Without solving, determine whether the solution of 1/3x=21 is
greater than
or less than 21. Explain.

Answer:

Option 2, option 3, option 4

Answer:

$27.69

Step-by-step explanation:

Given

Monthly budget (See attachment)

\(Month = 4\ weeks\)

\(Week = 40 \ hour\)

Required

Determine the closest hourly wage

From the attachment, the monthly budget is:

\(Budget = \$ 4430\)

First, we calculate the closest weekly earnings.

Since a month = 4 weeks.

Then

\(Weekly\ Earnings = \frac{\$4430}{4}\)

\(Weekly\ Earnings = \$1107.5\)

Next, we calculate the hourly earnings:

Since 1 week = 40 hour

Then

\(Hourly\ Earnings = \frac{\$1107.5}{40}\)

\(Hourly\ Earnings = \$27.6875\)

From the list of options, the closest is: $27.69

Answer:

7 Cows and 8 Chickens

Step-by-step explanation:

Note that cows have four legs each and chickens have two legs each.

if there were only cows, then 15 cows times 4 legs for each cow would give 15 x 4 = 60 legs. 60 is greater than 44, so some (maybe all) of the animals are chickens.

If there were only chickens, then 15 chickens times 2 legs for each chicken would give 15 x 2 = 30 legs. 30 is less than 44, so we have confirmed that there is a mixture of both cows and chickens on the farm.

One approach would be to build a table of possibilities:

Total legs will equal number of cows times 4 plus number or chickens times 2 and we know the total number of animals is 15, so we keep cows plus chickens equal to 15 and just keep adding a cow and subtracting a chicken and do the math until.we get 44 legs. We know that it will take less than 13 tries, since we already ruled out 15 cows or 15 chickens. We'll start with 1 cow and 14 chickens and go from there

1 Cow + 14 Chickens = (1 x 4) + (14 x 2) = 4 + 28 = 32 legs

2 Cows + 13 Chickens = (2 x 4) + (13 x 2) = 8 + 26 = 34 legs

3 Cows + 12 Chickens = (3 x 4) + (12 x 2) = 12 + 24 = 36 legs

4 Cows + 11 Chickens = (4 x 4) + (11 x 2) = 16 + 22 = 38 legs

5 Cows + 10 Chickens = (5 x 4) + (10 x 2) = 20 + 20 = 40 legs

6 Cows + 9 Chickens = (6 x 4) + (9 x 2) = 24 + 18 = 42 legs

7 Cows + 8 Chickens = (7 x 4) + (8 x 2) = 28 + 16 = 44 legs

We can stop here because we can see that 7 Cows and 8 Chickens have a total of 44 legs.

Another way to approach this is to use algebra and to make is shorter to write we can assign a variable to each item and relate them in some way.

Let's use the letter x to stand for cows and the letter y to stand for chickens so we don't have to keep writing chickens and cows. x and y are just common letters to use, by the way, could use w and k perhaps since cow has a w and chicken has a k...sadly they both start with c, so we can't use that for both.

We know a couple different, but related, things.

One thing we know is that the total number of animals is 15. We can write that as:

x + y = 15

That means cows (x) plus chickens (y) equals 15.

A second thing we know is that the total number of legs is 44. We can write that as

4x + 2y = 44

That means 4 times x (cow) plus 2 times y (chicken) is equal to 44 since each cow has 4 legs and each chicken has 2 legs.

Since we now have two related equations and two variables we can solve for the variables.

If we take the first equation and rearrange it, by subtracting x from both sides, we can see that one way to do it is the following

y = 15 - x

That means the number of chickens (y) is equal to 15 minus the number of cows (x). As long as we do the same thing on both sides of the equals sign the equation is still.equal...you will see this again below.

Now we can then substitute 15 - x for y in the second equation and then all we have is x in that equation. (We can do this because y is equal to 15 minus x...they both have the same value and mean the same thing...they are equal to each other)

4x + 2(15 - x) = 44

As you can see, we now have 2 times 15 minus x where we had 2 times y before. If we multiply the 2 through we get because 2 times 15 is 30 and 2 times x is 2x

4x + 30 - 2x = 44

We can subtract the 2x from 4x and we get

2x + 30 = 44

Now we can subtract 30 from both sides of the equation because as long as we do the same thing on both sides of the equals sign the equality holds true

2x + 30 - 30 = 44 - 30

30 minus 30 is zero and 44 minus 30 is 14 so now we have

2x = 14

If we divide both sides by two, we still maintain the equality and we get x on one side as 2x divided by 2 is 1x or just x and we get 7 on the other side as 14 divided by 2 is 7

x = 7

That means we have 7 Cows as x represents cows, so half the problem solved

If we now go back to our first equation,

x + y = 15

We can replace x with 7 and get

7 + y = 15

We can subtract 7 from both sides and maintain the equality and isolate y

7 - 7 + y = 15 - 7

Again, 7 minus 7 is zero so we have isolated y and 15 minus 7 is 8

y = 8

This means we have 8 Chickens since y represents chickens

Once again we have shown that Old MacDonald has 7 Cows and 8 Chickens

The possible values of x are 51% < x < 59%.

When you are given various values, the range of those values is how big the difference is between the largest value and the smallest value. In other words, the range is what you get when you subtract the smallest value in the group from the largest value in the group.

Its possible values are 1, 2, 3, 4, 5, and 6; each of these possible values has a probability of 1/6. 4. The word “random” in the term “random variable” does not necessarily imply that the outcome is completely random in the sense that all values are equally likely.

Let K represent Kofi

1st paper = 45/100

2nd paper = x / 100

Mean score = ( 45 + x ) % / 2

The possible range of x = 48% < (45+X)/2 < 52%

Cross multiplying

96% < 45 + x < 104%

Subtract 45 from both sides

Range = 51% < x < 59%

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Answer:

5 seconds

Step-by-step explanation:

just divide 60 by 12 ( a dozen) and your answer is 5

Answer:

0.2

Step-by-step explanation:

60 ÷ 12 = 5 that's how many donuts she eats in 1 second

12 ÷ 60 = 0.2 how long it takes her to eat one donut

Answer:

y = ⅓(x - 1425)

Step-by-step explanation:

Given

Budget = x

Mortgage = 1425

Required

Determine the amount spent on recreational activities.

First, we need to get the balance after she pays her mortgage.

Balance = Budget - Mortgage

Balance = x - 1425

From the question, we understand that she spends ⅓ of the balance on recreational activities.

Represent this with y.

y is calculated as thus:

y = ⅓ of Balance

y = ⅓ * (x - 1425)

y = ⅓(x - 1425)

Hence, the above equation y = ⅓(x - 1425) can be used to calculate the amount spent on recreational activities

Answer:

Excise tax

Step-by-step explanation:

Correct me if I'm wrong <3

Answer:

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle. In this case, the diameter is given as 14 cm, so we can substitute that into the formula:

C = π(14 cm)

Multiplying, we get:

C = 14π cm

So the circumference of the circle is 14π cm. The units are centimeters, since circumference is a length measurement.

The Vales of x in the equations are : 1) 3 (2) 1  (3) 5  (4) 14  (5) 10 respectively

A linear equation in one variable is that in which the highest power of its variable is 1

The given equations and their solutions are

2x +1 = 7

By collecting like terms we have

2x = 3

x = 3

2) The given equation is 4x +7 = 11

By collecting like terms we have

4x = 4

Making x the subject we have

x = 1

3) 2x -3 = 7

By collecting like terms we have

2x = 10

Making x the subject we have

x = 5

4) 1/2 x - 3 = 7

By collecting like terms we have

1/2x = 7

x= 14

5) The given equation is 3x - 11 = 19

By collecting like terms we have

3x= 30

Therefore x= 10

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Answer:

\(sqrt{-64} =8i\\\\sqrt{-15} =isqrt{15} \\sqrt{-100} =10i\\sqrt{-25} =2i\sqrt{6}\)

Step-by-step explanation:

I hope this helps

Derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.

What is differentiation?

In arithmetic, the derivative of a function of a true variable measures the sensitivity modification of the perform price with relation to a change in its argument. Derivatives are a elementary tool of calculus.

Main body:

by using product rule;

Let = u = x² + 4x + 6

⇒ du/dx = 2x + 4 .

Now y = u⁵

⇒ dy/dx = 5u⁴ .

dy/dx = dy/dx * du/dx = 5u⁴ * (2x + 4)

= 5 * (x² + 4x + 6)⁴ * (2x + 4)

= 5(2x + 4) * (x² + 4x + 6)⁴

hence , derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.

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Answer:

B

Step-by-step explanation:

Answer:

x=-pie/12

sinxcosx=-1/4

multiply both sides by 2

sin2x = 2sinxcosx we know

now equation will be

sin2x = -1/2

2x=-pie/6

x=-pie/12

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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Answer:

Nah bro I gotchu! 2x+28=42

2x=42-28

2x=14

x=7

:)

Step-by-step explanation:

The step that is not allowed is (b) add the left side of equation 2 to the left side of equation 1

The system of equations is given as:

2x - 3y = 12

-2x + y = 8

This means that the step that is not allowed is (b)

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Answer:A

Step-by-step explanation:

Answer:

-6r+6

Step-by-step explanation:

Let us expand the expression:

8-(6r+2)=

8-6r-2=

6-6r

OR

-6r+6

I hope this helps! :)

Answer:

6r+6

Step-by-step explanation:

we dont know the variable's number value yet so you can't solve anything with the 6r. We use distribbutive property and solve 8-2 since the 8 is just subtracting everything in the parenthesis. 8-2=6 and you can't do anything with the 6r so the expression would end up as 6r+6.

Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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Answer:

Hey 2923928 !

Answer: The second choice

\( \dashrightarrow \: { \tt{(x + 3)( - {x}^{2} + 4x - 2)}}\)

• from distributive property;

\(\dashrightarrow \: { \tt{( - {x}^{3} + 4 {x}^{2} - 2x - 3 {x}^{2} + 12x - 6) }}\)

• simplify:

\(\dashrightarrow \: { \tt{ - {x}^{3} + {x}^{2} + 10x - 6}}\)

Answer:

-x^3 + x^2 + 10x - 6

Step-by-step explanation

1. distirbute the x and 3(multiply) into this equation -x^2+4x-2

2. add all similar numbers

3. Profit.

The error interval for m is 6.58 ≤ m < 6.59

Truncation is a process of dropping all decimal places after a certain point without rounding the number.

Given that, the mass, m, of the lorry is 6.58 tonnes truncated to 2 decimal places.

Since the number is truncated to two decimal places, the error interval is,

6.58 ≤ m < 6.59

Hence, the error interval for m is 6.58 ≤ m < 6.59.

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There are 4 hundred billions in the number 432,845,979,484.

To determine how many hundred billions are in the number 432,845,979,484, we need to consider the place value of the hundred billions digit.

The number 432,845,979,484 has 12 digits, and we count the digits from right to left, starting with the units place. The digit in the hundred billions place is the seventh digit from the right.

Let's break down the number:

4 hundred billions (4 x 100,000,000,000)

3 ten billions (3 x 10,000,000,000)

2 billions (2 x 1,000,000,000)

8 hundred millions (8 x 100,000,000)

4 ten millions (4 x 10,000,000)

5 millions (5 x 1,000,000)

9 hundred thousands (9 x 100,000)

7 ten thousands (7 x 10,000)

9 thousands (9 x 1,000)

4 hundreds (4 x 100)

8 tens (8 x 10)

4 units (4 x 1)

As we can see, there are 4 hundred billions in the number 432,845,979,484.

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This answer was deemed incorrect, so sorry for posting this!

Answer:

1).00390625

2).216

3).0231481481481

Step-by-step explanation:

Answer:

\((-\infty,2)\)

Step-by-step explanation:

Since \(-3x+6\nless 0\), then \(x\ngtr 2\), therefore, the domain of the function is \((-\infty,2)\).

Answer:

you would still have 10 snles

The resistance is 540 ohms, the current in the conductor is approximately 5.33 amperes.

According to the given information, the current in an electrical conductor varies inversely to the resistance of the conductor. Inverse variation can be represented mathematically as follows:

Current * Resistance = Constant

Let's denote the constant as 'k'. We can use the initial values to find the value of 'k'.

When the resistance is 240 ohms and the current is 12 amperes:

12 * 240 = k

k = 2880

Now that we have the value of 'k', we can use it to find the current when the resistance is 540 ohms:

Current * 540 = 2880

Current = 2880 / 540

Current ≈ 5.33 amperes

Therefore, when the resistance is 540 ohms, the current in the conductor is approximately 5.33 amperes.

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