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marishachu [46]
3 years ago
11

Answer these 2 questions please

Mathematics
1 answer:
Whitepunk [10]3 years ago
8 0

Hi there!

Question 1:

For this, we are taking away 1/4 yards of spring from 7/8 yards. This is essentially just subtracting 1/4 from 7/8. This then gives us the equation:

\frac{7}{8}-\frac{1}{4}

Now, to subtract these, we want to make it so the denominators are the same, or the numbers on the lower half are the same. (One way to explain why this is true is: \frac{a}{b}-\frac{c}{b}=a\frac{1}{b}-c\frac{1}{b}=(a-c)\frac{1}{b}=\frac{a-c}{b}). Now, to make it so the denominators are the same, we can multiply the second fraction, 1/4, by 2/2 as 2/2 is essentially 1, and multiplying by 1 will get the same result, just with a denominator switched in this case. Doing this, we get:

\frac{7}{8}-\frac{1}{4}\cdot\frac{2}{2}

\frac{7}{8}-\frac{2}{8}

Now, subtracting the numerators, we get:

\frac{5}{8} yards of string will remain.

Question 2:

For this, we are combining these two thicknesses, and thus we add 1/4 to 7/12. This gives us the equation:

\frac{1}{4}+\frac{7}{12}

Now, we again want to make it so the denominators are the same. (Here's a similar proof but for addition this time: \frac{a}{b}+\frac{c}{b}=a\frac{1}{b}+c\frac{1}{b}=(a+c)\frac{1}{b}=\frac{a+c}{b}). Now, to make the denominators the same, we can multiply the first fraction, 1/4, by 3/3 (also equivalent to 1). Doing this, we get:

\frac{1}{4}\cdot\frac{3}{3}+\frac{7}{12}

\frac{3}{12}+\frac{7}{12}

\frac{10}{12}, which is equivalent to (dividing both the top and the bottom by 2) \frac{5}{6} inches.

Hope this helps!

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Is 4.5 natural number?​
vfiekz [6]

Answer:

No

Step-by-step explanation:

4.5 IS NOT A WHOLE NUMBER!

4 0
3 years ago
Read 2 more answers
I have 10 goats, n of which are male. I need to choose 2 of them to make a casserole.
snow_tiger [21]

Answer: There are 4 male goats.

Step-by-step explanation:

We know that n of the 10 goats are male.

The probability that in a random selection, the selected goat is a male, is equal to the quotient between the number of male goats (n) and the total number of goats (10)

The probability is;

p = n/10

Now the total number of goats is 9, and the number of male goats is n -1

then the probability of selecting a male goat again is:

q = (n-1)/9

The joint probability (the probability that the two selected goats are male) is equal to the product of the individual probabilities, this is

P = p*q = (n/10)*((n-1)/9)

And we know that this probability is equal to 2/15

Then we have:

(n/10)*((n-1)/9) = 2/15

(n*(n-1))/90 = 2/15

n*(n-1) = 90*2/15 = 12

n^2 - n = 12

n^2 - n - 12  = 0

This is a quadratic equation, we can find the solutions if we use Bhaskara's formula:

For an equation:

a*x^2  + b*x + c =  0

The two solutions are given by:

x = \frac{-b +- \sqrt{b^2 - 4*a*c} }{2*a}

For our case, the solutions will be:

n = \frac{1 +- \sqrt{(-1)^2 - 4*1*(-12)} }{2*1 } = \frac{1+- 7}{2}

The two solutions are:

n = (1 - 7)/2 = -3    (this solution does not make sense, we can not have a negative number of goats)

The other solution is:

n = (1 + 7)/2 = 4

This solution does make sense, this means that we have 4 male goats.

5 0
2 years ago
Please answer this question now
soldier1979 [14.2K]

Answer:

6 km

Step-by-step explanation:

You use Pythagoras

{QN}^2 = (PN)^{2}+(PQ)^{2} \\PQ = \sqrt{(QN)^{2}-(PN)^{2}  }\\ PQ = 6 km

7 0
3 years ago
Please help me solve this equation
elena-s [515]

Answer:

m<U = 38degrees

Step-by-step explanation:

From the given diagram, <B = <U since both triangles are similar, hence;

Hence;

2y+2 = 3y-16

2y - 3y = -16 - 2

-y = -18

y = 18

Get m<U

m<U = 3y-16

m<U = 3(18) -16

m<U = 54 - 16

m<U = 38degrees

3 0
2 years ago
What is the volume of the figure?
Fynjy0 [20]
Volume of Cylinder

V = \pi r^2 h

V = \pi \times (11~yd)^2 \times 9~yd

V = 1089 \pi~yd^3

V = 3421~yd^3
3 0
3 years ago
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