You can use the notation P(A), read “the probability of event B, given event A” to write a conditional probability. The correct answer is C.
Conditional probability refers to the probability of one event occurring given that another event has already occurred. In this case, we are interested in the probability of event B occurring given that event A has already occurred, and we can represent this using the notation P(B|A), where '|' means 'given'.
For example, let's say we are interested in the probability of getting a head on a coin toss (event B), given that the coin was flipped and landed on heads (event A). We could represent this using the notation P(B|A). The value of P(B|A) would be 1, because if the coin already landed on heads, then the probability of getting a head on the next flip is certain.
Conditional probability is an important concept in probability theory and is often used in real-world applications, such as predicting the likelihood of a disease given certain symptoms, or the probability of an event occurring given certain conditions.
The correct answer is C.
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A company has recently been hiring new employees. Today the company has 33% more employees than it did a year ago. If there are currently
66,500 employees, how many employees did the company have a year ago?
employees
If the company has 33% more employees than it did a year ago and there are currently 66,500 employees, the number of employees the company had a year ago was proportionately, 50,000 employees.
What is proportion?Proportion refers to the ratio of one quantity or value compared to another.
Proportions are fractional values, representing using fractions, decimals, or percentages.
The current population of a company's employees = 66,500
The percentage increase in the population from last year's = 33%
Proportionately, last year's population = 100%, while this year's population is 133% (100 + 33).
If 66,500 = 133% (1.33), then 100% = 50,000 (66,500 ÷ 1.33)
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What is 3/10 + 1/4 + 4/5 enter your answer in the box as a mixed number in simplest form
Answer:
[tex]1 \frac{7}{20} [/tex]
Step-by-step explanation:
Well you should find a common denominator for 10, 4 and 5 first to be able to mix them. Let's take 20 because it's the smallest number we can convert 10, and 4 and 5 to.
So
[tex] \frac{3 \times 2}{10 \times 2} + \frac{1 \times 5}{4 \times 5} + \frac{4 \times 4}{5 \times 4} [/tex]
And you get
6/20 + 5/20 + 16/20 (now you can add them because they all have 20 as denominator) so = 27/20 = 1 7/20
Do the following using Matlab: Generate 10 numbers between 1 and 6, calculate the mean. Generate 100 numbers between 1 and 6. calculate the mean. Generate 1000 numbers between 1 and 6, calculate the mean. There is a command in Matlab to generate numbers. Do not include the numbers when you submit the project. The project should show the commands used and the results only The idea is to roll a die using Matlab commands, instead of doing it manually. Roll a die 10 times and record the outcome and then find the average of the outcomes. Then compare the means for the cases of 10, 100 & 1000. On page 2 of lecture 10, we found that the mean of rolling a die to be 3.5. Therefore, your answer will be close to 3.5 every time you repeat the experiment for larger numbers.
We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.
We have,
To generate numbers between 1 and 6 in Matlab, we can use the "randi" command.
To generate 10 numbers, we can use:
```matlab
numbers10 = randi([1, 6], [1, 10]);
mean10 = mean(numbers10);
disp(mean10);
```
To generate 100 numbers, we can use:
```matlab
numbers100 = randi([1, 6], [1, 100]);
mean100 = mean(numbers100);
disp(mean100);
```
To generate 1000 numbers, we can use:
```matlab
numbers1000 = randi([1, 6], [1, 1000]);
mean1000 = mean(numbers1000);
disp(mean1000);
```
After running these commands, we will get the means for generating 10, 100, and 1000 numbers between 1 and 6.
As mentioned in the question, the mean of rolling a die is 3.5.
Therefore,
We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.
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Each week, Nursen saves $5 and shares $3.75. She also spends $4.95 on bus fare to get home from music lessons. This week she earned $24 babysitting. How much money does Nursen have left that she can spend?
Answer: In one week, Nursen saves $5 and shares $3.75, so she has $5 + $3.75 = $8.75 per week.
She spends $4.95 on bus fare, so she has $8.75 - $4.95 = $3.80 per week to spend.
This week, Nursen earned $24 babysitting, so she has an additional $24 to spend.
Therefore, Nursen has $3.80 + $24 = $27.80 to spend.
Step-by-step explanation:
Write in terms of x and y only.
Result:
sin(tan⁻¹(x) - tan⁻¹(y)) in terms of x and y only = (x - y) / (1 + xy).
How do we express the equation in term of x and y?For us to write the expression, we shall use this formular formula:
tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))
where:
a = tan⁻¹(x)
b = tan⁻¹(y)
Next, we have:
tan(tan⁻¹(x) - tan⁻¹(y)) = (tan(tan⁻¹(x)) - tan(tan⁻¹(y))) / (1 + tan(tan⁻¹(x))tan(tan⁻¹(y)))
= (x - y) / (1 + xy)
From both sides, we have sine:
sin(tan⁻¹(x) - tan⁻¹(y)) = sin(tan(x - y / 1 + xy))
So, sin(tan⁻¹(x) - tan⁻¹(y))
= sin(tan⁻¹(x) - tan⁻¹(y))
= (x - y) / (1 + xy) in terms of x and y.
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help please
(instructions: chose from the word bank below to describe the type of multiplication being used. you may use an answer more than once.)
[ identity commutative associative inverse distributive]
1. 14 x 6 = 6 x 14 ________
2. 4(5 + 7) = (4 x 5) + (4 x 7) ________
3. 8 x 1 = 8 ________
4. 7 x (6 x 2) = (7 x 6) x 2 ________
5. 12 x 3 = 3 x 12 ________
6. 1/8 x 8/1 = 1 ________
7. 1 x 9 = 9 ________
8. 3 x (7 x 2) = (3 x 7) x 2 ________
9. 2(8 + 5) = (2 x 8 ) + (2 x 5) ________
(page 2)
(instructions: choose the correct multiplication property for the problems below)
10. which property is demonstrated below?
12 x 1 = 12
A. identity
B. commutative
C. associative
D. inverse
E. distributive
11. which property is demonstrated below?
2/5 x 5/2 = 1
A. identity
B. commutative
C. associative
D. inverse
E. distributive
12. which property is demonstrated below
5 x 8 = 8 x 5
A. identity
B. commutative
C. associative
D. inverse
E. distributive
13. which property is demonstrated below?
8 x (7 x 9) = (8 x 7) x 9
A. identity
B. commutative
C. associative
D. inverse
E. distributive
14.which property is demonstrated below?
4(6 + 3) = (4 x 6) + (4 x 3)
A. identity
B. commutative
C. associative
D. inverse
E. distributive
The blanks are filled as follows
1. Commutative
2. Distributive
3. Identity
4. Associative
5. Commutative
6. Inverse
7. Identity
8. Associative
9. Distributive
10. A. Identity
11. A. Identity
12. B. Commutative
13. C. Associative
14. E. Distributive
What is distributive law of multiplication?The distributive law of multiplication is a distinct attribute in mathematics that distinguishes how multiplication interacts with the operations of addition or subtraction.
It is exemplified in the problem as
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A 138 foot antenna is on top of the top of a tall building. From a point on the ground, the angle of elevation to the top of the antenna is 30.5ﾟ while the angle of elevation to the bottom of of the antenna from the same point is 23.5ﾟHow tall is the building
Answer:
289
Step-by-step explanation:
Let's call the height of the building "h" and the distance from the point on the ground to the base of the building "d".
From the point on the ground, the distance to the top of the antenna is d + 138, and the distance to the bottom of the antenna is d.
Using trigonometry, we can set up two equations:
tan(30.5°) = (d + 138) / h (1)
tan(23.5°) = d / h (2)
We can solve equation (2) for d:
d = h tan(23.5°)
Substituting this into equation (1), we get:
tan(30.5°) = (h tan(23.5°) + 138) / h
Simplifying:
tan(30.5°) = tan(23.5°) + 138/h
tan(30.5°) - tan(23.5°) = 138/h
h = 138 / (tan(30.5°) - tan(23.5°)) ≈ 289.12 feet
Therefore, the height of the building is approximately 289.12 feet.
Which pair of points are both located less than 3 units from the point (3,8) on a coordinate grid?
The required pair of points that are both located less than 3 units from points (3, 8) is (2, 7).
Following the condition given in the question,
Assuming there are 3 points on the graph beside (3, 8) are (2, 7), (5, 5), and (6, 10)
The distance formula between two points is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
So, for each point, we can plug in the coordinates and simplify the following:
Point (2, 7):
d = √[(2 - 3)² + (7 - 8)²]
d = √[1² + 1²]
d = √2 (<3)
Points (6, 10):
d = √[(6 - 3)² + (10 - 8)²]
d = √[3² + 2²]
d = √13 (>3)
Point (5, 5):
d = √[(5 - 3)² + (5 - 8)²]
d = √[2² + 3²]
d = √13 (>3)
Point (1, 1):
d = √[(1 - 3)² + (1 - 8)²]
d = √[(-2)² + (-7)²]
d = √53 (>3)
Thus, the pair of points that are both located less than 3 units from points (3, 8) is (2, 7).
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An appropriate tip for a waiter at a restaurant is at least 15%. For a tab of $20, how much money should be left, including tip?
An appropriate tip for a waiter at a restaurant is at least 15% of the total bill. For a tab of $20, the tip would be:
Tip amount = 15% of $20
Tip amount = 0.15 x $20
Tip amount = $3
Therefore, the total amount of money that should be left, including tip, is:
$20 (tab) + $3 (tip) = $23.
Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run?
A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by.
Select all that apply.
You know the difference in the distances the boys ran, so this is a subtraction problem.
You are finding the total distance the boys ran, so this is an addition problem.
Dean ran part of the distance Sam ran, so this is a multiplication problem.
The correct equation is s + 2.3 = 6.8.
The correct equation is s – 2.3 = 6.8.
The correct equation is 2.3s = 6.8.
Answer:
A,E
Step-by-step explanation:
Operation: Minus
To find how far Sam ran, we need to subtract 2.3 from Dean's distance of 6.8 km.
6.8 km - 2.3 km = 4.5 km
Therefore, Sam ran 4.5 km, since Dean ran 2.3 km fewer than Sam.
Answer:
a and e
Step-by-step explanation:
got it right on homework
How many 1/4 cups of water fit inside of a 2 1/2 cup water bottle?
Answer:
There are 10 1/4 cups of water that fit inside a 2 1/2 cup water bottle.
To see why, note that 2 1/2 cups is equivalent to 10 quarter cups (2 x 4 = 8 and 8 + 2 = 10). Therefore, you can fill the water bottle with 10 1/4 cups of water.
Select the correct answer. What is the solution to 4|x − 3| + 1 = 1? A. x = 3 B. x = 3 or x = 4 C. x = 3 or x = 6 D. No solutions exist.
Answer:
a
Step-by-step explanation:
Please find the surface area of this figure. Ps pls show your work on how you got your answer or explain.
Answer:
2(1/2)(11)(13) + 2(1/2)(10)(13.2) + 10(11)
= 143 + 132 + 110 = 385 square feet
B is the correct answer.
The histogram displays the ages of 50 randomly selected users of an online music service. Based on the data, if the service has 25,000 users, how many of them are 30 and older?
The number of users that are 30 and older is 10,500.
We have,
From the histogram,
The number of users that are 30 and older.
= 7 + 9 + 3 + 2
= 21
Now,
The percentage of 30 and older users.
= 21/50 x 100
= 21 x 2
= 42%
Now,
Total users = 25,000
So,
The percentage of 30 and older users.
= 42% of 25,000
= 42/100 x 25,000
= 42 x 250
= 10500
Thus,
The number of users that are 30 and older is 10,500.
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Triangle ABC shown below has m∠B=36∘, a=5, and c=13. Find the area of the triangle.
Answer: 19.1 is correct
Step-by-step explanation:
where a and c are the lengths of two sides of the triangle and C is the angle between them. To use this formula, we need to find side b and angle A.
We can use the Law of Cosines to find side b:
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional
fee of $200.25 for each ton of sugar.
The second company charges $4995 to rent trucks plus an additional fee of $225.50 for each ton of sugar.
For what amount of sugar do the two companies charge
the same?
What is the cost when the two companies charge the
same?
$
Let’s solve this problem by setting the cost of the two companies equal to each other and solving for the amount of sugar. Let x be the amount of sugar in tons.
The cost for the first company is 5500 + 200.25x and the cost for the second company is 4995 + 225.50x.
Setting these two expressions equal to each other, we get:
5500 + 200.25x = 4995 + 225.50x
Solving for x, we get:
25.25x = 505
x = 20
So, the two companies charge the same when the amount of sugar is 20 tons.
The cost when the two companies charge the same is:
5500 + 200.25 * 20 = $9505
So, when the two companies charge the same, the cost is $9505.
Received message. Let's solve this problem by setting the cost of the two companies equal to each other and solving for the amount of sugar. Let x be the amount of sugar in tons. The cost for the first company is 5500 + 200.25x and the cost for the second company is 4995 + 225.50x. Setting these two expressions equal to each other, we get: 5500 + 200.25x = 4995 + 225.50x Solving for x, we get: 25.25x = 505 x = 20 So, the two companies charge the same when the amount of sugar is **20 tons**. The cost when the two companies charge the same is: 5500 + 200.25 * 20 = $9505 So, when the two companies charge the same, the cost is **$9505**.
MARK ME BRAINLEISTSelective serotonin reuptake inhibitors (SSRIs) are drugs that
Oprevent unused neurotransmitters from being transported back to the neuron.
increase reuptake of unused serotonin
Ostrengthen the effect of a neurotransmitters by mimicking it at the receptor site.
block effects of neurotransmitters by binding to receptors without activating them.
Selective serotonin reuptake inhibitors (SSRIs) are drugs that A. prevent unused neurotransmitters from being transported back to the neuron.
What are Selective serotonin reuptake inhibitors ?By inhibiting the serotonin transporter, SSRIs prevent the reuptake of serotonin into neurons after synapse release, thereby increasing available serotonin in the brain. Such changes help to alleviate symptoms associated with anxiety, depression and other mood disorders.
Overall, a rise in serotonin activity is significant in transforming an individual's mood pattern. When more serotonin remains within synapses, it binds with and activates its receptors, leading to increased levels of hormonal activity proven to be effective in treating various mood imbalances in patients.
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A manufacturer cuts a piece of metal for a microscope. The resulting piece of metal can be
represented in a coordinate plane by a triangle with vertices A (8,8), B(5, 3), and C(11,3)
. One unit in the coordinate plane represents one millimeter.
Prove that AABC is isosceles.
Find the exact length of each side.
AB =
BC =
AC =
We can actually see here that the triangle ABC is an isosceles triangle. This is because two sides of the triangle are equal.
What is an isosceles triangle?An isosceles triangle is actually a geometric shape having three sides, two of which are equal in length. Consequently, two of the angles that are across from those sides are also equal.
In order to prove that the triangle is an isosceles triangle, we will find the following:
Distance between vertices A and B:
AB = √((8-5)² + (8-3)²) = √(3² + 5²) = √34 = 5.83mm
Then, we also find the distance between vertices B and C:
BC = √((11-5)² + (3-3)²) = 6mm
Finally, we find the distance between vertices A and C:
AC = √((11-8)² + (3-8)²) = √(3² + 5²) = √34 = 5.83mm
Thus, we see here that AB and AC are actually equal which makes the triangle an isosceles.
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At Dela's Deli, Dela fills containers with homemade vinaigrette salad dressing. The table shows the amount of vinegar and olive oil used for the dressing.
Number of containers Vinegar (tsp) Olive Oil (tsp)
1 4 12.5
6
At this rate, how much vinegar and olive oil will be used to make 6 containers of salad dressing?
Dela will use 10 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 10 teaspoons of vinegar and 18.5 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 18.5 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
We have,
Dela uses a ratio of 4 teaspoons of vinegar to 12.5 teaspoons of olive oil.
So, for 6 containers
= 4 x 6
= 24 teaspoons of vinegar
and, = 12.5 x 6
= 75 teaspoons of olive oil
Thus, Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
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Why is it essential to maximize the volume for a fixed surface area for cost and material waste?
It is essential to maximize the volume for a fixed surface area for cost and material waste.
Because it can help to optimize the efficiency of material usage and minimize the cost of production.
In many manufacturing and construction processes, the cost of materials is a significant expense.
By maximizing the volume of an object for a fixed surface area, we can reduce the amount of material needed to construct the object.
This means that we can save money on material costs and reduce waste by using fewer materials overall.
In addition, minimizing the surface area of an object for a fixed volume can also help to reduce production costs.
This is because the surface area of an object is often a factor in determining the time and labor required to produce it.
By minimizing the surface area, we can reduce the amount of time and labor needed to produce the object.
Which can help to reduce production costs.
Therefore, maximizing volume for fixed surface area is an essential consideration in many manufacturing and construction processes.
It help to optimize material usage, minimize waste, and reduce production costs.
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Find the missing angle
Answer:
I Think 62°
Step-by-step explanation:
If the diameter of a circle is 8.4 in.. find the area and the circumference of the circle. Use 3.14 for pl. Round your answers to the nearest
hundredth.
Given that the diameter of a circle is 8.4 inches.
The radius (r) of the circle can be found by dividing the diameter by 2:
r = d/2 = 8.4/2 = 4.2 inches
The area (A) of a circle can be found using the formula:
A = πr^2
Substituting the value of r, we get:
A = 3.14 x 4.2^2 = 55.3896 ≈ 55.39 square inches
The circumference (C) of a circle can be found using the formula:
C = 2πr
Substituting the value of r, we get:
C = 2 x 3.14 x 4.2 = 26.3896 ≈ 26.39 inches
Therefore, the area of the circle is approximately 55.39 square inches and the circumference of the circle is approximately 26.39 inches.
We know that the area of a circle is given by the formula A = π×r²
Given the diameter of the circle = 8.4 in
Therefore radius of the circle = 8.4/2 = 4.2 in (diameter/2 = radius)
Now Area of the circle = π × 4.2²
= 3.14 × 17.64
= 55.3896
= 55.39 (round up to the nearest hundredth)
Circumference of the circle = 2 × π × r
= 2 × 3.14 × 4
= 26.376
= 26.38 (round up to the nearest hundredth)
Therefore the area of the circle is 55.39 in² and the circumference is 26.38 in.
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Hurry up please time limit
State the domain and range and tell if the graph is a function yes or no?
What’s the domain and range ?
Answer:No, X=-3, yly =-4,0,4
Step-by-step explanation:
30 POINTS ANSWER FOR BRAINLIST
Solve m^2 − 6m = 3. Use the Quadratic Formula. Leave your answers as simplified radicals.
Answer:
To solve m^2 - 6m = 3 using the quadratic formula, we first need to put the equation in standard form, which is ax^2 + bx + c = 0.
m^2 - 6m - 3 = 0
Now we can identify a, b, and c:
a = 1, b = -6, c = -3
Next, we can plug these values into the quadratic formula:
m = (-b ± sqrt(b^2 - 4ac)) / 2a
m = (-(-6) ± sqrt((-6)^2 - 4(1)(-3))) / 2(1)
m = (6 ± sqrt(48)) / 2
Simplifying the square root of 48, we get:
m = (6 ± 4sqrt(3)) / 2
Now we can simplify by factoring out a 2 from the numerator:
m = 3 ± 2sqrt(3)
So the solutions to the equation are:
m = 3 + 2sqrt(3) or m = 3 - 2sqrt(3)
Step-by-step explanation:
Answer: 3±2√3
Step-by-step explanation:
see image for explanation
Let me know if you more explanation with simplifying the root. That is a whole lesson in itself.
∠A and ∠B are vertical angles. If m ∠ A=(2x−2) ∘ and B=(3x−15) ∘ , then find the value of x
The value of x is 13°
What are Vertical Angles?When two lines intersect, four angles are formed. There are two pairs of nonadjacent angles. These pairs are called vertical angles.
In a coordinate plane, a line parallel to the Y-axis is called Vertical Line. It is a straight line which goes from top to bottom and bottom to top. Any point in this line will have the same value for the x-coordinate.
We have:
The angles are:
m ∠ A=(2x−2) ∘ and ∠ B=(3x−15) ∘
We have to find the value of x
Now, We know that :
m ∠A = m ∠B (Def. of Vertical Angles)
(2x−2) = (3x−15)
Combine the like terms:
2x - 3x = -15 + 2
-x = -13
x = 13
The value of x is 13°
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Michael checked several websites and stores around town for the television he wanted to purchase. He saw eight different prices: $273 $267 $276 $297 $264 $294 $264 $269 What is the mean, median, and mode of this data set?
The mean is 270.75 and the median is 271. While there is no single mode, then we conclude that our mode is 264 and 294 respectively.
Understanding how to calculate mean, median, modeBy definition:
Mean is the sum of all the numbers in the set divided by the total number of numbers.
Median is the middle value in the set when the numbers are arranged in order.
Mode is the number that appears most frequently in the set.
If we re-arrange the data given in ascending order, we have:
264 264 267 269 273 276 294 297
To calculate Mean:
Add up all the numbers and divide by the total number of numbers:
Mean = (264 + 264 + 267 + 269 + 273 + 276 + 294 + 297) / 8
Mean = 270.75
To calculate Median:
We need to find the middle number in the set. Since there are 8 numbers in the set, the median is the average of the 4th and 5th numbers:
Median = (269 + 273) / 2
Median = 271
To calculate Mode:
We need to determine which number appears most frequently in the set. In this case, there are two numbers that appear twice (264 and 294), and the rest of the numbers appear only once. Therefore, there is no single mode for this data set.
Mode = 264 and 294
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Abdoulaye is planning to drive from City X to City Y. The scale drawing below shows the distance between the two cities with a scale of 1 inch = 5 miles. City X and City Y are 11/2 between
City X ---------- 11/2 ------------- City Y
What is the actual distance between the two cities?
The actual distance between the two cities is [tex]7\frac{1}{2}[/tex] miles .
What is the actual distance?A scale drawing is the reduced version of a larger image. The scale drawing is reduced at a constant proportion to the original image using a scale. An example of a scale drawing is a map of the city.
Actual distance between the cities can be determined by multiplying the distance in the scale drawing by the scale.
Actual distance = 1[tex]\frac{1}{2}[/tex] x 5
= [tex]\frac{3}{2}[/tex] x 5 = [tex]\frac{15}{2}[/tex] = [tex]7\frac{1}{2}[/tex] miles
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Please help its due soon
The ratio of sec θ is determined as 5/3.
option A.
What is the ratio of secθ?The ratio is sec θ is calculated by applying the following method;
sec θ = 1/cosθ
Given that tanθ = -4/3 = oppo/adjacent
The hypotenuse side is calculated by applying Pythagoras theorem as shown below;
h = √ 4² + 3²
h = 5
The ratio of sec θ is calculated as follows;
sec θ = 1/cosθ
1/cosθ = 1/(3/5)
1/cosθ = 5/3
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in a certain lottery, you must correctly select 6 numbers (in any order) out of 39 to win.
The calculated value of the probability of winning is 3.06501854e-7
Calculating the probability of winningFrom the question, we have the following parameters that can be used in our computation:
Select 6 numbers out of 39 to win
This means that when a number is selected, the number is returned and the total numbers reduces by 1
i.e. P(Current) = n/(39 - n)
Using the above as a guide, we have the following:
P(Win) = 6/39 * 5/38 * 4/37 * 3/36 * 2/35 * 1/34
Evaluate the product of tthe expressions
So, we have
P(Win) = 3.06501854e-7
Hence, the probability of winning is 3.06501854e-7
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Complete question
In a certain lottery, you must correctly select 6 numbers (in any order) out of 39 to win You purchase one lottery ticket What is the probability that you will win?
The probability of winning is
I REALLY NEED THIS IMMEDIATELY PLEASE HELP !
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Patrica is building a garden in her backyard that is shaped like a triangle. She has already built two sides of the garden and they have lengths of 6 feet and 7 feet.
Answer:
Step-by-step explanation:
The third side of Patricia's garden should be approximately 10.64 feet long.
To determine the length of the third side of Patricia's garden, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we have two known side lengths (6 feet and 7 feet) and the angle between them (110 degrees).
The Law of Cosines states that for a triangle with side lengths a, b, and c, and angle C opposite side c:
c² = a² + b² - 2ab*cos(C)
We want to find the length of the third side, so let's call it c. Plugging in the known values:
c² = 6² + 7 - 267*cos(110°)
Simplifying the equation:
c² = 36 + 49 - 84*cos(110°)
Now, we can calculate the value of cos(110°) using a calculator or trigonometric tables. Once we have that value, we can substitute it back into the equation to find c². Taking the square root of c² will give us the length of the third side.
Note: The value of cos(110°) is approximately -0.342.
c² = 36 + 49 - 84*(-0.342)
c² ≈ 36 + 49 + 28.248
c^2 ≈ 113.248
Taking the square root:
c ≈ √113.248
c ≈ 10.64
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