Larry Mitchell invested part of his $25,000 advance at 5% annual simple interest and the rest at 9% annual simple interest. If his total yearly interest from both accounts was $1,850, find the amount invested at each rate.

Answer: 8.4 feet

Step-by-step explanation:

Given: Lumber required for each shelf = [tex]8\dfrac{3}{4}\ inches[/tex]

For each base side = [tex]12\dfrac12\ inches[/tex]

For each door stile = [tex]29\dfrac18\ inches[/tex]

Total lumber required = [tex](2\times 8\dfrac34 + 2\times12\dfrac12+2\times29\dfrac18)\ \ in.[/tex]

[tex]=(2\times\dfrac{35}{4}+2\times\dfrac{25}{2}+2\times\dfrac{233}{8})\ in\\\\= (\dfrac{35}{2}+25+\dfrac{233}{4})\ in.\\\\=\dfrac{403}{4}\ in. =\dfrac{403}{4}\times\dfrac1{12}\ feet \ \ \ \ [1 feet = 12 \ in.]\\\\\approx8.4\ feet[/tex]

Hence, we will need 8.4 feet lumber.

Answer:

See explanation below.

Step-by-step explanation:

Given: 100 lbs on Earth is 16.6 lbs on the moon.

a. The independent variable is weight. The gravity of the Moon and the gravity of the Earth are constant. Weight can change, but gravity is a constant.

b. An equation that relates the weight of someone on the Moon who travels to the Earth:

100 / 16.6 = 6.02. Take the Moon weight and multiply by 6.02:

Moon Weight * 6.02 = Earth Weight.

Proof:

16.6 * 6.024 = 99.99 - approximately 100 lbs Earth weight.

c. A 185 lb astronaut on Earth would weigh:

16.6 / 100 = .166. Take the Earth weight and multiply by .166:

185 * .166 = 30 lbs on the Moon.

d. A person who weighs 50 lbs on the Moon:

50 * 6.024 = 301.2 lbs on Earth.

Hope this helps! Have a good day and year! :)

Answer:

18

Step-by-step explanation:

[tex]{82 { }^{2} } - 80 {}^{2} = 324 \\ \sqrt{324 } = 18[/tex]

Answer:

x=62

Step-by-step explanation:

all angles should add to 180

180-56=124

124÷2=62

Answer:

Step-by-step explanation:

1st notice that two of the sides are the same length?   ( isosceles ) that mean the two angles at the "base" which is the side that both of the same size legs tie into... that's the side that is 4.5 in the picture.  soooo if both of those angles are the same.. and we know that the angles are going to add to 180 then....  we can say    the the 56° is the same as the one at the other end of the 4.5 side (base) so  2*56°=112°

and then 112° + x = 180°

x = 180-112

x = 68°

:)

Answer:

Step-by-step explanation:

1:4:7

1+4+7=12

120+12+10

Answer:

Step-by-step explanation:

first divide 120/4 = 30

so everything needs to be multiplied by 30

new ratio is 30:120:210

add them together

30 + 120 + 210 = 360

hope this helps <3

Answer:

w = 1.5

Step-by-step explanation:

if x equals 36 you have to figure out what 36 divided by equals 6 and thats 6 so y=6 then you have to take 6 and figure out what divided by it equals four and that is going to be 1.5

Answer:

w=3/2

Step-by-step explanation:

x/y=6 here x=36

then, 36/y=6

6y=36

y=36/6

y=6

here y/w=4

6/w=4

6=4w

w=6/4

w=3/2

Answer:

10

Step-by-step explanation:

Each trailer of each truck can cart away (10)(15)(6.5) = 975 cubic feet of debris.

To cart 45 tons of debris i.e. 200 x 45 = 9000 cubic feet of debris away, we need

9000/975 = 9.23 trucks.

Since you need at least 9.23 trucks, and you cannot have a decimal number of trucks, 10 trucks are needed to cart away 45 tons of debris from a demolition site.

Answer: 0.7

Step-by-step explanation:

Answer:

0.7 is the decimal

Answer:

The expression T = 15*3 + 32  could be used to correctly calculate the amount Roberta owes Mr. Jones

Step-by-step explanation:

Given that:

Amount charged for parts = $32

Per hour labor = $15

Time spent on repairing = 3 hours

Total amount = Per hour labor * Number of hours + Amount of parts

T = 15*3 + 32

Hence,

The expression T = 15*3 + 32  could be used to correctly calculate the amount Roberta owes Mr. Jones

Answered que aca ases copiando Jsjs NO ERES EL UNICO COPION the daria la respuesta pero no me la set ni yo

Step-by-step explanation:

Answer: True

The set of whole numbers is {0, 1, 2, 3, 4, 5, ...}

The set of natural numbers is {1, 2, 3, 4, 5, ...}

Both sets describe numbers that are positive and without any fractional or decimal component. The only difference is that 0 is included in the first set, but exclude from the second. If you want to include negative whole numbers as well, then you'd use the set of integers.

The given statement is true.

A number is an arithmetic value used to represent quantity. Hence, a number is a mathematical concept used to count, measure, and label. Thus, numbers form the basis of mathematics.

The statement given is says that, the set of whole numbers includes zero, but the natural numbers do not.

So, if we see the definition of both types of numbers, we can say that the whole numbers are the natural starting from 0, and the natural numbers are the one which includes only counting numbers used in our daily life.

Hence, the given statement is true.

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Step-by-step explanation:

Prime Factorization of 12

2 12

2 6

3 3

1

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 22×31

Prime Factorization of 27

3 27

3 9

3 3

1

Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:

27 = 33

Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 27.

LCM(12,27) = 22×33

LCM(12,27) = 108

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

Factors of 27

List of positive integer factors of 27 that divides 27 without a remainder.

1, 3, 9, 27

Least Common Multiple of 12 and 27 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).

We need to calculate greatest common factor 12 and 27, than apply into the LCM equation.

GCF(12,27) = 3

LCM(12,27) = ( 12 × 27) / 3

LCM(12,27) = 324 / 3

LCM(12,27) = 108

Least Common Multiple of 12 and 27 by Listing Multiples

Multiples of 12

12, 24, 36, 48, 60, 72, 84, 96,108

Multiples of 27

27, 54, 81,108

Find the smallest number that is on all of the lists. We have it in bold above.

∴ Least Common Multiple of 12 and 27 is 108

Properties of LCM 12 and 27

(i) The LCM of 27 and 12 is associative

LCM of 12 and 27 = LCM of 27 and 12

Frequently Asked Questions on LCM of 12 and 27

1. What is the LCM of 12 and 27?

Answer: LCM of 12 and 27 is 108.

2. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

3. What are the Factors of 27?

Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.

4. How to Find the LCM of 12 and 27?

Answer:

Least Common Multiple of 12 and 27 = 108

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 27

27 = 3 x 3 x 3

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 108 = 2 x 2 x 3 x 3 x 3

Step 4: Therefore, the least common multiple of 12 and 27 is 108.

The LCM (least common multiple) of 12 and 27 using prime factorizations​ would be 108.

Used the concept of least common multiple that states,

The Least common multiple of two or more numbers is the smallest number that is a multiple of two or more numbers.

Given that the two numbers are 12 and 27.

Hence, the prime factorizations​ of 12 and 27 are,

12 = 2 × 2 × 3

27 = 3 × 3 × 3

So, the LCM of 12 and 27 is,

2 × 2 × 3 × 3 × 3

= 108

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Answer:

A. Graph attached

B. It's a function. One input has only one output, it passed the vertical line test.

Step-by-step explanation:

a₀ = 3  a₁ = 6 = 3 x 2¹   a₂ = 6 x 2 = 3 x 2²  ..... aₙ = 3 x 2ⁿ

answer graph attached

A list of ordered pairs may or may not represent a function.

(a) The ordered pair

Let x represent the number of folds, and y represent the thickness.

So, the first ordered pair is:

[tex]\mathbf{(x,y) = (0,3)}[/tex]

When x increases by 1, the value of y gets doubled.

So, the six ordered pairs are:

[tex]\mathbf{(x,y) = \{(0,3),(1,6),(2,12),(3,24),(4,48),(5,96)\}}[/tex]

(b) Is the ordered pair, a function

In (a), we have:

Every x value has a different corresponding y value.

This means that the ordered pair is a function.

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Answer:

7 1/2

Step-by-step explanation:

convert mixed numbers to fractions to get 1/2 and 15/1

then, multiply the two to get 15/2

then simplify for the answer 7 1/2

answer 7.5

Step-by-step explanation:

convert the fraction to a decimal by dividing the numerator by the denominator

Answer:

parallelogram

Step-by-step explanation:

Answer

15:5, or 3:1

Step-by-step explanation:

Answer:

the answer is x=-9

Step-by-step explanation:

The value of a solution of the rational equation that must discard and nullify the context of the equation is -9

Word problems in mathematics require crucial understanding because they are used to solve a real-life scenario. It entails the gathering of all information necessary to arrive at the solution.

From the information given:

where x represents the number of minutes

The equation representing the above information is given as:

[tex]\mathbf{\mathbf{\dfrac{1}{x}+ \dfrac{1}{x+15}= \dfrac{1}{18}}}[/tex]

The objective of this question is to determine the value in which it will discard and nullify the context of the above equation.

In that case, the number must be a number in which when substituted into the above equation will result in having the same value on the left-hand side and the right-hand side.

From the given option, the number that results in that is -9

[tex]\mathbf{\mathbf{\dfrac{1}{-9}+ \dfrac{1}{-9+15}= \dfrac{1}{18}}}[/tex]

[tex]\mathbf{\mathbf{0.05555555556= 0.05555555556}}[/tex]

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Answer:

-1/2  is the answer

Step-by-step explanation:

Answer:

steps in the pic

Step-by-step explanation:

n=7 or n=-6

Answer:

180-(61+59) should give you the answer

Answer:

61+59

Step-by-step explanation:

gives u your answer

Answer:

What Problem?

Step-by-step explanation:

Answer:

1.0E+15

Step-by-step explanation:

im sure this is right

Answer:

Step-by-step explanation:

To find the answer divide a 1 kilometer by x amount of picometers.

K= x of p

K = 1000000000000000

or in short text

=1e+15

Answer:

2). As x-> -∞, f(x)->∞

    As x-> ∞, f(x)-> -∞

5). As x-> -∞, f(x)-> -∞

    As x-> ∞, f(x)-> ∞

3). As x-> -∞, f(x)-> -∞

    As x-> ∞, f(x)-> ∞

6). As x-> -∞, f(x)-> ∞

    As x-> ∞, f(x)-> ∞

Step-by-step explanation:

I just watched a quick video so you can't completely trust me, but i tried my best. Hopefully someone more trustworthy for this comes in.

Answer: Choice A) If Amber and Jorge each sell 5 trees in one week, they will earn the same amount

The amount they earn is $200 each.

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

Explanation:

Let's form the equation for the amount Amber earns.

She starts off at $150, and then we add on 10x dollars. The 10x is because she earns 10 dollars per tree, and we have x be the number of trees sold.

Overall we can say her equation is y = 150+10x

This is the same as y = 10x+150

----------

Since Jorge's equation is y = 25x + 75, we can apply substitution to solve for x

y = 10x+150

25x+75 = 10x+150 .... replace y with 25x+75

25x+75-10x = 150 ... subtract 10x from both sides

15x+75 = 150

15x = 150-75 ... subtract 75 from both sides

15x = 75

x = 75/15 .... divide both sides by 15

x = 5

If they sell 5 trees per week, then Amber and Jorge earns the same amount of money.

That amount earned is

Amber: y = 10x+150 = 10*5+150 = 50+150 = 200 dollars

Jorge: y = 25x+75 = 25*5+75 = 125+75 = 200 dollars

Both earn $200 per week from selling 5 trees for that week. This helps confirm we have the right answer.

Answer: 3/4

Step-by-step explanation:

Answer:

true value received 58.93% or the order.