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 station 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 under 3 minutes?

Find the z-table here.

6.68%
10.56%
89.44%
93.32%

The best first step in solving m–2(m–4)≤3m for m will be A. Distribute -2 through the parentheses.

It should be noted that an inequality simply means a relation between the expressions that are unequal.

It should be noted that the best first step in solving m–2(m–4)≤3m for m will be to distribute -2 through the parentheses.

This is important in order to have variables of m and then solve accordingly.

In conclusion, the best option is A.

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Answer:

28

Step-by-step explanation:

Answer:

A. [0, 65]

Step-by-step explanation:

Given that

Distance that Marcus drives every day = 32 miles.

The table having average speed as input and time taken as output is shown below in the table format:

\(\begin{center}\begin{tabular}{ c c}Speed(mph) & Time(minutes) \\ 60 & 32 \\ 45 & 43 \\ 55 & 35 \\ 50 & 38 \\ 62 & 31 \\\end{tabular}\end{center}\)

To find:

The domain that includes all possible average speeds using interval notation = ?

Solution:

First of all, let us understand what is a domain of a function.

Domain of a function is set of valid input values that can be provided to the function so that it has a valid output.

If a function is written as:

\(y=f(x)\) then values of \(x\) are the input given to the function.

In the given question statement, we are given that maximum Average speed attained by Marcus is 65 miles per hour.

That means domain has a maximum value of 65.

Let us learn something about interval notation.

( or ) means the value is not inclusive.

[ or ] means the value is inclusive.

Here 65 will be inclusive.

On the left side of comma, lower value is written and on the right side of comma, larger value is written.

So, domain for the current situation will be:

[0, 65]

0 is taken as the minimum value of domain here, because average speed value can not be negative.

This interval will contain all the possible values of input (average speed) as shown in the above table of values.

Answer:

Step-by-step explanation:

Typically yes you need to know

Mean

Median

Mode

and Range

Mean = average, add all numbers then divide by how many

Median = midpoint, middle number.  Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers

Mode = numbers that occurs the most in the list of numbers

Range = This is the largest number minus the smallest number.  

Given that the inequalities and that

x ⇒ pep club donations

y ⇒ represent donations raised by the honor society

The inequality is represented by x + y≥ 500

The solution for this is the shaded area above the solid line.

Given x ≥ 100, this is also indicated by the shaded region to the right

The point (300,100) indicates that the contributions made for the pep club were $300 and the donations raised by the honor society were $100.

The point (300,100) is NOT a feasible solution since it does not conform to the gray area of the system of inequalities solution.

To proof the above,

Let x = 300; and y = 100

Plugin in both values in the inequalities we have:

300 + 100 \(\ngeq\) 500

400 \(\ngeq\) 500 ; Hence it is NOT true; also

300 \(\ngeq\) 500.

The point (500,200) indicates that the contributions raised for the pep club were $500 and the donations raised by the honor society were $200.

The point (500,200) IS A possible solution since it falls inside the darkened area of the system of inequalities solution.

To proof the above,

Let x = 500; and y = 200

Plugin in both values in the inequalities we have:

500 + 200 ≥ 500

700 ≥ 500; hence, this is true and it is safe to indicate that the ordered pair satisfies the inequality A.

Conclusion:
The point (500, 200) is a viable solution.

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The option that can be used to verify the trigonometric identity, \(tan\left(\dfrac{x}{2}\right)+cot\left(x \right) = csc\left(x \right)\) is option C;

C. \(tan\left(\dfrac{x}{2} \right) + cot\left(x \right) = \dfrac{1-cos\left(x \right)}{sin\left( x \right)} +\dfrac{cos \left(x \right)}{sin\left(x \right)} =csc\left(x \right)\)

A trigonometric identity is an equations that consists of trigonometric functions that remain true for all values of the argument of the functions

The specified identity is presented as follows;

\(tan\left(\dfrac{x}{2} \right)+cot(x)=csc(x)\)

The half angle formula for tangent indicates that we get;

\(tan\left(\dfrac{1}{2} \cdot \left(\eta \pm \theta \right) \right) = \dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}\)

\(\dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}=\dfrac{sin \left(\eta\right) \pm sin\left(\theta \right)}{cos \left(\eta \right) + cos \left(\theta \right)} = -\dfrac{cos \left(\eta\right) - cos\left(\theta \right)}{sin \left(\eta \right) \mp sin \left(\theta \right)}\)

When η = 0, we get;

\(-\dfrac{cos \left(0\right) - cos\left(\theta \right)}{sin \left(0 \right) \mp sin \left(\theta \right)}=-\dfrac{1 - cos\left(\theta \right)}{0 \mp sin \left(\theta \right)}=\dfrac{1 - cos\left(\theta \right)}{sin \left(\theta \right)}\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)=\dfrac{1 - cos\left(x \right)}{sin \left(x \right)}\)

\(cot\left(x \right) = \dfrac{cos(x)}{sin(x)}\)

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1-cos(x)+cos(x)}{sin(x)} = \dfrac{1}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1}{sin(x)}=csc(x)\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)} = csc(x)\)

The correct option that can be used to verify the identity is option C

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The pair of ratios that does not form a proportion is 103/24 and 5/40.

To check if two ratios form a proportion, we need to simplify them to their simplest form and compare them. If the two ratios are equal after simplification, then they form a proportion.

In this question, we are given five ratios: 103/24, 5/40, -30/15, 10/5, and 3/S.

To simplify the first ratio, we can divide both the numerator and denominator by their greatest common factor, which is 1. Therefore, the simplified form of 103/24 is 4.29 (rounded to two decimal places).

To simplify the second ratio, we can also divide both the numerator and denominator by their greatest common factor, which is 5. Therefore, the simplified form of 5/40 is 0.125.

When we compare these two simplified ratios, we can see that they are not equal. Therefore, the pair of ratios that does not form a proportion is 103/24 and 5/40.

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Which pair of ratios does NOT form a proportion?

103 24

5 40

-30 15

10 5

3 S

The length of the base of the triangle is 8 yards whose height is half of 28 yards.

A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.

The following formula provides the area of a triangle:

Area = (1/2) x base x height

We are given that the height of the triangle is half of 28 yards, which is:

height = 1/2 x 28 = 14 yards

We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:

56 = (1/2) x base x 14

Simplifying this equation, we get:

56 = 7 x base

Dividing both sides by 7, we get:

base = 8

Therefore, the length of the base of the triangle is 8 yards.

The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.

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Therefore , the solution of the given problem of inequality comes out to be x + 15 < x - 3  and x - 3 > x + 15

In mathematics, a connection or group of integers can be an inequality without the equal sign. Equilibrium  is always followed by equity. Inequality occurs when norms are still incompatible. Disparity and fairness have distinct traits. We chose to use the most typical symbol because components aren't always equivalent or similar to one another (). Any disparity, no matter how small or large, can also be used to evaluate values.

Here,

Let x represent the weather today.

The difference between today's temperature and last year's is three degrees, so last year's temperature was x - 3.

Since the weather was 15 degrees higher five years ago, the previous temperature was x + 15.

We can use the following language to describe the relationship between the temperature today and one year ago today but instead five years ago today with respect to the current temperature:

=> x + 15 < x - 3 (five years ago temperature is less least 1 year ago temperature) 

=> x - 3 > x + 15 (one year ago temperature is bigger than five years ago temperature) 

Therefore, the proper disparities are:

=> x + 15 < x - 3

=>x - 3 > x + 15

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Then you can state that angle DEF is congruent to angle GHJ.

The postulate or theorem that allows you to state that angle DEF is congruent to angle GHJ is the Angle-Angle (AA) Postulate.

This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles must also be congruent.

In this case, if you have two triangles, one with angles DEF and the other with angles GHJ, and

you know that angle D is congruent to angle G and angle E is congruent to angle H, then by the AA Postulate, you can conclude that angle F is congruent to angle J.

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Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

Answer:

Step-by-step explanation:

hello :

g(x) = (x+5)²

Answer:

20. A. 357.8 in³

B. 1231.5 yd³

Step-by-step explanation:

20.

A.

Volume of Pyramid : ⅓*base area * height

here,

Base area = area of rectangle=length*breadth =10*8=80in²

Now

Height can be calculated by using Pythagorous theorem

height =\(\sqrt{(slant\: height)^2-(\frac{breadth}{2})^2}\)

height =\(\sqrt{14^2-(\frac{8}{2})^2}=\sqrt{196-16}=\sqrt{180}=13.42 in\)

height =13.4 in

Now

Volume of pyramid = ⅓*base area *height

Volume of Pyramid=⅓*80*13.42

Volume of Pyramid=357.8 in³

B.

Volume of cone = ⅓*area of base* height

Here

slant height=24 yd

height =?

diameter=14yd

radius =14/2=7 yd

Let's find the height:

By using the Pythagorous theorem,

slight height²=radius²+height²

substituting value

25²=7²+height²

height²=25²-7²

height =\(\sqrt{576}\)=24 yd

Now

Area of Base= πr²=π*7²=153.94 yd²

Now

Volume = ⅓*area of base*height =⅓*153.94*24=1231.5 yd³

So,

Volume of cone is 1231.52 yd³.

The number of M&M's that were in the bowl before Amelia arrived is; 12

Let the original amount in the bowl be x. Thus;

If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x

Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x

Now, we are told that there were finally 3 left after all the deductions. Thus;

0.25x = 3

x = 3/0.25

x = 12

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Answer:

2

Step-by-step explanation:

The equation has 2 terms in it which means 2 is the answer.

Answer:

1kg of onion is $1.5

Step-by-step explanation:

He paid $10 and got $1.50 back, meaning that the total price for the 2kg and 3kg of the potato and onion is:

10 - 1.5 = $8.50

Now, equating the prices of the two (take x as the cost of the potato per kg and take y as the cost of the onion per kg):

x -0.5 = y

x - y = 0.5  ---- Eq 1

Equating the total costs:

2x + 3y = 8.5 ---- Eq 2

Multiplying Eq 1 by 2:

2x - 2y = 1 ---- Eq 1'

Subtracting Eq 2 from Eq 1':

2x - 2x +3y - (-2y) = 8.5 - 1

5y = 7.5

y = 1.5

Substituting this into the first equation:

x - 1.5 = 0.5

x = 2

Hence,

the cost of the Potato is $2, and

the cost of the Onion per kg is $1.5

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Answer:

3000 is the answer this question.

120 many combinations are possible.

The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.

Consider a collection of three integers P, Q, and R. The number of ways that we may choose two numbers from each group is thus determined by combination.

It is represented as: \(^nC_r\)

where, n = total number of objects in the set

r = number of choosing objects from the set

Given that,

Cell Phone Models A particular cell phone company offers:

4 models of phones

each in 6 different colors

each available with any one of 5 calling plans

Thus, possible combination numbers are:

= (No. of models) × (No. of colors) × (No. of calling plans)

= (4)× (6)× (5)

= 120 possibilities

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Answer:

t- critical value =1.721

Step-by-step explanation:

Given

Sample size =n=22

Degree of freedom = sample size -1 = 22-1 =21

The significance level is 5%. This indicates that the test is right tailed.

The alpha value = 0.05

For given right tailed test, with value of alpha = 0.05 and degree of freedom = 21, the  t- critical value =1.721

Answer:

\(S=\frac{C}{2}\)

Step-by-step explanation:

From the graph B,

Let the equation of the line representing the relation between hours spent in studying 'S' and hours spent in class 'C' is,

S = mC + b

Where m = Slope of the line

b = y-intercept of the line

We choose two points (2, 1), and (4, 2) lying on the line.

Slope 'm' = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

m = \(\frac{2-1}{4-2}\)

m = \(\frac{1}{2}\)

y-intercept 'b' = 0

Equation of the line will be

S = \(\frac{1}{2}C\)

Answer:

d. I and III only

Step-by-step explanation:

I. The seeds should be randomly assigned to a treatment.

III. The number of successful seeds and unsuccessful seeds in each group should be at least 10.

The distribution of difference between two sample proportions :

Given :

Proportion 1 = P1 ;

Proportion 2 = P2 ;

Sample assignment for both samples 1 and 2 into the different treatment groups should be randomized, that is a simple random sampling of subjects into the treatment and control group. The sample design for difference between two sample proportions should be independent.

Finally each of the two proportions P1 and P2 should record a minimum of 10 successes and 10 non - successful Occurrences.

The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

When given two points and asked to find the equation of the line in slope-intercept form, the correct steps, the correct order is 2 , 1 , 4 , 3.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

Given that,

given two points and asked to find the equation of the line in slope-intercept form.

Find that,

what are the correct steps? Place a number next to the step to put them in order.

Explanation:

to find the equation of the line in slope intercept form form given two points.

step 1 :

find the slope.

step 2

write equation in point slope form

step 3.

pick a point form the given points , substitue it into the point slope form

step 4.

write the equation in slope intercept form by simplifying

Final Answer.

Hence , the correct order is 2 , 1 , 4 , 3.

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The integers that are in order from least to greatest will be C. -13, -2, 6, 20.

It should be noted that an integer simply means a natural number or a whole number that given. It should be noted that they can either be positive or negative.

In this case, the numbers will be illustrated as thus:

The smallest number is -13.

The biggest number is 20.

Therefore, the arrangement is -13, -2, 6, 20.

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Answer:

seconds

Step-by-step explanation:

Answer:

48s= number of scarves

Step-by-step explanation:

48 represents the price of scarf

Thank me later :)

Milan has two coupons for a jacket.

Coupon A:$16 rebate on a $55 jacket.

Coupon B:35% off of a $55 jacket.

Choose the coupon that gives the lower price.

Then fill in the blank with the correct value.

First case

Coupon A:$16 rebate on a $55 jacket.

the final price is ------> 55-16=$39

second case

Coupon B:35% off of a $55 jacket.

Remember that

100%-35%=65%=65/100=0.65

so

the final price is

0.65*55=$35.75

therefore

Answer:

What do you mean?

Step-by-step explanation:

I don’t understand.

Answer:4 times 5

Step-by-step explanation: