What is the range of the given data set?

2) P(did not exercise | did not catch a cold) = 1/16

3) P(did not catch a cold | did not exercise) = 1/6

4) The events "did not exercise" and "did not catch a cold" are dependent events.

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

P(A) = n(A) / n(S)  

where, n(A) is the number of favorable outcomes and n(S) is the total number of events in the sample space.

For events A, B,

P(A|B) means, event A and event B are depends on each other.

P(A | B) = n(A ∩ B) / P(B)

For given situation:

the total number of doctor’s patients: 8 + 30 + 10 + 2 =50

⇒ n(S) = 50

Let event A: did not exercise

⇒ n(A) = 10 + 2

⇒ n(A) = 12

⇒ P(A) = 12/50

event B: did not catch cold

⇒ n(B) = 30 + 2

⇒ n(B) =32

⇒ P(B) = 32/50

patient who did not catch a cold as well as who did not exercise = A ∩ B

⇒ n(A ∩ B) = 2

⇒  P(A ∩ B) = 2/50

2) To find: P(did not exercise | did not catch a cold)

⇒ P(A | B) = P(A ∩ B) / P(B)

⇒ P(A | B) = [tex]\frac{\frac{2}{50} }{ \frac{32}{50} }[/tex]

⇒ P(A | B) = 2/32

⇒ P(A | B) = 1/16

3) To find: P(did not catch a cold | did not exercise)

⇒ P(B | A) = P(B ∩ A) / P(A)

⇒ P(B | A) = [tex]\frac{ \frac{2}{50} }{ \frac{12}{50} }[/tex]

⇒ P(B | A) = 2/12

⇒ P(B | A) = 1/6

4) Since P(B | A) ≠ P(B)

i.e., P(did not catch a cold | did not exercise) ≠ P(did not catch a cold)

This means, the events "did not exercise" and "did not catch a cold" are dependent.

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Answer:   x = 30

==========================================================

Explanation:

When adding three angles of any triangle, they always add up to 180

3x+2x+x = 180

6x = 180

x = 180/6

x = 30

This then means,

This triangle is a 30-60-90 triangle.

Answer:

23ft longer

Step-by-step explanation:

The shorter piece is 15 feet, while the longer piece is 25 feet

Let the longer piece be y, and the shorter piece be x.

So, we have:

[tex]x + y = 40[/tex] --- the length of the rope

[tex]y =2x - 5[/tex] --- the relationship between the short and the long piece

Substitute 2x - 5 for y in [tex]x + y = 40[/tex]

[tex]x + 2x - 5 =40[/tex]

[tex]3x - 5 =40[/tex]

Add 5 to both sides

[tex]3x =45[/tex]

Divide both sides by 3

[tex]x =15[/tex]

Substitute 15 for x in [tex]y =2x - 5[/tex]

[tex]y =2 \times 15 -5[/tex]

[tex]y =30 -5[/tex]

[tex]y =25[/tex]

Hence, the shorter piece is 15 feet, while the longer piece is 25 feet

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Answer:

[tex]y=-\frac{5}{3} x+5[/tex]

Step-by-step explanation:

Points on the graph: (0, 5) and (3, 0)

Slope:

m=(y2-y1)/(x2-x1)

m=(0-5)/(3-0)

m= (-5)/3

m= -5/3

Slope-intercept:

y - y1 = m(x - x1)

y - 5 = -5/3(x - 0)

y - 5 = -5/3x

y = -5/3x + 5

Answer: 89,596

Step-by-step explanation:Hope I helped

Step-by-step explanation:

First

since its follow the pattern Intercept Max... Intercept Min...

Its a positive sine graph

Asin(B(x-0))<0.25

A=1

B=2π/period

period From the graph = 2π

B=2π/2π

B=1

Sin(x)<0.25

I'd go with C.

Answer:

mode-6

median-5.5

range-7

Answer:

The first one is correct.

The unit rate is 18 commercials per hour.

A division is a process of splitting a specific amount into equal parts.

On Saturday morning, Wendy watched one and a half hours of her favorite shows on television.

During the shows there were 27 commercials.

We need to find the unit rate of commercials per hour.

To find this we have to divide 27 by number of hours

27/[tex]1\frac{1}{2}[/tex]

Convert [tex]1\frac{1}{2}[/tex] to improper fraction

27/(3/2)

When whole number is divided by fraction, the denominator is multiplied with whole number

27×2/3

54/3

18

Hence, the unit rate is 18 commercials per hour.

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Answer:18 commercials per hour

Step-by-step explanation:

Answer:

Use L x W x H

Step-by-step explanation:

So...

5 x 12 x 8 = 480

Answer: The largest number of groups they can be split into and have the same number of boys and girls on each team is 6 groups with 2 boys and 2 girls in each group.

Answer:

-14

Explanation:

3 x -3 - 5 = -14

Answer:

-14, -5, 4, and 13

Step-by-step explanation:

For each x value, substitute it for x in the equation.

For the first one where x = -3,

y = 3(-3) - 5

y = -9 - 5

y = -14

So the first one is -14. The next x value is 0

y = 3(0) - 5

y = 0 - 5

y = -5

Second one is -5. The next x value is 3

y = 3(3) - 5

y = 9 - 5

y = 4

Third is 4. The next x value is 6

y = 3(6) - 5

y = 18 - 5

y = 13

So the last one is 13.

Answer:

56.55 in is the answer

Hope this helps

Have a good day :)

Step-by-step explanation:

Answer:

your answer is right

Step-by-step explanation:

adjacent angles = angles with a common side and corner point

Answer:

u are correct bc adjacent means: next to or adjoining something else.

hope u get a good mark gl

Step-by-step explanation:

Answer:

O V=3(10XB)(12)

Step-by-step explanation:

Answer:

A 50% chance.

Step-by-step explanation:

After subtracting 1 yellow sock and 1 blue sock, there are 11 blue and 11 yellow socks left.

So a 22 sock total.

The probability of picking another blue sock on the third try is the ratio of blue socks to total socks:

11/22 = 1/2=50%

The price of a seven minute call direct to New York, in the evening, is given as follows:

$5.82.

The cost of the call is obtained considering the information given in the table, for which the proportions are applied.

We have a direct call, meaning that it is a person-to-person call, thus the flat rate is of $3.00 per minute.

Then the minute proportions, considering that the call happens in the evening, are given as follows:

A seven minute call is composed by six additional minutes after the first, hence the total cost is obtained as follows:

0.38 x 3 + 6 x 0.26 x 3 = $5.82.

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Answer:

6√2

Step-by-step explanation:

-√2×2×2 -√2×3×3×3 + 2√3×3

-2√2 - 3✓6 + 2×3

-2√2 - 3√2×2 +2 + 6

6√2

After simplification we got the above expression in the form 3f + 16m -56

The word "simplify" implies to turn something in a simpler form.

In mathematics, simplify an expression means write an expression in such a way that is comparatively less complicated than before. The main purpose of simplify an expression is to make it easy to solve as well as calculation.

3f + 8(2m-7)

we rearrange the expression by removing the parenthesis.

we remove the parenthesis by multiplying the factors.

3f + 8 × 2m - 8 × 7

3f + 16m -56

the above expression has no like terms to add or subtract so it is kept in this form.

Hence, 3f + 16m -56 is the simpler form.

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Answer:

The answer is A

Step-by-step explanation:

The shape is a rhombus when plotted on a quardanent plane. The shape is similar to a diamond.

Answer:

Mrs. Perry

Step-by-step explanation:

find the ratio by dividing the petunias by the daffodils

Ms. H =3

Mr. M = 3.5

mrs. P= 3.75

Answer:

B

Step-by-step explanation:

Its B

Answer:

(3,5,4)

Step-by-step explanation:

B

Answer:

40 failed

Step-by-step explanation:

2/3 of 120 is 80, so you subtract the 80 who passed from the 120 total to get 40 students who failed

Answer:

Step-by-step explanation:

If [tex]\frac{2}{3}[/tex] passed the exam then:

[tex]\frac{3}{3} -\frac{2}{3} = \frac{1}{3}[/tex] failed the exam

now to find the number which failed we multiply:

[tex]\frac{1}{3} \cdot 120 = 40[/tex] and 40 is our answer

Answer:

The p-value is of 0.046 < 0.05, which means that there is a low probability of the results happening by random chance, and thus there is significant evidence to conclude that the new formula cleaned the shirts significantly better than the old formula.

Step-by-step explanation:

If the p-value is less than the significance level, it means that there is a low probability of the results happening by random chance.

In this question:

The p-value is of 0.046 < 0.05, which means that there is a low probability of the results happening by random chance, and thus there is significant evidence to conclude that the new formula cleaned the shirts significantly better than the old formula.

Answer:

[tex]5370^{0}=1 [/tex] is a required answer.

Answer:

Step-by-step explanation:

Steps to find the equation of a line from two points:

   1) Find the slope using the slope formula. ...

   2) Use the slope and one of the points to solve for the y-intercept (b). ...

   3) Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = MX + b) to get the equation for the line.

The numeric value of the expression ((2.1)² + 5.2 - 7.2) x 7.1 is given as follows:

17.1.

The expression for this problem is defined as follows:

((2.1)² + 5.2 - 7.2) x 7.1

The precedence of operators follows the PEMDAS acronym, as follows:

Hence the parenthesis takes precedence, thus:

(2.1)² + 5.2 - 7.2.

Then the power takes precedence, thus:

(2.1)² + 5.2 - 7.2 = 4.41 + 5.2 - 7.2

Addition and subtraction can be done in any order, hence:

4.41 + 5.2 - 7.2 = 2.41.

Then the multiplication is given as follows:

2.41 x 7.1 = 17.1.

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Therefore the solution of the given question of equation comes out to be the object will hit the ground after 6 seconds.

Two variables that are equal—one on each side of a "equals" sign—are represented mathematically by an equation. Equations can be used to solve problems in daily life. To tackle challenges in real life, we frequently seek pre algebra assistance. The very foundation of mathematics is pre-algebra.

Here,

Given : -4.9t² + 2.94t + 25.48

Then,

To find the When does the object strike the ground :

We get :

=> -4.9t² + 2.94t + 25.48 = 0

Using discriminant formula

We find the value of t:

=> t = -19.6 ±[tex]\sqrt{19.6^{2} - 4 (-4.9)(25.48)}[/tex] /  2(-4.9)

=> t =-2 or 6

So we neglect -2

So solution for t = 6 seconds

Therefore the solution of the given question of equation comes out to be the object will hit the ground after 6 seconds.

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