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3 years ago

Just wondering is 71 a PRIME number? ≡≡≡

Mathematics

2 answers:

Sergeu [11.5K]3 years ago

7 0

Yes 71 is a Prime Number

maxonik [38]3 years ago

7 0

Yes it is. When a number has more than two factors it is called a composite number

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4 2/5 + 3 1/10 + 2 3/5

ElenaW [278]

Answer:

10 1/10

Step-by-step explanation:

22/5 + 31/10 + 13/5

44/10 + 31/10 + 26/10

101/10

10 1/10

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2 years ago

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Solve the equation. 5x + 8 - 3x = -10 x = -9 X = -1 x = 1 X = 9 Cand

katovenus [111]

Here is how I solved it and the answer

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3 years ago

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Tyler has 120 linear feet of fencing to put around his garden. If he uses the fence to border a rectangular garden, what is the

Travka [436]

Answer:

The maximum area is $900\ ft^{2}$

Step-by-step explanation:

Let

x----> the length of rectangle

y---> the width of rectangle

we know that

The perimeter of rectangle is equal to

$P=2(x+y)$

we have

$P=120\ ft$

$120=2(x+y)$

$60=(x+y)$

$y=60-x$ ------> equation A

Remember that

The area of rectangle is equal to

$A=xy$ -----> equation B

substitute equation A in equation B

$A=x(60-x)$

$A=-x^{2} +60x$

This is a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex of the graph is the maximum area of the garden and the x-coordinate is the length for the maximum area

using a graphing tool

The vertex is the point $(30,900)$

see the attached figure

Find the value of y

$y=60-x$ -----> $y=60-30=30\ ft$

The dimensions of the rectangular garden is $30\ ft$ by $30\ ft$

For a maximum area the garden is a square

The maximum area is $900\ ft^{2}$

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4 years ago

Starting at 6 a.m. every morning, Matilda receives text messages on her cell phone from her mother, her best friend, and her bro

Dafna1 [17]

Answer:

a) 0.0013 = 0.13% probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.

b) $1.6 \times 10^{-9}$ probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

A) Find the probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.

Two from the best friend:

Her best friend sends a message once every 10 minutes.

From 6 to 7:30, there is an hour and a half, that is, 90 minutes, so the mean for her best friend is $\mu = \frac{90}{10} = 9$

Two messages is P(X = 2). So

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 2) = \frac{e^{-9}*9^{2}}{(2)!} = 0.0050$

Two from the mother:

Message every hour = 60 minutes. So $\mu = \frac{90}{60} = 1.5$ . This is P(X = 2).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 2) = \frac{e^{-1.5}*1.5^{2}}{(2)!} = 0.2510$

Two of her best friend and two of her mother:

Independent events, so the probability of both happening is the multiplication of their separate probabilities.

$p = 0.005*0.251 = 0.0013$

0.0013 = 0.13% probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.

B) With a chance of 75% a text message contains a typo independent of the sender. Find the probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.

In 3 hours, she is expected to receive:

3*60/10 = 18 messages from her best friend.

3*60/60 = 3 messages from her mother.

3*60/30 = 6 messages from her brother.

In total, 27 messages.

75% probability of a typo, so $\mu = 0.75*27 = 20.25$

This is P(X = 0).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-20.25}*20.25^{0}}{(0)!} = 1.6 \times 10^{-9}$

$1.6 \times 10^{-9}$ probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.

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3 years ago

Find an order pair (x, y) that is a solution to the equation -x+6y=3

Lelu [443]

One solution is the y intercept (0,1/2)

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3 years ago