Write both the explicit and recursive equations for this sequence: 7, 10, 13, 16,…. Show yourwork/explain your thinking for how you get each component of both of the equations.

Answer:

wouldt be 112,000?

Step-by-step explanation:

Dont you do 10x9x4x4??

That is how i was tought how to do it. I dont know about you.

Answer:

80

Step-by-step explanation:

The 4 doesn't matter right now unless you were solving for area. Visualize the shape as a normal rectangle with no cut out. That would make the bottom line 10+10+10 which equals 30. The top line is the same as the bottom, so that would also be 30. Then you just have the two sides which are both 10, combined them and they would add up to 20. Perimeter is the distance around the edge of a shape. You find the perimeter by adding up the distance of all the sides. So in conclusion, you're answer will be 30+30+10+10 which equals 80.

Answer:

Step-by-step explanation:

\( \space\)

A = b × h

=> 154.5 = b × 15

=> b = \( \sf{\frac{154.5}{15} }\)

=> 10.3 cm

\( \space\)

Hope it helps!

Have a great day! :)

Answer:

She should have 8 5/8 reams of paper left

1. Based on the producer theory, an increase in the demand for labor (L) would be caused by An increase in the productivity of labor, A decrease in the wage rate and A decrease in the rental rate of capital.

2. Missing variables in this simple producer theory would include The technology used to produce output, The preferences of consumers and Quality of labor and capital.

In the standard producer theory, a producer minimizes costs for a given level of output.

This involves choosing the optimal mix of inputs, such as labor (L) and capital (K), to produce the desired output (y).

The cost function is represented by C = wL + rK, where w is the wage rate (cost of labor) and r is the rental rate (cost of capital).

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Answer:

6x2-10x-4

Step-by-step explanation:

hx=(2x-4)(3x+1)

hx=2x(3x+1)-4(3x+1)

hx=6x2+2x-12x-4

hx=6x2-10x-4

a. The proportion of students have scores less than 380 is 11.51%.

b. The proportion of students have scores greater than 639 is 8.23%.

1. Using the z-score formula:

We can calculate that score of 380 corresponds to a z-score of -1.2 since z = (x - μ) / σ.

Using a standard normal distribution table, we find that:

2. Similarly, a score of 639 corresponds to a z-score of 1.39.

Using a standard normal distribution table, we find that:

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Answer:

(2a^3a^4)^5 simplifies to 32a^35.

Step-by-step explanation:

To simplify (2a^3a^4)^5, we can use the properties of exponents which states that when we raise a power to another power, we can multiply the exponents. Therefore, we can rewrite the expression as:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5

Next, we can simplify the expression inside the parentheses by multiplying the exponents:

a^3a^4 = a^(3+4) = a^7

Substituting this into our expression, we get:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5 = 2^5 * a^35

Finally, we can simplify this expression by using the property of exponents that states that when we multiply two powers with the same base, we can add their exponents. Therefore, we can rewrite the expression as:

2^5 * a^35 = 32a^35

Therefore, (2a^3a^4)^5 simplifies to 32a^35.

Answer:

Yes, it is a linear function

Step-by-step explanation:

A linear function is always in the form of y=mx+b. In this case, 1/2 is the "m" and 10 is the "b." Since the function is in this form, it must be a linear function.

The domain of \(y=4\log_5(x-3)\) is (d) all real numbers greater than 3.

The function is given as:

\(y=4\log_5(x-3)\)

Set the expression in bracket greater than 0

x -3 > 0

Add 3 to both sides

x > 3

Hence, the domain of \(y=4\log_5(x-3)\) is (d) all real numbers greater than 3.

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Answer:

125/6(In(x-25)) - 5/6(In(x+5))+C

Step-by-step explanation:

∫x2/x1−20x2−125dx

Should be

∫x²/(x²−20x−125)dx

First of all let's factorize the denominator.

x²−20x−125= x²+5x-25x-125

x²−20x−125= x(x+5) -25(x+5)

x²−20x−125= (x-25)(x+5)

∫x²/(x²−20x−125)dx= ∫x²/((x-25)(x+5))dx

x²/(x²−20x−125) =x²/((x-25)(x+5))

x²/((x-25)(x+5))= a/(x-25) +b/(x+5)

x²/= a(x+5) + b(x-25)

Let x=25

625 = a30

a= 625/30

a= 125/6

Let x= -5

25 = -30b

b= 25/-30

b= -5/6

x²/((x-25)(x+5))= 125/6(x-25) -5/6(x+5)

∫x²/(x²−20x−125)dx

=∫125/6(x-25) -∫5/6(x+5) Dx

= 125/6(In(x-25)) - 5/6(In(x+5))+C

Answer:

a = 8

b = 2

c = 48

Step-by-step explanation:

3 cups of flour is needed to make 24 servings.

3:24

Simplify. First, divide 3 from both sides of the ratio.

(3)/3 : (24)/3

1:8

Next, solve for b. You multiply 2 to 8 to get 16. Next, multiply 2 to 1

1 x 2 = b = 2

Finally, multiply 8 to 6 to get c.

8 x 6 = c = 48

~

Thanh's cost per month (four weeks) will be $300.00.The given fixed rate for Thanh is $49.00 per week. Thanh also pays $14.00 per week for the optional insurance and $12.00 weekly on gas.

To find Thanh's cost per month (four weeks), we need to multiply his weekly cost by 4.We can use the formula below to calculate Thanh's monthly cost.

Total weekly cost = Fixed rate + Insurance cost + Gas cost

Total weekly cost = $49.00 + $14.00 + $12.00

Total weekly cost = $75.00

The cost for Thanh per month (four weeks) = Total weekly cost × 4

Cost for Thanh per month (four weeks) = $75.00 × 4

Cost for Thanh per month (four weeks) = $300.00

Therefore, Thanh's cost per month (four weeks) will be $300.00.

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The population of US is 330 million approx.

A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." The number "%" is used to symbolize it.

Given

population of new york = 2.727272% population of US

population of new york = 9 million

population of US = 1/2.727272% of new york

population of US =  36.6666 x 90,00,000

population of US = 33,00,00,087.9 = 330 million approx

Hence population of US is approx 330 million.

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Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Answer:

Якщо ти перекладаєш це, то ти неписьменний. якщо ти читаєш це, я пишаюся тобою. Його коричневий. Лол. Нані, УуУ, Оні-Чан.

Step-by-step explanation:

Jolie's working time increased by 20 %

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, Jolie’s time at work increases from 25 hours per week to 30 hours per week, we need to find that by  what percentage did the time at work per week increase,

Using the concept of percentage,

Initial working hours = 25 hours per week

Final working hours = 30 hours per week

Increased hour = 30 - 25 = 5 hours

Percentage increased = 5 / 25 x 100 = 20%

Hence, Jolie's working time increased by 20 %

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They will be when they pass each other at 44 4/9 mins.

This is a classic question on Speed, time, & distance.

1. When time traveled in each segment is constant, then average speed is simple mean of speeds.

2. When distance traveled in each segment is constant, then average speed is reciprocal of simple mean of reciprocal of speeds. It is basically called Harmonic mean.

So this question falls in the category of 2.

=> So, average speed = Reciprocal of mean of reciprocals of 40 & 50.

=> Average speed = Reciprocal of mean of 1/40 & 1/50.

=> Average speed = Reciprocal of (1/40 + 1/50)/2

= Reciprocal of (5+4)/400

= 44 4/9 mins

Hence, they will be when they pass each other at 44 4/9 mins.

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Total number of people surveyed = 118

Number of people who own dogs = 78

Number of people who own cat = 44

Number of people who own both cats and dogs = 26

Number of people who only own dogs = 78 - 26 = 52

Number of people who own only cats = 44 - 26 = 18

Only dog owners + Only cat owners + Both + Neither = Total people surveyed

52 + 18 + 26 + Neither = 118

Neither = 22(answer)

Answer: E

Step-by-step explanation:

Answer:

3 is the right one

Step-by-step explanation:

Simple math you know

Answer:

$5.91

Step-by-step explanation:

The amount of simple interest gained from a sum of money can be represented as:

\(\textrm{Interest} = P\cdot r\cdot t\)

where \(P\) is the principal amount (original sum of money), \(r\) is the rate of simple interest per time period, and \(t\) is the period of time in relation to a year.

To solve this problem, we simply have to plug the given values into the above formula and round the result to the hundredths place (cents).

\(P = \$525\),  \(r = \dfrac{4.5\%}{\textrm{month}}\),  \(t = 3 \textrm{ months} = \dfrac{1}{4} \text{ year}\)

\(\textrm{Interest} = \$525 \cdot 4.5\% \cdot \dfrac{1}{4}\)

\(\boxed{\textrm{Interest} \approx \$5.91}\)

Answer:

$5.91 (nearest cent)

Step-by-step explanation:

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I=Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

As the value of t has been given in months, we need to convert it to years before inputting it into the formula.

\(\sf \implies 3\; months=\dfrac{3}{12}\;year=\dfrac{1}{4}\; year\)

Therefore, the values to input into the formula are:

Substitute the values into the formula and solve for I:

\(\implies I=525 \cdot 0.045 \cdot \dfrac{1}{4}\)

\(\implies I=23.625 \cdot \dfrac{1}{4}\)

\(\implies I=5.90625\)

Therefore, the amount of interest you would receive on a deposit of $525 for three months at a rate of 4.5% is $5.91 (nearest cent).

Answer:

3.43 I think that's it.

\(2x^2 -5x-8 =0\\\\\implies x = \dfrac{ -(-5) \pm \sqrt{(-5)^2 - 4\cdot 2 \cdot (-8)}}{2 \cdot 2}\\\\\\\implies x = \dfrac{5 \pm \sqrt{89}}{4}\\\\\\\text{Hence}~ x = \dfrac{5 + \sqrt{89}}{4},~~ x = \dfrac{5 - \sqrt{89}}{4}\)

Answer:

\(\sf \boxed{\sf x=\frac{5+\sqrt{89}}{4}}\)

\(\sf \boxed{\sf x=\frac{5-\sqrt{89}}{4}}\)

\(\sf 2x^2-5x-8=0\)

☁ We'll solve this equation using The Quadratic Formula:

\(\boxed{\sf \cfrac{-b\pm \sqrt{b^2-4ac}}{2a}}\)

A= 2, b= -5, c= -8

\(\sf x=\cfrac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\times \:2\left(-8\right)}}{2\times \:2}\)

\(\mapsto \sf \sqrt{\left(-5\right)^2-4\times \:2\left(-8\right)}\)

\(**\sf \left(-5\right)^2=5^2\)

\(\mapsto \sf \sqrt{5^2+4\times \:2\times \:8}\)

\(\mapsto \sf \sqrt{5^2+64}\)

\(\mapsto \sf \sqrt{89}\)

______________

\(\sf x=\cfrac{-\left(-5\right)\pm \sqrt{89}}{2\times \:2}\)

☁ Now, we'll Separate solutions, first, we'll solve the equation when ± is plus:

\(\mapsto \sf \cfrac{-\left(-5\right)+\sqrt{89}}{2\times \:2}\)

☁ Multiply 2*2 =4

\(\boxed{\sf \cfrac{5+\sqrt{89}}{4}}\)

_________________

☁ Now solve the equation when ± is minus:

\(\mapsto \sf \cfrac{-\left(-5\right)-\sqrt{89}}{2\times \:2}\)

☁  Multiply 2*2 =4

\(\boxed{\sf \cfrac{5-\sqrt{89}}{4}}\)

\(\sf Solution \:1:\boxed{\sf x=\frac{5+\sqrt{89}}{4}}\)

\(\sf Solution \:2:\boxed{\sf x=\frac{5-\sqrt{89}}{4}}\)

☁❅☁❅☁☁❅☁❅☁☁❅☁❅☁❅☁

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Answer:

the answer is D. F(x) = 1/x(x-3)

Step-by-step explanation:

Using a linear function, it is found that the monthly cost for 19 HCF is of $41.43.

A linear function, in slope-intercept format, is modeled according to the rule presented below:

y = mx + b

In which the parameters of the function are described as follows:

As stated in the problem, the slope is of 1.45, hence:

y = 1.45x + b.

The monthly cost for 22 HCF is $45.78, hence when x = 22, y = 45.78, meaning that the intercept b can be found as follows:

45.78 = 1.45(22) + b

b = 45.78 - 1.45 x 22

b = 13.88.

Then the function is:

y = 1.45x + 13.88.

And the cost for 19 HCF is given by:

y = 1.45(19) + 13.88 = $41.43.

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Answer:

Step-by-step explanation:

2 1/8 = 17/8

4/8 + 17/8 = 21/8

21/8 = 2 5/8

Therefore, Tom took 2 and 5/8 hours to clean the two rooms

Answer: 2 5/8 hours ( 2 hours and 38 mins [rounded])

Step-by-step explanation: For the best experience, look at the attachment:

So, first I took the numbers and set up an addition problem. But we have a problem. They both don't have the same denominator. So first, we need to find a common denominator before we add. So, luckily we know that 2 is a factor of 8. So 1/8 would stay the same and we'd multiply the 2 by 4 to get the denominator, and 1 by 4 to get the denominator. Then, you'd add 2 1/8 to 4/8 to get 2 5/8. Also, I converted 5/8 of an hour to get 37.5 mins, so I rounded up to 2 hrs and 38 mins.

Answer:

jack is 54 and lacey is 13.5. I think

Step-by-step explanation:

Let Jack be J and Lacy be L.

First equation:   J=4L

Second equation:    (J+9)+(L+9)=63

Solving using substitution:

4L+9+L+9=63

5L+18=63

5L= 45

L = 9

L=9 and J=4L  = 4*9 = 36

So Jack is 36 years old and Lacy is 9 years old.