Response time is an important statistic for measuring the effectiveness of a fire department, and is measured as the difference between the time a fire house receives a call and the time the first piece of fire equipment leaves the station. The response times for fire departments in a large city are found to have an approximately Normal distribution, with a mean of 4.5 minutes and a standard deviation of 1.2 minutes. What percentage of fire station response times are between 4 and 6 minutes?
37.7%
44.3%
55.7%
62.3%

More students received a 94 than any other score on the test. So, option B is the correct answer.

The mode of any given data set is the value that occurs in the given data set the most. This is that one value that occurs more than any other value in any given data set. From the given problem, we can easily understand that 94 is the mode of the set since it is the average score. This means that more students received a 94 than any other score on the test.

The first option is not the correct answer because we have not been told that 99 was the highest score on the test. We have also not been told no student scored below 50 or that a score of 91 was slightly below average.

This means option B is the correct answer.

The question you might be looking for is -

The mode score on the 6th-grade math test was 94! Which of these interpretations must be correct?

a. 99 was the highest score on the test.

b. More students received a 94 than any other score

c. No student scored below a 50

d. A score of 91 was slightly below average.

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Answer: -5,4

Step-by-step explanation:

2,1 x 2 = 4,2

-3,2 x 3 = -9,6

-9,6

- 4,2 = -5,4

The required  the average daily census for this period is 12.

A Average can be characterized as the amount of all numbers isolated by the all out number of values. A mean can be characterized as a normal of the arrangement of values in an example of information. At the end of the day, a normal is likewise called the math mean. It is known as a mean to Depict the average.

there were 2,200 inpatient service days.

Number of days between this period = 184 days

So, average daily census = 2200/184

11.95

⇒ 12 up to whole number.

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By using the concept of probability, it can be calculated that

Probability that it will rain on both the days = 0.04

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Probability of rain on the first day = 0.2

Probability of rain on the second day = 0.2

Assuming that the chance of rain is independent of the day

Probability that it will rain on both the days = 0.2 [tex]\times[/tex] 0.2 = 0.04

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Complete Question

The Smith family is planning to build a 3-room cabin which consists of 2 bedrooms (BR) and 1 living room (LR). Shown below are the rectangular floor plan (left figure) and a side view of the cabin (right figure). In the side view, the roof forms an isosceles triangle (ABC), the walls are perpendicular to the level floor (ED), AC || ED, F is the midpoint of AC, and BF ⊥ AC.

During the week the Smiths plan to roof the cabin, there is a 20% chance of rain each day.

Mr. and Mrs. Smith plan to roof the cabin on 2 consecutive days. Assuming that the chance of rain is independent of the day, what is the probability that it will rain both days?

The required projection of u onto v is the vector (-23/20)i - (23/10)j, or approximately <-1.5, -2.13>.

To calculate the projection of vector v onto vector u (proj_vu), we can use the formula:

[tex]proj_{vu} =\dfrac {(v \times u)}{||u||^2} *v[/tex]

Here, u is the vector -11i - 5j and v is the vector 4i + 8j.

Compute the dot product of u and v.
u · v = (-11)(4) + (-5)(8)
      = -92

Compute the magnitude of v.
[tex]||v|| = \sqrt{(4^2 + 8^2)} \\= \sqrt{80}\\ = 4\sqrt{5[/tex]

Compute [tex]proj_{vu}[/tex]using the formula.
[tex]proj_{vu} = \dfrac{u \times v} {||v||^2} * v\\ proj_{vu} = (-92 / (80)) * (i + 2j)\\proj_{vu} = (-23/20)i - (23/10)j[/tex]

Therefore, the projection of u onto v is the vector (-23/20)i - (23/10)j,  or approximately <-1.5, -2.13>.

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The question is incomplete, the complete question is given below:

Find the projection of vector v onto vector u or what is proj_vu?

Where.

Vector u = <-11, -5>

Vector v = <4, 8>

It is untrue that it can build cause-and-effect relationships.

When the following criteria are met, a cause-and-effect relationship is asserted: the two occurrences take place at the same time and location; one event occurs right before the other; and it seems doubtful that the second event would have happened without the first event first occurring.

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In fractional form, the answer is 397/55 and in decimal form it is 7.2181.

The equation can be written as 22/5+k= -31/11

transferring 22/5 to the R.H.S., the sign will turn negative.

thus, k=-31/11-22/5

Further solving the equation by taking L.C.M. of 11 and 5 which comes to 55,

k=(155+242)/55

we get the value of k= 397/55

If we convert the given value of k into decimal, it can also be written as, 7.2181.

Thus, the value of k can b expressed in both numerical and fractional forms.

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There are 4 outcomes in the sample space.

There are 2 outcomes in event A.

There are 2 outcomes in event B.

Sample Space:

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes. The random experiment's sample spaces are written in curly brackets, " ".

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There are 4 outcomes in the sample space.

There are 2 outcomes in event A.

There are 2 outcomes in event B.

Sample Space:

Several possible outcomes from a random experiment make up a sample space. The sample space is designated with the letter "S".

Events are a subset of potential experiment outcomes.

A sample region could have a range of outcomes, depending on the experiment.

Any sample space with a finite number of outcomes is said to be discrete or finite. Sample spaces for the random experiment are denoted by " " curly brackets.

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A function z(x, y) and its partial derivative (∂z/∂y)x is aslo a function.

Function:

In set math, function refers an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)

Given,

Consider a function z(x, y) and its partial derivative (∂z/∂y)x.

Here we need to identify that the partial derivative still be a function of x.

In order to find the solution for this function, we must know the definition of partial derivative,

The definition of partial derivative is, "partial derivative of any function having several variables is its derivative with respect to one of those variables where the others are held constant."

Here the partial derivative of a function f with respect to the differently x is variously denoted by f’x, fx, ∂xf or ∂f/∂x.

The symbol ∂ is partial derivative.

So, as per the definition of the partial derivative, the given partial derivative  (∂z/∂y)x is also a function.

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Answer:

Step-by-step explanation: 70 2.5 60

Using the equation of the proportional relationship, the number of miles she would drive on 50 gallons is: 1,660 miles.

A direct proportional relationship can be defined by the equation, y = kx, where the constant of proportionality between the variables is given as the value of k.

First, we need to write an equation that defines the table of values given. To do this, find the constant of proportionality by using any pair of values from the table, say (6, 199.2):

Number of gallons used = x

Number of miles driven = y

Constant of proportionality, k = y/x = 199.2/2

k = 33.2

To write the equation for the proportional relationship, substitute k = 33.2 into y = kx:

y = 33.2x

To find the how many miles she would drive on 50 gallons, substitute x = 50 into y = 33.2x:

y = 33.2(50)

y = 1,660 miles.

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The approximate value for the probability that at least 80 flips are necessary is 0.3897.

Given:

a fair coin is flipped repeatedly until 50 heads are observed

using the central limit theorem, calculate an approximate value for the probability that at least 80 flips are necessary.

P (h>25)=p(h>=26)= 1-p(h<=26)

Assume the situation is approximately normal

u= np =50(1/2)=25 , s=√(npq) = √( 50)(.5)(.5) =√12.5

z=(x-u)/s = ( 26–25)/√12.5 = 0.283

P(z=0.283) =0.1103

Edit p(z>0.283)=0.1103

P(h <= 80)= 0.5+ 0.1103= 0.6103

P(h>=80) 1 - 0.6103 = 0.3897

Hence we get the required answer.

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Answer: no i need this too :(

Step-by-step explanation:

Answer:

The rule of the translation is (x,y) ------> (x-1,y-5)

B'(-2,1)

C'(3,2)

Step-by-step explanation:

The null hypothesis states that the probability of reader has personal computer is 0.52 whereas alternative hypothesis states opposite

Its given that

The probability that readers has a personal computer = 0.52

The null hypotheses is that the proportion of readers who own a personal computer is equal to 0.53

Null hypotheses = H₀: p = 0.55

The alternate hypotheses is that the proportion of readers who own a personal computer is not equal to 0.55

Alternate hypotheses = H₁: p ≠ 0.55

Determine the  type of test:

Since the alternate hypothesis states that the proportion of readers who own a personal computer is different, therefore it is a two-tailed test.

To determine the z-score,

Given level of significance : ∝ = 0.05

So, the z-score at 0.05

Z-score = 1.960 (two tailed)

We Reject H₀ if Z > 1.960

And we accept H₀ if Z < 1.960

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Answer: The base is 4 units and the height is 9 units.

Step-by-step explanation: To find the dimensions of the rectangle, we can use the coordinates of the points A, B, C, and D. The base of the rectangle is the distance between the points A and B, or the distance between the points C and D. We can find this distance by subtracting the x-coordinates of the points: 1 - (-4) = 5. Therefore, the base of the rectangle is 5 units.

Next, we can find the height of the rectangle by subtracting the y-coordinates of the points A and C, or the points B and D. We can do this by subtracting the y-coordinates of the points: 8 - (-1) = 9. Therefore, the height of the rectangle is 9 units.

Therefore, the dimensions of the rectangle are a base of 5 units and a height of 9 units, so the correct answer is A; The base is 4 units and the height is 9 units.

Answer:

Step-by-step explanation:

Using ( 0,0) and (1,1 ). the slope is 1 and the y intercept is 0 because the line cuts the y axis at the origin. The equation of the line is y=1x

The  null and alternative hypothesis test the economist's claim is-

H₀: u = 863 ,H₁: u < 863

What is hypothesis test?

A applied math hypothesis test may be a technique of applied math abstract thought accustomed decide whether or not the info at hand sufficiently support a selected hypothesis. Hypothesis testing permits us to create probabilistic statements regarding population parameters.

Main body:

Let ц =average calories of virginia school lunches

The average calories in the school lunch is 863

Here the economists claims that after the testing period ends, the average caloric content in the lunches were dropped

The null hypothesis is H₀ц = 863

Means H₀ ;The average caloric content in the school lunch is 863

The alternative hypothesis is H₁ц <863

Hence , H₁; the average caloric content in the lunches was dropped.

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Answer: This is what I came up with after a few tries! 1/9x

Answer:

x+y=5

Step-by-step explanation:

Formula= Ax+By=C

change the equation up a little and get

x+y=5

Answer:

26.9%

Step-by-step explanation:

538/2000 =  0.269

Multiply this by 100 to get the percentage

= 26.9%

At a 4.5% annual growth rate, it will take 8.4 years to double the population from 15,000 to 20700.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Here,

The initial population=15000

Growth rate=4.5%

Final population=20700

Population growth=15000*4.5%

=675

Let n be the number of years.

Final population=initial population + Population growth*number of years

20700=(15000+675n)

675n=20700-15000

675n=5700

n=5700/675

n=8.4 years

It will take 8.4 years to grow the population from 15000 to 20700 at the growth rate of 4.5% per year.

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Observe from the data that a director of manufacturing must persuade management that the proposed production process cuts costs in order for the new way to be implemented.

The average cost of the present production process is $220 per hour.

What does "cost" mean?

The sum paid for anything, or its equivalent, is referred to as the price. the investment or expenditure (as of labor or sacrifice) made to obtain a thing; the average cost of a college education has increased significantly.

a)

In this instance, note how the researcher conducts experiments to ensure that the new method will function with a

mean price was under $220. Which is.µ < 220

The following is the Null and Alternative Hypothesis:

Negative hypothesis H.: The new technique will be operational at a mean cost of at least $220.

Therefore, H: µ > 220

An alternative theory. H.: The new technique will function at a mean cost that is lower than

$220

Meaning H µ < 220

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Answer: 5 minutes

Step-by-step explanation: The total change in the amount of water in the trough is the difference between the final amount and the initial amount, which is 80 gallons - 25 gallons = 55 gallons.

Since the rancher is adding 11 gallons of water per minute, the time it will take for the trough to have 80 gallons of water is the total change in the amount of water divided by the rate at which the water is being added, which is 55 gallons / 11 gallons/minute = 5 minutes.

Therefore, it will take the rancher 5 minutes to fill the trough with 80 gallons of water.

The amount of 198 liters of water weights 4.45 Pound force on the earth.

The density of the water is 1 kg/L.

It means that 1 L of water has 1 kg of water.

So, we can write,

1 liter water = 1 kg water

1.98 liters water = 1.98 kg water.

So, the mass of the water is 1.98 kg.

The weight of a body is given as,

W = Mg

Where,

M is mass of the body and g is the gravitational acceleation,

putting values to find the weight of 1.98 L of water,

W = 1.98 x 10

W = 19.8N.

Converting it into Pounds,

W = 4.45 Pounds force.

Hence, the weight of 1.98 liters of water on earth surface is 4.45 Pound force.

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The solution set of the given inequality -7x < -21 is {x | x > 3}.

For the stated question-

The given inequality is-

-7x < -21

Dividing both side by -1 will change the direction of the sign.

7x > 21

Now, divide both side by 7

7x/7 > 21/7

x > 3 (solution set)

Thus, the solution set of the given inequality -7x < -21 is {x | x > 3}.

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The characteristic of any function created by the product of two linear factors has two x-intercepts.

According to the question;

We are required to determine which is a characteristic of any function created by the product of two linear factors.

The product of two linear factors results in a quadratic function.

Since a quadratic function is a polynomial of degree two, 2.

In essence, the resulting function created by the product of two linear factors has two x-intercepts.

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Answer: 3y= 4x-6

Step-by-step explanation:

  given line = 4y= -3x+12

            slope= -3/4

           so the perpendicular lines slope will be 4/3

               new line  = y = (4/3)x+c

                            ==>    2 = (4/3)3+c

                           ==>   2 = 4+c

                           ==> c= -2

                          3y= 4x-6

Answer:

Step-by-step explanation:

4y=12-3X

divide both sides by4

y=-3x/4 +3

m1×m2= -1

m1= -3/4

-3/4× m2=-1

m2=4/3

Gradient is now=4/3

m= y -y1/x-x1

4/3= y-2/x-3

3y - 6= 4x - 12

3y= 4x - 12 +6

3y= 4x -6

divide both sides by 3

y =4/3x - 2

As per the given sample size, the shape of the population distribution when conducting t test is approximately normal.

Sampling.

in statistics, sampling refers the statistical procedure that is concerned with the selection of the individual observation; it helps us to make statistical inferences about the population.

Given,

Here we have the sample size is 81.

Now, we need to find the shape of the population distribution when conducting the t test.

Let us consider you are the manager of a restaurant for a fast-food franchise. And in last month, the mean waiting time at the drive-through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.9 minutes.

Now, you are selecting a random sample of 81 orders.

As per the sample size, the sample mean waiting time is 3.72 minutes, with a sample standard deviation of 0.8 minute.

Now, we complete parts (a) and (b) below.

a. here at the 0.01 level of significance, is there evidence that the population mean waiting time is different from 3.9 minutes.

And state the null and alternative hypotheses.

H0: μ▼ H1: μ ▼

So, H0 is sufficient insufficient evidence to conclude that the population mean waiting time is different from 3.9 minutes .

b. According to the sample size is 81,

The shpe of the population distribution when conducting t test is approximately normal. As in the t test is appropriate for a large sample size.

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Answer: Length 3, width is 1.

Step-by-step explanation: L + W = 4

L = 2W + 1

Answer:

12x + 6

Step-by-step explanation:

4x + 3 = 12 + (2x)  y / x

10x + 6 = X

= 12x + 6 = (18x)

Answer:

12x+6

Step-by-step explanation:

Perimeter is adding all sides or 2(l)+2(w)

it is no different in this so we fill in formula

2(4x+3)+2(2x)

Distribute the 2

2(4x)+2(3)+2(2x)

8x+6+4x

Combine like terms

8x+6+4x

8x+4x+6

12x+6

hopes this helps please mark brainliest