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3 years ago

Find the measure of <3.

Mathematics

1 answer:

miss Akunina [59]3 years ago

7 0

Measure of angle 3 is 31

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Ronch [10]

Answer:

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Step-by-step explanation:

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3 years ago

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a carnival game consists of 3 dart throws at a target. The probability of scoring a hit on any one throw is 30%. Using the binom

Ghella [55]

Answer: Probability of scoring 2 hits = 0.63.

Step-by-step explanation:

Since we have given that

Number of dart throws at a target = 3

Probability of scoring a hit on any one throw = 30%

We will use "Binomial Distribution" i.e.

$P=^nC_rp^r(1-p)^{n-r}$

where,

n denotes number of dart throws at a target,

r denotes number of required throws

p denotes probability of success

(1-p) denotes probability of failure

So, Probability of success is given by

$\frac{30}{100}=\frac{3}{10}$

Probability of failure is given by

$1-\frac{30}{100}=\frac{70}{100}=\frac{7}{10}$

We will use "Binomial Distribution" i.e.

$P(X=2)=^3C_2(\frac{3}{10})^2\times (\frac{7}{10})\\\\P(X=2)=\frac{9}{100}\times \frac{7}{100}\\\\P(X=2)=\frac{63}{100}\\\\P(X=2)=0.63$

Hence, Probability of scoring 2 hits = 0.63.

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3 years ago

A sports writer wished to see if a football filled with helium travels farther, on average, than a football filled with air. To

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Step-by-step explanation:

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3 years ago

Select the expressions that are equivalent to 12n – 8. Select all that apply.

Lostsunrise [7]

Answer:

B and D

Step-by-step explanation:

B= 4(3n-2)

D=12n-8 which equals 4(3n-2)

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3 years ago

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Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3

nlexa [21]

Answer:

$(x,y) = (5,-6)$

Step-by-step explanation:

$\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\$

$~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)$

$\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\$

$\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5$

$y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6$

$\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)$

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2 years ago