The weight of an organ in adult males has a bell-shaped distribution with a mean of 330 grams and a
standard deviation of 50 grams. Use the empirical rule to determine the following.
(a) About 95% of organs will be between what weights?
(b) What percentage of organs weighs between 280 grams and 380 grams?
(c) What percentage of organs weighs less than 280 grams or more than 380 grams?
(d) What percentage of organs weighs between 180 grams and 430 grams?

Answer:

x = 58.67

Step-by-step explanation:

[tex]\frac{-8.8}{x}[/tex] = [tex]\frac{1.5}{10}[/tex]

Cross multiply

1.5x = (-8.8)(10)

1.5x = -88

Divide, solve for x

x = -88/1.5 = -58.6666667 = around -58.67

Answer: To graph the equation y = 2/3x - 1, we can start by finding some points that satisfy the equation.

We can pick any value for x and substitute it into the equation to find the corresponding y-value.

For example:

When x = 0, y = (2/3)(0) - 1 = -1

When x = 1, y = (2/3)(1) - 1 = -1/3

When x = 2, y = (2/3)(2) - 1 = 1/3

When x = 3, y = (2/3)(3) - 1 = 2/3

We can plot these points on a coordinate plane and then connect them with a straight line to graph the equation.

The graph will be a line that passes through the points (0, -1), (1, -1/3), (2, 1/3), and (3, 2/3).

Step-by-step explanation:

Answer: Lisa will receive 475 Euros.

Step-by-step explanation: 500x0.95 = 475.

Answer:

Step-by-step explanation:

2

Answer:

Step-by-step explanation:

O gráfico  de g(x) = [x+3] é uma Reta que passarum pelo pno (3,0) e tem inclinação 1.

1.  Every composite number can be expressed as a product of primes - True

2.  Some quadratic equation has infinite solution - True

3. False (ix-yl = |x-y|, which may not equal ly = |y|)

4. 2(3+√7)-2√7 = 6√7 - False

5. False (25,471,287 is divisible by 3)

6. √6 is not rational number - True

7. Between every two real numbers there is another real number -True

8. For any natural numbers a and b GCF (a, b) * LCM (a, b) = a*b. -True

9. Integer is not closed under division -True

10. False (The product of a non-zero rational number and an irrational number is not necessarily rational)

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Using what we know about lines and vertical angles we will see that:

m∠3 = 35°.

Remember that when two lines intercept and 4 angles are formed, the vertical angles (these ones connected only by the vertex) have the same measure.

For example, 2 and 5 are vertical angles in this case.

Angles 6 and 3 also are vertical angles, and if both white lines are parallel, then the measures of angle 1 and 6 will be equal (because both are on the same quadrant) then:

m∠6 = 35°

Then the measure of angle 3 is:

m∠3 = 35°.

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Answer:

seventy-five thousand two hundred thirty-two

Step-by-step explanation:

The expression after simplification is -6x¹¹.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is (-4x²) (3x⁵) / (2x⁻⁴).

We have the rule for exponents,

xᵃ . xᵇ = xᵃ⁺ᵇ

xᵃ / xᵇ = xᵃ⁻ᵇ

(-4x²) (3x⁵) = (-4 × 3) x²⁺⁵ = -12x⁷

-12x⁷ / 2x⁻⁴ = (-12 / 2) x⁷⁻⁻⁴

                   = -6x¹¹

Hence the simplification of the expression (-4x²) (3x⁵) / (2x⁻⁴) is -6x¹¹.

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Answer:

4.5

Step-by-step explanation:

4.5 times 2 = 9

9 divided by 2 =4.5

(i) 0

(ii) inifinity(very large value)

(iii) undefined

(iv) positive value

(v) negative value

A limiting value of a function is a value that the function approaches as the input (or independent variable) approaches a certain value. It is also called the function's limit at that point. This concept is used in calculus to understand the behavior of functions and their derivatives.

so in all the cases we have to find the limiting value of f(x)

1. if the value of f(b) is very large the 1/f(b) is very small.

2. if f(b) is small then the value of 1/f(b) is very large

3. if f(b) is 0 then 1/f(b) is not defined.

4. if f(b) is positive then its reciprocal is also positive.

5. if f(b) is negative then its reciprocal is also negative.

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(I) 0

(ii) The infinite (very large value)

IIII, undefinable

(iv) A favorable value

(v) negative value

A function's limiting value is a point that the function approaches as the input (or independent variable) gets closer to a particular value. At that time, it is also known as the function's limit. Calculus makes use of this idea to comprehend how functions behave and how their derivatives work.

Therefore, we must always determine the limiting value of f. (x)

1. The value of 1/f(b) is very small if the value of f(b) is very large.

2. The value of 1/f(b) is very large if f(b) is tiny.

3. 1/f(b) is not defined if f(b) is 0.

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Answer: So Here you go I got the perfect answer with a explanation

Step-by-step explanation:

A unit rate is a rate in which the second term is 1. To find a unit rate, we need to divide the first term by the second term.

A) 40:5 has a unit rate of 8 (40/5 = 8)

C) 96:12 has a unit rate of 8 (96/12 = 8)

D) 48:6 has a unit rate of 8 (48/6 = 8)

So options A, C and D has a unit rate of 8.

Answer:

the ration has a unit rate of 8 A - 40:5C - 96:12 D - 48:6Dividable by 8

Step-by-step explanation:

The total price is obtained following these two steps:

The first step is obtain the price without taxes, which is done adding the price of all the items in the data-set.

Then the proportion is applied, relative to the sales tax of 7%.

The percentage of a sales tax of 7% is given as follows:

107%.

Hence the multiplier relative to this sales tax is given as follows:

1.07.

The problem is incomplete, hence the answer was given in general terms.

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Answer:

Yes, a transformation of f in the form g(x) =f(x)+k can have no x-intercepts. This will occur if the constant k is added to the y-value of every point on the f(x) graph, resulting in the chart of g(x) being shifted upward by k units. If the original diagram of f(x) had no x-intercepts, then the graph of g(x) would also have no x-intercepts because the x-coordinate of each point on the graph of f(x) is unchanged by the transformation.

Step-by-step explanation:

Answer:

f(x) = 0.5x

Step-by-step explanation:

For this problem, we simply have to find the constant of proportionality between x and f(x). In other words, what x is multiplied by to get f(x).

Since this proportion is constant (meaning it doesn't change), all we have to do is divide an f(x) value in the table by its corresponding x value.

p = f(x) / x

p = -2 / -4

p = 1/2 = 0.5

We can show the relationship of x to f(x) with the equation f(x) = px, which can be simplified using the constant of proportionality that we just solved for.

f(x) = 0.5x

The linear function that gives the number of matchsticks required to make the nth pattern is given as follows:

M(n) = 15n.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

When a linear function represents a proportional relationship, it means that the intercept is of zero.

As for each pattern the number of sticks is increased by 15, the slope is of 15 and the equation is given as follows:

M(n) = 15n.

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Answer:

uh 6

Step-by-step explanation:

10??????????????????????????6????

The interquartile range?

I believe it is 65.

Answer: -56/55

Step-by-step explanation:

2 4/5x = -11/4

14/5x = -11/4

Cross multiply:

-55x = 14 * 4 = 56

x = -56/55

The solution to the system is (7.5, 1)

From the question, we have the following parameters that can be used in our computation:

2x−3y=12

−12y+8x=48

divide the first equation by 2

So, we have

x - 1.5y = 6

This gives

x = 6y + 1.5

By substitution, the second equation becomes

-12y + 8 (6y + 1.5) = 48

So, we have

-12y + 48y + 12 = 48

Evaluate

36y = 36

Divide by 36

y = 1

So, we have

x = 6 + 1.5

x = 7.5

Hence, the solution is (7.5, 1)

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The ΔABC reflects across x-axis with point a=2 and scale factor of x+2 to form the ΔA'B'C'.

What is reflection?

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.

The vertices of ΔABC is given as -

A(–4, –2), B(–2, 6), and C(4, 4)

The vertices of ΔA'B'C' is given as -

A′(–2, –2), B′(0, –10), and C′(6, –8)

To find the scale factor of the reflection use the formula -

x + a = x' and y + b = y'

Substitute the values in the equation.

For vertex A and A' -

x1 + a = x1'

-4 + a = -2

a = -2 + 4

a = 2

y1 + b = y1'

-2 + b = -2

b = -2 + 2

b = 0

For vertex B and B' -

x2 + a = x2'

-2 + a = 0

a = 0 + 2

a = 2

y2 + b = y2'

6 + b = -10

b = -10 - 6

b = -16

For vertex C and C' -

x3 + a = x3'

4 + a = 6

a = 6 - 4

a = 2

y3 + b = y3'

4 + b = -8

b = -8 - 4

b = -12

It can be seen that the values of a is constant whereas the values of y varies. This happens due to reflection of coordinates across the x-axis.

Therefore, the reflection happens across the x axis.

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Step-by-step explanation:

based on you input, I would suggest you divide 70 by 4 to get 17.5.

that is the answer. trust.

#quanta #vesperdiagram

The absolute value function for f(e) is given as follows:

f(e) = |e|

The piece-wise definition of the function is given as follows:

The absolute value of a number is the number without the signal, representing the difference between the number and zero.

This means that the elevation function gives just elevation, without considering if the elevation is positive or negative, and thus the function is defined as follows:

f(e) = |e|

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Answer: Let's call the first number "x" and the second number "y".

From the problem statement, we know that:

x = 3y - 6 (because one number is six less than three times the other number)

x + y = 38 (because the sum of the numbers is 38)

We can substitute the first equation into the second equation to solve for one of the variables:

3y - 6 + y = 38

4y - 6 = 38

4y = 44

y = 11

Now we can substitute this value of y back into the first equation to find the value of x:

x = 3(11) - 6

x = 29

So the two numbers are:

x = 29

y = 11

Step-by-step explanation:

Mallory is further from the surface than Eva. So, Mallory > Eva. Therefore, option D is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Mallory is exploring at an elevation of -25 feet.

So, distance between Mallory and the surface of water is 25 feet

Jacob is standing on the boat, at an elevation of 15 feet.

Distance between Jacob and the surface of water is 15 feet

Eva just jumped in and is 5 feet below the surface of the water.

Distance between Eva and the surface of water is 5 feet

In this case, the person closest to the surface is Eva, who is 5 feet from the surface.

So, the inequality is Mallory > Eva

Therefore, option D is the correct answer.

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The simplified form of the given expression is x raise to the power of one-thirty.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

Simplifying indices expressions

Given the indices expression (x^1/2/(x^1/3)^1/5

Using the indices law below:

a^m/a^n = a^m-n

(a^m)^n

Applying the law above to the given equation

(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5

(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5

(x^1/2/(x^1/3)^1/5 = x^1/30

Hence the simplified form of the given expression is x raise to the power of one-thirty.

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The likelihood of randomly selecting a chocolate chip cookie from the batch is unlikely. Therefore, option C is the correct answer.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

Given that, the baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies.

P(chocolate chip) = 0.25

In probability, larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 0.5 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Here, 0.25<0.5

Therefore, option C is the correct answer.

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Answer:unlikely

Step-by-step explanation:

The person walks 128 feet if she walked around the square pathway.

The plane forms that can be sketched on a flat (or plane) surface or a piece of paper are known as 2D shapes. Every 2D shape has different attributes, like area and perimeter. Some of the two-dimensional objects have sides and corners, while others have curved edges.

Given two pathways,

circular and square, and the circular pathway is inscribed inside of a square pathway,

area of circular pathway = 768 square feet

area of circle = π/4*d²

where d is the diameter

768 = π/4*d²

768*4 = πd² (π = 3)

3072/3 = d²

d = √1024

d = 32 feet

since the circle is inscribed in a square the length of a side of square is equal to the diameter of the circle,

d = a = 32 feet

to find the perimeter of the square path,

perimeter of square = 4a

perimeter of square = 4*32

perimeter of square = 128 feet

Hence the person has to cover 128 feet if she walked around the square pathway.

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(a) Sample space: 2^50 (1,024,000). Probability of exactly 20 heads: 0.000244140625.

(b) 6^2 (36). Probability of a sum of 4: 1/9.

(c) C(52,5) (2,598,960). Probability of a full house: 0.001441.

(d) 10^20 (10^19). Probability of bin 1 containing exactly 3 balls: 1/10^19.

(e) C(54,3) (19,323). Probability of at least one psychologist: C(24,1)/C(54,3) (0.841). Probability of exactly three psychologists: C(24,3)/C(54,3) (0.037).

(f) 3^10 (590,490). Probability of at least one of each type: 0.001690.

(a) The sample space consists of all the possible outcomes of flipping a fair coin 50 times, which is 2^50 (1,024,000). There are only two possible outcomes for each flip, heads or tails. The probability of getting exactly 20 heads is 0.000244140625.

(b) The sample space consists of all the possible outcomes of rolling a red and a blue 6-sided die, which is 6^2 (36). The probability of getting a sum of 4 is 1/9.

(c) The sample space consists of all the possible 5 card poker hands (selected from a single deck), which is C(52,5) (2,598,960). The probability of getting a full house (3 cards of one rank and 2 cards of another rank) is 0.001441.

(d) The sample space consists of all the possible ways of placing 20 labeled balls into 10 labeled bins, which is 10^20 (10^19). The probability of bin 1 containing exactly 3 balls is 1/10^19.

(e) The sample space consists of all the possible ways of selecting 3 of the 54 people attending the conference, which is C(54,3) (19,323). The probability of at least one psychologist being chosen is C(24,1)/C(54,3) (0.841). The probability of exactly three psychologists being chosen is C(24,3)/C(54,3) (0.037).

(f) The sample space consists of all the possible ways of buying ten cupcakes from the 3 different types, which is 3^10 (590,490). The probability that you have at least one of each type is 0.001690.

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To much to right but have it in pic: \/ \/

Answer:

-13a +10b

Step-by-step explanation:

          [tex]-3a-4b-2(5a-7b)[/tex]

[tex]=-3a-4b-10a+14b[/tex]

[tex]=-13a+10b[/tex]

Hope this helps