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olchik [2.2K]
3 years ago
8

What strategy would be the best to solve this problem?A theater charges $8 for an adult ticket, and $6 for a children's ticket.

On a certain day, a total of 255 tickets were sold for a total cost of $1,850. How many more children's tickets were sold than adult tickets?
Mathematics
2 answers:
stich3 [128]3 years ago
7 0
8a + 6c = 1850
a + c = 255

system of equations
Lynna [10]3 years ago
7 0

Your answer for T4L quiz is Guess, Check, and Revise

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A circle with radius 9 has a sector with a central angle of 120 degrees. What is the area of the sector?
lara31 [8.8K]

Answer:

A =  27π units²

Step-by-step explanation:

Note that a central angle of 120 degrees corresponds to 1/3 of a full circle.

The area of the full circle is A = πr², or A = π(9 units)² = 81π units², and so

the area of the sector in question is 1/3 of that, or   A =  27π units²

5 0
4 years ago
What is −183 ? Group of answer choices
vitfil [10]

Answer:

it is b because I did the problem yes it is b

7 0
3 years ago
A cone with a radius of 12 cm and a height of 12 cm has the same volume as a cylinder with a radius of 8 cm. What is the height
Dmitry [639]
First, substitute the given radius and given height of the cone into the formula for the volume of a cone. 

Volume of a cone:  (1/3) pi r^2 h
In this case, the cone volume is (1/3) pi (12 cm)^2 (12 cm) = 576 cm^3

Vol. of a rt. cylinder:  pi r^2 h
In this case, the vol. of the rt. cyl. is pi (8 cm)^2 h.

The two different shapes have the same volume.  Therefore, set the two formulas (above) equal to each other:

576 pi cm^3 = pi (8cm)^2 h.  This becomes

576 pi cm^3 = pi (64 cm^2) h.  "pi" cancels out, leaving us with

576 cm^3
------------- = h.       This is the height of the cylinder, in cm.
 64 cm^2



3 0
4 years ago
Match each vector operation with its resultant vector expressed as a linear combination of the unit vectors i and j.
Cloud [144]

Answer:

3u - 2v + w = 69i + 19j.

8u - 6v = 184i + 60j.

7v - 4w = -128i + 62j.

u - 5w = -9i + 37j.

Step-by-step explanation:

Note that there are multiple ways to denote a vector. For example, vector u can be written either in bold typeface "u" or with an arrow above it \vec{u}. This explanation uses both representations.

\displaystyle \vec{u} = \langle 11, 12\rangle =\left(\begin{array}{c}11 \\12\end{array}\right).

\displaystyle \vec{v} = \langle -16, 6\rangle= \left(\begin{array}{c}-16 \\6\end{array}\right).

\displaystyle \vec{w} = \langle 4, -5\rangle=\left(\begin{array}{c}4 \\-5\end{array}\right).

There are two components in each of the three vectors. For example, in vector u, the first component is 11 and the second is 12. When multiplying a vector with a constant, multiply each component by the constant. For example,

3\;\vec{v} = 3\;\left(\begin{array}{c}11 \\12\end{array}\right) = \left(\begin{array}{c}3\times 11 \\3 \times 12\end{array}\right) = \left(\begin{array}{c}33 \\36\end{array}\right).

So is the case when the constant is negative:

-2\;\vec{v} = (-2)\; \left(\begin{array}{c}-16 \\6\end{array}\right) =\left(\begin{array}{c}(-2) \times (-16) \\(-2)\times(-6)\end{array}\right) = \left(\begin{array}{c}32 \\12\end{array}\right).

When adding two vectors, add the corresponding components (this phrase comes from Wolfram Mathworld) of each vector. In other words, add the number on the same row to each other. For example, when adding 3u to (-2)v,

3\;\vec{u} + (-2)\;\vec{v} = \left(\begin{array}{c}33 \\36\end{array}\right) + \left(\begin{array}{c}32 \\12\end{array}\right) = \left(\begin{array}{c}33 + 32 \\36+12\end{array}\right) = \left(\begin{array}{c}65\\48\end{array}\right).

Apply the two rules for the four vector operations.

<h3>1.</h3>

\displaystyle \begin{aligned}3\;\vec{u} - 2\;\vec{v} + \vec{w} &= 3\;\left(\begin{array}{c}11 \\12\end{array}\right) + (-2)\;\left(\begin{array}{c}-16 \\6\end{array}\right) + \left(\begin{array}{c}4 \\-5\end{array}\right)\\&= \left(\begin{array}{c}3\times 11 + (-2)\times (-16) + 4\\ 3\times 12 + (-2)\times 6 + (-5) \end{array}\right)\\&=\left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle\end{aligned}

Rewrite this vector as a linear combination of two unit vectors. The first component 69 will be the coefficient in front of the first unit vector, i. The second component 19 will be the coefficient in front of the second unit vector, j.

\displaystyle \left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle = 69\;\vec{i} + 19\;\vec{j}.

<h3>2.</h3>

\displaystyle \begin{aligned}8\;\vec{u} - 6\;\vec{v} &= 8\;\left(\begin{array}{c}11\\12\end{array}\right) + (-6) \;\left(\begin{array}{c}-16\\6\end{array}\right)\\&=\left(\begin{array}{c}88+96\\96 - 36\end{array}\right)\\&= \left(\begin{array}{c}184\\60\end{array}\right)= \langle 184, 60\rangle\\&=184\;\vec{i} + 60\;\vec{j} \end{aligned}.

<h3>3.</h3>

\displaystyle \begin{aligned}7\;\vec{v} - 4\;\vec{w} &= 7\;\left(\begin{array}{c}-16\\6\end{array}\right) + (-4) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}-112 - 16\\42+20\end{array}\right)\\&= \left(\begin{array}{c}-128\\62\end{array}\right)= \langle -128, 62\rangle\\&=-128\;\vec{i} + 62\;\vec{j} \end{aligned}.

<h3>4.</h3>

\displaystyle \begin{aligned}\;\vec{u} - 5\;\vec{w} &= \left(\begin{array}{c}11\\12\end{array}\right) + (-5) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}11-20\\12+25\end{array}\right)\\&= \left(\begin{array}{c}-9\\37\end{array}\right)= \langle -9, 37\rangle\\&=-9\;\vec{i} + 37\;\vec{j} \end{aligned}.

7 0
3 years ago
A researcher claims that the incidence of a certain type of cancer is less than 5%. To test this claim, the a random sample of 4
DedPeter [7]

Answer: The test statistic value is -0.95.

Step-by-step explanation:

Since we have given that

H_0:p=0.05\\\\H_a:p

Here, n = 4000

x = 170

So, \hat{p}=\dfrac{170}{4000}=0.0425

So, Test statistic value would be

\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\=\dfrac{0.0425-0.05}{\sqrt{\dfrac{0.5\times 0.5}{4000}}}\\\\=-0.95

Hence, the test statistic value is -0.95.

3 0
4 years ago
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