Fraction equivalents
7/15 = ?/45

Answer:

A. x^2 – 2x – 8

Step-by-step explanation:

Answer:

D. He recorded his paycheck amount for April 23rd incorrectly. Yes, this was Adam's mistake. The correct amount should be 341.60 and not 338.45.

Step-by-step explanation:

1. Let's review the information given to us to help Adam to determine where his error is.

A. He completely forgot to include the clothes he bought from Bargains RUS. No, he didn't. It was recorded properly,  including the sales tax amount.

B. He made an arithmetic error in the balance column. No he didn't, the balance was calculated correctly after each transaction.

C. He recorded one of his withdrawals in the deposit column. No, he didn't. All of the withdrawals are in the right column.

D. He recorded his paycheck amount for April 23rd incorrectly. Yes, this was Adam's mistake. The correct amount should be 341.60 and not 338.45.

Adam's error in the register lies in the paycheck amount recorded for the April 23rd deposit. His hourly wage is $9.76 and he worked for 35 hours, which should result in a pay of $341.60, but he recorded it as $338.45.

The error in Adam's register appears to be in the paycheck amount recorded for the April 23rd deposit. Here's how we can figure it out

So, Adam recorded his paycheck amount for April 23rd incorrectly.

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Answer:

Step-by-step explanation:

10 and 6/10 = 10.6

4 hundredths = 4/100 =  0.04

10.6 / 0.04 = 265 <==

Answer:

(A) [tex]4.9\times 10^{-7}\ m[/tex]

Step-by-step explanation:

Given:

Frequency of the wave (f) = [tex]6.1\times 10^{14}\ Hz[/tex]

Speed of the wave (v) = [tex]3.00\times 10^8\ m/s[/tex]

The wavelength equation of the wave is given as:

[tex]\lambda=\dfrac{v}{f}[/tex]

Here, [tex]\lambda \to wave\ wavelength[/tex]

Now, plug in the given values and simplify.

[tex]\lambda=\frac{3\times 10^8}{6.1\times 10^{14}}\\\\\lambda=4.9\times 10^{-7}\ m[/tex]

Therefore, the wavelength of the wave is option (A) [tex]4.9\times 10^{-7}\ m[/tex]

Answer:

3.229 revolutions per minute

Step-by-step explanation:

The angular velocity of an object is the rate at which it rotates around a fixed axis. In this case, the hamster wheel is rotating.

To find the angular velocity of the wheel, we need to convert the linear velocity of the hamster into angular velocity.

The linear velocity of the hamster is given as 17 centimeters per second. This means that for every second, the hamster moves 17 centimeters along the circumference of the wheel.

To find the angular velocity, we need to find the distance traveled along the circumference of the wheel in one revolution. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the wheel.

In this case, the radius of the wheel is 10 centimeters. So, the circumference of the wheel is C = 2π(10) = 20π centimeters.

Since the hamster runs at a speed of 17 centimeters per second, in one revolution of the wheel, it covers a distance of 20π centimeters.

Now, we can find the angular velocity by dividing the linear velocity by the distance traveled in one revolution.

Angular velocity = linear velocity / distance traveled in one revolution

Angular velocity = 17 centimeters per second / (20π centimeters per revolution)

Simplifying the expression, we get:

Angular velocity = 17 / (20π) revolutions per second

To convert the angular velocity from revolutions per second to revolutions per minute, we need to multiply it by 60 (since there are 60 seconds in a minute).

Angular velocity in revolutions per minute = (17 / (20π)) * 60

Calculating the value, we get:

Angular velocity in revolutions per minute ≈ 3.229 revolutions per minute

Therefore, the wheel will s

AI-generated answer

The angular velocity of an object is the rate at which it rotates around a fixed axis. In this case, the hamster wheel is rotating.

To find the angular velocity of the wheel, we need to convert the linear velocity of the hamster into angular velocity.

The linear velocity of the hamster is given as 17 centimeters per second. This means that for every second, the hamster moves 17 centimeters along the circumference of the wheel.

To find the angular velocity, we need to find the distance traveled along the circumference of the wheel in one revolution. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the wheel.

In this case, the radius of the wheel is 10 centimeters. So, the circumference of the wheel is C = 2π(10) = 20π centimeters.

Since the hamster runs at a speed of 17 centimeters per second, in one revolution of the wheel, it covers a distance of 20π centimeters.

Now, we can find the angular velocity by dividing the linear velocity by the distance traveled in one revolution.

Angular velocity = linear velocity / distance traveled in one revolution

Angular velocity = 17 centimeters per second / (20π centimeters per revolution)

Simplifying the expression, we get:

Angular velocity = 17 / (20π) revolutions per second

To convert the angular velocity from revolutions per second to revolutions per minute, we need to multiply it by 60 (since there are 60 seconds in a minute).

Angular velocity in revolutions per minute = (17 / (20π)) * 60

Calculating the value, we get:

Angular velocity in revolutions per minute ≈ 3.229 revolutions per minute

Therefore, the wheel will spin at a rate of approximately 3.229 revolutions per minute.

Answer:

[tex]\frac{12q^{\frac{7}{3}}}{p^{3}}[/tex]

Step-by-step explanation:

Here are some rules you need to simplify this expression:

Distribute exponents: When you raise an exponent to another exponent, you multiply the exponents together. This includes exponents that are fractions. [tex](a^{x})^{n} = a^{xn}[/tex]

Negative exponent rule: When an exponent is negative, you can make it positive by making the base a fraction. When the number is apart of a bigger fraction, you can move it to the other side (top/bottom). [tex]a^{-x} = \frac{1}{a^{x}}[/tex], and to help with this question: [tex]\frac{a^{-x}b}{1} = \frac{b}{a^{x}}[/tex].

Multiplying exponents with same base: When exponential numbers have the same base, you can combine them by adding their exponents together. [tex](a^{x})(a^{y}) = a^{x+y}[/tex]

Dividing exponents with same base: When exponential numbers have the same base, you can combine them by subtracting the exponents. [tex]\frac{a^{x}}{a^{y}} = a^{x-y}[/tex]

Fractional exponents as a radical: When a number has an exponent that is a fraction, the numerator can remain the exponent, and the denominator becomes the index (example, index here ∛ is 3). [tex]a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}[/tex]

[tex]\frac{(8p^{-6} q^{3})^{2/3}}{(27p^{3}q)^{-1/3}}[/tex]        Distribute exponent

[tex]=\frac{8^{(2/3)}p^{(-6*2/3)}q^{(3*2/3)}}{27^{(-1/3)}p^{(3*-1/3)}q^{(-1/3)}}[/tex]        Simplify each exponent by multiplying

[tex]=\frac{8^{(2/3)}p^{(-4)}q^{(2)}}{27^{(-1/3)}p^{(-1)}q^{(-1/3)}}[/tex]        Negative exponent rule

[tex]=\frac{8^{(2/3)}q^{(2)}27^{(1/3)}p^{(1)}q^{(1/3)}}{p^{(4)}}[/tex]        Combine the like terms in the numerator with the base "q"

[tex]=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)}q^{(1/3)}}{p^{(4)}}[/tex]        Rearranged for you to see the like terms

[tex]=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)+(1/3)}}{p^{(4)}}[/tex]        Multiplying exponents with same base

[tex]=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(7/3)}}{p^{(4)}}[/tex]        2 + 1/3 = 7/3

[tex]=\frac{\sqrt[3]{8^{2}}\sqrt[3]{27}p\sqrt[3]{q^{7}}}{p^{4}}[/tex]        Fractional exponents as radical form

[tex]=\frac{(\sqrt[3]{64})(3)(p)(q^{\frac{7}{3}})}{p^{4}}[/tex]        Simplified cubes. Wrote brackets to lessen confusion. Notice the radical of a variable can't be simplified.

[tex]=\frac{(4)(3)(p)(q^{\frac{7}{3}})}{p^{4}}[/tex]        Multiply 4 and 3

[tex]=\frac{12pq^{\frac{7}{3}}}{p^{4}}[/tex]        Dividing exponents with same base

[tex]=12p^{(1-4)}q^{\frac{7}{3}}[/tex]        Subtract the exponent of 'p'

[tex]=12p^{(-3)}q^{\frac{7}{3}}[/tex]        Negative exponent rule

[tex]=\frac{12q^{\frac{7}{3}}}{p^{3}}[/tex]        Final answer

Here is a version in pen if the steps are hard to see.

Answer:

[tex] - 10 \div 9 = \frac{ - 10}{9} [/tex]

[tex]10 \div ( - 9) = \frac{10}{ - 9} [/tex]

[tex] - ( - 10 \div ( - 9)) = - (10 \div 9) = - \frac{10}{9} [/tex]

[tex] - \frac{10}{9} = \frac{10}{ - 9} = - \frac{10}{9} [/tex]

A and B are the correct choices.

Answer:

[tex]\sqrt[3]{0.000004913}=0.017[/tex]

Step-by-step explanation:

Cubic Root

The cubic root of a number N is M, if

[tex]M^3=N[/tex]

It's usually tedious to manually compute cubic roots, but if we use some basic algebra concepts, the job is easily done.

Let's compute

[tex]M=\sqrt[3]{0.000004913}[/tex]

The argument can be expressed in scientific notation as

[tex]0.000004913= 4913\ 10^{-9}[/tex]

The power of 10 has an exact cubic root since the exponent is a multiple of 3. To find the cubic root of the mantissa, we note it's the triple product of 17, i.e.

[tex]4913=17*17*17=17^3[/tex]

Thus our number is

[tex]M=\sqrt[3]{17^3\ 10^{-9}}=17\ 10^{-3}=0.017[/tex]

We have then

[tex]\boxed{\sqrt[3]{0.000004913}=0.017}[/tex]

Answer:

The population of moose after 12 years will be 7,692

Step-by-step explanation:

we know that

In this problem we have a exponential function of the form

[tex]y=a(b^x)[/tex]

where

y ----> population of moose

x ----> the time in years

a is the y-intercept or initial value

b is the base of the exponential function

we have

[tex]a=40[/tex] ----> the y-intercept is given in the table (value of y when the value of x is equal to zero)

substitute

[tex]y=40(b^x)[/tex]

Find the value of b

For x=1, y=62

substitute in the equation

[tex]62=40(b^1)\\b=62/40\\b=1.55[/tex]

therefore

[tex]y=40(1.55^x)[/tex]

What will be the population of moose after 12 years?

For x=12 years

substitute in the exponential equation

[tex]y=40(1.55^{12})[/tex]

[tex]y=7,692[/tex]

Answer:

A, (5x + 3)(5x – 3)

B, (7x + 4)(7x + 4)

E, (x – 9)(x – 9)

F, (–3x – 6)(–3x + 6)

Step-by-step explanation:

Answer:

A, B, E, F

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

23 - 9 = 14

Answer:

14

Step-by-step explanation:

23-9=14

Answer:

The interest rate should be 11.6%.

Step-by-step explanation:

Let us assume that at r% rate of interest compounded annually is required to triple an investment of $P in 10 years.

So, using the formula of compound interest, we can write

[tex]3P = P(1 + \frac{r}{100})^{10}[/tex]

⇒ [tex]3 = (1 + \frac{r}{100})^{10}[/tex]

⇒ [tex](1 + \frac{r}{100}) = 1.116[/tex]

⇒ [tex]\frac{r}{100} = 0.116[/tex]

⇒ r = 11.6 %

Therefore, the interest rate should be 11.6%. (Answer)

Answer:

80 is the height of the platform

the rocket didnt launch from the ground so u need to add it in

Answer:

The rocket was launched from a platform 80 feet above the ground.

Step-by-step explanation:

The + 80 is where it starts

Answer:

(20 + n)¢

Step-by-step explanation:

With Company X, it costs 35¢ to connect  and then 5¢ for each minute.

So, for n minutes of calling the company X charges, C(x) = (35 + 5n)¢

Again,  With Company Y,  it costs 15¢ to connect and then 4¢ for each  minute.

So, for n minutes of calling the company Y charges, C(y) = (15 + 4n)¢.

Therefore, the company Y charges for n minutes of calling less than company X is [(35 + 5n) - (15 + 4n)]¢ = (20 + n)¢ (Answer)

To find how much more Company X charges than Company Y for n minutes, subtract the cost of Company Y from the cost of Company X. The expression to represent the difference in charges is 0.2 + 0.01n.

To find how much more Company X charges than Company Y, we need to subtract the cost of Company Y from the cost of Company X for n minutes.

Let's denote the cost of Company X as CX and the cost of Company Y as CY.

For Company X, the cost is $0.35 to connect and $0.05 for each minute. So, the cost of CX for n minutes is given by CX = 0.35 + 0.05n.

Similarly, for Company Y, the cost is $0.15 to connect and $0.04 for each minute. So, the cost of CY for n minutes is given by CY = 0.15 + 0.04n.

To find the difference in charges, we subtract CY from CX:

Company X charges (CX - CY) = (0.35 + 0.05n) - (0.15 + 0.04n) = 0.2 + 0.01n

Answer:

2.736

Step-by-step explanation:

5 it more --> round up

4 or less --> leave it how it is

Answer:

i think its 2.74

Step-by-step explanation:

Answer:

x = -4/5 = -0.800

Step-by-step explanation:

Pull out like factors :

-12 - 15x  =   -3 • (5x + 4)

Solve :  

-3   =  0

Solve  :

5x+4 = 0

5x = -4

x = -4/5 = -0.800

Answer:

B

Step-by-step explanation:

2x-5y=13.........(1) × 3

-3x+2y=13.......(2) × 2

6x - 15y = 39

-6x + 4y = 26

Adding

6x - 6x - 15y + 4y = 13 + 13

Answer:

Step-by-step explanation:

2x - 5y = 13

-3x + 2y = 13

multiply the top equation by 3 and the bottom one by 2, then add <==

watch...

2x - 5y = 13.....multiply by 3

-3x + 2y = 13....multiply by 2

-----------------

6x - 15y = 39 (result of multiplying by 3)

-6x + 4y = 26 (result of multiplying by 2)

-----------------add

- 11y = 65.....notice how out x terms were eliminated :)

The square root of 25/35, which simplifies down to the square root of 5/7 is an irrational number because the decimal form of the square root doesn't terminate or repeat.

The question is asking about the nature of the square root of the fraction 25/35. To solve it, we first simplify the fraction to its lowest terms, which is 5/7. The square root of 5/7 is a decimal that doesn't terminate or repeat, which means that it is an irrational number. In contrast, 25/35 rational refers to numbers that can be expressed as a ratio of two integers, which the square root of 5/7 cannot be.

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Explanation: Calculation of the general sales taxes of Connecticut State for 2019 ... combined rates mentioned above are the results of Connecticut state rate (6.35%). There is no county sale tax for Connecticut. There is no city sale tax for the Connecticut cities. ... The Connecticut's tax rate may change depending of the type of purchase.

Answer:

0.84+1.00=1.84 +14=15.

Answer:

the 6.192# melebulated by 59 and devide it by 597 your answere is 64

Step-by-step explanation:

Answer:

AC = 52.8

Step-by-step explanation:

33/20 = 1.65

12*1.65 = 19.8

BA = 19.8

CB + BA = AC

33 + 19.8 = 52.8

Answer:

AC = 52.8

Step-by-step explanation:

Since BE is parallel to CD and intersects the 2 sides of the triangle then it divides those sides proportionally, that is

[tex]\frac{BC}{AB}[/tex] = [tex]\frac{DE}{AE}[/tex], substituting values

[tex]\frac{33}{AB }[/tex] = [tex]\frac{20}{12}[/tex] ( cross-  multiply )

20AB = 396 ( divide both sides by 20 )

AB = 19.8

Thus

AC = AB + BC = 19.8 + 33 = 52.8

Because there are parentheses we distribute the negative signs:

3 - 20i + (-14) - 6i + (-8) + 2i

Next combine like terms:

3 + (-14) + (-8) and -20i - 6i + 2i

-19 -24i

Answer:

378

Step-by-step explanation:

First: Start with the parentheses

Meaning to add 27 + 36 then divide by 3.

Second: You should have 21 afterwards,

when you have this number you can use the number

outside of the parentheses a.k.a (21 x 18)

Third: You should get the answer "378" unless you do something wrong.

To calculate the expression 18•(27+26/3), follow the order of operations: division, addition, and then multiplication. The result is approximately 642.006.

To calculate the expression 18•(27+26/3), we need to follow the order of operations. First, we perform the division 26/3 which gives us 8.66666... (rounded to the nearest thousandth, this is 8.667). Next, we add 27 and 8.667 which equals 35.667. Finally, we multiply 18 by 35.667 to get the final result of 642.006 (rounded to the nearest thousandth, this is 642.006).

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There are approximately 745 pages in main story

Solution:

Let "x" be the number of pages in main story

Let "y" be the number of pages in prologue

Given that there are 750 pages in all

Therefore,

number of pages in main story + number of pages in prologue = 750

x + y = 750 ---------- eqn 1

The main story has 150 times as many pages as the prologue

Therefore, a equation is framed as:

number of pages in main story = 150(number of pages in prologue)

x = 150y ----------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 2 in eqn 1

150y + y = 750

151y = 750

y = 4.967

Substitute y = 4.967 in eqn 2

x = 150(4.967)

x = 745.05

Thus there are approximately 745 pages in main story

Answer:

central

Step-by-step explanation:

greetings the correct answer is central odyssey ware

Answer:

Hence (3, -3)   is  on the given line y = -2x + 3

Step-by-step explanation:

For a point on the Line, It must Satisfy the Equation of a line

Therefore for

[tex]y=-2x+3[/tex]

For (-2,-1)

Substitute x = - 2 and y = -1 in above equation

Left Hand Side = y

                         = -1

Right Hand Side = -2 × (-2) +3

                           = 4 +3

                           = 7

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (-2,-1)  is NOT on the given line

For (3, -3)

Substitute x = 3 and y = -3 in above equation

Left Hand Side = y

                         = -3

Right Hand Side = -2 × (3) +3

                           = -6 +3

                           = -3

Left Hand Side = Right Hand Side

Satisfied

Hence (3, -3)   is  on the given line y = -2x + 3

For (3, 3)

Substitute x = 3 and y = 3 in above equation

Left Hand Side = y

                         = 3

Right Hand Side = -2 × (3) +3

                           = -6 +3

                           = -3

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (3,3)  is NOT on the given line

For (-3,-9)

Substitute x = -3 and y = -9 in above equation

Left Hand Side = y

                         = -9

Right Hand Side = -2 × (-3) +3

                           = 6 +3

                           = 9

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (-3,-9)  is NOT on the given line

Only the point (3, -3) lies on the line y = -2x + 3. None of the other points satisfy the equation.

To determine which point lies on the line y = -2x + 3, we need to substitute the coordinates of each point into the equation:

(-2, -1): Substitute x = -2 into y = -2x + 3:

y = -2(-2) + 3 = 4 + 3 = 7. Since y = -1, this point does not lie on the line.

(3, -3): Substitute x = 3 into y = -2x + 3:

y = -2(3) + 3 = -6 + 3 = -3. Since y = -3, this point lies on the line.

(3, 3): Substitute x = 3 into y = -2x + 3:

y = -2(3) + 3 = -6 + 3 = -3. Since y = 3, this point does not lie on the line.

(-3, -9): Substitute x = -3 into y = -2x + 3:

y = -2(-3) + 3 = 6 + 3 = 9. Since y = -9, this point does not lie on the line.

The only point that satisfies the equation is (3, -3).

Complete question:

Which point is on the line y = -2x + 3?

A. (-2,-1)

B. (3, -3)

C. (3, 3)

D. (-3,-9)

Answer:

[tex]\sqrt{10}[/tex]

Step-by-step explanation:

Since this is a right triangle then we can apply the Pythagorean theorem

look at the photo below for the details.

:)

We can model the statement "one-third the sum of eleven and [p]" as y = (1/3)(11 + p)

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have one-third the sum of eleven and [p].

We can model the given question as -

y = (1/3)(11 + p)

Therefore, we can model the statement "one-third the sum of eleven and [p]" as y = (1/3)(11 + p)

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Answer:

24 + x = 60

Owen earns $36 in the Saturday afternoon.

Step-by-step explanation:

On Saturday morning, Owen earned $ 24. By the end of the afternoon, he had earned a total of $ 60.

Now, if Owen earned $x on Saturday afternoon, then the equation of x that models the situation will be  

24 + x = 60 (Answer)

Solving the above equation we get

x = $36

Therefore, Owen earns $36 on Saturday afternoon. (Answer)