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3 years ago

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Mrs. Lawson brought 15 bags of candy to give away for prizes. her third cllass wonf 3 3/4 bags of candy. her second class won 2

3/8 bags of candy. her third class won 2 5/8 of candy. how much candy does mrs. Lawson have left.

1 answer:

GuDViN [60]3 years ago

7 0

Mrs. Lawson has 6 2/8 bags of candy left.

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You go shopping at a local department store with your friend and cousin. You buy one pair of jeans, four pairs of shorts, and tw

VashaNatasha [74]

Answer: Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8

Step-by-step explanation:

Let x= cost per pair of jeans

y = Cost per pair of shorts

z= cost per shirt.

For you, total cost = x+4y+2z= 84

For your friend, total cost = 2x+y+3z=76

For cousin, total cost = x+2y+z= 52

Required system:

$x+4y+2z=84\ (i)\\ 2x+y+3z=76\ (ii)\\ x+2y+z=52\ (iii)$

from (i), $x=84-4y-2z$ (*)

put this in (ii) and (iii) we get

$2\left(84-4y-2z\right)+y+3z=76\\\Rightarrow\ -7y-z+168=76\ (iv)\\\\ 84-4y-2z+2y+z=52\\\Rightarrow\ -2y-z+84=52 \ (v)$

from (iv), $y=-\frac{z-92}{7}\ (vi)$

$\mathrm{Subsititute\:}y=-\frac{z-92}{7}\ \text{in}\ (v)$

$-2\left(-\frac{z-92}{7}\right)-z+84=52\\\\\Rightarrow\ -2\left(-\frac{z-92}{7}\right)-z=-32\\\\\Rightarrow\ -\frac{5z}{7}-\frac{184}{7}=-32\\\\\Rightarrow\ -5z-184=-224\\\\\Rightarrow\ -5z=-40\\\\\Rightarrow\ z=8$

$\mathrm{Subsititute\:}z=8\text{ in (vi)}$

$y=-\frac{8-92}{7}\\\\\Rightarrow \ y=12$

$\mathrm{Subsititute\:}z=8,\:y=12\text{ in (*)}$

$x=84-4\cdot \:12-2\cdot \:8\\\\\Rightarrow\ x= 20$

Hence, x= 20, y= 12 , z=8

So, Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8

7 0

3 years ago

The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont

BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

$\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)$

and its cumulative distribution function (CDF) is

$\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}$

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

$\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347$

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so A∩B = B and

$\bf P(A | B) = P(B)P(B) = (P(B))^2$

We have

$\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237$

hence,

$\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313$

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

If the distribution of lifetime of each bulb is independent, then we have here a binomial distribution of six trials with probability of “success” (one bulb needs replacement at the first inspection) p = 0.39347

Now the probability that exactly k bulbs need replacement is

$\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}$

<em>Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection. </em>

This means that,

<em>Probability that at least one of them needs replacement at the first inspection = </em>

$\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021$

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3 years ago

The ___ is the average of the sum of the squared differences of the mean from each element in a set of numerical data.

Bess [88]

Answer:

Variance.

Step-by-step explanation:

that is the variance of the data.

The square root of the variance is the Standard Deviation.

4 0

1 year ago

Length = 4 + x Width = x Height = x2 + 1 What is the base area of Box 3?

Simora [160]

Answer:

Base area of box = $x^2 +4$

Step-by-step explanation:

$Length = 4+x$

$Width = x$

$Height = x^2 + 1$

Base area of a rectangular box is a rectangle

Area of a rectangle (base area)= length times width

$Length = 4+x$

$Width = x$

Base area = $(4+x) \cdot x$

Multiply x inside the parenthesis

Base area of box = $4x +x^2$

8 0

3 years ago

Read 2 more answers

For which value of x does f(x) = 2

laila [671]

Answer:

<h2>x = -4</h2>

Step-by-step explanation:

<em>Look a the picture</em>.

Draw the horizontal line <em>y = 2</em>.

Common point: (-4, 2).

Conclusion: f(x) = 2 → x = -4

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3 years ago