Which choice is the correct answer for: 2.78 * 6?

12.78
16.28
13.18
16.68

Answer:

Explained below.

Step-by-step explanation:

The random variable X is defined as the number of missing pulses and follows a Poisson distribution with parameter (μ = 0.50).

The probability mass function of X is as follows:

\(P(X=x)=\frac{e^{-\mu}\ \mu^{x}}{x!};\ x=0,1,2,3...\)

(a)

Compute the probability that a disk has exactly one missing pulse as follows:

\(P(X=1)=\frac{e^{-0.50}\ 0.50^{1}}{1!}=0.3033\)

Thus, the probability that a disk has exactly one missing pulse is 0.3033.

(b)

Compute the probability that a disk has at least two missing pulses as follows:

\(P(X\geq 2)=1-P(X<2)\\\)

                \(=1-[P(X=0)+P(X=1)]\\=1-[\frac{e^{-0.50}\ 0.50^{0}}{0!}+\frac{e^{-0.50}\ 0.50^{1}}{1!}]\\=1-0.6065-0.3033\\=0.0902\)

Thus, the probability that a disk has at least two missing pulses is 0.0902.

(c)

It is provided that the two disks selected are independent of each other.

The probability that a disk has no missing pulses is:

\(P(X=0)=\frac{e^{-0.50}\ 0.50^{0}}{0!}=0.6065\)

Compute the probability that neither of the two disks contains a missing pulse as follows:

\(P(X_{1}=0,\ X_{2}=0)=P(X_{1}=0)\times P(X_{2}=0)\)

                               \(=0.6065\times 0.6065\\=0.367842\\\approx 0.3678\)

Thus, the probability that neither of the two disks contains a missing pulse is 0.3678.

The measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees

To find the measure of the angle to the nearest degree given trigonometric ratios, we can use inverse trigonometric functions.

Here are the steps to determine the angles:

a) sin A = 0.6018

Taking the inverse sine (arcsin) of both sides:

A = arcsin(0.6018)

Using a calculator, we find A ≈ 36 degrees (rounded to the nearest degree).

b) cos B = 0.9205

Taking the inverse cosine (arccos) of both sides:

B = arccos(0.9205)

Using a calculator, we find B ≈ 23 degrees (rounded to the nearest degree).

c) tan C = 0.0349

Taking the inverse tangent (arctan) of both sides:

C = arctan(0.0349)

Using a calculator, we find C ≈ 2 degrees (rounded to the nearest degree).

Therefore, the measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees.

Note: Trigonometric functions have periodicity, meaning there may be multiple angles with the same trigonometric ratio.

To determine the principal angle within a specific range, we use the inverse trigonometric functions.

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Answer:  

470

Step-by-step explanation:

Replace x with 10:  470

5(10)(10 - 3( = 500 - 30 = 470

470

If we increase each value by 7 grams, we get: {2507, 2707, 2807, 2907, 3107} this would change the rage median iqr of the data set.

what is the median?

The median is a measure of central tendency in a set of data, which represents the middle value of the data when it is arranged in order.

If each birth weight needs to be increased by 7 grams due to a calibration error in the scale being too low, this would affect all the values in the dataset equally, without changing the distribution of the data. Therefore, the range and median of the data set would be increased by 7 grams, while the IQR (interquartile range) would remain the same since it is calculated based on the middle 50% of the data.

For example, suppose we have the following birth weight data set:

{2500, 2700, 2800, 2900, 3100}

The range of the data set was originally 600 (3100 - 2500) but now it is 607 (3107 - 2507), an increase of 7. Similarly, the median of the data set was originally 2800 but now it is 2807, an increase of 7. However, the IQR of the data set, which is the difference between the third quartile (Q3 = 3000) and the first quartile (Q1 = 2700), remains the same at 300 - 270 = 30.

Therefore, If we increase each value by 7 grams, we get:

{2507, 2707, 2807, 2907, 3107}

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Complete Question:

You realize your scale was calibrated too low by 7 grams meaning each birth weight needs to be increased by 7 grams. How would this change the rage median IQR of the data set?

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:

y = x + 4

Step-by-step explanation:

From point (-1, 3) to point (0, 4), go up 1 (rise = 1) and go right 1 (run = 1).

slope = m = rise/run = 1/1 = 1

The y-intercept is b = 4

y = mx + b

y = x + 4

(-32)

Step-by-step explanation:

(-24)+(-8)

= -24 -8

= -32

Answer:

4.75 megabytes per second

Step-by-step explanation:

500-25 = 475

475 / 100 = 4.75

The x-intercepts represent a zero profit, the maximum value of the graph represents the maximum profit, An approximate average rate of change of the graph from x=3  to x=5 represents the reduction in profit from 3 to 5 and the domain is constrained by x=0.

Part A:

The x-intercepts represent a zero profit.

The maximum value of the graph represents the maximum profit.

The function increases up till the vertex and decreases after it.

This means that the profit increases as it reaches the peak at the vertex.

It decreases after the vertex up till it reaches zero.

On the left of the first zero and on the right of the second zero, the profits are negative.

Part B:

An approximate average rate of change of the graph from x=3  to x=5 represents the reduction in profit from 3 to 5.

Part C:

Simply, the domain is constrained by x=0.

We are obliged at x=6 .

This is because we have to avoid a negative profit.

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The graph of function y = (1/2)ˣ is shown in figure.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The function is,

⇒ y = (1/2)ˣ

Now, We can draw the graph of exponential function y = (1/2)ˣ.

Hence, The graph of function y = (1/2)ˣ is shown in figure

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Answer:

= √b/2a⁴

Step-by-step explanation:

First, we can simplify the ³⁄₁₂ to ¼

Next, we can simplify the a⁻³/a⁵ to a⁻⁸ which is ¹⁄ₐ⁸

Then we can simplify the b²/b to b

Now we should have:

√(b/4a⁸)

= √b/√(4a⁸)

= √b/2a⁴

Answer:x=58

Step-by-step explanation:

Did it already

Answer:

Hope the picture will help you

Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

Answer:

The circumference of the drive wheel is 10 feet * 3.14 = 31.4 feet.

The circumference of the vat is 18 feet * 3.14 = 56.52 feet.

The total length of belt needed to go around the drive wheel and the vat is 31.4 + 56.52 = 87.92 feet.

Answer:

the answer is 5.44 feet

Step-by-step explanation:

Add me

Answer:

Step-by-step explanation:

The composition (f o g)(x) = 10/(x+10) and its domain is all real numbers except x = -10.

a) To find (f o g) (x), we need to substitute g(x) into f(x) wherever we see x. That is,

(f o g) (x) = f(g(x)) = f(10/x) = (10/x) / (10/x + 1)

b) To find the domain of (f o g) (x), we need to look for any values of x that make the denominator of the expression equal to zero, since division by zero is undefined. Thus, we solve the equation:

10/x + 1 = 0

10/x = -1

x = -10

Therefore, the domain of (f o g) (x) is all real numbers except x = -10, since that value makes the denominator equal to zero. In interval notation, the domain is:

(-∞, -10) U (-10, ∞)

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2. The transformations are given as follows:

3. The transformations are given as follows:

For item 2, the transformations in this problem are given as follows:

For item 3, the transformations are given as follows:

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y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the slope-intercept equation for a line that goes through the point (4,-3)--with a slope of -2

m=-2

Now let us find the y intercept

-3=-2(4)+b

-3=-8+b

-3+8=b

5=b

Hence, y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

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Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.

The most common symbols used in inequalities are:

">" (greater than): indicates that the value on the left side is larger than the value on the right side.

"<" (less than): indicates that the value on the left side is smaller than the value on the right side.

"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.

"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.

"≠" (not equal to): indicates that the values on both sides are not equal.

Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

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The population of the country will be 796 million approximately in the year 2022.

To find when the population of the country will be 796 million, we can set the equation equal to 796 and solve for t:

\(A = 433.4e^{(0.032t)}\\796 = 433.4e^{(0.032t)}\)

Divide both sides by 433.4:

\(e^{(0.032t)} = 1.836\)

Take the natural logarithm of both sides:

\(ln(e^{(0.032t)}) = ln(1.836)\)

0.032t = 0.605

Divide both sides by 0.032:

t = 18.91

Therefore, the population of the country will be 796 million approximately 19 years after 2003. To find the year, we add 19 to 2003:

2003 + 19 = 2022

Therefore, the population of the country will be 796 million approximately in the year 2022.

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The value of x will be 18.67 for the given data of the triangle.

We have,

Thale's theorem:

When a line parallel to one side of a triangle intersects the other two sides in distinct points, the other two sides are divided in the same ratio.

Given that the sides of the triangle are divided into two parts,

For the left part the parts will be x and x + 7 for the right side the parts will be 16 and 22.

The ratio will be the same according to Thale's theorem. The value of x will be calculated as:-

x / ( x + 7 ) = 16 / 22

22x = 16x + 112

6x = 112

x = 112 / 6

x = 18.67

Therefore, the value of x will be 18.67.

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complete question;

Find the values of x and y. Find value of x.

It would take 10 men approximately 7.2 hours to dig the hole if they work at the same rate.

To find out how long it would take 10 men to dig the same hole if they work at the same rate, we can use the concept of man-hours.

We are given that 8 men can dig the hole in 9 hours.

This means that the total man-hours required to complete the task is 8 men \(\times\) 9 hours = 72 man-hours.

Since the number of men has increased to 10, we need to determine the new time it would take for them to complete the task at the same rate.

If we assume that the work rate remains constant, the total man-hours required to dig the hole would still be the same, which is 72 man-hours.

To find the new time, we divide the total man-hours by the number of men:

72 man-hours / 10 men = 7.2 hours.

Therefore, it would take 10 men approximately 7.2 hours to dig the hole if they work at the same rate.

Note: It's important to keep in mind that this calculation assumes a linear relationship between the number of men and the time taken.

In practice, other factors such as coordination and efficiency may come into play, potentially affecting the actual time required.

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The total money spent on a pass and lunch for each student is $850.14.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.

here,

As mentioned in the question, Passes for 28 pupils and 4 teachers cost the school $778.88 and the school also spends $241.64 on lunch for kids only.

Total number of person  = 28 + 4
                                     = 32
Cost per pass = 778.88 / 32
                     = $24.34
Total passes of students = 25 × 24.34 = 608.5
Total spend on lunch of student = 241.64
Total spend on lunch = 241.64 + 608.5 = $850.14

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From a group of 15 randomly selected residents , the probability that at least thirteen of them shop at Walmart is 0.0271  .

6 out of 10 Niceville residents shop at Walmart

So, the probability of shopping at Walmart (p) is = 6/10 = 0.6

The probability of not shopping at Walmart is (q) = 1 - 0.6 = 0.4 .

The number of members in the group is(n) = 15 ;

We have to find the probability that, at least thirteen of them shop at Walmart

By the Binomial Probability Distribution,

we know that ; P(x = a) = ⁿCₐ×pᵃ×qⁿ⁻ᵃ

So , P(x ≥ 13) = P(x=13) + P(x=14) + P(x=15)

Substituting the values of a , n and p and q ,

We get ;

= ¹⁵C₁₃p¹³q² + ¹⁵C₁₄p¹⁴q¹ + ¹⁵C₁₅p¹⁵q⁰

= ¹⁵C₁₃(0.6)¹³(0.4)² + ¹⁵C₁₄(0.6)¹⁴(0.4)¹ + ¹⁵C₁₅(0.6)¹⁵(0.4)⁰

= 0.0219 + 0.0047 + 0.0004

= 0.0271

Therefore, the required probability is 0.0271

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The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.

To determine the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.

Preferred Stock:

Dividends per share of preferred stock = Total dividends for preferred stock / Number of preferred shares

Year 1:

Dividends per share of preferred stock for Year 1 = $50,000 / 40,000 shares = $1.25

Year 2:

Dividends per share of preferred stock for Year 2 = $90,000 / 40,000 shares = $2.25

Year 3:

Dividends per share of preferred stock for Year 3 = $130,000 / 40,000 shares = $3.25

Common Stock:

Dividends per share of common stock = Total dividends for common stock / Number of common shares

Year 1:

Dividends per share of common stock for Year 1 = ($50,000 - Total dividends for preferred stock) / 100,000 shares = ($50,000 - $50,000) / 100,000 shares = $0

Year 2:

Dividends per share of common stock for Year 2 = ($90,000 - Total dividends for preferred stock) / 100,000 shares = ($90,000 - $90,000) / 100,000 shares = $0

Year 3:

Dividends per share of common stock for Year 3 = ($130,000 - Total dividends for preferred stock) / 100,000 shares = ($130,000 - $130,000) / 100,000 shares = $0

The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.

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The measure of the arc AT in this problem is given as follows:

mAT = 159º.

The measure of arc AT is obtained applying the two secant theorem, which states the angle measure of intersection of the two secant segments is half the difference of the measure of the far arc by the measure of the near arc.

The parameters for this problem are given as follows:

Hence the measure of the arc AT in this problem is given as follows:

(mAT - 59)/2 = 50

mAT - 59 = 100

mAT = 159º.

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well, the numeric difference will be 136 - 80 = 56, now, if we take 80 (original price) to be the 100%, what is 56 (the increase) in percentage off of it?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 80&100\\ 56&x \end{array}\implies \cfrac{80}{56}=\cfrac{100}{x}\implies \cfrac{10}{7}=\cfrac{100}{x} \\\\\\ 10x=700\implies x = \cfrac{700}{10}\implies x = \stackrel{\%}{70}\)