Suppose the value of x varies from x = a to x = b . There are at least two ways of thinking about what percent x changed by. We'll explore two of them here. For each of the following questions, write an expression in terms of a and b to answer the question. Method 1 b is how many times as large as a ? times as large Therefore, b is what percent of a ? % Hence, if x varies from x = a to x = b , x changes by what percent?

Using the binomial distribution, it is found that:

a) There is a 0.0162 = 1.62% probability that among 12 randomly observed individuals, exactly 7 do not cover their mouth when sneezing.

b) There is a 0.5958 = 59.58% probability that among 12 randomly observed individuals, fewer than 5 do not cover their mouth when sneezing.

c) The probability is higher than 5%, so it would not be unusual.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, with p probability.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]  

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]  

In this problem:

Item a:

This probability is P(X = 7), so:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 7) = C_{12,7}.(0.267)^{7}.(0.733)^{5} = 0.0162[/tex]

There is a 0.0162 = 1.62% probability that among 12 randomly observed individuals, exactly 7 do not cover their mouth when sneezing.

Item b:

The probability is P(X < 4), which is:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

Then

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{12,0}.(0.267)^{0}.(0.733)^{12} = 0.0241[/tex]

[tex]P(X = 1) = C_{12,1}.(0.267)^{1}.(0.733)^{11} = 0.1052[/tex]

[tex]P(X = 2) = C_{12,2}.(0.267)^{2}.(0.733)^{10} = 0.2107[/tex]

[tex]P(X = 3) = C_{12,3}.(0.267)^{3}.(0.733)^{9} = 0.2558[/tex]

Then

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0241 + 0.1052 + 0.2107 + 0.2558 = 0.5958[/tex]

There is a 0.5958 = 59.58% probability that among 12 randomly observed individuals, fewer than 5 do not cover their mouth when sneezing.

Item c:

This probability is:

[tex]P(X < 6) = P(X < 4) + P(X = 5) = 0.5958 + P(X = 5)[/tex]

Negative probabilities do no exist, thus, this probability is guaranteed to be above 0.05, which means that it would not be unusual if fewer than half covered their mouth when sneezing.

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Answer:

The value of 9 + c= 14 because 9 + 5=14

Answer: $10 each

Step-by-step explanation:

130*2

260+1040

=1300

1300/130

=10

Answer:

$160 in 10 hours

Step-by-step explanation:

We know that Kevin earns $112 for working 7 hours. To find the answer for 10 hours, we need to find the unit rate.

Divide 112÷7= $16 for every 1 hour he works.

Now, we can use the unit rate to find the amount earned for 10 hours.

16×10= $160

Answer:

Perpendicular slope: -3/2

Y-value of the y-intercept:  6

Linear equation of the perpendicular line: y = -3/2x + 6

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes, which means that multiplying the slopes of both lines will result in -1.

Given the linear equation, y = 2/3x - 5/3, and the point, (0, 6):

Let m1 = slope of line 1

     m2 = slope of the other line

Since the slope of y = 2/3x - 5/3 is 2/3, then the other line must have a slope of -3/2 because:

m1 × m2 = -1

[tex](\frac{2}{3}) (-\frac{3}{2}) = -1[/tex]

Therefore, the slope of the other line (m2) = -3/2.

The y-intercept is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0. The given point has coordinates (0, 6), which means that it is the y-intercept.  Its y-coordinate, (b) = 6.

Therefore, given the slope m = -3/2, and the y-value of the y-intercept, b = 6, then the equation of the perpendicular line is: y = -3/2x + 6.

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Answer:

40 table spoons

Step-by-step explanation:

We need to divide 16 by 2 because it says for every 2 color tablets she need 5 table spoons of vinegar

16/2 = 8

8 x 5 = 4

Answer:

Quizziz (Another educational site) or asking questions about the Exam/Quiz on Brainly.

Step-by-step explanation:

Answer:

[tex]9 \frac{ {d}^{2}y }{ {dx}^{2} } - 12 \frac{dy}{dx} + 4y = 0) \div 9 \\ \frac{ {d}^{2}y }{ {dx}^{2} } - \frac{4}{3} \frac{dy}{dx} + \frac{4}{9} y = 0 \\ y_{1}(x) = {e}^{ \frac{2}{3} x} \\ p(x) = - \frac{4}{3} \\ y_{2}(x) = y_{1}(x) \int \frac{ {e}^{ - \int \: p(x)dx} }{ {(y_{1}(x))}^{2} } dx \\ = {e}^{ \frac{2}{3} x} \int \frac{ {e}^{ \int \: \frac{4}{3} dx} }{ { ({e}^{ \frac{2}{3} x})}^{2} } dx \\= {e}^{ \frac{2}{3} x} \int \frac{ {e}^{ \frac{4}{3} x} }{ { {e}^{ \frac{4}{3} x}}} dx \\ = {e}^{ \frac{2}{3} x} \int dx \\ \boxed{y_{2}(x) =x{e}^{ \frac{2}{3} x}}[/tex]

Answer:

10x+276

Step-by-step explanation:

multiply length times width to get the area

12(5/6x +23)

simplify

10x +276

i hope your test is going well <3

Step-by-step explanation:

The number of employees before the layoff = 2000

"It is a number can be expressed as a fraction of 100."

For given question,

Let 'n' be the the number of employees before layoff.

A company laid off 80% of its work force.

The number of employees after the layoff is 400.

The number of employees after the layoff would be,

⇒ n - (80 percent of n) = 400

[tex]\Rightarrow n-(n\times \frac{80}{100} )=400\\\\\Rightarrow n[1-0.8]=400\\\\\Rightarrow n\times 0.2=400\\\\\Rightarrow n=2000[/tex]

Therefore, the number of employees before the layoff = 2000

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Step-by-step explanation:

defined by 0 ifr> Let e > 0. Prove that there exists a partition, P. of (0,1) with ... - did not match any documents.

Suggestions:

Answer:

45 - big boxes, 200 - small boxes

Step-by-step explanation:

45 x 10 = 450

200 x 20 = 4000

Total = 4,450

Hope it's correct

The total length of 9 rods will be 72 units.

What is Addition?

A process of combining two or more numbers is called addition.

Given that;

The length of 6 identical iron rods is 48 unit.

Now,

Since, the length of 6 identical iron rods is 48 unit.

Hence, the length of 9 identical iron rods = 9 × 48 / 6

                                                                = 9 × 8

                                                                = 72 units

Thus, The total length of 9 rods will be 72 units.

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Answer:

3900 x.094 = 366.60

366.6+3900=4266.60

7

Step-by-step explanation:

(x - 3)² = 16

x² - 6x + 9 = 16

x² - 6x + 9 - 16 = 0

x² - 6x - 7 = 0

(x - 7)(x + 1)

x = 7 \/ x = -1

so positive value of x = 7

Answer:

-38

Step-by-step explanation:

(-21 + -24 + -37 + -52 + - 56)/5 = -38

Answer:

x = - 3/7

y = - 8/7

Step-by-step explanation:

(2x - 6y = 6)/2 =

x - 3y = 3

x = 3y + 3

Substitution:

6 (3y +3) - 4y = 2

18y + 18 - 4y = 2

14y = -18+2

y = -16/14

y = - 8/7

Substitution:

x = 3(-8/7)+3

x = -24/7 + 3

x = -3/7

9514 1404 393

Answer:

  (x, y) = (-3/7, -1 1/7)

Step-by-step explanation:

We can divide each equation by 2 and subtract the constant to put them in general form.

  x -3y -3 = 0

  3x -2y -1 = 0

This form facilitates use of the "cross multiplication method" of solution. That method tells us ...

  1/d1 = x/d2 = y/d3

where the differences d1, d2, d3 are the differences of cross-products:

  d1 = 1(-2) -(3(-3)) = 7

  d2 = -3(-1) -(-2(-3)) = -3

  d3 = -3(3) -(-1(1)) = -8

Then the solutions are ...

  x = d2/d1 = -3/7

  y = d3/d1 = -8/7

(x, y) = (-3/7, -8/7)

_____

Additional comment

When the general form equations ax+by+c=0 and dx+ey+g=0 have their coefficients written in two rows: (note the repeated first coefficient)

The pattern in the cross-differences is relatively easy to see:

The expressions for the solution values, (x, y) = (d2/d1, d3/d1), are substantially identical to those of Cramer's method.

Answer:

17/24

Step-by-step explanation:

With the understanding that the three given cars form three mutually exhaustive and disjoint sets i.e., they form the partition of sample space, the probability that the selected car would be white is [tex]\frac{17}{24}[/tex].

A collection of sets B1, B2, . . . , Bn is said to partition the sample space if the sets (i) are mutually disjoint and (ii) have as union the entire sample space.

In this question, we take three sets - set of all red cars, white cars and green cars.

A car can be either red, white or green. Thus they are mutually exclusive.

Also, let the cars in parking lot be the sample space. Every car we pick has to be of one of the three colors. This imply that the three sets of the three cars are mutually exhaustive.

P(selecting a red car) + P (selecting a green car) + P(selecting a white car) = 1

[tex]\frac{1}{8} + \frac{1}{6} + P(selecting\ a\ white\ car) = 1\\\\ P(selecting\ a\ white\ car) = \frac{17}{24}[/tex]

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6 is a whole number so the answer is 6

Answers:

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

Explanation:

The y intercept is where the curve crosses the y axis. The curve appears to do so just below y = 10, so y = 9 seems like a good estimate. I'm basing this off of the answer choices given. The y intercept always occurs when x = 0.

The zeros, aka roots or x intercepts, are where the curve crosses or touches the x axis. This occurs in four locations: x = -3, x = -1, x = 1 and x = 3. The x intercepts always occur when y = 0.

Answer:

x = 70

Step-by-step explanation:

Step 1: Simplify both sides of the equations.

Step 2: Subtract 5/7x from both sides.

Step 3: Multiply both sides by 70/(-43).

Step 4: Check if solution is correct.

Therefore, x = 70.

Answer:

30 inches into feet

12 inches = 1 feet

12in = 1ft

24in = 2ft

30 - 24 = 6

The answer is 2 ft and 1/2

or 2 ft and 6 inches

***hope this helps

Step-by-step explanation:

Answer:

3x+5+2y

Step-by-step explanation:

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Answer:

[tex] = > 5 + 3x + 2y[/tex]

Answer:

recipe 1 and recipe 2 will taste the same while recipe 3 will taste different

Step-by-step explanation:

Let's look at the Mix ratio

for recipe 1 the mix ratio is 2:3

recipe 2 ratio is 2:3

and recipe 3 ratio is 3:4