the refreshment stand at the fair was open for 3 hours four people took turns working at the stand for the same amount of time how many minutes did each person work

Answers

Answer 1

Answer: first off, simplify 3 hours. One hour is equal to 60 minutes, so we get 180 minutes. Next we divide 180 by four. We can make this easier by dividing 180 by ten, and multiplying it by 10 after we do everything. 4 times 4 is 16, and then the remaining 2 divided by 4 is .5. We have 4.5, but now we need to multiply 4.5 by 10, and we get 45. The answer is 45.

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Tom has taken out a loan for college. He started paying off the loan with a first payment of $200. Each month he pays, he wants to pay back 1.2 times as the amount he paid the month before. Explain to Tom how to represent his first 30 payments in sigma notation. Then explain how to find the sum of his first 30 payments, using complete sentences. Explain why this series is convergent or divergent.

Answers

Answer:

In this geometric series, a represents the first term, what he pays back monthly is the common ratio which is 1.2, and the first 30 payments are what is being used to find the total amount which is represented by n. Thus, a=$200, n=30 and r=1.2. The sum is found by sn=(a((r^n)-1))/(r-1), which will be 200((1.2^30)-1))/(1.2-1). The solution is = $ 236,376 and the series is divergent because of the common ratio being greater than 1.

Step-by-step explanation:

This is a geometric series. The first payment represents the first term, a. The number of times he wants to pay back for subsequent payments represent the common ration, r. The first 30 payments represents the number of terms to use in finding the sum, n.

Hence, a = $ 200, n = 30 and r = 1.2.

The sum of a geometric sequence is given as:

Sn = (a((r^n)-1))/(r-1)

=(200((1.2^30)-1))/(1.2-1)

= $ 236, 376. 31

Explain why this series is convergent or divergent.

Since the common ratio, r, is greater than 1, the series is divergent

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Answers

easy, the degree of the function equals the number of roots it has
degree is the highest placeholder exponent

we have
7x^0
5x^4
-3x^2
which is highest?

4th

means 4 roots
means
(x-r1)(x-r2)(x-r3)(x-r4) where r1,r2,r3,r4 are the roots

4 roots

Which linear inequality is represented by the graph?

Answers

Linear inequality represented by the graph is

$\displaystyle y\leq (1)/(3)x-4$

Further explanation

Straight-line equations are mathematical equations that are described in the plane of cartesian coordinates

General formula

$\large{\boxed{\bold{y-y1=m(x-x1)}}$

y = mx + c

Where

m = straight-line gradient which is the slope of the line

x1, y1 = the Cartesian coordinate that is crossed by the line

c = constant

The formula for a gradient (m) between 2 points

$\large{\boxed{\bold{m= (y2-y1)/(x2-x1)}}$

If the intersection of the x-axis (b, 0) and the y-axis (0, a) then the equation of the line:

ax + by = ab

It says inequality if there are symbol forms like <,>,≤ or ≥

Whereas linear inequality can have forms: ax + by> cax + by ≥ cax + by <cax + by ≤ c

In graphical form, line inequality can be

dashed line because y does not include equals to
a solid line because y includes equal to

For line inequality (positive coefficient y)

ax + by ≥ c then the solution is shaded upwards

ax + by ≤ c then the solution is shaded down

Or we input the values x, y from the point in the shaded area and put in the inequality line

From the picture we can determine the equation of the line

Line through 2 points (0, -4) and (-3, -5)

the gradient: $\displaystyle =(-5+4)/(-3-0)\n\n=(1)/(3)$

the equation of the line:

$\displaystyle y-y1=m(x-x1)\n\ny+4=(1)/(3)(x-0)\n\n=(1)/(3)x-4$

We check the point in the area of shading, for example (0, -6)

we input in the equation :

$\displaystyle -6=(1)/(3).0-4\n\n-6=-4$

Because -6 < -4 and the graph is solid line so the inequality line will be

$\displaystyle y\leq (1)/(3)x-4$

Learn more

F (x) = x2 + 1 g (x) = 5 - x

htps: //brainly.com/question/2723982

the inverse of the function f (x) = 2x-10

brainly.com/question/628130

domain of the function

brainly.com/question/4135536

Keywords: linear inequality,graph

In the given graph the line is having the y intercept as -4.

The slope of line = $(Rise)/(Run) =(1)/(3)$

The equation of the line is $y=(1)/(3)x-4$

The line is a dark line so inequality will be either ≤ or ≥.

Consider point (0,-5)which lie in the shaded region.

Plug x=0 and y=0 in the equation of line,

-5= $(1)/(3)(0)-4=-4$

-5≤ -4 .

The inequality equation for the given graph is

y≤ $(1)/(3)x-4$

Solve 2 log2 2 + 2 log2 6 − log2 3x = 3.

Answers

Answer:

x = 6

Step-by-step explanation:

Given : $2\:log_2\:2\:+\:2\:log_26−\:log_2\:3x\:=\:3$

We have to solve the given expression $2\:log_2\:2\:+\:2\:log_26−\:log_2\:3x\:=\:3$

Subtract $2\log _2\left(2\right)+2\log _2\left(6\right)$ both sides , we have,

$2\:log_2\:2\:+\:2\:log_26-\:log_2\:3x-(2\log _2\left(2\right)+2\log _2\left(6\right)):=\:3-(2\log _2\left(2\right)+2\log _2\left(6\right))$

Simplify, we have,

$\log _2\left(3x\right)=3-2\log _2\left(2\right)-2\log _2\left(6\right)$

Divide both side by -1, we have,

$(-\log _2\left(3x\right))/(-1)=(3)/(-1)-(2\log _2\left(2\right))/(-1)-(2\log _2\left(6\right))/(-1)$

Simplify, we have,

$\log _2\left(3x\right)=-3+2\log _2\left(2\right)+2\log _2\left(6\right)$

Apply log rule, $a=\log _b\left(b^a\right)$

$2\log _2\left(6\right)-1=\log _2\left(2^(2\log _2\left(6\right)-1)\right)=\log _2\left(18\right)$

When log have same base,

$\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)$

$\mathrm{For\:}\log _2\left(3x\right)=\log _2\left(18\right)\mathrm{,\:\quad solve\:}3x=18$

3x = 18

x = 6

log(base2)[2² * 6² / 3x] = 3
144 / 3x = 2^3 = 8
144/8 = 3x
18 = 3x
x = 6

there are 7 gray kittens. 2 kittens are black. how many fewer black kittens are there than gray kittens?

Answers

5 kittens, because seven gray kitties minis two black kitties equals five fewer black kitties!

this is part 2 and you just have to find the total area in sq ft and also answer how much material do you need to make 3 backpacks

Answers

1. 1 1/8= 18/16

5/16*2= 10/16

4/16*2= 8/16

9/16= 9/16

1/2= 8/16

18/16 + 10/16 + 8/16 + 9/16 + 8/16= 53/16

Simplify:

4 & 5/16sq ft

2. All you do is multiply that by 3... so 4 & 5/16 = 53/16 53/16*3 = 159/16 = 9 & 15/16 sq ft

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