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3 years ago

What is the value of y? Enter your answer, as an exact value, in the box.

Mathematics

1 answer:

OLga [1]3 years ago

7 0

We know the bottom triangle is a 45, 45, 90 triangle, so the hypotenuse is √2 times the value of the legs:

(√2)(√2)
=√4
=2

Now, we can use this to solve for y. The top triangle is a 30, 60, 90 triangle. The side we found above is the side across from the 30 degree angle. The side opposite the 60 degree angle is √3 times the side across the 30 degree angle. Therefore, we can solve for y by multiplying 2 by √3

y=2√3

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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 44 o

Cerrena [4.2K]

Answer:

a) No 95% of values will fall between (24;64); 68,27% will fall between (34;54)

b)71,83 % will fall between 34 and 64 ounces

Step-by-step explanation:

Empirical rule establishes, for a normal distribution with mean μ and σ as standard deviation:

In interval μ ± σ or ( μ + σ ; μ - σ) we should find 68.27 % of all values of the population, and by simmetry 68.27/2 = 34,14 % should be over the mean and the other half would be values below the mean

Therefore in our case

μ + σ = 44 + 10 = 54

And

μ - σ = 44 - 10 = 34

a) Then 68,34 % of values will fall in this interval

We know now that value 34 is 1* σ below the mean, and is at the limit of 34,14 %

b) μ + 2*σ = 44 * 2*10 = 44 + 20 = 64

64 is the upper limit for the interval μ + 2*σ and we know that 95.45 % of all values will fall between ( μ - 2*σ ; μ + 2*σ ) and by simmetry just one side of this interval (the right side ) will have 95.45/2 = 47;73 %

Then in interval going from ( 34 ; 64 ) we shoud find 47.73 + 34,14

71,83 % of all values will fall between 34 and 64

7 0

4 years ago

The student council has 10 members where 5 of the members are Seniors. They need to choose a President, Vice President, Secretar

natima [27]

Answer:

P=1/42.

Step-by-step explanation:

We know that the student council has 10 members where 5 of the members are Seniors. They need to choose a President, Vice President, Secretary and Treasurer. We calculate the probability that the President is a Senior:

We calculate the number of possible combinations:

$C_4^{10}=\frac{10!}{4!(10-4)!}=210$

Number of favorable combinations is 5.

Threfore, the probability is

P=5/210

P=1/42.

8 0

3 years ago

A set of data has the trend line modeled by the equation Y =1.5x + 11. What value of X corresponds to y =56?

erica [24]

Answer:

x = 30

Step-by-step explanation:

Plug in 56 in place of y, then solve for x.

56 = 1.5x + 11

Subtract 11.

45 = 1.5x

Divide both sides by 1.5.

45/1.5 = x

30 = x

8 0

3 years ago

Read 2 more answers

Impossible question for me plz help

klio [65]

Answer:

The line x = 3 is simply a vertical line that passes through every single point where x is equal to 3.

One that is is parallel and passes through (-4, 7) will be in the same format, just with another number. The given point has an x-coordinate of -4, so the line is:

x = -4

8 0

3 years ago

Can someone please help me I’ll give brilliant thingy

cricket20 [7]

Answer:

Yes, the shapes are similar. Note, the angles are equivalent and the sides are scales of each other satisfying the requirements for similarly.

Step-by-step explanation:

For a shape to be similar there are two conditions that must be met. (1) Must have equivalent angles (2) Sides must be related by a scalar.

In the two triangles presented, the first condition is met since each triangle has three angles, 90-53-37.

To test if the sides are scalar, each side must be related to a corresponding side of the other triangle with the same scalar.

9/6 = 3/2

12/8 = 3/2

15/10 = 3/2

Alternatively:

6/9 = 2/3

8/12 = 2/3

10/15 = 2/3

Since the relationship of the sides is the scalar 3/2 (Alternatively 2/3), then we can say the triangles meet the second condition.

Given that both conditions are satisfied, then we can say these triangles are similar.

Note, this is a "special case" right triangle commonly referred to as a 3-4-5 right triangle.

Cheers.

8 0

3 years ago