a track star runs two races on a certain day. the probability that she wins the first race is 0.7, the probability that she wins the second race is 0.6, and the probability that she wins both races is 0.5. what is the probability that: note: define your events, and write the probability statement before you calculate an answer. you can show your work using equations or venn diagrams.

A' = (-1, 3)

B' = (-4, 0)

C' = (1, 6)

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

Reason:

The notation [tex]T_{ < -3, 5 > }[/tex] means "translate 3 units left, 5 units up".

Another way to write out this rule is [tex](\text{x},\text{y}) \to (\text{x}-3,\text{y}+5)[/tex]

-------------------

Let's apply that rule to the coordinates of point A.

[tex](\text{x},\text{y}) \to (\text{x}-3,\text{y}+5)\\\\(2,-2) \to (2-3,-2+5)\\\\(2,-2) \to (-1,3)\\\\[/tex]

Point A' is located at (-1, 3)

-------------------

Repeat for the coordinates of point B.

[tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+5)\\\\(-1,-5)\to(-1-3,-5+5)\\\\(-1,-5)\to(-4,0)\\\\[/tex]

Point B' is located at (-4, 0)

-------------------

Lastly do the same for point C.

[tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+5)\\\\(4,1)\to(4-3,1+5)\\\\(4,1)\to(1,6)\\\\[/tex]

Point C' is located at (1, 6)

Answer:

(8,6×10^-3) (8×10^-1)

=(0,0086). ( 0.8)

The missing angles are as calculated below. Fill them accordingly.

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Check the attached image for labeling

a = 125° (vertically opposite angles are equal)

a + b = 180 (sum of angles on a line)

b = 180 - 125 = 55°

b + c = 90  (sum of angles in a triangle)

c = 90 - 55 = 35°

d = b   (alternate angle)

d = 55°

e =   125° (alternate angle)

Fill in the missing angles accordingly

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Answer: 40°

Step-by-step explanation:

David's method to find the height of the tree is the use of the properties of similar triangles. The height of the tree is approximately 24 feet

According to the laws of reflection, we have;

Angle of incidence of the light from the top of the tree = Angle of the reflected light ray David sees.

The possible values in the question are;

Distance of the mirror from the tree = 37 feet

Distance from where David is standing to the mirror = 9.3 ft.

Height of his eyes above the ground = 6 ft.

Required: Height of Tree

Therefore;

The triangle formed by David's height, the reflected ray from the mirror and his distance from the mirror is similar to the right triangle formed by the tree, which by the relationship of similar triangles, gives;

[tex]\frac{9.3}{37}[/tex] = [tex]\frac{6}{Height of the Tree}[/tex]

Height of the tree × 9.3 = 6 × 37

Height of the tree = [tex]\frac{6 X 37}{9.3}[/tex] = 23.87 ≅ 24 feet

Therefore, the tree is approximately 24 feet tall

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The measure of the longer leg of the triangle is given as follows:

6.93 cm.

The three trigonometric ratios are defined as follows:

The longer leg is opposite to the angle of 60º, hence the sine relation is used to find the length, as follows:

sin(60º) = x/8

x = 8 x sine of 60 degrees

x = 6.93 cm.

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The value of X is 40/3ft, Y is 27/4ft and Z is 469/27ft. The solution has been obtained by using the properties of triangle.

What is a triangle?

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point. The triangle's three angles add up to a total of 180 degrees.

We know that if a line is parallel to the third side of the triangle, then the ratio of the sides is equal.

So,

⇒10/6 = x/8

⇒80/6 = x

⇒40/3 = x

Similarly,

⇒y/10 = 9/(40/3)

⇒y/10 = 27/40

⇒y = 27/4

Similarly,

⇒y/(y+10) = 7/z

⇒(27/4)/((27/4)+10) = 7/z

⇒469/27 = z

Hence, the value of X is 40/3ft, Y is 27/4ft and Z is 469/27ft.

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Using the laws of exponential used to simplify the expression, we have; 1/x^2.

When a given expression has an exponent, this implies that the degree of one of its variable is more than 1. So that the laws of exponent which is also law of indices can be used to determine the required simplification of the expression if required.

From the given question, we have;

x^3/ x^5

So that from the law of indices,

x^3/ x^5 = x^3 x^-5

              = x^(3 - 5)

              = x^-2

From the inverse law of exponent,

x^-2 = 1/ x^2

Using the law of exponents, the simplified form of the expression is 1/ x^2.

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The value of average rate of change of y = 0.5x - 3 over the interval

- 3 ≤ x ≤ 4 is, 0.5.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The function is,

⇒ y = 0.5x - 3

Now, The average rate of change is,

⇒ y = 0.5x - 3

⇒ dy / dx = 0.5

Hence, The value of average rate of change of y = 0.5x - 3 over the interval  - 3 ≤ x ≤ 4 is, 0.5.

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The required measure of the smallest angle in the triangle is 37°.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The sum of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

We know that one angle in right angled triangle is 90 degree and sum of other two angle is 90 degree.

So, acute angles are (2x -3) and (3x-7).

Then

(2x -3) +  (3x-7) = 90

5x - 10 = 90

5x = 100

x = 20

Smallest angle = 2x - 3

= 2(20) - 3

= 40 - 3

= 37°

Thus, required Smallest angle is 37°

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Answer: $6

Step-by-step explanation:

60% of 3.75

3.75 * 0.60 = 2.25

2.25 + 3.75 = 6

Step-by-step explanation:

The answer is 2.25 because 60% of 3.75 is equal to 2.25

The length of Sarah's drawing is given by the following equation:

0.1g = 0.8.

The scale of the drawing is obtained applying the proportions in the context of this problem.

The scale is defined as the division of the drawn length by the actual length.

Sarah's drawing has a scale factor of 1 inch to 0.1 inch, meaning that each inch she draws has an actual length of 0.1 inch.

The rule of three is defined as follows:

1 inch - 0.1 inches

g inches - 0.8 inches

Hence the equation is:

0.1g = 0.8.

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Answer:    It is the last one on he far right.

Step-by-step explanation:

;)

Answer: y = x - 2

Step-by-step explanation:

The equation representing the relationship between the ages of Debra and Pam is y = x + 2. This is determined by analyzing the table provided, which shows the ages of Pam (x) and Debra (y) in years. From the table, we can see that for every 1 year increase in Pam's age, Debra's age also increases by 1 year. This is represented in the equation y = x + 2, where y (Debra's age) is equal to x (Pam's age) plus 2 years. This equation is supported by the data in the table, as all of the ordered pairs (x, y) in the table satisfy the equation y = x + 2.

Answer:

Obtuse and isosceles

Step-by-step explanation:

Cuz 2 sides and angles are equal and there is one obtuse angle

Answer:

obtuse and isoscelies

Step-by-step explanation:

120 is greater than 90 so obtuse

isoscelies means to sides of equal length and one of different length

2 sides are 3ft and one is 5ft

The maximum number of philodendron plants that will occupy the whole area is 256.

The term area in math is defined as the region bounded by the shape of an object

Here we have given that your mother is very fond of collecting rare philodendron and here we have know that If she has a garden which measures 100 m² and each philodendron will occupy an estimated area of 0. 6 x 0. 6 m of the garden.

Here we have to 10 meters divided by 0.6 of a meter gives 16 philodendrons in one direction and the same number in the other direction.

Then the maximum number of plants is calculated as,

=> 16 x 16 = 256

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the average rate of change of the function over the interval 1 ≤ x ≤ 9​ is 3.75.

It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

Given the function g(x)=-x²+5x+14, within the interval 1 ≤ x ≤ 9

At the lower interval x = 1

g(x) = -1 +5 + 14

g(x) = 18

At the lower interval x = 9

g(x) = -9²+5*9+14

g(x) = -22

The average change of the function will be expressed as:

Δy/Δx = (-22 - 8)/ (9-1)

Δy/Δx = -30/8

Δy/Δx = 3.75

therefore, the average rate of change of the function over the interval 1 ≤ x ≤ 9​ is 3.75.

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The rational exponent form is 5^3/5x. Option D

We know that a rational function would be the function that does not have the radical sign in it. We can see that we have the expression that have been written for us here as; 5√125x^5.

When we open up the radical we would have;

125^1/5 * 5^5/5

But we know that;

125 = 5^3

We now have;

5^3/5 * x

This becomes;

5^3/5x

Thus we are going to end up in the rational exponent form of the expression as 5^3/5x.

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There is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games and no convincing evidence that her average is less than 80%.

Based on the dot plot of the simulation results, it appears that the player's true probability of sinking at least one ball on her break is not 80%. In the simulation, there were only 12 trials out of 100 where the player sank at least one ball on her break 14 or fewer times in 20 games. This corresponds to a probability of 12/100, or 12%.

Since the player's actual performance in the last 20 games (14 out of 20) is less likely to occur than what was observed in the simulation, we can get the conclusion that the player has a lower than 80% chance of sinking at least one ball during her break.

Therefore, the correct conclusion is, "there is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games. This result is not unusual and there is no convincing evidence that her average is less than 80%."

The question is incomplete. The complete question is 'The player’s true probability of sinking at least one ball on her break is 27%. another 100 simulated trials would show a much different outcome; therefore, we cannot draw any conclusions. it is most likely that she would sink at least one ball during her break exactly 16 times. there is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games. this result is not unusual and there is no convincing evidence that her average is less than 80%.'

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Answer:

d

Step-by-step explanation:

edge 2020

Answer:

[tex]\frac{9}{20}[/tex]

Step-by-step explanation:

45% = [tex]\frac{45}{100}[/tex]

[tex]\frac{45}{100}[/tex] ÷ [tex]\frac{5}{5}[/tex] = [tex]\frac{9}{20}[/tex]

Answer:45%=9/20 I hope this helps

Step-by-step explanation:

45%
By definition p%=p/100 which something like this

45/100

then you Cancel out the common factor 5

45/100 cancel these numbers out by 5

Then you will get your answer which is something like this

9/20

So 45%=9/20 as a fraction

The values in the result of the division operation, 7 ÷ 6 are as follows;

The quotient = 12

The remainder = 4

Please find attached the diagram with the correct values in the boxes created with MS Word

The quotient is the result following the complete division by the devisor. The remainder is the part of the dividend yet to be divided by the divisor.

The division operation is 76 ÷ 6

The quotient is the integer value obtained following the division operation of 76 by 6 which is 12 times. Therefore, the quotient is 12

The values in each box are therefore;

The value at the top left box, is 10

The value in the box below 2 and to the right of 60 is 12

The value outside to the top right of the rectangle is the remainder

The remainder is the difference between the dividend and the product of the quotient and the divisor as follows;

Remainder = 76 - 12 × 6 = 4

The remainder is 4

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The proportion taken by John 3:4 = 5:12 is correct.

The term called proportion in math is defined as the values of the proportion that are close to each other when written in ratio form using a colon.

Here we know that the  a 3-4-5 right triangle and a 5-12-13 right triangle are set by John.

And the taken proportion is written as,

=> 3:4 = 5:12

Here we have to use the Pythagoras theorem to verify this one, then we get,

=> 3² + 4² = 5²

=> 9 + 16 = 25

=> 25 = 25

Now, we have to take the other values and verify that one also,

=> 5² + 12² = 13²

=> 25 + 144 = 169

=> 169 = 169

Therefore the proportion is correct.

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Answer: No real "space" exists. There is plenty of air all around us

Step-by-step explanation: I'm sorry If I am wrong tysm

-☈⊙⌘☿

Answer:

cosmic microwave background radiation

Step-by-step explanation:

The area of the shaded region is equal to 116 sq units.

It is given that we can assume the angles to be right angle. So from the fig we  can see that it is a quadrilateral and  length and breadth for the given figure are different. So the given fig is a rectangle.

The area of a rectangle = length × breadth

∴ The area of the bigger rectangle = 10×20=200 sq units

Similarly,

The area of the smaller rectangle = 14 × 6 = 84 sq units

Now,

The area of the shaded region = Bigger rectangle - Smaller rectangle

⇒ 200 - 84 = 116 sq units

Therefore, The area of the shaded region is equal to 116 sq units.

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Since the value of y can be known from equation 1, we can use the substitution method to solve the system of equations. By entering the value of y in equation 2, we can quickly get the value of x. So the option B is correct.

The system of equation are:

y = 1/2x...................(1)

2x + 3y = 28...................(2)

To solve the system of equation we use substitution method because the value of y is know from the equation 1. We can find easily the value of x by putting the value of y in equation 2.

Now putting the value of y in equation 2.

2x + 3(1/2x) = 28

2x + 3/2 x = 28

7/2 x = 28

Multiply by 2 on both side, we get

7x = 56

Divide by 7 on both side, we get

x = 8

Now putting the value of x in equation 1

y = 8/2 = 4

The solution of the system of equation is (8, 4).

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Answer: 33.93 in

Step-by-step explanation:

we can see it is a right angle there. h is oppsite line of the right triangle and 70in is Hypotenuse. So, we can use the formula sin29 = h/70. Then sin29*70=h. h=33.93 in.

Quantitative variables provide numerical measures of individuals. The measurements yield useful results and can be added to or removed from.

A quantitative variable is one for which the data display amounts (e.g. height, weight, or age). A categorical variable is one where the data indicate categories. As was discussed in the chapter's section on variables, quantitative variables are those that are measured on a numeric scale.

Height, weight, reaction speed, subjective pain rating, temperature, and exam score are a few examples of quantitative variables.

A quantitative study works with numbers and data, whereas a qualitative study concentrates on words and meanings. Variables can be quantified, and hypotheses can be tested quantitatively. You can go more deeply into concepts and experiences by using qualitative research methods.

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The approximate range will be 56.25 gm. after the end of 3 years.

As per the question,

We have, the value of the weight of the bacteria = 450 gm

As the rate of bacteria is decreasing with rate of 1/2

So, after 1 year the number of bacteria will be half as it was at the start of the year.

So, the number of bacteria after 1 year will be = 450 *(1/2)=225

As the rate of bacteria is again decreasing with the rate of 1/2

So, after 2 years the number of bacteria will be half as it was at the start of the year.

So, the number of bacteria after 2 years will be = 225 *(1/2)=112.5

As the rate of bacteria is decreasing with the rate of 1/2

So, after 3 year the number of bacteria will be half as it was at the start of the year.

So, the number of bacteria after 3 years will be = 112.5*(1/2)=56.25

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Answer:

$560

Step-by-step explanation:

if 25% is the discount than the total of the item after the discount is .75x. So to find the original total we need the equation 420=.75x

first we need to isolate x so we divide both sides by .75, doing this will give us 560= x

to check our answer you need to multiply 560 by .75 (which I got by subtracting the discount, .25, from 1) which gives us our discounted total of $420

The probability that the result was a 6 is P(A)=1/3 the die is tossed and we are told that a result is a number greater than 4.

A standard 6-sided die numbered 1 to 6 has 2 sides that meet the criterion of greater than 4, which are 5 and 6. So out of 6, there are 2 ways.

A die has 6 faces with the numbers 1,2,3,4,5 and 6 on each of the six faces. Now consider an unbiased die and the probability of any of the faces appearing in a single roll is 1/6.

So,

P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=1/6

The numbers that are greater than 4 are 5 and 6

So it can be P(5) or P(6)=

P(5)+P(6)=2/6=1/3.

If you had stated at least a 4, then there are three chances which are to be 4,5,6 that meet the criterion, and the chance would be 3/6=1/2.

Hence, by the classical definition of probability, the probability of getting a number more than 4 in a single throw of a die is 1/3.

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