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2 years ago

1. Are these two lines parallel, perpendicular or neither?

Mathematics

1 answer:

kolezko [41]2 years ago

8 0

Answer:

parallel

Step-by-step explanation:

they have the same slope, but different y intercepts

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Your neighbor has a bag with 5 oranges and 7 apples in it. You will be receiving two pieces of fruit from your neighbor. What is

Snezhnost [94]

Answer:

31.82% probability that you will receive 2 apples.

Step-by-step explanation:

The fruits are removed from the bag, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

5 + 7 = 12 total fruits, which means that $N = 12$

7 apples, which means that $k = 7$

You receive 2 fruits, which means that $n = 2$

What is the probability, in percent, that you will receive 2 apples, assuming she removes them from the bag in random order?

This is, as a proportion, P(X = 2). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,12,2,7) = \frac{C_{7,2}*C_{5,0}}{C_{12,2}} = 0.3182$

0.3182*100% = 31.82%

31.82% probability that you will receive 2 apples.

4 0

3 years ago

1) Determine the discriminant of the 2nd degree equation below:

Aleksandr-060686 [28]

$\LARGE{ \boxed{ \mathbb{ \color{purple}{SOLUTION:}}}}$

We have, Discriminant formula for finding roots:

$\large{ \boxed{ \rm{x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }}}$

Here,

x is the root of the equation.
a is the coefficient of x^2
b is the coefficient of x
c is the constant term

1) Given,

3x^2 - 2x - 1

Finding the discriminant,

➝ D = b^2 - 4ac

➝ D = (-2)^2 - 4 × 3 × (-1)

➝ D = 4 - (-12)

➝ D = 4 + 12

➝ D = 16

2) Solving by using Bhaskar formula,

❒ p(x) = x^2 + 5x + 6 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5\pm \sqrt{( - 5) {}^{2} - 4 \times 1 \times 6 }} {2 \times 1}}}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm \sqrt{25 - 24} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm 1}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = - 2 \: or - 3}}}$

❒ p(x) = x^2 + 2x + 1 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 1 \times 1} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{4 - 4} }{2} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm 0}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = - 1 \: or \: - 1}}}$

❒ p(x) = x^2 - x - 20 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 1) \pm \sqrt{( - 1) {}^{2} - 4 \times 1 \times ( - 20) } }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ 1 \pm \sqrt{1 + 80} }{2} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{1 \pm 9}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = 5 \: or \: - 4}}}$

❒ p(x) = x^2 - 3x - 4 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 3) \pm \sqrt{( - 3) {}^{2} - 4 \times 1 \times ( - 4) } }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm \sqrt{9 + 16} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm 5}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = 4 \: or \: - 1}}}$

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5 0

2 years ago

Read 2 more answers

Write an equation for a line that is parallel to 2x+5y=15 and passes through the point (-10, 3)

Lyrx [107]

Answer:

The equation of the line is,

$y = - \frac{2}{5} x - 1$

Step-by-step explanation:

First, you have to write it in a form of y = mx + b :

$2x + 5y = 15$

$5y = 15 - 2x$

$y = 3 - \frac{2}{5} x$

$y = - \frac{2}{3} x + 5$

When both lines are parallel to each other, they will have to same gradient value. So the equation of the line is y = (-2/5)x + b. Next, you have to find the value of b by substutituting (-10,3) into the equation :

$y = - \frac{ 2}{5}x + b$

$let \: x = - 10,y = 3$

$3 = - \frac{2}{5} ( - 10) + b$

$3 = 4 + b$

$3 - 4 = b$

$b = - 1$

3 0

3 years ago

Read 2 more answers

How do u write One fifth the difference of 5 and b

ivanzaharov [21]

Answer:5-b=1/5

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

"a u.S. 1-cent coin (a penny) has a diameter of 19 mm and a thickness of 1.5 mm". Assume the coin is made of pure copper, whose

choli [55]

the question is Calculate the value of the copper in the coin

Step 1

Find the volume of the coin

we know that

the volume of a cylinder is equal to

$V=\pi r^{2}h$

where

r is the radius of the coin

h is the thickness of the coin

in this problem we have

Diameter=19 mm=1.9 cm

r=D/2------> r=1.9/2=0.95 cm

h=1.5 mm=0.15 cm

substitute the values in the formula

$V=\pi*0.95^{2}*0.15=0.425\ cm^{3}$

Step 2

Find the mass of copper in the coin

we know that

the density is equal to

$Density=mass/volume$

Solve for the mass

$mass=Density*volume$

we have

$Density=8.9\ gr/cm^{3}\\Volume=0.425\ cm^{3}$

substitute in the formula

$mass=8.9*0.425=3.785\ gr$

Step 3

Find the cost

we know that

the market price of the copper is $2.15 per pound

1 pound=453.592 grams

convert gram to pounds

3.785 gr=3.785/453.592=0.0083 pounds

0.0083*$2.15=$0.018=$0.02

therefore

the answer is

$0.02

3 0

3 years ago