If the dimensions of a shipping box are all doubled, how many staplers can the larger box hold?

Answer:

a) 0.4215 = 42.15% probability that all are repaired in less than 6 hours.

b) 0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours

Step-by-step explanation:

To solve this question, we need to understand the normal and the binomial probability distributions.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Normal Probability Distribution:

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

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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.

Proportion repaired below 6 hours:

Mean 5 hours and standard deviation 1 hour, which means that \(\mu = 5, \sigma = 1\)

This proportion is the p-value of Z when X = 6. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{6 - 5}{1}\)

\(Z = 1\)

\(Z = 1\) has a p-value of 0.8413.

0.8413 repaired below 6 hours.

For the binomial distribution, this means that \(p = 0.8413\)

5 are chosen:

This means that \(n = 5\)

a) Probability that all are repaired in less than 6 hours

This is P(X = 5). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 5) = C_{5,5}.(0.8413)^{5}.(0.1587)^{0} = 0.4215\)

0.4215 = 42.15% probability that all are repaired in less than 6 hours.

b) Probability that exactly 3 of them repaired below 6 hours

This is P(X = 3). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 3) = C_{5,3}.(0.8413)^{3}.(0.1587)^{2} = 0.15\)

0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours

The ratio of b to a is b/a = 2. This is option B.

We can say that both triangles ABE and BCE are equilateral triangles.

The length of each side of the triangle ABE is a.

So, BE = a ………. (1)

The length of each side of the triangle BCE is 2a.

So, BE = 2a ………. (2)

From equation (1) and (2), we can say that a = 2a or a = a ⇒ a = 2a ⇒ a/2 = a/2

Again, let us consider the triangles ABD and CBD.The length of each side of triangle ABD is a.

So, BD = a ………. (3)

The length of each side of the triangle CBD is a.So, BD = a ………. (4)

From equation (3) and (4), we can say that a = a or a = a ⇒ a = a

Again, let us consider the triangles ADE and CDE.

The length of each side of triangle ADE is b.

So, DE = b ………. (5)

The length of each side of the triangle CDE is 2a.So, DE = 2a ………. (6

)From equation (5) and (6), we can say that b = 2a or b = 2a ⇒ b/2 = a

So, the ratio of b to a is b/a = 2

Hence, the Answer is option (B) 2.

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The value of the exponent (2/5)^3 is \(\frac{8}{125}\)

In the above question, it is given that

(2/5)^3

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 2^3) signifies 2 x 2 x 2 = 8.

We need to solve it and then find the value of the exponent

(2/5)^3

= \(\frac{2}{5}\) x \(\frac{2}{5}\) x \(\frac{2}{5}\)

= \(\frac{2 . 2. 2}{5 . 5 . 5}\)

= \(\frac{8}{125}\)

Therefore the value of the exponent (2/5)^3 is \(\frac{8}{125}\)

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Answer:

yes it is true

hope my answer help you

Answer:

x = 28

Step-by-step explanation:

\( \tan(2x - 65) \degree = \cot(3x + 15) \degree \\ \\ \tan(2x - 65)\degree = \tan \{90 \degree - (3x + 15)\degree \} \\ \\ (2x - 65)\degree = \{90 \degree - (3x + 15)\degree \} \\ \\ (2x - 65)\degree + (3x + 15)\degree = 90 \degree \\ \\ (2x - 65 + 3x + 15)\degree = 90 \degree \\ \\ 5x - 50 = 90 \\ \\ 5x = 90 + 50 \\ \\ 5x = 140 \\ \\ x = \frac{140}{5} \\ \\ x = 28\)

a) Build the probability distribution of X =  0.125.  b) Find the mean value of X= 1.875.  c) Find the standard deviation of X = 1.0533

a)

For a fair coin,

P(H) = P(T) = 0.5

Outcome X Probability

T 1 0.5

HT 2 0.5*0.5 = 0.25

HHT 3 0.5*0.5*0.5 = 0.125

HHHT 4 0.5*0.5*0.5*0.5 = 0.0625

HHHH 4 0.5*0.5*0.5*0.5 = 0.0625

So, the probability distribution of X is

X P(X)

1 0.5

2 0.25

3 0.125

4 0.0625+0.0625 = 0.125

b)

X P(X) X*P(X) X2*P(X)

1 0.5 0.5 0.5

2 0.25 0.5 1

3 0.125 0.375 1.125

4 0.125 0.5 2

\(\sum\) 1 E(X) = 1.875 E(\(x^{2}\)) = 4.625

Mean = \(\sum\)X* P(X) = 1.875

c)

Variance = E(\(x^{2}\)) - E\((x^{2} )\)= 4.625 – \(1.875^{2}\)  = 1.1094

Standard Deviation = \(\sqrt{variance} = \sqrt{1.1094} = 1.0533\)

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The type of quadrilateral is formed by the points A(1, 2), B(3, 5), C(3, 8), and D(1, 5) is parallelogram.

Given points:

A(1, 2), B(3, 5), C(3, 8), and D(1, 5)

we know that distance formula,

Distance between AB = \(\sqrt{(x_{2} - x_{1})^{2} +( y_{2} - y_{1})^{2} }\)

= \(\sqrt{(3 - 1)^{2} +( 5 - 2)^{2} }\)

= \(\sqrt{2^{2}+3^{2} }\)

AB = \(\sqrt{13}\)

BC = \(\sqrt{(3 - 3)^{2} +( 8 - 5)^{2} }\)

= \(\sqrt{0^{2}+3^{2} }\)

= \(\sqrt{9}\)

= 3

BC = 3

CD = \(\sqrt{(1 - 3)^{2} +( 5 - 8)^{2} }\)

= \(\sqrt{(2^{2} +3^{2} }\)

CD = \(\sqrt{13}\)

AD = \(\sqrt{(1 - 1)^{2} +( 5 - 2)^{2} }\)

= \(\sqrt{0^{2}+3^{2} }\)

AD = 3

AC = \(\sqrt{(3 - 1)^{2} +( 8- 2)^{2} }\)

= \(\sqrt{2^{2} +6^{2} }\)

AC = \(\sqrt{40}\)

BD = \(\sqrt{(1 - 3)^{2} +( 5 - 5)^{2} }\)

= \(\sqrt{2^{2} +0^{2} }\)

BD = 2

Here AB = CD,BC = DA . But AC ≠ BD

Hence the pairs of opposite sides are equal but diagonal are not equal so it is a parallelogram.

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Answer:

Step-by-step explanation:

Wheat flour

Rye flour

Equation for total:

A cylinder which is option B is a geometric figure which has two circular bases lying in parallel planes.

One of the fundamental three-dimensional forms in geometry is the cylinder, which has two distant, parallel circular bases. At a certain distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.

The cylinder has two key characteristics, namely surface area and volume, because it is a three-dimensional form. The combined curved surface area of the cylinder and the areas of the two circular bases make up its whole surface area. A cylinder's volume is the term used to describe the three-dimensional space it takes up.

A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centres of the two bases.

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Answer:

i need help on this question too

Step-by-step explanation:

Answer:

I think X=10 but im not for sure.

Step-by-step explanation:

150 (X+10) = 200 (X+5)

150x+1500   200X+1000

-150X            -150X

1500               50X+1000

-1000                      -1000

500                50X

50                   50

10=X

By using Pythagorean identities the expression can be written as

         -8 (sin ( x ) + 1 -sin 2x)

The Pythagorean identity is an important identity in trigonometry derived from the Pythagorean theorem. These identities are used to solve many trigonometric problems where, given a trigonometric ratio, other ratios can be found. The basic Pythagorean identity, which gives the relationship between sin and cos, is the most commonly used Pythagorean identity:

sin2θ + cos2θ = 1 (gives the relationship between sin and cos)

There are two other Pythagorean identities as follows :

sec2θ - tan2θ = 1 (gives the relationship between sec and tan)

csc2θ - cot2θ = 1 (gives the relationship between csc and cot)

Given expression is:

-8tanx/ 1 +tan2x

we know that:

By the Pythagorean Theorem:

1 + tan²x = sec²x

and tan x = sin x/cos x

and, sec x = 1/cos x

Now, we can write as:

   -8tanx / 1 +tan²x

= -8 tan x / sec²x

= -8 sin x /cos x ÷ 1/cos²x

= -8 sin x/cos x × cos²x/1

= -8 (sin ( x ) + 1 -sin 2x)

Complete Question:

Use appropriate identities to rewrite the following expression in terms containing only first powers of sine:

−8tan 1 + tan2x.

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1

The exact value of tan(π4) tan ( π 4 ) is 1 .

Answer:

(a) $1.98

(b) $6.30

Step-by-step explanation:

(a)

The new value =

1.80 + The value of the percentage increase =

1.80 + (10% × 1.80) =

1.80 + 10% × 1.80 =

(1 + 10%) × 1.80 =

(100% + 10%) × 1.80 =

110% × 1.80 =

110 ÷ 100 × 1.80 =

110 × 1.80 ÷ 100 =

198 ÷ 100 =

1.98

Calculate the actual change (the absolute difference) between the two values

The actual change =

The new value - 1.80 =

1.98 - 1.80 =

0.18

Proof of calculation.

Calculate the percentage increased value...

... and see if we get as a result...

... the actual change (the absolute difference).

Calculate the percentage increased value:

The value of the percentage increase =

10% × 1.80 =

10 ÷ 100 × 1.80 =

10 × 1.80 ÷ 100 =

18 ÷ 100 =

0.18

So we have proven that the calculations are correct.

For positive numbers

The actual change =

The value of the percentage increase

The answer:

1.80 increased by 10% = 1.98

The actual change:

1.98 - 1.80 = 0.18

(b)

Calculate the New value
The new value =

42.0 + The value of the percentage increase =

4.20 + (50% × 4.20) =

4.20 + 50% × 4.20 =

(1 + 50%) × 4.20 =

(100% + 50%) × 4.20 =

150% × 4.20 =

150 ÷ 100 × 4.20 =

150 × 4.20 ÷ 100 =

63,000 ÷ 100 =

630

(but its as a dollar so its 6.30)

Calculate the actual change (the absolute difference) between the two values

The actual change =

The new value - 4.20 =

6.30 - 4.20 =

2.10

Proof of calculation.

Calculate the percentage increased value...

... and see if we get as a result...

... the actual change (the absolute difference).

Calculate the percentage increased value:

The value of the percentage increase =

50% × 4.20 =

50 ÷ 100 × 4.20 =

50 × 4.20 ÷ 100 =

21,000 ÷ 100 =

210

(but its as a dollar so its 2.10)

So we have proven that the calculations are correct.

For positive numbers

The actual change =

The value of the percentage increase

The answer:

4.20 increased by 50% = 6.30

The actual change:

6.30 - 4.20 = 2.10

The equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).

If we assume that the growth rate of the world population was constant from 1997 to 2017, then we can use the following equation:

Population in 2017 = Population in 1997 × (1 + r)²⁰

where r is the annual growth rate, and the exponent 20 represents the number of years between 1997 and 2017.

We can rewrite this equation to solve for r:

(7.53 ) = (5.88 ) × (1 + r)²⁰

Divide both sides by (5.88 ):

(7.53 ) / (5.88 ) = (1 + r)²⁰

Take the 20th root of both sides:

\((7.53 / 5.88 )^{(1/20)} = 1 + r\)

Subtract 1 from both sides:

\(r = (7.53 / 5.88 )^{(1/20)} - 1\)

Therefore, the equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).

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Answer: 24.33

Step-by-step explanation:

looked it up

Answer:

Given data:

The given expression is 1+1.

The value of the given expression is,

Thus, the value of 1+1 is 2.

Step-by-step explanation:

you don't know the meaning of

\(y = {h}^{ - 1} (x)\)

it means it is the inverse function to h(x).

the regular function assigns an y value to every x value.

the inverse function now turns this around and finds for a given y value the original x value.

so, the inverse function is easier understood, if we would write it

\(x = {h}^{ - 1} (y)\)

but just for formal reasons, we don't define functions this way but do it like above (x is the input, y the output value).

just, the understanding of an inverse function is a I just described it.

that means for the points, simply x and y values trade places.

the point (1, 9) turns into (9, 1) (it means 1 was the original x value when the original function delivered 9 a result).

and the point (3, 2) turns into (2, 3).

so, move the 2 green dots to these coordinates.

The simplified sum of the expression ∑+1=−1 (2 − 1) is 2.

The given expression is the sum of (2 - 1) from i = -1 to n, where n = 1. Therefore, the expression can be simplified as follows:

∑+1=−1 (2 − 1) = (2 - 1) + (2 - 1) = 1 + 1 = 2

In this case, the value of n is 1, which means that the summation will only be performed for i = -1. The expression inside the summation is (2 - 1), which equals 1. Thus, the summation is equal to 1.

Adding 1 to the result of the summation gives:

∑+1=−1 (2 − 1) + 1 = 1 + 1 = 2

Therefore, the simplified sum of the expression ∑+1=−1 (2 − 1) is 2.

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Answer:

- 1

Step-by-step explanation:

8m + 5n

8(3) + 5(- 5)

24 + (- 25)

24 - 25

- 1

Answer:

-1

Step-by-step explanation:

8m + 5n

8(3) + 5(-5)

24 - 25

-1

The coordinates for the center and length of the radius of this circle are equal to (½, 1), 2 units.

Mathematically, the standard form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

In order to determine the coordinates for the center and the length of the radius of this circle, we would use completing the square method:

x² + y² - x - 2y - 11/4 = 0

x² - x + ¼ + y² - 2y = 11/4 + ¼

(x - ½)² + y² - 2y + 1 = 12/4 + 1

(x - ½)² + (y - 1)² = 4

Comparing with the standard form, we have:

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Complete Question:

A circle is defined by the equation given below.

x^2 + y^2 − x − 2y − 11/4 = 0

What are the coordinates for the center of the circle and the length of the radius?

The expected value of perfect information (EVPI) is calculated as EVwPI minus maximum EMV. It quantifies the value of perfect information in decision-making.


The expected value of perfect information (EVPI) is a concept used in decision analysis. It represents the maximum amount of money an individual would pay to have perfect information about an uncertain event before making a decision.

To calculate EVPI, you start with the expected value with perfect information (EVwPI), which is the expected value when you have complete and accurate information about the uncertain event. Then, you subtract the maximum expected monetary value (EMV) from the EVwPI.

The EMV represents the expected monetary value of the decision without any additional information. By subtracting the maximum EMV from the EVwPI, you are essentially measuring the value of the additional information in terms of monetary gain.

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Answer:

m = - 1

Step-by-step explanation:

m = -4 - m + 2    Combine

m = -2 - m          Add m to both sides

m+m = - 2          Combine

2m = - 2            Divide by 2

m = -2/2

m = - 1

m=−(4+m)+2

Simplify both sides of the equation.

m=−(4+m)+2

m=−m+−4+2

m=(−m)+(−4+2)

m=−m+−2

m=−m−2

Add m to both sides.

m+m=−m−2+m

2m=−2

Divide both sides by 2.

2m/2=−2/2

m=−1

hope this helps!

Answer:

48c-8c is the answer to the question above

Answer:12.5

Step-by-step explanation:

50 divided by 4 = 12.5

Answer:

The answer is C

I turned it in and it was correct

Step-by-step explanation:

Please mark brainliest

Answer:

c

Step-by-step explanation: