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4 years ago

The line plots show the number of hours two groups of kids spent studying last weekend.

Mathematics

2 answers:

bixtya [17]4 years ago

5 0

Answer: A: The 14- to 17-year olds spent more hours studying, on average, last weekend than the 10- to 13-year olds

Step-by-step explanation:

From the given line plot we observe the total number of hours spent by 10 to 13 years olds is 1+1+2+4+4+4+4+6+6+7+8= 47 hours and for 14 to 17 years old is 4+4+4+4++6+7+8+9+9+10+10= 105 hours.

Median for 10 to 13 years = 4hours

Median for 14 to 17 years = 7 hours

Average hours spent by 10 to 13 years =47÷2=23.5

Average hours spent by 14 to 17 years =105÷2=52.5

Range of hours spent by 10 to 13 years = 8-1=7

Range of hours spent by 14 to 17 years =10-4=6

Among all the given options option A is right.

A: The 14- to 17-year olds spent more hours studying, on average, last weekend than the 10- to 13-year olds

erik [133]4 years ago

3 0

The 14- to 17-year olds spent more hours studying, on average, last weekend than the 10- to 13-year olds.

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A farmer finds that if she plants 100 trees per acre, each tree will yield 35 bushels of fruit. She estimates that for each addi

castortr0y [4]

Answer:

126 trees should she plant per acre to maximize her harvest.

Step-by-step explanation:

Let x be the additional tress that must be plant after planting 100 tress.

So, total number of trees = 100 + x trees

Also, Each additional tree planted decreases the yield of each tree by 3 bushels.

So , net bushels by each tree = 35 - 3x

The revenue function becomes

f(x) = (100 + x)(35 - 3x)

Thus,

Differentiating it by using chain rule as:

f'(x) = (100 + x)35 + 100(35 - 3x)

f'(x) = 3500 + 35x + 3500 - 300x

f'(x) = 7000 - 265x

For maxima of f(x), f'(x) = 0

7000 - 265x = 0

Thus,

x = 26.4151

Since, x represents tress, so, x is 26.

So, total tress she would plant to earn maximum revenue = 100 + 26 = 126 trees

3 0

3 years ago

i need help with the last two. I forgot the formula and wondering if you will help me find which one is and isnt a triangle

Nimfa-mama [501]

Answer:

3. D) 26, 7, 31

4. B) 6, 34, 27

Step-by-step explanation:

Both #3 and #4 use the same strategy: the two shorter sides' sum has to be greater than the longer side.

#3:

2 + 8 is 10, which is less than 13. So A wouldn't form a triangle.

12 + 22 is 34, which is the length of the longer side. So B wouldn't form a triangle either.

14 + 18 is 32, which is less than 40. So C wouldn't form a triangle.

7 + 26 is 33, which is greater than 31. So D would form a triangle.

D. 26, 7, and 31 are the only lengths of the ones shown that form a triangle.

#4:

17 + 18 is 35, which is greater than 19. So A would form a triangle.

11 + 22 is 33, which is greater than 25. So C would also form a triangle.

5 + 18 is 23, which is greater than 20. So D would form a triangle.

6 + 27 is 33, which is less than 34. So B wouldn't form a triangle.

B. 6, 34, and 27 are the only lengths of the ones shown that don't form a triangle.

6 0

3 years ago

I like you cookie want go out what me :]

Gelneren [198K]

Answer: lol wut

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

One side of a right triangle is 2 cm shorter than the hypotenuse and 7 cm longer than the third side. find the lengths of the si

astra-53 [7]

The right angles triangle has three sides including the hypotenuse which is opposite to the right angle.
If the hypotenuse - H
Then one side is - H - 2
Third side is 7 cm shorter then H-2
Therefore it’s H -2-7 = H -9
According to Pythagoras theorem
Square of hypotenuse = sum of the squares of the other 2 sides
H² = (H-9)² + (H-2)²
H² = H² -18H + 81 + H² -4H + 4
0 =H² -22H +85
This is a quadratic equation
0 = H² - 17H -5H +85
0 = H (H - 17) -5(H-17)
(H-17) (H-5) =0
H -17=0 or H-5=0
H could be 17 cm or 5 cm
If H =5 cm then
Side 1 -H-2 = 3 cm
And side 2 - H-9 = -4 cm
Since lengths cannot be negative values
H isn’t 5 cm
Therefore H =17 cm
1 side is H-2 = 15 cm
2nd side H -9 = 8 cm
Three sides are 17 cm, 15 cm and 8 cm

8 0

3 years ago

The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is form

ZanzabumX [31]

Draw ΔABC as shown in the figure below.
m∠B = 137°, b = 14, c = 9.

From the Law of Sines,
sin(C)/c = sin(B)/b
or
sin(C)/9 = sin(137°)/14
sin(C) = (9/14)*sin(137°) = 0.4384
m∠C = arcsin(0.4384) = 26°

Because the sum of angles in a triangle is 180°, therefore
m∠A = 180 -137 - 26 = 17°

From the Law of Sines,
a/sin(A) = b/sin(B)
or
a/sin(17°) = 14/sin(137°)
a = (sin(17°)/sin(127°))*14 = 6

Answer:
The solution for the triangle is
a = 6, b = 14, c = 9
m∠A = 17°, m∠B = 137°, m∠C = 26°

3 0

3 years ago