Could someone help me with this probelm

Answer:

According to my problem solving, the answer should be B. 4

Step-by-step explanation: it might be wrong but worth a shot

we have shown that P(X = k) reaches its largest value when k is the largest integer less than or equal to np.

To show that P(X = k) reaches its largest value when k is the largest integer less than or equal to np, we can consider the ratio P(X = k + 1) / P(X = k).

Using the probability mass function (PMF) of a binomial random variable, we have:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where C(n, k) is the binomial coefficient given by n! / (k!(n - k)!), p is the probability of success, and (1 - p) is the probability of failure.

Now, let's calculate the ratio:

P(X = k + 1) / P(X = k) = [C(n, k + 1) * p^(k + 1) * (1 - p)^(n - k - 1)] / [C(n, k) * p^k * (1 - p)^(n - k)]

Simplifying, we can cancel out some terms:

P(X = k + 1) / P(X = k) = [n! / ((k + 1)!(n - k - 1)!)] * [(k!(n - k)! / n!)] * [p / (1 - p)]

This further simplifies to:

P(X = k + 1) / P(X = k) = (n - k) * (k + 1) * p / ((k + 1) * (1 - p))

Now, we want to find when this ratio is less than 1 and when it is greater than 1 to determine where P(X = k) reaches its maximum.

1. When the ratio is less than 1:

For the ratio to be less than 1, we need (n - k) * p < (1 - p). Rearranging, we get:

p < (1 - p) / (n - k)

Since p is the probability of success and (1 - p) is the probability of failure, this inequality implies that the probability of success should be less than the probability of failure for the ratio to be less than 1.

2. When the ratio is greater than 1:

For the ratio to be greater than 1, we need (n - k) * p > (1 - p). Rearranging, we get:

p > (1 - p) / (n - k)

This inequality implies that the probability of success should be greater than the probability of failure for the ratio to be greater than 1.

From these inequalities, we can see that the ratio is less than 1 when p < 1/2 and greater than 1 when p > 1/2. This means that the ratio is decreasing when p < 1/2 and increasing when p > 1/2.

Now, let's consider the expression np. When np is an integer, k = np is an integer as well. In this case, we have either p = 1/2 or p ≠ 1/2.

If p = 1/2, then k = np is an integer, and both the inequalities are satisfied for k and k + 1. Therefore, both P(X = k) and P(X = k + 1) are at their maximum, and P(X = k) reaches its largest value.

If p ≠ 1/2, then either p > 1/2 or p < 1/2. In both cases, the ratio P(X = k + 1) / P(X = k) will be either decreasing or increasing, respectively. Therefore, P(X = k) reaches its largest value when k is the largest integer less than or equal to np.

In conclusion, we have shown that P(X = k) reaches its largest value when k is the largest integer less than or equal to np.

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Answer:

1) n=±2\(\sqrt{5}\)

2) a=±3\(\sqrt{10}\)

Step-by-step explanation:

1) \(n^{2}\) =20

✰Take the square root of both sides n=±\(\sqrt{20\\}\)

✰ Simplify \(\sqrt{20\\}\) to 2\(\sqrt{5}\)

→ n=±2\(\sqrt{5}\)  

⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆

2) \(a^{2}\) =90

✰ (Same as above) Take the square root of both sides ​a=±\(\sqrt{90\\}\)

✰ Simplify \(\sqrt{90}\) to 3\(\sqrt{10}\)

→ a=±3\(\sqrt{10}\)

The boundary lines are y > -3x + 4: dotted line and  y <= 8x + 1: solid line

From the question, we have the following parameters that can be used in our computation:

y > -3x + 4

y <= 8x + 1

The boundary line for the inequality "<" is a dotted line, which means that the endpoint is not included in the solution set.

The boundary line for the inequality ">=" is a solid line, which means that the endpoint is included in the solution set.

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Answer:

is it 6 with the 10

Step-by-step explanation:

Answer:

y = 6/5 x + 2/3

Step-by-step explanation:

A equation is given to us and we need to express it in , mx + b form . The given equation to us is,

\(\rm\implies 6 = \dfrac{15y - 10}{3x} \)

Move 3x to LHS , we will get ,

\(\rm\implies 6 * 3x = 15y - 10 \\\\\rm\implies 18x = 15y - 10 \\\\\rm\implies 15y = 18x + 10 \\\\\rm\implies y =\dfrac{18x+10}{15} \\\\\rm\implies \boxed{ \bf y = \dfrac{6}{5}x + \dfrac{2}{3}}\)

This is the required answer .

Answer:

35.8

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

Sample space = {(2,2) (2,4) (2,6) (4,2) (4,4) (4,6) (6,2) (6,4) (6,6)}

= 9/36

= 1/4

Jennifer has 48 nickels, which means she has 144 quarters.

Let's call the number of nickels Jennifer has "n".

Since Jennifer has three more dimes than nickels, she has n + 3 dimes.

And since she has three times as many quarters as nickels, she has 3n quarters.

We can start by figuring out the total value of the nickels and dimes in terms of cents:

n * 5 cents + (n + 3) * 10 cents = 750 cents

Expanding the right side of the equation and solving for n:

5n + 10n + 30 cents = 750 cents

15n + 30 cents = 750 cents

15n = 720 cents

n = 48

So Jennifer has 48 nickels, which means she has 3 * 48 = 144 quarters.

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Answer:

Cause it is more than 50 pounds

Step-by-step explanation:

Answer:

-2/11

Step-by-step explanation:

y2-y1/x2-x1

8-10 / -5 -(-16)

-2/-5 + 16

-2/11

Answer:

The answer is true......

The correct decimal number for 17/22 will be equal to 0.7(727)bar.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system. Decimal refers to the base-10 number system, which is perhaps the most widely used number system. The term "decimal number" refers to a number that has a decimal point followed by digits with values less than one.

Here,

17/22=0.772727.....

For 17/22, the proper decimal number is 0.7(727)bar.

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The form of the likelihood function to proceed with deriving the conditional MLE estimator of θ.

what is decision boundaries.?

Decision boundaries refer to the dividing lines or regions that separate different classes or categories in a classification problem. They are determined based on the features or attributes of the data and the classification algorithm being used. The decision boundary serves as a threshold or criterion for assigning new or unseen data points to specific classes based on their feature values.

To derive the decision boundaries in the given case, more specific information or context is needed. Decision boundaries are determined based on the specific classification or grouping criteria and the underlying data distribution. Please provide additional details or specifications regarding the problem or classification task.

Regarding the conditional maximum likelihood estimator (MLE) of θ, more information is required to proceed with the derivation. The MLE involves finding the parameter value that maximizes the likelihood function based on the observed data and any relevant assumptions or models. Please provide the specific context, assumptions, and the form of the likelihood function to proceed with deriving the conditional MLE estimator of θ.

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Answer:

The answer is D

Step-by-step explanation:

I just took the quiz

Answer:

The answer would be the 4th option

Step-by-step explanation:

The critical value of f(x) = 5x⁶ - 3x⁵ is x = 0.5 which is also its maxima point

f(x) = 5x⁶ - 3x⁵

differentiation w.r.t x

=> f'(x) = 30x⁵ - 15x⁴

Putting f'(x) = 0

30x⁵ - 15x⁴ = 0

=> x⁴(30x - 15) =0

=> 30x - 15 = 0

=> x = 15/30

=> x = 0.5 , 0

Critical number is 0.5 , 0

(B) To find where f(x) is increasing

for x > 0.5 ,

(30x-15) > 0 => x⁴(30x - 15) > 0

Therefore , f(x) is increasing at ( 0.5 , ∞ )

(C)To find where f(x) is decreasing

for x < 0.5 ,

(30x-15) < 0 => x⁴(30x - 15) < 0

Therefore , f(x) is decreasing at ( -∞ , 0.5)

(D) Differentiation f'(x) again w.r.t to x

f'(x) = 30x⁵ - 15x⁴

f"(X) = 150x⁴ - 60x³

Substituting critical values of x

=> 150(0.5)⁴ - 60(0.5)³

=>9.375 - 7.5

=> -1.875 < 0 , Hence , x = 0.5 is point of maxima

(E) no point of minima

Similarly , we can solve other parts

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According to the above, the perimeter of this figure is 61 yards. Moreover, the area is: 255yds

To find the area and perimeter of that figure we must perform the following mathematical procedure: To find the perimeter we must add the length of all the sides as shown below:

On the other hand, to calculate the area of the trapezoid we must apply the following mathematical formula:

So we can infer that the perimeter of this figure is 61yds and the area is 255yds².

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Based on the given options, the correct answer is: OC. Jack interpreted the mean as the median. Half the cats weighed less than 7.96 pounds and half weighed more.

The mean is a measure of central tendency that represents the average of a set of data. It is calculated by adding up all the values in the data set and then dividing by the total number of values.

In this case, Jack interpreted the mean of 7.96 as meaning that half the cats weighed less than 7.96 pounds and half weighed more. However, this is incorrect because the mean does not necessarily divide the data set into two equal halves.

The median, on the other hand, is the middle value in a sorted list of numbers. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values.

If Jack had interpreted the median as meaning half the cats weighed less than its value and half weighed more, he would have been correct. However, he incorrectly interpreted the mean as the median.

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The rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.

The volume of a sphere is given by the formula V = 4/3πr³, where r is the radius of the sphere. To find the rate at which the volume is changing, we need to take the derivative of this equation with respect to time, using the chain rule.

dV/dt = 4/3π(3r²) dr/dt

We know that the radius of the snowball is decreasing at a constant rate, so we can find the value of dr/dt by using the information given in the problem. The radius is decreasing from 34 cm to 18 cm in 30 minutes, which means that:

dr/dt = (34 - 18) cm / 30 minutes = -0.5333 cm/min

Now that we know the rate at which the radius is changing, we can substitute it into the equation for dV/dt and find the rate at which the volume is changing.

We know that the radius is 6 cm at the instant the volume is changing, so we can substitute that into the equation:

dV/dt = 4/3π(3r²) dr/dt = 4/3(π)(3)(6 cm)²(-0.5333 cm/min) = -241.27 cm³/min

So, the rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.

Note that the negative sign indicates that the volume is decreasing.

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Option D is correct.

is a function that is defined on a sequence of intervals and built from the piece of different functions. It is one that is defined not by a single equation, but by the two or more each equation is valid for some interval.

Given

f(x) = x +1, is a function.

The domain for the piece of the function.

From the graph, we can clearly see that at x = 1, there is a jump of 1 unit in y. hence it is divided into two parts.

For x > 1 the domain is defined up to ∞.

For x ≤ 1 the domain is defined up to -∞.

Thus the option D is correct.

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Answer:

5

Step-by-step explanation:

Natalie

100 + 10x

Her sister

25 + 25x

Where

x = number of months

Equate Natalie and her sisters equation

100 + 10x < 25 + 25x

100 - 25 < 25x - 10x

75 < 15x

Divide both sides by 15

x < 75 / 15

x < 5

Answer:

m∠B would be 45°

Step-by-step explanation:

Since m∠C is a right angle (90°) and m ∠B is half of a right angle, it would be 45°.

Answer: $ 7.20

Step-by-step explanation:

(9x4)/5

36/5

= 7.2

= $7.20

Answer:

A) 10-14

B) 45

C) 6.7%

Step-by-step explanation:

A) The interval that contain the most values can be gotten by looking at the histogram and selecting the interval with the highest frequency. Hence the interval 10-14 contains the most values because it has a frequency of 20.

B)The total number of swimmers is gotten by summing all the frequency of each individual lap. Hence:

Total swimmers on team = 10 + 12 + 20 + 0 + 3 = 45 swimmers

C) The percentage of swimmers who swam more than 14 laps = (number of swimmers that swam more than 14 laps/total swimmers) * 100%

The percentage of swimmers who swam more than 14 laps = [(0 + 3)/45] * 100% = (3/45) * 100% = 6.7%

The area of the shaded region in terms of the integrals is: (a) 12.5 (b) A = 5/2= 2.5

The shaded region is bound by the x-axis and the line y = 5x. To find the equation of this line, we can set y = 5x and solve for x in terms of y:

x = y÷5

To find the area of the shaded region with respect to x, we need to integrate the function with respect to x. The bounds of integration will be from 0 to the x-value of the line y = 5x.

the integral with respect to x is:

\(∫[0, 5] y/5 dx\)

To find the area of the shaded region with respect to y, we need to integrate the function with respect to y. The bounds of integration will be from 0 to the y-value of the line x = 5y.

\(∫[0, 1] 5y dy\)

Simplifying the integrals:

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Answer:

f(-3) = 6

Step-by-step explanation:

\(f(-3)=\frac{2}{3} (-3)+8=\frac{2(-3)}{3} +8=-\frac{6}{3}+8= -2+8=6\)

Hope this helps.

Answer:

f(x) = 6

Step-by-step explanation:

f(-3) means replace the x in f(x) with a -3, and replace every x in the equation with -3.

f(-3) = (2/3)x + 8

      = (2/3) (-3) + 8

      = (2 X -3)/3 + 8

      = -6/3   + 8

      = - 2 + 8

      = 6

Value = -3.5

The answer would be -15.95°

Rounded

The answer would be -16°

The polynomial k - 6k + 12k² - 3k⁵ when categorized is a fifth-degree polynomial

The expression of the polynomial from the question is given to be

k - 6k + 12k² - 3k⁵

When the terms of the polynomial are rearranged, the polynomial becomes

-3k⁵ + 12k² + k - 6k

Evaluate the like terms to reduce the expresson to minimum

-3k⁵ + 12k² -5

The degree of the above polynomial is 5

This means that, the polynomial is a fifth-degree polynomial with coefficients -3, 0, 0, 12, and -5

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The wire that connects the top of the tower to the point of the ground is thus the hypotenuse and its length is 84 foot.

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Given that the height of the tower is 168 foot, and the angle is 30 degrees.

The wire that connects the top of the tower to the point of the ground is thus the hypotenuse.

To find the hypotenuse, we use the trigonometric ratios as follows:

Sin 30 = 168 / Hypotenuse

0.5 = 168 / Hypotenuse

Hypotenuse = (168)(0.5)

Hypotenuse = 84.

Hence, the wire that connects the top of the tower to the point of the ground is thus the hypotenuse and its length is 84 foot.

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Step-by-step explanation:

-4x-10 willl be the answer I think question is not complete it should be equal to 0 or something

-4x - 10

The properties of equality allow us to simplify algebraic expressions.

Distributive Property

In order to simplify the expression, the first thing we need to do is simplify the parentheses. One of the properties of equality is the distributive property. The distributive property states that we can multiply each term inside the parentheses individually. This means that:

So, we can rewrite the expression as -4x - 4 - 6.

Combining Like Terms

The next step in simplifying the expression is combining like terms. Like terms are terms that contain the same variable to the same power. By this definition, all constants are like terms. So, we can combine -4 and -6 in order to rewrite the equation.

The fully simplified expression is -4x - 10. This expression can also be factored into the form -2(2x + 5).

Answer:

-8

Step-by-step explanation: