Give an example of an event for which the probability equals 1. Justify your answer

Answer:

yes

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Recall that a rational number is a number that results from dividing 2 integers

I'm not sure if your question refers to (√4) / 9 or √(4/9), but either way both are rational numbers:

If (√4) / 9, Then,

(√4) / 9

= 2/9

Since both 2 and 9 are integers, then 2/9 is a rational number

If √(4 / 9), Then,

√(4 / 9)

= √4 / √9

= 2/3

Since both 2 and 3 are integers, then 2/3 is also a rational number

The square root of 16 is rational 4.

The ratio of 4 and 7 is rational 0.5714285714285

The product is hence rational.

The product of the square root of 16 and 4/7 (which equals 16/7) is rational.

Rational numbers can be expressed as fractions of integers, while irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions.

The square root of 16 is 4, and 4/7 is a rational number. When you multiply a rational number (4/7) by an integer (4), the result remains rational.

Calculation: √16 * 4/7 = 4 * 4/7

= 16/7

16/7 is the product which is a rational number.

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Answer:

y=10x+2

Step-by-step explanation:

y-y1=m(x-x1)

y-2=10(x-0)

y-2=10(x)

y-2=10x

y=10x+2

Question:

Katy makes 48 cookies an hour. If she has 24 already, how long would it take her to make 120?

Answer:

It takes 2.5 hours for Katy to make  120 cookies

Step-by-step explanation:

Given:

Time taken to make 48  cookies = 1 hour

To Find:

Time taken to make 120 cookies = ?

Solution:

Time taken to make 48 cookies  = i hour

So now time taken to make 1 cookie  = [tex]\frac{1}{48} hour[/tex]

So time taken to make 120 cookies

= Number of cookies X time taken to make one cookie

=>[tex]120 \times  \frac{1}{48}[/tex]

=>[tex] \frac{120}{48}[/tex]

=> 2.5 hours

Answer:

the domain of the function f(x) is [tex]x\ge 7[/tex]

the range of the function f(x) is [tex]f(x)\ge 9[/tex]

Step-by-step explanation:

Consider the parent function [tex]y=\sqrt{x}.[/tex]

The domain og this function is [tex]x\ge 0,[/tex] the range of this function is [tex]y\ge 0.[/tex]

The function [tex]f(x)=\sqrt{x-7}+9[/tex] is translated function [tex]y=\sqrt{x}[/tex] 7 units to the right and 9 units up, so

the domain of the function f(x) is [tex]x\ge 7[/tex]

the range of the function f(x) is [tex]f(x)\ge 9[/tex]

Answer:

C

Step-by-step explanation:

Just took quiz

The perimeter of a triangle with midpoints d, e, and f on each side is twice the sum of segments d, e, and f. However, without specific numerical values for d, e, and f, the exact numerical measurement for the perimeter of triangle ABC cannot be determined.

The question is referring to a specific characteristic of geometry known as the midpoint. The midpoints, in this case d, e, and f, divide each side of the triangle into two equal parts. The side length of ABC is equal to double the sum of segments d, e, and f since they represent the half lengths of the sides.

However, please note that without any additional information or numeric representation, we cannot compute the exact numerical measurement of the perimeter of triangle ABC.

To illustrate, if we were given that the lengths d, e, and f were respectively 5 units, 6 units, and 7 units, we would calculate the perimeter of triangle ABC by adding the lengths of d, e, and f and multiplying the sum by 2.

In such a scenario: Perimeter of ABC = 2 * (d + e + f) = 2 * (5 units + 6 units + 7 units) = 2 * 18 units = 36 units.

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Answer:

[tex]\frac{(x-1)^{2}}{4}+\frac{y^{2}}{25}=1[/tex]

Step-by-step explanation:

we have

[tex]25x^{2}+4y^{2}-50x-75=0[/tex]

Convert to standard form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](25x^{2}-50x)+4y^{2}=75[/tex]

Factor the leading coefficient of each expression

[tex]25(x^{2}-2x)+4y^{2}=75[/tex]

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

[tex]25(x^{2}-2x+1)+4y^{2}=75+25[/tex]

[tex]25(x^{2}-2x+1)+4y^{2}=100[/tex]

Rewrite as perfect squares

[tex]25(x-1)^{2}+4y^{2}=100[/tex]

Divide both sides by the constant term to place the equation in standard form

[tex]\frac{25(x-1)^{2}}{100}+\frac{4y^{2}}{100}=\frac{100}{100}[/tex]

Simplify

[tex]\frac{(x-1)^{2}}{4}+\frac{y^{2}}{25}=1[/tex]

Correct answer:

D. (-5,-4)

In order to solve this problem,  let's plot each point. So, see the attached file below and keep in mind the following:

As you can see on the graph, only point (-5, -4) lies on the given line. Therefore, the conclusion is that this point could be a solution to a system of linear equations including the line graphed below.

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Answer:

a) The Inequality representing this problem is [tex]13+2.35x\leq 29.45[/tex].

b) Annie Marie can play maximum of 7 hours.

Step-by-step explanation:

Given:

Entry fee charge of game room = $13

Cost of hourly playtime = $2.35 per hour

Total Money Annie Marie has = $29.45

We need to find number of hours she can play with this amount.

Let number of hours she will play be 'x'.

No we know that Total Money she has should be less than or equal to sum of Entry fee charge of game room and Cost of hourly playtime multiplied by number of hours she can play.

Framing in equation form we get;

[tex]13+2.35x\leq 29.45[/tex]

Hence The Inequality representing this problem is [tex]13+2.35x\leq 29.45[/tex].

On Solving this equation we get;

Subtracting both side by 13 we get;

[tex]13+2.35x-13\leq 29.45-13\\\\2.35x\leq 16.45[/tex]

Now dividing both side by 2.35 using division property of Inequality we get;

[tex]\frac{2.35x}{2.35}\leq \frac{16.45}{2.35}\\\\x\leq 7 \ hrs.[/tex]

Hence Annie Marie can play maximum of 7 hours.

Answer:

(-3, -14)

Step-by-step explanation:

the difference between 9 and 3 is 6 so subtract 6 from 3 to get negative 3. the difference between 4 and - 5 is 9 so subtract 9 from -5

Answer:

10-10=10+10 its the same it will increase and decrease the increased level

Answer:

[tex]\frac{8}{5}[/tex]

Step-by-step explanation:

Given that [tex]g(x) = \frac{x + 1}{x - 2}[/tex] and h(x) = 4 - x

Now, if y = f(x) and y = g(x) then the composite function (f∘g)(x) is given by f[g(x)].

Hence, (g∘h)(x) = [tex]g[h(x)] = \frac{(4 - x) + 1}{(4 - x) - 2} = \frac{5 - x}{2 - x}[/tex] .......... (1)

Now, from equation (1) we get,

(g∘h)(x) = [tex] \frac{5 - x}{2 - x}[/tex]

⇒ (g∘h)(- 3) = [tex]\frac{5 - ( - 3)}{2 - ( - 3)} = \frac{8}{5}[/tex] (Answer)

Answer:

The answer is 8/5

Step-by-step explanation:

Answer:

The equation of line is y = 3 x - 1 , i.e option A  .

The rate of change = m = 3

Step-by-step explanation:

Given as :

The points are

([tex]x_1[/tex],[tex]y_1[/tex] ) = (- 2, -7)

([tex]x_2[/tex],[tex]y_2[/tex] ) = (1 , 2)

Let The slope = m

Now, The slope is calculated in points form

So, Slope = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

I.e m = [tex]\dfrac{2-(-7)}{1-(-2)}[/tex]

or, m = [tex]\dfrac{9}{3}[/tex]

I.e m = 3

So, The slope of points = m = 3

I,e Rate of change = m = 3

Now, the equation of line in slope - point form can be written as

y -[tex]y_1[/tex]  = m ( x -  [tex]x_1[/tex])

where m is the slope of line

i.e y - (-7) = ( 3 ) × ( x - (-2) )

or, y + 7 =  3 × (x + 2)

∴ y + 7 = 3 x + 6

Or, y = 3 x + 6 - 7

Or, y = 3 x - 1

So, The equation of line is y = 3 x - 1

Hence, The equation of line is y = 3 x - 1 , i.e option A  .

And The rate of change = m = 3   Answer

Answer:

Never mind, but your question makes no sense.

Step-by-step explanation:

List the rest of the question.

Answer:

1200

Step-by-step explanation:

its just common sense that 2*2=4  and 10*4=40 so now all you have to do is 40*30 which its just common knowledge that 4*3=12 now just add the zeros 1200

Answer:

The Total number of people were surveyed is 1,350 people.

Step-by-step explanation:

Given as :

The total number of people who preferred walking = 540 people

The percentage of people who preferred walking to running = 40% of the total people

Let The Total number of people were surveyed = n people

Now, According to question

The total number of people who preferred walking = 40% of the total number of people were surveyed

Or, 40% of n = 540

Or, [tex]\dfrac{40}{100}[/tex] × n = 540

Or, n = [tex]\frac{540\times 100}{40}[/tex]

∴ n = 1350

So,Total number of people were surveyed = n = 1350 people

Hence,The Total number of people were surveyed is 1,350 people. Answer

Answer:

Option b) is correct.

The completed factor of given expression is  [tex]2(x-2)(x+2)(x^2+4)[/tex]

Step-by-step explanation:

Given expression is [tex]2x^4-32[/tex]

To find the completed factor for the given expression:

[tex]2x^4-32[/tex]:

Taking the common number "2" outside  to the above expression we get

[tex]2x^4-32=2(x^4-16)[/tex]

Now rewritting the above  expression as below

[tex]=2(x^4-2^4)[/tex]  (since 16 can be written as the number 2 to the power of 4)

[tex]=2((x^2)^2-(2^2)^2)[/tex]

The above expression is of the form [tex]a^2-b^2=(a+b)(a-b)[/tex]

Here [tex]a=x^2[/tex] and  [tex]b=2^2[/tex]

Therefore it becomes

[tex]=2(x^2+2^2)(x^2-2^2)[/tex]

[tex]=2(x^2+4)(x^2-2^2)[/tex]  

The above expression is of the form [tex]a^2-b^2=(a+b)(a-b)[/tex]

Here [tex]a=x[/tex] and  [tex]b=2[/tex]

Therefore it becomes

[tex]=2(x^2+4)(x+2)(x-2)[/tex]  

[tex]=2(x+2)(x-2)(x^2+4)[/tex]  

Therefore [tex]=2(x+2)(x-2)(x^2+4)[/tex]  

[tex]2x^4-32=2(x-2)(x+2)(x^2+4)[/tex]  

Option b) is correct.

The completed factor of given expression is  [tex]2(x-2)(x+2)(x^2+4)[/tex]

Answer:

b

Step-by-step explanation:

Answer:

y = 139x + $ 799

y = 587x + $ 285

Step-by-step explanation:

Let x represent the number of days spent at the resort and y represent the total cost.

for the first option

y = 139x + $799 since $ 139 is the amount per night at the resort, $139x must be the cost for x number of days

y = 587x + $285  similarly x number of days should equal $587x

A. Mr. Babe made a commission of $14.85

B. He makes $15.75 per hour after the raise.

Step-by-step explanation:

A. While he worked there, Mr. Babe earned 3% on how much he sells. If he sold $495 couch, how much commission did he make?

Worth of sold couch = $495

Commission = 3%

Amount of commission = 3% of total worth sold

Amount of commission = [tex]\frac{3}{100}*495[/tex]

Amount of commission = [tex]\frac{1485}{100}=\$14.85[/tex]

Mr. Babe made a commission of $14.85

B. On top of his commission, Mr. Babe made $15 per hour. He eventually got a raise with an increase of 5% per hour. After the raise, how much did he make per hour?

Amount earned per hour = $15

Increase = 5%

As the increment is on per hour amount, therefore,

Amount of increase = 5% of per hour amount

Amount of increase = [tex]\frac{5}{100}*15=\frac{75}{100} = \$0.75[/tex]

New amount per hour = Per hour amount + amount of increase

New amount per hour = 15+0.75 = $15.75

He makes $15.75 per hour after the raise.

Keywords: percent, addition

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To calculate the total hours you will be paid for this week, subtract the total lunch break time from the total working hours. Therefore, the total hours you will be paid for this week is 19 hours and 45 minutes.

To calculate the number of hours you will be paid for this week, you need to subtract the total lunch break time from the total working hours.

On Monday, you worked from 8 AM to PM, which is 10 hours.

On Tuesday, you worked from 9 AM to 3 PM, which is 6 hours.

On Thursday, you worked from 8:30 AM to 2:15 PM, which is 5 hours and 45 minutes.

Overall, your total working hours for the week are 10 + 6 + 5 hours and 45 minutes.

Each day you have a 30-minute unpaid lunch break, so for the entire week you would have 4 lunch breaks x 30 minutes = 2 hours taken for lunch breaks.

Therefore, the total hours you will be paid for this week are 10 + 6 + 5 hours and 45 minutes - 2 hours = 19 hours and 45 minutes.

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Answer:

The minimum is the point (-3,2)

Step-by-step explanation:

we have

[tex]x^{2} +6x+11[/tex]

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

Convert the equation in vertex form

Complete the square

[tex]f(x)=(x^{2} +6x+3^2)+11-3^2[/tex]

[tex]f(x)=(x^{2} +6x+9)+11-9[/tex]

[tex]f(x)=(x^{2} +6x+9)+2[/tex]

Rewrite as perfect squares

[tex]f(x)=(x+3)^{2}+2[/tex] ----> equation in vertex form

The vertex is the point (-3,2)

therefore

The minimum is the point (-3,2)

Answer:

The arc is 3/10 of the circumference

Step-by-step explanation:

we know that

The complete circumference subtends a central angle of 2π radians

so

using proportion

Find out what fraction of the circumference represent an arc with a central angle of 3pi/5 radians

[tex]\frac{1}{2\pi}=\frac{x}{(3\pi/5)}\\\\x=\frac{(3\pi/5)}{2\pi}\\\\x=\frac{3}{10}[/tex]

Answer:

Step-by-step explanation:

5a^2 - 44 = 81

5a^2   = 81  + 44   {add 44 both the sides}

5a^2  = 125

a^2 = 125/5    {divide both sides by 5}

a^2 = 25

a^2 = 5*5

a =  ±5

Answer:

Option c) is correct

ie, a=plus minus 5 or [tex]a=\pm 5[/tex]

Step-by-step explanation:

Given equation is [tex]5a^2-44=81[/tex]

To find the solution of the given equation we have to solve the equation

[tex]5a^2-44=81[/tex]

[tex]5a^2=81+44[/tex]

Now applying the algebraic sum to the terms on the right hand side of the equation

[tex]5a^2=125[/tex]

[tex]a^2=\frac{125}{5}[/tex]

Now applying the division rule

[tex]a^2=25[/tex]

Therefore [tex]a=\pm 5[/tex]

Therefore option c) is correct

ie, [tex]a=\pm 5[/tex].

Answer:

290

Step-by-step explanation:

Answer:

n=-4

Step-by-step explanation:

56/-14=n

n=-4

Final answer:

The expressions that correctly represent an 8% increase from T are (1 + 8/100)T, which simplifies to 1.08T, and 1.08T directly. So, choices (A) 1.08T and (C) 1.08T are correct.

Explanation:

The student is asked to determine which expression represents the average temperature last Sunday when it was 8% higher than the temperature two Sundays ago, given as T degrees Celsius. To find 8% of T, the student would multiply T by 0.08. To calculate the total average temperature last Sunday, the student would then add this to T.

The correct expressions that represent this situation are:

Expressions (Choice B) B: T + 8 and (Choice D) D: 1.8T incorrectly represent an absolute increase of 8 degrees and an 80% increase, respectively, not an 8% increase. Expression (Choice E) E: T + 0.08T is equivalent to 1.08T and is also correct.

Therefore, the correct answers are (Choice A) and (Choice C).

Answer:

fevervrv

Step-by-step explanation:

3v43gvr3r54v4bv

As per question, Mandy has a 10.02-ounce container of mustard. The required Amount of Mustard left after she has eaten 6 hot dogs is 8.16 ounce.

Given:

Mandy has a 10.2-ounce container of mustard.

She uses 1/30 of the mustard to put on her hot dog each time.

According to question, Mandy has a 10.2-ounce container of mustard.

Now, 1/30 of the mustard to put on her hot dog each time to 6 hot dogs, so weight of mustard used is calculated as,

[tex]\frac{1}{30}\times10.2\times 6=2.04\;\rm{ounce}[/tex]

So, Amount of Mustard left after eating 6 hot dogs is,

[tex]10.2-2.04=8.16\;\rm{ounce[/tex]

Therefore, the required amount of mustard left after eating 6 hot dogs is 8.16 ounce.

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Answer:

[tex]x >\frac{3}{2}[/tex]

Step-by-step explanation:

The complete question is

Three times the sum of a number and two is less than seven times the number. Find the number

Let

x -----> the number

we know that

The linear equation that represent this problem is

[tex]3(x+2) < 7x[/tex]

Solve for x

Apply distributive property left side

[tex]3x+6 < 7x[/tex]

Subtract 3x both sides

[tex]6 < 7x-3x[/tex]

[tex]6 < 4x[/tex]

Divide by 4 both sides

[tex]\frac{6}{4}< x[/tex]

Simplify

[tex]\frac{3}{2}< x[/tex]

Rewrite

[tex]x >\frac{3}{2}[/tex]

Step-by-step explanation:

AC ≅ EF, given

AB ≅ ED, given

∠C ≅ ∠F, right angles are congruent

ΔABC ≅ ΔEDF, SSA congruence

BC ≅ DF, corresponding parts of congruent triangles are congruent