Find the area of the region enclosed by​ f(x) and the​ x-axis for the given function over the specified interval.

Answer:

18 is a composite number. 18 = 1 x 18, 2 x 9, or 3 x 6. Factors of 18: 1, 2, 3, 6, 9, 18. Prime factorization: 18 = 2 x 3 x 3, which can also be written 18 = 2 x 3².

All the prime factorization of 18 are,

⇒ 2, 3, 3

Because 2×3×3 = 18

We have to given that,

To find all the prime factorization of number 18.

Now, We need to find all the factors of 18.

Hence,

18 = 2 x 9

   = 2 x 3 x 3

Therefore, All the prime factorization of 18 are,

⇒ 2, 3, 3

Because 2×3×3 = 18

Learn more about the Greatest common factors visit:

https://brainly.com/question/219464

#SPJ6

Answer:

Step-by-step explanation:

you have to keep going cause if you count the fives there's a 25 but right next to the 25 there's 24 all you have to do is watch what your doing just watch your steps

Answer:

Please refer to the graph in the attached area.

Step-by-step explanation:

Given:

Total money available with the customer is $10.

Cost of each hotdog is $2.

Cost of each drink is is $2.50.

To find:

The graph of inequality.

Solution:

Let number of hotdogs bought = [tex]x[/tex]

Total cost of hotdogs = [tex]2x[/tex]

Let number of drinks bought = [tex]y[/tex]

Total cost of drinks = [tex]2.5y[/tex]

Total cost = [tex]2x+2.5y[/tex]

And total money available is $10.

So, the total cost calculated above must be lesser than or equal to $10.

Hence, the inequality is:

[tex]2x+2.5y<10[/tex]

Also there will be two conditions on variables [tex]x[/tex] and [tex]y[/tex]:

[tex]x\ge0\\y\ge0[/tex]

To graph this, let us find the points on the equivalent equation:

[tex]2x+2.5y = 10[/tex]

Finding two points on the equation.

First put x = 0 [tex]\Rightarrow[/tex] y = 4    

Then put y = 0, [tex]\Rightarrow[/tex] x = 5

So, two points are (0, 4) and (5, 0).

Now, plotting the line.

Having point (1,2) in the inequality:

2 + 5 < 10 (True) hence, the graph of inequality will contain the point (1,2)

Please refer to the graph of inequality in the attached graph.

Answer:

Option A - There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%

Step-by-step explanation:

The police officers claim is that the proportion of people wearing seat belts is less than 65%.

Now, we are told that the p - value is 0.277.

In hypothesis, for a significance value of 0.05, if the P value is less than 0.05, we reject the null hypothesis and if P value is greater than or equal to 0.05, we fail to reject the null hypothesis.

Now, since the significance level is 5% = 0.05,we can see that the P-value is greater than the significance value of 0.05. Thus, we fail to reject the police claim that the proportion of people wearing seat belts is less than 65%.

So the correct option is A.

Answer:

Option (D)

Step-by-step explanation:

In the picture attached,

An obtuse angle triangle ABC has been given.

By applying Sine rule in the triangle,

[tex]\frac{\text{SinB}}{b}=\frac{\text{SinA}}{a}=\frac{\text{SinC}}{c}[/tex]

Since, m∠A + m∠B + m∠C = 180°

45° + 110° + m∠C = 180°

m∠C = 180°- 155° = 25°

[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=\frac{\text{Sin25}}{7}[/tex]

[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=0.060374[/tex]

[tex]\frac{\text{Sin110}}{b}=0.060374[/tex]

b = [tex]\frac{\text{Sin110}}{0.060374}[/tex]

b = 15.56

b ≈ 15.56

[tex]\frac{\text{Sin45}}{a}=0.060374[/tex]

a = [tex]\frac{\text{Sin45}}{0.060374}[/tex]

a = 11.712

a = 11.71

Therefore, Option (D) will be the answer.

Answer:

  [tex]\boxed{2144}[/tex]

Step-by-step explanation:

The sum can be found by adding the parts:

  [tex]\sum\limits_{n=1}^{32}{(4n+1)}=4\sum\limits_{n=1}^{32}{n}+\sum\limits_{n=1}^{32}{1}=4\cdot\dfrac{32\cdot 33}{2}+32\\\\= 2112+32=\boxed{2144}[/tex]

__

The sum of numbers 1 to n is n(n+1)/2.

Answer:

[tex]\large \boxed{\sf \ \ \dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{2x+1}{x^2(x+1)} \ \ }[/tex]

Step-by-step explanation:

Hello,

This is the same method as computing for instance:

[tex]\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{3+2}{2*3}=\dfrac{5}{6}[/tex]

We need to find the same denominator.

Let's do it !

For any x real different from 0, we can write:

[tex]\dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{1}{x^2}+\dfrac{1}{x(x+1)}\\\\=\dfrac{x+1+x}{x^2(x+1)}=\dfrac{2x+1}{x^2(x+1)}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

3.54%

Step-by-step explanation:

This question represents a binomial distribution. A binomial distribution is given by:

[tex]P(x)=\frac{n!}{(n-x)!x!} p^xq^{n-x}[/tex]

Where n is the total number of trials, p is the probability of success, q is the probability of failure and x is the number of success.

Given that:

A basketball player scores 70% of his shots on average, therefore p = 70% = 0.7. Also q = 1 - p = 1 - 0.7 = 0.3.

The total number of trials (n) = 20 shots

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20)

P(x = 18) = [tex]\frac{20!}{(20-18)!18!}*0.7^{18}*0.3^{20-18}=0.0278[/tex]

P(x = 19) = [tex]\frac{20!}{(20-19)!19!}*0.7^{19}*0.3^{20-19}=0.0068[/tex]

P(x = 20) = [tex]\frac{20!}{(20-20)!20!}*0.7^{20}*0.3^{20-20}=0.0008[/tex]

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20) = 0.0278 + 0.0068 + 0.0008 = 0.0354 = 3.54%

Answer:

5+2+1 - 4 -3 = 1

5+4 - 3-2-1 =

Step-by-step explanation:

we have to ad and subtract number in such a way that result is 1.

1, 2, 3, 4, 5

5+2+1 - 4 -3 = 1

8-7 = 1

___________________________________________

In this problem we have use mathematical signs to get 3.

we add 5 and 4 which gives 9

and subtract 3,2 and 1 from it.

5+4 - 3-2-1 = 9 - 6 = 3

Answer: see below

Step-by-step explanation:

[tex]f(x)=-x^2\qquad g(x)=\dfrac{1}{\sqrt x}[/tex]

[tex]f og(x)=f\bigg(\dfrac{1}{\sqrt x}\bigg)\\\\.\qquad =-\bigg(\dfrac{1}{\sqrt x}\bigg)^2\quad \\\\.\qquad =-\dfrac{1}{x}\\\\\text{Domain:}\ x>0[/tex]

[tex]gof(x)=g(-x^2)\\\\.\qquad =\dfrac{1}{\sqrt{-x^2}}\\\\.\qquad =\dfrac{1}{xi}\\\\\text{Domain: Does Not Exist since result is an imaginary number}[/tex]

Answer:

Hey there!

Jimmy has 15-7, or 8 apples left.

Hope this helps :)

Answer: 8.5 sq. units.

Step-by-step explanation:

Formula:

Area of triangle : [tex]\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

Given: Triangle IJK, with vertices I(3,-7), J(7,-4), and K(4,-2)

Then, Area of triangle  IJK = [tex]\dfrac{1}{2}|3(-4-(-2))+7(-2-(-7))+4(-7-(-4))|[/tex]

[tex]\dfrac{1}{2}|3(-2)+7(5)+4(-3)|\\\\=\dfrac{1}{2}|-6+35-12|\\\\=\dfrac{1}{2}(17)\\\\=8.5\text{ sq. units}[/tex]

Hence, the area of this triangle  IJK on a Coordinate Grid = 8.5 sq. units.

Answer:

y = 2/3x+1/3

Step-by-step explanation:

2x−3y+1 = 0

Solve for y

Add 3y to each side

2x−3y+1 +3y= 0+3y

2x +1 = 3y

Divide by 3

2/3 x + 1/3 =3y/3

2/3x +1/3 = y

The slope is 2/3 and the y intercept is 1/3

y = 2/3x+1/3

Answer:

450 mins/night

Step-by-step explanation:

The average of a data set is the sum of all of the data divided by the number of data elements in the set. In this case, that would be:

(8 + 6.5 + 7 + 8.5) / 4

= 30 / 4

= 7.5 hours

7.5 hours is 7.5 * 60 = 450 mins/night

Answer:

450 mins per night

Step-by-step explanation:

average = [tex]\frac{sum \: of \: terms}{number \: of \: terms}[/tex]

average = (8 + 6.5 + 7 + 8.5)/4

average = 30/4

average = 7.5

The average is 7.5 hrs.

Convert hrs to mins.

7.5 × 60 = 450

Answer:

Step-by-step explanation:

Part A

(m + n)x = 4x + 5 + 8x - 5

(m + n)x = 12x   The fives cancel

Part B

(m - n)x = 4x + 5 - 8x + 5

(m - n)x = -4x + 10

Part C

The trick here is to put n(x) into m(x) wherever m(x) has an x.

m[n(x)] = 5(n(x)) + 5

m[n(x)] = 5(8x - 5) + 5

m[n(x)] = 40x - 20 + 5

m[n(x)] = 40x - 15

Answer:

The cost to rent each chair is $2.75 and the cost to rent each table is $8.50

Step-by-step explanation:

Let the:

Cost to rent a chair = x

Cost to rent a table = y

We would form an algebraic equation.

The total cost to rent 2 chairs and 3 tables is $31

2x + 3y = 31 ...... Equation 1

The total cost to rent 6 chairs and 5 tables is $59

6x + 5y = 59 ......... Equation 2

We solve the above equation above using elimination method

Multiply Equation 1 all through by the coefficient of x = 6 in Equation 2

Multiply Equation 2 all through by the coefficient of x = 2 in Equation 1

Hence, we have:

2x + 3y = 31 ...... Equation 1 × 6

6x + 5y = 59 ......... Equation 2 × 2

12x + 18y = 186........ Equation 3

12x + 10y = 118 .…...... Equation 4

Subtracting Equation 4 from Equation 3

= 8y = 68

y = 68/8

y = 8.5

Therefore, the cost to rent a table = $8.50

Substituting 8.5 for y in Equation 1 to get the value of x

2x + 3y = 31 ...... Equation 1

2x + 3(8.5) = 31

2x = 31 - 3(8.5)

2x = 31 - 25.5

2x = 5.5

x = 5.5/2

x = 2.75

The cost to rent a chair = $2.75

Therefore, the cost to rent each chair is $2.75 and the cost to rent each table is $8.50

Answer:

128

Step-by-step explanation:

You have two jars and seven marbles.

You do 2^{7}.

That is 128

Answer:

16384

Step-by-step explanation:

Its correct :)

Answer:

g(2) =10x+6

Step-by-step explanation:

g(x) =5x+3

g(2)=5x+3

g(2)=10x+6

have a great day

Answer:

1295$

Step-by-step explanation:

Let's denote the monthly salary of Barry A.

Then we have:

A - (1/5)A - (1/7)A = 851

or

(35A - 7A - 5A)/35 = 851

or

23A = 851 x 35

or

23A = 19785

or

A = 1295$

Answer:

  152.53°

Step-by-step explanation:

The Law of Cosines is useful for finding an angle when sides are given.

  a^2 = b^2 +c^2 -2bc·cos(A)

  A = arccos((b^2 +c^2 -a^2)/(2bc))

  A = arccos((18^2 +17^2 -34^2)/(2(18)(17))) = arccos(-543/612)

  A ≈ 152.53°

Answer:

cos -60° = [tex]\frac{1}{2}[/tex] ,

cos 660° =  [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

hope it helps

Answer:

-60 and 660

Step-by-step explanation:

Edge 2020

Answer:

a=90 degrees

b=90 degrees

x=22 degrees

Step-by-step explanation:

3x+22+(5x-18)=180

8x=176

x=22

Answer:

x = 22°, ∠a = 88°, ∠b = 92°.

Step-by-step explanation:

Angle b has the same measurement as the angle of 5x - 18, since the two angles are corresponding angles.

Angle a has the same measurement as the angle of 3x + 22, since the two angles are alternate interior angles.

Since angle a and the angle of 5x - 18 form a straight line, the two angles add up to be 180 degrees. Since angle a is the same as the angle of 3x + 22, we can substitute the angle for angle a.

(5x - 18) + (3x + 22) = 180

5x + 3x - 18 + 22 = 180

8x + 4 = 180

8x = 176

x = 22°.

3(22) + 22 = 66 + 22 = 88 degrees.

That means that ∠a = 88°.

5(22) - 18 = 110 - 18 = 92 degrees.

That means that ∠b = 92°.

Hope this helps!

This question is incomplete

Complete Question

A normal population has a mean of 61 and a standard deviation of 13. You select a random sample of 16. Compute the probability that the sample mean is: (Round z values to 2 decimal places and final answers to 4 decimal places.)

(a) Greater than 64

(b) Less than 57

Answer:

(a) Greater than 64 = 0.1788

(b) Less than 57 = 0.1094

Step-by-step explanation:

To solve the above questions we would be using the z score formula

The formula for calculating a z-score :

z = (x - μ)/σ,

where x is the raw score

μ is the population mean = 61

σ is the population standard deviation = 13

(a) Greater than 64

z = (x - μ)/σ,

where x is 64

μ is the 61

σ is the 13

In the above question, we are given the number of samples = 16

Sample standard deviation = popular standard deviation/ √16

= 13/√16

z = 64 - 61 ÷ 13/√16

z = 3/3.25

z = 0.92308

Approximately, z values to 2 decimal places ≈ 0.92

Using the z score table of normal distribution to find the Probability (P) value of z score of 0.92

P(z = 0.92) = 0.82121

P(x>64) = 1 - P(z = 0.92)

= 1 - 0.82121

= 0.17879

Approximately , Probability value to 4 decimal places = 0.1788

(b) Less than 57

z = (x - μ)/σ,

where x is 57

μ is the 61

σ is the 13

In the above question, we are given the number of samples = 16

Sample standard deviation = popular standard deviation/ √16

= 13/√16

z = 57 - 61 ÷ 13/√16

z = -4/3.25

z = -1.23077

Approximately, z values to 2 decimal places ≈ -1.23

Using the z score table of normal distribution to find the Probability (P) value of z score of -1.23

P(z = -1.23) = P(x<Z) = 0.10935

Approximately , Probability value to 4 decimal places = 0.1094

Answer:

60

Step-by-step explanation:

x + 0.30x = 78

1.30x = 78

x = 60

Answer:

The answer is 60.

Step-by-step explanation:

here, let another number be x.

according to the question the number when increased by 30% will be 78. so,

x+ 30% of x =78

now, x+ 30/100×x =78

or, x+0.3x=78

or, 1.3x=78

Therefore the another number is 60.

Hope it helps...

Answer:

[tex]\boxed{\sf \ \ \ 10^2+11^2+12^2=13^2+14^2 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let's note a a positive integer

5 consecutive integers are

a

a+1

a+2

a+3

a+4

so we need to find a so that

[tex]a^2+(a+1)^2+(a+2)^2=(a+3)^2+(a+4)^2\\<=>\\a^2+a^2+2a+1+a^2+4a+4=a^2+6a+9+a^2+8a+16\\<=>\\3a^2+6a+5=2a^2+14a+25\\<=>\\a^2-8a-20=0\\<=>\\(a+2)(a-10)=0\\<=>\\a = -2 \ or \ a = 10\\[/tex]

as we are looking for positive integer the solution is a = 10

do not hesitate if you have any question

Answer:

2m - 9

Step-by-step explanation:

To simplify this, we need to combine like terms. m + m = 2m and -4 - 5 = -9 so the simplified version would be 2m - 9.

Answer:

Step-by-step explanation:

Hello!

Miguel has four chips, two have the number "1", one has the number "3" and the other has the number "5"

If the experiment is "choosing two chips and looking at their numbers" there are the following possible outcomes:

S= {(1,1)(1,3)(1,5)(3,1)(5,1)(3,5)(5,3)}

The sample space for the experiment has 7 possible combinations.

a)

Be X: the amount of money Miguel will receive or owe.

If two chips with the same number are chosen he will receive $2

If the chips have different number he will owe $1

Looking at the possible outcomes listed above, out of the 7, in only one he will select the same number (1,1)

So the probability of him receiving $2 will be 1/7

Now out of the 7 possible outcomes, 6 will make Miguel owe $1, so you can calculate its probability as: 6/7

  xi  | $2 | -$1

P(xi) | 1/7 | 6/7

b)

To calculate the expected value or mean you have to use the following formula:

[tex]\frac{}{X}[/tex]= ∑[xi*P(xi)]= (2*1/7)(-1*6/7)= -4/7= $-0.57

c)

The expected value is $-0.57, meaning that Miguel can expect to owe $0.57 at the end of the game.

d)

To make the game fair you have to increase the probability of obtaining two chips with the same number. Any probability close to 50% will make the game easier. For example if you change the experiment so that for earning $2 the probability is 4/7 and for owing $1 the probability is 3/7, the expected earnings will be:

(2*4/7)+(-1*3/7)= $0.71

I hope this helps!

Answer:

A. 1.812

B. 1.753

C. 2.602

D. 3.747

E. 2.069

F. 2.453

Step-by-step explanation:

A. 95% confidence level, the level of significance = 5% or 0.05

Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 10 degrees of freedom = 1.182

B. 95% confidence interval = 0.05 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 15 degrees of freedom = 1.753

C. 99% confidence interval = 0.01 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 15 degrees of freedom = 2.602

D. 99% confidence interval = 0.01 level of significance; DF (n - 1) = 5- 1 = 4

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 4 degrees of freedom = 3.747

E. 98% confidence interval = 0.02 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.02 significance level with 23 degrees of freedom = 2.069

F. 99% confidence interval = 0.01 level of significance; df (n - 1) = 32 - 1 = 31

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 31 degrees of freedom = 2.453

Answer:

[tex]\boxed{\sf 2737.5 \ hours}[/tex]

Step-by-step explanation:

The average is 7.5 hours of sleep each night.

There are 365 nights in 1 year.

[tex]\sf Multiply \ the \ value \ by \ 365.[/tex]

[tex]7.5 \times 365[/tex]

[tex]2737.5[/tex]

Answer:

2,737 hours for a normal year, 2,745 if it is a leap year.

Step-by-step explanation:

Because there 365 days in a year, you should multiply the amount you sleep every day (7.5) by the number of days in a year (365)

[tex]7.5*365[/tex]

Multiply 7.5 by 365 to get

[tex]2,737.5[/tex]

Every year you will sleep 2,737 hours if you sleep 7.5 hours each day.

(If it is a leap year, just change 365 to 366 which will give you 2,745 hours)

I hope this helps. If you have any follow-up questions, feel free to ask.

Have a great day! :)

Answer:

3:06

Step-by-step explanation:

primero debemos calcular a cuántos minutos equivale un ángulo de 54°. Para hacer esto utilizamos una regla de 3 simple donde 60 minutos equivale a 360° grados, entonces:

60 minutos ----- 360°

x minutos -------- 54°

Resolviendo para x, tenemos:

[tex]x=\frac{54*60}{360}=9[/tex]

Entonces si las manecillas están a 9 minutos de diferencia, el ángulo será 54°. Si la hora es después de las 3, significa que la manecilla de la hora estará en el minuto 15 y la otra debe estar 9 minutos antes, es decir en el minuto 6.

Por lo tanto, la hora después de las 3 en la cual se forma un ángulo de 54° por primera vez es a las 3:06