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3 years ago

A postal carrier can

Mathematics

1 answer:

ioda3 years ago

6 0

Answer: 6 hours or 360 minutes

Step-by-step explanation:

First find out how long it takes to deliver to one house.

Convert hours to minutes.

2.5 x 60 = 150 minutes total

Divide to find the time per house

150 minutes / 130 houses = 1.15 minutes per house

Now multiply this rate by the number of houses (312).

312 x 1.15 = 360 minutes

If you want it in hours then divide by 60.

360/60 = 6 hours.

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How to factorize (1-x)(4x-9)+(x^2-6x+5)

adell [148]

-1(x-1)(4x-9) +(x-1)(x-5)
(x-1)(-1(4x-9) +x-5)
(x - 1)(-4x + 9 + x - 5)
(x - 1)(-3x + 4)

3 0

3 years ago

Savannah is 24 years older than Ryan, while Sebastian is 5 times as old as Ryan. If Savannah and Sebastian are twins, which equa

IRISSAK [1]

Answer: I think the answer would be b) 24+2x=5x

sry if it's wrong

3 0

4 years ago

"If you subtract 16 from my number and multiply the difference by -5 , the result is 20 ." What is 's number?

Phoenix [80]

Answer:

Let the original number be x.

Thus,

$\\ - 5(x - 16) = 20 \\ \\ - 5x + 80 = 20 \\ \\ 5x = 60 \\ \\ x = 12$

So, The original number is 12.

4 0

3 years ago

<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

3 years ago

7. On a map of a local community college, the cafeteria is located at point (-4,3) and the

marishachu [46]

Answer: C. 10.2

Step-by-step explanation: because in decimal form 10.19803902 to the nearest is 10.2

7 0

3 years ago

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