evaluate 16 3/4
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

Answer:

(0,-3)

Step-by-step explanation:

left 2 puts you at (0,3) and flipping over x axis makes the y value negative, so it's (0,-3)

The probability that the child must wait at least 9 minutes on a given morning is approximately 0.2231.

Let X be the waiting time at the bus stop. We know that X is exponentially distributed with mean 6 minutes. Therefore, the probability density function (PDF) of X is given by:

f(x) = 1/6 * e^(-x/6) for x >= 0

To find the probability that the child must wait at least 9 minutes, we need to calculate the following probability:

P(X >= 9) = integral of f(x) from 9 to infinity

= integral from 9 to infinity of (1/6 * e^(-x/6)) dx

Using integration by substitution, let u = x/6, du = 1/6 dx, so that:

P(X >= 9) = integral from 3/2 to infinity of e^(-u) du

= [e^(-u)] evaluated from 3/2 to infinity

= e^(-3/2)

≈ 0.2231

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The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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The fund balance at the end of 2019 will be $8,000.

The given problem has four different parts, where we are supposed to calculate the accumulation of funds at the end of 2019 in different scenarios.

Scenario 1In the first scenario, the first deposit is made on December 31, 2016, and interest is compounded annually.

Using the FVA of $1 table; Payment: $2,000n = 4i = 12%

Fund balance 12/31/2019: $9,559

Hence, the fund balance at the end of 2019 will be $9,559.Scenario 2In the second scenario, the first deposit is made on December 31, 2015, and interest is compounded annually.

Using the FVAD of $1 table;Payment: $2,000n = 4i = 12%

Fund balance 12/31/2019: $10,706 Therefore, the fund balance at the end of 2019 will be $10,706.Scenario 3In the third scenario, the first deposit is made on December 31, 2015, and interest is compounded quarterly. Using the FV of the $1 chart, we get the following calculation:

Deposit Date i = n = Deposit Fund Balance 12/31/2015 3% 16 $2,000 $3,20912/31/2016 3% 12 $2,000 $2,85212/31/2017 3% 8 $2,000 $2,53412/31/2018 3% 4 $2,000 $2,251

The interest rate is 3%, and the payment is $2,000. Hence, the fund balance at the end of 2019 will be $10,846.Scenario 4In the fourth scenario, the first deposit is made on December 31, 2015, interest is compounded annually, and interest earned is withdrawn at the end of each year.

Deposit Amount No. of Payments Interest left in Fund Fund Balance 12/31/2019$2,000 $8,000 Hence, the fund balance at the end of 2019 will be $8,000.

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Answer:a square

Step-by-step explanation:

The probability of Z being greater than 4 is nearly 0 (option D). Therefore, the answer is D.

Let's assume that the weight of a grapefruit follows a normal distribution with mean 0.9 pounds and standard deviation 0.1 pounds. Then, the weight of three grapefruits will follow a normal distribution with mean 2.7 pounds (3 x 0.9) and standard deviation 0.1732 pounds (sqrt(3) x 0.1).

Now, we need to find the probability that the total weight of three grapefruits is more than 3.4 pounds. We can standardize the distribution by subtracting the mean from 3.4 and dividing by the standard deviation:

Z = (3.4 - 2.7) / 0.1732 = 4

Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than 4 is nearly 0 (option D). Therefore, the answer is D.

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d) Tthe probability that there is a moving object given that both sensors detect motion is approximately 0.98.

(a) To find the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

A = Movement outside

B = Sensor V does not detect motion

C = Sensor L detects motion

We are given:

P(A) = 0.7 (probability of movement outside)

P(B|A) = 0.05 (probability of sensor V not detecting motion given movement outside)

P(C|A) = 0.8 (probability of sensor L detecting motion given movement outside)

We want to find P(C|A', B), where A' denotes the complement of event A.

Using Bayes' theorem:

P(C|A', B) = [P(A' | C, B) * P(C | B)] / P(A' | B)

We can calculate the values required:

P(A' | C, B) = 1 - P(A | C, B) = 1 - P(A ∩ C | B) / P(C | B) = 1 - [P(A ∩ C ∩ B) / P(C | B)]

             = 1 - [P(B | A ∩ C) * P(A ∩ C) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / [P(B | C) * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A')]]

P(B | C) = 0 (since sensor V does not detect motion when there is motion outside)

P(C | A') = 0 (since sensor L does not detect motion when there is no motion outside)

Substituting these values:

P(C | A', B) = 1 - [0 * P(A) * P(C | A) / (0 * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A'))]

             = 1 - [0 / (0 + P(B | C') * P(A') * P(C | A'))]

             = 1 - 0

             = 1

Therefore, the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion is 1.

(b) To find the probability that the home security system alerts the police given that there is a moving object, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

M = There is a moving object

We need to calculate P(D | M). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | M) = P(D, V detects motion, L detects motion | M) + P(D, V does not detect motion, L detects motion | M)

We know:

P(D, V detects motion, L detects motion | M) = P(V detects motion | M) * P(L detects motion | M) = 0.95 * 0.8 = 0.76

P(D, V does not detect motion, L detects motion | M) = P(V does not detect motion | M) * P(L detects motion | M) = (1 - 0.95) * 0.8 = 0.04

Substituting

these values:

P(D | M) = 0.76 + 0.04

        = 0.8

Therefore, the probability that the home security system alerts the police given that there is a moving object is 0.8.

(c) To find the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

NM = There is no movement

We need to calculate P(D | NM). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | NM) = P(D, V detects motion, L detects motion | NM) + P(D, V does not detect motion, L detects motion | NM)

We know:

P(D, V detects motion, L detects motion | NM) = P(V detects motion | NM) * P(L detects motion | NM) = 0.1 * 0.05 = 0.005

P(D, V does not detect motion, L detects motion | NM) = P(V does not detect motion | NM) * P(L detects motion | NM) = (1 - 0.1) * 0.05 = 0.045

Substituting these values:

P(D | NM) = 0.005 + 0.045

         = 0.05

Therefore, the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, is 0.05.

(d) To find the probability that there is a moving object given that both sensors detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

M = There is a moving object

V = Sensor V detects motion

L = Sensor L detects motion

We want to find P(M | V, L).

Using Bayes' theorem:

P(M | V, L) = [P(V, L | M) * P(M)] / [P(V, L)]

We can calculate the values required:

P(V, L | M) = P(V | M) * P(L | M) = 0.95 * 0.8 = 0.76

P(M) = 0.7 (given probability of movement)

P(V, L) = P(V, L | M) * P(M) + P(V, L | M') * P(M')

        = 0.76 * 0.7 + 0.04 * 0.3

        = 0.532 + 0.012

        = 0.544

Substituting these values:

P(M | V, L) = (0.76 * 0.7) / 0.544

           ≈ 0.98

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the minimum value of the function subject to the constraint is 0, and the maximum value is 10

To find the minimum and maximum values of the function f(x, y) = x^2y subject to the constraint g(x, y) = x + y = 9, we can use the method of Lagrange multipliers.

Let L(x, y, λ) = f(x, y) - λ(g(x, y) - 9) be the Lagrangian function, where λ is the Lagrange multiplier.

Taking the partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we get:

∂L/∂x = 2xy - λ = 0 ...(1)

∂L/∂y = x^2 - λ = 0 ...(2)

∂L/∂λ = -(x + y) + 9 = 0 ...(3)

From equation (2), we have x^2 - λ = 0, which implies x^2 = λ.

Substituting this into equation (1), we get 2xy - x^2 = 0, which can be simplified to x(2y - x) = 0.

This equation gives us two possibilities:

x = 0

2y - x = 0 --> 2y = x --> y = x/2

Now, let's substitute these values into equation (3):

For x = 0: -(0 + y) + 9 = 0 --> y = 9

So, one critical point is (0, 9).

For y = x/2:

-(x + x/2) + 9 = 0 --> -(3x/2) + 9 = 0 --> 3x/2 = 9 --> x = 6

Substituting x = 6 into y = x/2, we get y = 6/2 = 3.

So, another critical point is (6, 3).

Now, we need to evaluate the function f(x, y) = x^2y at the critical points:

f(0, 9) = (0)^2(9) = 0

f(6, 3) = (6)^2(3) = 108

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Answer:

The measures of this complementary angles is:

45°

Step-by-step explanation:

Complementary angles sum 90°

∡A + ∡B= 90°

∡A = ∡B

Then:

∡A + ∡A = 90°

2∡A = 90°

∡A = 90/2

∡A = 45°

∡B = 45°

Answer:

A. square root of 3 times 5

Step-by-step explanation:

a) The coefficient of determination is also known as R-squared and it measures the proportion of the variance in the dependent variable (outcome variable) that is explained by the independent variable (predictor variable) in a linear regression model.

b) The coefficient of determination (R-squared) tells us how much of the variation in the outcome variable is explained by the least squares regression line. Specifically, R-squared ranges from 0 to 1 and indicates the proportion of the variance in the dependent variable that can be explained by the independent variable in the model.
A high value of R-squared (close to 1) means that the regression line explains a large proportion of the variation in the outcome variable, while a low value of R-squared (close to 0) means that the regression line explains very little of the variation in the outcome variable.

a) To compute the coefficient of determination, we need to first calculate the correlation coefficient (r) between the predictor variable and the outcome variable. Once we have the correlation coefficient, we can square it to get the R-squared value.
For example, if the correlation coefficient between the predictor variable and the outcome variable is 0.75, then the R-squared value would be:
R-squared = 0.75^2 = 0.5625
Therefore, the coefficient of determination is 0.5625.
b) The coefficient of determination (R-squared) tells us how much of the variation in the outcome variable is explained by the least squares regression line. Specifically, R-squared ranges from 0 to 1 and indicates the proportion of the variance in the dependent variable that can be explained by the independent variable in the model.
For example, if the R-squared value is 0.5625, then we can say that the regression line explains 56.25% of the variation in the outcome variable. The remaining 43.75% of the variation is due to other factors that are not included in the model.

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The simplest form of the given expression ( x⁴ )⁸ exists x³².

Expression in Math exists described as the collection of numbers variables and functions by utilizing characters like addition, subtraction, multiplication, and division.

The given expression will be simplified as:-

( x⁴ )⁸ = x ⁴ ⁽⁸⁾

( x⁴ )⁸ = x ³²

Therefore the simplest form of the given expression exists as x³².

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Answer:

Step-by-step explanation:

OMG! Don't do that! I am so sorry this is happening to you. Look I don't know how to comfort you. IF he keeps doing this tell your mom or litterally call 911. If he did it just on that day then try confronting him on it. And ask him why he did that! Don't self-harm you deserve so much more than that! You are awesome!

By finding the linear equation that relates distance and time, we can see that the complete table is:

time (hours)   distance (miles)

2                              100

1.5                             75

t                              (50)*t

1                                50

6                               300

d/(50)                          d

After a small online search, I've found that the table is:

time (hours)   distance (miles)

2

1.5

t  

                                50

                               300

                                  d

Now, remember the relation:

distance = speed*time.

In this case, we know that the speed is 50 mi/h, so if we define d as the distance and t as the time, we can write:

d = (50mi/h)*t

To complete the table, we just replace the value that appears in the table, and then we solve the equation for the other variable.

First we have t = 2 hours:

d = (50 mi/h)*2h = 100 mi

Then we have t = 1.5 hours

d = (50 mi/h)*1.5 h = 75 mi

Then we assume that we evaluate in t, so there we just write the equation:

d = (50 mi/h)*t

Now we go to the other side of the table, now we evaluate d, so we can write:

t = d/(50 mi/h)

(that is what goes in the table when we need to evaluate in d).

Then the fourth place in the table has d = 50 mi, replacing that:

t = (50mi)/(50 mi/h) = 1h

And finally, we evaluate in d = 300mi

t = (300 mi)/(50 mi/h) = 6h

Then the complete table is just:

time (hours)   distance (miles)

2                              100

1.5                             75

t                              (50)*t

1                                50

6                               300

d/(50)                          d

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Answer:

41

Step-by-step explanation:

FG = EH ( being opposite sides of parallelogram)

3z + 8 = 5z - 14

5z - 3z = 8 + 14

2z = 22

z = 11

Now

FG = 3z + 8 = 3 *11 + 8 = 33 + 8 = 41

Hope it will help :)❤

The option that is not a factor of capacity planning is the option d

d) Proximity to suppliers

The process of ascertaining the production capacity an organization needs in order to meet changing demand for the products and services of the organization is known as capacity planning.

The factors considered in capacity planning are factors which include the capacity measurement approach, the economies of scale, preparedness to deal with the capacity in chunks, and activities towards identifying the best operating level.

Therefore, from the listed options, the option that is not a factor in capacity planning is the option (d) proximity to suppliers

Other aspects of the operations of an organization, such as supply chain management and logistics can be affected by the proximity of suppliers, but the proximity of suppliers is not directly linked to the determination process for the production capacity needed to meet the market demand.

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Answer:

There are $\boxed{3}$ paths from $A$ to $B.$

Answer:

H.C.F = 15

Step-by-step explanation:

60 = 2 × 2 × 3 × 5

75 = 3 × 5 × 5

90 = 2 × 3 × 3 × 5

HCF = 3 × 5 = 15

Answer:

1 km per minute

Step-by-step explanation:

Because if 30 km in 30 min 1km in 1 min.

Answer:

a) 1/30

b) 1/6

Step-by-step explanation:

a) There are 10 people total and a group of 3 is being chosen. However, they all need to be women:

For the first person, the probability of it being a woman is 4/10

For the second person, the probability of it being a woman (with the prerequisite that the first was a woman) is 3/9

For the third (with the same requirements) is 2/8

If we multiply all of the fractions together, we get: \(\frac{1}{30}\)

b) There are 10 people total and a group of 3 is being chosen. However, two of them need to be men, and 1 needs to be a woman:

For the first person, the probability of it being a man is 6/10

For the second person, the probability of it being a man (with the prerequisite that the first was a man as well) is 5/9

For the third person, the probability of it being a woman (because it can only be two men) is 4/8

If we multiply all the fractions together, we get: \(\frac{1}{6}\)

30% of the eligible students voted.

It is given to us that 650 students at the high school are eligible to vote and 195 of them voted in the last election.

Now let us take the percent of students to be 'x'

x% of 650 students voted whose value is given to be 195.

So the equation can be written as

( x / 100 ) * 650 = 195

x = ( 195 * 100 ) / 650

x = 30

Therefore 30% of  the eligible students voted in the last election.

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Answer:

x=2

Step-by-step explanation:

Answer:

\( \huge \boxed{ \boxed{ \tt x = 2}}\)

Step-by-step explanation:

The time it takes to paint the whole bookcase is 50 minutes.

From the information, Wilson paints 40% of a bookcase in 20 minutes.

Let the time taken to paint the whole bookcase be x. This will be illustrated as:

20/x = 40/100

Cross multiply

40x = 100 × 20

40x = 2000.

Divide

x = 2000 / 40

x = 50

The time taken is 50 minutes.

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The given expression is

First, we express the first number in scientific notation. We have to make sure that both scientific notations have the same exponent.

Then, we subtract the coefficients.

Answer: financially irresponsible

Step-by-step explanation:

Kendall is buying 5 for $9.95 when she could buy 6 for $9.65 which would get her another bottle and save 30 cents

Answer:

y-2/3x-4

the answer is (0,3)

3x+4y-12

the answer is (0,3)

The distance between the two parallel sides of the trapezium is 8 cm.

A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other.

The area of a trapezium is expressed as:

Area = 1/2 × ( a + b ) × h

Where a and b are base a and base b, h is height.

Given that:

Area of the trapezium = 36 cm²

Base a = 3 cm

Base b = 6 cm

Height h =?

Plug the given values into the above formula and solve for height:

Area = 1/2 × ( a + b ) × h

36 = 1/2 × ( 3 + 6 ) × h

36 = 1/2 × ( 9 ) × h

36 = 4.5 × h

h = 36 / 4.5

h = 8 cm

Therefore, the height of the trapezium is 8 cm.

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Brendan needs to purchase 45 bags of rock salt to cover the entire parking lot around his building. Each bag of rock salt covers an area of 1,500 square feet, and the total area of the parking lot is 67,500 square feet. Therefore, by dividing the total area of the parking lot by the area covered by each bag of rock salt, we can determine the number of bags needed.

To calculate the total area of the parking lot, we need to find the length and width of the shaded area in the diagram. From the diagram, we can see that the length of the shaded area is 150 feet, and the width is 450 feet. Therefore, the area of the shaded region can be calculated by multiplying the length and width:

150 ft x 450 ft = 67,500 sq ft

To determine the number of bags of rock salt needed, we divide the total area of the parking lot by the area covered by each bag of rock salt:

67,500 sq ft ÷ 1,500 sq ft per bag = 45 bags

Therefore, Brendan needs to purchase 45 bags of rock salt to cover the entire parking lot around his building

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