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The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

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Answer:

hundreths the 9 represents 900

Step-by-step explanation:

Answer:

900

Step-by-step explanation:

1,905

Expand the number

1000 + 900 + 5

900 is the value of the 9

Answer:

x = 13

y = 9

Step-by-step explanation:

Answer:

\((5x + 2)(x - 1)\)

Step-by-step explanation:

1. Split the second term in  into two terms.

\(5x ^2 +2x - 5x - 2\)

2. Factor out common terms in the first two terms, then in the last two terms.

\(x(5x+2) - (5x+2)\)

3. Factor out the common term .

\((5x+2)(x - 1)\)

The power series for f(x) 1/(1-x²) centered at 0 is:

1 + x² + x⁴ + x⁶ + ...

The first four nonzero terms are 1, x², x⁴, x⁶.

The power series expansion for the function f(x) = 1/(1-x²) centered at 0 can be found using the geometric series formula.

By letting a=1 and r=x²,

we get the series 1 + x² + x⁴ + x⁶ + ..., which converges for |x|<1.

This is because as x approaches 1 or -1, the terms of the series diverge.

Thus, the first four non-zero terms of the series are 1 + x² + x⁴ + x⁶.

This power series expansion is useful in many applications, such as in approximating the function near x=0 or in solving differential equations using power series methods.

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Mutually exclusive events are two events that cannot occur at the same time. The conditional probability of B given A is also equal to zero, since P(B|A)=P(A and B)/P(A)=0.

This means that their intersection is empty, or P(A and B)=0.This also means that their union is the sum of individual probabilities, P(A)+P(B). This is because the intersection of two mutually exclusive events is equal to the product of their probabilities, or P(A and B)=P(A)P(B). Therefore, the probability of either event occurring is the sum of the probability of each event since the intersection of both events is zero. As a result, the conditional probability of B given A is also equal to zero, since P(B|A)=P(A and B)/P(A)=0.

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Answer:

last one

Step-by-step explanation:

6 3x2/8x2= 6 6/16

6 +5=11

6/16+11/16=17/16

11 17/16

Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

The answer for this question is 8 because 7.954 the 9 is the ones the 5 is the hundreds the 4 is the thousands. Also whenever a number is or up it goes up or increases by one.

Hope that helped plz give me brainiest if I did thx!!! <3

Answer: 321-134= 187

Step-by-step explanation:

Answer:

187

Step-by-step explanation:

Total People: 321

Total People Younger than 10 years old: 134

Take the total people and subtract all people younger than 10 years old. All you have left is people who are NOT younger than 10 years old.

321(Total People) - 134(People younger than 10 years old) = 187 people NOT younger than 10 years old.

Using BODMAS, the solutions of the expressions are: (1) 9, (2)-12, (3) 0.27, and (4) 0.24

We should know that BODMAS is a mathematical approach which means

In each of the expressions, we must follow the approach

1)    \(\frac{(6+3)^{2} }{3*9}\)

Simplifying this we have 9²/9=81/9

=9

2)  \(\frac{3^{2} -6*2}{(12-8)/2^{2} *10}\)

Using BODMAS we have

(9-12)/4/40

-3÷1/9

⇒-3*4

=-12

(3)   \(\frac{4.5+2*2.5^{2}-6 }{8*4+9}\)

Using BODMAS we have

(4.5+2*6.25-6)/32+9

⇒(4.5+12.5-6)/41

=11/41=0.27

4     (\(\frac{3.5+16-2.5^{2} }{10.5-6*11}\))

Using BODMAS we have  

(3.5+16-6.25)/10.5-66

Simplifying

(13.25)/-55.5

=0.24

Therefore, the values when simplified are  (1) 9, (2)-12, (3) 0.27, and (4) 0.24

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Answer:

5 23/100

Step-by-step explanation:

Answer:

523/100 (Mixed number - 5  23/100)

Answer:

length of rectangle = 5

width of rectangle = 5

Area of rectangle = 25

Step-by-step explanation:

Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:

\(y=x\,(10-x)=10x-x^2\)

Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.

Recall that the formula for the x of the vertex of a quadratic of the form :

\(y=ax^2+bx+c\)

is given by the formula:

\(x_{vertex}=-\frac{b}{2\,a}\)

which in our case gives:

\(x_{vertex}=-\frac{b}{2\,a}\\x_{vertex}=-\frac{10}{2\,(-1)}\\x_{vertex}=5\)

Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.

The area of the rectangle is therefore the product of these two values: 5 * 5 = 25

Which should coincide with the value we obtain when we replace x by 5 in the area formula:

\(y=10x-x^2\\y=50-(5)^2\\y=50-25\\y=25\)

Answer:

Combine like terms

Step-by-step explanation:

+ 8x

+4y

+4

8x + 4y + 4

Answer:

B

Step-by-step explanation:

2x+6x=8x

7y-3y=4y

Add the new terms into the equation and you get 8x+4y+4

Answer:

C-true

Step-by-step explanation:

A-false

B-false

C-true

D-false

used substitution

The product of the two expressions (m - n)(m + n) gives x² - 4

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the expression (m - n)(m + n):

Multiplying the two expressions gives:

m² + mn - mn - n²

This gives:

m² - n²

The product of the two expressions (m - n)(m + n) gives x² - 4

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Answer:

5d-10 =0

Step-by-step explanation:

Answer: 5d - 10 = C

-tay

The root of the function f(x) = -12 – 21x + 18x² - 2.75x³, obtained using the false-position method with initial guesses of x1 = -1 and xu = 0, and a stopping criterion of 1%, is approximately x = -0.2552.

The false-position method is an iterative root-finding algorithm that narrows down the search for a root of a function within a given interval. In this case, we have the function f(x) = -12 – 21x + 18x² - 2.75x³.
To apply the false-position method, we need two initial guesses, x1 and xu, such that f(x1) and f(xu) have opposite signs. Here, x1 = -1 and xu = 0.
Next, we calculate the value of f(x1) and f(xu):
F(x1) = -12 – 21(-1) + 18(-1)² - 2.75(-1)³ = -12 + 21 – 18 + 2.75 ≈ -6.25
F(xu) = -12 – 21(0) + 18(0)² - 2.75(0)³ = -12 ≈ -12
Since f(x1) and f(xu) have opposite signs, we can proceed with the false-position method.
Now, we find the next guess, x2, using the formula:
X2 = xu – (f(xu) * (x1 – xu)) / (f(x1) – f(xu))
X2 = 0 – (-12 * (-1 – 0)) / (-6.25 – (-12)) ≈ -0.3548
We repeat the process until the stopping criterion is met. Since the criterion is 1%, we continue until the difference between consecutive x-values is less than 1% of the previous x-value.
After several iterations, we find that the approximate root is x ≈ -0.2552.
Therefore, the root of the given function using the false-position method is approximately x = -0.2552.

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Answer:

27, 28, 29

Step-by-step explanation:

If you divide 84 by 3, the quotient will be in the middle of the three integers. We get 28 from dividing 84 by 3, therefore our string of numbers are 27, 28, and 29.

Answer:

x = 15.9

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

6^2 + x^2 = 17^2

36+ x^2 = 289

x^2 = 289-36

x^2 =253

Take the square root of each side

sqrt(x^2) = sqrt( 253)

x = 15.90597

Rounding to the nearest tenth

x = 15.9

The volume of the right pyramid with a square base and each edge 4 inches long is 32/3√3 cubic inches. We used the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.

We found the area of the base to be 16 square inches and the height of the pyramid to be 2√3 inches, using the Pythagorean theorem.

To find the volume of the right pyramid, we first need to understand what a right pyramid is. A right pyramid is a pyramid where the apex is directly above the center of the base and the lateral edges are perpendicular to the base. In this case, we have a right pyramid with a square base, which means that the base of the pyramid is a square and the apex is directly above the center of the square.

To find the volume of this pyramid, we can use the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. In this case, the base is a square with side length 4 inches, so the area of the base is 4 x 4 = 16 square inches.

To find the height of the pyramid, we can use the Pythagorean theorem, since we know that each edge of the pyramid is 4 inches long. The height is the distance from the apex of the pyramid to the center of the square base. Using the Pythagorean theorem, we can find that the height of the pyramid is √(4^2 - 2^2) = √12 = 2√3 inches.

Now we can plug in the values we've found into the formula V = (1/3)Bh. We get V = (1/3)(16)(2√3) = 32/3√3 cubic inches. This is the volume of the pyramid in cubic inches.

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Answer:

2.25 dollars per pound

Step-by-step explanation:

Take the cost and divide by the number of pounds

11.25 dollars / 5 pounds

2.25 dollars per pound

Answer:

The cat food costs 2.25 dollars per pound

Step-by-step explanation:

First let's write this like an equation. Let's add a variable instead of pounds and you can name that anything you like. I prefer to use X. And since we have 5 pounds of cat food, we put 5x.

X = 1 Pound of cat food

11.25$ = 5x

Now we want X alone, so we divide both sides by 5

11.25$/5 = 5x/5

Now if we divide we get

2.25$ = X

And if we turn x back into pounds of cat food, we get that, for 2 dollars and 25 cents we have 1 bag of cat food

2.25$ = 1 Pound of cat food

the magnitude of the resultant force acting on the object is approximately 36.06 N

To determine the magnitude of the resultant force acting on the object, we can use the law of cosines.

Let F₁ = 20 N be the magnitude of the first force and F₂ = 30 N be the magnitude of the second force. The angle between the two forces is given as 20°.

According to the law of cosines, the magnitude of the resultant force R is given by:

R² = F₁² + F₂² - 2F₁F₂cos(θ)

where θ is the angle between the two forces.

Plugging in the values, we have:

R² = (20²) + (30²) - 2(20)(30)cos(20°)

R² = 400 + 900 - 2(20)(30)cos(20°)

R² = 1300 - 1200cos(20°)

Now, we can calculate the value of R by taking the square root of R²:

R = √(1300 - 1200cos(20°))

R ≈ 36.06 N

Therefore, the magnitude of the resultant force acting on the object is approximately 36.06 N.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct

option is 50% (option 3).

Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".

According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original

wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,

development, and urbanization. Therefore, the correct answer to the question is 50%.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%.

Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.

There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.

Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.

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Answer:

There will be 2,547 bacteria after 7 days.

Step-by-step explanation:

\(87*1.62^{7} =2547\)

After 7 days there will be 2547.55 cells in a petri dish if the number of fungi in a petri dish on the first day was 87 cells. If the number of fungi increases at a rate of 62% per day.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent y = a×

where a is a constant and a>1

We have:

The number of fungi in a petri dish on the first day was 87 cells. If the number of fungi increases at a rate of 62% per day.

As we know,

The standard form of the exponential growth equation:

y = a(1 + r)×

Here,

a is the starting value:

a = 87 cells

r = 62% = 0.62

x = 7 days

y = 87(1 + 0.62)⁷

After solving:

y = 2547.55 cells

Thus, after 7 days there will be 2547.55 cells in a petri dish if the number of fungi in a petri dish on the first day was 87 cells. If the number of fungi increases at a rate of 62% per day.

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Answer:

A. $157,775.90

Step-by-step explanation:

\(224,725(0.9925)^7^2^-^m\)

Where m is the number of months remaining in the lease

m = 25

\(P(m)= 224725(0.9925)^7^2^-^2^5\\\\P(m) = 157,755.90\)

Answer:

∠A = 45°

Step-by-step explanation:

◺ABC is a right angled triangle.

Sum of interior angles in a triangles is 180.

∠A + ∠B + ∠C = 180°

∠A + 90° + 45° = 180°

∠A = ( 180 - 90 - 45 )°

∠A = 45°

Note : -

□ is 90°

Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

The new dimensions of the shapes after transformation are;

1) Altitude = 9 in * 1/3 = 3 in

Hypotenuse = 24 in * 1/3 = 8 in

Leg = 18 in * 1/3 = 6 in

2) Length = 3.5 in * 2 = 7 in

Width = 12.4 in * 2 = 24.8 in

3) Altitude = 9 in * 1.5 = 13.5 in

Hypotenuse = 24 in * 1.5 = 36 in

Leg = 18 in * 1.5 = 12 in

4) Length = 3.5 in * 1/4 = 0.875 in

Width = 12.4 in * 1/4 = 3.1 in

5) Altitude = 9 in * 1/2 = 4.5 in

Hypotenuse = 24 in * 1/2 = 12 in

Leg = 18 in * 1/2 = 9 in

6) Length = 3.5 in * 4 = 14 in

Width = 12.4 in * 4 = 49.6 in

When we transform an object with a scale factor, if the scale factor is less than 1, then it will be reduced or shrinked while if the scale factor is greater than 1, it will be enlarged.

Dimensions of rectangle are;

Length = 3.5 in

Width = 12.4 in

Dimensions of triangle;

Altitude = 9 in

Hypotenuse = 24 in

Leg = 18 in

1) Shrinking the triangle by a scale factor of 1/3 will yield;

Altitude = 9 in * 1/3 = 3 in

Hypotenuse = 24 in * 1/3 = 8 in

Leg = 18 in * 1/3 = 6 in

2) Expanding the rectangle by a scale factor of 2 gives;

Length = 3.5 in * 2 = 7 in

Width = 12.4 in * 2 = 24.8 in

3) Expanding the triangle by a scale factor of 1.5 gives;

Altitude = 9 in * 1.5 = 13.5 in

Hypotenuse = 24 in * 1.5 = 36 in

Leg = 18 in * 1.5 = 12 in

4) Shrinking the rectangle by a scale factor of 1/4 will yield;

Length = 3.5 in * 1/4 = 0.875 in

Width = 12.4 in * 1/4 = 3.1 in

5) Shrinking the triangle by a scale factor of 1/2 will yield;

Altitude = 9 in * 1/2 = 4.5 in

Hypotenuse = 24 in * 1/2 = 12 in

Leg = 18 in * 1/2 = 9 in

6) Expanding the rectangle by a scale factor of 4 gives;

Length = 3.5 in * 4 = 14 in

Width = 12.4 in * 4 = 49.6 in

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The set of parameters that would give this person the worst grade on the exam relative to others is µ = 70 and σ = 5. This can be found using z-score. The correct option is option c).

To determine which set of parameters would give this person the worst grade on the exam relative to others, we need to find the z-score for the score of 65 under each set of parameters and see which one is the lowest. The z-score is a measure of how many standard deviations a particular value is from the mean.

The formula for calculating the z-score is:

z = (x - µ) / σ

where x is the score, µ is the mean, and σ is the standard deviation.

a. µ = 60 and σ = 5

z = (65 - 60) / 5 = 1

b. µ = 70 and σ = 10

z = (65 - 70) / 10 = -0.5

c. µ = 70 and σ = 5

z = (65 - 70) / 5 = -1

d. µ = 60 and σ = 10

z = (65 - 60) / 10 = 0.5

The lowest z-score is -1, which corresponds to option c. This means that most people scored higher than 65, and those who scored lower did so by a smaller margin.

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Answer:

c = 25,000 - 2000y

Step-by-step explanation: