My age is the difference between twice my age in 5 years and twice my age 5 years ago

The total amount is $ 780

Solution:

Let the total amount be "x"

Given that,

First person gets $ 268

Second person gets $ 200

Third person gets 40 %

This means, third person gets 40 % of total amount

Third person = 40 % of x

[tex]Third\ person = 40 \% \times x\\\\Third\ person = \frac{40}{100} \times x\\\\Third\ person = 0.4x[/tex]

We know that, total amount is equal to sum of amount got by all three persons

Total amount = first person + second person + third perosn

[tex]x = 268 + 200+ 0.4x\\\\x - 0.4x = 268 + 200\\\\0.6x = 468\\\\x = \frac{468}{0.6}\\\\x = 780[/tex]

Thus the total amount is $ 780

Answer:

The plumber worked for 43 minutes.

Step-by-step explanation:

A plumber charged $70 for the first 30 minutes of each house call plus $4 for each additional minute he works.

Now, the total amount to be paid to the plumber C(x) as a function of x number of minutes that he works can be modeled by the equation

C(x) = 70 for x ≤ 30 minutes and C(x) = 70 + (x - 30)4 for x > 30 minutes.

Now, the plumber charges Hayden $122 for the house visit. In that case, x must be greater than 30 minutes.

So, we can write

122 = 70 + (x - 30)4

⇒ 122 = 70 + 4x - 120

⇒ 4x = 172

⇒ x = 43 minutes.

Therefore, the plumber worked for 43 minutes. (Answer)

Answer:

2(x-7) = 2

Step-by-step explanation:

First, let's look at the first part -- "Twice the difference of a number and 7".  The difference between a number (x) and 7 means x-7.  It also says twice the difference, so we are going to multiply x-7 by 2.  So that ends us with 2(x-7)

The last part -- "equals 2" means we will set what we currently have to 2.  2(x-7) = 2

Answer:

2(x-7)=2

Step-by-step explanation:

The difference of a number and 7 is x-7 (difference means subtract)

Now the question says twice so that is what we do 2(x-7) now equal that to two 2(x-7)=2

Answer:

12 m apart

Step-by-step explanation:

Final answer:

To find the distance between Ernie and Trevor in the camping scenario, trigonometry principles utilizing the law of sines can be applied effectively, resulting in a distance of approximately 15.54m between them.

Explanation:

To find the distance between Ernie and Trevor, we can use trigonometry. Let's focus on the triangle formed by Bert, Ernie, and Trevor. Since Bert and Ernie are 10m apart with a 30-degree angle at Bert, we can use the law of sines to find Ernie and Trevor's distance. By the law of sines:

Answer:

x = 28.3

Step-by-step explanation:

3.5 belongs to Rational number sets mainly and also belongs to Real Numbers.

Step-by-step explanation:

Number Sets are nothing but group of number classified into groups.

They are Natural, Whole, Integers, Rational, Irrational and Real numbers.

Natural number set = {1,2,3...},

Whole number set= {0,1,2,3...},

Integers = { ....-2, -1, 0, 1, 2, ....},

Rational numbers = { Integers, Decimals, Fractions},

Irrational numbers = { non fractional numbers eg: π,[tex]\sqrt{2}[/tex] etc.}

Real = { Natural, Whole, Integers, Rational, Irrational }.

Any number which is a fraction resulting in a decimal value is Rational Number sets.

3.5 is a decimal number so it can be Rational Number sets also Real Number sets.

BB's parents should choose the option with a 4% annual increase on the accumulated amount because it leverages compound interest, likely resulting in significantly higher growth over time compared to the fixed contribution strategy.

The question involves deciding between two financial strategies for Baby Bertha's (BB) savings account: a fixed annual contribution ($1,000 at birth plus $50 per year) versus a dynamic contribution that includes an initial amount plus an annual percentage increase ($1,000 at birth plus an additional 4% of the accumulated amount each year). To determine which option BB's parents should select, we must understand the impact of compound interest and how it can significantly increase the future value of a savings account over time.

With the fixed contribution strategy, the amount added each year is constant, leading to linear growth. In contrast, the 4% annual increase on the accumulated amount option leverages the power of compound interest, likely resulting in exponential growth of the account's value over time. This strategy takes advantage of the principle that earnings are reinvested to generate their own earnings in subsequent years, a core tenet of compound growth.

Given the long-term nature of the saving plan (assuming BB won't withdraw the funds prematurely), the option with a 4% annual increase on the accumulated amount is more advantageous. This decision leverages compound interest, which is known to significantly increase the value of investments over extended periods. Hence, BB's parents should select Grandpa's option for the potential of greater financial growth.

Answer:

60(if you sell all)

Right now you have: 41 dollars

Step-by-step explanation:

Answer: you will have 41 dollars.

Step-by-step explanation:

because if you had 60 chocolate and now you had 19 left you sold 41 chocolate bars and you multiply that by how much there are which is 1 dollar and 41 time 1 is 41.

Answer:

12.3 + 0.61 +100= 112.91

Step-by-step explanation:

All you have to do is make all the values have two place values and then add.

Answer:

34 is the answer

Step-by-step explanation:

Answer:

the answer is 70/2+(5-6) i think. Sorry if it is wrong

Step-by-step explanation:

Answer:

Step-by-step explanation:

132,874,015 rounded to the nearest hundred thousand....

132,900,000 <===

Answer:

0.9

Step-by-step explanation:

i) 1 nickel is equal to 5 cents

ii) 36 nickels will equal to = 36 × 5 = 180 cents

iii) 1 dime is equal to 10 cents

iv) 20 dimes will equal to = 20 × 10 = 200 cents

v) the ratio of 36 nickels to 20 dimes will equal to

  =  36 nickels ÷ 20 dimes

 = 180 cents ÷ 200 cents

 = [tex]\frac{9}{10}[/tex]

 = 0.9

To express the comparison of 36 nickels to 20 dimes as a ratio in lowest terms, calculate the value of nickels and dimes in pennies, then simplify the ratio. By converting to pennies and reducing, the ratio of 36 nickels to 20 dimes is 9:10.

The question asks to write the comparison of 36 nickels to 20 dimes as a ratio reduced to lowest terms. To compare the value of nickels and dimes, we must know their value in pennies, the smallest unit of US currency. Since 1 nickel is worth 5 pennies and 1 dime is worth 10 pennies, we can express 36 nickels and 20 dimes in terms of pennies.

36 nickels = 36 x 5 pennies = 180 pennies

20 dimes = 20 x 10 pennies = 200 pennies

Now, we write the comparison as a ratio:

180 pennies : 200 pennies

Next, we reduce this ratio to lowest terms by dividing both numbers by their greatest common divisor, which is 20 in this case:

180 ÷ 20 : 200 ÷ 20

9 : 10

Therefore, the ratio of 36 nickels to 20 dimes reduced to lowest terms is 9:10.

c = 2πr = 2π(8) = 16π = 50.3 ft rounded to the nearest tenth

There are 28 students in first period and 56 students in sceond period and 74 students in third period

Solution:

Let the number of students in first period be "x"

Let the number of students in second period be "y"

Let the number of students in third period be "z"

There are 158 students registered for American History classes.

Therefore,

x + y + z = 158 ---------- eqn 1

There are twice as many students registered in second period as first period

number of students in second period = twice of number of students in first period

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

There are 10 less than three times as many students in third period as in first period

number of students in third period = 3 times number of students in first period - 10

z = 3x - 10 ------ eqn 3

Substitute eqn 2 and eqn 3 in eqn 1

x + 2x + 3x - 10 = 158

6x = 168

Substitute x = 28 in eqn 2

y = 2(28)

Substitute x = 28 in eqn 3

z = 3(28) - 10

z = 84 - 10

Thus there are 28 students in first period and 56 students in sceond period and 74 students in third period

Question: Which situation is represented by [tex]\frac{25}{9}[/tex]?

Option A: Melanie equally shares 25 meters of paper to create 9 banners

Option B: Quill gives way 9 baseball cards from a pack of 25 cards.

Option C: George invites 25 kids and 9 adults to his birthday party.

Option D: Becca create 9 rows with 25 buttons.

Answer:

Solution:

Option A: Melanie equally shares 25 meters of paper to create 9 banners.

The fraction is [tex]\frac{25}{9}[/tex].

Option B: Quill gives way 9 baseball cards from a pack of 25 cards.

The fraction is [tex]\frac{9}{25}[/tex]

Option C: George invites 25 kids and 9 adults to his birthday party.

Here, 25 + 9.

Option D: Becca create 9 rows with 25 buttons.

Here, 9 × 25.

Hence the answer is Option A: Melanie equally shares 25 meters of paper to create 9 banners.

Answer:

d = 5t + 20

Step-by-step explanation:

d represents the distance and t represents the time, in hours

Let he equation which model this situation ⇒ d = a t + b

Where a and b are constant.

Let the gas station is the starting point

So, at gas station t = 0 , d = 20

∴ 20 = 0 * a + b ⇒ b = 20

When he reaches home 2 hours later notes that he has traveled 30 miles.

and with substituting with b = 20

∴ 30 = 2 * a + 20

2a = 30 - 20 = 10  ⇒ a = 10/2 = 5

∴ d = 5t + 20

The equations that can be used to model this situation d = 5t + 20

Answer:

Answer is √7 ( not A, not B)

Step-by-step explanation:

BD/AB = sin 60°

BD/2 = √3/2

BD = √3

AD/AB = cos 60°

AD/2 = 1/2

AD = 1

CD = 3 -1 = 2

BC = √BD² + CD² = √(3 + 4) = √7

Answer:

17

Step-by-step explanation:

x + 2x + 3 + 2x = 88

5x = 85

x = 17

Final answer:

To find the sides of the triangle, set the shortest side as x cm, leading to the calculation that the shortest side is 17 cm, the second side is 37 cm, and the third side is 34 cm.

Explanation:

The question is based on finding the lengths of the sides of a triangle given the perimeter and relationships between the sides. Let the shortest side be x cm. Therefore, according to the information given, the second side is 3 cm longer than twice the shortest side, which makes it 2x + 3 cm, and the third side is twice as long as the shortest side, so it is 2x cm. The perimeter of the triangle, which is the sum of the lengths of its sides, is 88 cm. We can set up the equation to solve for x:

x + (2x + 3) + 2x = 88

5x + 3 = 88

5x = 85

x = 17 cm

Thus, the shortest side of the triangle is 17 cm, the second side is 2(17) + 3 = 37 cm, and the third side is 2(17) = 34 cm.

To find the width of a 16-inch laptop screen that is 8 inches tall, we can use the 16:9 aspect ratio typical for screens and calculate that the width is approximately 14.22 inches.

Finding the Width of the Laptop Screen

To find out how wide a 16-inch laptop screen is, given that it is 8 inches tall, we can use the Pythagorean theorem assuming the screen has a 16:9 aspect ratio which is typical for laptop screens. To use the Pythagorean theorem, we first need to establish the diagonal (16 inches) as the hypotenuse of a right-angled triangle, with the height and width as the other two sides.

As per the given scale factor for this problem (1/160), it does not seem relevant to finding the width using the Pythagorean theorem. Instead, we can use the aspect ratio to find the width. For a 16:9 aspect ratio:

Height = 9x

Width = 16x

Given the height (8 inches) and assuming it to be 9x:

9x = 8 inches

x = 8 / 9

Now to find the width which is 16x:

Width = 16 * (8 / 9)

Width = 14.222... inches (approximately)

The width of the screen is therefore approximately 14.22 inches.

The solution is [tex](3,4)[/tex]

Step-by-step explanation:

To solve the equation by substitution method, we need to substitute an equivalent value of a variable in one equation to an another equation.

The given two equations are [tex]y=4x-8[/tex] and [tex]y=2x-2[/tex] .

Thus, we know the equivalent value of y from one equation, let us subsitute the value of y from the equation [tex]y=2x-2[/tex] to the equation [tex]y=4x-8[/tex]

[tex]4x-8=2x-2[/tex]

Subtracting 2x from both sides of the equation, we get,

[tex]2x-8=-2[/tex]

Adding 8 to both sides of the equation, we get,

[tex]2x=6[/tex]

Dividing by 2 on both sides of the equation,

[tex]x=3[/tex]

Now, substituting [tex]x=3[/tex] in the equation [tex]y=2x-2[/tex], we get,

[tex]\begin{aligned}y &=2 x-2 \\&=2(3)-2 \\&=6-2 \\y &=4\end{aligned}[/tex]

Thus, the solution is [tex](3,4)[/tex]

Answer:

$14,800 at 10.5%

$38,850 at 12%

Step-by-step explanation:

Investment at 10.5% (x):

(0.12[$53,650 - x])/0.105x = 3

$6,438 - 0.12x = 0.315x

0.435x = $6,438

x = $14,800

Investment at 12%:

= $53,650 - $14,800

= $38,850

Answer: Investments: @ 10.5%, $14,800; @ 12%, $38,850

Proof: (income from 1st is 1/3 that of the income from the 2nd):

= (0.105[$14,800])/(0.12[$38,850])

= $1,554/$4,662

= 1/3

Let's denote as 'x' the amount of money invested by Ms. Burke at the rate of 10.5%. Given that the total amount of investment is $53,650, it follows that the remaining money invested at 12% is given by $53,650 minus 'x'.

The income from the 10.5% investment is 0.105 multiplied by 'x' and the income from the 12% investment is 0.12 multiplied by the quantity $53,650 minus 'x'.

According to the problem statement, the income from the 10.5% investment is one-third of the income from the 12% investment. Therefore, we can write down the following equation:

0.105*x = (1/3)*0.12*($53,650 - x)

We solve this equation to determine 'x'. The solution for this equation yields 'x' equal to approximately $14,800. This means Ms. Burke invested approximately $14,800 at 10.5%.

Also, we know that the difference between the total amount invested and the amount invested at 10.5% will give us the amount invested at 12%. Hence, by subtracting $14,800 from $53,650, we obtain $38,850.

Therefore, Ms. Burke invested approximately $14,800 at the rate of 10.5% and $38,850 at the rate of 12%.

Learn more about investment here:

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For this case we have the following equation:

[tex]p + 2p + 3p = 12[/tex]

To solve we follow the steps below:

We add similar terms from the left side of the equation:

[tex]6p = 12[/tex]

We divide between 6 on both sides of the equation:

[tex]p = \frac {12} {6}\\p = 2[/tex]

Finally, we have to:

[tex]5p-1 = 5 (2) -1 = 10-1 = 9[/tex]

Answer:

[tex]p = 2\\5p-1 = 9[/tex]

Answer:

X=5 and y=-6

Step-by-step explanation:

Positive five cancels out -5 and—6 cancels out positive six, so you are left with 0 which equals 0.

Answer:

The answer to your question is A = 648 u²

Step-by-step explanation:

I attach the solution because it said that I was writing improper words.

Answer:

Step-by-step explanation:

c = cooks, w = waiter

4c + 4w = 360....multiply by -5

5c + 6w = 480...multiply by 4

=================

-20c - 20w = - 1800 (result of multiplying by -5)

20c + 24w = 1920 (result of multiplying by 4)

=================

4w = 120

w = 120 / 4

w = 30 <=== waiters make $ 30

4c + 4w = 360

4c + 4(30) = 360

4c + 120 = 360

4c = 360 -120

4c = 240

c = 240/4

c = 60 <=== cooks make $ 60

Question:

Evaluate the expressions 3x - 2 and 4x + 4 for the following values of x. When you have found the value for each expression, write a statement using <, >, or = that shows how the two values are related. a. x = 0 b. x = -6 c. x = 5 d. x = -2

Answer:

Part a: [tex]4x+4>3x-2[/tex]

Part b: [tex]4x+4=3x-2[/tex]

Part c: [tex]4x+4>3x-2[/tex]

Part d: [tex]4x+4>3x-2[/tex]

Explanation:

Part a: Substituting [tex]x=0[/tex], we get,

[tex]\begin{aligned}3 x-2 &=3(0)-2 \\&=-2\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(0)+4 \\&=4\end{aligned}[/tex]

The value of [tex]3x-2[/tex] is less than [tex]4x+4[/tex]

Thus, [tex]4x+4>3x-2[/tex]

Part b: Substituting [tex]x=-6[/tex], we get,

[tex]\begin{aligned}3 x-2 &=3(-6)-2 \\&=-18-2 \\&=-20\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(-6)+4 \\&=-24+4 \\&=-20\end{aligned}[/tex]

The value of [tex]3x-2[/tex] and [tex]4x+4[/tex] are equal.

Thus, [tex]4x+4=3x-2[/tex]

Part c: Substituting [tex]x=5[/tex], we get,

[tex]\begin{aligned}3 x-2 &=3(5)-2 \\&=15-2 \\&=13\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(5)+4 \\&=20+4 \\&=24\end{aligned}[/tex]

The value of [tex]3x-2[/tex] is less than [tex]4x+4[/tex]

Thus, [tex]4x+4>3x-2[/tex]

Part d: Substituting [tex]x=-2[/tex], we get,

[tex]\begin{aligned}3 x-2 &=3(-2)-2 \\&=-6-2 \\&=-8\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(-2)+4 \\&=-8+4 \\&=-4\end{aligned}[/tex]

The value of [tex]3x-2[/tex] is less than [tex]4x+4[/tex]

Thus, [tex]4x+4>3x-2[/tex]

Final answer:

The value of 3x-2 is less than 4x+4

Thus, 4x+4>3x-2

Explanation:

Part a: 4x+4>3x-2

Part b: 4x+4=3x-2

Part c: 4x+4>3x-2

Part d: 4x+4>3x-2

Part a: Substituting x=0, we get,

[tex]\begin{aligned}3 x-2 &=3(0)-2 \n&=-2\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(0)+4 \n&=4\end{aligned}[/tex]

The value of 3x-2 is less than 4x+4

Thus, 4x+4>3x-2

Part b: Substituting x=-6, we get,

[tex]\begin{aligned}3 x-2 &=3(-6)-2 \n&=-18-2 \n&=-20\end{aligned}\begin{aligned}4 x+4 &=4(-6)+4 \n&=-24+4 \n&=-20\end{aligned}[/tex]

The value of 3x-2 and 4x+4 are equal.

Thus, 4x+4=3x-2

Part c: Substituting x=5, we get,

[tex]\begin{aligned}3 x-2 &=3(5)-2 \n&=15-2 \n&=13\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(5)+4 \n&=20+4 \n&=24\end{aligned}[/tex]

The value of 3x-2 is less than 4x+4

Thus, 4x+4>3x-2

Part d: Substituting x=-2, we get,

[tex]\begin{aligned}3 x-2 &=3(-2)-2 \n&=-6-2 \n&=-8\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(-2)+4 \n&=-8+4 \n&=-4\end{aligned}[/tex]

The value of 3x-2 is less than 4x+4

Thus, 4x+4>3x-2

Answer:

D. 5/12

Step-by-step explanation:

I will have a picture attached to the answer. But I will explain it overall.

So let's start off with what information we have: Bella ate 1/4 of the bar and Owen at 1/3 of the same bar.

So how much overall was gone by the two? Well, in this part we will add the two fractions.

1/3 + 1/4 =?

Yet, here's the thing, these two fractions have different denominators. What we have to do is make them the same denominator. In order to do so we have to find the Least Common Multiple of the denominators.

So with that in mind...

Multiples of 3: 3,6,9,12,15,18,21,...

Multiples of 4: 4,8,12,16,20,24...

Do you see a number that 3 and 4 have? Welp, I do! It's 12! So here is what going to happen! We will set up the problem like this!

1/3 times ? equal x/12

+ 1/4 times ? equal x/12

Now you may be wondering what is the question mark for and what is "x"? Here's the thing, since we know the new fraction we have to figure out what times the original denominators equal the new denominator! So with 1/3, what or how do we make the 3 into 12? Well 3 times 4 equals 12! So that is ?. The ? will be 4/4. Because whatever you do to the bottom you do to the top.

1/3 times 4/4 equals 4/12

Now we do the same thing for the 1/4 fraction. Except the question mark will be 3/3 since 4 times 3 equals 12

1/4 times 3/3 equals 3/12

Okay, now we have 4/12 + 3/12= x/12. Let's add the fractions. 4+3=7 and the 12 of the denominator will stay the same. So 1/3+1/4 or 4/12+3/12 now equals 7/12.

The real question is what is LEFTOVER of the granola bar? So we have what was devoured of the bar, so now we can subtract the part that was gone with the whole bar. So...

1 whole bar equals 12/12

- the devoured part equals 7/12

left over or untouched = 5/12

So the answer to the question is D. 5/12

I hope this helps you, I'm sorry this took me a long time, I again do have a picture attached to the answer. If you need any help or have a question please don't be afraid to ask! Have a good day!

Answer: option D.

The total amount of the granola bar is = 1.

Given that they have eaten 1/4 and 1/3 of the bar.

So they have eaten a total of [tex]\frac{1}{4}+\frac{1}{3}=\frac{7}{12}[/tex] of the bar.

So the remaining amount is = [tex]1-\frac{7}{12}=\frac{12}{12}-\frac{7}{12}=\frac{5}{12}[/tex].

So option D is right.

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420 gallons of 90% antifreeze must be mixed with 60 gallons of 10% antifreeze to get mixture that is 80% antifreeze

Solution:

Let "x" be the gallons of 90% antifreeze

The, final mixture would contain (x + 60) gallons

Then by given question, we can say,

"x" be the gallons of 90% antifreeze must be mixed with 60 gallons of 10% antifreeze to get 80 % of (x + 60) gallons

Thus we frame a equation as:

[tex]x \times 90 \% + 60 \times 10 \% = (x + 60) \times 80 \%[/tex]

Solve the above equation for "x"

[tex]x \times \frac{90}{100} + 60 \times \frac{10}{100} = (x + 60) \times \frac{80}{100}\\\\0.9x + 6 = (x+60) \times 0.8\\\\0.9x + 6 = 0.8x + 48\\\\\text{Combine the like terms }\\\\0.9x - 0.8x = 48 - 6\\\\0.1x = 42\\\\x = \frac{42}{0.1} = 420[/tex]

Thus, 420 gallons of 90% antifreeze is used

The given equation is not the conditional equation.

Step-by-step explanation:

A conditional equation is true only certain values of the numbers present in it.

    for example  x + 3 = 9  is true only, if x = 6

                         3x - 5 = 10 is true only, if x = 5

The given equation is an Identity equation in which both sides of the equation is equal.    

                     3(x - 4) + 5x = 4x + 4(x - 3)

                     3x - 12 + 5x = 4x + 4x - 12

                                   8x  = 8x.