If height is normally distributed, which of the following percentages represents the number of women in this country who are between 63 and 70.5 inches tall?

Answer:

The formula for ordinary interest is:

I = P * r * t

where:

I = the interest

P = the principal

r = the interest rate per year

t = the time in years

In this case, the principal is $12,500, the interest rate is 4%, and the time is 292/360 years (since there are 360 days in a year according to the problem statement). Therefore, we have:

t = 292/360 = 0.811111111

I = 12500 * 0.04 * 0.811111111 = 405.5555555

To find the maturity value, we add the interest to the principal:

M = P + I = 12500 + 405.5555555 = 12905.56

Therefore, the maturity value of the promissory note is $12,905.56 rounded to the nearest cent.

Step-by-step explanation:

V = 4/3 pi r^3

64 pi = 4/3 pi r^3      divide both sides of the equation by pi :

64  = 4/3 r^3              multiply both sides by 3/4

3/4 * 64  = r^3              simplify a bit

48   = r^3                     take cube root of both sides

r = 3.63     units

Answer:

Number of Hours | Money

0 hrs — 22$ (+0$)

1 hrs — 27$ (+5$)

2 hrs — 32$ (+5$)

3 hrs — 37$ (+5$)

(he would gain 15$ after 3 hours of baby sitting)

Step-by-step explanation:

Y = 5x + 22

5x is the amount being added each time, 22 is the y-intercept of the slope; the slope is going at a linear rate of 5 per hour.

Step-by-step explanation:

Circumference of a circle is found by:

Circ = pi * d

      = pi * 9.7 cm = 30.5 cm

If the water were redistributed equally among the 4 glasses, the fractional part of each glass that would be filled include the following: K. 31/80.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided above, the division can be calculated as follows;

Fraction = (1/4 + 1/2 + 4/5) ÷ 4

Fraction = 31/20 ÷ 4

Next, we would multiply the fraction 31/20 by the reciprocal of 4 as follows;

Fraction = 31/20 × 1/4

Fraction = 31/80

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Missing information:

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

The probability that Tally is on the red team would be 1/4

Probability means a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that Tally's teacher divides her class of 16 students into 4 equally sized teams: red team, yellow team, green team and the blue team.

Therefore, the probability that Tally is on the red team will be;

P(E) = Number of favorable outcomes / total number of outcomes

P(E) = Number of teams / total number of students

P(E) = 4/16

P(E) = 1/4

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When analyzing a resultant vector, the equation to find the magnitude of the vector is the Pythagorean theorem. This equation states that the magnitude of the resultant vector is equal to the square root of the sum of the squares of its components.

To find the direction of the resultant vector, the trigonometric function of inverse tangent or arctan can be used. This involves taking the inverse tangent of the vertical component divided by the horizontal component, which gives the angle of the vector with respect to the positive x-axis.

Alternatively, the direction can also be found using the trigonometric functions of sine and cosine by dividing the vertical and horizontal components of the vector by its magnitude.

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The equation about the conic is r = 6/(4|sinθ| - 3cosθ).

We have,

Since the focus is at the pole, the conic is a polar equation with the form

r = e d / (1 - e cosθ), where d is the distance from the pole to the directrix and e is the eccentricity.

In this case,

e = 3/4 and the directrix is r sinθ = -2.

We can rewrite the equation of the directrix in Cartesian coordinates as

y = -2/sinθ.

Now we can use the formula for the distance from a point (x, y) to a line Ax + By + C = 0, which is:

d = |Ax + By + C| / sqrt(A^2 + B^2)

In our case,

The equation of the directrix is y + 2/sinθ = 0, which we can rewrite as

y = -2/sinθ.

The coefficients of x and y are both 0 and the constant term is 2/sinθ, so

A = 0, B = 1, and C = -2/sinθ.

Substituting into the formula.

d = |-2/sinθ| / √(0² + 1²)

d = 2/|sinθ|

Now we can write the equation of the conic as:

r = e d / (1 - e cosθ) = (3/4) (2/|sinθ|) / (1 - (3/4) cosθ)

Simplifying.

r = 6/(4|sinθ| - 3cosθ)

This is the polar equation of the conic with focus at the pole and directrix r sinθ = -2, and eccentricity e = 3/4.

Thus,

The equation about the conic is r = 6/(4|sinθ| - 3cosθ).

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After discount the cost is $53.6 and  the processing fee is $5.36

The discount reduces the price of the shoes by 20%, which means Evan only has to pay 80% of the original price.

To find the price after the discount

we multiply the original price by 0.8:

Price after discount = 0.8 × $67 = $53.60

Next, the website applies a 10% processing fee to this discounted price. To find the processing fee, we can multiply the discounted price by 0.1:

Processing fee = 0.1 × $53.60

= $5.36

Hence, the processing fee is $5.36 and after discount the cost is $53.6

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A table that matches the data in the graph include the following:

Correct answers       Points

0                                   0

5                                   30

12                                  72

18                                  108

20                                 120

In Mathematics, a proportional relationship produces equivalent ratios and it can be represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points contained in the table as follows:

Constant of proportionality, k = y/x = t/d

Constant of proportionality, k = 30/5 = 72/12 = 108/18 = 120/20

Constant of proportionality, k = 6.

Therefore, the required equation is given by;

y = kx

y = 6x

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Missing information:

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

The type of error occurs when certain sample elements are excluded is sample frame error. Then the required answer for the given question is Option B.

The type of error that takes place when a particular sample elements are eliminated or when the whole population is not accurately projected in the sampling frame is called sample frame error.

There are 4 types of sampling error

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Using A linear equation, It ia found that:

• The equation is: L = 56 + 3d

Where D is representing the number of day crew has worked and L presenting the total length of the road. So let's solve this.

Step by step Explanation:

= L = 56 + 3d

= L = 56 + 3(36)

= L = 54 + 108

= L = 162

Answer:  Hence sum of interior angles of a convex 16-sided polygon would be 180∘×(16−2)=180∘×14=2520∘

Step-by-step explanation:

Answer:

------------------------

To find the sum of the interior angles of a 16-sided polygon, you can use the formula:

In our case, n = 16.

Substitute the value of n into the formula:

The matching choice is D.

Answer: 2.333  

Step-by-step explanation:

Since 3 feet equal 1 yard, we can divide 7 feet by 3 to get the equivalent distance in yards:

7 feet ÷ 3 feet/yard = 2.333 yards (rounded to 3 decimal places)

Therefore, 7 feet is equivalent to approximately 2.333 yards.

hope this help mark me brainst  

Independent events- events that do not affect each other's probability of occurring. Dependent events- events where the occurrence of one event affects the probability of the other event happening. Mutually exclusive events- events that cannot occur at the same time. Exhaustive events- events that cover all possible outcomes.


1. Independent events: Independent events are events in which the occurrence of one event does not affect the probability of the occurrence of another event. In other words, the outcome of one event has no impact on the outcome of the other event.

2. Dependent events: Dependent events are events in which the occurrence of one event does affect the probability of the occurrence of another event. The outcome of one event is influenced by the outcome of the other event.

3. Mutually exclusive events: Mutually exclusive events are events that cannot occur at the same time. The occurrence of one event means the other event cannot occur. For example, flipping a coin and getting both heads and tails at the same time is a mutually exclusive event, as it is impossible for both to happen simultaneously.

4. Exhaustive events: Exhaustive events are a set of events that include all possible outcomes in a given situation. They are complete and cover every possibility, leaving no room for additional outcomes. For example, when flipping a coin, the set of exhaustive events includes both heads and tails, as there are no other possible outcomes.

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For a sample of room temperature during winter, an upper bound of the probability that the temperature in your room deviates from the mean by at least 4 degrees is equals to the 0.25.

For a sample of temperature during winter, Average temperature of room

= 70 degree

Standard deviations = 2 degrees

We have to determine upper bound of the probability that the temperature in your room deviates from the mean by at least 4 degrees. According to chebyehev's theorem, [tex]P( | X - μ |≥ k σ ) ≤ \frac{ 1 }{k²} [/tex].

here , σ = 2 , μ = 70, kσ = 4

=> k = 2

So, the required upper bound of probability is [tex]P( | X - μ |≥ k σ ) ≤ \frac{ 1 }{k²} [/tex]

≤ [tex]\frac{ 1 }{2²} [/tex]

≤ [tex]\frac{ 1 }{4} [/tex]

= 0.25

Hence, required upper bound value is 0.25.

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The measure of variability that the Charity should use is B. The IQR of 13 is the most accurate to use, since the data is skewed.

Adopting the IQR gives a better picture of the standard donations, since it is less responsive to outliers and unbalanced data than the range. The charity must take advantage of the Interquartile Range (IQR) for an exact depiction of the data, as it is less impressionable to outliers and skewed data.

The IQR would be:

= Q3 - Q1

Q1 from the data is:

= (6 + 8) / 2 = 7

Q3 is :

(20 + 20) / 2 = 20

The IQR is:

= 20 - 7

= 13

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The Rutherford model of the atom is known to be a term that is also seen as planetary model. It was said to have been proposed by Ernest Rutherford in 1911. It was a vital improvement over previous models, but it had some few limitations.

Below are some advantages and disadvantages of the Rutherford model:

In terms of Advantages:

In terms of Disadvantages:

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See text below

advantages and disadvantages of the rutherford model of the atom

Answer:

6 tins of red paint

Step-by-step explanation:

blue = 1, red = 3 so:

from 1 to 2 tins of blue, you multiply 1 x 2 = 2 tins. Now we have to multiply by 2 on the other side

So: 3 x 2 = 6 tins of red

In ratios, multiplying or dividing has to be applied to both sides

1 : 3 becomes 2: 6

If each bag of chips costs $1 less than a granola bar, and jack buys 2 more items than jane buys, Jack buys 15 bags of chips

Let's assume that Jack buys x bags of chips and Jane buys y granola bars. We know that they each spend $24 on snacks, so we can set up the following equation:

x*(price of one bag of chips) + y*(price of one granola bar) = $24

We also know that each bag of chips costs $1 less than a granola bar, so we can write:

(price of one bag of chips) = (price of one granola bar) - $1

Substituting this into the first equation, we get:

x*((price of one granola bar) - $1) + y*(price of one granola bar) = $24

Expanding and simplifying, we get:

x*(price of one granola bar) + y*(price of one granola bar) - x = $24

We also know that Jack buys 2 more items than Jane, so we can write:

x = y + 2

Substituting this into the previous equation, we get:

(y + 2)(price of one granola bar) + y(price of one granola bar) - (y + 2) = $24

Simplifying, we get:

2*(price of one granola bar) + y = $26

We can now solve for y:

(price of one granola bar) = ($26 - y)/2

Substituting this back into the equation for x, we get:

x = y + 2

x = (26 - y)/2 + 2

Simplifying, we get:

x = (28 - y)/2

We know that x and y must be whole numbers, so we can test different values of y until we find one that makes x a whole number. Starting with y = 2, we get:

(price of one granola bar) = ($26 - 2)/2 = $12

2*(price of one granola bar) + y = $26

2*($12) + 2 = $26

Therefore, Jack buys 15 bags of chips (x = (28 - y)/2 = (28 - 2)/2 = 15) and Jane buys 13 granola bars (y = 2).

In summary, Jack and Jane each spend $24 on snacks. Jack buys bags of chips and Jane buys granola bars. Each bag of chips costs $1 less than a granola bar, and Jack buys 2 more items than Jane buys. We can solve for the number of bags of chips Jack buys by setting up and solving equations based on these facts. We find that Jack buys 15 bags of chips.

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The requried measure of the hypotenuse of the given right triangle is 37.

The hypotenuse of the right angle triangle can be evaluated by Pythagoras' theorem, which states that the sum of squares of the legs of a right triangle is equal to the square of the third side.

Hypotensue² =  12²+35²
Hypotensue = √1369 = 37

Thus, the requried measure of the hypotenuse of the given right triangle is 37.

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Step-by-step explanation:

When x = 0    y = 20      Plug in:

20 = 20 b^0  

20 = 20      true , but we didn't find 'b'

when x = 1   y = 10        Plug in:  

10 = 20 * b^1

10 = 20 b

b = 1/2

Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

To establish that S is a subspace of ℝ^3, we must confirm that S is closed under vector summation and scalar multiplication.

A pertinent theorem from linear algebra that can be applied here is the "Subspace Criterion" theorem. This principle states that a non-empty subset S of a vector space V is a subspace if and only if it fulfills the following conditions:

For any vectors a, b ∈ S, their addition a + b ∈ S.

For any vector a ∈ S and any scalar k, the product ka ∈ S.

Now, let's define a vector m = v - e.

Observe that for any y in S, we have:

m • y = (v - e) • y = (v • y) - (e • y) = 0.

This implies that y is orthogonal to the vector m.

Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

As the plane is closed under vector summation and scalar multiplication, S is indeed a subspace of ℝ^3.

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Suppose v = (2, 4, 5) and e = (6, 7, 3) are a pair of vectors in ℝ^3. Let S be the collection of all y in ℝ^3 such that the inner product of v and y equals the inner product of e and y (i.e., v • y = e • y).

What principle can be utilized to demonstrate that S is a subspace of ℝ^3? Describe S in geometric terms.

Using similar side theorem and taking the ratios of similar sides, the value of AD is 3.6 units

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.

In this problem, we can use the similar side theorem by taking ratios of similar sides.

4.5 / 5 = AD / 4

Cross multiply both sides

AD = (4.5 * 4) / 5

AD = 18/5

AD = 3.6

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Answer:

The volume of a pyramid can be calculated using the formula:

V = (1/3) * base area * height

where "base area" is the area of the base of the pyramid.

In this case, the base of the pyramid has a length of 9 meters and a width of 7 meters, so its area is:

base area = length * width = 9 m * 7 m = 63 m^2

The height of the pyramid is 13 meters.

Now we can calculate the volume:

V = (1/3) * base area * height

= (1/3) * 63 m^2 * 13 m

= 273 m^3

Therefore, the volume of the pyramid is 273 cubic meters.

Decision variables are the unknown quantities that need to be determined in a linear programming problem.

The objective function is a mathematical expression that needs to be maximized or minimized. It represents the goal or objective of the problem. Constraints are the restrictions or limitations that need to be satisfied in a linear programming problem. These constraints limit the feasible region of the problem and provide boundaries for the decision variables. Linear programming involves finding the optimal solution by maximizing or minimizing the objective function, subject to the constraints. The solution must satisfy all the constraints and provide the best possible value for the objective function.

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The largest possible number that he could be thinking of is given as follows:

3.

A number a is said to be a factor of another number b when the divisibility of b by a has a remainder of zero, that is, it is an exact division.

The factors of 18 are given as follows:

{1, 2, 3, 6, 9}.

The factors of 30 are given as follows:

{1, 2, 3, 5, 6, 10, 15, 30}

The number is odd, hence the largest possible number is of 3.

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The inequality for the shaded region shown in the figure is; y ≥  x^2 - 1

We can see that the shaded region seems to be a parabola, and we also can see that the lines of the parabola are solid lines (which means that the points on the curve itself are solutions, so the symbol ≥ is used)

Then:

y ≥ ax^2 + bx + c

where ax^2 + bx + c is the general quadratic equation.

Now to find the equation for the parabola:

f(x) = ax^2 + bx + c

We also can see that the vertex of the parabola is at the point (0, -1)

This means

f(0) = -1 = a0^2 + b0 + c

     -1 = c

c = -1

Then:

f(x) = ax^2 + bx - 1

Now we can see at the graph again, to see that the zeros of the parabola are at +1 and -1

Which means that:

f(1) = 0 = a*1^2 + b*1 - 1 = a + b - 1

f(-1) = 0 = a*(-1)^2 + b*(-1) - 1 = a - b - 1

Then we have two equations:

a + b - 1 = 0

a - b - 1 = 0

b = 0

these equations become:

a - 1 = 0

a - 1 = 0

Then solving for a, a = 1

Then the quadratic equation is:

f(x) = 1*x^2 + 0*x - 1

f(x) = x^2 - 1

And the inequality is y ≥  x^2 - 1

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