1. A landscaper can rent a backhoe for $45,000 a year. He could purchase the equipment for
monthly costs of $2,500 plus $20 for each hour it is used. How many hours per year must
the equipment be used to justify purchasing it rather than renting it?

The difference between the cost of one candy per ounce and the other candy is that: Almond bark costs $0.50 more per ounce than peanut brittle.

Mathematically, a direct proportion can be represented the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for each candy as follows:

For Peanut Brittle, we have the following:

Constant of proportionality (k) = 10/10

Constant of proportionality (k) = 1.0

For Almond Bark, we have the following:

Constant of proportionality (k) = 3/2

Constant of proportionality (k) = 1.5

Next, we would determine the difference in cost:

Difference in cost = 1.5 - 1.0

Difference in cost = $0.50.

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The given equation solved for u is u = 7 or u = -7

From the question, we are to solve the given equation.

The given equation is

u^6 − 49 u^4 = 0

First, we will write the equation properly

The given equation written properly is

u⁶ - 49u⁴ = 0

Now,

To solve the equation, we will determine the value(s) of the variable. The variable in the given equation is u.

Thus,

We will solve for u

u⁶ - 49u⁴ = 0

Add 49u⁴ to both sides of the equation

u⁶ = 49u⁴

Divide both sides by u⁴

u⁶/u⁴ = 49u⁴/u⁴

u² = 49

Then,

u²- 49 = 0

u² - 7² = 0

Factorize by applying the rule for difference of two squares

(u + 7)(u - 7) = 0

Then,

u + 7 = 0 OR u - 7 = 0

u = -7 OR u = 7

Hence, the value of u is -7 OR 7

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Answer:

25

Step-by-step explanation:

2000/4=500

500/20=25

Answer: 125

Step-by-step explanation: you see if you take your 20$ you ern of of selling a shirt then the price you buy it for 4$ then defied it by 2000$ you get 125.

The number of guests at the wedding is 276.

Since 1/3 of the guests choose beef and 5/12 choose chicken, the fraction for vegetarian will be:

= 1 - (1/3 + 5/12)

= 1 - 3/4

= 1/4

Therefore, let the total number of guests be x.

This will be illustrated as:

1/4 × x = 69

0.25x = 69

Divide

x = 69 / 0.25

x = 276

Therefore, there are 276 guests.

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Answer:

Todd's conclusion is logical. I know this because all people named Todd are logical beings who always come to logical conclusions. But seriously though, please comment down below more of your question so I can accurately answer it, thanks!

Step-by-step explanation:

Answer:

22.3 gm

Step-by-step explanation:

720 is this many half lives :   720 / 1690

   so there will be this much left   30 gm ( 1/2)^(720/1690) = 22.3 gm

Answer:

The slope of the line passing through the points [tex](-2, 2)[/tex] and [tex](-5, 5)[/tex] is equal to: [tex]-1[/tex]

Step-by-step explanation:

The slope of a line can be found with the following formula

[tex]m=\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where [tex]x_2 > x_1[/tex]

Then substituting the values ​​with the given ones we have

[tex]m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{2-5}{-2-(-5)}=\frac{-3}{-2+5}=\frac{-3}{3} =-1[/tex]

So the slope of the line passing through the given points is [tex]-1[/tex]

Answer: 25 1/3

Step-by-step explanation:

The simplest radical form of the radicals given are:

1. The simplest radical form of √175 is 5 √7.

2. The simplest radical form of √5 / 12 is √5 / 12.

First, let us understand the radical:

A radical can also be called a surd. A surd is an irrational number. We say that it is irrational because it can not be expressed as a terminating decimal.

1.

We are given:

√175

We need to write in the simplest radical form.

175 can be written as:

175 = 5 * 5 * 7

√175 = √ 5 * 5 * 7

√175 = √ 5 * 5 * √7

√175 = 5 √7

So, the simplest form of √175 is 5 √7.

2.

We are given:

√5 / 12

We need to write in the simplest radical form.

√5 / 12 is already in the simplest form.

So, the simplest form of √5 / 12 is √5 / 12.

Thus, the simplest radical form of the radicals given are:

1. The simplest radical form of √175 is 5 √7.

2. The simplest radical form of √5 / 12 is √5 / 12.

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Answer:

x = 4 ; y = -1

Step-by-step explanation:

y = -2x + 7

x + 2(-2x+7) = 2

x -4x + 14 = 2

-3x = 2 -14

-3x = -12

-3/-3 x = -12/-3

x = 4

y = -2* 4 + 7

y = -8 + 7

y = -1

Answer:

x = 105

Step-by-step explanation:

To solve for x, we simply need to isolate it:

[tex]\frac{2}{7}x+\frac{1}{5}x=51\\ \frac{17}{35}x=51\\ x=105[/tex]

Answer:

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

The given function is the combination of three lines:

The values of the function at the given points are:

Answer:

Below

Step-by-step explanation:

The equation ( you need to commit to memory) is:

FV = PV ( 1+i)^n      FV = future value    PV = present value(110 000)

                               i = decimal interest per PERIOD = .08 /4 = .02

                                 n = # of periods = 40  (it is a quarterly period by 10 yrs)

FV = 110 000 ( 1 + .02)^40 =  242 884 .36 dollars

Answer:

124.644

Step-by-step explanation:

28.2*4.42=124.644.

Answer:

28.2 × 4.42= 124.644

and in non-decimal it's 124644 removing 3 decimal places

Step-by-step explanation:

Brainiest, please

thank you

Answer:$583.93 is the original price

Each individual paid the sum of $23.4 including state tax at the restaurant

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%".

In the problem, their total bill is $50.88 and they gave a 30% tip

We should fid 30% of 50.88

0.3 * 50.88 = $15.264

30% of $50.88 is $15.264

If we add this up and then find the state tax to it.

15.264 + 50.88 = 66.144.

Find 6% of 66.144 to determine the state tax.

0.06 * 66.144 = 3.96864

The total amount spent is 66.144 + 3.96864 = 70.11264

We can divide this equally amongst the three people to get the individual payment = 70.11264/3 = 23.37088

Rounding this to the nearest cent, we have 23.4.

We can say each person paid $23.4 at the end of the day

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If a population was 5000 in 2010 and grew to 6000 by 2015. What is the annual percentage rate of growth is 9.6%

The initial population was 5000

The population in 2015 is 6000

let the rate of growth be r

aₙ = arⁿ-¹

6000 = 5000 r⁵⁻¹

6000/5000 = r⁴

6/5 = r⁴

r = 1.2⁻⁴

r = 0.48

r = 48%

the annual percentage rate of growth 48/5 = 9.6

Therefore, if a population was 5000 in 2010 and grew to 6000 by 2015. What is the annual percentage rate of growth is 9.6%

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Answer:384

Step-by-step explanation:

first you multiply 2 times 2= 4 then 4 times 4 times 4= 64 then you multiply 3 times 2= 6 lastly you multiply 6 and 64. your welcome:)

Step-by-step explanation:

if p(A)=0.17, p(B)=0.42 and p(AorB)=0.59, are A and B mutually exclusive

Answer:

63 is the answer.

Step-by-step explanation:

9p=9xp, p=7, so 9x7=63. ;)

to get the slope of any straight line, we simply need two points off of it, let's use those two from the picture below

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{(-3)}}} \implies \cfrac{-4}{-1 +3} \implies \cfrac{ -4 }{ 2 } \implies - 2[/tex]

Answer:

3+4x>-5

4x>-5-3

4x>-8

x>-8/4

x> -2

Answer: 4

Step-by-step explanation:  your going to divide -2 by 1 and you get 2 then add 4 and you get 6 pls give me brainliest :)

The number of  turkeys that they sold on Sunday is 90 turkeys

Total number of turkeys = 240

On Sunday, they sold 3/8 of them

The fraction of turkeys they sold on Sunday = 3/8

To find the number of turkeys that they sold on Sunday we have to find the 3/8 fraction of 240

Then,

The number of turkeys that they sold on Sunday = Total number of turkeys × The fraction of turkeys they sold on Sunday

Substitute the values in the equation

The number of turkeys that they sold on Sunday = 240 × 3/8

= 240 × 0.375

= 90 turkeys

Hence, the number of  turkeys that they sold on Sunday is 90 turkeys

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The slope of the line is -3 and the equation of the line formed by the points is y + 3x = 6.

From the table we can see that the line passes through the points:

(-6,6) ,(5,-3) ,(4,0) and (3,3) .

Let us consider any two points on the line (4,0) and (3,3) .

We know that the slope of the line can be found by using the intercept formula

Hence slope = (3-0) / (3-4) = 3/ -1 = -3

Now the equation of the line is :

y - 3 = -3(x-3)

or, y - 3 = -3x +9

or, y + 3x = 6

The letter m is frequently used to represent the slope of an object that resembles a line in the plane that contains the x and y axes. The slope is defined as the difference in two independent locations along the line expressed in y coordinate less by the equivalent difference in x coordinate.

Therefore slope of the line is -3.

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The number of groups, using the combination formula, for each case, is given as follows:

a) Same number of students from each grade: 1,245,816,000

b) At least two grade nine students: 31,650,886,995.

c) James and Lucy are in it: 2,481,256,778.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

For item a, the groups are taken as follows:

Hence the number of groups is:

[tex]C_{10,3}C_{11,3}C_{12,3}C_{13,3} = \frac{10!}{7!3!} \times \frac{11!}{8!3!} \times \frac{12!}{9!3!} \times \frac{13!}{10!3!} = 120 \times 165 \times 220 \times 286 = 1,245,816,000[/tex]

For item b, the total number of groups, without considering the restriction, is:

[tex]C_{46,12} = \frac{46!}{12!34!} = 38,910,617,655[/tex]

The number of groups with none students from grade 9 is:

[tex]C_{36,12} = \frac{36!}{12!24!} = 1,251,677,700[/tex]

The number of groups with one student from grade 9 is:

[tex]C_{10,1}C_{36,11} = 10 \times \frac{36!}{11!25!} = 6,008,052,960[/tex]

Using complementary events, the number of groups with at least two grade 9 students is:

38,910,617,655 - (1,251,677,700 + 6,008,052,960) = 31,650,886,995.

For item c, considering Jamie and Lucy in it, the remaining 10 students are taken from a set of 44, hence:

[tex]C_{44,10} = \frac{44!}{10!34!} = 2,481,256,778[/tex]

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Answer: y = 5x - 3

Step-by-step explanation:

It is a line, so its formula is y = mx + b.

         [tex]y=5x+b\\7=5(2)+b\\7=10+b\\b=7-10=-3[/tex]

Therefore, the formula is y = 5x - 3.

Answer:

y=5x-3

Step-by-step explanation:

Answer:

12 inches

Step-by-step explanation:

Let be "x" the top inches (in the model) of a eighty four foot building.

According to the information provided in the exercise, we be aware of that the top of a two-story establishing is 21 toes and in the scale model its top is 3 inches.

Knowing this, we can set up the following proportion: 3/21=x/84

The final step is to get to the bottom of for "x" in order to calculate its value.

The probability of drawing the Blue 4 is an example of .R′f.E′

Red cards = 1,2,3

Blue cards =1,2,3,4,5,6

Pr(R) =  Drawing a red card = 3/9 = 1/3

Pr(B)= Drawing a blue card = 6/9 = 2/3

Pr(E) = Drawing an even card = 4/9

Pr(O) = Drawing an odd number card = 5/9

Probability of drawing the blue 4 ? = Pr(blue, 4) = 1/9

From the options

(A) R or O = Pr(R) + Pr(O)  = 1/3 + 1/9 = 8/9 ........(Not equal to 1/9)

(B) B and O = Pr(B) × Pr(O) =  2/3 × 5/9 = 10/21......(Not equal to 1/9)

(C) R or E = Pr(R) + Pr(E) = 1/3 + 4/9 = 7/9.......(Not equal to 1/9)

(D) R and O = Pr(R) + Pr(O) = 1/3 × 5/9 = 5/27.......(Not equal to 1/9)

(E) R'. E' = 1-Pr(R)-1-Pr(E) =

                1-1/3 =2/3- 1-4/9 =5/9

               2/3-5/9 = 1/9......( equal to 1/9).

Hence, the probability of drawing the Blue 4 is an example of .R′f.E′

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Disclaimer: the question given by you is incomplete, the solution is done as per a similiar question which is

A deck of cards contains RED cards numbered 1,2,3 and BLUE cards numbered 1,2,3,4,5,6. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card.Drawing the Blue 4 is an example of which of the following events? Select all correct answers.Select all that apply:a.R OR Ob.B AND Oc.R OR Ed.R AND Oe.R′f.E′