Which expression is equivalent to the given expression?
4 ln r + In 3 – In r
O A. ln(3.13)
B. ln(3.1 + 3)
OC. In(x4 - x + 3)
D. ln(111)

Answer:

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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]

In this question, we have that:

[tex]\mu = 270, \sigma = 90, n = 18, s = \frac{90}{\sqrt{18}} = 21.2[/tex]

What is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days?

This is the pvalue of Z when [tex]X = 260[/tex]. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{260 - 270}{21.2}[/tex]

[tex]Z = -0.47[/tex]

[tex]Z = -0.47[/tex] has a pvalue of 0.3192.

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

Answer:

[tex] - \frac{1}{5 \sqrt{y} } [/tex]

Answer:

option 1

Step-by-step explanation:

[tex]\sqrt{y} =y^{\frac{1}{2}}\\\\(\frac{1}{\sqrt{y} })^{\frac{-1}{5}} =(\frac{1}{y^{\frac{1}{2}}})^{\frac{-1}{5}}\\\\= (y^{\frac{-1}{2}})^{\frac{-1}{5}}\\\\=y^{\frac{-1}{2}*\frac{-1}{5}}\\\\= y^{\frac{1}{10}}\\\\=\sqrt[10]{y}[/tex]

Answer:

[tex]6x^{2} -9x+3[/tex]

Step-by-step explanation:

[tex](3x-3) (2x-1)[/tex]

[tex]3x (2x-1)-3(2x-1)[/tex]

[tex]6x^{2} -3x-6x+3[/tex]

[tex]6x^{2} -9x+3[/tex]

Answer:

C.

Step-by-step explanation:

interior angles for ABCD is 360° and for ABO(triangle above) is 180°

from triangle,

you will get angle for OBA which is 180° - 38° - 90° = 52°

from angle B, we know that, straight line is 180°.

so,

180° = 52° +y- 12°

y = 140°

so, we can calculate x.

360° = 90° + 90° + 128° + x

x = 52°

Answer:

Per mile Chau takes 5.8 minutes per mile.

Step-by-step explanation:

To find this answer you would have to do the amount of time divided by the amount of miles. Always remember when dividing time most of the time goes first unless the problem / instructions say differently. So, when you do 50 divided by 10 you will get 5.8. So, Chau takes 5.8 minutes per mile.

Answer:

√(27/4) = 2.6

=> a.neartest integer: 2

   b.nearest tenth: 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Word problem is a topic in mathematics that involves the interpretation of a given question with a mathematical expression so as to determine the value of the required variable.

Example: The price of a pencil is $10, and that of a ruler is $15.25. If Charles bought 5 pencils and 4 rulers, calculate the total amount of money spent.

price of a pencil = $10

price of a ruler = $15.25

Then,

cost of 5 pencils = $10 x 5

                            = $50

cost of 4 rulers = $15.25 x 4

                         = $61

Total amount of money spent by Charles = $50 + $61

                              = $111

The total amount of money spent by Charles is $111.

Answer:

m=-18

Step-by-step explanation:

6m=-108

m=-108/6

m=-18

Answer:

okay so the answer is -18

9514 1404 393

Answer:

  $281.40

Step-by-step explanation:

A financial calculator tells you the payment for the 18-month loan is $361.46, so her total payback amount is $6506.28.

Similarly, the payment for the 24-month loan is $282.82, and the total amount repaid is 6787.68.

The shorter-term loan costs less by ...

  $6787.68 -6506.28 = $281.40

Ann can save $281.40 by choosing the shorter-term loan.

Answer:

a) The slope (m) of the equation y = x - 5 is 1 and the y-intercept (b) is -5.

b) The slope (m) of the equation 2x + y = 4 is -2 and the y-intercept (b) is 4.

Answer:

The slope = 5

y intercept = 0,0

Explanation:

Use the slope-intercept form

Use the slope-intercept form

y = m x + b to find the slope m and y-intercept b.

Graph:

Answer:

0.0132

Step-by-step explanation:

No

Carbon monoxide concentrations sample in air from a large city are not normally distributed. This is often so because of the time of the day and that of the night. There exists different concentrations during the day, with respect to during the night. The companies and factories work during the day, so does most vehicles. This means that there tend to be a higher concentration during the day, than there will be during the night.

b)

Assuming that Y' is approximately normal, we can say that

P(Y' > 14) = P(Z > [√100(14 - 12)/9]) and this is equal to

P(Z > 2.22) = 0.013

Here,

a+b=20

ab=50

we know that,

[tex]\tt{ (a+b)^2=a^2+b^2+2ab }[/tex] ⠀

According to the question,

[tex]\tt{(20)^2=a^2+b^2+2×50 }[/tex] ⠀

[tex]\tt{ 400=a^2+b^2+100 }[/tex] ⠀

[tex]\tt{ a^2+b^2=400-100 }[/tex] ⠀

[tex]\tt{a^2+b^2=300 }[/tex] ⠀

Answer:

      a² + b² = 300

Step-by-step explanation:

a + b = 20  ; ab = 50

(a +b)² = a²+ b² + 2ab

a² + b² + 2ab = (a + b)²

a² + b² + 2*50 = (20)²

a² + b² + 100 = 400

         a² + b² = 400 - 100

        a² + b² = 300

Answer:

The answer is below

Step-by-step explanation:

Trigonometric functions are functions used in right angled triangles to relate an angle in the triangle to the ratio of two side. The most common trigonometric functions are the sine, the cosine, and the tangent.

Some trigonometric identities are:

secθ = 1/ cosθ, cosecθ = 1 / sinθ, tanθ = sinθ / cosθ, cotθ = 1 / tanθ = cosθ / sinθ.

Hence simplifying the question:

[tex]\frac{sin\theta}{cos\theta tan\theta} =\frac{sin\theta}{cos\theta *\frac{sin\theta}{cos\theta} }\\\\=\frac{sin\theta}{sin\theta}\\\\=1[/tex]

Answer:

$22.50

Step-by-step explanation:

So if each topping cost 2.50 then just multiply by 9

Answer:

Hi! The answer is A hope I helped

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

Answer:

B 12.375 is the answer

Step-by-step explanation:

Key skills needed: Fraction to Decimal Conversion

1) The mixed number that is in the question is --> [tex]12\frac{3}{8}[/tex]

2) We need to find 12 and 3/8 as a decimal.

[tex]12\frac{3}{8}= 12 + \frac{3}{8}[/tex]

This means it would be 12."something"

We need to find out what [tex]\frac{3}{8}[/tex] as a decimal is.

3) To do this, we do 3 ÷ 8 (to find the decimal form of a fraction, you do the numerator divided by the denominator).

4) Check the image I posted to see how I did 3 ÷ 8.

5) Well based on the division, 3 divided by 8 is 0.375

This means that [tex]12 + \frac{3}{8} = 12 + 0.375 = 12.375[/tex]

Therefore 12.375 is your answer

Hope you understood and have a nice day!! :D

Answer:

43

Step-by-step explanation:

PEMDAS 19 times 2 is 38 plus 5 equals 43

Answer:

No, he does not have enough money to buy the grapes because he only has 15$ when in total the the grapes are $28.35.

Step-by-step explanation:

Answer:

2x-3y+z

Step-by-step explanation:

-2x-y-2z+4x-2y+3z

combine like terms

-2x+4x= 2x

-y-2y= -3y

-2z+3z= z

so..

2x-3y+z

Answer:

Correlation does not always imply causation. (It's not correct)

Step-by-step explanation:

Correlation tests 2 variables' relationship, but just because they are related does not mean they necessarily cause each other.

Answer:

90 degrees.

Step-by-step explanation:

Rotate it on Geogebra.

Answer:

28/7

Step-by-step explanation:

Answer:14.9129

Step-by-step explanation:

Answer:

hmmm sorry i dont really know

Answer:

45+3.x

Step-by-step explanation:

Each person gets a haircut --> 3.15= 45