Given the venn diagram below, what is the correct notation?

Answer:

see below

Step-by-step explanation:

Modified problem

(x)^2-3/x

Step 1: Find f(x+h)

(x+h)^2-3/(x+h)

x^2 +2hx + h^2 -3/(x+h)

Step 2: Find f(x + h) − f(x)

x^2 +2hx + h^2 -3/(x+h) - ( x^2-3/x)

Distribute the minus sign

x^2 +2hx + h^2 -3/(x+h) -  x^2+3/x

Combine like terms and get a common denominator

2hx + h^2  -3x/(x(x+h)) +3(x+h)/(x(x+h)

2hx + h^2  +3h/(x(x+h))

Step 3: Find (f(x + h) − f(x))/h

(2hx + h^2+3h/(x(x+h)) )/h

2hx/h  + h^2/h+3h/(x(x+h)) /h

2x +h +3/(x(x+h))

Step 4: Find lim  h→0  (f(x + h) − f(x))/h

2x+0 +3/(x(x+0))

2x +3/x^2

Answer:

  [tex]\dfrac{6^2-3^2}{2}=\dfrac{27}{2}[/tex]

Step-by-step explanation:

You can go to the trouble to integrate y = x from 3 to 6, or you can figure the area geometrically.

  [tex]\displaystyle\int_3^6{x}\,dx=\left.\dfrac{x^2}{2}\right|_3^6=\dfrac{6^2-3^2}{2}\quad\text{using integration}\\\\A=\dfrac{1}{2}(b_1+b_2)h=\dfrac{1}{2}(6+3)(6-3)=\dfrac{6^2-3^2}{2}\quad\text{using geometry}[/tex]

Answer:

100

Step-by-step explanation:

The Volume of the Rectangular prism on the left is 60

The Volume of the Rectangular prism on the right is 40

Answer:

Your correct answer is 40

Step-by-step explanation:

Multiply 8 x 5.

8 x 5 = 40

MUltiply 40 x 1.

40 x 1 = 40

So, it stays the same. Anything multiplied by 1 stays the same.

Therefore, your correct answer is 40.

Answer:

0.006772

If the last dropping digit is less than 5 then it will be ignored

0.00677

if the last dropping digit is greater than 5 than the the last retained digit increases by 1

0.0068

if  the last dropping digit is greater than 5 than the the last retained digit increases by 1

0.007

if  the last dropping digit is greater than 5 than the the last retained digit increases by 1

0.01

if the last digit is less than 5 so it will be ignored

0.0 is significant figure because zero to the right of decimal point are significant

Step-by-step explanation:

i hope this will help you :)

Answer:

0.007

Step-by-step explanation:

Rounding off 0.006772 to 1 significant figures:

=> 0.007

There is only 1 significant figure in this , since the zeroes on the left are not counted as significant figures.

Answer:

∠2 = 75° because of alternate interior angles. Since ∠1 and ∠2 form a linear pair, they are also supplementary which means that ∠1 = 180 - ∠2 = 180 - 75 = 105°.

The value of angles are,

⇒ ∠1 = 105°

⇒ ∠2 = 75°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Now, We get;

∠2 = 75°

Because of alternate interior angles.

And, Since ∠1 and ∠2 form a linear pair,

Hence,  they are also supplementary which means that;

⇒ ∠1 = 180 - ∠2

⇒ ∠1 = 180 - 75

⇒ ∠1 = 105°

Thus, The value of angles are,

⇒ ∠1 = 105°

⇒ ∠2 = 75°

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Hey there! :)

Answer:

y = 7/2x - 11

Step-by-step explanation:

Use the slope formula to calculate the slope:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the coordinates:

[tex]m = \frac{10-(-4)}{6-2}[/tex]

Simplify:

[tex]m= \frac{14}{4}[/tex]

[tex]m = \frac{7}{2}[/tex]

Slope-intercept form is y = mx + b. Plug in the slope, as well as the coordinates of a point given to solve for b:

10 = 7/2(6) + b

10 = 42/2 + b

10 = 21 + b

10 - 21 = b

b = -11.

Write the equation:

y = 7/2x - 11

Volume before the gold:

3 x 2 x 4 = 24 cubic cm.

Volume after gold:

3 x 2 x 4.25 = 25.5 cubic cm

Volume of gold is the difference:

25.5 - 24 = 1.5 cubic cm.

Answer:

[tex] \angle B[/tex]

Step-by-step explanation:

[tex] \angle B[/tex] is included by AB and BC, because B is the common vertex in AB and BC,

Answer:

x + (4x-85) = 90

Step-by-step explanation:

The two angles are complementary which means they add to 90 degrees

x + (4x-85) = 90

Answer: A

Step-by-step explanation:

Both angles are makes a right angle which adds up to 90 degrees so they both have to add up to 90 degrees.

Answer:

Step-by-step explanation:

33.3%

19.4%

Hope you understand :)

Answer:

DF = 3.0

<E = 31°

<F = 59°

Step-by-step explanation:

1. Use the Pythagorean Theorem to find side DF.

a² + b² = c²

5² + b² = 5.83²

25 + b² = 33.9889

b² = 8.9889

b = √8.9889

b = 2.998149429

b = 3.0

Side DF is equal to 3.0.

2. Use SOHCAHTOA to find the measure of <E. We know two sides: adjacent (5) and hypotenuse (5.83). So, we will use cosine.

Cosine = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{5}{5.83}[/tex] = 0.8576329331

Take the inverse cosine to find <E in degrees.

cos⁻¹ (0.8576329331) = 30.95 = 31°

<E is equal to 31°.

3. Add the two angles and subtract from 180° or use SOHCAHTOA to find the measure of <F.

90° + 31° + x = 180°

121° + x = 180°

x = 59°

or

We know two sides: adjacent (3.0) and hypotenuse (5.83). So, we will use cosine.

Cosine = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{3.0}{5.83}[/tex] = 0.5145797599

Take the inverse cosine.

cos⁻¹(0.5145797599) = 59.03063031 = 59°

<F is equal to 59°.

Hope that helps. :)

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

There is a 0.9986 probability that a randomly selected 27​-year-old male lives through the year. A life insurance company charges ​$174 for insuring that the male will live through the year. If the male does not survive the​ year, the policy pays out ​$90 comma 000 as a death benefit. Complete parts​ (a) through​ (c) below.

a. From the perspective of the 27​-year-old ​male, what are the monetary values corresponding to the two events of surviving the year and not​ surviving?

b. If the  27  -year-old  male purchases the policy, what is his expected value?

c. Can the insurance company expect to make a profit from many such policies? Why?  From the point of view of the insurance company, the expected value of the policy is

Answer:

a. The life insurance company charges ​$174 for insuring if the male survives

Value(survive) = -$174

The life insurance company pays ​$90,000 for insuring if the male does not survive.

Value(not survive) = $89,826

b. The expected value for a 27-year-old male is

E(x) = -$48

c. The expected value for the insurance company is

E(x) = $48

Step-by-step explanation:

The probability that a randomly selected 27​-year-old male survives is given by

P(survive) = 0.99864

The probability that a randomly selected 27​-year-old male does not survive is given by

P(not survive) = 1 - P(survive)

P(not survive) = 1 - 0.99864

P(not survive) = 0.0014

a. From the perspective of the 27​-year-old ​male, what are the monetary values corresponding to the two events of surviving the year and not​ surviving?

If 27​-year-old ​male survives:

The life insurance company charges ​$174 for insuring if the male survives

Value(survive) = -$174

If 27​-year-old ​male does not survive:

The life insurance company pays ​$90,000 for insuring if the male does not survive.

Value(not survive) = $90,000 - 174

Value(not survive) = $89,826

b. If the  27-year-old male purchases the policy, what is his expected value?

The expected value for a 27-year-old male is given by

E(x) = P(survive)×Value(survive) + P(not survive)×Value(not survive)

E(x) = 0.9986×-174 + 0.0014×89,826

E(x) = -$48

The negative sign indicates that it is a loss from the perspective of the 27​-year-old ​male.

c. Can the insurance company expect to make a profit from many such policies? Why?  From the point of view of the insurance company, the expected value of the policy is

The expected value for the insurance company is given by

E(x) = 0.9986×174 + 0.0014×-89,826

E(x) = $48

The positive sign indicates that it is a profit from the perspective of the insurance company.

Answer:

Step-by-step explanation:

Hello!

(a) Which genre has the highest mean audience score? The lowest mean audience score?

1) Action [tex]\frac{}{X}_1[/tex]= 58.63

2) Comedy [tex]\frac{}{X}_2[/tex]= 59.11

3) Drama [tex]\frac{}{X} _3[/tex] = 72.10

4) Horror [tex]\frac{}{X}_4[/tex]= 48.65

The lowest mean score is  [tex]\frac{}{X}_4[/tex]= 48.65

The highest mean score is  [tex]\frac{}{X} _3[/tex] = 72.10

(b) Which genre has the highest median score? The lowest median score?

1) Action Me₁= 51.00

2) Comedy Me₂= 58.00

3) Drama Me₃= 72.00

4) Horror Me₄= 52.00

The Lowest median is Me₁= 51.00

The Highest median is Me₃= 72.00

(c) In which genre is the lowest score, and what is that score? In which genre is the highest score, and what is that score?

Lowest or minimum scores:

1) Action 32.00

2) Comedy 31.00

3) Drama 46.00

4) Horror 25.00

The genre with the lowest score is "Comedy"

Highest or maximum scores:

1) Action 93.00

2) Comedy 93.00

3) Drama 91.00

4) Horror 78.00

There are two genres with the highest score "Action" and "Comedy"

(d) Which genre has the largest number of movies in that category?

The number of movies for each category corresponds to the sample sizes:

1) Action n₁= 32

2) Comedy n₂= 27

3) Drama n₃= 21

4) Horror n₄= 17

The largest number of movies sampled was for the genre "Action"

(e) Calculate the difference in mean score between comedies and horror movies, and give notation with your answer, using i, for the mean comedy score and, for the mean horror score.

Comedy [tex]\frac{}{X}_C[/tex]= 59.11

Horror [tex]\frac{}{X}_H[/tex]= 48.65

[tex]\frac{}{X}_C[/tex] -  [tex]\frac{}{X}_H[/tex]= 59.11 - 48.65= 10.46

I hope this helps!

Answer:

3003

Step-by-step explanation:

We want to find out how many ways we can choose 10 players among 15 players (since the goalie is not interchangeable)

The number of different lineups you can have can be found by using combination:

[tex]^{15}C_{10} = \frac{15!}{(15 - 10)! 10!}\\ \\= \frac{15!}{5! * 10!} \\\\= 3003[/tex]

There are 3003 different lineups that can be chosen.

Answer:

Volume of a cylinder is πr²h

Where

r is the radius

h is the height

Volume = 154cm³

radius = 3cm

height = ? cm

154 = π × 3² × h

154 = π × 9 × h

154 = 9πh

divide both sides by 9π

h = 154/9π

h = 5.4cm

Height is 5.4cm

Hope this helps

Answer:

(A)6 kilometers

Step-by-step explanation:

First, we determine the value of a using Pythagoras Theorem.

[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\17^2=a^2+15^2\\a^2=17^2-15^2\\a^2=289-225\\a^2=64\\a^2=8^2\\a=8$ km[/tex]

Therefore:

Distance along the long route = 8 + 15 =23 km

Distance along the shortcut =17 km

Difference =23-17 =6km

Therefore, Mr. Jones bikes 6km less when he takes the shortcut instead of the long route.

Answer:

a

Step-by-step explanation:

on edge

Answer:

b and I will be there at work and I will be there at work and I will be there at work and I will

Step-by-step explanation:

you are not going to be able to make it to the meeting tonight but I can tomorrow if you have time

Answer:

Option (3)

Step-by-step explanation:

Glide reflection of a figure is defined by the translation and reflection across a line.

To understand the glide rule in the figure attached we will take a point A.

Coordinates of the points A and A' are (2, -1) and (-2, 4).

Translation of pint A by 5 units upwards,

Rule to be followed,

A(x, y) → A"[x, (y + 5)]

A(2, -1) → A"(2, 4)

Followed by the reflection across y-axis,

Rule to be followed,

A"(x, y) → A'(-x, y)

A"(2, 4) → A'(-2, 4)

Therefore, by combining these rules in this glide reflections of point A we get the coordinates of the point point A'.

Option (3) will be the answer.

Answer:Reflection along the line y= -1

Step-by-step explanation:

took test

Answer:

66

Step-by-step explanation:

30+25+5+6 = 66.

There are 66 students in the class.

Answer:

  -1.9

Step-by-step explanation:

The opposite of the opposite is the original number, -1.9.

It is located at -1.9 on the number line.

Answer:

a

Step-by-step explanation:

Answer:d

Step-by-step explanation:

Answer:

It is increasing and the x-intercept is (1,0) so F and E

Step-by-step explanation:

A P E X

The true statements are F and E

The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

We need to graph the log function. F(x) = log6x

Domain: x>0 All real number greater than 0.

Range: All real number.

y-intercept: Put x=0 and solve for y. (Does not exist)

y-intercept: Put y=0 and solve for x. (1,0)

Log function is increasing function.

F is true. (It is increasing)

D is False. (Because Range is all real number)

E is true. (x-intercept (1,0))

A is false. (It is decreasing.)

B is false. (The y-intercept is (0, 6))

C is false. (Domain is x>0)

Hence, F and E are true.

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Answer:

  5.793 s

Step-by-step explanation:

On average she swam 1/10 the distance in 1/10 the time.

She took an average of 5.793 seconds to swim 10 m.

___

10 m is 1/10 of 100 m

Answer:

$10452958

Step-by-step explanation:

Initial profit = $11900848

Fall rate= $48263 per year

Equation:

where P(x)= profit at year of x, and 1990<x<2020

Divide the profit by the percentage:

98 / 0.0425 = 2305.88

The cost was $2,305.88

Answer:

n = 32

Step-by-step explanation:

an = a1 + (n - 1)d

a4 = a1 + 3d = 16

a8 = a1 + 7d = 32

7d - 3d = 32 - 16

4d = 16

d = 4

a4 = a1 + 3d = 16

a1 + 3(4) = 16

a1 + 12 = 16

a1 = 4

an = 4 + (n - 1)4 = 128

4 + 4n - 4 = 128

4n = 128

n = 32

Answer:

[tex]\mathbf{1 + \dfrac{x^2}{2!}+ \dfrac{5}{24}x^4+\dfrac{61}{720}x^6}[/tex]

Step-by-step explanation:

From the given information:

we are to find the first four nonzero terms of the Maclaurin series of the given function.

Sec x.

If we recall ; we will realize that the derivative of sec x = [tex]\dfrac{1 }{cos \ x}[/tex]

Also; for cos x ; the first four terms of its Maclaurin Series can be expressed as ;

=[tex]1- \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!}+...[/tex]

However, using the long division method: we have;

[tex]\dfrac{1}{1- \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!}}[/tex]

the rule of the long division method is to first use the 1 from the denominator to divide the 1 from the numerator. the multiply it with the answer we get which is (1) before subtracting it from  that answer (1).

i.e

1/1 = 1

1 × 1 = 1

1 - 1 = 0

Afterwards; we will subtract the remaining integers from this numerator.

So, we have:

[tex]\dfrac{-(1 - \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!} )}{0+ \dfrac{x^2}{2!}-\dfrac{x^4}{4!}+ \dfrac{x^6}{6!}}[/tex]

We are going to apply the same process to the remainder [tex]\dfrac{x^2}{2!}[/tex];

which is to divide the second integer with 1

[tex]\dfrac{\dfrac{x^2}{2!}}{1}= \dfrac{x^2}{2!}[/tex]

Then we will multiply the numerator with [tex]\dfrac{x^2}{2!}[/tex] ; the result will then be subtracted from the polynomial.

[tex]= \dfrac{-( \dfrac{x^2}{2!} - \dfrac{x^4}{2! 2!} + \dfrac{x^6}{2! 4!}- \dfrac{x^8}{2! 6!}) }{0 + \dfrac{5}{24}x^4 - \dfrac{7}{360}x^6- \dfrac{x^8}{2!6!} }[/tex]

Repeating the same process for remainder  [tex]\dfrac{5}{24}x^4[/tex]; we have:

[tex]\dfrac{ \dfrac{5}{24}x^4 }{1}= \dfrac{5}{24}x^4[/tex]

so; we will need to multiply 1 with [tex]\dfrac{5}{24}x^4[/tex] and subtract it from the rest of the polynomial

[tex]=\dfrac{{0 + \dfrac{5}{24}x^4 - \dfrac{7}{360}x^6- \dfrac{x^8}{2!6!} }}{ 1-x^2+ \dfrac{x^4}{4!} - \dfrac{x^6}{6!} }[/tex]

[tex]= \dfrac {- ( \dfrac{5}{24}x^4 -\dfrac{5}{2!4!}x^6 - \dfrac{5x^8}{4!4!} - \dfrac{5x^{10}}{6!4!} } {0+ \dfrac{61}{720}x^6}[/tex]

Here ; the final remainder is [tex]\dfrac{61}{720}x^6}[/tex]; repeating the usual process for long division method; we have:

[tex]\dfrac{\dfrac{61}{720}x^6}{1}= \dfrac{61}{720}x^6}[/tex]

So;

[tex]= \dfrac{0+ \dfrac{61}{720}x^6}{1-x^2+ \dfrac{x^4}{4!} - \dfrac{x^6}{6!} }[/tex]

[tex]= \dfrac{-( \dfrac{61}{720}x^6)}{0 }[/tex]

Now the  first four nonzero terms of the Maclaurin series is the addition of all the integers used as remainders ; i.e

[tex]\mathbf{1 + \dfrac{x^2}{2!}+ \dfrac{5}{24}x^4+\dfrac{61}{720}x^6}[/tex]

Answer:

Step-by-step explanation:

Area of triangle = 1/2 × b × h

69.3 = 8.4 × h

h = 69.3 / 8.4

h = 8.25 mm

hope this helps

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Answer:

16.5mm

Step-by-step explanation:

1. 69.3 x 2

2. 138.6 divided by 8.4

3. solve which equals 16.5mm

Hope this helps you:)

Answer:

Step-by-step explanation:

[tex]\sqrt{-16}=\sqrt{16i^{2}}\\\\ =\sqrt{4^{2}*i^{2}}\\\\=4i[/tex]

Answer:

$25.00 + $10x = $115.00

Step-by-step explanation:

We know that the initial charge of joining is $25. Each class costs $10 each. She spent a total of $115. What we don't know is how many classes she took. With this equation, we can easily find out how many classes she took.