Erin is making a jewelry box of wood in the shape of a rectangular prism. The jewelry box

A line passes through the point (–7, 5) and has a slope of 1/5. Which is another point that the line passes through?

A line passes through the point (–7, 5) and has a slope of 1/5.
So this line would be y=1/5x+b
If we substitute x and y into this formula
We can get b=5+7/5=32/5
Then y=1/5x+32/5
If x=0, then y=32/5
So another point on this line is (0,32/5)

8 0

2 years ago

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A stop sign is a regular octagon. The standard stop sign has a 16.2 inch radius. The area of a standard stop sign is ___________

juin [17]

The area of standard stop sign regular octagon is 742.3 squared inches, if the standard stop sign has a 16.2 inch radius.

Step-by-step explanation:

The given is,

Radius of standard stop sign is 16.2 inch radius

Step:1

The regular octagon is equal to the 16 right angled triangle,

Angle of right angle triangle = $\frac{360}{16}$ = 22.5°

Ref attachment,

From the OAB right angle triangle,

Trigonometric ratio,

sin ∅ = $\frac{Opp}{Hyp}$

Where, ∅ = 22.5°

Hyp = Radius = 16.2 inches

Ratio becomes,

sin 22.5°= $\frac{b}{16.2}$

b = (0.374607)(16.2)

b = 6.19947 inches

Trigonometric ratio,

cos ∅ = $\frac{Adj}{Hyp}$

Where, ∅ = 22.5°

Hyp = Radius = 16.2 inches

Adj = h

Ratio becomes,

cos 22.5°= $\frac{h}{16.2}$

h = (0.9238795)(16.2)

h = 14.967 inches

Step:2

From the triangle OAC,

Area, $A = \frac{1}{2} (Height )( Base)$

Where, Height = 14.967 inches

Base = b + x = 6.19947 + 6.19947

= 12.3989 inches

From the values equation becomes,

A = $\frac{1}{2} (14.967)(12.39894)$

A = 92.7875 Squared inches

Step:3

The octagon is equal to sum of 8 triangles

Area of octagon = 8 × Area of triangle

= 8 × 92.7875

= 742.3 squared inches

Result:

The area of standard stop sign regular octagon is 742.3 squared inches, if the standard stop sign has a 16.2 inch radius.

7 0

3 years ago

4. Geologists estimate the time since the most recent cooling of a mineral by counting the number of uranium fission tracks on t

MariettaO [177]

Answer:

In this case we use the Poisson distribution because we are talking about the occurrence of an event (number of tracks) over a specified interval (in this case an area interval).

The probability of the event occurring x times over an interval is:

P(x) = nˣ × e⁻ⁿ ÷ x!

where n is the mean.

a) P(7) = 6⁷ × e⁻⁶ ÷ 7! = 0.1376

b) P(x ≥ 3) = 1 - P(x < 3) = 1 - P(2) - P(1) - P(0)

P(2) = 6² × e⁻⁶ ÷ 2! = 0.0446

P(1) = 6¹ × e⁻⁶ ÷ 1! = 0.0149

P(0) = 6⁰ × e⁻⁶ ÷ 0! = 0.0025

P(x ≥ 3) = 0.9380

c) P(2 < x < 7) = P(3) + P(4) + P(5) + P(6) = 0.0892 + 0.1339 + 0.1606 + 0.1606 = 0.5443

d) The mean is going to be 6.

e) The standard deviation is √n = √6 = 2.4

3 0

2 years ago

For each container of tea, McKenzie uses 16 tea bags and 3 cups of sugar. If McKenzie uses 64 tea bags, how many cups of sugar w

cestrela7 [59]

So tis is a ratio 16 is to 3 or 16:3
if use 64 tea bags then how many cups of sugar so
turn 16:3 into fraction
16:3=16/3 or 3/16, it doesn't matter
then you want to find 64:x or 64/x or x/64

we know that 16/3=64/x because it tis an equivalent ratio
so 16/3=64/x
multiply both sdies by (3 times x)
16 times x times 3/3=64 times 3 times x/x
16 times x=64 times 3
16x=192
divide both sdies by 16
x=12
theanswer is 12 cups of sugar

5 0

2 years ago

Brenda throws a dart at this square-shaped target:

Klio2033 [76]

Answer: See below

Step-by-step explanation:

Area of the square = l*w = 11*11 = 121

Area of the circle = pi r^2 = pi*1^2 = 3.142

Part A

P(hitting the circle) = 3.142 / 121 = 0.026 which is closer to 0.

Part B

P(hitting the outside portion) = 1 - 0.026 = 0.974 which is closer to 1.

4 0

1 year ago

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