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3 years ago

12

Mathematics

1 answer:

marta [7]3 years ago

8 0

Step-by-step explanation:

-3 10

-1 4

10= -3m+b

4= -m+b

6= -2m

m= -3

10= 9+b

b= 1

y= mx+b

y= -3x+ 1

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She uses between 1515 and 2020 yellow and blue beads in a ratio of 44 yellow beads to 55 blue beads.

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3 years ago

Last year, your store's total revenue was $400,000. the store's total discounts were $10,000 and returns totaled $5,000. what we

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3 years ago

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What is the length of the altitude to the longest side of a triangle, if the lengths

sergeinik [125]

Answer:

hb ≈ 7.06cm

Step-by-step explanation:

Using the formulas:

A=hbb

A=s(s﹣a)(s﹣b)(s﹣c)

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6 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

A study shows that employees who begin their workday at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a

arlik [135]

Answer:

20 %

Step-by-step explanation:

This question can be easily solved using The Rectangular, or Uniform Distribution of Probability

The probability of people arriving between 8:40 am and 9:30 am is uniformly distributed and can be represented by a rectangle attached as figure 1 .

The total area of this green rectangle must be equal to 1 because the total probability is always equal to 1.

We are interested in finding the red region which is for the time range of 9:00 am to 9:10am shown in the figure 2 attached:

First we need to find the Height of this rectangle:

To find the value of Height:

The formula for the area of rectangle = Base x Height

Base = b – a

In our case b – a is the difference in time from 8:40 am to 9:30 am

So, b – a = 50 (mins)

Similarly, Height x Base = 1 because max probability is equal to 1

Height = 1/ (b – a) because Base x Height must be equal to 1 (max probability)

Height = 1/ (b – a )

Height = 1/(Base)

Height = 1/50

Now once we have the value of Height we can find the desired probability of any region by multiplying the Height with the given time range in the question. In our case the time range is 9:00 am to 9:10 am which means 10(mins). Therefore,

Probability = Height x 10

Probability = 1/50 x 10

Probability = 1/5

To convert it into percentage

1/5 x 100% = 20% (Answer)

3 0

3 years ago