Spinner B is the spinner that has a probability of 1/3 of spinning orange.
How to find the he probability of spinning orange is more than 40%a) For one of the spinners, the probability of spinning orange is 1/3. To identify which spinner this is, we need to find the spinner that has exactly one orange sector out of three total sectors.
From the given spinners, Spinner B is the only spinner that has one orange sector out of three, so Spinner B is the spinner that has a probability of 1/3 of spinning orange.
b) For two of the spinners, the probability of spinning orange is more than 40%. To find these spinners, we need to look for the spinners that have at least three orange sectors out of a total of eight sectors (since 3/8 is greater than 40%).
From the given spinners, Spinner A and Spinner C both have three orange sectors out of eight total sectors, so they are the two spinners for which the probability of spinning orange is more than 40%.
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the visual fraction model shows the fractions of 1 cup of each kind of yogurt thats add to the blender
Therefore , the solution of the given problem of fraction comes out to be 3/4 cups of yoghurt to the blender.
What is a fraction?Any configuration of identically sized parts can be combined to represent the total. In Standard English, quantity is defined as "a portion" within a specific measurement. 8, 3/4. Wholes also include fractions. These serve as the divisor of the ratio, which in mathematical terms would be a pair of numbers. Here are a few illustrations of how to convert simple halves into whole numbers.
Here,
A visual fraction model can be used to illustrate the various fractions in a cup of yoghurt that you want to add in portions to a blender.
For instance, you may divide the cup into four equal parts and use one of those parts to represent 1/4 cup of yoghurt in the blender.
You can divide the cup into two equal parts and display two of those parts to symbolise the addition of 1/2 cup of yoghurt.
You would have added
=> 1/4 + 1/2 = 3/4 cups of yoghurt to the blender.
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50 Points! Multiple choice algebra question. Suppose you deposit $1000 in an account paying 4% annual interest, compounded continuously. Find the balance after 10 years. Photo attached. Thank you!
The balance after 10 years is equal to: A. $1491.82.
How to determine the balance after 10 years?In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):
[tex]A(t) = P_{0}e^{rt}[/tex]
Where:
A(t) represents the future value.P₀ represents the principal.r represents the interest rate.t represents the time measured in years.When time, t = 10 years, the future value can be calculated as follows:
[tex]A(t) = 1000e^{0.04 \times 10}\\\\A(t) = 1000e^{0.4}[/tex]
A(t) = 1000(1.49182469764)
A(t) = 1491.82469764 ≈ $1491.82.
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A spherical balloon has a 20-in. diameter when it is fully inflated. Half of the air is let out of the balloon. What is the volume of the fully-inflated balloon?
The volume of the fully - inflated balloon is 4186.67 cubic inches. The solution has been obtained by using the formula for sphere.
What is a sphere?
The geometric equivalent of a circle in two dimensions in three dimensions is a sphere. A collection of three-dimensional points with the same r separation between them are referred to as a sphere.
We are given diameter as 20 inches.
So, the radius is half of the diameter which comes out to be 10 inches.
From this, we get the volume as
⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]r^{3}[/tex]
⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]10^{3}[/tex]
⇒ Volume = [tex]\frac{4000}{3}[/tex] π
⇒ Volume = 4186.67 cubic inches
Hence, the volume of the fully - inflated balloon is 4186.67 cubic inches.
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please help with an explanation
It is financially beneficial for Harris Fishing Tours to replace the old boat with the new fuel-efficient model, as it has a net benefit of $12,000 compared to continuing to use the old boat.
To determine whether Harris Fishing Tours should replace the old boat with the new fuel-efficient model, we need to compare the costs and benefits of each option.
Option 1: Replace the old boat with the new fuel-efficient model
If Harris replaces the old boat with the new fuel-efficient model, they will have to pay $80,000 for the new boat. They can sell the old boat for $32,000, so the net cost of the new boat will be $48,000 ($80,000 - $32,000).
The new boat is expected to be extremely fuel efficient, which means that the fuel costs will be $15,000 per year lower than the old boat. Over the remaining four years of the old boat's useful life, this represents a total savings of $60,000 ($15,000 x 4).
Therefore, the total cost of replacing the old boat with the new fuel-efficient model is $48,000 - $60,000 = -$12,000, which means that this option has a net benefit of $12,000.
Option 2: Continue to use the old boat until it wears out
If Harris decides to continue using the old boat until it wears out, they will not incur the $80,000 cost of purchasing the new boat.
However, they will continue to pay $15,000 per year more in fuel costs than they would with the new boat. Over the remaining four years of the old boat's useful life, this represents a total cost of $60,000 ($15,000 x 4).
In addition, at the end of the four years, the old boat will have no salvage value since it will have reached the end of its useful life.
Therefore, the total cost of continuing to use the old boat until it wears out is $60,000, which means that this option has a net cost of $60,000.
Conclusion
Based on the analysis above, it is more financially beneficial for Harris Fishing Tours to replace the old boat with the new fuel-efficient model. This option has a net benefit of $12,000, while continuing to use the old boat until it wears out has a net cost of $60,000.
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(40 POINTS)
Data based on past observations can sometimes predict future performance.
a. Give an example where past performance does predict future performance. Explain your reasoning.
b. Give an example where past performance does not predict future performance. Explain your reasoning.
An example of where past performance does predict future performance would be Mt. Kīlauea's eruption in 2018.
An example of where past performance does not predict future performance would be the eruption of Hualālai last happening in 1801.
What does the data show on volcanoes ?Using past data, there was a prediction that Mt. Kīlauea would erupt in the year 2018 and it did happen ( even though it was not very serious ) at the Lower East rift zone of the volcano. Past performance therefore predicted the future.
However, the same prediction said that Hualālai would erupt in 1854 and yet the volcano has not erupted since 1801 which shows that the prediction was wrong.
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Can you help me answer this question?
The constant of proportionality of the line is slope m = 2/3
Given data ,
Let the line be represented as A
Now , the value of A is
Let the point on the straight line be P ( 2 , 3 )
Now , from the proportionality , we get
y = kx
Divide by x on both sides , we get
k = y/x
So , the slope of the line is k
k = 2/3
Hence , the proportion is y = ( 2/3 )x
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NASA launches a rocket at
t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t^2+43t+339
.
(A) Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? (Round answer to 2 decimal places)
The rocket splashes down after
seconds._______
(B) How high above sea-level does the rocket get at its peak? (Round answer to 2 decimal places)
The rocket peaks at _____
meters above sea-level._____
Answer:
(A)
[tex] - 4.9 {t}^{2} + 43t + 339 = 0[/tex]
[tex]49 {t}^{2} - 430t - 3390 = 0[/tex]
[tex]t = \frac{ - ( - 430) + \sqrt{ {( - 430)}^{2} - 4(49)( - 3390)} }{2(49)} = \frac{430 + \sqrt{849340} }{98} = 13.79[/tex]
The rocket splashes down after 13.79 seconds.
(B) h'(t) = -9.8t + 43 = 0
t = 43/9.8 = 215/49 = 4.39 seconds
h(4.39) = 433.34 meters
At t = 4.39 seconds, the rocket peaks at
433.34 meters above sea level.
Match each drawing on the left with its word description on the right , some of the answer choices on the right may not be used. Line segment AB , Line AB , Point AB , Ray AB , Ray BA
1) Line AB
2) Ray AB
3) Line segment AB
4)Ray BA
The first drawing is a line AB because a line passing through two different points A and B
The second drawing is ray AB because it started at A
The third drawing is a line segment AB because it is part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints
The fourth drawing is ray BA
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I will give 30 points to whoever answers
|x +3| if x >5
|x +3| if x >2
|x +3| if x =2
|x − 3| if x >5
|120+x| if x < −120
|x − 120| if x < −120
|x − (−12)| if x > −12
|x − (−12)| if x < −12
|x − (−12)| if x = −12
|x ÷ 3| if x >0
|x ÷ 3| if x <0
|x ÷ 3| if x =0
These are absolute value expressions evaluated under different conditions:
How to solve|x + 3| if x > 5:
Here x is greater than 5, so x + 3 will also be positive. In this case, |x + 3| = x + 3.
|x + 3| if x > 2:
Similar to the above, x is greater than 2, so x + 3 will be positive. Thus, |x + 3| = x + 3.
|x + 3| if x = 2:
In this case, x + 3 = 2 + 3 = 5, and the absolute value of 5 is just 5. Thus, |x + 3| = 5.
|x - 3| if x > 5:
If x is greater than 5, then x - 3 will be positive. Hence, |x - 3| = x - 3.
|120 + x| if x < -120:
Since x is less than -120, 120 + x will be negative. But the absolute value of a negative number is its positive counterpart, so |120 + x| = -(120 + x).
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Find the length of the missing side
Step-by-step explanation:
This is a right triangle , so the Pythagorean theorem applies
c^2 = a ^2 + b^2 c is the hypotenuse a and b are the legs
15^2 = 9^2 + x^2
15^2 - 9^2 = X^2
x = 12 ft
AP calc please help me
a) over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.
b) the average temperature of the water in the system is 1527.
c) over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.
a) g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt
g'(-3) = -2
b) The absolute maximum value of g on the closed interval [-5, 5]=
10 + 2√7.
c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.
What is right Riemann sum formula?
The right Riemann sum formula uses the right-most value of each interval as the value of the function over that interval.
a) g(5) = 2(5) + [tex]\int\limits^5_0[/tex] ƒ(t) dt
= 10 + 2√7
g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt
g'(-3) = 2 + [tex]\int\limits^3_0[/tex]ƒ'(t) dt
= 2 - (4 + 0)
= -2
b) The absolute maximum value of g on the closed interval [-5, 5]=
10 + 2√7.
This is because the highest value of ƒ(t) dt on the interval= 4√7, which occurs at x = 2.
The highest value of g is thus given by 10 + 2√7.
c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.
This is because ƒ'(t) dt is undefined at these points, so the second derivative of g is also undefined.
a) To evaluate the S'(t) dt, we need to calculate the area under the curve of the temperature data given in the table. To do this, we use the trapezoidal rule. This gives us the following:
[tex]\int\limits^10_0[/tex] S'(t) dt = [(142 + 210 + 254 + 280 + 274 + 268)/2] × 8
= 17,088
This means that over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.
This can be interpreted in the context of the problem as the average rate at which the temperature of the water in the solar steam power system is changing over the given time interval.
b) To approximate the average temperature of the water in the system using a right Riemann approximation, we need to calculate the area under the curve of the temperature data given in the table. We can do this using the right Riemann sum formula, which gives us the following:
Right Riemann Approximation = [(210 + 254 + 280 + 274)/4] × 6 = 1527
In this case, the right-most value of each interval is lower than the true average over that interval, so the approximation will be lower than the true average.
c) To determine the total change in the temperature of the system for the interval 10≤t≤20, we need to calculate the area under the curve of the equation S'(t)=-√2xe (√x²-100)/x.
This can be done using the definite integral of the equation, which gives us the following:
Total Change = ∫1020-√2xe (√x²-100)/x dx
= -14,351
This means that over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.
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Help with math problems
The surd forms are simplified to give;
21. 10√6 - 12√10
23. -56a - 5√2a - 25
25. -4√15x - 25x + 3
What are surds?Surds are described as values in square root that can no longer be simplified into whole numbers or integers
They are also seen as irrational numbers.
From the information given, we have that;
√15(2√10 - 4√6)
Expand the bracket and multiply the surd forms
2√150 - 4√90
Factorize the forms
2√25 ×√6 - 4√9 × √10
find the square root
10√6 - 12√10
23. (√2a - 5)(7√2a - 5)
expand the bracket
7√4a² - 5√2a - 35√4a² + 25
find the square root, we have;
7×2a - 5√2a - 35×2a + 25
collect the like terms
14a - 70a - 5√2a - 25
-56a - 5√2a - 25
25. (√3 + √5x)(√3 - 5√5x)
expand the bracket
3 - 5√15x + √15x - 5√25x²
find the square root
3 - 5√15x + √15x - 25x
collect the like terms
-4√15x - 25x + 3
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A fair number cube is rolled twice. After 500 trials of the experiment, the experimental probability of rolling two 3s is 11/50. What is the difference between the number of expected outcomes and the number of actual outcomes?
Find the slope of the line that passes through A (3, 7) and B (7, 10).
Answer:
[tex]m = \frac{10 - 7}{7 - 3} = \frac{3}{4} [/tex]
A coach asked her athletes if they enjoy running. Fifty-five percent of the team do not like to run. Of those, 70% enjoy cycling, while 80% of those who enjoy running also enjoy cycling. The tree diagram shows how the athletes are divided into subgroups.
The tree diagram shows athletes branching off into two categories, enjoys running and does not enjoy running. Enjoys running branches off into two sub-categories, enjoys cycling and does not enjoy cycling. Does not enjoy running branches off into two subcategories, enjoys cycling and does not enjoy cycling.
What is the total percentage of the athletes who enjoy cycling?
9%
25.5%
55%
74.5%
Answer:
75%
Step-by-step explanation:
To determine the total percentage of athletes who enjoy cycling, we need to consider the percentages given in the problem.
According to the information provided:
55% of the team does not like to run.
Of those who do not like to run, 70% enjoy cycling.
Of those who enjoy running, 80% also enjoy cycling.
To calculate the total percentage of athletes who enjoy cycling, we need to consider the percentages from both branches of the tree diagram.
Percentage of athletes who do not like to run and enjoy cycling:
= (Percentage of athletes who do not like to run) * (Percentage of those who enjoy cycling within that group)
= 55% * 70% = 38.5%
Percentage of athletes who enjoy running and enjoy cycling:
= (Percentage of athletes who enjoy running) * (Percentage of those who enjoy cycling within that group)
= (100% - 55%) * 80% = 45% * 80% = 36%
Total percentage of athletes who enjoy cycling:
= Percentage of athletes who do not like to run and enjoy cycling + Percentage of athletes who enjoy running and enjoy cycling
= 38.5% + 36% = 74.5%
Therefore, the correct answer is:
74.5%
Please help!!!
Natalie gathered a random sample of flower bouquets at the florist. She calculated data on different variables. For one data that she collected, she constructed a bar graph
Which of the following variables did she use?
O Type of flowers in each bouquet
O Amount of water needed for each bouquet
O Number of flowers in each bouquet
O Price for each bouquet
The variables that Natalie used in the data collected was C. Number of flowers in each bouquet.
How to find the variable ?The bar graph that Natalie crafted utilized the variable "number of flowers in each bouquet." This particular type of graph reveals the frequency or count associated with every number of flowers contained within a single bouquet.
As an illustration, let us suppose there were 20 bouquets holding 5 flowers, 30 bouquets possessing 10 flowers, and 15 bouquets that had 15 flowers each; consequently, the bar chart would exhibit exactly three bars symbolizing the count for all three categories as outlined above.
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Liz opened a savings account and deposited $1,000.00 as principal. The account earns 8% interest, compounded quarterly. What is the balance after 4 years?
After the first quarter, the interest earned would be:
$1,000.00 * 0.02 = $20.00
So the new balance would be:
$1,000.00 + $20.00 = $1,020.00
After the second quarter, the interest earned would be:
$1,020.00 * 0.02 = $20.40
So the new balance would be:
$1,020.00 + $20.40 = $1,040.40
After the third quarter, the interest earned would be:
$1,040.40 * 0.02 = $20.81
So the new balance would be:
$1,040.40 + $20.81 = $1,061.21
After the fourth quarter, the interest earned would be:
$1,061.21 * 0.02 = $21.22
So the final balance after 4 years would be:
$1,061.21 + $21.22 = $1,082.43
Therefore, the balance after 4 years would be $1,082.43.
For f(x)=3x+4 and g(x)=x^2 find the following composite functions and state the domain of each.
The composite functions are:
a) f ∘ g = 3x² + 4, with domain of all real numbers.
b) g ∘ f = 9x² + 24x + 16, with domain of all real numbers.
c) f ∘ f = 9x + 16, with domain of all real numbers.
d) g ∘ g = x⁴, with domain of all real numbers.
To find the composite functions, we need to substitute the function g into the function f or vice versa, depending on the order of composition. The resulting composite function will have a domain that is restricted by the domains of the individual functions involved.
a) To find f ∘ g, we substitute g(x) = x² into f(x) = 3x + 4:
f(g(x)) = 3g(x) + 4 = 3x² + 4
The domain of f ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.
b) To find g ∘ f, we substitute f(x) = 3x + 4 into g(x) = x²:
g(f(x)) = (3x + 4)² = 9x² + 24x + 16
The domain of g ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.
c) To find f ∘ f, we substitute f(x) = 3x + 4 into f(x) = 3x + 4:
f(f(x)) = 3f(x) + 4 = 3(3x + 4) + 4 = 9x + 16
The domain of f ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.
d) To find g ∘ g, we substitute g(x) = x² into g(x) = x²:
g(g(x)) = (x²)² = x⁴
The domain of g ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.
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Pls Help Parallelogram PQRS is shown in the coordinate plane below. What is the perimeter of parallelogram PQRS?
1) Find the missing side using the right triangle shown. 2) Then find the perimeter by adding all four sides of the parallelogram!
Note that the perimeter of the parallelogram is 42
How is this so?recall that opposite sides of a parallelogram are congruent always
We have to to find the distance between the points Q(6, 6 ) and R(1, -6) using the distance formula which is
d = √[(x2 - x1) ² + (y2 - y 1)²]
where d is the distance between two points with paris (x1 , y1)
and (x2, y2).
PS = QR = √(6-1)² + (6+6)²
= √5² + 12²
= √(25+144
= √(169)
= 13
PQ = SR = 8
Perimeter = 13 + 13 + 8 + 8
Perimeter = 42.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
A box in the shape of a right rectangular prism has a length of 8.5 inches, a width of 4.5 inches, and a height of 3.75 inches, What is the volume, in cubic inches, of the box?
The volume of the prism is 143.44 in³
What is volume of a prism?A prism is a solid shape that is bound on all its sides by plane faces.
The general formula for the volume of a prism is expressed as;
V = base area × height
The prism is a rectangular prism, therefore the volume will be calculated as
V = l× w × h
where l is the length of the base and w is the width of the base
V = 8.5× 4.5 × 3.75
V = 143.44 in³
therefore the volume of the rectangular prism is 143.44 in³
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A binomial experiment with probability of success p=0.45 and n=7 trials is conducted. What is the probability that the experiment results in exactly 1 success?
The calculated value of the probability that the experiment results in exactly 1 success is 0.08719
Calculating the probability that the experiment results in exactly 1 success?From the question, we have the following parameters that can be used in our computation:
n = 7
x = 1
p = 0.45
The probability is then calculated as
P(x = x) = nCr * p^x * (1 - p)^(n - x)
Substitute the known values in the above equation, so, we have the following representation
P(x = 1) = 7C1 * (0.45)^1 * (1 - 0.45)^(7-1)
Evaluate the expression
So, we have
P(x = 1) = 0.08719
Hence, the probability is 0.08719
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A clock pendulum swings back and forth once every two seconds. If its length is one meter and the greatest
angle that it makes with the vertical is 12 degrees, how many kilometers does the bottom end of the pendulum travel in
one day?
The bottom end of the pendulum travels 18,115.2 meters/day, which is approximately 18.12 kilometers/day (since 1 kilometer = 1000 meters).
The motion of the pendulum is a simple harmonic motion and the period of oscillation can be calculated as follows:
T = 2π√(l/g)
where l is the length of the pendulum and g is the acceleration due to gravity (approx. 9.81 m/s²).
Substituting l = 1 m, we get
T = 2π√(1/9.81)
T ≈ 2.006 s.
In one day, there are
24 hours x 60 minutes/hour x 60 seconds/minute
= 86,400 seconds.
The pendulum makes half a period (i.e., one back-and-forth swing) in 2/2 = 1 second. Therefore, it makes
86,400/2
= 43,200 back-and-forth swings in one day.
The distance traveled by the bottom end of the pendulum in one complete swing is equal to the length of the pendulum times twice the maximum angle it makes with the vertical, which is
2 x 12 degrees
= 24 degrees
= 0.419 radians.
Therefore, the distance traveled by the bottom end of the pendulum in one complete swing is
1 meter x 0.419
= 0.419 meters.
Multiplying by the number of swings in one day, we get:
0.419 meters/swing x 43,200 swings/day
= 18,115.2 meters/day.
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ACTIVITY 4: Solve the following inequalities.
The solutions of the inequalities are shown below
x [tex]\geq[/tex] 5
x< 13
x[tex]\geq[/tex]1
x> 1
How do you solve inequalities?Solving inequalities involves finding all possible values of a variable that make the inequality true. The process for solving an inequality depends on the type of inequality and the operations involved.
[tex]6^x + 4 \leq 6^{2x - 1} \\x + 4 \leq 2x - 1\\x - 2x\leq -1 - 4\\-x \leq -5\\x \geq 5[/tex]
[tex]2^{x + 3} > 4x^{x - 5} \\2^{x + 3} > 2^{2x - 10}\\x + 3 > 2x - 10\\x - 2x > - 10 - 3\\-x > - 13\\x < 13[/tex]
[tex]9^x \leq 9^{2x - 1}\\ x \leq 2x - 1\\x - 2x \leq -1\\-x \leq -1\\x \geq 1[/tex]
[tex]5^4 > 25^{2x} \\5^4 > 5^{4x} \\4 > 4x\\x > 1[/tex]
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Find the trig ratio, reduce and enter your answer in the lowest terms. Please help!
The trigonometric ratio cosA = [tex]\frac{3}{5}[/tex] which is in the lowest form.
What does the trigonometric ratio mean? a trigonometric ratioTrigonometric ratios are the ratios of the sides of a right triangle. The sine, cosine, and tangent are three popular trigonometric ratios. (tan).
The given triangle is a right angle,
To find the cos angle we need to take the ratio of the length of the side which is next to the angle, it is also called an adjacent side to the length of the longest side of the triangle called the hypotenuse.
[tex]cosA = \frac{Length of the side next to the angle}{length of the longest side of the triangle} \\cosA = \frac{Adjacent side}{Hypotenuse} \\cosA = \frac{6}{10}\\ cosA = \frac{3}{5}[/tex]
Therefore [tex]cosA= \frac{3}{5}[/tex]
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Level E: The repair department of the bicycle shop repairs three things: flat tires, bent handle bars and ripped seats. Today in the repair department, 25% of the bikes had flat tires only, 5% had bent handlebars only, and 10% had ripped seats only. Just 1/12th of the bikes had all three repairs to do: flat tires, bent handlebars and ripped seats. No bikes were completely fixed and there are a total of 101 repairs to be made. How many bikes are in the repair department? How many bikes need two repairs? If less than half of all the bikes have a ripped seat, what is the range of bikes that need both the tires and handlebars repaired without needing to fix the seat?
Out of 60 bikes in the repair department, 25 need two repairs and the range of bikes that need both tire and handlebar repairs without needing to fix the seat is 25 out of 60 bikes.
Let's use F, H, and S to represent the events that a bike has a flat tire, bent handlebars, and ripped seat, respectively. Then, we are given:
P(F) = 0.25
P(H) = 0.05
P(S) = 0.10
P(F ∩ H ∩ S) = 1/12
We want to find the number of bikes in the repair department and the number of bikes that need two repairs.
Let N be the total number of bikes in the repair department. Then, the number of repairs needed for each category is:
Flat tires: 0.25N
Bent handlebars: 0.05N
Ripped seats: 0.10N
The number of bikes that need all three repairs is:
P(F ∩ H ∩ S)N = (1/12)N
The number of repairs needed for these bikes is:
3P(F ∩ H ∩ S)N = (1/4)N
The number of repairs needed for bikes that need only two repairs is:
2[P(F ∩ H) + P(F ∩ S) + P(H ∩ S)]N = (5/12)N
The number of repairs needed for bikes that need only one repair is:
[P(F) + P(H) + P(S)]N = 0.4N
The total number of repairs needed is given as 101, so we have:
(1/4)N + (5/12)N + 0.4N = 101
Simplifying this equation gives:
N = 60
Therefore, there are 60 bikes in the repair department.
The number of bikes that need two repairs is:
(5/12)N = 25
Next, we need to find the range of bikes that need both the tires and handlebars repaired without needing to fix the seat. Let's use T and H to represent the events that a bike needs tire and handlebar repairs, respectively. We want to find P(T ∩ H ∩ not S).
We know that P(T ∩ H ∩ S) = P(F ∩ H ∩ S) = 1/12. Also, P(S) = 0.10, so P(not S) = 0.90. Therefore:
P(T ∩ H ∩ not S) = P(T ∩ H) - P(T ∩ H ∩ S)
= 2[P(F ∩ H) + P(F ∩ H ∩ S) + P(H ∩ S)] - P(F ∩ H ∩ S)
= 2(5/12) - 1/12
= 5/12
So, less than half of all the bikes have a ripped seat, and the range of bikes that need both the tires and handlebars repaired without needing to fix the seat is 5/12 of all the bikes, or 25 out of 60 bikes.
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ERROR ANALYSIS Describe and correct the error in finding the area of sector XZY when the area of
OZ is 255 square feet.
X
W
Z
X
115°
Let n be the area
of sector XZY.
115
255
n≈ 162.35 ft²
n
360
=
The wrong formula was used. The correct method is: area of sector = 115/360 * 255 ≈ 81.46 square feet.
How to Find the Area of a Sector?The area of a sector is calculated by using the formula:
Area of sector = ∅/360 * πr², where:
r is the radius of the circle
∅ is the central angle measure.
The error made was that a wrong method/formula was used in finding the area of sector.
Given the following:
Area of circle = 255 square feet (πr²)
∅ = 115°
Note that πr² represents the area of a circle, therefore, substituting the values into the formula, we have:
Area of sector = 115/360 * 255
Area of sector ≈ 81.46 square feet
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pls help with this geometry asap
Area of sector XYZ is 81.45 feet².
Define area of sectorThe area of a sector is a measure of the size of a portion of a circle enclosed by two radii and an arc between them. It is expressed in square units, such as square centimeters, square meters, or square inches.
To find the area of a sector, you need to know the radius of the circle and the central angle of the sector.
The formula for the area of a sector is:
Area of sector = (central angle / 360°) x π x r²
where r is the radius of the circle, π is the mathematical constant pi (approximately 3.14), and the central angle is measured in degrees.
n is the area of sector XYZ
n/360=115/255(X)
n/255=115/360(V)
(The same elements are proportional)
n=115/360×255
n=81.4583≈81.45 feet²
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Solve the following by completing the square or squaring both sides using steps illustrated in the lesson content.. Leave answers in radical (EXACT) form. Do not use decimals. -2x+6=-x^2
Answer:
Starting with the equation:
-2x + 6 = -x^2
First, we can rearrange it to put it in standard quadratic form:
x^2 - 2x - 6 = 0
To complete the square, we need to add and subtract a constant term that will make the left-hand side of the equation a perfect square. The constant we need to add is (b/2)^2, where b is the coefficient of x. In this case, b = -2, so:
x^2 - 2x + 1 - 1 - 6 = 0
The first three terms can be written as a perfect square:
(x - 1)^2 - 7 = 0
Add 7 to both sides:
(x - 1)^2 = 7
Now we can take the square root of both sides:
x - 1 = ±√7
Add 1 to both sides:
x = 1 ± √7
So the solutions to the equation are:
x = 1 + √7 or x = 1 - √7
mark me brilliant
Which equation represents a line that passes through the point (−12, 6) and is perpendicular to the graph of the equation y = 34
x + 7?
A. y = 43
x + 18
B. y = 34
x + 15
C. y = −43
x − 10
D. y = −34
x − 3
Answer:
C
Step-by-step explanation:
If it is perpendicular to the line y = ¾x+7 then the gradient if the line must be the negative reciprocal of 3/4. The gradient must be - 4/3. So A, B and D are rejected. Left is C
Let's replace now.
For C,
Let's take y=-4/3x-10 into consideration at the point (-12,6)
Y should be equal to 6 when we replace x by -12
Let's try
Y = -4/3(-12) - 10 = 16 - 10 = 6
Yup. C is your answer.
Can anyone help me??
1. The coordinates of the vertices of the preimage in the first column of the table are; (2, 2), (-1, 2) (-1, 1) (-2, 1) (-2, -2) (1, -2) (1, -1) (2, -1).
2. The scale factor for the dilation is 3
3. The coordinates for the image are, (6,6) (-3, 6) (-3, 3) (-6, 3)(-6, -6) (3, -6) (3, -3)(6, -3)
4. The sketch has been attached below;
5. The dilation multiplies the length of line segments by the scale factor.
6. The dilation did not affect the angle measures. The angles in the image are the same as the angles in the preimage.
How to calculate the scale factor of the image?
To calculate the scale factor for the dilation, we look at what has been provided (x, y) → (3x, 3y)
x =1 x2 = 3
1 multiplied by what will give us 3
1×? = 3
1/1 = 3/1 = 3
If we multiply 3 to every vertices of the preimage, we will find the coordinated of the image.
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