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ivanzaharov [21]
3 years ago
10

Find each rate in 40 meters in 16 sec

Mathematics
1 answer:
lara31 [8.8K]3 years ago
4 0
<span> Rate = 40/16 = 10/4 = 5/2 = 2.5 meters/second Unit rate = ratio where denominator is 1 = 2.5/1 meters/second </span>
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Dylan opened a credit card account with $750.00 of available credit. Now that he has made some purchases, Dylan's account only h
barxatty [35]

Answer:

45%

Step-by-step explanation:

The formula to work out the decrease is:

Percentage Decrease= actual decrease / original amount X 100%

1) So firstly, we have to work out the decrease, to do this we have to do is do $750-$412.50= $337.50

2) We can now substitute this into our formula which will now be. (We will also add the original amount, which is $750.00)

Percentage Decrease= 337.50 / 750.00 X 100% = 45

The percentage decrease is 45%

8 0
2 years ago
Which expression is a fourth root of -1+isqrt3?
aleksklad [387]

Answer:

Step-by-step explanation:

\sf n^{th} roots of a complex number is given by DeMoivre's formula.

   \sf \boxed{\bf r^{\frac{1}{n}}\left[Cos \dfrac{\theta + 2\pi k}{n}+i \ Sin \ \dfrac{\theta+2\pi k}{n}\right]}

Here, k lies between 0 and (n -1) ; n is the exponent.

\sf -1 + i\sqrt{3}

a = -1 and b = √3

\sf \boxed{r=\sqrt{a^2+b^2}} \ and \ \boxed{\theta = Tan^{-1} \ \dfrac{b}{a}}

\sf r = \sqrt{(-1)^2 + 3^2}\\\\ = \sqrt{1+9}\\\\=\sqrt{10}

                   \sf \theta = tan^{-1} \ \dfrac{\sqrt{3}}{-1}\\\\ = tan^{-1} \ (-\sqrt{3})

                   \sf = \dfrac{-\pi }{3}

n = 4

For k = 0,

          \sf z = \sqrt[4]{10}\left[Cos \ \dfrac{\dfrac{-\pi}{3} +0}{4}+iSin  \ \dfrac{\dfrac{-\pi}{3}+0}{4}\right] \\\\\\z= \sqrt[4]{10} \left[Cos \ \dfrac{ -\pi  }{12}+iSin  \ \dfrac{-\pi}{12}\right]\\\\\\z = \sqrt[4]{10}\left[-Cos \ \dfrac{\pi}{12}-i \ Sin \ \dfrac{\pi}{12}\right]

For k =1,

         \sf z = \sqrt[4]{10}\left[Cos \ \dfrac{5\pi}{12}+i \ Sin \ \dfrac{5\pi}{12}\right]

For k =2,

       z = \sqrt[4]{10}\left[Cos \ \dfrac{11\pi}{12}+i \ Sin \ \dfrac{11\pi}{12}\right]

For k = 3,

      \sf z = \sqrt[4]{10}\left[Cos \ \dfrac{17\pi}{12}+i \ Sin \ \dfrac{17\pi}{12}\right]

For k = 4,

      \sf z =\sqrt[4]{10}\left[Cos \ \dfrac{23\pi}{12}+i \ Sin \ \dfrac{23\pi}{12}\right]

4 0
1 year ago
In a recent survey, 10 percent of the participants rated Pepsi as being "concerned with my health." PepsiCo's response included
hichkok12 [17]

Answer:

The statistic for this case would be given by:

z=\frac{0.18 -0.1}{\sqrt{\frac{0.1(1-0.1)}{100}}}=2.67  

Step-by-step explanation:

Infromation provided

n=100 represent the random sample selected

X=18 represent the people who rates Pepsi as being "concerned with my health"

\hat p=\frac{18}{100}=0.18 estimated proportion of people who rates Pepsi as being "concerned with my health"

p_o=0.1 is the value that reference to compare

z would represent the statistic

Hypothesis to test

For this case we can assume that the interest is check if the proportion of people who rates Pepsi as being "concerned with my health" is equal to 0.1 or not , then the system of hypothesis are:

Null hypothesis:p=0.1  

Alternative hypothesis:p \neq 0.1  

The satistic for this one sample proportion test is given by:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Replacing the info given we got:

z=\frac{0.18 -0.1}{\sqrt{\frac{0.1(1-0.1)}{100}}}=2.67  

7 0
2 years ago
Kelly earns $23.00 for 4 hours of work. At that rate, how long would she have to work to earn $57.50?
ankoles [38]

Answer:

10 hours

Step-by-step explanation:

5.75x 10= 57.50

8 0
2 years ago
Which expression is equivalent to (see attachment)
Kobotan [32]

Answer:

  see below

Step-by-step explanation:

8 can be factored from each of the terms of the sum. (It's the distributive property.)

  8·0 + 8·1 + 8·2 + ... + 8·26 + 8·27

  = 8·(0 +1 +2 + ... +26 +27)

8 0
2 years ago
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