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gavmur [86]
3 years ago
5

(1) An insurance agency sells various types of insurance policies. 40% of their clients buy auto insurance policies, 30% of thei

r clients buy home insurance policies, and 15% of their clients buy both home and auto insurance policies. a. Compute the probability a randomly selected client buys a home or auto insurance policy.
Mathematics
1 answer:
yaroslaw [1]3 years ago
6 0

Answer:

55% or 0.55(as a decimal)

Step-by-step explanation:

40% of their clients buy auto insurance policies = P(A)

30% of their clients buy home insurance policies = P(H)

15% of their clients buy both home and auto insurance policies = P( A ∩ H)

The probability a randomly selected client buys a home or auto insurance policy = P (A ∪ H) is calculated as

P ( A ∪ H) = P(A ) + P ( H ) - P( A ∩ H)

= 40% + 30% - 15 %

= 70% - 15%

= 55%

Therefore, the probability that a randomly selected client buys a home or auto insurance policy is 55% or expressed as decimal = 0.55

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3 years ago
Find the equation of the line that passes through (0, -3) and is parallel to
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Hey there!

\\

  • Answer:

\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}

\\

  • Explanation:

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be \: \sf{d_1} \: and the line that is parallel to \: \sf{d_1} \: be \: \sf{d_2} \: .

\sf{d_2} \: passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

\sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}}

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⇒Subtitute the values :

\sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )}

\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}

\sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}}.

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

\sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \:  the \: line \: and \: b \: is \: the \: y-intercept.}

\implies \sf{y = \bold{\dfrac{7}{6}}x + b} \\

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line \: \sf{d_1} \:. Now, replace y with -3 and x with 0:

\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:

Therefore, the equation of the line \: \bold{d_1} \: is \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}

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▪️Learn more about finding the equation of a line that is parallel to another one here:

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8 0
1 year ago
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BROOO HELP what is the slope of the line through (-3,3) and (-1,-1)?
lesya [120]

Answer:

C

Step-by-step explanation:

To find the slope between any two points, we can use the slope formula:

m=\frac{y_2-y_1}{x_2-x_1}

Where (x₁, y₁) and (x₂, y₂) are two, separate points.

We have the two points (-3, 3) and (-1, -1).

So, let (-3, 3) be (x₁, y₁) and let (-1, -1) be (x₂, y₂).

Substitute them into the slope formula to get:

m=\frac{-1-3}{-1-(-3)}

Subtract:

m=\frac{-4}{2}=-2

Hence, our slope is -2.

So, our answer is C.

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2 years ago
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Answer:

<h3>B. It has infinite solutions</h3>

Step-by-step explanation:

Given the system of equations:

2t + w = 10 ..... 1

4t = 20 − 2w ... 2

From 1:

w = 10-2t ...3

Substitute 3 into 2 to have;

4t = 20 - 2(10-2t)

4t = 20-20+4t

4t = 4t

Let t = k

Substitute t = k into 1 and get w;

From 1: 2t + w = 10

2k + w =10

w = 10 - 2k

<em>k can take any integers. This shows that the solution to the equation is infinite</em>

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