given a normal distribution with µ = 50 and σ = 10, find: (a) the area under the curve to the left of x = 34.5;; (b) the area under the curve to the right of x = = 42.7; (c) the area under the curve between x = 45.4 and x = 58.6; (d) the value of x that has 91% of the curve to its left; (e) the two values of x, symmetric around the mean, which contain 80% of the curve.

Answer:

See Explanation

Step-by-step explanation:

Given

Arun = ¼

Varun = ⅙

Required

Determine the possible initial number of chocolate

The question requires options to work with which are missing; however, I'll explain how to solve and also list out possible options to make use of.

The question says Arjun gave out fractions of his chocolate without breaking an of them; this means that he gave out whole chocolate (i.e. whole number)

So, to solve this, we multiply the fraction given to Arun and Varun.

Any of the options that results in non decimal integer answers the question.

Take for instance, the options are:

a) 8 b) 15 c) 20 d) 48

Option A: 8

Arun = ¼ * 8 = 2

Varun = ⅙ * 8 = 1.33

Option B: 15

Arun = ¼ * 15 = 3.75

Varun = ⅙ * 15 =2.5

Option C: 20

Arun = ¼ * 20 = 5

Varun = ⅙ * 20 = 3.33

Option D: 48

Arun = ¼ * 48 = 13

Varun = ⅙ * 48 = 8

Option D answers the question because other options resulted in decimals for either Arun or Varun or both of them.

Answer:

234565432344343

Carman buy the video game in the cost of $45.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Carman has saved 80% of the money she needs to buy a new video game.

And, she saved the cost $36.

Let total cost of the video game = x

So, We can formulate;

⇒ 80% of x = $36

⇒ 80/100 × x = 36

⇒ 8x = 360

⇒ x = $45

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The domain of the function is all positive real numbers, representing the possible diameters of the rope, while the range is all positive real numbers, indicating the potential breaking strengths of the manila rope.

The domain of the function is all positive real numbers since the diameter of a rope cannot be negative or zero. However, it is important to note that in practical terms, the diameter should also have a minimum value, typically determined by the manufacturing specifications or practical constraints.

The range of the function represents the possible breaking strengths of the manila rope. Since the function is defined as z = 8900d^2, where d is the diameter, the breaking strength (z) will always be a positive value. As the diameter increases, the breaking strength also increases, and there is no upper limit to the breaking strength. However, it is essential to consider practical limitations, such as the maximum load capacity of the material used or any physical constraints that may prevent the rope from achieving extremely high breaking strengths.

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Alex has $15.78 and Rick has $12.15 money.

According to the question,

We have the following information:

Alex had $3.63 more than Rick. Together they had $27.93.

Let's take the money Rick has to be $x.

Now, we have the following expression for the money Alex has:

3.63+x

Now, we have:

x+3.63+x = 27.93

2x+3.63 = 27.93

Subtracting 3.63 from both the sides:

2x = 27.93-3.63

2x = 24.3

Dividing by 2 on both the sides:

x = 24.3/2

x = $12.15

So, Rick has $12.15.

Now, the money Alex has:

3.63+12.15

$15.78

Hence, Alex has $15.78 and Rick has $12.15 money.

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This statement is true

A probability is a numerical value that indicates the chance, or likelihood, of a specific event occurring. Probability is the measure of the likelihood of a random event happening, and it is expressed as a number between 0 and 1, with 0 implying that the event would never occur and 1 implying that it is certain to happen.

The probability of an event happening is referred to as its likelihood. Probability can be expressed as a fraction, percentage, or decimal, and it is a vital tool in statistics. It is frequently utilized in mathematics to estimate real-world situations that involve random variables such as coin flips, weather patterns, stock market trends, and even sporting events.

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Answer:

-176

Step-by-step explanation:

Let x = -8

f(-8) = 11 (-8-24) / 2

         Simplify the parentheses

f(-8) = 11 ( -32)/2

        = 11 (-16)

        = 176

Answer:

Step-by-step explanation:

change in x (horizontal) = 4 - 1 = 3

Change in y (vertical)  = 9 - 3 = 6

Slope = change in x / change in y

slope = 3 / 6 = 1/2

C. When there is no outlier, the mean is the appropriate measure of center.

When there are no outliers in a dataset, the mean is a good measure of center because it takes into account the values of all the data points. The median is also a good measure of center, but it may not be the best choice if there are extreme values or outliers in the dataset, as it can be influenced by those values. However, when there are no outliers, both the mean and the median are appropriate measures of center.

Option A is not true because the mean is not skewed in one direction when there is no outlier. Skewness refers to the shape of the distribution, and it can be affected by outliers, but not by the absence of outliers.

Option B is not true because the median is not skewed in one direction when there is no outlier. Skewness refers to the shape of the distribution, and the median is not affected by the shape of the distribution, but by the position of the values.

Option D is not true because the median can be used as the measure of center even when there is no outlier. It is a robust measure of center that is not influenced by extreme values.

From the histogram,

The students securing 10-19 points are 14 and student securing 70-79 points are 16.

Thus there are more students securing 70-79 points thann student securing 10-19 points.

The answer is 70-79 points.

Answer:

Step-by-step explanation:

Given the equation used to calculate the amount of profit, p, made from selling n candy bars expressed as  p = 1.50n – 500

To find the number of candies sold for $700, we are going to substitute p = $700 into the given expression and find n as shown;

700 =  1.50n - 500

Add 500 to both sides

700+500 = 1.50n-500+500

1200 = 1.50n

Divide both sides by 1.50

1200/1.50 = 1.50n/1.50

800 = n

Rearrange

n = 800

Hence 800 candy bars must be sold to make $700 profit

Understanding a set’s nature or properties is made easier by its closure property

The set is closed if it has the closure property. This means that any operation performed on an element within a set will provide a result that belongs to that element’s set.

Why Closure Property is important?

Understanding a set’s nature or properties is made easier by its closure property. Mathematical applications of closure are numerous. Any operation that adheres to this condition is said to be “closed” or to have “fulfilled the operation’s closure property.”

Example – The set of even number is closed under subtraction

                   Even – Even = Even

                   6 – 4 = 2

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Answer: 52 inches

Step-by-step explanation:  To find the total length of the kite from point A to point C, we need to first find the length of the other two sides of the kite. Let's call the length of the side from point B to point C "x" and the length of the side from point A to point B "y".

Since the perimeter of the kite is the sum of all its sides, we can set up the equation:

x + y + x + y = 104

Simplifying, we get:

2x + 2y = 104

Dividing both sides by 2:

x + y = 52

We know that the distance from point A to point C is equal to the sum of the distances from point A to point B and from point B to point C:

AC = AB + BC = y + x

Substituting the value of (y + x) from the previous equation, we get:

AC = 52

Therefore, the total length of the kite from point A to point C should be 52 inches.

please mark this answer as brainlist

Answer:

The scale factor represents a proportional relationship between the scale drawing and the building’s dimensions. If the dimensions change, then the scale factor must also change to preserve the relationship.

Step-by-step explanation:

Hope it helps XD

Answer:

The scale factor represents a proportional relationship between the scale drawing and the building’s dimensions. If the dimensions change, then the scale factor must also change to preserve the relationship.

Step-by-step explanation:

Answer:

C=47.1

Step-by-step explanation:

take the diameter(15) and multiply it by pi(3.14).

15 x 3.14 = 47.1

Answer:

5 pears

Step-by-step explanation:

Given that

The  average of 20 pears were sold from Monday to Friday

But after the sales on Saturday and Sunday, the average pears sold per day were increased to 25

We need to determine the number of pears sold on Saturday and sunday

So, it is

= 25 pears - 20 pears

= 5 pears

Answer:

The answer is 720

Step-by-step explanation:

Got it right on edge. :)

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

a) Nonzero vector orthogonal to the plane through the point P(0, 0, -3), Q(4,2, 0), and R(3, 3, 1) would be (12, -6, -12)

b) Area of the triangle PQR would be 4.18

What is nonzero vector of orthogonal ?

Taking the cross product of two vectors in the plane yields a non-zero vector orthogonal to the plane across the points. Calculate the difference vector of two of the points, then take the cross product of that difference vector with the difference vector of the third point.

a) A nonzero vector orthogonal to the plane through the points P, Q, and R can be found by taking the cross product of two nonparallel vectors in the plane.

For example, the vector PQ = (4, 2, 0) - (0, 0, -3) = (4, 2, 3) and PR = (3, 3, 1) - (0, 0, -3) = (3, 3, 4). The cross product of these vectors is orthogonal to the plane:

PQ x PR = (12, -6, -12)

2) The area of triangle PQR can be found using the cross product formula for the area of a parallelogram. The area is given by the magnitude of the cross product of two sides of the triangle:

         \(Area =\frac{ |PQ * PR| }{2}\\\\Area =\frac{\sqrt{(12^2 + (-6)^2 + (-12)^2)} }{2}\\\\Area =3 * \sqrt(10) / 2\\\\Area =4.18\)

Thus, Nonzero vector orthogonal to the plane through the point P(0, 0, -3), Q(4,2, 0), and R(3, 3, 1) would be (12, -6, -12) and area of the triangle PQR would be 4.18.

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Answer:

1.5 hours

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

Aya and Mary distance = 12 miles

Let, meeting point from Aya = Z miles

So, Aya covers Z miles to reach Mary.

Hence, Mary covers (12 - Z ) miles to reach Aya

Here, Time = \(\frac{Distance}{Speed}\)

Aya = \(\frac{Z}{5}\)

Mary = \(\frac{12-Z}{3}\)

If, same time taken, then we can solve by following method,

\(\frac{Z}{5} = \frac{12-Z}{3}\)

By solving the equation, we get

Z = 60 ÷ 8

Or Z = 7.5 miles

Hence, time taken for both to meet = 7.5 ÷ 5

= 1.5 hours

The number of people who prefer eggs is 35.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent. A ratio might be formatted as a Part to Part or Part to Whole comparison. A Part to Part comparison looks at two individual quantities within a ratio of greater than two numbers, such as the number of dogs to the number of cats in a poll of pet type in an animal clinic. A Part to Whole comparison measures the number of one quantity against the total, such as the number of dogs to the total number of pets in the clinic.

Let the number of people who prefer eggs be x.

21 people said they prefer oatmeal.

The ratio of people who prefer oatmeal to those who prefer eggs is 3 to 5.

∴ \(\frac{21}{x} = \frac{3}{5} \\x = \frac{21*5}{3}\\ x = \frac{105}{3} \\x = 35\)

Thus, the number of people who prefer eggs is 35.

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Answer:

a = 22

AB = 50

Step-by-step explanation:

\(a-5=17\)

\(a=17+5\)

\(a=22\)

Line AB=2a+6

\(2(22)+6=44+6=50\)

\(AB=50\)

Hope this helps

The equation of the graph is (x-3)(x+1), the y-intercept of y=\(x^{2} -5x+4\) is "4" and the factors of  y=\(x^{2} -5x+4\) are (x-4) ad (x-1)

Given that a graph touch x-axis at 2 points i.e. 2 roots are there for given graph.The graph touches the x-axis at (3,0) and (-1,0) it implies x=3 and x=-1 are the solutions the equation,(x-3) and (x+1) are factors of equation

Therefore,the equation of graph is  (x-3)(x+1).

Given the equation y=\(x^{2} -5x+4\)

The y-intercept is defined as the graph passing a fixed point at x=0 line

i.e.(0,c) pass through it . c is the y-intercept

c=0-0+4

c=4

Therefore,The y-intercept of  the equation y=\(x^{2} -5x+4\) is 4

Factorising  y=\(x^{2} -5x+4\)

⇒  y=\(x^{2} -5x+4\)

⇒y=\(x^{2} -x-4x+4\)

⇒y=x(x-1)-4(x-1)

⇒y=(x-4)(x-1)

Therefore, the factors of  y=\(x^{2} -5x+4\) are (x-4) and(x-1)

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Answer:

your answer will be 172.8m³

Step-by-step explanation:

have a nice day!!!

Answer: 22 m

Step-by-step explanation:

I think it's 22 but not sure though.

Answer:

r = k/2 + 35/2

Using the normal distribution, there is a 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

For this problem, the parameters are given as follows:

\(\mu = 40, \sigma = 8, n = 16, s = \frac{8}{\sqrt{16}} = 2\)

The probability that the sample mean will be within 2 points of the population mean is the p-value of Z when X = 40 + 2 = 42 subtracted by the p-value of Z when X = 40 - 2 = 38, hence:

X = 42:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

Z = (42 - 40)/2

Z = 1

Z = 1 has a p-value of 0.8413.

X = 38:

\(Z = \frac{X - \mu}{s}\)

Z = (38 - 40)/2

Z = -1

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

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The number of additional days she wants to rent the car for the two specials are equivalent is 5 days.

Compact car:

y = 50 + 6x

Another special:

y = 40 + 8x

let

x = number of additional days

50 + 6x = 40 + 8x

50 - 40 = 8x - 6x

10 = 2x

x = 10/2

x = 5 days

Therefore, the number of additional days she wants to rent the car for, the two specials are equivalent is 5 days.

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The expression that represents the statement "the product of a number and eight" is 8x.

Expression:

Expression means the mathematical statement that consists of  minimum of two numbers/variables and at least one math operation(addition, subtraction, multiplication and division) in it.

Given,

The given statement is "the product of a number and eight".

Now, we have to find the suitable expression for this statement.

In order to find the suitable expression, we have to divide the given statement and then we have to identify the keyword in it.

By using those keywords, we have to solve it.

In the given statement we have identify the following:

product

number

eight

Here the product refers the multiplication

number is any unknown number that is x.

eight refers the number 8.

When we combine these keywords we can get the expression 8x.

Therefore, the resulting expression is 8x.

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