a binomial experiment with probability of success =p0.7 and =n7 trials is conducted. what is the probability that the experiment results in exactly 6 successes?

The null hypothesis for the chi-Squared test of independence is that the variables are independent.

In statistical analysis, the chi-squared test of independence is used to determine if there is a relationship between two categorical variables. The null hypothesis assumes that the variables are independent of each other, meaning that there is no association or relationship between them.

To conduct the test, we gather data and organize it into a contingency table, which displays the frequencies or counts of each combination of values for the two variables. The chi-squared test then calculates the expected frequencies under the assumption of independence, based on the observed frequencies.

The test statistic, known as the chi-squared statistic, measures the discrepancy between the observed and expected frequencies. If the observed frequencies deviate significantly from the expected frequencies, we reject the null hypothesis and conclude that there is evidence of a relationship between the variables.

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Answer:

1.50 $

Step-by-step explanation:

Hope this helps!

When a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

It's important to note that pressure increases as depth increases under water. The pressure in pounds per square foot, P, at a depth of d feet is given by the equation:

P = 0.433d + 14.7 where 0.433 is a constant for water, and 14.7 is the pressure at the surface.

In order to find the depth at which the pressure is 159 pounds per square foot, we need to solve the equation for

d.P = 0.433d + 14.7

Substitute P = 159 and solve for

d.159 = 0.433d + 14.7

Subtract 14.7 from both sides.

144.3 = 0.433d

Divide both sides by 0.433 to isolate d.

d ≈ 333.06

Hence, when a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

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Answer:

(96–72)/12

24/12 = 2

D is the answer

Answer:

-3 ≤ 3x ≤ 6

To solve for "x", we can divide each part of the inequality by 3:

-1 ≤ x ≤ 2

Therefore, the number "x" must lie between -1 and 2 in order to satisfy the condition in the sentence.

Step-by-step explanation:

The Taylor polynomial error bound provides an upper bound on the error between a Taylor polynomial approximation and the actual function value within a given interval.

Specifically, it guarantees that the absolute value of the difference between the actual function value and the Taylor polynomial approximation is no more than the maximum value of the absolute value of the (n+1)th derivative of the function within that interval, multiplied by the maximum distance between the point of approximation and the center of the Taylor series expansion. In other words, the error bound guarantees that the error in using the Taylor polynomial approximation is no larger than a certain value, which can be computed using the given formula.

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Algebraic expression for the length of Anna Quilt is X - 3. Here's the solution in more than 100 words.An algebraic expression is a mathematical phrase that contains letters, numbers, and arithmetic operations.

It can be solved by substituting values in place of the letters and performing the operations.In this problem, we are given that Anna and Diana are each making a quilt. The length of Anna Quilt is 3 fewer squares than X, which means we need to write an algebraic expression for the length of Anna's quilt.

Let's suppose the length of X is L. Then the length of Anna's quilt would be 3 fewer squares than L, which means it would be L - 3. However, since we are asked to write the expression in terms of X, we need to substitute L with X in the expression. Thus, the length of Anna's quilt as an algebraic expression is X - 3.So, X - 3 is the answer to this question.

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The value of "a" is approximately 1.83 given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive.

We are given that the absolute value of the difference between the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive. We need to find the value of "a".

Let the two roots of the equation be r1 and r2, where r1 is not equal to r2. Then, we have:

|r1 - r2| = √(61) / 3

The sum of the roots of the quadratic equation is given by r1 + r2 = -5 / a, and the product of the roots is given by r1 × r2 = -3 / a.

We can express the difference between the roots in terms of the sum and product of the roots as follows:

r1 - r2 = √((r1 + r2)² - 4r1r2)

Substituting the expressions we obtained earlier, we have:

r1 - r2 = √(((-5 / a)²) + (4 × (3 / a)))

Simplifying, we get:

r1 - r2 = √((25 / a²) + (12 / a))

Taking the absolute value of both sides, we get:

|r1 - r2| = √((25 / a²) + (12 / a))

Comparing this with the given expression |r1 - r2| = √(61) / 3, we get:

√((25 / a²) + (12 / a)) = √(61) / 3

Squaring both sides and simplifying, we get:

25 / a² + 12 / a - 61 / 9 = 0

Multiplying both sides by 9a², we get:

225 + 108a - 61a² = 0

Solving this quadratic equation for "a", we get:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61)

Since "a" must be positive, we take the positive root:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61) ≈ 1.83

Therefore, the value of "a" is approximately 1.83.

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The question is -

Given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive, what is the value of "a"?

This two points' required point slope equation is y -24 = -7 (x + 4).

A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its ascent, or vertical change, by its run, or horizontal change.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

According to our question-

x1,y1=4,-24

x2,y2=7,-53

m= -53-24/7+4

m= -7

equation is

y - 24 = -7 (x +4).

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Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer:

x

\( {x}^{2} - 3 \)

Answer:

a = 1.125

is your compleate full answer

Answer:

the factorised form is 4(8a+9)

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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If the function f (x) = 3 logx and g(x) \(=\) x² + 1 , then the value of composite function g[f(x)] is (3logx)² + 1 , the correct option is (a) .

In the question ,

it is given that ,

the function f(x) is

f(x) \(=\) 3logx

and the function g(x) is

g(x) \(=\) x² + 1 ,

the value of the composite function g[f(x)] will be

g[f(x)] = g(f(x))

Substituting the value of f(x) = 3logx , we get

g(f(x)) = g(3logx)

Substituting the value of 3logx in the place of x in the function  g(x) = x² + 1 ,

we get ,

= (3logx)² \(+\) 1

Therefore , If the function f (x) = 3 logx and g(x) = x² + 1 , then the value of composite function g[f(x)] is (3logx)² + 1 , the correct option is (a) .

The given question is incomplete , the complete question is

If f ( x ) = 3 log x and g( x ) = x² + 1 , find the value of composite function g[ f ( x )] .

(a) (3logx)² + 1

(b) 3log(x² + 1)

(c) 3(x² + 1)logx

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Answer:

C. Uniform circular motion is when a object travels on a circular path at a constant speed.

To partition a line segment with a given ratio, you can follow these steps:

1. Identify the two endpoints of the line segment. Let's call them point A and point B.

2. Determine the ratio in which you want to partition the line segment. For example, let's say the ratio is 2:1.

3. Use the ratio to divide the line segment into parts. To do this, you'll need to find a point, let's call it point C, that is a certain distance from point A and a certain distance from point B. The distance from point A to point C should be twice the distance from point C to point B.

4. To find point C, calculate the total length of the line segment by finding the distance between point A and point B. Let's say the length of the line segment is d.

5. Divide d by the sum of the ratio (2+1=3) to determine the length of each part. In this case, each part would be d/3.

6. Multiply the length of each part by the corresponding ratio factor to determine the distance from point A to point C. In this case, point C would be located at a distance of (2/3) * (d/3) from point A.

7. Similarly, multiply the length of each part by the remaining ratio factor to determine the distance from point C to point B. In this case, point C would be located at a distance of (1/3) * (d/3) from point B.

8. Once you have the coordinates of point C, you have successfully partitioned the line segment with the given ratio.

For example, let's say the line segment AB has a length of 12 units and we want to partition it with a ratio of 2:1. Using the steps above:

1. Identify the endpoints: A and B.
2. Ratio: 2:1.
3. Calculate each part: d/3 = 12/3 = 4 units.
4. Distance from A to C: (2/3) * (d/3) = (2/3) * 4 = 8/3 units.
5. Distance from C to B: (1/3) * (d/3) = (1/3) * 4 = 4/3 units.
6. Point C would be located at coordinates (8/3, 4/3) on the line segment AB.

Remember, these steps can be modified based on the specific ratio you are given.

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Question- Partitioning a line segment, AB, into a ratio a/b involves dividing the line segment into a + b equal parts and finding a point that is an equal part from A and b equal parts from B. When finding a point, P, to partition a line segment, AB, into the ratio a/b, we first find a ratio c = a / (a + b)

The correct option is option (B) .

In a Multiple regression Model , the value of adjusted r-Squared is positive.

Adjusted r-Squared :

Adjusted r-squared is a modified version of r-squared adjusted for the number of predictors in the model. The fitted r-squared increases only if the new term improves the model beyond what would be expected by chance. This is reduced if the predictor happens to not improve the model more than expected.

The formula for r-squared,

Adjusted r-squared= 1 - [ ( 1 -r²)(n-1)/(n-k-1)]

where

N --> number of points in the data sample.

K --> number of independent regressors, i. number of variables in the model excluding or constant.

r²--> Indicates how well a term (data point) fits a curve or line.

r-squared values range from 0 to 1 and are commonly stated as percentages from 0% to 100%.

100% r-squared means that all movements in the security are completely explained by movements in the index.

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Answer:

I think the answer is 7 or 4

Probability is a branch of mathematics that deals with the measurement of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.

The events A and B are not independent.

To see this, note that the probability of A is given by:

\(P(A) = 1/2\) , since there are 6 ways to get an odd sum\((1+2, 2+1, 3+4\) ,   \(4+3, 5+6, 6+5)\) out of a total of 12 possible outcomes when rolling two dice.

The probability of B is also 1/2, since there are 3 odd numbers on a standard die and 6 possible outcomes for the second die.

Now, to calculate P(A ∩ B), we need to find the probability that both events A and B occur simultaneously.

This happens when we roll an odd sum (which has a 1/2 probability) and then get an odd number on the second die (which has a 1/2 probability). Multiplying these probabilities together, we get:

\(P(A ∩ B) = (1/2) * (1/2) = 1/4\)

Finally, we can check whether the events A and B are independent by comparing P(A ∩ B) to P(A)P(B):

\(P(A)P(B) = (1/2) * (1/2) = 1/4\)

Therefore, Since \(P(A ∩ B) ≠ P(A)P(B)\)  , we can conclude that the events A and B are not independent.

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Events A and B are not independent. Let A = {the sum of the dice is odd}, and let B = {the second die shows an odd number}.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

The probability of two events A and B being independent is determined by whether the occurrence of one event affects the occurrence of the other. In the given problem, event A is the sum of two dice being odd, and event B is the second die showing an odd number.

The probability of A and B occurring separately can be calculated, as can the probability of A and B occurring together. While P(A ∩ B) = P(A) * P(B), the events are not independent since knowing that one event has occurred affects the probability of the other event.

If A occurs, the probability of B changes, and if B occurs, the probability of A changes.

No, because P(A∩B) = P({1,3,5})∩P({1,3,5}) = P({1,3,5}) = 1/2, and P(A)P(B) = (1/2) * (1/2) = 1/4, which are not equal.

Therefore, events A and B are not independent.

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Answer:

x = 3

Step-by-step explanation:

5(5 + 19) = 6(6 + 4x + 2)

5(24) = 36 + 24x + 12

120 = 48 + 24x

72 = 24x

x = 3

As given by the question

There are given that the right angle triangle

Now,

From the triangle, first, find the value of ST

So,

To find the value of ST, use the sine function

Then,

Then,

Now,

To find the value of RS, use sine function also

So,

Hence, the value of ST and RS is shown below:

Answer:

f(5) = -7

Step-by-step explanation:

f(5) means that x=5 so what you have to do if count +5 along the x axis and then count downward along the y axis until you touch the line. In this case, you count 7 down which is -7

Answer: $9095.44

Step-by-step explanation:

Given:

P=7380

r=1.9% = .019

t= 11

V = P\(e^{rt}\)                               >substitute

V = 7380 \(e^{(.019)(11)}\)              >Plug into calculator

V= $9095.44

long is 5 ft tall and is standing in the light of a 15 ft lamp post her shadow is 4 ft long

To solve the given problem, let's proceed to the solution-

          We know that the Height of the girl = is 5 ft

          The height of the lamp post = is 15 ft

          The length of the shadow = is 4 ft

          Distance between the girl and the lamp post (initially) = 15 - 5 = 10 feet

  the distance between the girl and the lamp post (after walking) is x.

        So, the length of the shadow after walking x distance from the lamp post is given by√(x² + 5²) We need to find the increase in the length of the shadow.

      So, the increase in the length of the shadow is given by(√(x² + 5²) - 4) ft.

     We need to find this increase for x = 11. As x increases, the value of the above expression will also increase.

     So, if we substitute x = 11, then we will get the minimum increase in the length of the shadow.

     Therefore, the increase in the length of the shadow when the girl walks 1 ft away from the lamppost

            = (√(11² + 5²) - 4) ft

            = (sqrt(146)-4)ft ~ 10.6 ft.

  Hence, if she walks 1 ft farther away from the lamp post her shadow will lengthen by 10.6 ft.

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The volume of the cylinder is V = 6,430.72 yards³

Given data ,

Let the radius of the cylinder be r = d/2

r = 32/2 = 16 yards

Now , the height of the cylinder h = 8 yards

And , Volume of Cylinder = πr²h

On simplifying , we get

V = ( 3.14 ) ( 16 )² ( 8 )

V = 6,430.72 yards³

Hence , the volume is 6,430.72 yards³

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The values of z for the standard normal distribution are 1.17 and -1.17

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

Distribution type = standard normal distribution

The number z that has cumulative proportion 0.88.

This means that we calculate the z-score from the p-value

i.e p = 0.88

Using the z-score table of values, we have the following representation

z = 1.17

The number z such that the event z > z has proportion 0.12

This means that we calculate the z-score from the p-value

i.e. p = 0.12

Using the z-score table of values, we have the following representation

z = -1.17

Hence, the z-scores are 1.17 and -1.17

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The variable z follows a standard normal distribution. Let's solve the given problems step by step: (a) To find the number z that has a cumulative proportion of 0.88, we need to find the z-score that corresponds to this proportion. The cumulative proportion represents the area under the standard normal curve to the left of a given z-score.

Using a standard normal distribution table or a calculator, we can find the z-score associated with a cumulative proportion of 0.88. The z-score is approximately 1.175. Therefore, the value of z that corresponds to a cumulative proportion of 0.88 is approximately 1.175.

(b) To find the number z such that the event z > z has a proportion of 0.12, we need to find the z-score that corresponds to this proportion. The event z > z is equivalent to finding the area under the standard normal curve to the right of z. Using a standard normal distribution table or a calculator, we can find the z-score associated with a proportion of 0.12 to the right of z. The z-score is approximately -1.175.

Therefore, the value of z that corresponds to the event z > z having a proportion of 0.12 is approximately -1.175.

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Answer:

3

Step-by-step explanation:

dude kinda obv that its 3

Answer:

answer would be 3

Step-by-step explanation:

Answer:

29/35 less than 20/30

29/35 = 0.83

20/30 = 0.67