a particular fruit's weights are normally distributed, with a mean of 725 grams and a standard deviation of 29 grams. if you pick one fruit at random, what is the probability that it will weigh between 687 grams and 825 grams. round your probabilty accurate to 4 decimal places

a. Correct answer is C as sample contains more pink marbles than red marbles, so it's predicted that the bowl has more pink marbles.

b. With 750 marbles in the bowl and proportion of pink marbles being 0.7, there are approximately 525 pink marbles and 225 red marbles, thus you are more likely to pick a pink marble.

a. The correct answer is C. Yes. Because the representative sample contains more pink marbles than red marbles, you can predict that the bowl contains more pink marbles than red marbles.

b. If there are 56 pink marbles and 24 red marbles in a sample of 80 marbles, then the proportion of pink marbles in the sample is 56/80 = 0.7, and the proportion of red marbles in the sample is 24/80 = 0.3. If there are 750 marbles in the bowl, then there are about 0.7750 = 525 pink marbles and 0.3750 = 225 red marbles. So, you are more likely to pick a pink marble.

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The simplification of the logarithm is determined as [tex]\log_32 - 11[/tex].

To solve the problem, we can first convert all the logarithms into the same base, which will be base 3. Using the logarithmic identity that

[tex]\log_a b = \frac{\log_c b}{\log_c a}[/tex]

where;

we get:

[tex]3\log_9(18) + \log_3\left(\sqrt{\frac{8}{27}}\right) - \log_{\frac{1}{27}}(81) - \log_{\sqrt{3}}(2\sqrt{2}) &\\\\= 3\frac{\log_3(18)}{\log_3(9)} + \frac{1}{2}\log_3\left(\frac{8}{27}\right) - \frac{\log_{3}(81)}{\log_{3}(1/27)} - \frac{\log_{3}(2\sqrt{2})}{\log_{3}(\sqrt{3})}[/tex]

[tex]= 6\frac{\log_3(2)+\log_3(3)}{2\log_3(3)} + \frac{1}{2}\left(\log_3(2^3)-\log_3(3^3)\right) - \frac{\log_{3}(3^4)}{\log_{3}(3^{-3})} - \frac{\log_{3}(2\sqrt{2})}{1/2}\\\\\= 3\left(\frac{\log_3(2)}{\log_3(3)}+1\right) + \frac{3\log_3(2)-9\log_3(3)}{6} - \frac{12}{3} - 2\log_{3}(2\sqrt{2})[/tex]

[tex]= 3\left(\frac{\log_3(2)}{\log_3(3)}+1\right) - \frac{3}{2} + \frac{\log_3(2) }{2} - 4 - \log_3(8) \\\\= 3\left(\frac{\log_3(2)}{\log_3(3)}\right) - \frac{5}{2} + \frac{\log_3(2) }{2} - \log_3(2^3)\\\\= 3\left(\frac{\log_3(2)}{\log_3(3)}\right) - \frac{5}{2} + \frac{1}{2} (\log_3(2) )- \log_38\\\\= 6\left (\frac{\log_3(2)}{\log_3(3)}\right) -5+ \log_3(2) - 2\log_3(8)\\\\= 6\log_32 \ - \ 6\log_33 - 5 + \log_32-2\log_38\\\\= \log_3\left (\frac{2^6\times 2 }{3^6\times 8^2}\right) - 5\\\\[/tex]

[tex]= \log_3\left (\frac{2^7 }{3^6\times 2^6}\right) - 5\\\\= \log_3\left (\frac{2 }{3^6}\right) - 5\\\\= \log_32 - \log_33^6 - 5\\\\= \log_32 - 6 - 5\\\\=\log _32 \ - 11[/tex]

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the end behavior of the polynomial function f(x) = [tex]2x^3 + 5x^2 - 2x - 3[/tex] is that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.

To describe the end behavior of a polynomial function, we need to examine the degree and leading coefficient of the function. In the polynomial function f(x) =[tex]2x^3 + 5x^2 - 2x - 3[/tex], the degree is 3 and the leading coefficient is 2.

The end behavior of the polynomial function f(x) is determined by the behavior of the function as x approaches positive infinity and negative infinity.

As x approaches positive infinity, the leading term dominates the behavior of the function. Since the leading coefficient is positive and the degree is odd, the function will increase without bound, or approach positive infinity. In other words, as x becomes very large and positive, the function will also become very large and positive.

As x approaches negative infinity, the leading term also dominates the behavior of the function. However, since the degree is odd, the function will decrease without bound, or approach negative infinity. In other words, as x becomes very large and negative, the function will also become very large and negative.

Therefore, the end behavior of the polynomial function f(x) = [tex]2x^3 + 5x^2 - 2x - 3[/tex] is that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.

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Both Option C. 5k+5 and Option D. 5(k+1) are equivalent expressions to 2k+2+k+3+2k.

To simplify the expression 2k+2+k+3+2k, we can combine like terms, as follows:

2k + k + 2k + 2 + 3 = 5k + 5

Therefore, the expression 2k+2+k+3+2k is equivalent to 5k+5. We can also write this expression as 5(k+1), since we can factor out the common factor of 5 from both terms:

5(k+1)

Therefore, both Option C. 5k+5 and Option D. 5(k+1) are equivalent expressions to 2k+2+k+3+2k.

Option A, [tex]5k^5[/tex], is not equivalent to the given expression, as it contains an exponent of 5, which is not present in the original expression.

Option B, [tex]5+k^5[/tex], is also not equivalent to the given expression, as it contains a term k^5, which is not present in the original expression.

Option C, 5k+5, is equivalent to the given expression, as shown above.

Option D, 5(k+1), is also equivalent to the given expression, as shown above.

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The complete question is :

Select all expressions that are equivalent to 2k+2+k+3+2k.

A. [tex]5k^5[/tex]

B. [tex]5+k^5[/tex]

C. [tex]5k+5[/tex]

D. [tex]5(k+1)[/tex]

Answer:

[tex]x = \frac{5}{p - 1} [/tex]

p ≠ 1

Step-by-step explanation:

20 = 4x (p - 1)

20 = 4xp - 4x

4xp - 4x = 20

(4p - 4)x = 20 / : (4p - 4)

[tex]x = \frac{20}{4p - 4} = \frac{20}{4(p - 1)} = \frac{5}{p - 1} [/tex]

we determine the scope of the definition:

4p - 4 ≠ 0

4p ≠ 4 / : 4

p ≠ 1

Answer:-72x

Step-by-step explanation:

The sample mean for the given data set is 3.044 miles.

Let's use the given data to calculate the sample mean. We have the distances in miles that 10 visitors live from the library: 0.5, 0.8, 0.8, 1.5, 1.8, 3.5, 4.8, 6.2, and 8.3.

To find the sample mean, we first add up all the distances:

0.5 + 0.8 + 0.8 + 1.5 + 1.8 + 3.5 + 4.8 + 6.2 + 8.3 = 27.4

Next, we divide the sum by the total number of distances, which is 9 (since we have data for 10 visitors):

27.4 / 9 = 3.044 (rounded to three decimal places)

This means that, on average, the visitors to the library live about 3.044 miles away from the library.

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Answer:

[tex]90 { \: cm}^{2} [/tex]

Step-by-step explanation:

First, we can find one triangle's area (they are all the same and isosceles):

h = XY = 6 cm, a = BC = 5 cm

[tex]s(triangle) = \frac{1}{2} \times h \times a = \frac{1}{2} \times 6 \times 5 = 15[/tex]

And now, multiply this number by 6 (since there are 6 of these identical triangles):

S(hexagon) = 15 × 6 = 90 cm^2

Answer:

C

Step-by-step explanation:

P and N are a linear pair and sum to 180° , that is

P + 67° = 180° ( subtract 67° from both sides )

P = 113°

Answer:

360∘

The sum of the exterior angles of a polygon is always 360∘ . Therefore, the sum of the exterior angles of a 25-gon is 360∘ .

An expression for the number of bracelets of n beads, where rotations.

Whats an expression for the bracelets?

In mathematics, the term "bracelets" can refer to a type of combinatorial object, specifically, a set of beads arranged in a circular pattern. An expression for the number of bracelets of n beads, where rotations and reflections are considered identical, can be given as follows:

B(n) = (1/n) * (2raise to the power (n-1) + Σ(d|n, d<n) μ((n/d)) * 2 raise to the power ((n/d)-1))

Here, B(n) represents the number of distinct bracelets of n beads, Σ denotes the summation, d|n denotes "d divides n", and μ is the Möbius function.

The first term in the expression, (1/n) * (2 raise to the power (n-1)), represents the number of bracelets that are invariant under rotation. The second term takes into account the bracelets that are not invariant under rotation, but are invariant under reflection, and involves the Möbius function.

This expression can be used to calculate the number of bracelets for any value of n, by plugging in the value of n and evaluating the expression.

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Answer:

3/4.

Step-by-step explanation:

y = x^1/2

dy/dx = 1/2 x^-1/2

dy/dt = dy/dx * dx/dt

        =  1/2 x^-1/2 * 3

         = 3/2 x^-1/2

When x = 4:

dy/dt = 3/2 * 4 ^-1/2

         = 3/2* 1/ √4

         = 3/2 * 1/2

         = 3/4.

Answer:

Step-by-step explanation:

Answer:

Let x be Taub and y for Chloe

y-x=1. since their ages are consecutive

y-1=x

xy=12.…..... eq 1

(y-1)y=12....... eq 2

y²-y-12=0

y=4 or y=-3

since age can never be a negative, we choose y=4 and substitute in eq 1

4x=12

x=12/4=3

Taub is 3 years old

The non - markup price of the pair of shoes is $103. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

It is believed that the four fundamental operations, often known as "arithmetic operations," adequately explain all real numbers. After division, multiplication, addition, and subtraction in mathematics are the operations quotient, product, sum, and difference.

We are given that the store sells the shoes for $193.21 which includes the 87% markup.

So, using the subtraction operation, we get

⇒ Non - markup price = ($193.21 * 100) ÷ 187

⇒ Non - markup price = $19321 ÷ 187

⇒ Non - markup price = $103.3208

Hence, the non - markup price of the pair of shoes is $103.

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The probability that less than four students out of fifty students registered for a general education course will pass/fail the course is 0.9601 (rounded to four decimal places).

The probability of an event is defined as the number of ways the event can occur divided by the total number of possible outcomes. To solve the given problem, we will use the binomial distribution formula.

The formula for the probability of less than 4 successes in n trials, given the probability of success p, is:P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)Where X is a binomial random variable with n = 50 trials and p = 0.03 probability of success, i.e., taking general education courses on a pass/fail basis.

Now, let's calculate each term:

P(X = 0) = C(50, 0) (0.03)⁰ (0.97)⁵⁰P(X = 0) = 1 × 1 × 0.97⁵⁰ ≈ 0.3669P(X = 1) = C(50, 1) (0.03)¹ (0.97)⁴⁹P(X = 1) = 50 × 0.03 × 0.97⁴⁹ ≈ 0.3937P(X = 2) = C(50, 2) (0.03)² (0.97)⁴⁸P(X = 2) = 1225 × 0.0009 × 0.97⁴⁸ ≈ 0.1872P(X = 3) = C(50, 3) (0.03)³ (0.97)⁴⁷P(X = 3) = 19600 × 0.000027 × 0.97⁴⁷ ≈ 0.0123P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)P(X < 4) = 0.3669 + 0.3937 + 0.1872 + 0.0123P(X < 4) ≈ 0.9601

Hence, the probability that less than four students out of fifty students registered for a general education course will pass/fail the course is 0.9601.

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The exponential function in the graph can be written as:

h(x) = 3*2^x

We can see that h(x) is an exponential function, so we can write this in a general form as:

h(x) = a*b^x

Where a is the initial value and b is the base of the exponential.

First, we can see that it passes through the ponit (0, 3), replacing these values we will get:

3 = a*b^0

3 = a

So the equation is:

h(x) = 3*b^x

We also can see that it passes through (1, 6), replacing these values we will geT:

6 = 3*b^1

6 = 3*b

6/3 = b

2 =b

The exponential function is:

h(x) =3*2^x

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Answer:

2.64

Step-by-step explanation:

b*h=5.28

5.28/2=2.64

The number of sacks of trash that Jorge's brother picked up is given as follows:

3.75 sacks.

The number of sacks of trash that Jorge's brother picked up is obtained applying the proportions in the context of the problem.

Jorge picks up 2 1/2 sacks of trash, which is a mixed number, hence the decimal number that represents this amount is given as follows:

2 + 1/2 = 2 + 0.5 = 2.5 sacks.

His brother picks up 1 1/2 times as much as Jorge, which is 1 + 1/2 = 1.5 times the amount picked by Jorge, hence the number of sacks of trash that Jorge's brother picked up is obtained as follows:

2.5 x 1.5 = 3.75 sacks.

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Answer:

1. is the distance from the center of the circle to any point on it's circumference

The probability that p falls between 0 and 0.06 is 0.00000205.

How to calculate the probability

Based on the information, to calculate the probability that p falls between 0 and 0.06, we need to first calculate the standard error (SE) of the sample proportion, which can be calculated as:

SE = ✓[ p * (1-p) / N ]

where p is the sample proportion and N is the sample size.

In this case, we have:

p = 25/85 = 0.2941

N = 85

SE = ✓[ 0.2941 * (1-0.2941) / 85 ] = 0.0545

Next, we need to calculate the z-score corresponding to the upper limit of the interval (0.06). This can be calculated as:

z = (0.06 - p) / SE = (0.06 - 0.2941) / 0.0545 = -4.4702

Using the dCMP normal distribution tool, we can find the probability that a standard normal random variable falls below this z-score as:

P(z < -4.4702) = 0.00000205

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Answer:

1.28*10^6

Step-by-step explanation:

It is up to you whether you convert 1400000 into scientific notation or convert 1.2*10^5 into decimal notation, subtract, and then convert once more into scientific notation for your final answer.

Either way, it will come out to be 1.28*10^6

Work is below:

1.2*10^5 = 120,000

1400000 - 120000 = 1280000

= 1.28*10^6 (remember it is every number behind the decimal)

Answer:

  25 cm

Step-by-step explanation:

You want to know the length of the hypotenuse in a right triangle with legs 15 cm and 20 cm.

The given leg lengths have the ratio ...

  15 : 20 = 3 : 4 . . . . . . . scale factor of 5

This means they are part of a 3 : 4 : 5 right triangle.

The length "t cm" is 5·5 cm = 25 cm.

The value of t is 25.

__

Additional comment

In case you've never heard of a {3, 4, 5} right triangle, you can figure the missing hypotenuse from the Pythagorean theorem:

  c² = a² +b²

  t² = 15² +20² = 225 +400 = 625

  t = √625 = 25

The {3, 4, 5} Pythagorean triple is used repeatedly in algebra, geometry, and trig problems, along with some others: {5, 12, 13}, {7, 24, 25}, {8, 15, 17}. These can appear as multiples of the basic triple, as here, where the multiple is 5 × {3, 4, 5} = {15, 20, 25}.

Answer:

Step-by-step explanation:

The required larger and smaller number is 7 and 3 respectively.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,

Let the larger number be x and smaller number be y,

According to the question,

the sum of the larger and twice the smaller is equal to 13.

x + 2y = 13 - - - -(1)

And, twice their positive difference is equal to eight.

2(x - y) = 8

x - y = 4 - - - -(2)

Subtracting equation 1 by 2

3y = 9

y = 3

Now,

x - y =4

x -3 = 4

x = 7

Thus, the required larger and smaller number is 7 and 3 respectively.

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The probability that a basketball player makes all four of his free throws when the probability of making one is 80% is 0.4096.

This is calculated using the binomial probability formula, which states that the probability of k successes in n trials is given by the following:

P(k successes in n trials) = [tex](n!/(k!(n-k)!))\timespk(1-p)(n-k)[/tex]

In this case, the probability of making a single free throw is 80% (0.8),

so we can plug this into the formula.

We know that the player is taking 4 free throws, so k is 4 and n is also 4.

Plugging these values into the formula, we get:

P(4 successes in 4 trials) = [tex](4!/(4!(4-4)!))\times 0.84(1-0.8)(4-4) = 0.4096[/tex]

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Answer:

The answer to your problem is, A. The Allstars, with a mean of about 67.1 inches

Step-by-step explanation:

Allstars mean height:

= (73 + 62 + 60 + 63 + 72 + 65 + 69 + 68 + 71 + 66 + 70 + 67 + 60 + 70 + 71) / 15

= 1007 / 15

= 67.6 inches

Super Stars mean height:

= (66 + 68 + 62 + 63 + 47 + 64 + 65 + 50 + 60 + 64 + 65 + 65 + 58 + 60 + 55) / 15

= 912 / 15

= 60.2 inches

We can see that the Allstars team has a higher mean height than the Super Stars team, with an average of 67.6 inches compared to 60.2 inches. Therefore, the Allstars team typically has the tallest players

Thus the answer to your problem is, A. The Allstars, with a mean of about 67.1 inches

V = πr^2h

V1 = π14/2^2•9
V1 = π7^2•9

V1 = π49•9

V1 = 1,385.442360233099

V2 = π6/2^2•9

V2 = π3^2•9

V2 = π9•9

V2 = 254.4690049407733

V = V1 - V2

V = 1,385.442360233099 - 254.4690049407733

V = 1,130.973355292326 or 1,130.97

Thus, the volume of the cylinder is 1,130.97cm^3.

Answer:

41 chickens and 9 cows

Step-by-step explanation:

Chickens have 2 legs each.

Cows have 4 legs each.

There are 50 animals total.

There are 118 legs total.

You can set up a system to represent this situation.

Let x represent the number of chickens and y represent the number of cows.

x + y  = 50

2x + 4y = 118

Multiply the first equation by 2 and subract it from the second equation.

    2x + 4y = 118

-    2x + 2y = 100

_____________

2y = 18

y = 9

So there are 9 cows. There are 50 animals total so there must be 41 chickens.

There is a total of 50 chickens and cows.

Chickens have 2 legs each. Cows have 4 legs each.

There are 118 legs in total. We are focusing on how much chickens there are.

CHICKENS=50-COWS.

2CHICKENS+4COWS=118

2(50-COWS)+4COWS=118

100-2COWS+4COWS=118

2COWS=118-100

2COWS=18

C0WS=18/2

COWS=9

CHICKENS+9=50

CHICKENS=50-9

CHICKENS=41

PROOF:

2*41+4*9=118

82+36=118

118=118

This is a bit long and confusing but I hope this helps!