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2 years ago

In the library at Lenape Elementary School, there are

Mathematics

1 answer:

ValentinkaMS [17]2 years ago

5 0

Question:

In the library at Lenape Elementary School, there are 3/8 as many fiction books as there are nonfiction books. There are 44 books in the school library. How many books are fiction books?

Answer:

There are 12 fiction books in library

Solution:

Let "x" be the number of non fiction books

Then given that,

There are 3/8 as many fiction books as there are nonfiction books

$Fiction\ books = \frac{3}{8}x$

There are 44 books in the school library

Therefore,

Non fiction books + fiction books = 44

$x + \frac{3x}{8} = 44\\\\\8x + 3x = 44 \times 8\\\\11x = 44 \times 8\\\\x = 4 \times 8\\\\x = 32$

How many books are fiction books?

$Fiction\ books = \frac{3}{8}x = \frac{3 \times 32 }{8} = 12$

Thus there are 12 fiction books in library

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Two tangents drawn to a circle from a point outside it, are equal in length.prove it.

stiks02 [169]

Given: A circle with centre O; PA and PB are two tangents to the circle drawn from an external point P.
To prove: PA = PB
Construction: Join OA, OB, and OP.
It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact.
OA⊥PA
OB⊥PB
In △OPA and △OPB
∠OPA=∠OPB (Using (1))
OA=OB (Radii of the same circle)
OP=OP (Common side)
Therefor △OPA≅△OPB (RHS congruency criterion)
PA=PB
(Corresponding parts of congruent triangles are equal)
Thus, it is proved that the lengths of the two tangents drawn from an external point to a circle are equal.
The length of tangents drawn from any external point are equal.
So statement is correct

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1 year ago

A painter is painting a wall with an area of 150 ft2. He decides to paint half of the wall and then take a break. After his brea

fgiga [73]

First break= 1/2
second break = 1/2 of half= 1/4
third break = half of 1/4 = 1/8
forth break = 1/2 of 1/8 = 1/16
fifth break = 1/2 of 1/16 =1/32
fraction painted = 1 -1/32 =31/32
portion painted = 150*31/32 = 145.3125 ft^2

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2 years ago

A botanist collected one leaf at random from each of 10 randomly selected mature maple trees of the same species. The mean and t

Zarrin [17]

Answer:

One sample t-test for population mean would be the most appropriate method.

Step-by-step explanation:

Following is the data which botanist collected and can use:

Sample mean
Sample Standard Deviation
Sample size (Which is 10)
Distribution is normal

We have to find the best approach to construct the confidence interval for one-sample population mean. Two tests are used for constructing the confidence interval for one-sample population mean. These are:

One-sample z test for population mean
One-sample t test for population mean

One sample z test is used when the distribution is normal and the population standard deviation is known to us. One sample t test is used when the distribution is normal, population standard deviation is unknown and sample standard deviation is known.

Considering the data botanist collected, One-sample t test would be the most appropriate method as we have all the required data for this test. Using any other test will result in flawed intervals and hence flawed conclusions.

Therefore, One-sample t-test for population mean would be the most appropriate method.

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2 years ago

Dwayne buys ingredients to make a cake. He buys 112 pounds of flour, 12 ounces of coconut, and 114 pounds of sugar. What is the

Anastaziya [24]

Answer:

The only correct options are A, B and E.

Step-by-step explanation:

He buys $1\frac{1}{2}$ pounds of flour, 12 ounces of coconut, and $1\frac{1}{4}$ pounds of sugar.

We will add these together, but before that, we convert the 12 ounces to pounds, so that all the units are the same:

1 ounce = 0.0625 pounds

12 ounces = 12 * 0.0625 = $\frac{3}{4}$ pounds

He buys $\frac{3}{4}$ pounds of coconut.

Adding all of them together yields:

$1\frac{1}{2}$ + $\frac{3}{4}$ + $1\frac{1}{4}$ = $3\frac{1}{2}$ pounds

Let us also convert to ounces:

$3\frac{1}{2}$ / 0.0625 = 56 ounces

Let us also convert 1/2 pound to ounces:

1/2 / 0.0625 = 8 ounces

Hence, the total weight of ingredients that Dwayne bought is $3\frac{1}{2}$ pounds or 56 ounces or 3 pounds 8 ounces

Hence, options A, B and E are correct.

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1 year ago

bob is having a party and want to order some cake. there will be 57 guest and he wants to make sure that everyone gets a slice o

Leviafan [203]

Bob should by the 25cm cake for 18.75 each. He will need to buy 3 of these cakes in order to feed 57 guests. The total cost would be 56.25. If he were to buy the 20cm cake, he would need to purchase 5 cakes for a total of 67.50.

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1 year ago