3 5/10 as a improper fraction

When the expected value and variance are 3.5 and 15.25, the statistic probability distribution will be 5/10, 3/10, and 2/10.

Given that,

A box contains ten sealed envelopes labelled 1, 2, 3, and 10. Six of them are empty, two have $5 apiece, and the remaining two each contain a $10 bill. You obtain the most money in any chosen envelope when replacement is used; a sample of size 3 is selected (forming a random sample). The statistic of interest is m if the quantities in the selected envelopes are represented by x1, x2, and x3.

We know that,

The probability distribution will be

P(X=0) = 5/10

P(X=5) = 3/10

P(X=10) = 2/10

In probability theory, the expected value is a development of the weighted average. The arithmetic mean of a sizable number of outcomes of a random variable that were independently selected is, informally, the expected value.

The expected value is

E =0(5/10)+5(3/10)+10(2/10) = 3.5

The variance is

V = 0² x (5/10) + 5² ( 3/10 ) + 10² x (2/10) - 3.5² = 15.25

Therefore, the statistic probability distribution will be 5/10, 3/10, and 2/10 when the expected value and variance are 3.5 and 15.25.

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Answer:

An candy shop sells a box of chocolate for $30

Step-by-step explanation:

I used grammerly this BETTR be right.

Answer:

The improper way is "A candy shop sells chocolates for $30 each

Step-by-step explanation:

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following functions:

We calculate each operation, just like this:

Answer:

x=13

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    (2*x+14)-((3*x+1))=0

1.1      Solve  :    -x+13 = 0

Subtract  13  from both sides of the equation :

                     -x = -13

Multiply both sides of the equation by (-1) :  x = 13

Answer:

\(P(3\ or\ c) = 0.45\)

Step-by-step explanation:

Given

See attachment for spinner

Required

\(P(3\ or\ c)\)

From the first spinner, we have:

\(S = \{1,2,3,4,5\}\) --- Sample Space

\(n(S)=5\)

So, P(3) is:

\(P(3) = \frac{n(3)}{n(S)}\)

\(P(3) = \frac{1}{5}\)

\(P(3) = 0.20\)

From the second spinner, we have:

\(S = \{a,b,c,d\}\)

\(n(S) = 4\)

So, P(c) is:

\(P(c) = \frac{n(c)}{n(S)}\)

\(P(c) = \frac{1}{4}\)

\(P(c) = 0.25\)

The required probability is then calculated as:

\(P(3\ or\ c) = P(3) + P(c)\)

\(P(3\ or\ c) = 0.20 + 0.25\)

\(P(3\ or\ c) = 0.45\)

for the slope, the equation is:

in case you have two points

The equation of the line equation:

If you want to find the interception in x-axis, you have to change the y for a 0, like this

If you want to find the interception in y-axis, you have to change the x for a 0, like this, that is "b" in the equation

Since the values of \(\hat{p}_1, \hat{p}_2, n_1\), and n_2 are not given, it is not possible to determine the exact 95% confidence interval estimate.

A 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on a social networking site can be calculated using the formula for a difference in proportions:

\($$\hat{p}_1 - \hat{p}_2 \pm z^* \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$$\)

where \($\hat{p}_1$\) and \($\hat{p}_2$\) are the sample proportions of women and men who trust recommendations, respectively, n_1 and n_2 are the sample sizes of women and men, and z^* is the critical value from the standard normal distribution for a 95% confidence level (approximately equal to 1.96).

Since the values of \(\hat{p}_1, \hat{p}_2, n_1\), and n_2 are not given, it is not possible to determine the exact 95% confidence interval estimate.

However, this formula can be used to calculate the estimate once the sample data is available.

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Answer:

Check Explanation

Step-by-step explanation:

- Write a statement that interprets that prediction interval.

The prediction interval (58.2 kg, 124.6 kg) represents the range of values that the true predicted weight for a height of 185 cm using the regression obtained from the data can actually, possibly take on to a certain level of confidence.

- What is the major advantage of using a prediction interval instead of simply using the predicted weight of 91.4 kg​?

The prediction interval is better to use instead of just using a predicted weight because in computing the prediction interval, we consider all the factors, biases and significant factors that can introduce uncertainties into the regression used to just find the predicted weight.

So, the prediction interval is more encompassing and has a better chance of containing the true weight that corresponds to the height 185 cm because it incorporates so many things thay can go wrong with the regression into its computation unlike the predicted weight.

- Why is the terminology of prediction interval used instead of confidence​ interval?

This is because the interval is obtained from the regression results, used in predicting weights, given height.

Confidence interval is used for numerical distributions to estimate the interval of range of values where the true population mean can be found with a certain level of confidence.

Hope this Helps!!!

Interval values describes a range of values in which the the true or actual value will likely reside based on a certain level of Confidence.

1.)

Tbe prediction interval describes a range of values which will contain the actual value based on a certain level of confidence.

2.)

The prediction interval gives an interval estimate rather than a point estimate, which increases the probability of obtaining a true value.

3.)

The prediction interval is used instead of confidence interval, because it is concerned with prediction using a linear model while confidence interval is associated with estimating the population mean from a sample.

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Answer:

C

Step-by-step explanation:

10 = 10(4) - 30

10 = 40 - 30

10 = 10

Recall the trigonometric function tangent.

We can use either 30° or 60° as our basis for the angle. In this case, we will use 60° (using 30° works just as well, we just have to determine its corresponding opposite and adjacent sides)

Substitute these values to the tangent function and we have

Multiply both sides with square root of 8, to get rid of the fraction in the right side.

Recall that tan 60° = square root of 3 therefore

Given the formula

Hence, the probability that the student passes the second professor's class is 0.955.

Using the parallelogram law to find m, the value of m is 50°.

The parallelogram law states that the sum of the squares for a parallelogram's four sides is equal to the sum of the squares for its two diagonals.

The parallelogram must have equal opposed sides in Euclidean geometry.

If ABCD is a parallelogram, then AB = DC and AD = BC, the parallelogram law is stated as:

2(AB)² + 2 (BC)² = (AC)² + (BD)²

If the parallelogram is a rectangle, the parallelogram law is stated as:

2(AB)² + 2 (BC)² = 2(AC)²

The value of the unknown angles in the parallelogram are as follows:

CED = 180 - (60 + 33 + 37)

CED = 50°

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Answer:

52.5 inch square

Step-by-step explanation:

Area of pentagon: A = 1/2 × p × a;

where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.

A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5

The area of the regular pentagon with apothem 3.5 and side 6 is 52.5

In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.

Given the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.

In order to find the area, the formula to calculate the area of the regular pentagon is given by:

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

Now,

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5\)

\(\text{Area of pentagon} =52.5\)

Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5

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Answer:

---------------------------------

Answer:

$582.68

Step-by-step explanation:

Total amount will be,

→ $266.63 + $317.29 + $62.78

→ 266.63 + 380.07

→ $646.7

Then the final price will be,

→ ($646.7 - 15%) + 6%

→ (646.7 - (646.7/100) × 15) + 6%

→ (646.7 - 97.005) + 6%

→ 549.695 + (549.695/100) × 6

→ 549.695 + 32.9817

→ 582.6767

→ $582.68

Hence, the answer is $582.68.

Answer:

option 3

Step-by-step explanation:

4x+8<-16

x<-6

4x+8_>-16

x_>-1

(it's more and equal .so the circle has to be shaded and move to the right of -1)

Answer:C

Step-by-step explanation:

After solving, the regular singular points are x=0, 5i, -5i.

We have to determine the singular points of the given differential equation. Classify each singular point as regular or irregular.

(x^3+25x)y"–5xy'+6y = 0

On comparing with the equation P(x)y''+Q(x)y'+R(x)y=0

P(x) = (x^3+25x)

P(x)=0

x^3+25x = 0

x=0, 5i, –5i be the singular point.

Now write equation 1 in the standard form

Divide by x^3+25x on both side, we get;

y"–5x/(x^3+25x) y'+6/(x^3+25x) y = 0

y"–5/(x^2+25) y'+6/x(x^2+25) y = 0

Comparing with the standard form of equation;

y''+P(x)y'+Q(x)y = 0

P(x) = –5/(x^2+25)      Q(x)=6/x(x^2+25)

We know that if \(\lim_{x \to x_{o}}(x-x_{o})p(x)\text{ and }\lim_{x \to x_{o}}(x-x_{o})^2q(x)\) exist finite. Then the singular point \(x_{o}\) is regular singular point else irregular singular point.

(a) At \(x_{o}\)=0

\(\lim_{x \to 0}(x-0)p(x)=\lim_{x \to 0}\frac{-5x}{x^2+25}\)

\(\lim_{x \to 0}(x-0)p(x)\) = 0 (Finite)

\(\lim_{x \to 0}(x-0)^2p(x)=\lim_{x \to 0}\frac{6x^2}{x(x^2+25)}\)

\(\lim_{x \to 0}(x-0)^2p(x)=\lim_{x \to 0}\frac{6x}{(x^2+25)}\)

\(\lim_{x \to 0}(x-0)p(x)\) = 0 (Finite)

So x=0 is a regular singular point.

(b) At \(x_{o}\)=5i

\(\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{-5(x-5i)}{(x+5i)(x-5i)}\)

\(\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{-5}{(x+5i)}\)

\(\lim_{x \to 5i}(x-5i)p(x)\) = -1/i (Finite)

\(\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{6(x-5i)^2}{x(x+5i)(x-5i)}\)

\(\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{6(x-5i)}{x(x+5i)}\)

\(\lim_{x \to 5i}(x-5i)p(x)\) = 0 (Finite)

So x=5i is a regular singular point.

(c) At \(x_{o}\)=-5i

\(\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{-5(x+5i)}{(x+5i)(x-5i)}\)

\(\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{-5}{(x-5i)}\)

\(\lim_{x \to -5i}(x+5i)p(x)\) = 1/i (Finite)

\(\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{6(x+5i)^2}{x(x+5i)(x-5i)}\)

\(\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{6(x+5i)}{x(x-5i)}\)

\(\lim_{x \to -5i}(x+5i)p(x)\) = 0 (Finite)

So x=-5i is a regular singular point.

Hence, the regular singular points are x=0, 5i, -5i.

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Answer

Given the 2 equations

x = y + 4 → (1)

2x - 3y = - 2 → (2)

Substitute x = y + 4 into (2)

2(y + 4) - 3y = - 2 ← distribute and simplify left side

2y + 8 - 3y = - 2

- y + 8 = - 2 ( subtract 8 from both sides )

- y = - 10 ( multiply both sides by - 1 )

y = 10

Substitute y = 10 into (1) for corresponding value of x

x = 10 + 4 = 14

Solution is (14, 10 ) → D

Step-by-step explanation:

Answer:

x=3

x=3y=1

I hope this helps!

Step-by-step explanation:

x+y=4

2x-3y=3

y = 4-x

2x-3(4-x) = 3

2x-12+3x = 3

5x = 15

x = 3

y = 4-x

4-3 = 1

y = 1

Answer:

The answer is b

Step-by-step explanation:

Answer:

10.79 m

Step-by-step explanation:

The relationship between the area A of a square and the side S is given as

A = S²

Where A is measured in Units square and S is measured in Units.

As such, given that the area of the square lawn is  72 796/625m^2. If the length of each side of the lawn is S then

72 796/625m^2 = S²

S = √( 72 796/625m^2)

S = 10.79 m

Each side of the lawn is 10.79 m long

Answer:

Σ( xi ) / n ; $29

Step-by-step explanation:

Given the following data:

X= $27, $31, $30, $26, $25, $27, $37, $33, $32, $28, $26, $26

Number of observations (n) = 12

Mean formula (m) = ( Σ xi ) / n

Where i = each individual value in X

Mean water bill for the years is thus :

m = Σ [(27 + 31 + 30 + 26 + 25 + 27 + 37 + 33 + 32 + 28 + 26 + 26)] / 12

m = 348 / 12

m = 29

Hence, the mean water bill for the year is $29

Answer:

Mathwords: Multiplicity. How many times a particular number is a zero for a given polynomial. For example, in the polynomial function f(x) = (x – 3)4(x – 5)(x – 8)2, the zero 3 has multiplicity 4, 5 has multiplicity 1, and 8 has multiplicity 2.

Extra:

How do you find the multiplicity?

Image result for Multiplicity example

The factor is repeated, that is, (x−2)2=(x−2)(x−2), so the solution, x=2, appears twice. The number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity. The zero associated with this factor, x=2, has multiplicity 2 because the factor (x−2) occurs twice.

HOPE THIS HELPS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial has a root at a given point is the multiplicity of that root.

Step-by-step explanation:

Answer:

\(g(x) = 30\cdot x +40\); \(a \approx 1.898\), \(k = 40\).

Step-by-step explanation:

The resultant function is obtained by multiplying \(f(x)\) by a real number \(k\). That is:

\(g(x) = k \cdot f (x)\)

If \(k = 5\) and \(f(x) = 6\cdot x + 8\), then \(g(x)\) is:

\(g(x) = 5\cdot (6\cdot x + 8)\)

\(g(x) = 30\cdot x +40\)

Given that presence of the expression \(g(x) = 6^{a}\cdot x + k\), then:

\(6^{a} = 30\) and \(k = 40\)

The value of a is obtained by applying the definition of logarithms:

\(a = \log_{6}30\)

\(a \approx 1.898\)

Finally, the value of k is found by direct comparison:

\(k = 40\)

Answer: 1/5 and 8

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Answer:

\(4^2=5^2+7^2-2(5)(7) cos A\\\\\)

\(A=34.0^o\)

-----------------

\(\frac{4}{Sin34^o} =\frac{5}{SinB} \\\\\)

\(B=44.4^o\)

--------------

\(7^2=4^2+5^2-2(4)(5)CosC\)

\(C= 101.5^o\)

\(---------\)

hope it helps...

have a great day!!

All the missing elements of the triangle by the Cosine rule are A = 40°, B = 45°, and C = 102°.

Given that,

Three sides on a triangle are,

a = 4

b = 5

c = 7

Used the formula of the Cosine rule which states that,

a² = b² + c² - 2bc cos A

b² = a² + c² - 2ac cos B

c² = a² + b² - 2ab cos C

Where, a, b, and c are three sides and A, B, and C are angles of a triangle.

Now, apply the Cosine rule to find the all angles of a given triangle,

a² = b² + c² - 2bc cos A

Substitute a = 4, b = 5 and c = 7,

4² = 5² + 7² - 2 × 5 × 7 cos A

16 = 25 + 49 - 70 cos A

70 cos A = 74 - 16

70 cos A = 58

Divide both sides by 58,

cos A = 58/70

cos A = 0.83

A = cos ⁻¹ (0.83)

A = 33.9°

Round to the whole number,

A = 40°

b² = a² + c² - 2ac cos B

Substitute a = 4, b = 5 and c = 7,

5² = 4² + 7² - 2 × 4 × 7 cos B

25 = 16 + 49 - 56 cos B

25 = 65 - 56 cos B

56 cos B = 65 - 25

56 cos B = 40

cos B = 40/56

cos B = 0.71

B = cos ⁻¹ (0.71)

B = 44.7°

Round to the whole number,

B = 45°

c² = a² + b² - 2ab cos C

Substitute a = 4, b = 5 and c = 7,

7² = 4² + 5² - 2 × 4 × 5 cos C

49 = 16 + 25 - 40 cos C

49 = 41 - 40 cos C

40 cos C = 41 - 49

40 cos C = - 8

cos C = - 8/40

cos C = - 1/5

cos C = - 0.2

C = cos ⁻¹ (0.2)

C = 101.5°

Round to the whole number,

C = 102°

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We must construct a polynomial with the following characteristics:

0. degree: 3,

1. zeros: x₁ = -3, x₂ = -1 and x₃ = 2,

2. passes through the point (3, 5).

The general form for this polynomial is:

Where a is a constant factor and x₁, x₂ and x₃ are the zeros of the polynomial.

Replacing the values of the zeros, we have:

Using the condition that the polynomial passes through (3, 5), we have:

Solving for a, we get a = 5/24. Replacing this value in the equation above, we get:

If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~

The roots of the quadratic equation \(3x^2 - 14x - 5 = 0\), in exact square root form, are x = 5 and x = -1/3.

Using the quadratic formula to solve the quadratic equation \(3x^2 - 14x - 5 = 0\),we have

\(x = (-(-14) ± sqrt((-14)^2 - 4(3)(-5))) / (2(3))\\x = (14 ± sqrt(14^2 + 4(3)(5))) / (2(3))\\x = (14 ± sqrt(196 + 60)) / 6\\x = (14 ± sqrt(256)) / 6\\x = (14 ± 16) / 6\\\)

Therefore, the two roots of the quadratic equation in exact square root form are:

\(x = (14 + 16) / 6 = 5\\x = (14 - 16) / 6 = -1/3\\\)

Thus, the roots of the quadratic equation \(3x^2 - 14x - 5 = 0\), in exact square root form, are x = 5 and x = -1/3.

A quadratic equation is a second-degree polynomial equation in one variable of the form:

\(ax^2 + bx + c = 0\)

where x is the variable, and a, b, and c are constants. In this equation, the highest power of x is 2, and it is called the coefficient of x^2. The coefficient of x is b, and the constant term is c.

The quadratic equation is called "quadratic" because the highest power of x is a square (i.e., x^2), and the graph of the equation is a parabola.

The quadratic equation can have zero, one, or two real solutions, depending on the values of a, b, and c. The solutions can be found by using the quadratic formula:

\(x = (-b ± √(b^2 - 4ac)) / 2a\)

where the symbol ± means "plus or minus" and the square root is of the discriminant (b^2 - 4ac).

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F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.

If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.

Explanation:

Instance 1

Inverse functions of both functions can be found using the first method.

Example.

Inverse of f (x) = x + 7 is what we're looking for.

We attempt to determine x using the equation y = x + 7.

y = x + 7

Inferring that g (x) is the inverse of f (x) from the fact that x = y 7

Finding g (x inverse )'s is now necessary.

g( x ) = x − 7

y = x − 7

x = y + 7

As a result, we discovered that f (x) is the inverse function of g (x).

f and g are equal if g is inverse of f and vice versa.

The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.

Example:

f ( g ( x ) =  [ x − 7 ] + 7

G ( x ) placed as x is the expression in brackets.

f ( g ( x ) ) = x − 7  + 7 = x

g (f ( x ) =  [ x + 7 ] − 7

f ( x ) inserted as x is the expression in brackets.

g ( f ( x ) ) = x + 7 − 7 = x

The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.

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