How to solve step by step

The expected number of classes a student will take in a given semester is 1.89

Expected value is defined as the predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.

Given :

x|  0       1        2       3      45  

p| 0.4 0.25  0.15  0.08  0.02

where x = number of classes

p = probability

The expected value of x, E(x) =Σ xp

E(x) = (0×0.4) + (1×0.25) + (2×0.25) + (3×0.08) + (45×0.02)

E(x) = 0 + 0.25 + 0.5 + 0.24 + 0.9

E(x) = 1.89

Therefore, the expected number is 1.89.

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Answer:

6.4

Step-by-step explanation:

I guessed and got it right.

Answer:

Step-by-step explanation:

Velocity = distance / time

In this problem, we need to calculate for distance, knowing time and velocity.

multiply time on both sides, on the right side the time will cancel out leaving time alone.

velocity * time = distance

40m/s * 0.46s = distance

distance = 18.4 meters

Hope it helped!

Answer:

SAS

Step-by-step explanation:

We now that 2 sides are congruent because of the congruent marker, and the bases of the triangles are the same, meaning they are congruent. And we also have a congruent pair of angles. So we can tell if they are congruent by using the SAS theorem.

-Hope this helped

Answer:

Total Cost = $186

Step-by-step explanation:

All but 8 means that All of them participated except for 8 of them

Since there is 39 Students in the Club

Then the Number of Students participated = 39 - 8 = 31 Students

Total Cost = (Cost per Student ) * ( Number of Students )

                 =$6 * 31 = $186

Glad to Help

Answer:

a = [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

[tex]\frac{a}{4}[/tex] - [tex]\frac{5}{6}[/tex] = - [tex]\frac{1}{2}[/tex]

multiply through by 12 ( the LCM of 4, 6 and 2 ) to clear the fractions

3a - 10 = - 6 ( add 10 to both sides )

3a = 4 ( divide both sides by 3 )

a = [tex]\frac{4}{3}[/tex]

Answer:

[tex]a=\frac{4}{3}[/tex]

Step-by-step explanation:

Move all terms not containing [tex]a[/tex] to the right side of the equation.

Add [tex]\frac{5}{6}[/tex] to both sides of the equation.

[tex]\frac{a}{4}=-\frac{1}{2} +\frac{5}{6}[/tex]

To write [tex]-\frac{1}{2}[/tex]  as a fraction with a common denominator, multiply by [tex]\frac{3}{3}[/tex].

[tex]\frac{a}{4}=-\frac{1}{2}*\frac{3}{3} +\frac{5}{6}[/tex]

Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.

[tex]\frac{a}{4}=-\frac{3}{2*3} +\frac{5}{6}[/tex]

[tex]\frac{a}{4}=-\frac{3}{6} +\frac{5}{6}[/tex]

Combine the numerators over the common denominator.

[tex]\frac{a}{4}=\frac{-3+5}{6}[/tex]

Add [tex]-3[/tex] and [tex]5[/tex] .

[tex]\frac{a}{4}=\frac{2}{6}[/tex]

Cancel the common factor of [tex]2[/tex] and [tex]6[/tex].

Factor [tex]2[/tex] out of [tex]2[/tex].

[tex]\frac{a}{4}=\frac{2(1)}{6}[/tex]

[tex]\frac{a}{4}=\frac{2*1}{2*3}[/tex]

Cancel the common factor.

[tex]\frac{a}{4}=\frac{1}{3}[/tex]

Multiply both sides of the equation by [tex]4[/tex].

[tex]4\frac{a}{4} =4(\frac{1}{3})[/tex]

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of [tex]4[/tex].

[tex]a=4(\frac{1}{3})[/tex]

Simplify the right side.

Combine [tex]4[/tex] and [tex]\frac{1}{3}[/tex]

[tex]a=\frac{4}{3}[/tex]

The derivative of f(x) is option A.

What is derivative?

The instantaneous pace at which one quantity changes in relation to another is referred to as a derivative in mathematics.

Main Body:

Since the derivative of [tex]e^{x}[/tex] is just [tex]e^{x}[/tex] , application of the chain rule to a composite function with [tex]e^{x}[/tex] as the outside function means that:

         [tex]\frac{dy}{dx} (e^{f(x)} )= e^{f(x) }.f'(x)[/tex]

Now the derivative of 1/x = [tex]\frac{-1}{x^{2} }[/tex]

Hence derivative of f(x) = [tex]-e^{\frac{1}{x} } /x^{2}[/tex].

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The ΔABC placed on top of ΔADE, and having angles ∠ABC and ∠BAC congruent to ∠ADE and ∠DAE in ΔADE is similar to ΔADE. The side CB is 3 indicating that the side ED, which has a length of x = 5

Similar triangles are triangles that have similar (the same shape), such that one triangles has side lengths that are a constant multiple of the other.

Please find attached a possible drawing that is based on the parameters of the question

From the question and the drawing created with MS Word, we have;

Length of AB = 9

Side CB = 3

Segment BD = 6

∠ABC = ∠ADE = 90°

∠ABC ≅ ∠ADE by definition of congruency

From the drawing, ∠BAC ≅ ∠BAC by reflexive property of equality

Triangle ΔBAC is similar to triangle ΔDAE by AA similarity postulate

Segment AD = Segment AB + Segment BD by segment addition postulate

AD = 9 + 6 = 15

The pair of corresponding sides of similar triangles are proportional, therefore;

[tex]\dfrac{\overline{AB}}{\overline{AD}} = \dfrac{\overline{BC}}{\overline{DE}}[/tex]

Which gives;

[tex]\dfrac{9}{15} = \dfrac{3}{x}[/tex]

9 × x = 15 × 3 = 45

x = 45 ÷ 9 = 5

The  length of side ED, x = 5

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Answer: 12

Step-by-step explanation: Because 9 x 2 is 18, and 7 x 2 is 14, we want to multiply 6 by 2. This gives us the answer 12.

9 x 2 = 18

7 x 2 = 14

6 x 2 = 12

Answer:  The correct answer is D. (2.5,1.5)

Step-by-step explanation:

As noted in the graph, the lines intersect at the location where x=2.5 and y=1.5 in Quadrant I (both positive).

x is equal to 125°  in the triangle

The figure given here is a triangle. And we know that the sum of the angles in a triangle is 180°. So we can apply this concept by writing the expression below:

x + 25° + 30° = 180°

x + 55° = 180°

x = 180° - 55°

x = 125°

Therefore, the value of x is 125°. So x is equal to 125°

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The letter has reflection symmetry only. When one half of an object or form reflects the other half, this is known as reflection symmetry. The line where you cut is referred to as the line of symmetry, generating the two equal portions, and the two halves are reflections of one another.

Mirror symmetry, line symmetry, reflection symmetry, and mirror-image symmetry are all terms used in mathematics to describe symmetry with respect to a reflection. To put it another way, a figure with reflectional symmetry is unaffected by reflection. There is a symmetry line or axis in 2D and a symmetry plane in 3D.

A sort of symmetry that pertains to reflections is called reflection symmetry. Line symmetry and mirror symmetry are other names for reflection symmetry. If a figure has at least one line dividing it into two halves, one half is said to be the mirror image of the other half.

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Answer:

The equation for the slope-intercept form is y = 4x - 10

Hope this helps!

Step-by-step explanation:

Slope = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]   Equation = y = mx + b

The two points given are ( -5, 10 ) and ( 0, -10 ).

Putting in the values gives you [tex]\frac{-10-10}{0-(-5)} = \frac{-20}{5} =-4[/tex].

y = 4x + b, to find b, insert one of the points:

-10 = 4(0) + b    ->   -10 = 0 + b,    b = -10

Putting it all together gives you y = 4x - 10

Answer:

x = 14

Step-by-step explanation:

the inscribed angle JKL is half the measure of its intercepted arc, that is

83 = [tex]\frac{1}{2}[/tex] arc JL = [tex]\frac{1}{2}[/tex](9x + 40) ← multiply both sides by 2 to clear the fraction

166 = 9x + 40 ( subtract 40 from both sides )

126 = 9x ( divide both sides by 9 )

14 = x

Answer:

SA(surface area) of the rectangular prism is 1,510 in inches

Step-by-step explanation:

SA=2(lh+lw+hw)

2inch=24ft

lh=264

lw=336

wh=154

755*2=1,510

Jimmy will take 24 hours to do the given job alone.

What is the teamwork equation for problem solving?
Problems with teamwork are resolved using this technique. If the first person completes a task in 'A' units of time and a second person completes a task in 'B' units of time, they can complete a task in 'T' units of time together (total).
The teamwork equation can be applied, that is: (1/A) + (1/B) = (1/T)

Given, time taken by Britney to do the job individually = B = 12 hours
Also, time taken by Britney and Jimmy to do the job together = A = 8 hours
Let the time taken by Jimmy to do the job individually = A hours
Thus, using the equation established in the literature above and substituting the given values, we have:
(1/A) + (1/B) = (1/T) ⇒ (1/A) + (1/12) = 1/8 ⇒ 1/A = (1/8) - (1/12)
⇒ 1/A = (3/24) - (2/24) ⇒ 1/A = 1/24 ⇒ A = 24
Thus, Jimmy will take 24 hours to do the given job alone.

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Step-by-step explanation:

[tex]4pound \: roast \: = 140 \: minutes \\ 5 \: pounds \: roast \: = {?} \\ then cross multiplication \\ 140 \times 5 \: divide \: by \: 4 \\ 700 \div 4 = 175 \\ 5 \: pound \: roast \: take \: 175 \: minutes[/tex]

The recursive formula is an = a(n-1) +4. A recursive formula is one that defines each term in a sequence by using the term before it (s)

The sequence's first term

The pattern rule for obtaining any term from its preceding term

Recursive Arithmetic Sequence Formula

To find the nth term of an arithmetic sequence, use the recursive formula:

an = an-1 + d for n ≥ 2

Where

an is the nth term of a A.P.

d is the common difference.

Given:

14, 18, 22, 26, 30, …

a1 = 14

and, d = 18-14

d = 4

a2 = a1 + 4

a2 = 14 + 4 = 18

Similarly, going this way

an = a(n-1) +4

Hence, the recursive formula is an = a(n-1) +4

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Answer:

  45,000

Step-by-step explanation:

Given a 30 minute sample of a constant stream shows 2250 people entered the gate, you want an estimate of the total number of people through the gate in 10 hours.

A half-hour period is 1/20 of the 10-hour period the gate was open. The rate is assumed constant, so the 2250 people entering in that half-hour period is presumed to be 1/20 of the total attendance.

  20 · 2250 = 45000

The estimated festival attendance is 45,000 people.

The measure of the exterior angle of the triangle is 144 degrees.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Therefore, the measure of the two remote interior angles of a triangle are x - 10 and 4x + 4. The exterior angle of the triangle measures 3x + 54 .

Let's solve for the exterior angle.

x - 10 + 4x + 4 = 3x + 54

5x - 6 = 3x + 54

5x - 3x = 54 + 6

2x = 60

x = 60 / 2

x = 30

Therefore,

exterior angle = 3x + 54 = 3(30) + 54 = 90 + 54 = 144 degrees

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The different two-letter initials can people have using the upper case characters in the English alphabet is 676 (if no specifications are given)

The question has not specified other conditions so we have assumed it by cases and solved it

Case 1 -

“Everything” allowed, means that we are considering solutions like “AA” and “BA, AB”

If this is the case then there are => 26 x 26 = 676 Combinations,

Case 2-

No repetition allowed

Here, we are excluding cases like “AA, BB” etc so here we have

26 x 25 = 650 as our answer

Case 3-

no repetition allowed + unique set every time, So

here we will have ²⁶C₂ (this is basic combinatorics formula )

= (26 x 25)/2

= 325 combinations possible

Case 4 -

Repetition allowed + unique set every time

here we will assume along with the uniqueness of each combination we will add Repeated combinations, Here we have “AA, BB, CC,……..ZZ” 26 new combinations along with unique ones So,

²⁶C₂+ 26 = 325 + 26 = 391 possible cases.

and I would recommend adding more detail to your question specifying the conditions in a better way, but the technically correct answer to your questions if no conditions are CASE 1.

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The correct multiplication of 1.8 and 2.4 will be 4.32.The product 0.432 calculated by Maura was incorrect.

For the given question-

Maura divide 1. 8 by 2. 4 and enter 0. 432 as the result.

Tom claims her product is unreliable.

Tom is able to make this deduction without the need for multiplication because the value 0.432 is less than even 1.8, which is not conceivable.

Thus,when multiplying by a number bigger than 1, the result will always be greater than the starting numbers.

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The equation the function after the transformation is (c) g(x) = -√x  - 3

The equation of the function is given as

f(x) = √x ---- i.e the square root parent function

The sequence of transformations is given as follows:-

When the above transformations are combined, we have:

Translate up by 3 units: g(x) = f(x) + 3

Reflection across the x-axis: g(x) = -(f(x) + 3)

So, we have

g(x) = -(√x + 3)

Expand

g(x) = -√x  - 3

Hence, the function g(x) is (c) g(x) = -√x  - 3

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Answer: g= 61/5 or 12.2

Step-by-step explanation:

The percentage that Richard get is 8%

The statement can be interpreted as:

He answered 52 correctly from a total of 65 questions

From the above statement, we have the following parameters

Dividend = 52

Divisor  = 65

The percentage is then calculated as

Percentage = Dividend/Divisor  x 100%

Substitute the known values in the above equation

So, we have

Percentage = 52/65 x 100%

Evaluate the quotient

Percentage = 0.8x 100%

Evaluate the product

Percentage = 8%

Hence, the percentage is 8%

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The solutions to the equation [tex]2x^{2} +3x=-8\\[/tex] are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex] respectively.

What is a quadratic equation?

A second-degree algebraic equation is a quadratic equation in x.

[tex]ax^{2} +bx+c=0[/tex] is the quadratic equation in standard form, where a and b are the coefficients, x is the variable, and c is the constant term.

To find the root value of x, [tex]x= \frac{-b}{2a}[/tex] ± [tex]\frac{\sqrt{b^{2} -4ac} }{2a}[/tex]

Given, [tex]2x^{2} +3x=-8\\[/tex]

or, [tex]2x^{2} +3x+8=0[/tex]

Comparing the equation [tex]2x^{2} +3x+8=0[/tex] with the equation  [tex]ax^{2} +bx+c=0[/tex] , we get

[tex]a=2, b=3, c=8[/tex]

Then, [tex]x= \frac{-3}{2*2}[/tex] ± [tex]\frac{\sqrt{3^{2} -4*2*8} }{2*2}[/tex]

or,  [tex]x= \frac{-3}{4}[/tex] ± [tex]\frac{i\sqrt{55} }{4}[/tex]

Taking '+' sign, we get [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex]  and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex]

Therefore, the solutions of the given equation are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex].

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An airplane can fly 374.4 miles in 3 hours.

A small airplane flew 104 miles in 50 minutes.

So, the rate would be,

rate  = distance / time

rate = 104/50

rate = 2.08 miles/minute

We need to find the distance the airplane can flay in 3 hours.

3 hours = 180 minutes

t = 180 minutes

r = d/t

2.08 = d/180

d = 2.08 * 180

d = 374.4 miles

Therefore, an airplane can fly 374.4 miles in 3 hours.

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