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Katyanochek1 [597]

2 years ago

7

Daniella has a box of 525 markers that she wants to share with 15 of her friends. If each of her friends gets the same number of

markers, how many markers will each friend get?
please help me!

1 answer:

Semenov [28]2 years ago

6 0

Answer:

Each friend will get 35 markers

Step-by-step explanation:

525 / 15 = 35

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Find the missing dimension of each prism: volume= 56 1/4 ft | width= 3 3/4 ft | length= 7 1/2 ft

Juliette [100K]

Prism volume = width*length*height
56 1/4 = 3 3/4 * 7 1/2 * h

56.25=3.75*7.5*h

h=(56.25)/(3.75*7.5)=2

So that the missing dimension (height) is 2 ft

4 0

3 years ago

Suppose that 12% of test scores for the unit 1 test were above 85 and 8% were below 70. Assuming a normal

Doss [256]

Answer:

Mean = 78.2

Standard deviation = 5.8

Step-by-step explanation:

Mathematically z-score;

= (x-mean)/SD

From the question;

12% of test scores were above 85

Thus;

P( x > 85) = 12%

P(x > 85) = 0.12

Now let’s get the z-score that has a probability of 0.12

This can be obtained from the standard normal distribution table and it is = 1.175

Thus;

1.175 = (85 - mean)/SD

let’s call the mean a and the SD b

1.175 = (85-a)/b

1.175b = 85 - a

a = 85 - 1.175b ••••••••(i)

Secondly 8% of scores were below 70

Let’s find the z-score corresponding to this proportion;

We use the standard normal distribution table as usual;

P( x < 70) = 0.08

z-score = -1.405

Thus;

-1.405 =( 70-a)/b

-1.405b = 70-a

a = 70 + 1.405b ••••••(ii)

Equate the two a

70 + 1.405b = 85 - 1.175b

85 -70 = 1.405b + 1.175b

15 = 2.58b

b = 15/2.58

b = 5.81

a = 70 + 1.405b

a = 70 + 1.405(5.81)

a = 78.16

So mean = 78.2 and Standard deviation is 5.8

4 0

2 years ago

f) The life of a power transmission tower is exponentially distributed, with mean life 25 years. If three towers, operated indep

Step2247 [10]

Answer:

15.24% probability that at least 2 will still stand after 35 years

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution and the exponential distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Probability of a single tower being standing after 35 years:

Single tower, so exponential.

Mean of 25 years, so $m = 25, \mu = \frac{1}{25} = 0.04$

We have to find $P(X > 35)$

$P(X > 35) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-0.04*35} = 0.2466$

What is the probability that at least 2 will still stand after 35 years?

Now binomial.

Each tower has a 0.2466 probability of being standing after 35 years, so $p = 0.2466$

3 towers, so $n = 3$

We have to find:

$P(X \geq 2) = P(X = 2) + P(X = 3)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{3,2}.(0.2466)^{2}.(0.7534)^{1} = 0.1374$

$P(X = 3) = C_{3,3}.(0.2466)^{3}.(0.7534)^{0} = 0.0150$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.1374 + 0.0150 = 0.1524$

15.24% probability that at least 2 will still stand after 35 years

4 0

2 years ago

What does P(X4=2,X3=3,X2=3,X1=2)

Dmitriy789 [7]

Answer:

its b

Step-by-step explanation:

3 0

2 years ago

Katya made another set of dolls. In the new set, the largest doll has a diameter of 8.75 cm and a height of 15.6 cm. Is this a d

Natali5045456 [20]

<em>Complete Question:</em>

<em>Katya creates handmade sets of dolls, which is sold to craft and souvenir stores. The first set of dolls has a middle diameter of 7cm and a height of 12cm.</em>

<em>Katya made another set of dolls. In the new set, the largest doll has a diameter of 8.75 cm and a height of 15.6 cm. Is this a dilation of the first set of dolls? </em>

<em></em>

Answer:

The new set is not a dilation of the first set

Step-by-step explanation:

Given

First Set:

$Height = 12cm$

$Diameter = 7cm$

New Set:

$Height = 15.6cm$

$Diameter = 8.75cm$

Required

Determine if the new set is a dilation of the second

To do this, we pass through the following steps:

1. Divide the height of the first set by the new set

2. Divide the diameter of the first set by the new set

3. Result in (1) and (2) must be equal if the new set is a dilation of the first set

Following the steps above:

(1)

$Height\ Ratio = \frac{H_2}{H_1}$

$Height\ Ratio = \frac{15.6}{12}$

$Height\ Ratio = 1.3$

(2)

$Diameter\ Ratio = \frac{D_2}{D_1}$

$Diameter\ Ratio = \frac{8.75}{7}$

$Diameter\ Ratio = 1.25$

(3) Make comparison

The ratio in (1) does not equal the ratio in (2)

i.e.

$1.3 \neq 1.25$

<em>Hence, the new set is not a dilation of the first set</em>

7 0

2 years ago