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Mrrafil [7]
2 years ago
13

="absmiddle" class="latex-formula">
Mathematics
1 answer:
inn [45]2 years ago
5 0

Step-by-step explanation:

({ \sqrt{x} }^{2})  = 16 \\  \sqrt{x } =  \sqrt{16}   \\  \\ sqrt \: root  \: will \: be \: cancelled \\ so \:  \\ x \: \:  = 16

You might be interested in
An Eastbound train (E) traveling 95 mph and a Westbound train (W) traveling 110 mph leave the same train station at different ti
Simora [160]

Answer:

The system of linear equations that can be used to determine the time that each of the trains has been traveling is:

E + W = 4 ....... Equation 1

95 E + 110W = 400  ......Equation 2

Hence,

An Eastbound train has been travelling for =  (E) = 2.67 hours

A Westbound train has been travelling for =  (W) = 1.33 hours

Step-by-step explanation:

An Eastbound train (E) traveling 95 mph and a Westbound train (W) traveling 110 mph leave the same train station at different times. After 4 hours, they are 4 00 miles apart. Which system of linear equations can be used to determine the time that each of the trains has been traveling?

Speed = Distance/Time

Distance = Speed × Time

Let the time

An Eastbound train =  (E)

A Westbound train =  (W)

E + W = 4 hours ....... Equation 1

95mph × E + 110mph × W = 400 miles

95 E + 110W = 400 miles ......Equation 2

The system of linear equations that can be used to determine the time that each of the trains has been traveling is:

E + W = 4 ....... Equation 1

95 E + 110W = 400  ......Equation 2

E = 4 - W

We substitute 4 - W for E in Equation 2

95 (4 - W) + 110W = 400  

380 - 95W + 110W = 400

Collect like terms

95W - 110W = 400 - 380

15W = 20

W = 20/15

W = 1.3333333333 hours

≈ 1.33 hours

E = 4 - W

E = 4 - 1.33 hours

E = 2.67 hours

Therefore,

An Eastbound train has been travelling for =  (E) = 2.67 hours

A Westbound train has been travelling for =  (W) = 1.33 hours

8 0
3 years ago
Suppose we have three urns, namely, A B and C. A has 3 black balls and 7 white balls. B has 7 black balls and 13 white balls. C
professor190 [17]

Answer:

a. 11/25

b. 11/25

Step-by-step explanation:

We proceed as follows;

From the question, we have the following information;

Three urns A, B and C contains ( 3 black balls 7 white balls), (7 black balls and 13 white balls) and (12 black balls and 8 white balls) respectively.

Now,

Since events of choosing urn A, B and C are denoted by Ai , i=1, 2, 3

Then , P(A1 + P(A2) +P(A3) =1 ....(1)

And P(A1):P(A2):P(A3) = 1: 2: 2 (given) ....(2)

Let P(A1) = x, then using equation (2)

P(A2) = 2x and P(A3) = 2x

(from the ratio given in the question)

Substituting these values in equation (1), we get

x+ 2x + 2x =1

Or 5x =1

Or x =1/5

So, P(A1) =x =1/5 , ....(3)

P(A2) = 2x= 2/5 and ....(4)

P(A3) = 2x= 2/5 ...(5)

Also urns A, B and C has total balls = 10, 20 , 20 respectively.

Now, if we choose one urn and then pick up 2 balls randomly then;

(a) Probability that the first ball is black

=P(A1)×P(Back ball from urn A) +P(A2)×P(Black ball from urn B) + P(A3)×P(Black ball from urn C)

= (1/5)×(3/10) + (2/5)×(7/20) + (2/5)×(12/20)

= (3/50) + (7/50) + (12/50)

=22/50

=11/25

(b) The Probability that the first ball is black given that the second ball is white is same as the probability that first ball is black (11/25). This is because the event of picking of first ball is independent of the event of picking of second ball.

Although the event picking of the second ball is dependent on the event of picking the first ball.

Hence, probability that the first ball is black given that the second ball is white is 11/25

​​

8 0
2 years ago
Which of the following is not a Pythagorean triple?. . A.. 28, 45, 53. B.. 16, 63, 65. C.. 13, 84, 85. D.. 11, 61, 62.
Anna11 [10]
A set of numbers is said to be Pythagorean triple if the sum of the squares of the lesser numbers equal the square of the remaining number,

A. 28² + 45² = 2809    ;  53² = 2809     ; EQUAL
B. 16² + 63² = 4225    ;  65²= 4225      ; EQUAL
C. 13² + 84² = 7225    ;  85² = 7225     ; EQUAL
D. 11² + 61² = 3842    ;   62² = 3844     ; NOT EQUAL

The answer is letter D.
6 0
2 years ago
Read 2 more answers
Michmoo Computer Company sells computers and computer parts by mail. The company assures its customers that products are mailed
Anastaziya [24]

Answer: (60.858, 69.142)

Step-by-step explanation:

The formula to find the confidence interval for mean :

\overline{x}\pm z_c\dfrac{\sigma}{\sqrt{n}} , where \overline{x} is the sample mean , \sigma is the population standard deviation , n is the sample size and z_c is the two-tailed test value for z.

Let x represents the time taken to mail products for all orders received at the office of this company.

As per given , we have

Confidence level : 95%

n= 62

sample mean : \overline{x}=65 hours

Population standard deviation : \sigma=18 hours

z-value for 93% confidence interval: z_c=1.8119  [using z-value table]

Now, 93% confidence the mean time taken to mail products for all orders received at the office of this company :-

65\pm (1.8119)\dfrac{18}{\sqrt{62}}\\\\ 65\pm4.142\\\\=(65-4.142,\ 65+4.142)\\\\= (60.858,\ 69.142)

Thus , 93% confidence the mean time taken to mail products for all orders received at the office of this company : (60.858, 69.142)

8 0
3 years ago
The eagles had a record of 16 wins and 12 loses. What was the ratio of wins to losses?
nata0808 [166]

Answer:

16/12  or 4/3

Math

6 0
2 years ago
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