(r = 1) = 0.1468

Thus, P(r ≥ 4 | r ≥ 2) = (1 - 0.5584)/(1 - 0.1468)

= 0.5177

(d) P(r < 6 | r ≥ 3)

= P(3 ≤ r < 6)/P(r ≥ 3)

P(3 ≤ r < 6) = P(r = 3) + P(r = 4) + P(r = 5) = 0.5308

P(r ≥ 3) = 1 - {P(r = 0) + P(r = 1) + P(r = 2)}

= 0.6603

Thus, P(r < 6 | r ≥ 3) = 0.5308/0.6603 = 0.8309

Answer:

About 8.2 cm

Step-by-step explanation:

Assuming that a is one of the legs of this right triangle, then using the Pythagorean Theorem:

[tex]a=\sqrt{15.3^2-12.9^2}\approx 8.2[/tex]

Hope this helps!

Answer:

55.32% probability that a late package was delivered by express delivery service 2

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Late delivery.

Event B: Service 2 was used.

A certain company sends 35% of its overnight mail parcels via express delivery service 1 and the rest by express delivery service 2.

100 - 35 = 65%.

So [tex]P(B) = 0.65[/tex]

Service 2 has a record of 2.0% of packages being delivered late.

This means that [tex]P(A|B) = 0.02[/tex]

Probability of a late delivery.

35% from service 1. Of those, 3% are late.

65% from service 2. Of those, 2% are late.

So

[tex]P(A) = 0.35*0.03 + 0.65*0.02 = 0.0235[/tex]

What is the probability that a late package was delivered by express delivery service 2

[tex]P(B|A) = \frac{0.65*0.02}{0.0235} = 0.5532[/tex]

55.32% probability that a late package was delivered by express delivery service 2

Answer:

850

Step-by-step explanation:

Current profit per year = $ 20

Number of subscribers = 3000

For each additional subscriber over 3000, the profit will increase by 1 cent or by $ 0.01. For example, for 3001 (3000 + 1) subscribers, the profit will be $ 20.01 per year. Similarly, for 3002 (3000 + 2) subscribers, the profit will be $20.02 per year and so on.

So, for x additional subscribers over 3000, the profit will increase by 0.01(x). i.e. for (3000 + x) subscribers, the profit will be $(20 + 0.01x)

Since, profit per each subscriber is $(20 + 0.01x), the profit for (3000 + x) subscribers will be:

Total profit = Number of subscribers x Profit per each subscriber

Total profit = (3000 + x)(20 + 0.01x)

We want to calculate how many subscribers will be needed to bring a profit of $109,725. So, we replace Total profit by $109,725. The equation now becomes:

Using quadratic formula, we can solve this equation as:

x = -5850 is not a possible solution as this would make the total number of subscribers to be negative. So we reject this value.

Therefore, the answer to this question is 850. 850 more subscribers are needed to being a total profit of $109,725

Answer:

  a) $115,840.97

  b) $306,000

  c) $190,159.03

Step-by-step explanation:

Loan payment calculations can be done using the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where A is the monthly payment, P is the principal value of the loan, r is the annual interest rate, and t is the loan duration in years.

The principal amount of the loan can be found by filling in the given values and solving for P.

  850 = P(0.08/12)/(1 -(1 +0.08/12)^(-12·30))

  P = 850(1 -1.0066667^-360)/0.0066667 ≈ 850×136.283494

  P = 115,840.97

You could afford a loan of $115,840.97.

The total amount paid is the sum of 360 payments of $850 each:

  360 × $850 = $306,000

You will pay $306,000 to the loan company.

The amount of interest is the difference between the amount paid and the amount borrowed:

  $306,000 -115,840.97 = $190,159.03

$190,159.03 of the amount paid is interest.

__

Additional comment

A variety of apps, calculators, and spreadsheets can do these calculations for you. The result from one of these calculators is attached. The PV is the Present Value of the series of 360 payments of $850 each. It is the loan amount.

Answer:

a) zw = 8 (Cos 40° + i Sin 40°)

b) (z/w) = 2 (Cos 260° + i Sin 260°)

Step-by-step explanation:

z = 4(Cos 150° + i Sin 150°)

w = 2 (Cos 250° + i Sin 250°)

To first simplify,

Cos 150° = -0.8660

Sin 150° = 0.50

Cos 250° = -0.3420

Sin 250° = -0.9397

z = 4(Cos 150° + i Sin 150°)

z = 4 (-0.866 + 0.5i)

z = (-3.464 + 2i)

w = 2 (Cos 250° + i Sin 250°)

w = 2 (-0.342 -0.9397i)

w = (-0.684 - 1.8794i)

a) zw = (-3.464 + 2i) (-0.684 - 1.8794i)

zw = 2.369376 + 6.5102416i - 1.368i - 3.7588i²

Note that i² = -1

zw = 2.369376 + 5.1422416i + 3.7588

zw = (6.128176 + 5.1422416i)

A general complex number z = x + it has the Polar form = r (cos θ + i sin θ)

r = √(x² + y²)

θ = arctan (y/x)

zw = (6.128176 + 5.1422416i)

x = 6.128176

y = 5.1422416

r = √(6.128176² + 5.1422416²) = 7.99997 = 8

θ = arctan (5.1422416/6.128176) = 40°

zw = 8 (Cos 40° + i Sin 40°)

b) (z/w) = (-3.464 + 2i) / (-0.684 - 1.8794i)

To simplify This, we first rationalize, that is, multiply numerator and denominator by (-0.684 + 1.8794i)

(z/w) = [(-3.464 + 2i)×(-0.684 + 1.8794i)] ÷ [((-0.684 - 1.8794i)×((-0.684 + 1.8794i)

(z/w) = [2.369376 - 6.5102416i - 1.368i + 3.7588i²] ÷ [0.467856 - 3.53214436i²]

Note that i² = -1

(z/w) = [2.369376 - 3.7588 - 7.8782416i] ÷ [0.467856 + 3.53214436]

(z/w) = (-1.389424 - 7.8782416i)/4

(z/w) = (-0.347356 - 1.9695604i)

x = -0.347356

y = -1.9695604

r = √[(-0.347356)² + (-1.9695604)²] = 1.9997 = 2

θ = arctan (-1.9695604)/(-0.347356) = 80° on the first quadrant, but the signs on x and y indicates that this is the third quadrant, hence

θ = 180° + 80° = 260°

(z/w) = 2 (Cos 260° + i Sin 260°)

Hope this Helps!!!

Answer:

  15 litres

Step-by-step explanation:

  (1/2 litre/day)(30 days) = 15 litres

__

Multiply rate by time to get quantity.

Answer:

  23,325 ft, about 4.42 miles

Step-by-step explanation:

The geometry of the situation can be modeled by a right triangle, where the side adjacent to the 2.7° angle of climb is the horizontal distance, and the side opposite is the vertical change in altitude. That change is ...

  5600 ft -4500 ft = 1100 ft

and the angle relation is ...

  tan(2.7°) = opposite/adjacent = (1100 ft)/(horizontal distance)

Multiplying this equation by (horizontal distance)/tan(2.7°) gives ...

   horizontal distance = (1100 ft)/tan(2.7°) ≈ 23,325 ft

Dividing this by 5280 ft/mi gives ...

  horizontal distance ≈ 4.42 mi

The airplane travels about 23,325 ft, or 4.42 miles, horizontally as it climbs.

Answer:

a) Mean blood pressure for people in China.

b) 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c) 71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d) 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e) Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg

f) 157.44mmHg

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

If X is two standard deviations from the mean or more, it is considered unusual.

In this question:

[tex]\mu = 128, \sigma = 23[/tex]

a.) State the random variable.

Mean blood pressure for people in China.

b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.

This is 1 subtracted by the pvalue of Z when X = 135.

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

[tex]Z = \frac{135 - 128}{23}[/tex]

[tex]Z = 0.3[/tex]

[tex]Z = 0.3[/tex] has a pvalue of 0.6179

1 - 0.6179 = 0.3821

38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.

This is the pvalue of Z when X = 141.

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

[tex]Z = \frac{141 - 128}{23}[/tex]

[tex]Z = 0.565[/tex]

[tex]Z = 0.565[/tex] has a pvalue of 0.7140

71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d.)Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

This is the pvalue of Z when X = 125 subtracted by the pvalue of Z when X = 120. So

X = 125

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

[tex]Z = \frac{125 - 128}{23}[/tex]

[tex]Z = -0.13[/tex]

[tex]Z = -0.13[/tex] has a pvalue of 0.4483

X = 120

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

[tex]Z = \frac{120 - 128}{23}[/tex]

[tex]Z = -0.35[/tex]

[tex]Z = -0.35[/tex] has a pvalue of 0.3632

0.4483 - 0.3632 = 0.0851

8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?

From b), when X = 135, Z = 0.3

Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f.) What blood pressure do 90% of all people in China have less than?

This is the 90th percentile, which is X when Z has a pvalue of 0.28. So X when Z = 1.28. Then

X = 120

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

[tex]1.28 = \frac{X - 128}{23}[/tex]

[tex]X - 128 = 1.28*23[/tex]

[tex]X = 157.44[/tex]

So

157.44mmHg

Answer:

x = 24

Step-by-step explanation:

Of means multiply and is means equals

1/4 * x = 6

Multiply each side by 4

1/4*4 x = 6*4

x = 24

Answer:

idk

Step-by-step explanation:

Answer:

The object hits the ground 5 seconds after being launched.

Step-by-step explanation:

The height of the object in t seconds after being launched is given by the following equation:

[tex]h(t) = 80t - 16t^{2}[/tex]

When will the object hit the ground after it is launched?

This is t for which h(t) = 0.

So

[tex]80t - 16t^{2} = 0[/tex]

[tex]16t(5 - t) = 0[/tex]

Then

[tex]16t = 0[/tex]

[tex]t = 0[/tex]

This is the launch point

[tex]5 - t = 0[/tex]

[tex]t = 5[/tex]

So

The object hits the ground 5 seconds after being launched.

Answer:

The object will hit the ground after 5 seconds. You can rewrite the quadratic function as a quadratic equation set equal to zero to find the zeros of the function 0 = –16t2 + 80t + 0. You can factor or use the quadratic formula to get t = 0 and t = 5. Therefore, it is on the ground at t = 0 (time of launch) and then hits the ground at t = 5 seconds.

Step-by-step explanation:

This is the exact answer on edg 2020

Answer:

40m

Step-by-step explanation:

5.25 divided by 1.75=3

120 divided by 3=40

Answer:

131,200 units

Step-by-step explanation:

The number of units transferred to Department 2 from Department 1 is the total units to be accounted for  which is 180,200 units minus the ending work in process of 49,000 units.

The logic here is that Department 1 is to account for 180,200 units ,part of which is the ending working process while the remainder which was transferred out is the difference between the two figures

units transferred to Department 2=180,200-49,000= 131,200.00  units

Answer:

Suppose that a white ball is selected, the probability that the coin landed tails = (12/37) = 0.3243

Step-by-step explanation:

Complete Question

Urn A has 5 white and 7 black balls. Urn B has 3 white and 12 black balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?

Solution

Let the probability of that a head turns up and urn A is selcted be P(A) = (1/2)

Probability that a tail turns up and urn B is selected = P(B) = (1/2)

Probability that a white ball is picked = P(W)

The probability that a white ball is picked given that the coin toss gives a head and urn A is selected = P(W|A) = (5/12)

The probability that a white ball is picked given that the coin toss gives a tail and urn B is selected = P(W|B) = (3/15) = (1/5)

We now require the probability that the coin lands on a tail and urn B is selected given that a white ball is picked, P(B|W)

Note that the conditional probability P(X|Y) is expressed mathematically as

P(X|Y) = P(X n Y) ÷ P(Y)

And P(X n Y) = P(X|Y) × P(Y)

Hence, the required probability

P(B|W) = P(B n W) ÷ P(W)

Although, we do not have the probabilities P(B n W) and P(W), we can calculate them

P(B n W) = P(W n B) = P(W|B) × P(B) = (1/5) × (1/2) = (1/10)

P(W) = P(W n A) + P(W n B) (Since the events A and B are mutually exclusive)

P(W n A) = P(W|A) × P(A) = (5/12) × (1/2) = (5/24)

P(W n B) = (1/10)

P(W) = (5/24) + (1/10) = (37/120)

P(B|W) = P(B n W) ÷ P(W) = (1/10) ÷ (37/120) = (12/37) = 0.3243

Hope this Helps!!!

Answer:

Approximately 28 times

Step-by-step explanation:

The tires are circular in shape.

We first need to find the circumference of the tire and then divide the length of the road by that circumference.

The circumference of a circle is given as:

C = πD

where D = diameter

The diameter of the tires is 1.7 m. Its circumference is therefore:

C = π * 1.7 = 5.34 m

Therefore, the number of times that the tire has to turn in traveling the length of the street is:

149 / 5.34 = 27.9 ≅ 28

Answer:

The answer is commutative and associative.

Step-by-step explanation:

Answer:

17.7

Step-by-step explanation:

62.3-7=55.3

55.3-19.9=35.4

35.4/2 = 17.7

brainliest pzz

Answer:

The value of s is 17.7mm.

Step-by-step explanation:

Given that perimeter of a shape happens when all sides are add up together. So for this question :

[tex]perimeter = 7 + 19.9 + s + s[/tex]

[tex]perimeter = 26.9 + 2s[/tex]

Let perimeter = 62.3mm,

[tex]62.3 = 26.9 + 2s[/tex]

[tex]2s = 62.3 - 26.9[/tex]

[tex]2s = 35.4[/tex]

[tex]s = 35.4 \div 2[/tex]

[tex]s = 17.7mm[/tex]

Answer:

2

Step-by-step explanation:

g(1) = 1² + 1 = 2

Step-by-step explanation:

it is 2

Answer:

(a). 72.9%.

(b). 13.6 hr.

Step-by-step explanation:

So, we are given the following data or parameters or information which is going to assist us in solving this question/problem;

=> "A welder produces 7 welded assemblies during the first day on a new job, and the seventh assembly takes 45 minutes (unit time). "

=> The worker produces 10 welded assemblies on the second day, and the 10th assembly on the second day takes 30 minutes"

So, we will be making use of the Crawford learning curve model.

T(7) + 10 = T (17) = 30 min.

T(7) = T1(7)^b = 45.

T(17 ) = T1(17)^b = 30.

(T1) = 45/7^b = 30/17^b.

45/30 = 7^b/17^b = (7/17)^b.

1.5 = (0.41177)^b.

ln 1.5 = b ln 0.41177.

0.40547 = -0.8873 b.

b = - 0.45696.

=> 2^ -0.45696 = 0.7285.

= 72.9%.

(b). T1= 45/7^ - 045696 = 109.5 hr.

V(TT)(17) = 109.5 {(17.51^ - 0.45696 – 0.51^ - 0.45696) / (1 - 0.45696)} .

V(TT) (17) = 109.5 {(4.7317 - 0.6863) / 0.54304} .

= 815.7 min .

= 13.595 hr.