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2 years ago

Here are sketches of four triangles.

Mathematics

1 answer:

baherus [9]2 years ago

7 0

Answer:

3.4

Step-by-step explanation:

If we look at the top left triangle and the triangle with x, we notice that they are similar (since they have a 57° and a right angle). This means that 4 / 1 = x / 0.84, which means that x = 3.4.

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Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. how high

bezimeni [28]

Given that grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height.

So if D is the diameter and h is the height of the conical pile then we can write:

D=3h

We know that diameter = 2r, where r is the radius

2r=3h

$r=\frac{3h}{2}$

Volume of conical pile is given by formula

$V=\frac{1}{3}\pi r^2h$

Given that volume is 1110 cubic feet.

Now plug the values of Volume and r into equation of volume

$1110=\frac{1}{3}\pi (\frac{3h}{2})^2h$

$1110=\frac{1}{3}\pi\cdot\frac{9h^2}{4}\cdot h$

$1110=\pi\cdot\frac{3h^3}{4}$

$1110\cdot\frac{4}{3\pi}=h^3$

$471.098631552=h^3$

take cube root of both sides

7.78103342467=h

Hence height is approx 7.78 feet.

7 0

3 years ago

Suppose that a random sample of 10 adults has a mean score of 62 on a standardized personality test, with a standard deviation o

aniked [119]

Answer:

The 90% confidence interval for the mean score of all takers of this test is between 59.92 and 64.08. The lower end is 59.92, and the upper end is 64.08.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.05 = 0.95$ , so $z = 1.645$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.645*\frac{4}{\sqrt{10}} = 2.08$

The lower end of the interval is the sample mean subtracted by M. So it is 62 - 2.08 = 59.92

The upper end of the interval is the sample mean added to M. So it is 62 + 2.08 = 64.08.

The 90% confidence interval for the mean score of all takers of this test is between 59.92 and 64.08. The lower end is 59.92, and the upper end is 64.08.

5 0

2 years ago

Ants have 6 legs. Elena and Andre write equations showing the proportional relationship between the number of ants, a, to the nu

Vlad [161]

Answer:

I agree with Elena

Step-by-step explanation:

Ants have 6 legs. Elena and Andre write equations showing the proportional relationship between the number of ants, a, to the number of ant legs, v.

Elena writes a = 6 times v

Andre writes v =1/6 times a.

Mathematically

The number of ants a is directly proportional to the number of legs

=a ∝ v

Because if

1 ant = 6 legs

2 ants = x legs

x = 6 legs × 2

x = 12 legs

The number of ants is directly proportional to the number of legs

Therefore, Elena is correct and Andre is wrong.

8 0

3 years ago

let t : r2 →r2 be the linear transformation that reflects vectors over the y−axis. a) geometrically (that is without computing a

tangare [24]

(a) ( 1, 0 ) is the eigen vector for '-1' and ( 0, 1 ) is the eigen vector for '1'.

(b) two eigen values of 'k' = 1, -1

for k = 1, eigen vector is $\left[\begin{array}{c}0\\1\end{array}\right]$

for k = -1 eigen vector is $\left[\begin{array}{c}1\\0\end{array}\right]$

See the figure for the graph:

(a) for any (x, y) ∈ R² the reflection of (x, y) over the y - axis is ( -x, y )

∴ x → -x hence '-1' is the eigen value.

∴ y → y hence '1' is the eigen value.

also, ( 1, 0 ) → -1 ( 1, 0 ) so ( 1, 0 ) is the eigen vector for '-1'.

( 0, 1 ) → 1 ( 0, 1 ) so ( 0, 1 ) is the eigen vector for '1'.

(b) ∵ T(x, y) = (-x, y)

T(x) = -x = (-1)(x) + 0(y)

T(y) = y = 0(x) + 1(y)

Matrix Representation of $T = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right]$

now, eigen value of 'T'

$T - kI = \left[\begin{array}{cc}-1-k&0\\0&1-k\end{array}\right]$

after solving the determinant,

we get two eigen values of 'k' = 1, -1

for k = 1, eigen vector is $\left[\begin{array}{c}0\\1\end{array}\right]$

for k = -1 eigen vector is $\left[\begin{array}{c}1\\0\end{array}\right]$

Hence,

(a) ( 1, 0 ) is the eigen vector for '-1' and ( 0, 1 ) is the eigen vector for '1'.

(b) two eigen values of 'k' = 1, -1

for k = 1, eigen vector is $\left[\begin{array}{c}0\\1\end{array}\right]$

for k = -1 eigen vector is $\left[\begin{array}{c}1\\0\end{array}\right]$

Learn more about " Matrix and Eigen Values, Vector " from here: brainly.com/question/13050052

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6 0

1 year ago

10/24 and 5/12 what are the porportions

anyanavicka [17]

4 and 2 are the porportions

3 0

3 years ago

Read 2 more answers