Which is the logarithmic form of the exponential equation 2³=8 ?
(A) logB 2=3
(B) log₈ 3=2
(C) log₃ 8=2
(D) log₂ 8=3

Answer:

Rs 140

Step-by-step explanation:

Rs 25 is the amount of money she bought the apples

Rs 32 is the amount of money she sold the apples

32 - 25 = $7 profit per apple

7 Rs multiplied by 20 apples is equal to Rs 140 in profit.

Hope this helps!

The given equation 5n – 6 > 8n – 3n does not satisfy the inequality conditions.

The given inequality is;

5n – 6 > 8n – 3n

Ad 3n on the both side of inequality.

5n – 6 + 3n > 8n – 3n + 3n

Now, subtract the variable part,

8n - 6 > 8n

Subtract 8n both side.

8n - 6 - 8n > 8n - 8n

0 - 6 > 0

-6 > 0

But, -6 not not greater than 0.

Thus, the inequality is not valid.

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In the given statement is:

The Personal identification numbers (pins) for automatic teller machines (atms) usually consist of four digits. suppose pins are assigned at random so that all 4-digit numbers are equally likely.

To find probability that a pin assigned at random has at least one 0

To create a PIN that doesn't include any zeroes means choosing each digit from among the 9 non - zero digits. The number of such PINs is

[tex]9^{4}[/tex] = 6,561

The rest of the PINs must then include one or more zeroes, and the number of is

10,000 - 6,561 = 3, 439

If a PIN is chosen at random, the probability that it does include at least one zero is then the ratio

Hence, The final answer is : [tex]\frac{3,439}{10,00} = 0.3439[/tex]  

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The relative change in weekly sales is  mathematically given as

relative change= -12.857%

This is further explained below.

This Sale per week after the price decreases

=350-45  

=305

Generally, the equation for relative change is  mathematically given as

[tex]\left(\frac{\text { final Value - Intial value }}{\text { Intial value }}\right) \times 100 \%$[/tex]

Hore final value =305 week

Initial Value =350 week

Relative Change[tex]=\left(\frac{305-350}{350}\right) \times 100[/tex]

[tex]&=\frac{-45}{350} \times 100[/tex] \\

=-12.857%

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You can replace the values in a problem with letters or words so that it's easier to use mental math to complete the computation.

This is further explained below.

Generally, A word may also refer to both a string of letters that are denoted by a certain meaning and the space that separates those characters from one another.

A graphic representation of a spoken sound is often written or printed and is the basic building block of an alphabet.

In conclusion, You may make it simpler to compute using mental math by changing the numbers in a problem to letters or words, which will make it possible for you to solve the issue more quickly.

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The inverse for the function f (x) = 2 / 3 x - 3 will be f ⁻¹ (x) = 3 / 2 x + 9 / 2.

We are given the function:

f (x) = 2 / 3 x - 3

we need to find the inverse of the function.

First we will write the function in the form of x.

y = 2 / 3 x - 3

y + 3 = 2 / 3 x

2 x = 3 y + 9

x = 3 / 2 y + 9 / 2

So, the inverse function will be:

f ⁻¹ (x) = 3 / 2 x + 9 / 2.

Therefore, the inverse for the function f (x) = 2 / 3 x - 3 will be f ⁻¹ (x) = 3 / 2 x + 9 / 2.

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If you are emphasizing on the fact that these are its only real roots, then maybe the function has any other 2 imaginary roots, so there wouldn't be any specific equation that you're looking for.

However if you mean that these real roots are the only roots of this function, meaning that they are double roots, we can argue that:

[tex]f(x) = (x + 4) {}^{2} (x + 1) {}^{2} \\ f(x) = (x {}^{2} + 8x + 16)(x {}^{2} + 2x + 1) \\ expand \: by \: multiplying \: each \: term \: by \: the \: other \: 3 \\ f(x) = x {}^{4} + 10x {}^{3} + 33x {}^{2} + 40x + 16[/tex]

The total amount of that Harry will need for the project is nineteen and one third feet and Hence the option B is correct.

Addition of Fraction

Wood 1:

Length of each = 2 3/4 feet

Number of pieces = 4

Total = Length of each × Number of pieces

= 2 3/4 × 4

= 11/4 × 4

= 11 meters

Wood 2:

Length of each = 1 2/3 feet

Number of pieces = 5

Total = Length of each × Number of pieces

= 5/3 ×5

= 25/3 meters

Total amount of wood needed for the project = 11meters + 25/3 meters

= 11 +25/3

= (33+25)/3

= 58/3

=19 1/3 meters

Therefore, the total amount of wood that Harry will need for the project is nineteen and one third feet

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Answer:

(x-1)(x+1+3)=(x-1)(x+4)

The probability of taking out a pencil from the bag having 9 pens, 7 pencils and 6 crayons is 0.32.

We are given that:

We have-

Number of pens = 9

Number of pencils = 7

Number of crayons = 6

Now, the total number of objects in the bag = 9 + 7 + 6

Now, the total number of objects in the bag = 22

We have to find the probability of taking out a pencil from the bag.

P ( taking out a pencil from the bag ) = 7 / 22

P ( taking out a pencil from the bag ) = 0.32

Therefore, we get that, the probability of taking out a pencil from the bag having 9 pens, 7 pencils and 6 crayons is 0.32.

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It should be noted that writing 6300kg in grams, and giving your answer in standard form is 6.3 × 10^6.

From the information, a bricklayer needs to order 6300kg of building sand. Write 6300kg in grams, giving your answer in standard form.

1 kilogram = 1000 grams

6300 kilograms = x grams

6300 × 1000 = x

x = 6,300,000 grams

Therefore, writing 6300kg in grams, and giving your answer in standard form is 6.3 × 10^6.

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The expression for the total number of baseball cards he has now is

b + 11.

It is given that Carlos had " b " baseball cards.

Then, he got 11 more baseball then the number of baseballs will be

         [tex]b+11[/tex]

Hence , the total number of baseballs are b + 11

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Answer:

3 7/10

Step-by-step explanation:

8 4/5 - 5 1/10

8 8/10 - 5 1/10

8 - 5 = 3       8/10 - 1/10 = 7/ 10

3 7/10

Answer:

Javier gets to 1000 first in 23 weeks

Step-by-step explanation:

Let J = Javier

Let S = Shane.

S = 640 + 15 every week.

J = 425 +25 every week. Make a time chart.

640 (week 0), 655 (week 1), 670 (week 2), 685 (week 3), 700 (week 4), 715 (week 5), 730 (week 6), 730 (week 7), 745 (week 8), 760 (week 9), 775 (week 10), 790 (week 11), 805 (week 12), 820 (week 13), 835 (week 14), 835 (week 15), 850 (week 16), 865 (week 17), 880 (week 18), 895 (week 19), 910 (week 20), 925 (week 21), 940 (week 22), 955 (week 23),

425 (week 0), 450 (week 1), 475 (week 2), 500 (week 3), 525 (week 4), 550 (week 5), 575 (week 6), 600 (week 7), 625 (week 8), 650 (week 9), 675 (week 10), 700 (week 11), 725 (week 12), 750 (week 13), 775 (week 14), 800 (week 15), 825 (week 16), 850 (week 17), 875 (week 18), 900 (week 19), 925 (week 20), 950 (week 21), 975 (week 22), 1000 (week 23)

Answer:

[tex]y = \dfrac{1}{4} x - 4[/tex]

Step-by-step explanation:

Slope intercept form of line equation is y = mx + b, m = slope, b = y-intercept

Slope of line perpendicular to y =m x + b will have slope   - (1/m)

4x+y=3 can be re-written as
y = -4x + 3

Slope = -4

Slope of line perpendicular to this line is - (1/-4)  = 1/4

Line equation: y = (1/4) x + b

Plug in x, y values from given point into this line equation to find b
-3 = 1/4 x 4 + b

-3 = 1 + b

-3 -1 = b

b = -4

So equation of perpendicular line is y = (1/4)x - 4

Answer:

d=1, 1+12=13 Variable can be a number or any number .

Answer:

8.5

Step-by-step explanation:

11-3/2-1

11-1.5-1

9.5-1

8.5

Solution :

Properties of Functions:

Definition of a Function: A function is a rule or formula that associates each element in the set X (an input) to exactly one and only one element in the set Y (the output). Different elements in X can have the same output, and not every element in Y has to be an output.

Definition of the Domain of a Function: The set of all possible inputs of a function is defined as the domain. The domain of a real-valued function defined by a formula for y in terms of x will be the set of all x input-values that result in a real y output-value unless the domain of the function is further restricted.

Definition of the Range of a Function: The set of all possible outputs of a function is defined as the range. The range of a real-valued function defined by a formula for y in terms of x will be the set of all y output-values that result from the x input-values in the domain.

Function Notation: Given that f(x) is given by some formula containing x, f(B) will be the same formula with each x replaced by B.

Linear Function Definition: If a function may be written in the form f(x) = mx + b where x is the independent variables and m and b are constants, then f(x) represents a linear function. The variable m is defined as the slope and the point (0, b) represents the y-intercept. An equation in this form is known to be in Slope-Intercept Form.

Linear Function Slope Definition: Given that f(x) = mx + b, then m is defined as the slope where:

for any two points (x1, y1) and (x2, y2) on the line.  Graphically, the slope represents the change in y with respect to x on the graph of the line.

Linear Functions of Parallel Lines If two linear functions are given by f(x) = m1x + b and g(x) = m2x + b, and m1 = m2, then the graphs of f(x) and g(x) will consist of two lines that are parallel to each other.

Linear Functions of Perpendicular Lines If two linear functions are given by f(x) = m1x + b and g(x) = m2x + b, and m1 = -1/m2, then the graphs of f(x) and g(x) will consist of two lines that are parallel to each other.

Graphs of Even Functions Given a function f(x), if f(c) = f(-c) for all c in the domain, then f(x) is an even function and its graph will have symmetry with respect to the y-axis.

Graphs of Odd Functions Given a function f(x), if f(c) = -f(-c) for all c in the domain, then f(x) is called an odd function and its graph will have symmetry with respect to the origin.  Symmetry with respect to the origin implies that a 180-degree rotation of the graph about (0,0) results in an identical graph.

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-7² = -49

Given options are as follows -

a. (-6)^2

b. (1/3)^2

c. 0.5^2

d. -7^2

by solving 1 option we get

(-6)×(-6)

= 36

we get a positive value

because we know that (-)×(-) = +

so this option is not less than zero

again by solving 2 option we get

1/3^2

1/3× 1/3

= 1/9

it is also a positive value

because we know that (+)×(+) = +

so this option is not less than zero

Further by solving 3 option we get

(0.5)²

(0.5)×(0.5)

= 0.25

again it is also a positive value

so this option is not less than zero

but for the option 4

-(7)²

= -49

which is a negative value .

A negative number is any number that is less than zero

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The inequality to represent the last statement that was made by Mai will be t <= 2.

It should be noted that an equation simply means the relationship that can be used to show the relationship among the variables.

It should be noted that the last statement made by Mai is that I think triathlon athletes generally train for no more than 2 hours a day.

Therefore, the inequality to represent this will be t <= 2.

where t = number of hours trained.

This implies that t is less than or equal to 2 hours

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Mai said, "I'm not sure the graph is right. For example, the point is in the shaded region, but it's not realistic for an athlete to swim for 10 hours and bike for 3 hours in a training session! I think triathlon athletes generally train for no more than 2 hours a day."

Write an inequality to represent Mai's last statement.

The wage of Katie before pay rise or the value of old wage is equal to $220.

What is percentage ?

Percentage is calculated by dividing the value by the total value, and then multiplying the result by 100.

It is given that the new wage is $264 as Katie gets a 20% pay rise.

Let's assume the old wage be x.

The new wage can be written as :

x + (20x / 100)

This is equal to $264.

i.e.,

(x + 20x/100) = 264

or

120x/100 = 264

Let's solve this expression to get the value of old wage.

120x = 264 × 100

or

120x = 26400

or

Old wage (x) = $220

Therefore , the wage of Katie before pay rise or the value of old wage is equal to $220.

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The total number of boxes required to cover the kitchen floor is 14.

The dimensions of the kitchen floor are 14' × 24'

⇒Length of the kitchen floor = 14 feet

⇒Width of the kitchen floor= 24 feet

The area of the kitchen floor= Length × Width

⇒ Area = 14 × 24

⇒ Area = 336 sq. ft.

Since, 4 boxes of flooring cover 100 sq. ft.

∴1 box will cover = 100/4 sq. ft.

⇒25 sq. ft.

Now, Number of boxes required to cover the floor of the kitchen will be,

⇒ Area of the floor / Area covered by 1 box of flooring

⇒336/25

⇒ 13.44

∴ The total number of boxes required to cover the kitchen floor is 14 (rounded up from 13.44).

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Answer:

x = 8

Step-by-step explanation:

3 + 10(9X + 4) = 763  Distribute the 10

3 + 10(9x) + 10(4) = 763

3 + 90x + 40 = 763  Combine like terms

90x + 43 = 763  Subtract 43 from both sides

90x = 720  Divide both sides by 90

x = 8

Answer:

x=8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let,

One of the siblings age be = x

So, the other siblings ages are = x+2, x+4 and x+6

Since,

Ashley is the oldest sibling so his age is x + 6

∴ By the problem,

=> x + (x+2) + (x+4) + (x+6) = 100

=> 4x + 12 = 100

=> 4x = 100 - 12

=> 4x = 88

=> x = 22

Now,

We got the age of the youngest one that is 22 years

As,

Ashley is the oldest sibling so his age is

= 22 + 6 = 28 years

Hence,

The age of Ashley is 28 years (Ans)

Answer:

28 years old

Step-by-step explanation:

100/4 = 25

The ages are consecutive even numbers,

so add 1 to and subtract 1 from 25.

Add 3 to and subtract 3 from 25.

Ages: 22, 24, 26, 28

Ashley is the oldest: 28 years old

Answer:

0<x<4

Step-by-step explanation:

Ok, so the question is basically asking where balls height goes up, then down. So the x has to be in the middle of a bounce. That means that x has to be 0, 4, 6, or 8. So the number on the left side must be one of the numbers I just listed. And then the number on the right must be the end of the bounce, so it would be either 4, 6, 8, or 10. So then your answer after looking must be 0<x<4

Step-by-step explanation:

first question:

1/7 - 3/4 LCM : 28

4/28 - 21/28

= -17/28

second equation:

1/6 - 4/9 LCM : 36

6/36 - 16/36

= -10/36

= -5/14

( I believe these are the answers )

Answer:

[tex] \sf \: 12x−1[/tex]

Step-by-step explanation:

Let's simplify step-by-step.

4(3x+2)−9

Distribute:

=(4)(3x)+(4)(2)+−9

=12x+8+−9

Combine Like Terms:

=12x+8+−9

=(12x)+(8+−9)

=12x+−1

=12x−1

The required set of positive two-digit even numbers less than 25 that do not contain the digit 0 is 12,14,16,18,22,24.

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.

Given:

Set D is the set of positive two-digit even numbers less than 25 that do not contain the digit 0.

According to given question we have

2-digit numbers are the numbers that have two digits and they start from the number 10 and end on the number 99.

Starting at 12 going up the two digit numbers even numbers less than 25 that do not contain the digit 0.

12,14,16,18,22,24

Therefore, the required set of positive two-digit even numbers less than 25 that do not contain the digit 0 is 12,14,16,18,22,24.

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Answer:

9.53 x 10^5

Step-by-step explanation:

a x 10b

a = 9.53

b = 5

Answer:

9.53

Step-by-step explanation:

math math math math math math

Answer:

Step-by-step explanation:

if you're using Del Math (yk what i'm talking about) it requires you to have a specific way of putting it.

The equation is going to be:

4.25x + 167 = 655.75

your x is going to be:

115

I hope this helps!

For the explanation hopefully, this will make sense (english isn't my first language)

So you know the number of hours: 4.25

cost of the parts: 167

total cost: 655.75

then finally the cost per hour: x

----

so now when you write your equation you're going to end up with the total number of hours (times the cost per hour) added to the cost of the parts, then the remaining will be your total cost. This is how I pictured the equation portion in my head.

for the actual solving part you subtract the cost of the parts from itself as well as the total which should leave you with: 4.25x = 488.75

then you're going to divide 4.25 from each side, as you do.

Then you have the cost of labour per hour: 115

The equation to find the cost of the labor per hour is:

167 + 4.25C = 655.75

The cost of the labor per hour is $115.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

Number of hours worked = 4.25

Cost of the parts used = $167

Total cost = $655.75

Now,

We can write an equation to find the C = cost per hour.

167 + 4.25C = 655.75

Solve for C.

167 + 4.25C = 655.75

4.25C = 655.75 - 167

4.25C = 488.75

C = 115

Thus,

The cost of the labor per hour is $115.

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