Homer and Mike were replacing the boards on​ Mike's old deck. Mike can do the job alone in 1 hour less time than Homer. They worked together for 6 hours until Homer had to go home. Mike finished the job working by himself in an additional 6 hours. How long would it have taken Homer to fix the deck​ himself?

[tex]\bf \begin{array}{ccll} cans&\$\\ \cline{1-2} 12&33\\ 5&x \end{array}\implies \cfrac{12}{5}=\cfrac{33}{x}\implies 12x=165 \\\\\\ x=\cfrac{165}{12}\implies x=13.75[/tex]

Answer:

$13.75

Step-by-step explanation:

Divide $33 by 12 to find out how much each can of nuts costs, which is $2.75. Now multiply that by 5 to get the cost of 5 cans of nuts. $13.75.

Answer:

Linear  

Step-by-step explanation:

Each time x increases by one unit, y increases by three units.

The table represents a linear function of x.

Answer:

[tex]5\frac{23}{64}\approx 5.36 [/tex] cubic meters.

Step-by-step explanation:

We have been given that the surface area of a cube is [tex]18\frac{3}{8}[/tex] square meters and we are asked to find the volume of the cube.

Since we know that surface area of a cube with each edge equals a units is:

[tex]\text{Total surface area of cube}=6a^2[/tex]

Let us find length of each edge using surface area formula.

[tex]18\frac{3}{8}=6a^2[/tex]

Let us convert our given area into mixed fraction.

[tex]\frac{147}{8}=6a^2[/tex]

Upon dividing both sides of our equation by 6 we will get,

[tex]\frac{147}{8*6}=a^2[/tex]

[tex]\frac{147}{48}=a^2[/tex]  

Upon taking square root of both sides we will get,

[tex]\frac{7\sqrt{3}}{4\sqrt{3}}=a[/tex]  

[tex]\frac{7}{4}=a[/tex]

Now we will use volume of cube formula with each side length 'a'.

[tex]\text{Volume of cube}=a^3[/tex]

[tex]\text{Volume of cube}=(\frac{7}{4})^3[/tex]

[tex]\text{Volume of cube}=\frac{343}{64}[/tex]

[tex]\text{Volume of cube}=5\frac{23}{64}[/tex]

[tex]\text{Volume of cube}=5.359375\approx 5.36[/tex]

Therefore, the volume of cube will be [tex]5\frac{23}{64}[/tex] cubic meters.

Answer:x<=(20)/(a)

Step-by-step explanation:

With a principal of $5,000, an interest rate of 3.8%, over 22 years, Jackson's principal will grow to $11,535

Given: principal is $5000, interest rate is 3.8% and it is compounded continuously

To find: amount when Jackson is 40 years old

To solve this problem, we use the formula for continuous compounding interest:

[tex]A = P \times e^{rt}[/tex]

where:

A is the total amount of money

P is the principal

r is the annual interest rate (decimal form, so 3.8% becomes 0.038)

t is the time in years

Time here will be 22 years as Jackson deposited the money when he was 18 years old. So, the difference of 40 and 18 gives us 22 years.

Now we can find the total amount by plugging in the values:

[tex]A = 5000 \times e^{0.038 \times 22}\\[/tex]

[tex]A= 5000 \times e^{0.836}\\[/tex]

[tex]A= 5000 \times 2.307\\[/tex]

[tex]A = 11535[/tex]

Therefore, Jackson's account will have $11,535 when he is 40 years old.

Final answer:

To find the measure of angle K in the isosceles trapezoid JKLM, set the expressions for angle J and angle M equal to each other and solve for x. Substituting the value of x into one of the angle expressions will give the measure of angle K.

Explanation:

To find the measure of angle K in the isosceles trapezoid JKLM, we can use the fact that the opposite angles in an isosceles trapezoid are congruent. Since angle J and angle M are given in terms of x, we can set them equal to each other and solve for x:

17x + 7 = 11x + 13

Simplifying the equation, we get:

6x = 6

x = 1

Now that we have the value of x, we can substitute it back into one of the angle expressions to find the measure of angle K:

m∠K = 17(1) + 7 = 24 degrees

Answer:

28%

Step-by-step explanation:

Percentage mark up = (new - original) / original  * 100 %

     new = 704

     original =  550                              

Substituting these values in

     Percentage mark up = (704 - 550) / 550  * 100 %

                                         =154/550 * 100%

                                         =.28*100%

                                            28%

Step-by-step explanation:

so for example lets say the fractions are 1/4 and 2/3

you would multiply them to make the eqution look like this-                 [tex]\frac{1}{4}[/tex]·[tex]\frac{2}{3}[/tex]

so then you would cross simplify, since 2 is a factor of 4 we will factor them out, so itll look like this=

[tex]\frac{1}{2}[/tex]·[tex]\frac{1}{3}[/tex]

then you multiply the denominator with denominato and numerator with numerator, so the answer is 1/6

Hello There!

To multiply fractions, you first want to line up the numerator and the denominator together so they line up with each other.

Next, you want to multiply across. This includes multiplying the numerators together and then multiplying the denominators together.

Finally, you want to find the greatest common factor but only if the fraction can be simplified.

That Is How To Multiply Fractions

Answer:

D

Step-by-step explanation:

The quadratic formula is

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].

It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions.  Using the formula will require less work than finding the factors if factorable. We will substitute a=2, b=16 and c=-9.

[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-(16)+/-\sqrt{(16)^2-4(2)(-9)} }{2(2)}\\x=\frac{-16+/-\sqrt{256+72} }{4}[/tex]

We will now simplify and solve.

[tex]x=\frac{-16+/-\sqrt{328}}{4}\\x=-4+/-\sqrt{\frac{328}{16}}\\x=-4+/-\sqrt{\frac{41*8}{2*8}}\\x=-4+/-\sqrt{\frac{41}{2}}[/tex]

Answer:

The correct answer option is A. x2 – 3x + 15.

Step-by-step explanation:

We are given the following expression and we are supposed to simplify it:

[tex]7x^2+6x-9x-6x^2+15[/tex]

Before solving it, a good idea will be to arrange all the like terms together in their decreasing power and write the expression as:

[tex]7x^2-6x^2+6x-9x+15[/tex]

Simplifying it to get:

[tex]x^2-3x+15[/tex]

Therefore, the first option A is the correct answer x2 – 3x + 15.

Answer:

A. [tex]x^{2} - 3x +15[/tex]

Step-by-step explanation:

Given:

7x^2 + 6x – 9x – 6x^2 + 15.

On combining the x^2, and "x" terms we get,

= (7x^2 – 6x^2) + (6x – 9x)  + 15

Now, here simple addition of integers takes places

=  x^ - 3x + 15

Answer:

∠CAT = 140°

Step-by-step explanation:

Since AB bisects ∠CAT then ∠BAT = ∠CAB, hence

5x + 20 = 2x + 50 ( subtract 2x from both sides )

3x + 20 = 50 ( subtract 20 from both sides )

3x = 30 ( divide both sides by 3 )

x = 10

∠CAT = ∠BAT + ∠CAB = 5x + 20 + 2x + 50 = 7x + 70

substitute x = 10 into the expression

∠CAT = (7 × 10) + 70 = 70 + 70 = 140°

Answer:

Since AG = GC then AD must equal DC

2x -3 = x +2

x = 5

Step-by-step explanation:

Answer:

Since you want me to answer 3 lb 1 oz - 1 lb 15 oz instead, the answer is 18 oz

Step-by-step explanation:

First, convert pounds and ounces to just ounces, then subtract the total ounces. Finally, convert back to pounds and ounces to get the result of 8 lb 1 oz minus 3 lb 6 oz, which is 4 lb 11 oz.

Subtracting Mixed Measurements

To find the result of 8 lb 1 oz − 3 lb 6 oz, follow these steps:

Convert everything to ounces for easier subtraction (since there are 16 ounces in a pound).

Subtract the ounces first, then subtract the pounds.

Step-by-Step Solution

Step 1: Convert to ounces
8 lb 1 oz = (8 × 16) + 1 = 128 + 1 = 129 ounces
3 lb 6 oz = (3 × 16) + 6 = 48 + 6 = 54 ounces

Step 2: Subtract the ounces
129 ounces - 54 ounces = 75 ounces

Step 3: Convert back to pounds and ounces
75 ounces = 4 lb 11 oz (since 75 ÷ 16 = 4 remainder 11)

Therefore, 8 lb 1 oz − 3 lb 6 oz = 4 lb 11 oz.

Answer:

30% of the meat on the platter is ham.

Step-by-step explanation:

90 slices = 100%

10% = 9 slices

90 - 63 = 27 slices (this is the amount of ham)

10% x 3 = 30% = 27 slices of ham

Answer:

27 slices of ham which is about 30% of the meat.

Step-by-step explanation:

In this problem we have given

no. of slices of meat=90

no of slices of turkey's meat=63

Percent of ham in platter=?

No of ham slices= Total slices -turkey slices

=90 - 63

= 27 slices

therefore no of ham slices=27

percent of ham slices=Ham slicesx100/total slices

=27x100/90%

=30%

Therefore  percent of ham's in patter=30%

Answer:

they are different numbers

Step-by-step explanation:

when you subtract 35-15 it comes out to 20 and the other one comes out to 17

I'm guessing 10 days, since you lost a bit more than half of the workers, and it would take longer for the job to get done.

Answer:

20 Centimeters

Step-by-step explanation:

did it on edge

Answer:

C. 81[-4/3]^n-1

Step-by-step explanation:

The explicit formula for a geometric sequence is given by a_n = a * r^(n-1). Using the provided values of a2 = 108 and a5 = 256, we can establish two equations to solve for 'a' and 'r'. This results in two possible explicit formulas for the sequence.

In a geometric sequence, each term after the first is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. If we denote the first term of the sequence by 'a' and the common ratio by 'r', then the explicit formula of the sequence is: a_n = a * r^(n-1). Given that a2 = 108 (the second term is 108) and a5 = 256 (the fifth term is 256), we have two equations: a*r = 108 and a*r^4 = 256. Dividing the second equation by the square of the first equation, we get r^2 = 256/108^2 = 0.022. So, r is about +- 0.148. Substituting r into the first equation, we can solve for a. This gives us two possible explicit formulas for the sequence depending on whether we take the positive or negative value of r.

https://brainly.com/question/33243139

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Answer:

Each adult ticket was $43

Step-by-step explanation:

2x+18.5 = 104.5

Simplify

2x = 86

x = $43

Answer:

see explanation

Step-by-step explanation:

given x² - 6x - 21 = 0 ( add 21 to both sides )

x² - 6x = 21

to complete the square

• add ( half the coefficient of the x-term)² to both sides

x² + 2 (- 3)x +9 = 21 + 9

(x - 3)² = 30 ( take the square root of both sides )

x - 3 = ± [tex]\sqrt{30}[/tex] ( add 3 to both sides )

x = 3 ± [tex]\sqrt{30}[/tex]

x = 3 - [tex]\sqrt{30}[/tex] = - 2.48 ( to 2 dec. places ) or

x = 3 + [tex]\sqrt{30}[/tex] = 8.48 ( to 2 dec. places )

Step-by-step explanation:

larger number = y

smaller number=x

y>2x+1

y<3x+6

Probably the first one, if I did this right.

To do this problem, you need to know how to read math, literally. The problem says that y is the larger number, so assume the smaller is x. So, y exceeds 2x by 1 (so, y>2x+1). then, it says 3x exceeds y by 6; therefore, 3x+6>y. I may have interpreted it wrong, though, so tell me if I made a mistake :))

Answer:

first one

A. y = 2x + 1 and 3x + 6 = y

Answer:

0.8

Step-by-step explanation:

We can solve P(A or B) by using the following:

[tex]P(AorB)=P(A)+P(B)-P(AandB)[/tex]

Since we know P(A) = 0.6, P(B) = 0.3 and P(A and B) = 0.1 we obtain:

[tex]P(AorB)=0.6+0.3-0.1=0.8[/tex]

Answer: 0.8

Step-by-step explanation:

Answer:

[tex]3\frac{1}{4}[/tex] divide by [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]3\frac{1}{4}[/tex] is a mixed fraction and it can be written as

[tex]\frac{3*4+1}{4}=\frac{13}{4}[/tex]

13/4 can be break into

[tex]\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{1}{4}[/tex]

[tex]\frac{13}{4}[/tex] can be divided into [tex]\frac{3}{4}[/tex] and it is left with

[tex]\frac{1}{4}[/tex]

[tex]3\frac{1}{4}[/tex] divide by [tex]\frac{3}{4}[/tex]

Answer:

As you did not provide any "next steps", I would do it this way:

2q - 4 = 20 // add 4 to both sides

2q = 24 // divide both sides by 2

q = 12

Answer:

2q-4=20

Step-by-step explanation:

Answer:

sin theta  = 3/5

cos theta = 4/5

tan theta = 3/4

Step-by-step explanation:

sin = opposite / hypotenuse

cos = adjacent / hypotenuse

tan = opposite / adjacent

sin theta = 18/ 30 = 3/5

cos theta = 24/30 = 4/5

tan theta = 18/24 = 3/4

Answer:

[tex]sin \theta = \frac{3}{5} = 0.6\\\\ cos \theta = \frac{4}{5} = 0.8\\\\tan \theta = \frac{3}{4} = 0.75\\[/tex]

Step-by-step explanation:

Use SOHCAHTOA for reference

[tex]sin = \frac{opposite}{hypotenuse} \\\\cos = \frac{adjacent}{hypotenuse} \\\\tan = \frac{opposite}{adjacent}[/tex]

[tex]sin \theta = \frac{18}{30} = \frac{3}{5} = 0.6\\\\cos \theta = \frac{24}{30} = \frac{4}{5} = 0.8\\\\tan \theta = \frac{18}{24} = \frac{3}{4} = 0.75[/tex]

Answer:

True

Step-by-step explanation: