When Aaron runs the 400 m dash is finishing times are normally distributed with a mean of 80 seconds and a standard deviation of 2. 5 seconds using the elliptical rule determine the interval of times that represent the middle 99. 7% of his finishing times in the 400 m race

Answer:

a)6

b)15 and -15

Step-by-step explanation:

a)5*5*5*5*5*5 there is 6 5's so, we  can show it as, [tex]5^{6}[/tex]

[tex]5^{6}[/tex]=[tex]5^{x}[/tex]

x=6

b) in this one you found one of the answers of y which is 15.

but [tex]15^{2}=-15^{2}\\so y=15\\and y=-15[/tex]

Answer:

The answer is down below

Step-by-step explanation:

a) 5×5×5×5×5×5=5^x

5×5×5×5×5×5=5⁶

b)y²=225

square both sides

√y²=√225

y=15

The maximum value of a full cycle can be 2700 mL, this gives the maximum volume of air inhaled by a person during one breath. The function C(t) = 250sin(2I/5(t))+2450.

It shows the capacity of the lung of a person at any point of time t in milliliters (mL).

We not only need to find the one full cycle but also determine the period of function and it is given by:

T = 2I/(2I/5)

T = 5 seconds.

This means that the function completes one full cycle every 5 seconds.

To find the maximum value of the function over one full cycle, we need to find the maximum value of sin(2π/5(t)). The maximum value of sin(2π/5t) is 1, this happens at 2π/5(t) = π/2 + nπ, and n is considered as an integer.

So, the maximum value of the function occurs when sin(2I/5(t)) = 1, Substituting this into the original function, we get maximum value, Cm:

Cm = 250(1) + 2450

= 2700 mL.

The maximum value of a full cycle can be 2700 mL, this gives the maximum volume of air inhaled by a person during one breath.

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The functions are classified as follows:

a) Linear.

b) Linear.

c) Linear.

d) Non-linear.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

Hence, from the definition, a function is classified as linear if the highest exponent of both x and y is of one.

A term x on the denominator has an exponent of -1, hence item d is not a linear function.

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The linear equations in the options are:

a) 5x - 9 + 7y = x - 4

b) 0.01x - 0.7y = 2.2

c) -3x = 4

We say that an equation is linear if the dependence with the veriables is only of first degree.

For example, equations of the form:

a*x + b*y = c

Are linear, because the variables x and y have an exponent of 1.

Then, the options that show linear equations are:

a) 5x - 9 + 7y = x - 4

b) 0.01x - 0.7y = 2.2

c) -3x = 4

The last option is non linear, because x is on the denominator.

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Answer:

D is the only possible answer

Answer:

66.67%

Step-by-step explanation:

There are two ways to solve this problem depending on which way you like. Percentages are based on a 0-100 system and thus you can start by dividing 100/90. This will give you an amount of 1 family. We are looking for 60 families, so multiply that value by 60 to get how much of a percentage 60 families is.

The other way is to divide 90 by 60, and then multiply that result by 100 to give you a percent.

Regardless of your preferred method, both answers are the same.

The length of the arc with a central angle of 45° is 4.24 cm

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The length of an arc formed on a circle with a central angle Ф and radius r is:

Length of arc = (Ф/360) * 2πr

Given the circle radius is 5.4 cm and the central angle is 45°, hence:

Length of arc = (Ф/360) * 2πr = (45/360) * 2π(5.4) = 4.24 cm

The length of the arc is 4.24 cm

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Therefore, any of these two points lies on the circle represented by the equation. [tex](x - 3)^2 + (y+4)^2=6^2.[/tex]

A circle is a geometric shape that consists of all the points that are a fixed distance, called the radius, from a given point, called the center. The distance from the center to any point on the circle is always the same. A circle can also be defined as the set of points in a plane that are equidistant from a given point, which is the center of the circle. Circles are often studied in geometry and have a number of important properties, such as their circumference, area, and diameter. They are also widely used in mathematics, physics, and engineering, and have many practical applications in fields such as architecture, art, and design.

by the question.

The equation of the circle in standard form is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where (h, k) is the center of the circle and r is the radius.

Comparing this with the given equation:

[tex](x - 3)^2 + (y + 4)^2 = 6^2[/tex]

we can see that the center of the circle is at point (3, -4) and the radius is 6.

To find a point on the circle, we can substitute any value for x or y and solve for the other variable. For example, let's choose x = 0:

[tex](0 - 3)^2 + (y + 4)^2 = 6^2[/tex]

[tex]9 + (y + 4)^2 = 36[/tex]

[tex](y + 4)^2 = 27[/tex]

[tex]y + 4=±\sqrt{27}[/tex]

[tex]y = -4±\sqrt{27}[/tex]

So, the two points on the circle are:

(0, -4 + √27) and (0, -4 - √27)

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The inclination or grade of the trail from the Alpine Hotel to the scenic overlook is 21.9%.

The inclination or grade of a trail is the ratio of the change in elevation to the length of the trail, expressed as a percentage. To find the inclination of the trail from the Alpine Hotel to the scenic overlook, we need to first calculate the change in elevation.

Change in elevation = 11,100 feet - 8,000 feet = 3,100 feet

Now we can calculate the inclination or grade of the trail as follows:

Grade = (change in elevation / length of trail) x 100%

Grade = (3,100 / 14,100) x 100%

Grade = 0.219 x 100%

Grade = 21.9%

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we have shown that [tex](3x)^2x = (9x^2)^2,[/tex] which is the equation you provided. This is true for any value of x, so the equation is valid. The statement you have provided is a mathematical equation that involves exponentiation. To understand this equation, we need to know the rules of exponents.

The rule for exponentiation with the same base states that when we have a base raised to multiple exponents, we can simply multiply the exponents. In other words, [tex](a^b)^c = a^(b*c).[/tex] Using this rule, we can simplify the right-hand side of the equation to [tex](9x^2)^2 = 81x^4.[/tex]

Now, let's look at the left-hand side of the equation:[tex](3x)^2x[/tex]. To simplify this expression, we can use the distributive property of exponents. That is, [tex](a^b)^c = a^(b*c).[/tex] Using this rule, we can write[tex](3x)^2x as (3x^2)^x.[/tex]Then, using the rule for exponentiation with the same base, we can write this as [tex]3^(2x) * x^(2x).[/tex]

So now we have the equation [tex]3^(2x) * x^(2x) = 81x^4.[/tex]We can simplify this equation further by dividing both sides by[tex]x^(2x) to get 3^(2x) = 81x^(4-2x).[/tex] Simplifying the right-hand side, we get [tex]3^(2x) = 81x^(2(2-x)) = 81x^(4-2x).[/tex]

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After 3 seconds, the rider is still at their starting height of 0 metres.

The height of a rider after 3 seconds can be calculated using the equation h(t) = v₀t - (1/2)gt², where h(t) is the height of the rider in metres at time t, v₀ is the initial velocity in metres per second, and g is the acceleration due to gravity in metres per second squared.

Assuming v₀ is 0, since the rider is just starting, and g is 9.81, then the height of the rider after 3 seconds is h(3) = 0 - (1/2)(9.81)(3²) = -44.355. Since this is a negative number, the rider is still at their starting height of 0 metres after 3 seconds.

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In a reaction that is first order reaction with respect to x and first order with respect to y, the change will have no effect overall on the rate is doubling [x]. The answer is option (b).

If the reaction is first order with respect to x and first order with respect to y, then the rate equation is given by Rate = k [x]^1 [y]^1 = k [x][y].Option (a) Doubling [x] and doubling [y] will increase the rate by a factor of Option (c) Quadrupling [y] will increase the rate by a factor of 4 x 4 = 16.

Option (d) Halving [x] and doubling [y] will have no overall effect on the rate since rate will increase by a factor of 2/1 = 2 and then decrease by a factor of 1/2 = 0.5, for an overall effect of 1. Option (e) Halving [x] and halving [y] will decrease the rate by a factor of 2 x 2 = 4.

Thus, option (b) Doubling [x] is the correct answer. If the concentration of a reactant is tripled and the rate increases by a factor of nine, then we can write k [x][y] = 9 k [x (3)][y]k = 9 k / 3 = 3 k. Since the concentration of x is raised to the power of 1, the order with respect to that reactant is 1.

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If the resort gets over 75 inches of snow 40% of years, between 40 and 75 inches 45% of years, and less than 40 inches 15% of years the resort's expected yearly profit is $161,500.

To find the resort's expected yearly profit, we need to calculate the weighted average of its profits under different snowfall conditions, using the probabilities of each condition occurring as weights.

Let P1, P2, and P3 be the probabilities of snowfall being over 75 inches, between 40 and 75 inches, and less than 40 inches, respectively. We are given that P1 = 0.4, P2 = 0.45, and P3 = 0.15.

Let R1, R2, and R3 be the profits that the resort makes under each of these snowfall conditions. We are given that R1 = $250,000, R2 = $160,000, and R3 = -$70,000 (since the resort loses money if snowfall is less than 40 inches).

Then the expected yearly profit, E, is:

E = P1R1 + P2R2 + P3R3

= 0.4250,000 + 0.45160,000 + 0.15(-70,000)

= 100,000 + 72,000 - 10,500

= $161,500

This means that, on average, the resort can expect to make a profit of this amount each year, taking into account the varying probabilities of different snowfall conditions.

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Answer:

refer to the attachment

Step-by-step explanation:

If the interest is not compounded, it means that Mabel will earn a simple interest of 11% per year on her principal amount of $30,000.

The formula for calculating simple interest is:

Interest = (Principal x Rate x Time)

Where:

Principal = $30,000

Rate = 11% = 0.11 (as a decimal)

Time = 2 years

So, substituting the values in the formula, we get:

Interest = (30,000 x 0.11 x 2) = $6,600

Therefore, Mabel will earn $6,600 in interest over a period of 2 years.

Answer:

It all depends on the linear system

Step-by-step explanation:

A system of linear equations usually has a single solution but sometimes it can have no solution (parrel lines) or infinite solutions (same line).

I hope this helped

The answer is Three.

One solution.

Infinitely many solutions.

No Solutions at all.

The location at which a function is not differentiable is a Vertical tangent line

A function may not be differentiable at some points. Such points are known as non-differentiable points. Let's take a look at each of the given terms to figure out the non-differentiable points. Discontinuity: A discontinuity is when a function's graph is interrupted by a break or hole.

It occurs when a function is undefined at a certain point. It may be classified into three categories: removable, jump, and infinite. Functions may not be differentiable at removable discontinuities but are differentiable at jump and infinite discontinuities. A discontinuous point is not the same as a non-differentiable point because it may be differentiable at other points of the function.

Cusp: A cusp is a sharp corner formed by a curve. It happens when the slope of the function approaches infinity. The curve is not differentiable at the cusp. Horizontal Tangent Line: When the slope of a function approaches zero, it creates a horizontal tangent line. The function may or may not be differentiable at this point depending on the shape of the graph.

It may be differentiable or not differentiable. Therefore, it is not a non-differentiable point. Vertical Tangent Line: When a function's slope approaches infinity, it creates a vertical tangent line. The function is non-differentiable at this point. A vertical tangent line is always a non-differentiable point.

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the number of goals Yolanda scores without penalties is x = 8, and the number of goals Neel scores without penalties is y = 0.

Let x be the number of goals Yolanda scores without penalties, and let y be the number of goals Neel scores without penalties.

According to the problem, Yolanda makes 6 goals and 2 penalties, so her total number of goals is:

x + 6

And her total number of points is:

(x + 6) + 2(1) = x + 8

Similarly, Neel scores 4 goals and 2 penalties, so his total number of goals is:

y + 4

And his total number of points is:

(y + 4) + 2(1) = y + 6

We know that Yolanda ends the game with 16 points, so we can write:

x + 8 = 16

Subtracting 8 from both sides, we get:

x = 8

We also know that Neel ends the game with 6 points, so we can write:

Y + 6 = 6

Subtracting 6 from both sides, we get:

y = 0

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Answer: x = 31 over 14 − 5y over 14

Step-by-step explanation: Move all terms that don't contain x to the right side and solve.

The probability that the sample of 50 rabbits contains exactly 2 marked rabbits is 1/2.

When sampling from either a small population without replacement, the hypergeometric distribution consists of a discrete probability distribution which determines the likelihood that an event occurs k times in n trials.

The given data:

Total market sample of rabbits = 100.

Randomly selected rabbits = 50.

Let the probability that the sample of 50 rabbits contains exactly 2 marked rabbits be P(E).

Then, using hypergeometric distribution;

P(E) = ⁵⁰C₂ / ¹⁰⁰C₂

Solve the probability using the combination.

P(E) = 25*49 / 50*49

P(E) = 25/50

P(E) = 1/2

Thus, the probability that the sample of 50 rabbits contains exactly 2 marked rabbits is 1/2.

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Answer:

0.099, 0.18, 0.2, 0.698.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

3x + 3 - x + (-7) > 6

2x + 3 - 7 > 6

2x - 4 > 6

2x > 10

x > 5

Answer:

B. x > 5

Step-by-step explanation:

3x + 3 - x + (-7) > 6

3x - x + 3 - 7 > 6

2x + (-4) > 6

2x - 4 > 6

2x > 6 + 4

2x > 10

x > 10 / 2

x > 5

:D

The scale that Wyatt used is 1 inch represents 0.36 yards

The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. The scale provides information on the proportional relationship between the scale of the drawing and the original image.

Scale of the drawing = original length / length of the drawing

84 / 231 = 0.36 yards

This means that 1 inch is represented by 0.36 yards

Alternatively, it can be written as 1 : 0.36 yards

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The given distribution is not a probability distribution.

The given distribution is not a probability distribution, since the sum of probabilities is not equal to 1. A probability distribution must satisfy two conditions: 1) the probabilities must lie inclusively between 0 and 1, and 2) the sum of probabilities must be equal to 1.

In this case, the sum of probabilities is 15+15+15 = 45, which is not equal to 1. Therefore, the given distribution is not a probability distribution. The other options are incorrect because they do not accurately describe the given distribution.

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The quadratic function represented by the given table is:

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

Here we have a table that defines a quadratic equation, remember a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:

y = a*(x - h)^2 + k

Here we can see that the vertex is (2, 3), then we can write:

y = a*(x - 2)^2 + 3

And we can see that it also passes through the point (0, -1), then:

-1 = a*(0 - 2)^2 + 3

-1 = a*4 + 3

-1 - 3 = a*4

-4 = a*4

-4/4 = a = -1

The quadratic function is:

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

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Answer: The comparison "3.4 < 3.36" is reasonable because 3.36 is greater than 3.4.

The decimal point separates the whole number part of a number from the fractional part. In this case, 3.36 has a greater whole number part (3) than 3.4, and both have the same decimal part (0.36). So, 3.36 is greater than 3.4.

Therefore, the statement "3.4 < 3.36" is a true and reasonable comparison.

Step-by-step explanation:

Answer:

s is inversely proportional to t

Step-by-step explanation:

As s increases, t decreases.  They are inversely proportioanl when that happens.

100

The suitable class width would be 3.5 if your highest observed value is equal to 400, your lowest observed value is equal to 50, and your number of observations is equal to 100.What is a class width?The class width is the width of each interval in a frequency distribution. It is found by subtracting the smallest value from the largest value and then dividing by the number of classes.Class width = (highest value - lowest value) / number of classesWhere,H = highest observed value = 400L = lowest observed value = 50n = number of observations = 100Using the formula:Class width = (H - L) / nClass width = (400 - 50) / 100Class width = 350 / 100Class width = 3.5Thus, the suitable class width would be 3.5 if your highest observed value is equal to 400, your lowest observed value is equal to 50, and your number of observations is equal to.

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The height of the mountain above sea level is 777.94 m.

The two engineers can calculate the height of the mountain by using the principle of trigonometry. Firstly, they must calculate the altitude of the mountain from the point A, which can be done by using the formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point A and d is the distance between point A and the mountain. In this case, the altitude from point A is h = tan(37°) * 1200 = 1645.58 m. Secondly, they can calculate the altitude from point B, which can be done by using the same formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point B and d is the distance between point B and the mountain. In this case, the altitude from point B is h = tan(45°) * 480 = 867.64 m. Finally, the height of the mountain above sea level can be calculated by subtracting the altitude from point B from the altitude from point A, i.e. h = 1645.58 m - 867.64 m = 777.94 m.

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To calculate the dosage strength of digoxin, which is supplied by the pharmacy in mg per tablet, the physician orders digoxin 0.25 mg po daily.

In other words, The physician ordered 0.25 mg of digoxin to be administered orally every day. The medication provided by the pharmacy is to be taken in tablet form. To calculate the amount of digoxin in each tablet, you need to divide the ordered dose by the amount of tablets.

The equation is:Dose Ordered / Tablets = Dose per tablet

Substitute the known values:Dose Ordered = 0.25 mgTablets = 1 tablet0.25 mg / 1 tablet = 0.25 mg per tablet.

Therefore, the dosage strength of the digoxin supplied by the pharmacy is 0.25 mg per tablet.

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Step-by-step explanation:

the midpoint between 2 points A (xa, ya) and B (xb, yb) is

M ((xa + xb)/2, (ya + yb)/2)

(xa + xb)/2 = 10.5

(ya + yb)/2 = 9

let's say R = A

(1 + xb)/2 = 10.5

(10 + yb)/2 = 9

1 + xb = 21

xb = 20

10 + yb = 18

yb = 8

S = (20, 8)