A vending machine dispenses coffee into a twenty-ounce cup. the amount of coffee dispensed into the cup is normally distriubuted with a standard deviation of 0.03 ounce. You can allow the cup to overfill 2% of the time. What amount should you set as the mean amount of coffee to be dispensed?

Answer:

Last answer: [tex]cot^{2} \alpha - csc^{2} \alpha = -1[/tex]

sorry couldn't find theata so I just used alpha.

Answer:

Step-by-step explanation:

A). Let the dimensions of the rectangular pen are,

Length = l

Width = x

Since, farmer has the wire measuring 80 feet to surround the the pen.

Perimeter of the pen = 80 feet

2(l + x) = 80

l + x = 40

l = 40 - x ------(1)

Area of the rectangular pen = Length × width

                                               = lx

By substituting the value of l from equation (1),

Area (A) of the pen will be modeled by the expression,

A = (40 - x)

A = 40x - x²

B). For maximum area of the pen,

Derivative of the area = 0

[tex]\frac{d}{dx}(A)=0[/tex]

[tex]\frac{d}{dx}(A)=\frac{d}{dx}(40x-x^2)[/tex]

         = 40 - 2x

And (40 - 2x) = 0

x = 20

Therefore, width of the pen = 20 feet

And length of the pen = 40 - 20

                                     = 20 feet

Dimensions of the pen should be 20 feet by 20 feet.

Answer:

55000×100/90

61,111.111

Answer:

Step-by-step explanation:

It depends on whether you mean ln(1/49k) or ln(1/(49k)).

Answer:

b

Step-by-step explanation:

You only need to add the real numbers and the ys.

Answer:

12 + 2y

Step-by-step explanation:

9+y+y+3

Combine like terms

9+3   + y+y

12 + 2y

9514 1404 393

Answer:

  a) 3092.5 (rounded to tenths)

  b) 39,600

  c) ₹28,755

Step-by-step explanation:

These are all simple calculator problems. The arithmetic involved is something you learned in 2nd or 3rd grade.

__

a) Since we divide using the division algorithm, it isn't clear what "check your answer by division algorithm" is intended to mean. The result of the division (stopping at 1 decimal place) is 3092.5.

The usual method of checking a division problem is to multiply the quotient by the divisor to see if the dividend value is the result. Here, we have ...

  13×3092.5 = 40202.5

This differs by from the dividend of 40203 by 0.5, which is the remainder showing in our long division. In short, the answer checks OK.

__

b) The value of each 4 is found by setting other digits to 0.

  Most significant 4: 40,000

  Least significant 4: 400

Difference in place value: 40,000 -400 = 39,600

__

c) The balance in the account is found by subtracting withdrawals from deposits:

  ₹35000 -6245 = ₹28,755

Answer:

Step-by-step explanation:

3. ZW ≅ WX

Step-by-step explanation:

x = goods y = $

x Sold = 40, Y = $90

x Sold = 80, Y = $210

sum of xHotdogs = 40+80 = 120 Hotdogs

Sum of Y$ = $90 + 210 = 300

so

X = 2A & Y = 3 its mean one hotdogs can sold for one each = $2.25 and we round it to $3

So = XY = 2A + 3

sorry if i wrong

Answer:

the answer is 2

Step-by-step explanation:

Given:

The equation of the hyperbola is:

[tex]xy=-42[/tex]

To find:

The the equation which is not an asymptote of the hyperbola.

Solution:

We have,

[tex]xy=-42[/tex]

It can be written as:

[tex]y=\dfrac{-42}{x}[/tex]

Equating denominator and 0, we get

[tex]x=0[/tex]

So, the vertical asymptotic is [tex]x=0[/tex].

The degree of numerator is 0 and the degree of denominator is 1.

Since the degree of numerator is greater that the degree of denominator, therefore the horizontal asymptote is [tex]y=0[/tex] and there is no oblique asymptote.

Therefore, [tex]y=x[/tex] is not an asymptote of the given hyperbola and the correct option is C.

Answer:

[tex] \frac{1}{9} [/tex]

Step-by-step explanation:

[tex]f( - 2) = {3}^{ - 2} [/tex]

[tex]1 \div 9 = .111[/tex]

Ethan will pay $31.99 with the discount.

How? This is the answer because:

If 39.99 is 100%, and you are trying to find 20%...

1. you need to set it up as a ratio (of course, you do not need to do this, but it is easier for me to do it this way)

2. the ratio will look like this: 39.99/100% x/20%

3. all we need to do from here is to cross multiply!

4 39.99 x

---------- = ----------

100 20

-price is on the top and percent on the bottom

-you would now do 39.99 times 20

-then divide by 100

5. once you have 20% of 39.99, you need to subtract that answer from the total

6. 39.99 - 7.998 = 31.992 (you need to round to the nearest hundredth)

Hope this helps <3

Answer:

24.4185<x<25.5815

Step-by-step explanation:

Given the following:

n = 64

mean x = 25

s = 2

z is the z score at 98% CI = 2.326

Get the Confidence Interval:

CI = x±z*s/√n

CI = 25±2.326*2/√64

CI = 25±2.326*2/8

CI = 25±0.5815

CI = (25-0.5815, 25+0.5815)

CI = (24.4185, 25.5815)

CI = 24.4185<x<25.5815

Hence the 98% confidence interval for the true average age of all students in the university is 24.4185<x<25.5815

Answer:

Step-by-step explanation:

Formula:

The total amount:

We have to find the,

Accumulated amount at end of 12 years.

The formula we use,

→ A = P(1+r)^t

It is given that,

→ P = $4000

→ t = 12 years

Then r will be,

→ 6%

→ 6/100

→ 0.06

Then the total amount is,

→ P(1+r)^t

→ 4000 × (1 + 0.06)^12

→ 8048.79

Thus, $ 8048.79 is the amount.

Given:

[tex]4\dfrac{1}{2}[/tex] subtracted from 5.33.

To find:

The value for the given statement.

Solution:

[tex]4\dfrac{1}{2}[/tex] subtracted from 5.33 can be written as:

[tex]5.33-4\dfrac{1}{2}[/tex]

On simplification, we get

[tex]=5.33-\dfrac{8+1}{2}[/tex]

[tex]=5.33-\dfrac{9}{2}[/tex]

[tex]=5.33-4.5[/tex]

[tex]=0.83[/tex]

Therefore, the correct option is C.

According to the question, our quadratic equation is :

\begin{gathered} \bf {x}^{2} - ( {r}^{2} + {s}^{2} )x + {r}^{2} {s}^{2} = 0 \\ \bf \implies \: {x}^{2} - ( - 91)x + {(rs)}^{2} = 0 \\ \bf \implies \: {x}^{2} + 91x + {(50)}^{2} = 0 \\ \bf \implies \: {x}^{2} + 91x + 2500 = 0\end{gathered}

x

2

−(r

2

+s

2

)x+r

2

s

2

=0

⟹x

2

−(−91)x+(rs)

2

=0

⟹x

2

+91x+(50)

2

=0

⟹x

2

+91x+2500=0

Answer:

4 e

Step-by-step explanation:

dz6dxrx xrrx6 xz33x4xr4x xrx

Answer:

4.629

Step-by-step explanation:

Hope it is helpful to you

Answer:

x = 50

y = 50

Step-by-step explanation:

[tex]\begin{bmatrix}x+y=100\\ 0.12x+0.38y=25\end{bmatrix}[/tex]

.12(100-y) + .38y = 25

x = 50

y = 50

Answer:

x = 1/8(k-c)

Step-by-step explanation:

8x + c = k

Subtract c from each side

8x +c-c = k-c

8x = k-c

Divide each side by 8

8x/8 = (k-c)/8

x = 1/8(k-c)

Answer:

x-1/8(k-c)

Step-by-step explanation:

Answer:

1 / 97290

Step-by-step explanation:

The number of ways of selecting 3 specific route capitals from 47 states can be obtained thus :

Probability = required outcome / Total possible outcomes

Total possible outcomes = 47P3

Recall :

nPr = n! / (n-r)!

47P3 = 47! / (47-3)! = 47! / 44! = 97290

Hence, probability of selecting route if 3 specific capitals is = 1 / 97290

Answer:

Graph (a)

Step-by-step explanation:

Given

[tex]y = \sqrt[3]{x+ 6} -3[/tex]

Required

The graph

First, calculate y, when x = 0

[tex]y = \sqrt[3]{0+ 6} -3[/tex]

[tex]y = \sqrt[3]{6} -3[/tex]

[tex]y = -1.183[/tex]

The above value of y implies that the graph is below the origin when x = 0. Hence, (c) and (d) are incorrect because they are above the origin

Also, only the first graph passes through point (0,-1.183). Hence, graph (a) is correct

Answer:

the answer is A

Step-by-step explanation:

Answer:

Kindly check explanation

Step-by-step explanation:

Rounding each number to 4 significant figures and expressing in standard notation :

(a) 102.53070,

Since the number starts with a non-zero, the 4 digits are counted from the left ;

102.53070 = 102.5 (4 significant figures) = 1.025 * 10^2

(b) 656.980,

Since the number starts with a non-zero, the 4 digits are counted from the left ; the value after the 4th significant value is greater than 5, it is rounded to 1 and added to the significant figure.

656.980 = 657.0 (4 significant figures) = 6.57 * 10^2

(c) 0.008543210,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

0.008543210 = 0.008543 (4 significant figures) = 8.543 * 10^-3

(d) 0.000257870,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

0.000257870 = 0.0002579 (4 significant figures) = 2.579 * 10^-4

(e) -0.0357202,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

-0.0357202 = - 0.03572 (4 significant figures) = - 3.572* 10^-2

Answer:

0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.

Step-by-step explanation:

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.

Mean of 10 minutes and a standard deviation of 3 minutes

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

Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.

This is 1 subtracted by the p-value of Z when X = 15, so:

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

[tex]Z = \frac{15 - 10}{3}[/tex]

[tex]Z = 1.67[/tex]

[tex]Z = 1.67[/tex] has a p-value of 0.9525.

1 - 0.9525 = 0.0475.

0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.

Answer:

4(a).

Expression of dy/dx :

[tex]{ \tt{ \frac{dy}{dx} = - 2(3 - 2x) {}^{2} + 24}}[/tex]

5(a).

[tex]{ \tt{ \frac{dy}{dx} = 54 - 2(2x - 7) {}^{2} }}[/tex]

Answer:

Orthocenter would be in the middle of the shape.

Step-by-step explanation:

B.

Answer:

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

Step-by-step explanation:

We have the mean during the interval, which means that the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Lost-time accidents occur in a company at a mean rate of 0.8 per day.

This means that [tex]\mu = 0.8n[/tex], in which n is the number of days.

10 days:

This means that [tex]n = 10, \mu = 0.8(10) = 8[/tex]

What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2?

This is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-8}*8^{0}}{(0)!} = 0.00034[/tex]

[tex]P(X = 1) = \frac{e^{-8}*8^{1}}{(1)!} = 0.00268[/tex]

[tex]P(X = 2) = \frac{e^{-8}*8^{2}}{(2)!} = 0.01073[/tex]

So

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00034 + 0.00268 + 0.01073 = 0.01375[/tex]

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

Answer:

0.2405 = 24.05% probability that the sample proportion of households spending more than $125 a week is less than 0.31.

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Assume the population proportion is 0.34 and a simple random sample of 124 households is selected from the population.

This means that [tex]p = 0.34, n = 124[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.34[/tex]

[tex]s = \sqrt{\frac{0.34*0.66}{124}} = 0.0425[/tex]

What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31?

This is the p-value of Z when X = 0.31, so:

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

[tex]Z = \frac{0.31 - 0.34}{0.0425}[/tex]

[tex]Z = -0.705[/tex]

[tex]Z = -0.705[/tex] has a p-value of 0.2405.

0.2405 = 24.05% probability that the sample proportion of households spending more than $125 a week is less than 0.31.

Answer:

12

Step-by-step explanation: