Determine if each statement is true or false. Justify your answer.
log (x-2)= log x/log 2

Answer: D y=4x   3=4y+x

Step-by-step explanation:

[tex]y=4x\ \ \ \ m=4\\\\3=4y+x\\3-x=4y+x-x\\3-x=4y\\-x+3=4y[/tex]

Divide both parts of the equation by 4:

[tex]\displaystyle\\-\frac{x}{4} +\frac{3}{4}=y \\\\-\frac{1}{4} x+0.75=y\\\\y=-\frac{1}{4} x+0.75\ \ \ \ m_{\perp}=-\frac{1}{m}=-\frac{1}{4}[/tex]

Aqil have 88 stickers.

Let Ryan have x stickers initially. Then Aqil will have (352-x) stickers. Ryan lost 25% of his stickers i.e., x-(25% of x)

= x- 25x/100

= x-x/4

= 3x/4

After Ryan lost 25% of his stickers, the ratio of Ryan's stickers to Aqil's stickers was 9:4 i.e.,

3x/4 : (352-x) = 9 : 4

⇒ 3x/4/(352-x) = 9/4

⇒3x/4 x 4 = 9 x (352-x)

⇒3x = 3168-9x

⇒3x+9x = 3168

⇒12x = 3168

⇒x = 3168/12

⇒x = 264

∴ Ryan have 264 stickers of the total 352 stickers and Aqil will have (352-x) i.e., 88 stickers.

Hence, Aqil have 88 stickers out of the 352 stickers.

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Step-by-step explanation:

or, y° + 40° + y + 30° = 180 [Sum of angle of a triangle]

or, 2y°+ 70° = 180°

or, 2y° = 180° - 70°

or, y = 110°/2°

or. y = 55°

Therefore the value of y is 55°

Step-by-step explanation:

the X is always O when we talk about the y intercept and the Y id always O when we talk about the x intercept

a. Mean and Median is 2.95 and 3 respectively

b. The  first and third quartiles5.25 and 15.75 respectively

c. Range and interquartile range is 7 and 4 respectively

d. Variance and Standard Deviation is 4.201 and 2.049 respectively

e. The skewness is not expected as it largely differs from the mean.

Rearranging the data.

0, 0, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6,7

Mean = ∑▒(x/N)

Mean = (6+1+ 5 +3+ 7+ 3 +0+ 3+ 1+ 3 +4 +1+ 2+ 4 +1+ 0 +5 +6 +3+ 1)/20

= 59/20

=2.95

Median = Sum of (10th and 11th number) /2

(3 +3)/ 2

=6/2

=3

Quartile = 0, 0, 1, 1, 1,     1, 1, 2, 3, 3,    3, 3, 3, 4, 4,    5, 5, 6, 6,7

Q1=Value of (((n+1))/4)

Q1=Value of ((1(20+1))/4)

Q1=Value of ((21))/4)

Q1= (5.25)

observation=Value of (5th)

observation= 1

Q3=Value of (((n+1))/4)

Q3=Value of ((3(20+1))/4)

Q3=Value of (((63))/4)

Q3= (15.75)

observation=Value of (16th)

observation = 5

Range = highest value - lowest value

= 7-0

= 7

Interquartile range = q3 – q1

=5 – 1

= 4

Variance =    Σ(Xi-¯X)2/N

x (x-xi) (x-xi)2

0 (0-2.95) -2.95

0 (0-2.95) -2.95

1 (1-2.95) -1.95

1 (1-2.95) -1.95

1 (1-2.95) -1.95

1 (1-2.95) -1.95

1 (1-2.95) -1.95

2 (2-2.95) 0.95

3 (3-2.95) 1.95

3 (3-2.95) 1.95

3 (3-2.95) 1.95

3 (3-2.95) 1.95

3 (3-2.95) 1.95

4 (4-2.95) 2.95

4 (4-2.95) 2.95

5 (5-2.95) 3.95

5 (5-2.95) 3.95

6 (6-2.95) 4.95

6 (6-2.95) 4.95

7 (7-2.95) 5.95

 Σ=(84.0125)

Variance = 84.0125/20

Variance = 4.201

Standard deviation = √variance

S.D = √4.201

S.D = 2.049

e. the skewness is not expected as it largely differs from the mean.

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The value of A is 954

According to the question we have been given that

The equation to be used is :   A = P(1+in)

The values we have been given are ;

       P = 900

       i = 0.03

      n = 2

We need to find the value of A. So to find the value of A we have to put the required values in the equation given to us. Thus,

       A = 900(1+0.03*2)

We will solve according to the BODMAS rule that is we have to first solve the bracket terms.

    A = 900(1 + 0.06)

   A = 900*1.06

    A = 954

Hence the value of A is 954.

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Answer: 38 and 24

Step-by-step explanation:

38 and 24

Answer:

A) The original price of music player is $170.66

B) If the item was marked up by 1/2 before it was placed on the sales floor, what was that the store paid for the digital player.?

Step-by-step explanation:

A)you would divide $128 by 4, getting $32. then add that to the original price, being $160.

B) you would divide $160 by 2, getting $80, then add those two together in order to find what it was marked up to, being $240. hopefully this helps

Answer:

(5,6)

The x axis is 5 and the y axis is 6.

I really hope this will help you. Good luck! Have a great day!!!! :)

The odds in favor of selecting an ace then a face card is 3/52.

Probability is used to determine the odds in favor of an event happening. The odds in favor of an event happening lies between 0 and 1. The greater the odds in favor of the event happening, the closer to one, the probability value would be. In a deck of cards, there are 13 aces and there are 12 face cards

The odds in favor of selecting an ace then a face card = (number of ace cards / total number of cards) x (number of face cards / total number of cards)

(13 / 52) x (12 / 52)

1/4 x 3/13 = 3/52

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Answer:

Step-by-step explanation:

It’s the 3rd and last one 0.5 swim and 1.5 bike and 0 hours swim and 2 bike

I’ve done the test

Answer:

Step-by-step explanation:

Answer:

-21 3/23

Step-by-step explanation:

-27 / 23 is -1 4/13, -1 4/23 *18 is -21.13 or -21 3/23

Taking into account the definition of probability, the probability for a customer to pick at least one item is 14/15.

Probability is the possibility that a phenomenon or an event will happen, given certain circumstances and it is expressed as a percentage.

The probability of any event A is defined as the ratio between the number of cases in which event A may or may not occur and the total number of possible cases. This is called Laplace's Law:

P(A)= number of favorable cases÷ total number of posible cases

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event is verified when one of the two, A or B, or both occurs and it is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B.

In first place, let's define the following events:

So you know:

In this case, considering the definition of union of events, the probability for a customer to pick at least one item is calculated as:

P(M∪F)= P(M) + P(F) -P(M∩F)

P(M∪F)= 17/30 + 5/6 -7/15

P(M∪F)= 14/15

Finally, the probability for a customer to pick at least one item is 14/15.

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The function that relates the sales and the number of muffins is :

S = 2.5 m

The sales amount can be find by the total sales. That is , if there are n products to sell and selling amount is x rs. then we can easily find the total sales by multiplying them and by this total sales we can easily find the number of items sold per units and vice versa.

In the question given,

amount (A) = $ 250.00

Now take any of two values from table ,

Choose any two points and calculate the slope:

slope = [tex]\frac{50 - 20}{20 - 8}[/tex] =  2.5

thus, y = 2.5x

Hence we can say the function that relates the sales and the number of muffins is :

S = 2.5 m

where, S = sales amount

           m = number of muffins to be sell

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The complete question is:

In a bake sale, you recorded the number of muffins sold and the amount of sales in a table as shown.

a. What is a function that relates the sales and the number of muffins?

b. How many muffins would you have to sell to make at least $ 250.00 in sales?

The transformations needed to sketch the graph of [tex]h(x) = \sqrt[3]{1 - x}[/tex] are described as follows:

Starting with the graph of the basic function [tex]y = \sqrt[3]{x}[/tex], horizontally shift the graph right one unit, and then reflected the graph about the x-axis.

A transformation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

The parent cube root function is given by:

[tex]y = \sqrt[3]{x}[/tex]

To have x -> x - 1, we reflect the function over the y-axis, hence:

[tex]y = \sqrt[3]{-x}[/tex]

To have -x -> 1 - x, we shift it one unit right, hence:

[tex]h(x) = \sqrt[3]{1 - x}[/tex]

The order of the transformations can be reversed, i. e., shift right then reflection.

Thus the correct statement to sketch the graph is given by:

Starting with the graph of the basic function [tex]y = \sqrt[3]{x}[/tex], horizontally shift the graph right one unit, and then reflected the graph about the x-axis.

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Answer:

y-2 = -5(x-8)

Step-by-step explanation:

y-y₁=m(x-x₁)

Answer: 2

Step-by-step explanation:

8+14-5-7+3-7-4

add first.

8+14+3=25

25-5-7-7-4

now subtraction, set aside the added solution, 25.

-5-7-7-4=-23

25-23=2

Answer:

2

Step-by-step explanation:

Parentheses

Exponents

Multiply

Divide

Addition

Subtraction

8+14-5-7+3-7-4

Do addition and subtraction what ever comes first from left to right.

22-5-7+3-7-4

17-7+3-7-4

10+3-7-4

13-7-4

6-4

2

On multiplying (√3+√5)(√3-√5), we get answer as -2

1. Split the radicands in half. A number known as a radicand appears underneath the radical symbol.

2. To multiple radicands, multiply the integers as if they were whole numbers. Always keep the item beneath a single radical sign.

3. Use factoring to exclude any perfect squares from the radicand. To achieve this, check whether any perfect squares have the radicand as a factor.

4. Position the square root of the ideal square before the radical sign. Don't change the second component of the radical symbol.

5. Square the square's root. Sometimes it is necessary to multiply a square root by itself.

We are given,

(√3+√5)(√3-√5)

⇒ (√3)² - (√5)²

⇒ 3 - 5

⇒ -2

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The value of the expression,  5([tex]2^{-3}[/tex]) is expressed as: 5/8.

We are given the expression, 5([tex]2^{-3}[/tex]), to find the value of the expression, the steps explained below should be taken.

5([tex]2^{-3}[/tex]) [given expression]

Apply the negative exponents rule to evaluate the exponent in the expression

5([tex]2^{-3}[/tex]) = 5(1/2³)

5([tex]2^{-3}[/tex]) = 5/2³

Solve the exponent to eliminate the power of minus 3

5([tex]2^{-3}[/tex]) = 5/(2 × 2 × 2)

5([tex]2^{-3}[/tex]) = 5/8

Thus, the value of the expression,  5([tex]2^{-3}[/tex]) is expressed as: 5/8.

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$4051.63 will be in the account after 18 years.

The formula to be used is given as follows :

               A(t) = a ( 1 + r )^t      (1)

 where,  A(t) = future value

                a = principal amount or amount initially deposited.

                r = annual interest rate

                t = time

According to the question we have been given that

             a = $2000

             r = 0.04

             t = 18 years

putting the required values in equation (1) we get

         A(t) = 2000 (1+0.04)^18

         A(t) = 2000 (1.04)^18

         A(t) = 2000*2.03

         A(t) = $4051.63

Thus $4051.63 will be in the account after 18 years.

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Answer:

square = width*height,

circle=pi*r^2

triangle = w * h * 0.5

Step-by-step explanation:

square = width*height,

circle=pi*r^2

triangle = w * h * 0.5

The trace of water left on the floor is the circumference of 565.2 cm.

Water traces are seen on the floor from a wet bicycle tire.

The bicycle wheel makes three complete rotations before coming to a stop, circumference  and the tire has a radius of 30 cm.

The circle of the cycle is indicated by the water stain left on the floor.

Given the radius = 30 cm

So,

C = 2 × 3.14 × 30

C = 188.4

Given that a bicycle wheel turns three times before pausing to pick up a trace of water, the answer is,

3 x 188.4 = 565.2 cm

the floor has a 565.2 centimeter trace of water.

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Answer:

He would have $100 in his bank account from the information provided

Step-by-step explanation:

A composite function exists as a function that depends on another function. The value for  (f⁰f)(0) = - 4/3

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

Let the two functions be g(x) = 3x + 2 and f(x) = x - 2/3

Now, (f⁰f)(x) = f[f(x)]

f(x) = x - 2/3

(f⁰f)(x) = f( x - 2/3)

simplifying the above equation, we get

(f⁰f)(x) = (x - 2/3) - 2/3  

(f⁰f)(0) = - 2/3 - 2/3

(f⁰f)(0) = - 4/3

Therefore, the value of (f⁰f)(0) = - 4/3.

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Answer:

Step-by-step explanation: the five was never in bracket and -2 times 2 = -4

(5)^2 -2(5-3)

=(5)^2  -2(2)

=25  -2(2)

25 (-4)

-100

Answer: 7a

Step-by-step explanation:

Step-by-step explanation:

do sum of 3a and 4a your answer will be 7a

All denominators are [tex]= -17-4\sqrt{5}[/tex].

The phrase simplifies manner to make something simpler to do or recognize. So, by decreasing or simplifying the fractions method we make the fraction as simple as feasible. We do this by dividing the numerator and the denominator with the aid of the most important range that could divide into both numbers precisely.

The only form is likewise known as the decreased form of a fraction. for instance, ¾ is the most effective shape of a fraction that has a not unusual thing equal to 1. but 2/4 is not the most effective form, because 2/four can in addition be simplified and written as ½.

Step one is to perceive a common issue between the denominator and numerator. The denominator and numerator are each divided by the commonplace thing. The department operation is repeated until there are not any extra elements. The fraction is said to be simplified if no greater factors go out.

Apply FOIL method : (a+b)(c+d)= ac+ad+bc+bd

[tex](3+2\sqrt{5} )(1-2\sqrt{5} =3.1.3(-2\sqrt{5} )+2\sqrt{5}.1+2\sqrt{5} (-2\sqrt{5} )[/tex]

[tex]= 3.1+3(-2\sqrt{5} )+2\sqrt{5} .1+2\sqrt{5} (-2\sqrt{5} )[/tex]

[tex]= -17-4\sqrt{5}[/tex]

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Answer:

C

6/13

Step-by-step explanation:

Comment

This is not a true sequence. It just has the same things done to the numerator as to the denominator.

The numerator (top part of the fraction).

Add 3 to the previous numerator's top

So 3 + 3 = 6 which is the numerator of the second term.

15 + 3 = 18 which is the numerator of the seventh term.

So the numerator of the 4th term is 9 + 3 = 12

The Denominator

The difference there is 5

So 21 + 5   = 26

The answer is

12/26

This reduces down to 6/13

Multiply by 2: Divide by (a+b)

Answer:

r=(a-1)/pt

Step-by-step explanation:

a=1+prt

a-1=prt

a-1/pt=r

r=a-1/pt

good luck buddy rip if you dont get the question