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3 years ago

Ratios equivalent to 16:12

Mathematics

1 answer:

Artyom0805 [142]3 years ago

4 0

Answer:

$\frac{16}{12}$ equivalent to $\frac{ 4}{3}$

Step-by-step explanation:

Given ratio, $\frac{16}{12}$

It can be written as $\frac{16}{12}=\frac{4 \times 4}{4 \times 3}$

cancel common factor,

$\frac{16}{12}=\frac{ 4}{3}$

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Answer:

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Step-by-step explanation:

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3 years ago

Let C = C1 + C2 where C1 is the quarter circle x^2+y^2=4, z=0,from (0,2,0) to (2,0,0), and where C2 is the line segment from (2,

trapecia [35]

Not much can be done without knowing what $\mathbf F(x,y,z)$ is, but at the least we can set up the integral.

First parameterize the pieces of the contour:

$C_1:\mathbf r_1(t_1)=(2\sin t_1,2\cos t_1,0)$
$C_2:\mathbf r_2(t_2)=(1-t_2)(2,0,0)+t_2(3,3,3)=(2+t_2, 3t_2, 3t_2)$

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$\mathrm d\mathbf r_1=(2\cos t_1,-2\sin t_1,0)\,\mathrm dt_1$
$\mathrm d\mathbf r_2=(1,3,3)\,\mathrm dt_2$

and so the work is given by the integral

$\displaystyle\int_C\mathbf F(x,y,z)\cdot\mathrm d\mathbf r$
$=\displaystyle\int_0^{\pi/2}\mathbf F(2\sin t_1,2\cos t_1,0)\cdot(2\cos t_1,-2\sin t_1,0)\,\mathrm dt_1$
${}\displaystyle\,\,\,\,\,\,\,\,+\int_0^1\mathbf F(2+t_2,3t_2,3t_2)\cdot(1,3,3)\,\mathrm dt_2$

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3 years ago

A random sample of 300 balls hit into play in college baseball games is taken. For each ball hit into play, it is recorded wheth

AlekseyPX

Answer:

Null hypothesis: There is no relationship between direction of the ball and if it resulted in a hit or an out.

Step-by-step explanation:

In this case, the experiment conducted is to determine whether there is any relationship between the direction of the ball and if it resulted in a hit or an out.

A random sample of 300 balls hit into play in college baseball games is taken. For each ball hit into play, it is recorded whether the ball was hit to the left, center, or right of the field, and whether the ball resulted in a hit or an out.

The regression analysis would be used to determine whether there is any relationship between direction of the ball and if it resulted in a hit or an out.

The hypothesis for the regression analysis is defined as follows:

<em>H</em>₀: There is no relationship between direction of the ball and if it resulted in a hit or an out.

<em>H</em>ₐ: There is a significant relationship between direction of the ball and if it resulted in a hit or an out.

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3 years ago

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = 5 over 5 and 59 hundredths.

Vikentia [17]

The relationship between Traingle XYZ and ACB is that they are similar triangles. tanX = tanA = 5 over 2 and 5 tenths, where

AC = 2 x XY
CB = 2 x YZ

<h3>What is the dilation about?</h3>

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB, hence XYZ and ACB are similar triangles.

Angles Y and C are said to measure 90 degrees, and angles A and X are known to be congruent. Thus:

tanX = tanA = 5 over 2 and 5 tenths

AC = 2 x XY

CB = 2 x YZ

Another way to solve for it is by:

Note that Dilation of the triangle ΔXYZ was by a factor of "2".

Since m∠Y = m∠C = 90º - given

ΔXYZ and ΔACB are said to be right triangles.

Since ∠X ≅ ∠A - given

Then ∠X and ∠Z are said to becomplementary angles

Since m∠Z = 90° - m∠X -- given

Then ∠A and ∠B are said to be complementary angles

Since m∠B = 90° - m∠A --- given

Then, ∠Z ≅ ∠B

Therefore ΔXYZ ∼ ΔACB are similar triangles because it has its corresponding sides to be proportional and its corresponding angles to be congruent.

Note:

sin ∠X = 5/5.59

sin ∠X = YZ/XY

YZ = 5 seen in ΔXYZ

XZ = 5.59 seen in hypotenuse of ΔXYZ

Then one need to Calculate the length of one aspect of XY:

XY = √((5.59)2 - 52)

= 2.4996

Note CB/YZ = 2

CD = 2*YZ = 2 x 5

= 10

AC/XY = 2

AC = 2* XY

= 2 x 2.4996

= 4.999

Learn more about dilation from:

brainly.com/question/27517432

#SPJ1

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2 years ago