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shusha [124]
3 years ago
5

"Bert has half as much money as Ernie. If Ernie loses $225 and Bert earns $675, Bert will have twice as much money as Ernie. How

much money do Bert and Ernie have before and after earning money
Mathematics
1 answer:
Rzqust [24]3 years ago
3 0

Answer: Ernie has $750 and Bert has \dfrac{750}{2}=\$375

Step-by-step explanation:

Let the amount that Ernie has be 'x'.

Let the amount that Bert has be \dfrac{x}{2}

Amount lost by Ernie = $225

Amount gained by Bert = $675

According to question, we get that

2(x-225)=\dfrac{x}{2}+675\\\\2x-450=\dfrac{x}{2}+675\\\\2x-\dfrac{x}{2}=675+450\\\\\dfrac{4x-x}{2}=1125\\\\\dfrac{3x}{2}=1125\\\\x=\dfrac{1125\times 2}{3}\\\\x=\$750

Hence, Ernie has $750 and Bert has \dfrac{750}{2}=\$375

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4 0
3 years ago
Based on information from Harper’s Index, 37% of adult Americans believe in Extraterrestrials. Out of a random sample of 100 adu
san4es73 [151]

Answer:

z(s)  is in the rejection zone , therefore we reject H₀

We have enough evidence to claim the proportion of individuals who attended college and believe in extraterrestrials is bigger than 37%

Step-by-step explanation:

We have a prortion test.

P₀  =  37 %         P₀  = 0,37

sample size  =  n  =  100

P sample proportion   =   P  = 47 %        P  =  0,47

confidence interval  95 %

α  =   0,05  

One tail-test  (right tail) our case is to show if sample give enough information to determine if proportion of individual who attended college is higher than the proportion found by Harper´s index.

1.-Hypothesis:

H₀      null hypothesis                        P₀  =  0,37

Hₐ  alternative hypothesis                P₀  >  0,37

2.-Confidence interval 95 %

α  =   0,05        and    z(c)  =  1.64

3.-Compute of z(s)

z(s)  =  [  P  -  P₀  ]  /√(P₀Q₀/n) ]  

z(s)  =  [ (  0,47  -  0,37  ) /  √0.37*0,63/100

z(s)  = 0,1 /√0,2331/100     ⇒   z(s)  = 0,1 /0,048

z(s)  = 2.08

4.-Compare  z(s)   and  z(c)

z(s) > z(c)        2.08  > 1.64

5.-Decision:

z(s)  is in the rejection zone , therefore we reject H₀

We have enough evidence to claim the proportion of individuals who attended college and believe in extraterrestrials is bigger than 37%

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2 years ago
In a circle of radius 10 cm, a sector has an area of 40 (pi) sq. cm. What is the degree measure of the arc of the sector?
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Answer:

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Step-by-step explanation:

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Plug in 10 as the radius, and solve

A = \pir²

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Using this, create a proportion that relates the area of the sector to the degree measure of the arc.

Let x represent the degree measure of the arc of the sector:

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Cross multiply and solve for x:

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                                              Hope this helps:)
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