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3 years ago

7

There are 30 blue balls, 40 red balls, and 30 white balls in a bag of balls. What is the conditional probability of choosing a b

lue ball, given that a white ball was not chosen?

2 answers:

lina2011 [118]3 years ago

7 0

Answer:

So, only 70 balls are left with us , from which we choose a blue ball

So, the probability will be

P( \text{getting a blue ball })=\frac{30}{70}=\frac{3}{7}

Step-by-step explanation:

natulia [17]3 years ago

4 0

Answer: So, the probability will be

$P( \text{getting a blue ball })=\frac{30}{70}=\frac{3}{7}$

Step-by-step explanation:

Since we have given that

Number of blue balls =30

Number of red balls = 40

Number of white balls = 30

Since there are 100 balls in total ,

As we have given that there is no white ball chosen.

So, only 70 balls are left with us , from which we choose a blue ball

So, the probability will be

$P( \text{getting a blue ball })=\frac{30}{70}=\frac{3}{7}$

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An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 1-ounce p

ludmilkaskok [199]

Answer:

a) $y=-0.317 x +46.02$

b) Figure attached

c) $S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03$

Step-by-step explanation:

We assume that th data is this one:

x: 30, 30, 30, 50, 50, 50, 70,70, 70,90,90,90

y: 38, 43, 29, 32, 26, 33, 19, 27, 23, 14, 19, 21.

a) Find the least-squares line appropriate for this data.

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 30+30+30+50+50+50+70+70+70+90+90+90=720$

$\sum_{i=1}^n y_i =38+43+29+32+26+33+19+27+23+14+19+21=324$

$\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200$

$\sum_{i=1}^n y^2_i =38^2+43^2+29^2+32^2+26^2+33^2+19^2+27^2+23^2+14^2+19^2+21^2=9540$

$\sum_{i=1}^n x_i y_i =30*38+30*43+30*29+50*32+50*26+50*33+70*19+70*27+70*23+90*14+90*19+90*21=17540$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=49200-\frac{720^2}{12}=6000$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=17540-\frac{720*324}{12}{12}=-1900$

And the slope would be:

$m=-\frac{1900}{6000}=-0.317$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{720}{12}=60$

$\bar y= \frac{\sum y_i}{n}=\frac{324}{12}=27$

And we can find the intercept using this:

$b=\bar y -m \bar x=27-(-0.317*60)=46.02$

So the line would be given by:

$y=-0.317 x +46.02$

b) Plot the points and graph the line as a check on your calculations.

For this case we can use excel and we got the figure attached as the result.

c) Calculate S^2

In oder to calculate S^2 we need to calculate the MSE, or the mean square error. And is given by this formula:

$MSE=\frac{SSE}{df_{E}}$

The degred of freedom for the error are given by:

$df_{E}=n-2=12-2=10$

We can calculate:

$S_{y}=\sum_{i=1}^n y^2_i -\frac{(\sum_{i=1}^n y_i)^2}{n}=9540-\frac{324^2}{12}=792$

And now we can calculate the sum of squares for the regression given by:

$SSR=\frac{S^2_{xy}}{S_{xx}}=\frac{(-1900)^2}{6000}=601.67$

We have that SST= SSR+SSE, and then SSE=SST-SSR= 792-601.67=190.33[/tex]

So then :

$S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03$

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3 years ago

The cube of the difference of a number and 4

lbvjy [14]

Answer:

(x - 4)³

Step-by-step explanation:

"The cube of x" would be x³. The difference of a number and 4 would be x - 4.

Therefore, "the cube of the difference of a number and 4" would be

(x - 4)³

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3 years ago

If you split a right angle with a ray going through the middle of the right angle, the two angles formed will be ______. Select

Tom [10]

Answer:

Complementary

Step-by-step explanation:

To be complementary, your two angles need to add up to 90 degrees

a right triangle is already 90 degrees so if you cut it through the middle they'd form complementary angles

8 0

3 years ago

Read 2 more answers

Peter selects a sock from his drawer. The sock is black. There are 4 white socks, 7 blue socks, and 12 black socks left in the d

max2010maxim [7]

Answer:

5/12

7/12

125/36 = 3,47%

50/11 = 4,54%

Step-by-step explanation:

Probability a black sock is selected when a person chooses 1 sock = 5/12

Probability a white or brown sock is selected when a person chooses 1 sock =

7/12

Probability a person chooses 3 socks and selects a white first, a black second, and a brown last if the socks are replace = (4/12 * 5/12 * 3/12)*100 =125/36 = 3,47%

Pobability a person chooses 3 socks and selects a white first, a black second, and a brown last if the socks are NOT replace = (4/12 * 5/11 * 3/ 10)*100 = 50/11 = 4,54%

3 0

3 years ago

Find the measure of the exterior angles of the following regular polygons: a triangle, a quadrilateral, a pentagon, an octagon,

musickatia [10]

Answer:

Triangle: 120

Quadrilateral: 90

Pentagon: 72

Octagon: 45

Decagon: 36

30-gon: 10

50-gon: 7.2

100-gon: 3.6

Step-by-step explanation:

360/n = the measure on the exterior angle

n = the number of sides

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3 years ago