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4 years ago

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A basket contained 75 brown eggs. 40% of them were used-up, and a third of them remaining were rotten and thrown out. What fract

ion of the initial number of brown eggs remained in the basket finally?

1 answer:

IceJOKER [234]4 years ago

6 0

Answer:

4/15

Step-by-step explanation:

40% is the same as .4.

.4 x 75 = 30

1/3 x 75 = 25

30 + 25 = 55

75 - 55 = 20

20 / 75

Simplify. Divide by 5.

4/15

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Mr. Huyck needs 8 gallons of punch for the school dance. How many<br> quarts of punch would he need?

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32 bc eight times four equals 32

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3 years ago

Read 2 more answers

A company surveyed 2400 men where 1248 of the men identified themselves as the primary grocery shopper in their household. a) E

polet [3.4K]

Answer:

a) With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

b) The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

c) $\alpha =1-0.98=0.02$

Step-by-step explanation:

If np' and n(1-p') are higher than 5, a confidence interval for the proportion is calculated as:

$p'-z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }\leq p\leq p'+z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }$

Where p' is the proportion of the sample, n is the size of the sample, p is the proportion of the population and $z_{\alpha/2}$ is the z-value that let a probability of $\alpha/2$ on the right tail.

Then, a 98% confidence interval for the percentage of all males who identify themselves as the primary grocery shopper can be calculated replacing p' by 0.52, n by 2400, $\alpha$ by 0.02 and $z_{\alpha/2}$ by 2.33

Where p' and $\alpha$ are calculated as:

$p' = \frac{1248}{2400}=0.52\\\alpha =1-0.98=0.02$

So, replacing the values we get:

$0.52-2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\leq p\leq 0.52+2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\\0.52-0.0238\leq p\leq 0.52+0.0238\\0.4962\leq p\leq 0.5438$

With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

Finally, the level of significance is the probability to reject the null hypothesis given that the null hypothesis is true. It is also the complement of the level of confidence. So, if we create a 98% confidence interval, the level of confidence $1-\alpha$ is equal to 98%

It means the the level of significance $\alpha$ is:

$\alpha =1-0.98=0.02$

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3 years ago

Find the x-intercept of the parabola of with vertex (1,20) and the y-intercept (0,16). write your answer in this form: (x1,y1),(

svetoff [14.1K]

I assume that the parabola in this particular problem is one whose axis of symmetry is parallel to the y axis. The formula we're going to use in this case is (x-h)2=4p(y-k). We know variables h and k from the vertex (1,20) but p is not given. However, we can solve for p by substituting values x and y in the formula with the y-intercept:

(0-1)^2=4p(16-20)

Solving for p, p=-1/16.

Going back to the formula, we can finally solve for the x-intercepts. Simply fill in variables p, h and k then set y to zero:

(x-1)^2=4(-1/16)(0-20)
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x-1=(+-)sqrt(5)
x=(+-)sqrt(5)+1

Here, we have two values of x

x=sqrt(5)+1 and
x=-sqrt(5)+1

thus, the answers are: (sqrt(5)+1,0) and (-sqrt(5)+1,0).

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4 years ago

A municipality has budgeted R80 000 for putting up new street name boards The street name boards cost R134 each. How many new st

ivanzaharov [21]

The Municipality we be able to set up 597 street name boards with R2 left in the budget.

Data;

Amount Budgeted = R80,000
Cost of each board = R134

<h3>Number of Street Boards in the Budget</h3>

The number of streets boards that can be produced in the budget is calculated by dividing the total amount budgeted by the cost of each street board. This is done mathematically as

$x = \frac{80000}{134}\\x = 597.01$

We would have a total of 597 street names on the budget with some amount left.

We can calculated this by multiplying 597 by 134 and then subtracting the value from R80,000

$597 * 134 = 79998 \\R80,000 - R79998 = R2$

The Municipality we be able to set up 597 street name boards with R2 left in the budget.

Learn more on division of numbers here;

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2 years ago

amirah ,who is at a point P ,observes a boat at pont B 1200m from P in direction 047 degrees. The boat is moving due north of B

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Answer:

about 2.81 km/h

Step-by-step explanation:

It can be useful to draw a diagram.

The lines pointing to due north from points B and P are parallel, so the angle BCP and the bearing of point C from P are the same, 30°. The angle BPC will be the difference of bearings of B and C at P, so is 47-30=17°. This is enough information to solve the triangle using the Law of Sines:

PB/sin(C) = CB/sin(P)

CB = PB·sin(P)/sin(C) = (1200 m)·sin(17°)/sin(30°) ≈ 701.7 m

The speed of the boat is then ...

x = distance/time = (0.7017 km)/(1/4 h) = 2.8068 km/h

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3 years ago