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antoniya [11.8K]
2 years ago
6

Find the LCM of 18 and 45 using prime factorizations. ​

Mathematics
2 answers:
Otrada [13]2 years ago
8 0

Answer:

90

Step-by-step explanation:

18/3

6/3

2/3

45/3

15/3

5/3

Take 5/3 and 2/3

5*3*2*3

90

Valentin [98]2 years ago
4 0

Answer:

The L.C.M. of 18 and 45 is 90.

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Ji-Hun and Kana are running a marathon. Due to the volume of people running, the starts occur in waves. Kana starts at 9:35 a.m.
iris [78.8K]

Answer:

23.52 miles

Step-by-step explanation:

Let us find the number of miles that they would have run.

Kana starts at 9:35 a.m. and runs at an average rate of 7 mph.

Let the time she has spent so far be t.

Speed is given as:

s = d / t

where d = distance and t = time

=> d = s * t

Therefore, for Kana:

d = 7 * t = 7t _____________(1)

Ji-Hun starts at 10:00 am (25 minutes after Hannah) and runs at an average rate of 8 mph.

25 minutes = 25/60 hour = 0.42 hour

So, his time (compared to Kana's) is t - 0.42.

therefore, for Ji-Hun:

d = 8 * (t - 0.42)

=> d = 8t - 3.36 ____________(2)

Equating (1) and (2):

7t = 8t - 3.36

=> 8t - 7t = 3.36

t = 3.36 hours

Therefore, let us find d:

d = 7 * 3.36 = 23.52 miles

So, Ji-Hun will catch up to Kana after 23.52 miles.

6 0
3 years ago
Below are the rates of travel of 4 shipping trucks. Which truck drove the fastest rate? Truck A: 300 miles in 4 hours Truck B: 2
Tasya [4]

Answer:

Truck D.

Step-by-step explanation:

Below are the rates of travel of 4 shipping trucks.

Truck A: 300 miles in 4 hours Truck B: 240 miles in 3 hours Truck C: 325 miles in 5 hours Truck D: 170 miles in 2 hours.

Speed = distance/time

Speed of Truck A,

v_A=\dfrac{300}{4}\\\\v_A=75\ mph

Speed of Truck B,

v_B=\dfrac{240}{3}\\\\v_B=80\ mph

Speed of Truck C,

v_C=\dfrac{325}{5}\\\\v_C=65\ mph

Speed of Truck D,

v_D=\dfrac{170}{2}\\\\v_D=85\ mph

It can be seen that the speed of Truck D is more out of Trucks A,B and C. Hence, Truck D is moving at a faster rate.

8 0
2 years ago
Please answer question in picture below
Sonja [21]
9×7=63
63÷2=31.5
31.5×4=126

7×7=49

126+49=175

175 is the answer
8 0
2 years ago
For the given hypothesis test, determine the probability of a Type II error or the power, as specified. A hypothesis test is to
erica [24]

Answer:

the probability of a Type II error if in fact the mean waiting time u, is 9.8 minutes is 0.1251

Option A) is the correct answer.

Step-by-step explanation:

Given the data in the question;

we know that a type 11 error occur when a null hypothesis is false and we fail to reject it.

as in it in the question;

obtained mean is 9.8 which is obviously not equal to 8.3

But still we fail to reject the null hypothesis says mean is 8.3

Hence we have to find the probability of type 11 error

given that; it is right tailed and o.5, it corresponds to 1.645

so

z is equal to 1.645

z = (x-μ)/\frac{S}{\sqrt{n} }

where our standard deviation s = 3.8

sample size n = 50

mean μ = 8.3

we substitute

1.645 = (x - 8.3)/\frac{3.8}{\sqrt{50} }

1.645 = (x - 8.3) / 0.5374

0.884023 = x - 8.3

x = 0.884023 + 8.3

x = 9.18402

so, by general rule we will fail to reject the null hypothesis when we will get the z value less than 1.645

As we reject the null hypothesis for right tailed test when the obtained test statistics is greater than the critical value

so, we will fail to reject the null hypothesis as long as we get the sample mean less than 9.18402

Now, for mean 9.8 and standard deviation 3.8 and sample size 50

Z =  (9.18402 - 9.8)/\frac{3.8}{\sqrt{50} }

Z = -0.61598 / 0.5374

Z = - 1.1462 ≈ - 1.15

from the z-score table;

P(z<-1.15) = 0.1251

Therefore, the probability of a Type II error if in fact the mean waiting time u, is 9.8 minutes is 0.1251

Option A) is the correct answer.

8 0
2 years ago
Please answer all of above worth 32 points !!
schepotkina [342]

Answer: A. 35+1

B. 20+ 5z

C. 4 + 12

Step-by-step explanation:

This is just using the distributive property which is like foiling

7 0
3 years ago
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