how do i find the percent of the area under the density curve where x is less than 2?

a.  The probability that a randomly selected adult female has a pulse rate less than 82 beats per minute is 0.7123.

b. The probability that 25 randomly selected adult females have a pulse rate with a mean less than 82 beats per minute is 0.9974.

c. The normal distribution can be used in part (b), even though the sample size does not exceed 30 as Option D: Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

a. Using the z-score formula, z = (x - μ) / σ, where x = 82, μ = 75, and σ = 12.5, we get -

z = (82 - 75) / 12.5

z = 0.56

Using a standard normal distribution table or calculator, we can find the probability that z is less than 0.56 is 0.7123.

Therefore, the probability value is obtained as 0.7123.

b. The central limit theorem states that as the sample size increases, the distribution of sample means becomes approximately normal, regardless of the shape of the original population distribution.

Therefore, we can use a normal distribution to approximate the sampling distribution of the sample mean, even if the sample size is less than 30.

The mean of the sampling distribution of the sample mean is the same as the mean of the original population, which is 75.

The standard deviation of the sampling distribution of the sample mean, also known as the standard error, can be calculated as σ / sqrt(n), where n = 25 is the sample size.

standard error = 12.5 / √(25) = 2.5

Using the z-score formula again, we can find the z-score for a sample mean of x' = 82 -

z = (x' - μ) / (σ / √(n))

z = (82 - 75) / (2.5)

z = 2.8

Using a standard normal distribution table or calculator, we can find the probability that z is less than 2.8 is 0.9974.

Therefore, the probability value is obtained as 0.9974.

c. The correct answer is the central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.

The requirement of a sample size greater than 30 applies to using a normal distribution to approximate the population distribution, not the sampling distribution of the sample mean.

Therefore, the correct option is D.

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Assume that females have pulse rates that are normally distributed with a mean of μ=75.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete parts​ (a) through​ (c) below.

a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 82 beats per minute.

The probability is ___.

b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 82 beats per minute.

The probability is ___.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

A. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.

B. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size.

C. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.

D. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

Answer:

82 ft^2

Step-by-step explanation:

To find the amount of glass needed to cover the entire rectangular pyramid, we need to calculate the combined surface area of all its faces.

The rectangular base of the pyramid has an area of 5 feet by 4 feet, or 20 square feet. The two large triangular faces each have an area of (1/2) x base x height = (1/2) x 5 feet x 6.8 feet = 17 ft^2. The two small triangular faces each have an area of (1/2) x base x height = (1/2) x 4 feet x 7 feet = 14 ft^2.

Therefore, the total surface area of the pyramid is:

20 ft^2 (for the base) + 17 ft^2 + 17 ft^2 + 14 ft^2 + 14 ft^2 = 82 ft^2

So, the amount of glass needed to cover the entire pyramid is 82 square feet.

Therefore, the answer is 82 ft^2.

Answer:82  ft2

Step-by-step explanation:

i did it in class

Answer:

Hey Sweetheart!

z=4

4x4x4= 64

Hope this Helps!!!

Answer:

[tex]\large\boxed{\tt m \angle p = 54.7^{\circ}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find the value of p.}[/tex]

[tex]\textsf{Note that we are given \underline{Vertical Angles}, and a \underline{perpendicular} set of lines.}[/tex]

[tex]\large\underline{\textsf{What are Vertical Angles?}}[/tex]

[tex]\textsf{Vertical Angles are 2 angles that are opposite from each other, and share a}[/tex]

[tex]\textsf{common vertex point. (center point) Vertical Angles are congruent as they are}[/tex]

[tex]\textsf{formed by the same 2 intersecting lines.}[/tex]

[tex]\large\underline{\textsf{What are Perpendicular Lines?}}[/tex]

[tex]\textsf{Perpendicular Lines are 2 sets of lines that intersect each other with opposite}[/tex]

[tex]\textsf{reciprocal slopes. Perpendicular Lines form 4 right angles that are 90}^{\circ}.[/tex]

[tex]\large\underline{\textsf{Identifying Vertical Angles;}}[/tex]

[tex]\textsf{Remember that vertical angles are opposite from each other, and are congruent.}[/tex]

[tex]\textsf{We are given 1 measure of an angle, and this angle has a measure of 35.3}^{\circ}.[/tex]

[tex]\textsf{The angle opposite to it, (below angle p) is opposite from our angle.}[/tex]

[tex]\textsf{We have identified our vertical angle, now let's identify p.}[/tex]

[tex]\large\underline{\textsf{Identifying m} \tt \angle p;}[/tex]

[tex]\textsf{We should know that we are Perpendicular lines, and angle p is overlapped in one.}[/tex]

[tex]\textsf{This means that these angles are \underline{Complements}, angles that add up to 90}^{\circ}.[/tex]

[tex]\textsf{Because we know that the other angle inside the right angle is 35.3}^{\circ}, \ \textsf{we are}[/tex]

[tex]\textsf{able to set up an equation to find p.}[/tex]

[tex]\tt p = 90^{\circ} - 35.3^{\circ}[/tex]

[tex]\underline{\textsf{Evaluate;}}[/tex]

[tex]\large\boxed{\tt m \angle p = 54.7^{\circ}}[/tex]

Answer:

y=1/4x

Step-by-step explanation:a direct variation equation is y=kx. if y=1/4x, then when x=8, y=2.

that's the final answer

The relationship between the types of quadrilaterals such as rectangles, trapezoids and rhombi can be quantified in terms of sides and angles.

Rectangles and trapezoids

Squares and rhombi

Squares and trapezoids

Rhombi and trapezoids

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The balance A for P dollars invested at a rate r for t years and compounded n times per year can be calculated using the formula: A = P (1 + r/n)^(n*t)

where:

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

t = the number of years the money is invested

n = the number of times the interest is compounded per year

A = the total amount including principal and interest

To solve for the balance A, simply substitute the given values for P, r, t, and n into the formula and evaluate:

For example, let's say we invest $5000 at an annual interest rate of 4.5% for 3 years, compounded monthly (n=12).

P = $5000

r = 0.045 (4.5% expressed as a decimal)

t = 3 years

n = 12 (compounded monthly)

A = 5000 (1 + 0.045/12)^(12*3)

= 5000 (1.00375)^36

= $5,838.27

Therefore, balance A is $5,838.27 after 3 years of investing $5000 at an annual interest rate of 4.5%, compounded monthly.

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The area of the walkway can be expressed as the sum of two terms is 9x + 7 and 10x + 4.

We are given that the area of the garden is 6(5.5x + 2.5). This means that the garden has a length of 5.5x + 2.5 units and a width of 6 units (since the problem doesn't specify which side is the length or width, we can assume either). We can use the formula for the area of a rectangle to find the area of the garden:

Area of the garden = length x width = (5.5x + 2.5) x 6 = 33x + 15

Next, we are given that the combined area of the garden and the walkway is 6.5(8x + 4). This means that the garden and the walkway together have a length of 8x + 4 units and a width of 6.5 units. We can again use the formula for the area of a rectangle to find the combined area:

Combined area = length x width = (8x + 4) x 6.5 = 52x + 26

To find the area of the walkway, we need to subtract the area of the garden from the combined area. This will give us the area of the walkway alone.

Area of the walkway = Combined area - Area of the garden

= (52x + 26) - (33x + 15)

= 19x + 11

Finally, we are asked to express the area of the walkway as the sum of two terms. This means we need to find two numbers that add up to 19 and two numbers that add up to 11. We can use trial and error to find these numbers. One possible solution is:

19x + 11 = (9x + 7) + (10x + 4)

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Answer:

[tex]60n - 97[/tex]

Step-by-step explanation:

[tex]3 - 5( - 3n + 5)3 - 5( - 3n + 5)[/tex]

[tex]3 + (15n - 25)3 + 15n - 25[/tex]

[tex]3 + 45n - 75 + 15n - 25[/tex]

[tex]60n - 97[/tex]

  LN/RT = NM/TS is the correct option in congruent triangle .

What in mathematics is congruent?

If two shapes are similar in size and shape, they are said to be congruent. The mirror image of one shape is the same as the other if two shapes are congruent.

                          Congruent refers to objects that are precisely the same size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.

  In ΔLMN ≅ ΔRST

 In triangle are congruent .

    LN/RT = NM/TS

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Answer:21

Step-by-step explanation:

5x=180-75

5x=105

x=105/5

x=21

Answer:

QS=24

Step-by-step explanation:

QS and QU is the radius of the circle so they well be congruent
using Pythagorean Theorem:

[tex]x^{2} +32^{2} =(x+16)^{2}[/tex]

[tex]x^{2} +1024=x^{2} +32x+256[/tex]

[tex]32x=768[/tex]

[tex]X=24[/tex]

So,

QS=24

Answer:

120

Step-by-step explanation:

Answer: 4.2 percent

Step-by-step explanation: Your welcome

There are 336 ways for the 8 team entrants to achieve the desired outcome of first, second, and third place positions.

The problem involves selecting 3 individuals out of 8 to fill the 1st, 2nd, and 3rd place positions. Since the order in which the individuals are selected matters, we need to use the permutation formula to determine the total number of ways to achieve the desired outcome.

The formula for permutation is:

P(n,r) = n! / (n-r)!

Where n is the total number of individuals, and r is the number of positions to be filled.

In this case, we need to select 3 individuals out of 8 to fill the 1st, 2nd, and 3rd place positions. Using the permutation formula, we get:

P(8,3) = 8! / (8-3)!

= 8! / 5!

= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (5 x 4 x 3 x 2 x 1)

= 8 x 7 x 6

= 336

In other words, the coach has 336 possible ways to select three team members for the podium, assuming all team members have an equal chance of winning.

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The median of 20 is the most accurate to use, since the data is skewed.

A histogram is a graphical representation of data that shows the frequency distribution of a set of continuous data. It is a bar graph-like structure where the bars represent the frequency or proportion of data in specific intervals or ranges of values. The x-axis represents the range of values, and the y-axis represents the frequency or proportion of data in each range. Histograms are commonly used in statistical analysis to represent the distribution of data, especially when dealing with large datasets.

Here,

The data is not evenly distributed, as there are many donations at the lower end and fewer donations at the higher end. Therefore, the median, which represents the middle value in the data set, is a better measure of center than the mean, which can be influenced by extreme values. The median donation in this data set is $20.

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One possible equation Ross can make is 9 - 7 + 8 = 10

Ross is given the numbers 6, 7, 8, and 9, and is asked to make an equation that equals 10. The equation can use each number only once, and can use any arithmetic operations (such as addition, subtraction, multiplication, and division) in any order.

One way Ross can approach this problem is to first think about what pairs of numbers can be combined to make 10. Ross could quickly see that there are no pairs of numbers that add up to 10, since the highest pair is 8 + 9 = 17.

Next, Ross could think about using subtraction or division to create a 10. However, there are no pairs of numbers that can be subtracted or divided to get 10 either.

Therefore, Ross needs to use a combination of addition, subtraction, and/or multiplication to create an equation that equals 10.

One possible equation Ross can make is:

9 - 7 + 8 = 10

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Answer:-1

Step-by-step explanation:

in order to solve this type questions you should "orginize" numbers same variables:

-6x+4x=6-4

-2x=2

x=-1

Factor  72 + 32 in the form of a ( b + c)  with A having gcf is 72 + 32 is 8(9 + 4).

To factor 72 + 32, we first need to find the greatest common factor (GCF) of 72 and 32.

The prime factorization of 72 is 2³ x 3², and the prime factorization of 32 is 2⁵.

The common factors of 72 and 32 are 1, 2, 4, 8, and 16. The greatest common factor is 8, since it is the largest factor that they both share.

So, we can write 72 + 32 as:

72 + 32 = 8 x (9 + 4)

Therefore, the factored form of 72 + 32 is 8(9 + 4).

To factor 72 + 32, we need to find the greatest common factor (GCF) of 72 and 32, which is 8. We can then use this GCF to write 72 + 32 in factored form as 8(9 + 4). This expression can also be simplified as 8(13), which equals 104. This means that 72 + 32 can be written as the product of 8 and 13, where 8 is the GCF of 72 and 32, and 13 is the sum of the quotients of 72 and 32 when divided by 8. Factoring expressions is an important skill in algebra and is used in many areas of mathematics and science.

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Step-by-step explanation:

2(x+10y)+2(7x^2-x+9y)

= 2x+20y+14x^2-2x+18y

= (14x^2+38y) units^2

None of these statements must be true

=========================================

Explanation:

Let's go through the answer choices one at a time.

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

A)

Consider the set {4,5,6}. It has a mean of (4+5+6)/3 = 15/3 = 5. We add up the values and then divide by the number of values (3 in this case).

Now consider the set {3,5,7}. I've added 1 to the largest element and subtracted 1 from the smallest. This will spread the data set out further. The mean is still 5 because (3+5+7)/3 = 15/3 = 5. The center hasn't changed. But the data is more spread out so the variance is larger for this new set.

Therefore, the sets {4,5,6} and {3,5,7} do NOT have the same variance. We cross choice A off the list.

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

B)

Recall that

[tex]\text{standard deviation} = \sqrt{\text{variance}[/tex]

For example, if the variance is 36 then the standard deviation would be [tex]\sqrt{36} = 6[/tex]

Because of the connection of the standard deviation and variance, both measure how spread out a set is. Furthermore, it means the sets {4,5,6} and {3,5,7} do NOT have the same standard deviation. We can cross choice B off the list.

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

C)

This statement is clearly not true because the sets {4,5,6} and {3,5,7} are not the same, but they produce the same mean. We can cross choice C off the list.

Choice D is the only thing left so it must be the final answer.

Answer:

Omg I HATE IXL sm!!

Step-by-step explanation:

$637.51

The symbol π and the word "pi" are both used to refer to the mathematical constant that represents the ratio of a circle's circumference to its diameter

The symbol π and the word "pi" are both used to refer to the mathematical constant that represents the ratio of a circle's circumference to its diameter. The symbol π is a Greek letter that has been used to represent this constant for centuries, while the word "pi" is the commonly accepted English-language term for this constant.

They are two different representations of the same mathematical concept. The symbol π is used extensively in mathematical formulas, while the word "pi" is used more colloquially to refer to this constant in everyday conversation.

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Aki's Bicycle Designs should build 1.75 hundred, or 175, bicycles to minimize the average cost per bicycle.

To find the number of bicycles Aki's Bicycle Designs should build to minimize the average cost per bicycle, we need to find the minimum point of the given quadratic function C(x).

First, we can find the derivative of C(x) concerning x:

C'(x) = 0.4x - 0.7

Then, we can set C'(x) equal to zero and solve for x:

0.4x - 0.7 = 0

0.4x = 0.7

x = 1.75

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Hence, the value of  variable in the given expression x is 8

An angle is formed when two straight lines  meet at a common endpoint.

∠1 = 7x - 4

∠2 = 3x + 28

A secant line that crosses two parallel lines produces these angles. After that, these angles were congruent, which means that their measures are equal.

Then, equaling  both given expressions and solving for x,  we get:

Step1: subtract 3x both sides

7x - 4 = 3x + 28

Step2: add 4 both sides

7x - 3x - 4 = 28

Step2: simplify like terms

7x - 3x = 28 + 4  

Step3: divide by 4 both sides

4x = 32  

x = 32/4

x = 8

Hence, the value of x is 8.

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The right triangle has a 90-inch perimeter.

A right triangle is one with a 90 degree inner angle. Its longest side is the hypotenuse, which is also the side of the right triangle that faces the right angle. The two arms of a right angle are made up of height and base.

To get the length of the other right triangle leg, let's apply the Pythagorean theorem: a2 + b2 = c2, where c is the hypotenuse and a and b are the triangle's legs.

We are aware that c = 41 inches and, let's say, a = 40 inches for one of the legs. Hence, we may find b:

40² + b² = 41²

1600 + b² = 1681

b² = 1681 - 1600

b² = 81

b = √81

b = 9

Hence, the other leg is 9 inches long.

We can now determine the triangle's perimeter:

Perimeter = a + b + c

Perimeter = 40 + 9 + 41

Perimeter = 90 inches

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The approximate percent decrease in the number of customers from Saturday to Sunday is 33%. Therefore, the answer is option A: 33%

To find the approximate percent decrease in the number of customers from Saturday to Sunday, we first need to calculate the decrease in the number of customers:

Decrease = Saturday customers - Sunday customers

Decrease = 135 - 90

Decrease = 45

The percent decrease can be found by taking the decrease as a percentage of the original value (Saturday customers):

Percent decrease = (Decrease / Saturday customers) x 100%

Percent decrease = (45 / 135) x 100%

Percent decrease = 33.33%

Rounding to the nearest percent, we get that the approximate percent decrease in the number of customers from Saturday to Sunday is 33%. Therefore, the answer is option A: 33%.

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Your question is incomplete, but probably the complete question is :

You work as a cashier in a supermarket. On Saturday, you had 135 customers. On Sunday, you had 90 customers. What is the approximate percent decrease in the number of customers from Saturday to Sunday?

33%

45%

50%

90%

225%