A 13-ounce can of coffee costs $2.73. What is the unit price per pound (1 pound=16 ounces)?

Answer:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are dismissed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

In this question:

Total of 7 + 18 = 25 employees, which means that [tex]N = 25[/tex]

7 over 50, which means that [tex]k = 7[/tex]

10 were dismissed, which means that [tex]n = 10[/tex]

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]

0.055 = 5.5% probability that exactly 5 employees were over 50.

Answer:

[tex]\sqrt{7}[/tex]

Step-by-step explanation:

Given

4[tex]\sqrt{7}[/tex] - 10[tex]\sqrt{7}[/tex] + 7[tex]\sqrt{7}[/tex] ( add the coefficients of the terms )

= (4 - 10 + 7) [tex]\sqrt{7}[/tex]

= 1[tex]\sqrt{7}[/tex]

= [tex]\sqrt{7}[/tex]

Picture cards are Jacks, queens and Kings. There are 4 of each for a total of 12 picture cards.

52-12 = 40 non picture cards.

Probability of being dealt a non picture card would be 40/52

The probability of not being dealt a non picture card would be 1 - 40/52 = 12/52 = 3/13

Answer: 3/13

Answer:

This rotational symmetry has 4 or more order .

OAmalOHopeO

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Answer:

  B.  1

Step-by-step explanation:

The figure has no symmetry, so only maps to itself with 360° of rotation.

The order of rotational symmetry is 1.

Answer

Together, they have 99 marbles.

Explanation

Ravi has 33 marbles.

His brother has twice (two times) as many marbles as him. Ravi's brother has 33×2=66 marbles.

Together, they have 33+66=99 marbles.

Together, they have 99 marbles.

A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics. For instance, the product of 5 and 6 is 30.

given

Ravi has 33 marbles.

His brother has twice (two times) as many marbles as him. Ravi's brother has 33×2=66 marbles.

Together, they have 33+66=99 marbles.

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Answer:

  3/(x +1) -4/(x +1)^2

Step-by-step explanation:

The partial fraction expansion will be of the form ...

  A/(x+1)^2 +B/(x+1)

We can find the values of A and B by writing the sum of these terms:

  = (A +B(x +1))/(x +1)^2

Then we require ...

  B = 3

  A +B = -1   ⇒   A = -4

So, the desired expansion is ...

  3/(x +1) -4/(x +1)^2

Answer:

3

Step-by-step explanation:

3t + 2 = 5t - 4

3t - 5t = -4 - 2

-2t = -6

t = 6/2

t = 3

Answer:

t = 3

Step-by-step explanation:

3t + 2 = 5t - 4

3t - 5t = - 4 - 2

-2t = -6

(Cut those two -)

t = 6÷2

t = 3

Answer:

(-2,2) and (-3,-4)

Step-by-step explanation:

by graphing the line and parabola, you should get this graph

Answer:

90

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

x+x+10 +x+50 = 180

3x+60= 180

3x = 180-60

3x = 120

Divide by 3

3x/3 = 120/3

x = 40

The largest angle is

x+50

40+50 = 90

We have to,

find the measure of the largest angle.

Given that,

The angles in a triangle are represented by x, x+10, and x+50.

Let's start to solve,

→ x+ (x+10) + (x+50) = 180°

→ x + x + x = 180° (-50-10)

→ 3x = 180° -60

→ 3x = 120

→ x = 120/3

→ [x = 40°]

Then the value of x + 10,

→ x + 10

→ 40 + 10

→ 50°

Then the value of x + 50,

→ x + 50

→ 40 + 50

→ 90°

The measure of the largest angle is,

→ D. 90 degrees

Thus, option (D) is the correct answer.

Answer:

[tex]\frac{dv}{dt} =7239.168 cm/sec[/tex]

Step-by-step explanation:

From the question we are told that:

Rate [tex]\frac{dh}{dt}=1cm[/tex]

Height [tex]h=12cm[/tex]

Radius [tex]r=4h[/tex]

Generally the equation for Volume of Cone is mathematically given by

[tex]V=\frac{1}{3}\pi r^2h[/tex]

[tex]V=\frac{1}{3}\pi (4h)^2h[/tex]

Differentiating

[tex]\frac{dv}{dt} =\frac{16}{3}\pi3h^2\frac{dh}{dt}[/tex]

[tex]\frac{dv}{dt} =\frac{16}{3}*3.142*3*12^2*1[/tex]

[tex]\frac{dv}{dt} =7239.168 cm/sec[/tex]

Answer:

sqrt( 150)

Step-by-step explanation:

it can also be 5sqrt(6)

The solution is,  the area of the triangle. ABC is 10 cm^2.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

from the given diagram, we get,

we have to find the area of the triangle. ABC

now, we have,

using the Pythagorean theorem, we get,

BD = √AB² - AD²

     =√50 - 45

     =√5

now, we know that,

area of triangle = 1/2 * base * height

                          = 1/2 * √5 * 4√5

                          = 10

Hence, The solution is,  the area of the triangle. ABC is 10 cm^2.

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Answer:

Domain: [-5, 4]

Range: [-5, 0] U (2, 4]

Step-by-step explanation:

The domain encompasses whatever the input (in this case, the horizontal values) can be and the range is what the output (in this case, the vertical values) can be.

As shown on the graph, all horizontal values including and between -5 and 4 are used on the graph. It does not matter that they are on two separate lines. Therefore, the domain is [-5, 4]. Note that the closed brackets signify that -5 and 4 are used

The y values used in the bottom line range from -5 to 0, and in the top one they range from 2 to 4 (not including the 2, as shown by the open circle). Therefore, the bottom range is [-5, 0] and the top range is (2, 4]. We can combine these to say the range is [-5, 0] U (2, 4]

Answer:

x=4

Step-by-step explanation:

[tex]\frac{16}{12}= \frac{6x}{5x-2}[/tex]

assuming that the triangles are similar, we can create this ratio of 16 or 12+4 to 6x and 12 to 5x-2

we can cross multiply to get 16(5x-2)=6x(12)

that leaves you with 80x-32=72x

we can then subtract 80x to both sides to get -32= -8x

solve by diving -8 from both sides which means that x=4

Answer:

[tex]this \: triangles \: are \: similar \: so \\ sides \: must \: be \: in \: a \: ratio \\ \frac{16}{12} = \frac{6x}{5x - 2} \\ \frac{4}{3} = \frac{6x}{5x - 2} \\ 4(5x - 2) = 3 \times 6x \\ 20x - 8 = 18x \\ x \: terms \: togather \\ 20x - 18x = 8 \\ 2x = 8 \\ x = \frac{8}{2} \\ x = 4 \\ thank \: you[/tex]

The answer at the end of the day would be 4

Answer:

I set up an equation to show that the number of bracelets multiplied by the cost of each bracelet minus the commission is equal to the total, 6(x – 1.25) = 16.50. I divided each side by 6, then added 1.25 to each side with a result of x = 4. Hyo-Jim sold each bracelet for $4.

Step-by-step explanation:

Answer: I believe that you have to do e^3 to find the volume of a cube.

If you had the side, you would do a^3 (a stands for the side length)

Answer:

"48" is the appropriate solution.

Step-by-step explanation:

Given:

Flow rate,

R = 2 people per sec.

Flow time,

T = 24 seconds

By using the Little's Law,

⇒ [tex]I = R\times T[/tex]

The no. of people during rush hour will be:

⇒    [tex]=24\times 2[/tex]

⇒    [tex]=48[/tex]

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Answer:

  x = 5

Step-by-step explanation:

The given side is opposite the angle, and the unknown is the hypotenuse. The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(30°) = (5/2)/x

  x = (5/2)/sin(30°) = (5/2)/(1/2) = 5/1

  x = 5

__

Additional comment

In this 30°-60°-90° "special" right triangle, the long leg is √3 times the short leg, so ...

  y = (5/2)√3

Answer:

x = 9/8

Step-by-step explanation:

The triangles are similar so we can use ratios to solve

AB         BC

----  = -----------

AD       ED

x            1

----  = -----------

x+9       9

Using cross products

9*x = 1(x+9)

9x = x+9

Subtract x from each side

9x-x = x+9-x

8x = 9

Divide by 8

8x/8 = 9/8

x = 9/8

Take the triangle as,

→ AB/AD = BC/ED

→ x/x+9 = 1/9

Now by using cross products,

→ 9 × x = 1(x+9)

→ 9x = x+9

Now subtract x from both sides,

→ 9x-x = x+9-x

→ 8x = 9

Then divide by 8 from both sides,

→ 8x/8 = 9/8

→ x = 9/8

So, the value of x is 9/8.

Answer:

Hello,

I don't know the words used for that binominal exercice.

Step-by-step explanation:

The probability that the waiter will drop exactly four of the next ten is 0.2

Probability is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases.

Now it is given that,

Waiter drops hamburgers = 30%

Therefore, Probability of drop, p = 0.3

Now For the next ten,

⇒ number of trials, n = 10

⇒ q = 1 - p = 1 - 0.3

⇒ q = 0.7

Thus, probability that he will drop exactly four of the next ten,

P(x = x) = nCx * p^x * q^(n-x)

For exactly 4, x = 4

⇒ P(x = 4) = ¹⁰C₄ * 0.3^4 * 0.7^(10 - 4)

⇒ P(x = 4) = 210*0.0081*0.1176

⇒ P(x = 4) = 0.2

Thus, the probability that the waiter will drop exactly four of the next ten is 0.2

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Answer:

Opposite sides

Step-by-step explanation:

Given equation of line is 

L=3x−2y+1=0

For the point (2,1), L=5>0

For the point (−3,5),L=−18<0

Opposite signs shows that the two points lies on the opposite side of the line  L=0.

Answer:

7

Step-by-step explanation:

1 hour = 118 guests

826 / 118 = 7 hours

Answer:

I think h is 7

Answer:

0.6121 = 61.21% probability that the sample average amount of time taken on each day is at most 11 min.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Normal distribution with mean value 10 min and standard deviation 3 min.

This means that [tex]\mu = 10, \sigma = 3[/tex]

First day:

5 individuals, so [tex]n = 5, s = \frac{3}{\sqrt{5}}[/tex]

The probability is the p-value of Z when X = 11. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{11 - 10}{\frac{3}{\sqrt{5}}}[/tex]

[tex]Z = 0.745[/tex]

[tex]Z = 0.745[/tex] has a p-value of 0.7719.

Second day:

6 individuals, so [tex]n = 6, s = \frac{3}{\sqrt{6}}[/tex]

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{11 - 10}{\frac{3}{\sqrt{6}}}[/tex]

[tex]Z = 0.817[/tex]

[tex]Z = 0.817[/tex] has a p-value of 0.793.

What is the probability that the sample average amount of time taken on each day is at most 11 min?

Each day is independent of other days, so we multiply the probabilities.

0.7719*0.793 = 0.6121

0.6121 = 61.21% probability that the sample average amount of time taken on each day is at most 11 min.

Answer:

[tex]LCL=1.94[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=15[/tex]

Mean [tex]\=x=63.45[/tex]

Range [tex]R=5.6[/tex]

Generally at [tex]n=15[/tex]

Value of Control chart constant,

 [tex]LCL=D*R[/tex]

Generally the equation for Lower Control Limit is mathematically given by

 [tex]LCL=D*R[/tex]

 [tex]LCL= 0.347*5.6[/tex]

 [tex]LCL=1.94[/tex]

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Answer:

  y = -9x +49

Step-by-step explanation:

The slope of line b is the same as the slope of line a. That can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -8)/(2 -1) = -9

The y-intercept can be found from the given point using the formula ...

  b = y - mx

  b = 13 -(-9)(4) = 13 +36 = 49

Then the slope-intercept equation of line b is ...

  y = -9x +49

Answer:

28

Step-by-step explanation:

The median is the middle number when the numbers are listed from smallest to largest

26, 27, 28, 31, 33

The middle number is 28

The median is 28

Answer:

[tex]y = 0.35x + 35[/tex]

Step-by-step explanation:

Linear equation:

A linear equation has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

Finding the slope:

We have two points: (110, 73.5) and (760, 301).

The slope is given by the change in y divided by the change in x. So

Change in y: 301 - 73.5 = 227.5

Change in x: 760 - 110 = 650

Slope: [tex]m = \frac{227.5}{650} = 0.35[/tex]

So

[tex]y = 0.35x + b[/tex]

Finding the y-intercept:

(760, 301) means that when [tex]x = 760, y = 301[/tex]. So

[tex]301 = 0.35(760) + b[/tex]

[tex]b = 301 - 0.35(760)[/tex]

[tex]b = 35[/tex]

So

[tex]y = 0.35x + 35[/tex]

Answer:

12

Step-by-step explanation:

12

For 3, 4 and 6 the smallest number which would be perfectly divisible by them is their LCM which is 12.

Have a nice day!

Answer:

12

Step-by-step explanation:

We want to find the least common multiple of 4,6,3

4:

4,8,12,16,20

6:

6,12,18,24

3:

3,6,9,12,15

The first number that appears in all 3 lists is 12

Answer:

Always. Always.

Step-by-step explanation:

All circles conform to the same equations such as using pie to calculate circumference. Unlike a rectangle, for example, all ratios used in a circle are the same.