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3 years ago

A bowl of grapes has a total mass of 265g. The bowl has a mass of 121g. What is the mass of the grapes?

Mathematics

1 answer:

stealth61 [152]3 years ago

8 0

Answer:

144g

Step-by-step explanation:

You know that the bowl itself has a mass of 121g. If you take that number away from the total amount, you will be left with only the mass of the grapes.

265g - 121g = 144g

I hope this helps!

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A researcher wants to estimate the percentage of all adults that have used the Internet to seek pre-purchase information in the

lara31 [8.8K]

Answer:

The sample size is 1875.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

Sampling error of 0.03.

This means that $M = 0.03$

99.74% confidence level

So $\alpha = 0.0026$ , z is the value of Z that has a pvalue of $1 - \frac{0.0026}{2} = 0.9987$ , so $Z = 3$ .

25% of all adults had used the Internet for such a purpose

This means that $\pi = 0.25$

What is the sample size

The sample size is n. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 3\sqrt{\frac{0.25*0.75}{n}}$

$0.03\sqrt{n} = 3\sqrt{0.25*0.75}$

Simplifying by 0.03 both sides

$\sqrt{n} = 100\sqrt{0.25*0.75}$

$(\sqrt{n})^2 = (100\sqrt{0.25*0.75})^2$

$n = 1875$

The sample size is 1875.

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Step-by-step explanation:

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2 years ago

Find the equation for the circle with a diameter whose endpoints are (3,-1) and (-2,-1)

cricket20 [7]

Answer:

The equation for the circle is: $(x-\frac{1}{2} )^2 + y^2 = (\frac{5}{2} )^2$

Step-by-step explanation:

Here, let us assume the two end points of the diameter are:

P (3,-1) and Q (-2,-1)

Now, as we knew diameter is the chord that passer through the center of the circle.

⇒ Mid point of DIAMETER = Center coordinates of the Circle

Let us assume O(x,y) is the center of the line segment PQ.

So, by MID POINT FORMULA:

$(x,y)= (\frac{3 -2}{2} , \frac{-1-1}{2} ) =( \frac{1}{2},\frac{-2}{2}) \\\implies (x,y) =( 0.5 , -1)$

⇒ The center coordinates of the circle = O(0.5,-1) ...... (1)

Now, RADIUS = Half of DIAMETER

Using DISTANCE FORMULA:

$PQ = \sqrt{(3-(-2))^2 + (-1 - (-1))^2} = \sqrt{(5)^2 + 0} = 5$

So, Radius = 5/2 = 2.5 units

Now, the equation of circle with radius r and center coordinate ( h,k) is given as: $(x-h)^2 + (y-k)^2 = r^2$

Substitute r = 2.5 and (h,k) = (0.5,0) we get:

$(x-0.5)^2 + (y-0)^2 = (2.5)^2\\\implies (x-\frac{1}{2} )^2 + y^2 = (\frac{5}{2} )^2$

Hence the equation for the circle is: $(x-\frac{1}{2} )^2 + y^2 = (\frac{5}{2} )^2$

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4 years ago