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nydimaria [60]
3 years ago
6

Find the values of x and y. Write your answer in simplest form.

Mathematics
1 answer:
nydimaria [60]3 years ago
7 0

Answer:

x=30°

y=30°

Step-by-step explanation:

x= 180-150=30°

y)

180=30 + 90 + z

z +120 = 180

z= 60

90-60=y

y=30

30°

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Please help ! The equation is attached in the photo above :)
qaws [65]

Step-by-step explanation:

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7 0
3 years ago
Read 2 more answers
Fugture out the question
levacccp [35]

Answer: Its right.

Step-by-step explanation:

5 0
3 years ago
Lowest common multiple of 3240 and 1007
xeze [42]

Answer:

3,262,680

Step-by-step explanation:

Hope this helps!

4 0
3 years ago
Suppose that the speed at which cars go on the freeway is normally distributed with mean 68 mph and standard deviation 5 miles p
denis23 [38]

Answer:

A)X \sim N(68 , 25)

B) the probability that is traveling more than 70 mph is 0.3446

C) the probability that it is traveling between 65 and 75 mph is 0.6449

D) 90% of all cars travel at least 56.85 mph fast on the freeway

Step-by-step explanation:

The speed at which cars go on the freeway is normally distributed with mean 68 mph and standard deviation 5 miles per hour.

Mean = \mu = 68 mph

Standard deviation = \sigma = 5 mph

A) X ~ N( _____, _______ )

In general X \sim N( \mu , \sigma^2)

\mu = 68 mph

\sigma = 5 mph

\sigma^2 = 5^2 = 25

So, X \sim N(68 , 25)

B) If one car is randomly chosen, find the probability that is traveling more than 70 mph.i.e.P(X>70)

So,Z = \frac{x-\mu}{\sigma}\\Z=\frac{70-68}{5}

Z=0.4

Using Z table

P(Z>70)=1-P(Z<70)=1-0.6554=0.3446

Hence the probability that is traveling more than 70 mph is 0.3446

C) If one of the cars is randomly chosen, find the probability that it is traveling between 65 and 75 mph.

P(65<X<75)

Z = \frac{x-\mu}{\sigma}

AT x = 65

Z=\frac{65-68}{5}

Z=-0.6

AT x = 75

Z=\frac{75-68}{5}

Z=1.4

Using Z table

P(65<X<75)=P(-0.6<Z<1.4)=P(Z<1.4)-P(Z<-0.6)=0.9192-0.2743=0.6449

Hence the probability that it is traveling between 65 and 75 mph is 0.6449

D)90% of all cars travel at least how fast on the freeway?

Since we are supposed to find at least how fast on the freeway

So,P(X>x)=0.9

1-P(X<x)=0.9

1-0.9=P(X<x)

0.1=P(X<x)

Z value at 10% =-2.23

So, Z=\frac{x-\mu}{\sigma}\\-2.23=\frac{x-68}{5}\\-2.23 \times 5 =x-68\\(-2.23 \times 5)+68=x

56.85 = x

Hence 90% of all cars travel at least 56.85 mph fast on the freeway

8 0
3 years ago
The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the o
Korvikt [17]

Answer:

a) k = 0.000124

b) According to these data, the Shroud of Turin has around 760 years.

Step-by-step explanation:

The amount of carbon-14 is modeled by the following equation:

C(t) = C_{0}e^{-kt}

In which C_{0} is the initial amount and k is the rate of decrease.

(a) Find the value of the constant k in the differential equation.

Half-life of 5595 years.

So C(5595) = 0.5C_{0}

C(t) = C_{0}e^{-kt}

0.5C_{0} = C_{0}e^{-5595k}

e^{-5595k} = 0.5

Applying ln to both sides

-5595k = -0.69

k = 0.000124

b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained about 91 percent of the amount of carbon-14 contained in freshly made cloth of the same material. How old is the Shroud of Turin, according to these data?

This is t when C(t) = 0.91C_{0}

C(t) = C_{0}e^{-kt}

0.91C_{0} = C_{0}e^{-0.000124t}

e^{-0.000124t} = 0.91

Applying ln to both sides

-0.000124t = -0.094

t = 760.57

According to these data, the Shroud of Turin has around 760 years.

8 0
4 years ago
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