Simon claims that Plant B will be taller than Plant A in 6 weeks because it has the greater initial value. Is he correct?

Answer:

EX=-$1

Step-by-step explanation:

Expected Value of Probability Distribution

Assume a discrete probability distribution is

[tex]P=\{p1,p2,p3,...pn\}[/tex]

For

[tex]X=\{x1,x2,x3,...xn\}[/tex]

The expected value is

[tex]EX=\sum x_i.p_i[/tex]

We have two possible outcomes from our random experience: The sum of the die is 7 or different from 7. If it sums 7, the player wins $9, otherwise, they lose $3. Thus

[tex]x=\{9,-3\}[/tex]

We must find the probability of having a 7. Each dice can be a 1, 2, 3 ,4 , 5, or 6. The combinations to sum 7 are 1+6, 2+5, 3+4, 4+4, 5+2, and 6+1. That is 6 possibilities out of 36 in total. The probability of having a 7 is

[tex]\displaystyle p_1=\frac{6}{36}=\frac{1}{6}[/tex]

The probability of not getting 7 is the negation of the previous event

[tex]\displaystyle p_2=1-\frac{1}{6}=\frac{5}{6}[/tex]

The probability set is:

[tex]\displaystyle P=\left\{\frac{1}{6},\frac{5}{6}\right\}[/tex]

The expected value is:

[tex]\displaystyle EX=9\cdot \frac{1}{6}-3\cdot \frac{5}{6}[/tex]

[tex]\displaystyle EX=\frac{3}{2}-\frac{5}{2}=-1[/tex]

Therefore, the player can expect to lose $1

The expected value of the game "Under-or-Over-Seven" is a loss of $1, computed by considering the probabilities of winning $9 or losing $3 based on dice sums.

To compute the expected value of the game, we need to consider all possible outcomes and their associated probabilities.

1. The sum of two fair dice can range from 2 to 12.

2. The probability of each sum can be calculated by considering all possible combinations of the dice.

Here's the breakdown of the sums and their probabilities:

- Sum of 2: Probability = 1/36

- Sum of 3: Probability = 2/36

- Sum of 4: Probability = 3/36

- Sum of 5: Probability = 4/36

- Sum of 6: Probability = 5/36

- Sum of 7: Probability = 6/36

- Sum of 8: Probability = 5/36

- Sum of 9: Probability = 4/36

- Sum of 10: Probability = 3/36

- Sum of 11: Probability = 2/36

- Sum of 12: Probability = 1/36

Now, let's calculate the expected value:

[tex]\[ E(X) = (P(X=7) \times \$9) + (P(X\neq7) \times (-\$3)) \][/tex]

[tex]\[ E(X) = (\frac{6}{36} \times \$9) + (\frac{30}{36} \times (-\$3)) \][/tex]

[tex]\[ E(X) = (\frac{6}{36} \times \$9) - (\frac{30}{36} \times \$3) \][/tex]

[tex]\[ E(X) = \frac{54}{36} - \frac{90}{36} \][/tex]

[tex]\[ E(X) = \frac{-36}{36} \][/tex]

E(X) = -$1

So, the expected value of the game is a loss of $1.

The plane would travel approximately 4533.33 miles in 6 hours.

To find the distance the plane would travel in 6 hours, we can use the formula:

Distance = Speed × Time

Given that the plane travels at 3400 miles in 8 hours, we can substitute the values into the formula:

Distance = 3400 × 8/6

Simplifying the expression:

Distance = 4533.33 miles

Therefore, the plane would travel approximately 4533.33 miles in 6 hours.

Final answer:

To simplify √72 by removing all perfect squares, you factor 72 into 2³ × 3², then take out the square root of 4 and 9 to get 6√(2) as the simplified result.

Explanation:

To simplify the square root of 72 and remove all perfect squares from inside the square root, you first need to factor 72 into its prime factors. The prime factorization of 72 is 2³ × 3². This can be rewritten as (2² × 3²) × 2, which simplifies to (4 × 9) × 2.

Since the square root of 4 and 9 are perfect squares, you can take them out of the square root, resulting in √(4) × √(9) × √(2) = 2 × 3 × √(2) = 6√(2).

Therefore, the simplified form of √72 is 6√(2), which removes all perfect squares from inside the square root.

Answer: The weekly demand equation would  be

[tex]p=-0.2m+84.8[/tex]

Step-by-step explanation:

Since we have given that

Number of units of their portable media player = 109 units per week

Cost per unit = $63.00

At unit price of $12.80, consumer are buying 360 units per week.

So, here, p = $63.00 and x = 109 units

Here, price and quantity are linearly related by

[tex]p=mx+b\\\\63=109m+b\\\\63-109m=b-----------------(1)[/tex]

If p = $12.80, x= 360

So, the equation of price would be

[tex]12.80=360m+b\\\\12.80-360m=b-------------(2)[/tex]

From eq(1) and (2), we get that

[tex]63-109m=12.80-360m\\\\63-12.80=-360m+109m\\\\50.20=-251m\\\\\dfrac{50.2}{251}=-m\\\\-0.2=m[/tex]

So, the value of b would be

[tex]63=109m+b\\\\63-109(-0.2)=b\\\\63+21.8=b\\\\84.8=b[/tex]

So, the weekly demand equation would  be

[tex]p=-0.2m+84.8[/tex]

Answer: Obviously chose Pizza Hut, as no other pizza place can out pizza the hut.

Answer:

I devour the souls of the innocent

Step-by-step explanation:

XD what question is this???

Answer:

16 apples.

Step-by-step explanation:

[tex]U(x, y) = x^2y^8[/tex]

[tex]MU_x =\frac{\partial U}{\partial x} = 2xy^8\\MU_y = \frac{\partial U}{\partial x} = 8x^2y^7\\[/tex]

Price of apples, Px=$4

Price of tomatoes,  Py=$3

Ratio of their Marginal Utilities

[tex]\frac{MU_x}{MU_y} = \frac{Px}{Py}[/tex]

[tex]\frac{y}{4x} = \frac{4}{3}[/tex]

[tex]y=\frac{16x}{3}[/tex]

Since Natalie’s income is $320

320 = xPx+yPy

[tex]320=4x + 3*\frac{16x}{3} \\320= 4x+16x = 20x\\x=\frac{320}{20} = 16\\Also\\y=\frac{16x}{3}=\frac{16X16}{3}=\$85.33[/tex]

Since x=16, Natalie will consume 16 apples.

Given Natalie's budget and the prices of apples and tomatoes, plus the fact that her utility function indicates she consumes two as many tomatoes as apples, we determined that Natalie will consume up to 32 apples under these conditions.

To determine how many apples Natalie will consume, we first need to solve the utility maximization problem where she chooses 'x' and 'y' to maximize her utility subject to her budget constraint. This problem is typically solved using calculus, but here is a simplified way of solving it:

Firstly, let's consider Natalie's budget constraint. With $320, the prices of apples and tomatoes being $4 and $3 respectively, her budget constraint is $4x + $3y ≤ $320.

Due to the nature of Natalie's utility function U(x, y) = x 2y 8, it's clear that for every apple she buys, she consumes twice as many tomatoes (since y=2x). Replacing 'y' in the budget constraint yields to $4x + $3(2x) ≤ $320, or $10x ≤ $320.

x ≤ 32, that is, Natalie will consume up to 32 apples.

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Her weekly allowance is $20

Step-by-step explanation:

Let her weekly allowance be 'a'

Given that,

She spent half of the allowance (a/2)

So,

Money left with her = (a/2)

She earned $6 by washing the car

She has $16 at the end.

So,

(a/2) + 6 = 16

(a/2) = 16 - 6

(a/2) = 10

a = 10 x 2

a = 20

So, her weekly allowance is $20

Answer:

n= - 11/3

Step-by-step explanation:

3(n+8)=13

3n+24=13

3n=13-24

3n-11

n= - 11/3

To find the surface area of ANY prism you need to find the area of individual shape first.

To find 2 faces of the prism, you will need to do bxh. As there is 2 of the same rectangle , you need to multiply it by 2. Therefore, the first number you need is 16m squared.

To find the next part of the prism, you will need to do 2m x 3m which is 6m. You need the area so 6m squared (The units are important). There are also 2 of these, so multiply it by 2 to get 12m squared.

For the final part of the prism, you will need to do 4m x 3m which is 12m squared. There are 2 of these so the it is 24m squared.

Finally, you will need to add all these figures up.

16m squared + 12m squared + 24m squared = 52m squared

Answer:

52 m

Step-by-step explanation:

Answer: the volume is: 280.8

Step-by-step explanation:

volume= length x width x height

Answer:

140.4 cm^3

Step-by-step explanation:

The formula for calculating volume of a triangular prism : 1/2 × h × l × b

1/2 × 4 × 9 × 7.2 = 140.4 cm^3

Answer:

(1,1) is a solution of the system.

Step-by-step explanation:

Let's solve the system.

y = 2x - 1

5x - 4y = 1

In the first equation, y is already separated as a function of x. So we replace in the second equation;

5x - 4(2x - 1) = 1

5x - 8x + 4 = 1

4 - 1 = 8x - 5x

x = 1

y = 2x - 1 = 2(1) - 1 = 1

(1,1) is a solution of the system.

Answer:

The ratio is 2:1

Step-by-step explanation:

This is since there are 2 times the amount of hands as there are phones

Answer:

9x - 3y = -12

-9x +5y = -1

2y = -13

y = -13/2

-3x - 13/2 = 8/2

-3x = 21/2

-6x = 21

x = -21/6 = -7/2

(-7/2, -13/2)

Answer:

473 milliliters in 1 pint

Step-by-step explanation:

divide 946 by 2

Answer:

There are 473 milliliters in 1 pint so 5 pints would be 2,365

Step-by-step explanation:

Final answer:

The expected value of the sample mean weight of watermelons, given a population mean of 21.3 pounds, is also 21.3 pounds.

Explanation:

Expected Value of the Sample Mean Weight of Watermelons

If we have a population in which the average watermelon weighs 21.3 pounds with a standard deviation of 1.07 pounds, and we consider the sample mean weight of 90 watermelons, we can calculate the expected value of this sample mean. In statistics, the expected value of the sample mean is the same as the population mean when the samples are drawn from the population independently. Thus, the expected value of the sample mean weight for the watermelons is 21.3 pounds.

The correct answer is 96 degrees for the circle.

Equation

Since angles KJL and KML are opposite angles of a cyclic quadrilateral, their sum is 180 degrees.

(7x - 8) + (3x + 8) = 180° is the equation.

10x = 172

x = 17.2

Therefore, angle KJL measures 7(17.2) - 8 = 115.4 degrees, and angle KML measures 3(17.2) + 8 = 52.6 degrees.

The measure of arc KL is equal to the sum of the measures of angles KJL and KML:

115.4 + 52.6 = 168

So the measure of arc KL is 168 degrees.

Therefore, the correct answer is 96 degrees, which matches one of the answer choices.

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Answer: 4/25

Step-by-step explanation:

Answer:

70%

Step-by-step explanation:

Answer:

Both of them are D

Step-by-step explanation:

1ST QUESTION

D. 18

2ND QUESTION

D. Any number greater than or equal to 55

brainliest?

Answer:

Type of investigation = Experimental

Dependent variable = The reaction time of the controllers

Independent variable =  Controlled breaks

Step-by-step explanation:

A researcher is examining the effects of controlled breaks on reaction times of Air Traffic Controllers.

The controllers are randomly assigned to two groups.

Group 1 and Group 2

Group 1 has 20 controllers who spend 45 minutes on a break in a quiet room, with no talking, TV, or other electronics.

Group 2 has 20 controllers who spend their 45 minutes on a break in a common area break room where people are allowed to talk, watch TV, or use electronic devices.

After the breaks, the reaction times of controllers in the two groups were measured.

Type of investigation?

This is clearly an experimental type of investigation where the researcher performs an experiment and after that measures the results.

Type of variables involved?

In this experimental investigation, we have both dependent as well as independent variable.

The controlled break is the independent variable since it can be manipulated by the researcher.

The reaction time of the controllers is the dependent variable since it is being measured and is expected to get affected when the independent variable is manipulated that is controlled breaks.

Final answer:

This is an experimental investigation where the effects of controlled breaks on reaction times of Air Traffic Controllers are examined. The independent variable is the type of break, and the dependent variable is the reaction times of the controllers.

Explanation:

The type of investigation used in this study is an experimental investigation. The independent variable in this study is the type of break given to the Air Traffic Controllers, with two levels: controlled breaks in a quiet room and breaks in a common area with allowed talking, TV, and electronic devices. The dependent variable is the reaction times of the controllers after their breaks. There are no extraneous variables mentioned in the given information.

Answer:

0.10

Step-by-step explanation:

The experimental likelihood of getting a 50% coupon is thus 2/20, or 0.1 to the decimal place.

The likelihood of rolling any one of the number cube's 6 equally likely results is 1/6. We must roll the number cube 20 times and tally how many times we receive a 50% discount in order to determine the experimental chance of doing so.

Assume that rolling a 1, 2, or 3 means you won't receive a coupon, a 4 means you'll receive a 25% coupon, a 5 means you'll receive a 50% coupon, and a 6 means you'll receive a 75% coupon.

The following outcomes are possible after 20 rolls of the number cube:

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The question is incomplete. The complete question is as follows.

Juan, Carlos and Maria went to the museum. The entrance ticket cost $5 per person, but, as they are students, there is a discount of $1 per ticket. After, they bought: 3 combos of chicken and fries costing $4 each; 3 bottles of water costing $1 each; 3 vanilla cookies costing $1 each; How much money each student paid if they divided the costs in equal amount?

Answer: $10

Step-by-step explanation: As each students split the bill in equal parts, to find how much they spent, we can calculate how much one of the three spent.

For ticket: 5 - 1 (because of the students discount) = $4

Each combo of chicken and fries cost $4, so: combo = $4

Each bottle of water costs $1, so: water = $1

and each vanilla cookie costs $1: cookie = $1

Total spent is:

T = 4+4+1+1

T = 10

Each student spent a total of $10 for this outing.

Answer:

$2,520

Step-by-step explanation:

The simple Interest earned on an deposit, P at a rate of r% for a period of t years is calculated using the formula:

[tex]\text{ Simple Interest}=\dfrac{Principal*Time*Rate}{100}[/tex]

P=$10,500

R=6%

T=4 years

Therefore:

[tex]\text{ Simple Interest}=\dfrac{10500*4*6}{100}\\=\$2,520[/tex]

Sally will earn $2520 interest after 4 years.

Answer:

-9

Step-by-step explanation:

Plug in 15 for x in the equation

you should get (1/5*15) -12

multiply 1/5 and 15 to get 3

then 3-12=-9

therefore the answer is -9

Answer:

a) We have evidence of the " center stage effect" pair number 3 was selected 34 times almost double the probability of random process

b) probability of ocurrency in random case is 20 %

Step-by-step explanation:

To answer this question we first look at the probability of chossing a pair in case of random selection

P = successful event / total outcomes

P₁ = 1/5

P₁ = 0,2    or   P₁ = 20 %

Then if the central pair was selected  34 times from 100 participants          ( almost the double ) we have evidence of the center stage effect

P₂  = 34/100   or   P₂  = 0,34

In this experiment, the data showing 34 subjects choosing the center pair of socks out of 100 participants does indicate evidence of the "center stage effect" as the observed frequency surpasses the expected frequency under randomness.

To determine if the data provided is evidence of the "center stage effect," we need to analyze whether the subjects' choices align with randomness or if there is a noticeable bias towards the center socks.

1. Calculate the expected frequency of selecting the center pair of socks under the assumption of randomness:
- Since there are 5 pairs of socks, the chance of randomly selecting the center pair would be 1 out of 5.
- This gives us a probability of 1/5  or 0.2.

2. Determine the expected number of subjects choosing the center pair out of 100 participants:
- Expected frequency = Probability of selection x Total number of participants
- Expected frequency = 0.2 x 100 = 20

3. Compare the expected frequency (20) with the actual frequency observed in the data (34):
- If the observed frequency significantly exceeds the expected frequency, it suggests a bias towards selecting the center pair of socks, supporting the "center stage effect" hypothesis.

Therefore, in this experiment, the data showing 34 subjects choosing the center pair of socks out of 100 participants does indicate evidence of the "center stage effect" as the observed frequency surpasses the expected frequency under randomness.

Answer:

0.00198

Step-by-step explanation:

The number of total ways that 5 cards can be selected from a deck of 52 cards is given as

⁵²C₅ = 2,598,960 ways.

Number of ways a flush, including straight and royal flushes, that is, five cards of the same suit can happen is given by

⁴C₁ × ¹³C₅ = 4 × 1287 = 5148

Note that of the 52 cards, each suit has 13 cards, So, ⁴C₁ represents selecting a suit out of 4 different suits and ¹³C₅ represents selecting 5 cards out of 13 cards thay a suit contains.

So, the probability of a flush

= 5148 ÷ 2,598,960 = 0.0019807923 = 0.00198 to 5 d.p

Hope this Helps!!!

The probability of  five cards of the same suit is 0.00198

Probability of any event happen is calculated by, divide favourable number of outcomes by total number of outcomes.

The number of total ways that 5 cards can be selected from a deck of 52 cards is given as

                    Total outcomes =     ⁵²C₅ = 2598960  

Number of ways a flush, including straight and royal flushes, that is, five cards of the same suit can happen is given by

         Number of favourable outcomes =       ⁴C₁ × ¹³C₅ = 4 × 1287 = 5148

 ⁴C₁ represents selecting a suit out of 4 different suits .

¹³C₅ represents selecting 5 cards out of 13 cards that a suit contains.

Therefore, the probability that a five-card poker hand contains a flush,

                              =[tex]\frac{5148}{2598960}=0.00198[/tex]

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Using a system of equations, it was determined there were 336 bottles worth 5 cents each and 82 bottles worth 10 cents each, summing up to a total of $25.

The local organization collected 418 returnable bottles and cans, some worth 5 cents each and the rest worth 10 cents each. The total value was $25.00. We need to find out how many bottles were worth 5 cents and how many were worth 10 cents.

We can set up two equations to solve this problem using algebra. Let's assume that the number of 5-cent bottles is x and the number of 10-cent bottles is y.

The first equation will represent the total number of bottles: x + y = 418.

The second equation will represent the total value of these bottles: 0.05x + 0.10y = 25.

To solve this system of equations, we can multiply the second equation by 100 to eliminate the decimals and then apply the method of substitution or elimination to find the values of x and y.

Rewrite the second equation without decimals: 5x + 10y = 2500.

Multiply the first equation by 5: 5x + 5y = 2090.

Subtract the modified first equation from the second equation: 5y = 410.

Divide both sides by 5 to find y: y = 82.

Substitute y = 82 into the first equation and solve for x: x = 418 - 82 = 336.

Therefore, there were 336 bottles or cans worth 5 cents each and 82 bottles or cans worth 10 cents each.

Answer:

- There is enough evidence to support the claim that the heart rate level lower than 120 bpm  (P-value=0.002).

- The 95% confidence interval for the population mean weight control heart rate of 20-year-olds is (98.07, 115.93).

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the heart rate level lower than 120 bpm

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=120\\\\H_a:\mu< 120[/tex]

The significance level is 0.05.

The sample has a size n=100.

The sample mean is M=107.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=45.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{45}{\sqrt{100}}=4.5[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{107-120}{4.5}=\dfrac{-13}{4.5}=-2.889[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=100-1=99[/tex]

This test is a left-tailed test, with 99 degrees of freedom and t=-2.889, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t<-2.889)=0.002[/tex]

As the P-value (0.002) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the heart rate level lower than 120 bpm .

Confidence interval:

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=107.

The sample size is N=100.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{45}{\sqrt{100}}=\dfrac{45}{10}=4.5[/tex]

The t-value for a 95% confidence interval is t=1.984.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.984 \cdot 4.5=8.929[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 107-8.929=98.07\\\\UL=M+t \cdot s_M = 107+8.929=115.93[/tex]

The 95% confidence interval for the population mean weight control heart rate of 20-year-olds is (98.07, 115.93).

Using the t-distribution, it is found that the 95% confidence interval for the population mean weight control heart rate is (98.07, 115.93). Since the entire interval is lower than 120 bpm, it is evidence to conclude that the expected level is actually lower than 120 bpm.

We are given the standard deviation for the sample, which is why the t-distribution is used to solve this question.

The information given is:

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 100 - 1 = 99 df, is t = 1.984.

Hence:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 107 - 1.984\frac{45}{\sqrt{100}} = 98.07[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 107 + 1.984\frac{45}{\sqrt{100}} = 115.93[/tex]

The 95% confidence interval for the population mean weight control heart rate is (98.07, 115.93). Since the entire interval is lower than 120 bpm, it is evidence to conclude that the expected level is actually lower than 120 bpm.

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Approximately 215 samples are needed for a 95% confidence interval estimating the mean breakdown voltage with a 2 kV width and a 1 kV margin of error, assuming the range is 40 to 70 kV.

To determine the required sample size for estimating the mean breakdown voltage with a 95% confidence interval (CI) width of 2 kV and an estimated margin of error (m) of 1 kV, you can use the formula:

[tex]\[ n = \left(\frac{{Z^2 \cdot \sigma^2}}{{m^2}}\right) \][/tex]

Where:

- n is the required sample size,

- Z is the Z-score corresponding to the desired confidence level (for 95%, it's approximately 1.96),

- [tex]\( \sigma \)[/tex] is the estimated standard deviation of the population.

Since you mentioned the investigator believes breakdown voltage is between 40 and 70, assuming a uniform distribution, you might consider using [tex]\( \sigma = \frac{{\text{{range}}}}{4} \)[/tex] as an approximation. Therefore,

[tex]\[ \sigma = \frac{{70 - 40}}{4} = 7.5 \][/tex]

Now plug these values into the formula:

[tex]\[ n = \left(\frac{{1.96^2 \cdot 7.5^2}}{{1^2}}\right) \][/tex]

Let's calculate the required sample size n:

[tex]\[ n = \frac{{(1.96)^2 \cdot (7.5)^2}}{{1^2}} \]\[ n = \frac{{3.841 \cdot 56.25}}{{1}} \]\[ n \approx \frac{{214.6}}{{1}} \]\[ n \approx 214.6 \][/tex]

So, the required sample size for the 95% confidence interval to have a width of 2 kV (with a margin of error of 1 kV) is approximately 215.

Therefore, the investigator would need a sample size of about 215 to estimate the mean breakdown voltage with the desired level of confidence and precision.

Answer:

Radius = 6.5cm

Diameter = 13cm (given)

Step-by-step explanation:

The diameter is the length of one side of a circle to the other. It's already given in the diagram as 13cm.

The radius is half of the diameter. 13 divided by 2 is 6.5cm.

The correct answer are as follows

Radius = 6.5 cm

Diameter = 13 cm

So , The diameter is 13cm

and The radius is 1/2 x diameter = 1/2 x13 = 6.5cm

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