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3 years ago

A mountain biker gets halfway up a hill and realizes he forgot his water, so he returns to his starting point

Mathematics

2 answers:

Vikentia [17]3 years ago

7 0

Step-by-step explanation:

The mountain bike goes back down the hill to get his water bottle

motikmotik3 years ago

3 0

Answer:

True

Explanation:

1/2 (up the hill) - 1/2 (down the hill) = 0

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Factor 5v^2 - 23v - 10

AfilCa [17]

Answer:

$(5v + 2)(v - 5)$

Step-by-step explanation:

Hello!

The expression is written in the form of $ax^2 + bx + c$

Let's factor by grouping:

$ac = -50$

The sum of the factors of -50 should add up to -23.

-25 and 2 work for this.

Expand and factor:

$5v^2 - 23v - 10$
$5v^2 - 25v + 2v - 10$
$5v(v - 5) +2(v -5 )$
$(5v + 2)(v - 5)$

The factored expression is $(5v + 2)(v - 5)$

7 0

2 years ago

What geometric term does the surface of a chalkboard represent?

Fittoniya [83]

A) Plane because it is a flat surface that extends in two dimensions but exists in a three-dimensional space, and also it isn't a point, a line, or an angle because a line is infinitely thin, a point is infinitesimally small, and an angle is a measurement, not a surface.

7 0

3 years ago

Read 2 more answers

2 Probability and Stats questions!!

mart [117]

1) To find the confidence interval
the sample mean x = 38 σ = 9; n = 85;
The confidence level is 95% (CL = 0.95) CL = 0.95
so α = 1 – CL = 0.05
α/2 = 0.025 Z(α/2) = z0.025
The area to the right of Z0.025 is 0.025 and the area to the left of Z0.025 is 1 – 0.025 = 0.975
Z(α/2) = z0.025 = 1.645 This can be found using a computer, or using a probability table for the standard normal distribution.
EBM = (1.645)*(9)/(85^0.5)=1.6058 x - EBM = 38 – 1.6058 = 36.3941 x + EBM = 38 + 1.6058 = 39.6058
The 95% confidence interval is (36.3941, 39.6058).
The answer is the letter D
The value of 40.2 is within the 95% confidence interval for the mean of the sample

2) To find the confidence interval 
the sample mean x = 76 σ = 20; n = 102; 
The confidence level is 95% (CL = 0.95) CL = 0.95
so α = 1 – CL = 0.05
α/2 = 0.025 Z(α/2) = z0.025
The area to the right of Z0.025 is 0.025 and the area to the left of Z0.025 is 1 – 0.025 = 0.975
Z(α/2) = z0.025 = 1.645 This can be found using a computer, or using a probability table for the standard normal distribution.
EBM = (1.645)*(20)/(102^0.5)=3.2575 x - EBM = 76 – 3.2575 = 72.7424 x + EBM = 76 + 3.2575 = 79.2575 
The 95% confidence interval is (72.7424 ,79.2575).
The answer is the letter A and the letter D
The value of 71.8 and 79.8 are outside the 95% confidence interval for the mean of the sample

5 0

3 years ago

Jill bought a lamp for $40. She sold it at a garage sale for $12. What was the approximate decrease?

Vesnalui [34]

Answer:

she was left with 28$ I'm in high school i think I'm right

Step-by-step explanation:

3 0

3 years ago

An open top rectangular box is to be made from a rectangular piece of metal that is 3cm wide and 8cm long by cutting a square fr

Tanzania [10]

Answer:

x = 0.67 cm

Step-by-step explanation:

Let call " x " the length of the side of the square to cut from each corner

then the sides of the future box would be

L = 8 - 2x and D = 3 - 2x

The volume of the box is:

V = L*D*x

And such volume as function of x is

V(x) = ( 8 - 2x ) * ( 3 - 2x ) * x ⇒ V(x) = ( 24 - 16x - 6x + 4x²) * x

V(x) = 4x³ - 22x² + 24x

Taking derivatives on both sides of the equation we get:

V´(x) = 12x² - 44x + 24

Then V´(x) = 0 ⇒ 12x² - 44x + 24 = 0 ⇒ 3x² - 11x + 6 = 0

We got a second degree equation solving for x

x₁,₂ = [11 ± √ 121 - 72 ] / 6

x₁ = ( 11 + 7 ) / 6 x₁ = 3 we dismiss this solution since according to problem statement one side would become negative

Then

x₂ = ( 11 - 7 ) / 6 ⇒ x₂ = 4/6 ⇒ x₂ = 0.67 cm

As the second drivative is smaller than 0 then there is a maximun in that point

V´´(x) = 12x - 44 < 0

Sides of the box

L = 8 - 2x ⇒ L = 8 - 2*(0.67) ⇒ L = 8 - 1.34 ⇒ L = 6.66 cm

D = 3 - 2x ⇒ D = 3 - 2* (0.67) ⇒ D = 3 - 1.34 ⇒ D = 1.66 cm

Heigh = x = 0.67 cm

V(max) = 6.66*1.66*0.67

V(max) = 7.41 cm³

5 0

3 years ago