Steve can complete the 100m dash in 10 seconds while Paul can run it in 12 seconds. How does Steve's time compare to Paul's?A. Steve is 5∕6 as fast as Paul
B. Steve is 5∕6 slower than Paul
C. Steve is 1∕2 as fast as Paul
D. Steve is 1∕2 slower than Paul

a survey in which 400 people were asked to identify the TV channel on which they preferred to watch the evening news.

How many more people preferred WWCN with 41% than WANR with 22%?
A. 164
B. 76
C. 236
D. 68

Answers

Answer 1

Answer: So, Steve's time in a ratio to Paul's time:

$(Steven's time)/(Pauls's time) = (10)/(12) = (5)/(6) .$ So Steven's time is $(5)/(6)$ times shorter, that is
"Steven is $(5)/(6)$ times faster than Paul (I find the phrasing "as fast as" problematic though)

In the second question 41% of 400, which is 4*41=164 people chose WWCN and 22% chose WANR, that is 22%*400=4*22=88.

And the difference is 76 people! ( 164-88=76)B)

Answer 2

Answer:

Answer:

Q-1 The correct option is A) Steve is 5∕6 as fast as Paul

Q-2 The correct option is 76.

Step-by-step explanation:

Consider the provided information.

Q-1

Steve can complete the 100m dash in 10 seconds while Paul can run it in 12 seconds.

Since, the distance for both are same,

$\frac{\text{Steve's time}}{\text{Paul's time}}=(10)/(12)=(5)/(6)\n\text{Steve's time}=(5)/(6)\text{ of Paul's time}}$

Hence, Steve's time is 5⁄6 of the time taken by Paul.

Therefore, the correct option is A) Steve is 5∕6 as fast as Paul

Q-2 a survey in which 400 people were asked to identify the TV channel on which they preferred to watch the evening news.

WWCN got 41% and WANR got 22%

For WWCN

41% of 400 is: $(41)/(100) * 400=164$

That means 164 people preferred WWCN.

For WANR

22% of 400 is: $(22)/(100) * 400=88$

That means 88 people preferred WANR.

We need to find how many more people preferred WWCN

For this subtract both the values: 164-88=76

Thus, 76 more people preferred WWCN

Hence, the correct option is 76.

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Rewrite each expression by completing the square.
a. z^2 − 5z + 8
b. x^2 + 0.6x + 1

Answers

Answer:

The answer to your question is below

Step-by-step explanation:

z² - 5z + 8

Equal to zero z² - 5z + 8 = 0

Subtract 8 in both sides z² - 5z + 8 - 8 = 0 - 8

Simplify z² - 5z = -8

Divide -5 by 2 write the result

in both sides of the equation z² - 5z + (-5/2)² = -8 + (-5/2)²

to the power of 2

Simplify z² - 5z + 25/4 = -8 + 25/4

z² - 5z + 25/4 = -32/4 + 25/4

z² - 5z + 25/4 = -7/4

Factor (z - 5/2)² = -7/4

x² - 0.6x + 1

Convert 0.6 to a fraction 0.6 = 6/10 = 3/5

x² - 3/5x + 1

Equal to zero x² - 3/5x + 1 = 0

Subtract -1 in both sides z² - 3/5z + 1 - 1 = 0 - 1

Simplify z² - 3/5z = - 1

Divide -3/5 by 2 write the result

in both sides of the equation z² - 3/5z + (-3/10)² = -1 + (-3/10)²

to the power of 2

Simplify z² - 3/5z + 9/100 = -1 + 9/100

z² - 3/5z + 9/100 = -100/100 + 9/100

z² - 3/5z + 9/100 = -91/100

Factor (z - 3/10)² = -91/100

Given the definition of rational numbers, are decimals like 0.5 and 0.3 rational numbers? Why or why not?

Answers

Givendecimals like 0.5 and 0.3 are rational numbers because they are terminating decimals and can be written as p/q

What are rational numbers?

Rational numbers are numbers which can be written in the form p/q , where p and q are integers ,q≠0, highest common factor of p and q is 1.

The decimal expansion of rational number are terminating decimal expansion or non terminating and recurring decimal expansions.

Examples of rational number: 1/2 , 3/4, 13/2, 0.125,0.5, 0.55555....,

0.1212121212.....

As the given decimals 0.5 and 0.3 have terminatingdecimal expansion therefore they are rational numbers.

The rational form of 0.5 and 0.3 are

0.5 = 5/10 = 1/2

∴ 0.5 is written as p/q with p= 1 and q =2≠0 , p and q are coprime

0.3 = 3/10

∴ 0.3 is written as p/q with p= 3 and q =10≠0 , p and q are coprime

Therefore, 0.5 and 0.3 are rational numbers.

Also, Learn more about rational numbers from the link below:

brainly.com/question/24398433

#SPJ2

Answer:

Yes they are rational numbers

Step-by-step explanation:

Use Pascal's triangle or the Binomial theorem to expand the binomials. 1. (3c-2d)^4
2. (2n+3)^5
3. (x^2+4)^3

Answers

$(3c-2d)^4=(3c)^4-4(3c)^3\cdot2d+6\cdot(3c)^2\cdot(2d)^2-4\cdot3c\cdot(2d)^3-(2d)^4\n\n=81c^4-216c^3d+216c^2d^2-96cd^3-16d^4\n-------------------------------\n(2n+3)^2\n=(2n)^5+5(2n)^4\cdot3+10(2n)^3\cdot3^2+10(2n)^2\cdot3^3+5\cdot2n\cdot3^4+3^5\n\n=32n^5+240n^4+720n^3+1080n^2+810n+243\n-------------------------------\n(x^2+4)^3=(x^2)^3+3(x^2)^2\cdot4+3x^2\cdot4^2+4^3\n\n=x^6+12x^4+48x^2+64$

What is the least common multiple (LCM) of 4 and 10?

Answers

Well, 4•1=4 4•2=8 and so on so 4•5=20. 20 is divisible by 10 (10•2=20) therefore 20 is the least common mutiple

Planck's constant is best described as which of the following?a. a very large positive number
b. a very small positive number
c. a very large negative number
d. a very small negative number

Answers

b is the answer i believe

Solutions

We know that the Planck constant is defined by the equation: E = h\nu. I believe the correct answer is (B)

(B) = a very small positive number

Triangle ABC is going to be reflected over the line y = X.If A is located at (1,-7), where will A' be located?

Answers

Answer:

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Step-by-step explanation:

Coordinate rules :]

Reflection over x-axis -- (x, y) -> (x, -y)

Reflection over y-axis -- (x, y) -> (-x, y)

Reflection over y = x -- (x, y) -> (y, x)

Reflection over y = -x -- (x, y) -> (-y, -x)

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