Tammy is planning to garden a plot of land in the shape of a right triangle.


The length of the base of the plot is 12 feet, and the length of one side is 5 feet, as shown in the diagram. Tammy makes a scale drawing of the plot using a scale of 1 inch to 2 feet. The area of the plot in the scale drawing is
square inches.

The linear function that represents the line is f(x) = -3x + 14

We can rewrite the point-slope equation y + 1 = -3(x - 5) in slope-intercept form, which has the general form of y = mx + b, where m is the slope and b is the y-intercept.

To do this, we first distribute the -3 on the right side of the equation:

y + 1 = -3x + 15

Then, we can isolate y by subtracting 1 from both sides:

y = -3x + 14

So the slope of the line is -3 and the y-intercept is 14. Therefore, the linear function that represents the line is:

f(x) = -3x + 14

Hence, the correct answer is f(x) = -3x + 14.

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The points or coordinates that will fall inside the parallelogram are 0,4 and 4,7.

Based on the above, the coordinates that would fit inside the parallelogram are:

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Answer: 55 degrees

Step-by-step explanation: 180-70-55=u

This answer is because the sum of all the angles is 180 degrees.

Answer:

u = 55°

Step-by-step explanation:

The sum of the internal angles of a triangle = 180°

Then:

70 + 55 + u = 180

125 + u = 180

u = 180 - 125

u = 55°

The area of the parallelogram is approximately 193.73 square meters.

How to find the area?

To find the area of a parallelogram, we need to multiply the length of one side of the parallelogram by the perpendicular distance between that side and the opposite side.

In this case, we know that one side of the parallelogram is 11.8 m and the other side is 18.5 m. Let's call these sides "a" and "b" respectively.

To find the perpendicular distance between these two sides, we need to draw a perpendicular line from one of the endpoints of side "a" to side "b". Let's call this perpendicular distance "h".

We can use the formula for the area of a parallelogram:

Area = base x height

where the base is side "a" and the height is "h".

To find "h", we can use the Pythagorean theorem:

h² = b² - (a/2)²

where "a/2" is half of side "a".

Plugging in the values we know, we get:

h² = 18.5² - (11.8/2)²

h² = 302.25 - 34.81

h² = 267.44

h ≈ 16.36

Now that we know the height of the parallelogram, we can calculate its area:

Area = 11.8 x 16.36

Area ≈ 193.73 m²

Therefore, the area of the parallelogram is approximately 193.73 square meters.

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Answer:

Step-by-step explanation:

1/2*base*height

The percentage of alcohol after an hour will be approximately 4.9%.

What is percentage?

A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Let p(t) be the percentage of alcohol at time t.

Where t is in minutes.

Amount of alcohol in vat = Volume of vat x p/100

Rate of change of alcohol in vat = Volume of vat x dp/dt time 1/100

Rate of change of alcohol in vat = 500 x dp/dt x 1/100

Rate of change of alcohol in vat = 5 x dp/dt

Net rate of change of alcohol = (Rate of inflow of alcohol) - (Rate of Outflow of alcohol)

Rate of Inflow of alcohol = 0.06 - 5 = -4.94 gal/min

Rate of outflow of alcohol = p(t)/100 x 5 = 0.05p(t) gal/min

Therefore, the rate of change of alcohol is 0.03 - 0.05 p(t) gal/min

Finally we can write

5 x dp/dt = 0.3 - 0.05 p

Divide both sides by 5

dp/dt = 0.06 - 0.01p

Integrate both sides

[tex]\int {dp} / 0.06 -0.01p = \int dt[/tex]

-100ln (0.06 - 0.01p) = t + C

At t=0, p=4, therefore

-100ln (0.06 - 0.04) = 0 + C

391.2 = C

Substitute the value of C, to get

-100ln (0.06 - 0.01p) = t + 391.2

Substitute t = 60 and solve for p

-100ln (0.06 - 0.01p) = 60 + 391.2

-100ln (0.06 - 0.01p) = 451.2

ln (0.06 - 0.01p) = -4.512

[tex]p = \frac{0.06 - e^{-4.512} }{0.01}[/tex] ≈ 4.9%

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7.68 pounds of honey remains after the bears ate 0.32 pounds.

What is a initial amount mean?

When referring to any Capital Appreciation Bond, Original Amount refers to the Bond's Accrued Value as of the date of issuance.

To find how much honey remains, we need to subtract the amount eaten by the bears from the initial amount produced:

Remaining honey = Initial honey - Honey eaten by bears

Remaining honey = 8 pounds - 0.32 pounds

Remaining honey = 7.68 pounds

Therefore, 7.68 pounds of honey remains after the bears ate 0.32 pounds.

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Answer:

The answer is:

[tex]l=\dfrac{S-\pi r^2}{\pi }[/tex]

Step-by-step explanation:

In order to determine the solution for I, we have to know about the equations.

In any equation there are variables. If we want to determine the value of one of them, we have to free that variable in any side of the equation.

Regarding the surface of a cone, i have attached an image that shows the real formula of the surface of a cone, We can see that in this case:

[tex]l=rI[/tex]

So, we have the next formula and we want to l:

[tex]S=\pi l+\pi r^2[/tex]

[tex]S-\pi r^2=\pi l[/tex]

[tex]\dfrac{S-\pi r^2}{\pi }=l[/tex]

Finally the solution for I is:

[tex]l=\dfrac{S-\pi r^2}{\pi }[/tex]

In conclusion  there are no points among the given options that are on the parabola.

why it is?

The vertex of the parabola is the midpoint between the point (6, 2) and the line y = 4, which is at (6, 3). Since the focus is below the vertex and the directrix is a horizontal line, the equation of the parabola is of the form:

(x - h)²2 = 4p(y - k)

where (h, k) is the vertex and p is the distance from the vertex to the focus (and from the vertex to the directrix).

Using the vertex and the given point (6, 2), we can find that p = 1. Therefore, the equation of the parabola is:

(x - 6)²2 = 4(y - 3)

Now we can check which of the given points satisfy this equation:

A. (4, 6)

(4 - 6)²2 = 4(6 - 3)

4 = 12 - 12

This point is not on the parabola.

B. (5, 7)

(5 - 6)²2 = 4(7 - 3)

1 = 16

This point is not on the parabola.

C. (6, 5)

(6 - 6)²2 = 4(5 - 3)

0 = 8

This point is not on the parabola.

D. (7, 6)

(7 - 6)²2 = 4(6 - 3)

1 = 12

This point is not on the parabola.

E. (8, 5)

(8 - 6)²2 = 4(5 - 3)

4 = 8

This point is not on the parabola.

Therefore, there are no points among the given options that are on the parabola.

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Complete question:

Which points are on the parabola defined as the set of points the same distance from (6,2) and the line y=4?

The ratio commonly used as an alternative to 3.14 is 22/7 whichj commonly represents the mathematical expression of pi.

This ratio is often used as an approximation for pi (π) which is the mathematical constant representing the ratio of the circumference of a circle to its diameter. While pi is an irrational number and has an infinite number of decimal places, 22/7 is a rational number and can be easily computed.

The value of 22/7 is approximately equal to 3.1428571, which is a fairly accurate approximation for most practical applications. It is often used in situations where a quick estimate is required or where a more accurate value of pi is not necessary.

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Answer:

12x-2

Step-by-step explanation:

-4(-3x-8)-34

12x+32-34

12x-2

Answer:Option B is correct.

Step-by-step explanation: Given:  

x+2

1

​

+

x+3

1

​

1        =

(x+3)(x+2)

x+3+x+2

1​      =

2

+5x+6

2x+5

​

1

​

       =

2x+5

x

2

+5x+6

​

The expression 1/(1/x+2) + (1/x+3) is equivalent to (x² + 4x + 44)/x(x + 11) when x > 3.

We have,

To simplify the expression 1/(1/x+2) + (1/x+3), we can apply the concept of finding a common denominator and combining fractions.

Let's start by finding the common denominator for the two fractions.

The denominators are (1/x + 2) and (1/x + 3).

To find the common denominator, we multiply the denominators together:

Common denominator = (1/x + 2) x (1/x + 3)

Expanding the expression:

Common denominator = (1/x * 1/x) + (1/x * 3) + (2 * 1/x) + (2 * 3)

Simplifying further:

Common denominator = 1/x^2 + 3/x + 2/x + 6

Combining the fractions with the common denominator:

1/(1/x+2) + (1/x+3) = (1/x) / (1/x^2 + 3/x + 2/x + 6) + (1/x+3)

To simplify the expression further, we can multiply the first fraction by x/x to clear the fraction in the numerator:

(1/x) / (1/x² + 3/x + 2/x + 6) + (1/x+3) = (x/x) * (1/x) / (1/x² + 3/x + 2/x + 6) + (1/x+3)

Simplifying:

= 1 / (x/x * 1/x) / (1/x² + 3/x + 2/x + 6) + (1/x+3)

= 1 / (1/x²) / (1/x² + 3/x + 2/x + 6) + (1/x+3)

= 1 / (1/x²) / (1/x² + (3 + 2)/x + 6) + (1/x+3)

= 1 / (1/x²) / (1/x² + 5/x + 6) + (1/x+3)

= 1 / (1/x²) / (1/x² + 5/x + 6) + (x/x) * (1/x+3)

Simplifying further:

= 1 / 1 / (1 + 5/x + 6x/x²) + (x/x² + 3x/x)

= 1 / (1 + 5/x + 6x/x²) + (x + 3x)/x²

= 1 / (1 + 5/x + 6/x) + (4x)/x²

= 1 / (1 + (5 + 6)/x) + (4x)/x²

= 1 / (1 + 11/x) + (4x)/x²

= 1 / (x + 11)/x + (4x)/x²

= x / (x + 11) + (4x)/x²

= (x² + 4(x + 11))/x(x + 11)

= (x² + 4x + 44)/x(x + 11)

Therefore,

The expression 1/(1/x+2) + (1/x+3) is equivalent to (x² + 4x + 44)/x(x + 11) when x > 3.

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The measure of ∠R in ΔPQR is option (a) 26⁰

Since angle P is a right angle (90 degrees), triangle PQR is a right triangle.

Using the Pythagorean theorem, we can find the length of the remaining side PQ

PQ^2 = PR^2 - QR^2

PQ^2 = 12.7^2 - 14.1^2

PQ^2 = 161.29 - 198.81

PQ^2 = 37.52

PQ ≈ 6.12

Now we can use the sine function to find the measure of angle R

sin(R) = opposite/hypotenuse = PQ/PR

sin(R) = 6.12/12.7

sin(R) ≈ 0.482

Taking the inverse sine (sin^-1) of both sides, we get:

R ≈ sin^-1(0.482)

R ≈ 26 degrees

Therefore, the correct option is (a) 26⁰

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The given question is incomplete, the complete question is

What is the measure of angle R in triangle PQR?

a) 26°

b) 42°

c) 45°

d) 64°

The value of b is -6

We know that the difference between two vectors with components (a1, a2) and (b1, b2) is given by (b1-a1, b2-a2).

So in this case, we have

[b1 - 3, b2 - 4] = [(-6) - 3, b - 4]

Simplifying the right-hand side gives us

[-9, b - 4]

So we can set the components of the left-hand side equal to the corresponding components of the right-hand side

b1 - 3 = -9

b2 - 4 = b - 4

Solving for b in the first equation gives us

b1 = -9 + 3 = -6

Substituting this into the second equation and simplifying gives us

-6 - 4 = b - 4

-10 = b - 4

b = -10 + 4 = -6

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We can begin by defining Penny's total wealth as a mix of a set sum and a portion of Susie's wealth to develop an expression of how much money she has. We are informed that Penny has at least $4.50 and an additional 2/5 of Susie's wealth. Hence, we can write:

p = $4.50 + (2/5)s

where p is Penny's wealth, s is Susie's wealth, and s is represented by the letters.

If Susie has $11.50, we may enter s = $11.50 into the formula for p to see how much Penny has:

p = $4.50 + (2/5)($11.50)

p = $4.50 + $4.60

p = $9.10

As a result, Penny has $9.10 and Susie has $11.50.

In conclusion, the equation for Penny's wealth in terms of Susie's wealth is p = $4.50 + (2/5)s. When we enter s = $11.50 into the formula, we obtain p = $9.10, which is how much money Penny has while Susie has $11.50.

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Answer:

False

Step-by-step explanation:

14.6/2 = 7.3

7.3 x 3 = 21.9

21.9 - 1.9 = 20

Other side:

8 - 4 = 4

4 x 3 = 12

20 does not equal 12

therefore false :)

Answer: To create a linear model that represents the amount of fuel on the plane as a function of flight time, we need to use the given information to calculate the fuel burn rate of the airplane in gallons per hour.

Fuel burn rate = Fuel capacity ÷ Range

Fuel burn rate = 63,500 gallons ÷ 14,430 km = 4.4 gallons per km

We need to convert km to miles, as flight time is usually measured in hours and miles. We can use the conversion factor 1 km = 0.621371 miles to convert kilometers to miles.

Range in miles = Range in km ÷ 0.621371

Range in miles = 14,430 km ÷ 0.621371 = 23,594 miles

Fuel burn rate = Fuel capacity ÷ Range in miles

Fuel burn rate = 63,500 gallons ÷ 23,594 miles = 2.69 gallons per mile

Therefore, the linear model that represents the amount of fuel on the plane as a function of flight time, in hours, is:

Fuel on plane (in gallons) = Fuel capacity - Fuel burn rate x Flight time (in hours)

F(t) = 63,500 - 2.69t

where F(t) is the amount of fuel on the plane (in gallons) after flying for t hours.

Step-by-step explanation:

The measure of angle subtended by the arc JR is determined as 74 ⁰.

The measure of arc JR is calculated by applying the following principle of circle geometry for a cyclic quadrilateral as shown below.

The measure of the angle tangent to the circle opposite the arc JR is given as 37 ⁰.

The measure of angle subtended by the arc JR is calculated as

m∠ JR = 2 x 37 ⁰ ( angle at the tangent is half of the angle subtended by the arc.

m∠ JR =74 ⁰

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Answer:

96

Step-by-step explanation:

Because you're increasing the number, you'll add the percentage to 100%. After that, use ratio to solve.

Therefore,

100% : 64

100% + 50%(150%) : ?

= 150/100 × 64

= 15/10 × 64

= 3/2 × 64

= 3/1 × 32

= 3 × 32

= 96

After tripling the sample size will reduce the standard error of the sample proportion by one-third we have:

The sample size in statistics is a measurement of the total number of samples utilised in an experiment. The sample size is 50, for instance, if we are evaluating 50 samples of city dwellers who watch TV. It is sometimes referred to as sample statistics.

One of the mathematical techniques used in statistics to calculate variability is the standard error. It is referred to as SE. The standard deviation of a sample distribution serves as the standard error of a statistic or estimate of a parameter. It may be characterised as a projection of that standard deviation.

a. true

population = 25% = 0.25

sample = n= 12

n x p

= 12 x o. 25 = 3 and 3 is less than 10

12(1 - p)

= 12 x 0.75

= 9 and is less than 10

b. True

the sample distribution of the population is normal when

sample size x population > or equal to 10

40 x 0.75

= 30 and 30 is greater than 10

c. false

50 x 0.25 = 12.5

50 x 0.20 = 10

[tex]z = 10 - \frac{12.5}{\sqrt{12.5} }[/tex]

= -2.5/3.54

= -0.70

H0: Young American family who delayed

H1: young American family who did not delay

p(z = -0.70)

0.2420>0.005

therefore we accept the null hypothesis.

d. false

150 x 0.20 = 30

150 x 0.75 = 37.5

[tex]z = 30 - \frac{37.5}{\sqrt{37.5} }[/tex]

= -7.5/6.12

= -1.22

p(z = -1.22) = 0.1112 > 0.05

therefore we do not reject the null hypothesis.

e. false

[tex]se1 = \sqrt{(p(1-p)/n}\\se2 = \sqrt{(p(1-p)/3n}\\se2 = 1/\sqrt{(3)se2}[/tex]

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Complete question:

About 25% of young Americans have delayed starting a family due to the continued economic slump. Determine if the following statements are true or false, and explain your reasoning.a. The distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump in random samples of size 12 is right skewed.b. In order for the distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump to be approximatly normal, we need random samples where the sample size is at least 40.c. A random sample of 50 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.d. A random sample of 150 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.e. Tripling the sample size will reduce the standard error of the sample proportion by one-third.

Answer: O: 252

Step-by-step explanation:

Theoretically, all of the letters would've been drawn 250 times as that is the theoretical possibility. The closest number to the theoretical number in this experiment would be 252 which belongs to O

The point (2, 7) lies on the line defined by the equation Y=3/2x+4

The given equation is [tex]Y = 3/2x + 4[/tex]

To find the point that lines on the line defined by this equation, we need to solve for x. Start by subtracting 4 from both sides of the equation:

[tex]Y - 4 = 3/2x[/tex]

Next, multiplying both sides by 2:

[tex]2Y - 8 = 3x[/tex]

Finally, divide both sides by 3:

[tex]x = (2Y - 8) /3[/tex]

Now, given a  value, we can calculate the corresponding x value. For example, if Y = 7, then:

[tex]x = (2 * 7 - 8) / 3x = (14 - 8) / 3x = 6 / 3x = 2[/tex]

Therefore, the point (2, 7) lies on the line defined by this equation.

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Complete question :

What is the value of x for the point (x,7) that lies on the line defined by the equation Y = 3/2x + 4?

A. 1

B. 2

C. 3

D. 4

[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{9\times 7}{63}\\ h=6 \end{cases}\implies V=\cfrac{(63)(6)}{3}\implies V=126~cm^3[/tex]

now, for the slanted cone, we can use Cavalieri's Principle for an slanted cylinder, thus we can say that the slanted cone will have the same volume of a non-slanted cone, now, since this one has a diameter of 6, that means is has a radius of 3.

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3} \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=7 \end{cases}\implies V=\cfrac{\pi (3)^2(7)}{3}\implies V=21\pi \implies V\approx 66~cm^3[/tex]

Answer:

64

Step-by-step explanation:

1. (5, 12, 13) is a Pythagorean triple.

2.  (20, 21, 27) is not a Pythagorean triple.

3. Fake triples are (7, 2, 25), (280, 450, 533), and (110, 60, 651)

4.  A Pythagorean triple that I know is (3, 4, 5).

5. a.Thus, (6, 8, 10) is also a Pythagorean triple.

b.  Thus, (30, 40, 50) is also a Pythagorean triple.

c. Thus, (1.5, 2, 2.5) is still a Pythagorean triple.

d. Yes, a Pythagorean triple consisting of three even numbers is (6, 8,

10). A Pythagorean triple consisting of three odd numbers is (5, 12, 13).

The Pythagorean theorem is a fundamental theorem in mathematics that relates to the sides of a right-angled triangle.

1. To prove that (5, 12, 13) is a Pythagorean triple, we need to show that

⇒ 5² + 12² = 13²

⇒ 5² + 12² = 169       (5² = 25 and 12² = 144 and 13² = 169)

Therefore, 5² + 12² = 13², which means that (5, 12, 13) is a Pythagorean triple.

2. To prove that (20, 21, 27) is not a Pythagorean triple.

Assuming that (20, 21, 27) is a Pythagorean triple, we would have:

⇒ 20² + 21² = 27²

⇒ 400 + 441 ≠ 729

Therefore, (20, 21, 27) is not a Pythagorean triple.

3. To find the fakes among the following list of triples, we need to check if there is a whole number solution for the sides of a right-angled triangle with these measurements.

Therefore, the fakes are (7, 2, 25), (280, 450, 533), and (110, 60, 651).

4. A Pythagorean triple that I know is (3, 4, 5).

Scaling up each side by the same amount should still result in a Pythagorean triple, as the relationship between the sides will remain proportional.

 5.  a) Multiplying each side by 2, we get (6, 8, 10). Verifying Pythagoras' theorem, we have:

6^2 + 8^2 = 36 + 64 = 100

10^2 = 100

Thus, (6, 8, 10) is also a Pythagorean triple.

b) Multiplying each side by 10, we get (30, 40, 50). Verifying Pythagoras' theorem, we have:

30^2 + 40^2 = 900 + 1600 = 2500

50^2 = 2500

Thus, (30, 40, 50) is also a Pythagorean triple.

c) Halving each side of (3, 4, 5), we get (1.5, 2, 2.5). Verifying Pythagoras' theorem, we have:

1.5^2 + 2^2 = 2.25 + 4 = 6.25

2.5^2 = 6.25

Thus, (1.5, 2, 2.5) is still a Pythagorean triple.

d) The observation is that scaling up or down a Pythagorean triple by the same amount results in another Pythagorean triple. This is because the sides of a Pythagorean triple are related by the Pythagorean theorem, which is a quadratic equation. Multiplying each side by the same amount simply scales the sides up or down proportionally, while preserving the quadratic relationship.

Yes, a Pythagorean triple consisting of three even numbers is (6, 8, 10). A Pythagorean triple consisting of three odd numbers is (5, 12, 13).

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1. (5, 12, 13) is a Pythagorean triple.

2.  (20, 21, 27) is not a Pythagorean triple.

3. Fake triples are (7, 2, 25), (280, 450, 533), and (110, 60, 651)

4.  A Pythagorean triple that I know is (3, 4, 5).

5. a.Thus, (6, 8, 10) is also a Pythagorean triple.

b.  Thus, (30, 40, 50) is also a Pythagorean triple.

c. Thus, (1.5, 2, 2.5) is still a Pythagorean triple.

d. Yes, a Pythagorean triple consisting of three even numbers is (6, 8,

10. A Pythagorean triple consisting of three odd numbers is (5, 12, 13).

The Pythagorean theorem is a fundamental theorem in mathematics that relates to the sides of a right-angled triangle.

1. To prove that (5, 12, 13) is a Pythagorean triple, we need to show that

⇒ 5² + 12² = 13²

⇒ 5² + 12² = 169       (5² = 25 and 12² = 144 and 13² = 169)

Therefore, 5² + 12² = 13², which means that (5, 12, 13) is a Pythagorean triple.

2. To prove that (20, 21, 27) is not a Pythagorean triple

Assuming that (20, 21, 27) is a Pythagorean triple, we would have:

⇒ 20² + 21² = 27²

⇒ 400 + 441 ≠ 729

Therefore, (20, 21, 27) is not a Pythagorean triple.

3. To find the fakes among the following list of triples, we need to check if there is a whole number solution for the sides of a right-angled triangle with these measurements.

Therefore, the fakes are (7, 2, 25), (280, 450, 533), and (110, 60, 651).

4. A Pythagorean triple that I know is (3, 4, 5).

Scaling up each side by the same amount should still result in a Pythagorean triple, as the relationship between the sides will remain proportional.

5.  a) Multiplying each side by 2, we get (6, 8, 10). Verifying Pythagoras' theorem, we have:

6² + 8² = 36 + 64 = 100

10² = 100

Thus, (6, 8, 10) is also a Pythagorean triple.

b) Multiplying each side by 10, we get (30, 40, 50). Verifying Pythagoras' theorem, we have:

30² + 40² = 900 + 1600 = 2500

50² = 2500

Thus, (30, 40, 50) is also a Pythagorean triple.

c) Halving each side of (3, 4, 5), we get (1.5, 2, 2.5). Verifying Pythagoras' theorem, we have:

1.5² + 2² = 2.25 + 4 = 6.25

2.5² = 6.25

Thus, (1.5, 2, 2.5) is still a Pythagorean triple.

d) The observation is that scaling up or down a Pythagorean triple by the same amount results in another Pythagorean triple. This is because the sides of a Pythagorean triple are related by the Pythagorean theorem, which is a quadratic equation. Multiplying each side by the same amount simply scales the sides up or down proportionally, while preserving the quadratic relationship.

Yes, a Pythagorean triple consisting of three even numbers is (6, 8, 10). A Pythagorean triple consisting of three odd numbers is (5, 12, 13).

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You need a sample size of approximately 82 students to estimate the average time college students spend studying per week with a 99% confidence interval and a margin of error of 30 minutes (0.50 hours).

To determine the sample size, we will use the formula given below;

Where, n = sample size

Zα/2 = the z-score associated with the level of confidence

α = level of significance

σ = population standard deviation

d = margin of error of the estimation.

Substituting the given values, we have; n = [(Zα/2 * σ)/d]^2

We are given the population standard deviation, σ = 3.5 hours.

We are also given the margin of error, d = 0.5 hours.

We need to find the value of Zα/2 at 99% confidence level.

Since the sample size is large enough, we can use the z-distribution to find the z-value.

The area under the standard normal distribution curve for a 99% confidence level is as shown below;

Using the z-tables, the value of Zα/2 for a 99% confidence level is 2.576.

Substituting the values into the formula; n = [(Zα/2 * σ)/d]^2n = [(2.576 * 3.5)/0.5]^2= (9.006)^2= 81.12

Since we need a whole number for the sample size, we round up the value to get 82.

However, since the standard deviation of the population is known, we can use the z-distribution to construct a confidence interval for the population mean. This will give us an accurate interval estimate of the population mean.

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Answer: A. Action: add 3 to both sides

Step-by-step explanation:

 The property that justifies this action is the addition property of equality, which states that if you add the same number to both sides of an equation, the equation remains true.

Answer:

[0,12]

Step-by-step explanation:

The unit of the domain is seconds

x is greater than or equal to zero because time can't be negative

Time stops at 12 seconds since the ball hits the ground.

Brackets are used to include both 0 and 12 as values

The new median of the data set is 616

Multiply all the numbers by 22

looking at this number they both are in the middle. So you add both numbers and divide by two.

440 + 792 = 1232

The length of the hypotenuse is the line connecting the two points (-3,-7) and (-7,-1), which has length 2√13, as calculated above.

A triangle is a clοsed, dοuble-symmetrical shape cοmpοsed οf three line segments knοwn as sides that intersect at three places knοwn as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factiοns equal), isοsceles, οr scalene based οn their sides.

Next, we can find the length of the hypotenuse by using the distance formula, which is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

So, in this case, we have:

d = √((-7 - (-3))² + (-1 - (-7))²)

= √((-4)² + (-6)²)

= √(16 + 36)

= √52

= 2√13

Therefore, the distance between the two points in simplest radical form is 2√13.

The length of the hypotenuse is the line connecting the two points (-3,-7) and (-7,-1), which has length 2√13, as calculated above.

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The indefinite integral is:

-10 ln|x| + 3 ln|x - 2| + 7 ln|x + 1| + C

First, we factor the denominator of the integrand using partial fractions:

x^3 - x^2 - 2x = (x - 2)(x + 1)x

We then express the integrand as:

10x^2 - 7x + 2 = A/(x - 2) + B/x + C/(x + 1)

Multiplying both sides by the denominator and solving for A, B, and C, we get:

A = -4, B = 10, C = 1

Thus, we can rewrite the integrand as:

-4/(x - 2) + 10/x + 1/(x + 1)

Integrating each term separately and combining the results, we obtain the final expression for the indefinite integral.

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