the respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes

Answer:

[tex]C = 25.1 \text{ cm}[/tex]

Step-by-step explanation:

We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:

[tex]C = \pi d[/tex]

Note: This formula can also be written as [tex]C = 2\pi r[/tex] because [tex]2r = d[/tex].

↓ plugging in the given radius

[tex]C = 8\pi \text{ cm}[/tex]

↓ rounding to the nearest tenth

[tex]\boxed{C = 25.1 \text{ cm}}[/tex]

Answer:

28 in²

Step-by-step explanation:

Area of parallelogram = base X vertical height

= 7 X 4

= 28 in²

Answer:

To many questions, and too many numbers

Step-by-step explanation:

Shakira needs to rent a car for one day and she is trying to decide which car rental company to use. Alpha Car Rental offers a Porsche for $29.17 per day, plus 57 cents per mile. Beta Car Rental also offers the same car for $50.23 per day, plus 44 cents per mile.

To determine which car rental is a better deal, Shakira needs to calculate at what number of miles the prices for both Alpha and Beta Car Rental are the same. To do this, she can use the following equation:

The variable of x is the number of miles. This equation simplifies to x = 21.06 miles. Therefore, at 21.06 miles, Alpha and Beta Car Rental will be the same price.

The given table represents a linear function with a constant rate of change of 2. Option D is the right answer.

To determine if the table represents a linear function and calculate the rate of change, let's examine the given values:

x   | y

-----------

1   | 3

2   | 5

3   | 7

4   | 9

By looking at the y-values, we can observe that for every increase of 1 in x, the corresponding y-value increases by 2. This indicates a constant rate of change, suggesting that the table represents a linear function.

To calculate the rate of change, we can use the formula:

[tex]\[\text{{Rate of Change}} = \frac{{\text{{Change in y}}}}{{\text{{Change in x}}}}\][/tex]

Taking any two points from the table, let's choose (1, 3) and (2, 5):

[tex]\[\text{{Rate of Change}} = \frac{{5 - 3}}{{2 - 1}} = \frac{2}{1} = 2\][/tex]

The table provided exhibits a linear function with a constant rate of change. As the x-values increase by 1 from [tex]1[/tex] to [tex]4[/tex], the corresponding y-values increase by [tex]2[/tex] from [tex]3[/tex] to [tex]9[/tex]. This consistent change in y for each unit change in x indicates a linear relationship between the variables.

The rate of change, also known as the slope of the function, is determined by the ratio of the change in y to the change in x. In this case, the rate of change is [tex]2[/tex], meaning that for every increase of [tex]1[/tex] in [tex]x[/tex], the y-value increases by 2.

Thus, the table represents a linear function with a rate of change of [tex]2[/tex].

Therefore, the correct answer is D) Yes; rate of change = [tex]2[/tex].

NOTE: The given question is incomplete. The complete question is:

Determine if the table below represents a linear function. If so, what's the rate of change?

options:

A)  Yes; rate of change = 4

B)  No; it's a non-linear function.

C)  Yes; rate of change = 3

D)  Yes; rate of change = 2​

Table:

x   | y

-----------

1   | 3

2   | 5

3   | 7

4   | 9

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Step-by-step explanation:

5 P 5 = 120 ways = 5!

The set of capacity measures related to cubic meter are ordered from the greatest to the least:

5.5 dam³, 5.480 m³, 5 dam³, 5 dam³, 530 m³, 61 m³

In this problem we need to order a group of capacity measures in cubic meters and its related units from the greateast to the least. To make this we need to understand the following relations:

Now we proceed to order the following set of information:

First, write the set of measures:

5 dam³, 530 m³, 5.480 m³, 5.5 dam³, 5 dam³, 61 m³

Second, convert all measures in cubic decameters into cubic meters:

5.000 m³, 530 m³, 5.480 m³, 5.500 m³, 5.000 m³, 61 m³

Third, order all the set from the greatest to the least:

5.500 m³, 5.480 m³, 5.000 m³, 5.000 m³, 530 m³, 61 m³

Fourth, rewrite the set of measures in its original units:

5.5 dam³, 5.480 m³, 5 dam³, 5 dam³, 530 m³, 61 m³

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The measure of angle QRS in triangle QRS is 56.8 degrees.

To find the measure of angle QRS in triangle QRS, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.

We know that:

- The measure of angle RSQ is 48.2 degrees

- The measure of angle SQR is 75 degrees

Let x be the measure of angle QRS. Then, we can write:

RSQ + SQR + QRS = 180

Substituting the known values, we get:

48.2 + 75 + x = 180

Simplifying and solving for x, we get:

x = 180 - 48.2 - 75x = 56.8

Therefore, the measure of angle QRS in triangle QRS is 56.8 degrees.

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After making payments for 15 years, the amount still owed on the mortgage would be approximately $145052.36.

To determine how much will still be owed after making payments for 15 years, we can use the formula for the remaining balance on a mortgage:

Remaining balance = P ((1 + r)ⁿ - (1 + r)ᵇ) / ((1 + r)ⁿ - 1)

where:

P = the initial loan amount (in this case, $219,000)

r = the monthly interest rate (which is the annual interest rate divided by 12)

n = the total number of monthly payments (which is 30 years times 12 months per year, or 360 months)

b = the number of monthly payments made so far (which is 15 years times 12 months per year, or 180 months)

First, we need to calculate the monthly interest rate:

r = 4.5% / 12 = 0.00375 = 0.375%

Next, we can plug in the values to get:

Remaining balance = $219,000 ((1 + 0.00375)³⁶⁰- (1 + 0.00375)¹⁸⁰) / ((1 + 0.00375)³⁶⁰ - 1)

= $145052.36

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The variables for this problem are given as follows:

a = 16, [tex]b = 16\sqrt{2}[/tex] , c = 16, d = 16.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

For side lengths a and c, we have a right triangle with angles of 45º, hence using the 45-45-90 Triangle Rule, with the hypotenuse of [tex]16\sqrt{2}[/tex], the lengths a and c are given as follows:

a = c = 16.

The length a is also the geometric mean of the lengths c and d, hence:

16² = 16d

d = 16.

Then the length b is obtained applying the Pythagorean Theorem as follows:

b² = 16² + 16²

[tex]b = \sqrt{2 \times 16^2}[/tex]

[tex]b = 16\sqrt{2}[/tex]

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The line of symmetry for the above figure is attached accordingly.

In mathematics, symmetry with regard to a reflection is known as reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry.

That is, a figure with reflectional symmetry does not alter when it is reflected. A line/axis of symmetry exists in 2D, while a plane of symmetry exists in 3D.

After inserting the symmetry lines, the above resulted in a kite.

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Answer:If the Diameter of a circle is 22 inches, the area will be 380.13in².

Step-by-step explanation:

These are the formulas you use:

Area=pi*Radius^2  or A=pi*Radius*Radius

Diameter=2*Radius

A=1

4*pi*Diameter*2=1 2

4*pi*222=380.13271in

380.13271in is approximately 380.13in².

Answer:True

Lower interest rates reuslt in saving more money.

The conic section of the equation 4x² + 9x +4y² - 36y - 125 = 0 is a circle

The given equation is

4x² + 9xy + 4y² - 36y - 125 =0

The above equation is an illustration of a circle equation

The standard form of a circle equation is

(x - a)² + (y - b)² = r²

Where

(a, b) is the center

r is the radius

While the general form of the equation is

ax² + fx + by² + gy + c =0

Where c is a constant

Recall that, we have

4x² + 9x + 4y² - 36y - 125 =0

This is the general form

We can convert to the standard form as follows

Divide through by 4

x² + 2.25x + y² - 9y - 31.25 =0

Next, we complete the square of the x-terms and the y-terms

For the x-terms, we have

x² + 2.25x = x² + 2.25x + (2.25/2)² - (2.25/2)²

x² + 2.25x = (x + 2.25/2)² - (2.25/2)²

For the y-terms, we have

y² - 9y = y² - 9y + (9/2)² - (9/2)²

y² - 9y = (y - 9/2)² - (9/2)²

Substitute the new x and y terms

So, x² + 2.25x + y² - 9y - 31.25 = 0 becomes

(x + 2.25/2)² - (2.25/2)² + (y - 9/2)² - (9/2)²- 31.25 =0

Evaluate the sum of like terms

(x + 2.25/2)² + (y - 9/2)² - 3377/64 = 0

So, we have

(x + 9/8)² + (y - 9/2)² = 3377/64

Using the above as a guide, we can conclude that the conic section of the equation is a circle

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From the calculation, she can't carry all but she can carry her suitcase with clothes in it and three out of the four gift items.

We know that we have to consider the restriction that the airline has placed. We have been told that the luggage that have to be packed in this case would have to be less than 22.7 kg.

We would now have to look at all the things that Haley would need to pack so as to determine what can be packed and what can not be packed.

Total luggage  that she has to pack;

Mass of empty suitcase + mass of her clothes + mass of 4 gifts

Total luggage = 5.1 Kg + 14.8 Kg + 4(0.87) = 23.38 Kg

This implies that she can't carry all but she can carry her suitcase with clothes in it and three out of the four gift items.

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Answer:

1?

Step-by-step explanation:

9 1/4 is the longest distance

2 times

According to the chart, the mile that she ran the fastest was [tex]9 \frac{1}{2}[/tex] miles. 1 dot equals 1 minute so her fastest mile was [tex]9 \frac{1}{2}[/tex].

I hoped this helped if not please tell me what I did wrong ૮ ˶ᵔ ᵕ ᵔ˶ ა

The reflection rule that maps triangle DEF onto triangle D'E'F' is a reflection across the line that passes through (2,2) and (−1.25,2.75).

A translation is a type of transformation that moves all the points of a figure the same distance and in the same direction.

The shape and size of the figure do not change, only its position in the plane.

(3, 6)--->(1,6)

3-x=1

x=-2

(x-2, y)

To find the reflection rule that maps the triangle D(3, 6), E(-4,-3), F(6, 1) onto its image D'(1, 6), E(8, -3), F'(-2, 1), we need to determine the line of reflection.

In triangle the point where the perpendicular bisectors intersect will be the center of the reflection.

We find that the midpoint of DE is (−0.5,1.5), the midpoint of DF is (4.5,3.5), and the midpoint of EF is (1,−1).

The perpendicular bisectors of DE and DF intersect at (2,2), and the perpendicular bisectors of DE and EF intersect at (−1.25,2.75).

Therefore, the reflection rule that maps triangle DEF onto triangle D'E'F' is a reflection across the line that passes through (2,2) and (−1.25,2.75).

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The interquartile range for the average of 15 cities is 1.8.

a) X ~ N(9.6, 1.3)

b) X bar ~ N(9.6, 0.13)

c) The probability that one randomly selected city's waterway will have less than 9.3 ppm pollutants can be calculated using the z-score formula: P(X < 9.3) = P(Z < (9.3 - 9.6) / 1.3) = 0.338.

d) The probability that the average amount of pollutants is less than 9.3 can be calculated using the z-score formula: P(Xbar < 9.3) = P(Z < (9.3 - 9.6) / 0.13) = 0.819.

e) The assumption that the distribution is normal is indeed necessary for part d.

f) The IQR for the average of 15 cities can be calculated as follows: Q1 = 8.7 and Q3 = 10.5. IQR = 10.5 - 8.7 = 1.8.

Therefore, the interquartile range for the average of 15 cities is 1.8.

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The measure of <BED = 135 degrees

To determine the value, we need to know the following;

From the information given, we have that;

Angle AED + Angle ACD are on a straight line

Now, susbtitute the values, we have that;

135 + ACD = 180

collect like terms

ACD = 180 - 135

subtract the values

ACD = 45

Then, we have that;

<BED = <ACD + <BEC

Substitute the values

<BED = 45 + 90

<BED = 135 degrees

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(a) The distribution of X ~ N(7.08, 2.29)

(b) The probability of a patron's lunch cost is 0.049

(b) The probability of a group patron's lunch cost is 0.049

(d) The assumption of normal distribution is not necessary

Given that

Mean = 7.08

Standard deviation = 2.29

The distribution of X is represented as

X ~ N(Mean , Standard deviation)

So, we have

X ~ N(7.08, 2.29)

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (6.9379  - 7.08)/2.29 and z = (7.2186 - 7.08)/2.29

Evaluate

z = -0.062 and z = 0.061

So, we have

P = P(-0.062 < z < 0.061)

Evaluate

P = 0.049039

Approximate

P = 0.049

This is same as part (b)

i.e. the probability that the average lunch is between $6.9379 and $7.2186 is 0.049

No, the assumption is not necessary

This is because

The distribution has a sample size less than 25 as required by the central limit theorem

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1. f(x) =  (2x² + 4x + 4) / x³ = 0; as lim x→∞, and lim x→-∞

2. g(x)  = (2x²  +  4x  + 4)/x² = ∞; as lim x→∞, and lim x→-∞]

3.  h(x)  = (2x²  +  4x  + 4)/x = ∞ as lim x→∞, and -∞ as lim x→-∞.

To find the end behavior of each of the functions, we can take the limit as x approaches infinity and negative infinity.

For  f(x)  = (2x²  +  4x  + 4)/x³;

lim x→∞ (2x² + 4x + 4) / x³ = 0

lim x→-∞ (2x² + 4x + 4) / x³ = 0

f(x) approaches zero as x approaches positive or negative infinity.

For  g(x)  = (2x²  +  4x  + 4)/x²;

lim x→∞ (2x² + 4x + 4) / x² = ∞

lim x→-∞ (2x² + 4x + 4) / x² = ∞

g(x) approaches infinity as x approaches positive or negative infinity.

For  h(x)  = (2x²  +  4x  + 4)/x

lim x→∞ (2x² + 4x + 4) / x = ∞

lim x→-∞ (2x² + 4x + 4) / x = -∞

h(x) approaches infinity as x approaches positive infinity, and negative infinity as well, but with a negative sign.

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Step-by-step explanation:

OK, 'Brainless'....  the triangle side length rule states that any two sides of a triangle must sum to greater than the remaining side length...

42 + 20 > x        then  12 , 20, 22, 32, 42, 50     will work here

42+x > 20            all of the possibles work here

20 + x > 42         32, 42, 50, 62 and 70 work here

   so   32 and 42 are in all of the lists ....that is your answer

Jeremy is wrong as I explained below.

As we know,

Thus, as we can see from the figure figure 1 is a rectangle and Figure 2 is a square so,

I do not agree with Jeremy.

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Complete question:

The value of the principal is $10,000.

The equation A = P(1 + 0.043t) represents the amount of money earned on a savings account with 4.3% annual simple interest A is the account balance after t years P is the principal amount, and 0.043 is the interest rate per year.

The account balance is $15,160 after 12 years.

Substituting these values into the equation, we get:

15,160 = P(1 + 0.043(12))

Simplifying the right-hand side, we get:

15,160 = P(1 + 0.516)

15,160 = P(1.516)

Dividing both sides by 1.516, we get:

P = 10,000

This means that the account was initially opened with a principal of $10,000 and it earned simple interest of 4.3% per year for 12 years resulting in an account balance of $15,160.

The principal and it does not take into account the interest that is earned on the interest itself.

In contrast compound interest takes into account the interest that is earned on both the principal and the previously earned interest.

The account in question had been earning compound interest instead of simple interest the final account balance after 12 years would have been higher than $15,160.

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The statement "When added, the sum of the y-intercepts must be 1" and "f(x) could have a rate of change equal to 1 and g(x) could have a rate of change of 2" can be used to describe the original functions f(x) and g(x).

Within mathematical study, we encounter various types of relations between objects – but none quite so distinctive as a function. These relations are essentially collections or sets composed solely from ordered pairs – pairings containing precisely two distinct elements each.

The defining trait for functions lies in how they operate with regards to these paired elements: specifically that every element comprising the domain – representing all potential inputs – correspond with absolute exclusivity to just one solitary member within the codomain – signifying all possible outputs.

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There are 35 different committees that can be formed, each consisting of one man and one woman.

To form the committee consisting of one man and one woman, we need to choose one man from the available seven men and one woman from the available five women.

Number of choices for selecting one man = 7

Number of choices for selecting one woman = 5

To find the total number of different committees that can be formed, we multiply these numbers together:

Total number of committees = 7 × 5

Total number of committees = 35

Therefore, there are 35 different committees that can be formed, each consisting of one man and one woman.

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The area of the figure is 183.5 ft².

We have,

The figure has two types of shapes.

Two rectangles and one triangle.

Now,

Area of rectangle = Length x Width

Area of triangle = 1/2 x base x height

Now,

Rectangle 1:

Area = 7 x 5 = 35 ft²

Rectangle 2:

Area = 4 x (4 + 5) = 4 x 9 = 36 ft²

Triangle:

Area = 1/2 x (11 + 4) x 15 = 1/2 x 15 x 15 = 112.5 ft²

Now,

The area of the figure.
= 35 + 36 + 112.5

= 183.5 ft²

Thus,

The area of the figure is 183.5 ft².

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