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Doss [256]
2 years ago
14

Charlotte is running at a rate of 9\,\dfrac{\text{km}}{\text{h}}9 h km ​ 9, start fraction, start text, k, m, end text, divided

by, start text, h, end text, end fraction. What is Charlotte's speed in \dfrac{\text{m}}{\text{s}} s m ​ start fraction, start text, m, end text, divided by, start text, s, end text, end fraction?
Mathematics
1 answer:
OverLord2011 [107]2 years ago
5 0

Answer:

2.5 meters per second

Step-by-step explanation:

Given,

The speed of Charlotte = 9 km/h

That is, the distance covered in 1 hour = 9 km,

∵ 1 km = 1000 m

So, the distance covered in 1 hour = 9000 m,

∵ 1 hour = 60 minutes and 1 minute = 60 seconds,

⇒ 1 hours = 3600 seconds,

∴ The distance covered in 3600 seconds = 9000 m,

⇒ Distance covered in 1 second = \frac{9000}{3600} = 2.5 m,

Hence, his/her speed = 2.5 meters per second

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X - the number of sandwiches ordered
y - the number of soups ordered

There were 18 people, and each person ordered either one soup or one sandwich.
x+y=18

The sandwiches cost $7.75 each, the soups cost $4.50 each. The total cost was $113.50.
7.75x+4.5y=113.5

Set up a system of equations:
x+y=18 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\times (-4.5) \\
7.75x+4.5y=113.5 \\ \\
-4.5x-4.5y=-81 \\
\underline{7.75x+4.5y=113.5} \\
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10 sandwiches were ordered.
The answer is D.
4 0
2 years ago
Factor the algebraic expression below in terms of a single trigonometric function. csc 2x - 1
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(csc(x) + 1)(csc(x) -1)
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2 years ago
a(0.3−y)+1.1+2.4x (y−1.2) ​ =0 =−1.2(x−0.5) ​ Consider the system of equations above, where aaa is a constant. For which value o
Veseljchak [2.6K]

Answer:

For a = 1.22 there is one solution where y = 1.3

Step-by-step explanation:

Hi there!

Let´s write the system of equations:

a(0.3 - y) + 1.1 +2.4x(y-1.2) = 0

-1.2(x-0.5) = 0

Let´s solve the second equation for x:

-1.2(x-0.5) = 0

x- 0.5 = 0

x = 0.5

Now let´s repalce x = 0.5 and y = 1.3 in the first equation and solve it for a:

a(0.3 - y) + 1.1 +2.4x(y-1.2) = 0

a(0.3 - 1.3) + 1.1 + 2.4(0.5)(1.3 -1.2) = 0

a(-1) + 1.1 + 1.2(0.1) = 0

-a + 1.22 = 0

-a = -1.22

a = 1.22

Let´s check the solution and solve the system of equations with a = 1.22. Let´s solve the first equation for y:

1.22(0.3 - y) + 1.1 +2.4(0.5)(y-1.2) = 0

0.366 - 1.22y + 1.1 + 1.2 y - 1.44 = 0

-0.02y +0.026 = 0

-0.02y = -0.026

y = -0.026 / -0.02

y = 1.3

Then, the answer is correct.

Have a nice day!

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2 years ago
8.1.3 A random sample has been taken from a normal distribution and the following confidence intervals constructed using the sam
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Answer:

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Step-by-step explanation:

a) Upper and lower values for the confidence intervals are at the same distance from the mean, as they represent an upper and lower limit for the value, and the most probable value is the one in the middle, which, in a normal distribution is the mean.

As they derive from the same data, both pairs of values should give us the same mean:

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b) The percentage of the confidence interval tells us which is the area below the bell curve (of the normal distribution) between the limits given.

One could give a value with a 100% CI, but limits should be minus and plus infinity, and as the interval gets smaller, less values are covered (less area), and less certain we are about our value being inside the interval.

Then, we can say that the widest interval must be the 95% CI, i.e. (38.02, 61.98).

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