If a deadly disease infected the hummingbird population, what would most likely happen to the plants option (b) They would become endangered
If a deadly disease infected the hummingbird population, it would most likely lead to a decrease in the pollination of plants that rely on hummingbirds for pollination. Without the hummingbirds to transfer pollen between flowers, these plants would have a reduced rate of successful pollination, which would result in a decrease in their ability to reproduce.
However, it is unlikely that the plants would die within hours or become endangered immediately, nor would they need to migrate. The effect of the loss of hummingbird pollinators on the plants would depend on the specific plant species, their pollination requirements, and the availability of alternative pollinators. Some plants may be more adaptable to using alternative pollinators, while others may suffer more severe consequences. It is also possible that the loss of hummingbirds could lead to a decline in the populations of other animals that depend on the plants, creating a ripple effect in the ecosystem.
Therefore, the correct option is (d) They would become endangered
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Find the area of the shaded polygon.
To find the area of the shaded polygon, we had to assume that each dotted line was one unit. In which case, the coordinates are:
A(1,4)B (5,6)C (6, 3)D (3, 2)Hence, the area of the polygon is A [tex]\approx[/tex] 11.15 units.
To get the area of the polygon, we must determine the length of all it's sides.
a) A-B is given by the distance formula:
distance = √((x2 - x1)² + (y2 - y1)²)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using this formula, we can calculate the distance between points A(1,4) and B(5,6) as follows:
distance = √((5 - 1)² + (6 - 4)²)
= √(16 + 4)
= √(20)
A-B = 4.47213595
A-B [tex]\approx[/tex] 4.47
b)
To find B-C we use the same method:
B-C = 3.16 units.
c)
To find C- D we use the same method:
C- D [tex]\approx[/tex] 3.16 units.
d) to find D-A we use the employ the same method:
D - A [tex]\approx[/tex] 2.83
Since this is an irregular quadrilateral, we will require the use of the
length of one of it's diagonals which is also computed using the distance formula to get: 4.47 Units.
Calculate the perimeter of ABCD
Perimeter of ABCD = AB + BC + CD + AD
Perimeter of ABCD = 4.4721359549996 + 3.1622776601684 + 3.1622776601684 + 2.8284271247462
Perimeter of ABCD = 13.625118400083
Calculate the semi-perimeter (s) of ABCD
s = Perimeter ÷ 2
s = 13.625118400083 ÷ 2
s = 6.8125592000413
Calculate the Area (A) using Brahmagupta's Formula
A = √[(s - a)(s - b)(s - c)(s - d)]
A = √(6.8125592000413 - 4.4721359549996)(6.8125592000413 - 3.1622776601684)(6.8125592000413 - 3.1622776601684)(6.8125592000413 - 2.8284271247462)
A = √(2.3404232450417)(3.6502815398729)(3.6502815398729)(3.9841320752951)
A = √(124.24555320337)
A = 11.14654893693
A [tex]\approx[/tex] 11.15 units.
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3×+9×=6×+42 solve for ×
Answer:
x=7
Step-by-step explanation:
First, try to bring all your X's together
3x+9x=6x+42
12x=6x+42
-6x -6x
6x=42
/6 /6
x = 7
Addison wanted to know if there was a connection between her coffee consumption and how
well she slept that night. For weeks, Addison recorded how many cups of coffee she drank in
the morning and how many hours she slept that night.
0 cups of coffee
1 cup of coffee
6 hours 7 hours
1
5
5
4
What is the probability that a randomly selected day is one when she drank exactly 1 cup of
coffee and is one when she slept about 6 hours?
Simplify any fractions.
Answer:
Step-by-step explanation:
[50 POINTS]
What is the remainder when 3x^3−x^2+2x−4
is divided by (x - 2)?
The remainder is _______________________
Step-by-step explanation:
To find the remainder when 3x^3 - x^2 + 2x - 4 is divided by (x - 2), we can use synthetic division.
First, we write the coefficients of the polynomial in descending order of powers of x, with any missing terms represented by a coefficient of 0:
3 1 -1 2 -4
To perform synthetic division, we bring down the first coefficient (1) and multiply it by the divisor (x - 2) to get the first entry in the second row, which we then add to the second coefficient:
3 1 -1 2 -4
1
1
We repeat the process with the new coefficient in the third row, multiplying it by the divisor and adding it to the next coefficient:
3 1 -1 2 -4
1 3
1 2
Finally, we repeat the process with the new coefficient in the third row to get the last entry in the second row:
3 1 -1 2 -4
1 3 8
1 2 4
The last entry in the third row is the remainder, which is 4. Therefore, the remainder when 3x^3 - x^2 + 2x - 4 is divided by (x - 2) is 4.
A standard size golf ball has a diameter of 1. 680 inches. The material used to make the golf balls weighs 0. 6523 ounces per cubic inch. What is the weight, to the nearest hundredth of an ounce of one golf ball
The volume of a standard size golf ball can be calculated using the formula for the volume of a sphere:
V = (4/3)πr^3
where r is the radius of the golf ball. The diameter of the golf ball is 1.680 inches, so the radius is 0.840 inches.
V = (4/3)π(0.840)^3
= 2.468 in^3
The weight of the golf ball can be calculated by multiplying its volume by the density of the material:
W = V × D
where D is the density of the material. The density of the material is 0.6523 ounces per cubic inch.
W = 2.468 in^3 × 0.6523 oz/in^3
= 1.6095 oz
Therefore, the weight of one golf ball is approximately 1.61 ounces (rounded to the nearest hundredth of an ounce).
A pyramid and a coke have the same base, area, slant height, and surface area. If the perimeter of the base of the pyramid is 314 centimeters, what is the radius of the cone
If the perimeter of the base of the pyramid is 314 centimeters, then radius of the cone is approximately 17.44 centimeters.
What is perimeter?Perimeter is a measurement of the distance around the outside of a two-dimensional shape. It is the sum of the lengths of the shape's sides.
Since the pyramid and cone have the same base and slant height, they are similar geometric figures. Therefore, their corresponding dimensions are proportional. Let's denote the radius of the cone as r.
Since the perimeter of the base of the pyramid is 314 centimeters, and the base of the pyramid is a square, we can find the length of one side of the square base by dividing the perimeter by 4:
Length of one side = Perimeter / 4 = 314 cm / 4 = 78.5 cm
Since the pyramid and the cone have the same area of the base, and the base of the pyramid is a square, we can find the area of the base by squaring the length of one side:
Area of the base = (Length of one side)² = (78.5 cm)²= 6,152.25 cm²
Since the pyramid and the cone have the same surface area, we can use the formula for the surface area of a cone to find the radius of the cone:
Surface area of the cone = πr(r + l), where l is the slant height.
The surface area of the cone is equal to the surface area of the pyramid, so we have:
πr(r + l) = 2 × Area of the base + Perimeter × l
Substituting the known values, we get:
πr(r + 13) = 2 × 6,152.25 cm² + 314 cm × 13 cm
Simplifying and solving for r, we get:
πr² + 13πr - 4,059.5 = 0
Using the quadratic formula, we find:
r ≈ 17.44 cm (rounded to two decimal places).
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during a football game,the ball is placed 20 yards 2 feet from the goal line.How many feet from the goal line is the football.
A boat is heading towards a lighthouse, where Tyee is watching from a vertical
distance of 115 feet above the water. Tyee measures an angle of depression to the boat
at point A to be 15°. At some later time, Tyee takes another measurement and finds
the angle of depression to the boat (now at point B) to be 50°. Find the distance from
point A to point B. Round your answer to the nearest foot if necessary.
In the given problem, the distance from point A to point B is approximately 658 feet (rounded to the nearest foot).
How to Calculate the Distance?Let's define some variables:
Let h be the height of the lighthouse (given as 115 ft).Let d be the distance from Tyee to point A.Let x be the distance from Tyee to point B.Using trigonometry, we can write the following equations:
For triangle ACT, we have:
tan(15°) = h/d
For triangle BCT, we have:
tan(50°) = h/(d+x)
We want to find the value of x, so let's rearrange the second equation:
tan(50°) = h/(d+x)
tan(50°)*(d+x) = h
d+x = h/tan(50°)
x = h/tan(50°) - d
Substituting the given values:
x = 115/tan(50°) - d
Now we need to find the value of d. For that, we can use the first equation:
tan(15°) = h/d
d = h/tan(15°)
Substituting the given value:
d = 115/tan(15°)
Now we can substitute both values into the equation for x:
x = 115/tan(50°) - 115/tan(15°)
Using a calculator, we get:
x ≈ 658.4 ft
Therefore, the distance from point A to point B is approximately 658 feet (rounded to the nearest foot).
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Which of the following is a TRUE statement about hypothesis testing?
A: If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.
B: Whether to use a one-sided or a two-sided test is typically decided before the data are gathered.
C: If a hypothesis test is conducted at the 1% level, there is a 1% chance of rejecting the null hypothesis.
D: The probability of a Type I error plus the probability of a Type II error always equals one.
E: The power of a test concerns its ability to detect a null hypothesis.
If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.
What is hypothesis testing?
A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters through hypothesis testing.
Here,
We have to find the correct statement about hypothesis testing.
We concluded that If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.
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Answer:
In this case, B is true.
Whether to use a one-sided or a two-sided test is typically decided BEFORE the data are gathered, not after.
Be careful while reading the options on the quiz, because depending on the question you get, the options may be worded slightly differently. Because of the wording, the answer may be different as well (on the FLVS quiz, I got different answer choices for this question). Be careful and read cautiously!
Have a great day.
All exponential functions can be written in many forms. Write the function
F(t)=9100(1.15)^t in the form
f(t)=ae^kt
Round all coefficients to four decimal places.
In conclusion Rounding to four decimal places, we get:
f(t) = 9100e²(0.1398t)
How to solve?
To write the function F(t) = 9100(1.15)²t in the form f(t) = ae²(kt), we need to first take the natural logarithm of both sides:
ln(F(t)) = ln(9100(1.15)²t)
ln(F(t)) = ln(9100) + ln(1.15²t)
ln(F(t)) = ln(9100) + t × ln(1.15)
Now, we have the form ln(F(t)) = ln(a) + kt, where k = ln(1.15) and a = 9100. We can exponentiate both sides of this equation to get:
F(t) = e²(ln(a) + kt)
F(t) = e²ln(a) × e²(kt)
F(t) = a × e²(kt)
Substituting the values of a and k, we get:
F(t) = 9100 × e²(0.1398t)
Rounding to four decimal places, we get:
f(t) = 9100e²(0.1398t)
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The distance from Sunderland to Wigan is 150 miles.
Mollie leaves Sunderland in her car at 07:50.
Her average speed on the journey is 60mph.
What time does she arrive in Wigan?
If a company understates its ending balance of inventory in year 1 and states its inventory correctly in year 2, which one of the following is true?a. Net income is overstated in year 1.b. Cost of goods sold is understand in year 2.c. Net income is understated in year 2.d. Retained earnings is understood in year 2.
If a company understates its ending balance of inventory in year 1 and states its inventory correctly in year 2, then the correct statement is option (c) Net income is understated in year 2
Understating the ending balance of inventory in year 1 would result in the cost of goods sold (COGS) being overstated and net income being understated in that year. This is because the COGS is calculated as the beginning inventory plus purchases minus ending inventory. By understating the ending inventory balance, the COGS for year 1 would be overstated, which would result in a lower net income for year 1.
In year 2, if the inventory is stated correctly, it would not have an impact on the COGS for that year. However, if the net income for year 1 was understated due to the understated ending inventory balance, the cumulative effect would be an understated net income for both years. This means that the correct answer is c. Net income is understated in year 2.
Therefore, the correct option is (c) Net income is understated in year 2
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In the figure DB bisects
So, the measure of angle B is 90 degrees.
What is angle?An angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. The two rays or line segments are called the sides or arms of the angle. Angles are typically measured in degrees or radians, and they are used to measure the amount of rotation between two lines or planes. A full rotation is 360 degrees or 2π radians, while a half rotation is 180 degrees or π radians. Angles play an important role in geometry, trigonometry, physics, engineering, and many other fields of science and mathematics.
by the question.
To find the measure of angle B, you need to use the fact that angle DB bisects angle ADC. This means that angle ADB and angle CDB are congruent, or have the same measure. So you can set the measure of angle ADB equal to the measure of angle CDB and solve for x.
Once you have found the value of x, you can substitute it into either equation for angle ADB or angle DBC to find the measure of that angle. Finally, since angle B is an exterior angle of triangle ADB, its measure is equal to the sum of the measures of angles ADB and DBC.
So, the steps to find the measure of angle B are:
Set the measure of angle ADB equal to the measure of angle CDB:
(3x - 12) = (2x + 6)
Solve for x:
x = 18
Substitute x = 18 into either equation for angle ADB or angle DBC to find the measure of that angle:
angle ADB = (3x - 12) = (318 - 12) = 48 degrees
angle DBC = (2x + 6) = (218 + 6) = 42 degrees
Find the measure of angle B as the sum of the measures of angles ADB and DBC:
angle B = angle ADB + angle DBC = 48 + 42 = 90 degrees.
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If two angles of a triangle are congruent to the corresponding angles of a second triangle,
then the third angle of the first triangle is congruent to the third angle of the second
triangle.
A. True
B. False
Answer:
A. True
Step-by-step explanation:
If two angles of a triangle are congruent to the corresponding angles or the second triangle than the third angles must be congruent to each other.
The sum of the interior angles of a triangle is 180. Let's say 2 angles to one triangle is 100 and the second angle is 35. That forces the third angle to be 45 (100 + 35 + 45 = 180)
Helping in the name of Jesus.
Answer:
A. True
Step-by-step explanation:
In congruent triangles...All angles and sides have to be equal.
Simplify the expression. Enter the answer in the box. 3 2/5 + (-7 1/5) = 3 + (-7) + 2/5 + (-1/5)
the masses, in grams, of ten ball bearings taken at random from a batch are: 25.9, 24.7, 23.4, 24.5, 25.0, 26.9, 26.4, 25.8, 23.2, 21.9. calculate a 95% confidence interval for the mean mass of the population, supposed normal, from which these masses were drawn? what is x2, the upper limit of the 95% confidence interval? enter your answer rounded to two decimal places. for example, if your answer is 12.345 then enter as 12.35 in the answer box.
The 95% confidence interval for the mean mass of the population is 24.57 ± 1.06. The upper limit of the 95% confidence interval is 25.63.
Given the masses, in grams, of ten ball bearings taken at random from a batch are: 25.9, 24.7, 23.4, 24.5, 25.0, 26.9, 26.4, 25.8, 23.2, 21.9
We have to calculate a 95% confidence interval for the mean mass of the population, supposed normal, from which these masses were drawn.The formula for the Confidence Interval is given by,
CI = X bar± tα/2 * (s/√n)
Where,
CI = Confidence Interval
Xbar = Sample mean
tα/2 = α level of significance/2 (α is the level of significance)
s = sample s
tandard deviationn = sample size
tα/2 = t-distribution value for α/2 and (n-1) degrees of freedomtα/2 for α = 0.05 and (n-1) degrees of freedom
tα/2 = 2.262
Hence,CI = X bar ± tα/2 * (s/√n)
CI = 24.94 ± 2.306 * (1.618/√10)
CI = 24.94 ± 1.36
Upper limit of 95% confidence interval
x2 = 24.94 + 1.36= 26.30
Rounded off to two decimal places, x2 is 26.30.
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Solve the radical equation.
negative 5 square root of 2 x minus 1 end root equals space minus 15
The sοlutiοn tο the radical equatiοn is x = 5.
What is radical equatiοn?In mathematics, a radical is the οppοsite οf an expοnent, which is symbοlised by the symbοl "," alsο referred tο as rοοt. A square rοοt οr a cube rοοt can be used, and the number befοre the symbοl οr radical is regarded as an index number οr degree. The expοnent οf this number cancels the radical and is a whοle number.
What is the basic arithmetic οperatiοns?The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.
Starting with:
-5√(2x - 1) = -15
Divide bοth sides by -5:
√(2x - 1) = 3
Square bοth sides:
2x - 1 = 9
Add 1 tο bοth sides:
2x = 10
Divide bοth sides by 2:
x = 5
Hence, the solution to the equation is x = 5.
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1. A car's speed increases as it merges onto a highway. The car travels at 65 mph on the highway until it slows to exit. The car then stops at three traffic lights before reaching its destination. Draw a sketch of a graph that shows the car's speed over time.
Just make a flat line for each time the car stops.
Hope this helps.
help asapp!!!!!!!!!!!!!
The total length of the cross-country course include the following: 16 miles.
How to calculate the perimeter of a rectangle?In Mathematics and Geometry, the perimeter of a rectangular shape such as a parallelogram can be calculated by using this mathematical expression;
P = 2(L + B)
Where:
P represent the perimeter of a rectangle.B represent the breadth of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the perimeter of a rectangular shape, we have the following;
P = 2(L + B)
P = 2(6 + 2)
P = 2(8)
P = 16 miles.
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Complete Question:
A cross-country course is in the shape of a parallelogram with a base of length 6 mi and a side of length 2 mi.
What is the total length of the cross-country course?
Answer: The total length of the cross-country course include the following: 16 miles.
How to calculate the perimeter of a rectangle?
In Mathematics and Geometry, the perimeter of a rectangular shape such as a parallelogram can be calculated by using this mathematical expression;
P = 2(L + B)
Where:
P represent the perimeter of a rectangle.
B represent the breadth of a rectangle.
L represent the length of a rectangle.
By substituting the given side lengths into the formula for the perimeter of a rectangular shape, we have the following;
P = 2(L + B)
P = 2(6 + 2)
P = 2(8)
P = 16 miles.
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Complete Question:
A cross-country course is in the shape of a parallelogram with a base of length 6 mi and a side of length 2 mi.
What is the total length of the cross-country course?
Step-by-step explanation:
A researcher looking for evidence of extrasensory perception (ESP) tests 1000 1000 subjects. Nine of these subjects do significantly better ( P < 0.01 ) (P<0.01) than random guessing.
(a) Nine subjects may seem like a lot of people, but can you conclude that these nine people have ESP? Select the appropriate statement that explains whether or not it is proper to conclude that these nine people have ESP.
Yes. This follows directly from the 1 % 1% significance level.
Yes. This follows directly from the statistical significance.
No. Since the tests were performed at the 1% significance level, as many as 10 subjects may have done significantly better than random guessing.
No. The sample size was not large enough for any statistical inference.
it is important to note that the sample size of 1000 subjects is large enough for statistical inference, but the significance level must be taken into account when interpreting the results.
No. Since the tests were performed at the 1% significance level, as many as 10 subjects may have done significantly better than random guessing.
When conducting hypothesis testing, the significance level (in this case, 0.01 or 1%) is the probability of rejecting the null hypothesis when it is actually true. This means that there is a 1% chance of observing a significant result purely by chance, even if the null hypothesis (in this case, that the subjects do not have ESP) is true.
In this scenario, nine subjects performed significantly better than random guessing, which may suggest that they have ESP. However, due to the possibility of observing significant results by chance, it is not proper to conclude that these nine people have ESP. There is still a chance that these results are purely coincidental.
Additionally, it is important to note that the sample size of 1000 subjects is large enough for statistical inference, but the significance level must be taken into account when interpreting the results.
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7 divided by 70.85 show work
the probability of a potential employee passing a drug test is 90%. if you selected 11 potential employees and gave them a drug test, how many would you expect to pass the test?
The required expected number of employees who will pass the test from given 11 potential employees is equal to 10.
Probability of passing a drug test is 90%,
Then the probability of failing is 10%.
For each potential employee,
Probability of passing is 0.9, and the probability of failing is 0.1.
The number of potential employees who would be expected to pass the test,
Calculated using the binomial distribution with n = 11 and p = 0.9.
P(A = x) = (ⁿCₓ) × pˣ × (1-p)ⁿ⁻ˣ
where,
A is the number of potential employees who pass the test
x is the number of potential employees who pass the test
n is the number of potential employees
p is the probability of passing the test
Using this formula, the expected number of potential employees who would pass the test is,
E(A) = n ×p
= 11 × 0.9
= 9.9
Rounding to the nearest whole number, we can expect 10 potential employees to pass the test.
Therefore, the expected number of employees from the given probability who would pass the the test is 10.
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Multiply x times (y + 2)
Step-by-step explanation:
[tex]{ \tt{x(y + 2)}}[/tex]
We need to multiply inner terms i.e. y+2 with x
[tex]{ \red{ \tt{xy + 2x}}}[/tex]
Answer:
xy +2x
Step-by-step explanation:
x(y+2)
Distribute the x to each term inside the parentheses.
x*y + x*2
xy +2x
Please Answer!!
After t years, the rate of depreciation of a car that costs $20,000 is 25%. What is the
value of the car 2 years after it was purchased?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 25\%\to \frac{25}{100}\dotfill &0.25\\ t=\textit{elapsed time}\dotfill &2\\ \end{cases} \\\\\\ A = 20000(1 - 0.25)^{2} \implies A=20000(0.75)^2\implies A = 11250[/tex]
Please help with this question.
Where the above mean exist, the values of x and y are 10.5 and 3.5 respectively.
What is the explanation for the above response?The total number of people surveyed is 24. So we can write:
Frequency of 0 sisters + Frequency of 1 sister + Frequency of 2 sisters + Frequency of 3 sisters = Total frequency
5 + x + 5 + y = 24
x + y = 14 --- (1)
Also, we know that the mean number of sisters is 1.25. This means that the total number of sisters divided by 24 should be equal to 1.25. So we can write:
0 × 5 + 1 × x + 2 × 5 + 3 × y = 1.25 × 24
x + 3y = 21 --- (2)
Now we have two equations (1) and (2) with two variables (x and y). We can solve for x and y by simultaneous equations.
Multiplying equation (1) by 3, we get:
3x + 3y = 42 --- (3)
Subtracting equation (2) from equation (3), we get:
2x = 21
x = 10.5
Substituting the value of x in equation (1), we get:
10.5 + y = 14
y = 3.5
Therefore, the values of x and y are 10.5 and 3.5 respectively.
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Amari gathered a random sample of oranges in her town. She calculated data on different variables. For one of the variables that she collected, she constructed a bar graph.
Which of the following variables did she use?
Type of orange
Diameter of the oranges
Number of navel oranges
Price per pound of oranges
"type of orange" because it is a bar graph therefore it is supposed to be categories, not numbers :)
If a shoe size of 4 is added to the data, how does the median change?
The median stays 6.5.
The median decreases to 6.5.
The median stays 6.75.
The median decreases to 6.75.
Answer: The median decreases to 6.5.
Step-by-step explanation:
The median before 4 was added was 6.75.
When 4 is added the median is 6.5.
Wants to buy new boots that cost $68. The sales tax rate in her city is 5-%. What is the total cost for the boots
Emily new boots cost a total of $71.4 with the tax included as 5% and the original cost of the boots being $68.
The sales tax rate in Emily's city = 5% and the cost of Emily's new boots is $68
we need to find the amount of sales tax Emily will pay for her boots,
The formula we will use =
Sale tax = Percent sales tax x Cost of the product
when we put the values in the formula, we get:
Sales tax = 5% x $68
= $3.4
now we need to also calculate the total cost for Emily's boots,
Therefore, the total cost = Cost of boots + Sales Tax
when we put the values in the formula, we get:
Total cost = $68 + $3.4
= $71.4
Therefore, the total cost Emily will pay for her boots is $71.4
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Dion brought $35.75 to the state fair. He bought a burger, a souvenir, and a pass. The burger was
1/6 as much as the souvenir, and the souvenir cost 3/4 the cost of the pass. Dion had $2.00 left over after buying these items. What was the cost of each item?
The burger costs $0.625, the souvenir costs $3.75, and the pass costs $5.00.
What was the cost of each item?Let's name the burger price "b," the souvenir price "s," and the pass price "p." Then, using the information provided, we can construct an equation system:
b + s + p = 35.75 (1) (The three things cost a total of $35.75.)
b = (1/6)s (2) (the burger was one-sixth the price of the memento).
s = (3/4)p (3) (the memento cost one-quarter the price of the pass)
b + s + p + 2 = 35.75 (4) (After purchasing these products, Dion had $2.00 left over.)
To remove s from the equations, we can apply equations (2) and (3):
b + (3/4)p + p = 35.75 (equations (1) and (3))
b = (1/6)(3/4)p (Applying Equation (2))
b = (1/8)p
This expression can now be substituted by Input b into equation (1):
(1/8)p + (3/4)p + p = 35.75
(7/8)p = 35.75
p = 35.75 / (7/8)
p = $5.00
We may calculate the cost of the keepsake using equation (3):
s = (3/4)p = (3/4)($5.00) = $3.75
Finally, we can calculate the cost of the burger using equation (2):
b = (1/6)s = (1/6)($3.75) = $0.625
As a result, the burger costs $0.625, the souvenir costs $3.75, and the pass costs $5.00.
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Find the area of the shaded segment of the circle
The area of the shaded segment of the circle is calculated by substracting the area of triangle from area of sector of circle So, area of shaded segment of the above circle is equals to the (12π - 9√3) cm².
Assume a sector having a radius r and a central angle of α degrees. The sector's area will be A= (α/360∘)πr². Similarly, different shapes have different area formulas. We have been provided a circle of radius 6cm. Assume that its center is O and the segment is AB. Radius of circle , r = 6 cm
Central angle,α = 120°
Area of shaded segment is calculated by the area of sector AOB of circle minus area of triangle AOB formed there. So, Area of sector AOB , A = (α/360∘)πr²
= ( 120°/360°) π6²
= (1/3) 36π = 12π cm²
As we know, OA = OB= 6cm
=> m∠OAB = m∠OBA
and m∠AOB + m∠OAB + m∠OBA = 180∘
=> 120∘ + m∠OAB + m∠OAB= 180∘
=> 2(m∠OAB) = 180∘− 120∘ = 60°
=> m∠OAB = 30° = m∠OBA
So, it is an isosceles triangle. Draw a perpendicular OC on AB then there is formed two right angled triangles. In right angled triangle OAC, 90°, 60°, 30° and OA = 6 cm then OC/6 = Sin 30°
=> OC= 3 cm and
AC = √36 - 9 = √27 = 3√3 cm
Similarly, BC = 3√3 cm so, AB = 6√3 cm. Now, area of triangle AOB = (1/2) × AB × OC = (1/2)× 6√3 ×3 = 9√3 cm²
So, required area = 12π cm² - 9√3 cm². Hence, required value is (12π - 9√3) cm².
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Complete question:
The above figure completes the question. Find the area of the shaded segment of the circle.