what is the area of a sector with a central angle of 8 π/11 radians and a radius of 7.2 ft? use 3.14 for π and round your final answer to the nearest hundredth. enter your answer as a decimal in the box.
this is just to help any of my fellow people who suck at math :)
Answers
Answer:
[tex]59.19 ft^2[/tex]
Step-by-step explanation:
step 1
Find the area of the circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=7.2\ ft[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]A=(3.14)(7.2)^{2}[/tex]
[tex]A=162.78\ ft^2[/tex]
step 2
we know that
The area of a circle subtends a central angle of 2π radians
so
using proportion
Find out the area of a sector with a central angle of 8 π/11 radians
[tex]\frac{162.78}{2\pi }\frac{ft^2}{rad} =\frac{x}{(8\pi/11)}\frac{ft^2}{rad} \\\\x=162.78(8/11)/2\\\\x=59.19\ ft^2[/tex]
Final answer:
The area of a sector with a central angle of 8π/11 radians and a radius of 7.2 ft, using 3.14 for π, is approximately 78.60 ft² when rounded to the nearest hundredth.
Explanation:
To calculate the area of a sector of a circle, we use the formula ½ θr², where θ is the central angle in radians, and r is the radius of the circle. For a sector with a central angle of ₈π/₁₁ radians and a radius of 7.2 ft, substituting 3.14 for π, we can find the area as follows:
Use the formula: Area = (½)(θ)(r²).
Substitute the given values to get: Area = (½)(₈π/₁₁)(7.2 ft)².
Calculating using 3.14 for π we get: Area = (0.5)*(8*3.14/11)*(7.2 ft)².
Simplify and calculate the result which gives us: Area = 78.5952 ft².
Round the final answer to the nearest hundredth: Area = 78.60 ft².
Related Questions
The angle of elevation of a ladder is 19∘ and the ladder is 12 feet from the wall. What is the height of the ladder in feet?
Answers
Answer:
(24x)(19x2) 12/2 19
Step-by-step explanation:
(24x)(19x2) 12/2 19
Answer:
12.7 ft
Step-by-step explanation:
You're going to need to use acos
so
12 = acos (19) = 12.69
Then round up to 12.7
Ajay sells two cycles at 2500$ each. If he makes a profit of 25% on one and incurs a loss of 25% on the other, find his net profit or loss percent.
Answers
Answer:
The total loss percentage is 6.25%.
Step-by-step explanation:
Let the cost price of the first cycle is $x.
So, for the first cycle, 25% profit is there for selling the cycle at $2500.
Then, [tex]x(1 + \frac{25}{100}) = 2500[/tex]
⇒ 1.25x = 2500
⇒ x = $2000
Again, let us assume that the cost price of the second cycle is $y.
So, by selling the cycle at $2500 there is a loss of 25%.
Therefore, [tex]y(1 - \frac{25}{100} ) = 0.75y = 2500[/tex]
⇒ y = $3333.33
Therefore, the total cost price of two cycles = $(2000 + 3333.33) = $5333.33 and total selling price is $(2500 + 2500) = $5000.
Therefore, the total loss percentage is [tex]\frac{5333.33 - 5000}{5333.33} \times 100 = 6.25[/tex] % (Answer)
If the graph is reflected over the x-axis, what is the domain of
the function?
Answers
The domain of a function is the set of all possible input values for the function. Reflecting a graph over the x-axis does not change the domain of the function.
Explanation:The domain of a function is the set of all possible input values for the function. When a graph is reflected over the x-axis, the y-values are negated. In this case, since the graph is a horizontal line, the y-values remain the same after reflection. Therefore, reflecting the graph over the x-axis does not change the domain of the function. The domain will still be the same set of real numbers that satisfy the given condition, which is 0 ≤ x ≤ 20.
When a function is reflected over the x-axis, the domain remains the same and the sign of each value in the range is negated.
When a function f(x) is reflected over the x-axis to form -f(x), it affects both the domain and the range. Let's break it down step by step:
Original Function: f(x)
Domain: The set of all possible input values for x in the function f(x).
Range: The set of all possible output values for f(x).
Reflected Function: -f(x)
Reflected Domain: The domain remains the same because reflecting over the x-axis does not change the x-coordinates. So, the reflected domain is the same as the original domain.
Reflected Range: The range is affected by the reflection. All the positive values in the original range become negative, and all the negative values become positive. If the original function had points (a, b), the reflected function will have points (a, -b). This essentially flips the original range values.
In summary:
Reflected Domain: Same as the original domain.
Reflected Range: The sign of each value in the original range is negated. For example, if the original function had a point (2, 3), the reflected function would have a point (2, -3).
The complete question is :
how does the reflection over the x-axis (-f(x)) affect the domain and range
Solve this equation for x. Round your answer to the nearest hundredth. 1 = In(x + 4)
Answers
Answer:
-1.28
Step-by-step explanation:
1=ln(x+4)
ln(x+4)=1
e^ln(x+4)=e^1
x+4=e
x=e-4=-1.28
HELP!
Use the distributive property to match equivalent expressions.
Answers
Answer:
Step-by-step explanation:
1d
2a
3b
4c
The distributive property states that performing an operation on a sum or difference (either multiplication or division) is equivalent to performing that operation on each addend separately and then summing or subtracting the results. As an example, the statement 2*(3 + 4) can be rewritten as (2*3) + (2*4) to demonstrate the application of the distributive property.
Explanation:The distributive property in mathematics states that the multiplication of a number by a sum is equivalent to the sum after each addend has been multiplied by that number individually. For example, if we had the expression 2*(3 + 4), using the distributive property, we could rewrite it as (2*3) + (2*4) which is 6 + 8, and both expressions equal to 14 (because 2*(3 + 4)=2*7=14).
So to match equivalent expressions using the distributive property, you would have to identify expressions that follow this rule. For example:
3*(x + 5) is equivalent to 3*x + 3*57*(y - 2) is equivalent to 7*y - 7*2Learn more about Distributive Property here:https://brainly.com/question/6276874
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I don't really understand :/
Remove all perfect squares from inside the square root.
√180
Answers
Answer:
6[tex]\sqrt{5}[/tex]
Step-by-step explanation:
We can factorize 180 to get 2^2*3^2*5.
We know that 2^2 and 3^2 are squares so we can remove them from under the radical.
So, the simplified square root would be 6[tex]\sqrt{5}[/tex]
To remove perfect squares inside a square root, we simplify the number using prime factorisation. In this case, √180 simplifies to 6√5.
Explanation:The given value is √180. To simplify it or remove perfect squares, we have to find the prime factors of the number under the square root. We can write 180 as 2 * 2 * 3 * 3 * 5. In square root simplifications, we usually group the factors into pairs, because a pair of same factors gives one factor outside the square root. Here, 2 * 2 becomes 2 and 3 * 3 becomes 3. There is an extra 5 inside the square root that cannot come out because it doesn't have a pair. Hence, √180 simplifies to 6√5.
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Drag the cards to create a three -digit number that matches these rules
Note:not all cards will be used
Answers
Selection of the digits, In accordance with the rules results to
671
What is place value
Place value is the value of a digit based on its position within a numeral, especially in the base-10 (decimal) number system.
Each digit in a number has a place value, and the position of the digit determines its contribution to the overall value of the number.
The digit in the hundreds place (6) comes first. Next is the tens digit (7) then lastly the ones digit (1)
This results to 671
Calibrating a scale:
Making sure that the scales used by businesses in the United States are accurate is the responsibility of the National Institute for Standards and Technology (NIST) in Washington, D.C. Suppose that NIST technicians are testing a scale by using a weight known to weigh exactly 1000 grams. The standard deviation for scale reading is known to be o 2.8. They weigh this weight on the scale 50 times and read the result each time. The 50 scale readings have a sample mean of x = 1001.1 grams. The calibration point is set too high if the mean scale reading is more than 1000 grams. The technicians want to perform a hypothesis test to determine whether the calibration point is set too high.
Use a = 0.01 level of significance and the critical value method.
(a) State the appropriate null and alternate hypotheses.
H0:
H1:
This hypothesis test is a left, right, or two tailed?
Answers
Answer:
We conclude that the calibration point is set too high.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 1000 grams
Sample mean, [tex]\bar{x}[/tex] = 1001.1 grams
Sample size, n = 50
Alpha, α = 0.05
Population standard deviation, σ = 2.8 grams
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 1000\text{ grams}\\H_A: \mu > 1000\text{ grams}[/tex]
We use One-tailed(right) z test to perform this hypothesis.
Formula:
[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]z_{stat} = \displaystyle\frac{ 1001.1 - 1000}{\frac{2.8}{\sqrt{50}} } = 2.778[/tex]
Now, [tex]z_{critical} \text{ at 0.01 level of significance } = 2.326[/tex]
Since,
[tex]z_{stat} > z_{critical}[/tex]
We reject the null hypothesis and accept the alternate hypothesis. We accept the alternate hypothesis. We conclude that the calibration point is set too high.
Final answer:
The null hypothesis is that the calibration point is set correctly and the alternate hypothesis is that the calibration point is set too high.
Explanation:
The appropriate null and alternate hypotheses for this hypothesis test are:
H0: The calibration point is set correctly (mean scale reading = 1000 grams)
H1: The calibration point is set too high (mean scale reading > 1000 grams)
This hypothesis test is a right-tailed test because the alternate hypothesis is testing for a value greater than the null hypothesis.
Lola charges $7 for 1/2 dozen cupcakes. What is the price per dozen?
Answers
Answer: $14
Step-by-step explanation: To find out the price per dozen, we first need to understand that the word "dozen" means a grouping of 12. This means that 1/2 a dozen would be half of 12 which is 6.
If we double 6 to 12, we multiply by 2. We will also multiply by 2 for the price so we have 7 × 2 which simplifies to 14.
Therefore, Lola will charge $14 for her cupcakes.
I also provided an image to show the 1/2 dozen and dozen cupcakes.
you jus drove your car 450 miles and used 50 gallons of gas. you know that the gas tank on your car holds 15 1/2 gallons of gas. what is the most number of miles you can drive on one tank of gas?
Answers
Final answer:
To find the most number of miles you can drive on one tank of gas, divide the total miles driven by the total gallons used to calculate the miles per gallon (MPG). Then, multiply the MPG by the number of gallons in the gas tank to find the maximum number of miles that can be driven on one tank.
Explanation:
To find the most number of miles you can drive on one tank of gas, you can use the given information. You know that you just drove your car 450 miles and used 50 gallons of gas. Therefore, to find the miles per gallon (MPG), divide the total miles driven by the total gallons used. In this case, 450 miles divided by 50 gallons gives you an MPG of 9. This means that for every gallon of gas, your car can travel 9 miles.
Now, you know that the gas tank on your car holds 15 1/2 (or 15.5) gallons of gas. To find the maximum number of miles you can drive on one tank of gas, multiply the MPG by the number of gallons in the tank. So, 9 MPG multiplied by 15.5 gallons equals 139.5 miles. Therefore, the most number of miles you can drive on one tank of gas is 139.5 miles.
The most number of miles you can drive on one tank of gas is 139.5 miles.
To determine the most number of miles you can drive on one tank of gas, follow these steps:
Calculate the car's average miles per gallon (mpg):
You drove 450 miles using 50 gallons of gas.
The average mpg is calculated by dividing the total miles driven by the total gallons of gas used: [tex]\frac{450 \text{ miles}}{50 \text{ gallons}} = 9 \text{ mpg}.[/tex]
Determine the capacity of one full tank of gas in your car:
The gas tank holds 15 1/2 gallons of gas. Convert 15 1/2 to a decimal: [tex]15 \frac{1}{2} = 15.5 \text{ gallons}.[/tex]
Calculate the most number of miles you can drive on one full tank of gas:
Multiply the car's average mpg by the gas tank's capacity: [tex]9 \text{ mpg} \times 15.5 \text{ gallons} = 139.5 \text{ miles}.[/tex]
2. The registration at a preschool is $125. Then,
parents must also pay $475 per month for
tuition. Write an equation to represent the
total cost after each month. Identify your
variables. a) What is the rate of change?
b) What is the initial value?
c) What is the Independent variable?
d) What is the dependent variable?
Answers
The equation of the total cost is y = 475 x + 125, where y is the total cost for x months
a) The rate of change is $475 per month
b) The initial value is $125
c) The independent variable is the number of months (x)
d) The dependent variable is the total cost after each month (y)
Step-by-step explanation:
The given is:
The registration at a preschool is $125The parents must also pay $475 per month for tuitionAssume that the total cost is y for x months
∵ The registration fee = $125 ⇒ paid once
∵ The parents pay $475 per month for tuition
∵ The number of months is x
∴ The total cost y = 475 x + 125
The equation of the total cost is y = 475 x + 125, where y is the total cost for x months
∵ y = 475 x + 125 is in the form of the linear equation y = m x + b,
m is the slope of the line and b is the y-intercept
∵ The slope of the line m is the rate of change y with respect to x
∴ m = 475
∴ The rate of change is $475 per month
a) The rate of change is $475 per month
∵ b is the initial value of y at x = 0
∴ b = 125
∴ The initial value is $125
b) The initial value is $125
∵ The independent variable is x
∴ The independent variable is the number of months (x)
c) The independent variable is the number of months (x)
∵ The dependent variable is y
∴ The dependent variable is the total cost after each month (y)
d) The dependent variable is the total cost after each month (y)
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Solve each equation using the quadratic formula x = =
a. x2 + 3x + 2 = 0
c. 2x2 + 5x = 1
b. 4x2 + 8x - 24 = 0
d. x2 + 14x + 33 = 0
Answers
Answer:
a: x=-2, x=-1
c:x=-2.68, x=0.186
b:x=-3.6, x=1.6
d:x=-11, x=-3
Need help with this math problem
Answers
The value of b is: 4
Step-by-step explanation:
The given polygon is a convex polygon with three sides. A polygon with three sides is called triangle. The sum of interior angles of a triangle is 180°
So,
[tex]Sum\ of\ Angles = 180\\(b+41)+(101)+(b+30) = 180\\b+41+101+b+30 = 180\\2b+172 = 180\\2b = 180-172\\2b = 8[/tex]
Dividing both sides by 2
[tex]\frac{2b}{2} = \frac{8}{2}\\b = 4[/tex]
Hence,
The value of b is: 4
Keywords: Polygons, Triangles
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What is the sum of the polynomials?(8x^2-9x^2-4x)+(x^2-3y^2-7x)
Answers
Answer:
-11x-3y^2
Step-by-step explanation:
(8x^2-9x^2-4x)+(x^2-3y^2-7x)
-x^2-4x+x^2-3y^2-7x
-4x-7x-3y^2
-11x-3y^2
Answer:
-3y² - 11xStep-by-step explanation:
[tex](8x^2-9x^2-4x)+(x^2-3y^2-7x)\\\\=8x^2-9x^2-4x+x^2-3y^2-7x\qquad\text{combine like terms}\\\\=(8x^2-9x^2+x^2)-3y^2+(-4x-7x)\\\\=-3y^2-11x[/tex]
Ingrid has $30 to buy oil paints for her painting class. Each tube of paint
costs $9. How many tubes can she buy? Do not include units in your answer.
Answers
Answer:
3
Step-by-step explanation:
She has enough money to buy 3 tubes which leaves with $3 for whatever else she desires
Determine the probability of being dealt 3 tens from a standard deck of 52 cards when 3 cards are dealt
Answers
Answer:
A standard deck contains 52 cards with 4 suits and hence 4 tens. The probability of being dealt 3 tens is thus 4/52 x 3/51 x 2/50. The denominator decreases as one card is removed from the deck each time. If the removed card is replaced, there would be no need for the decrease in the denominator.
Step-by-step explanation:
Adam has 16.45 kg of flour, he uses 6.4 kg to make hot cross buns. The remaining flour is exactly enough to make 15 batches of scones. How much flour in kg will be in each batch of scones?
Answers
Answer:
Each batch of scones needed 0.67 kg of flour
Step-by-step explanation:
16.45 - 6.4 = 10.05kg (remaining)
15 batches = 10.05kg
1 batch = 0.67kg
A coffee company surveyed 40 potential customers to see where they would
like the company's new organic coffee sold. Respondents were given the
following four locations and asked to choose as many as they liked: grocery
stores, drugstores, health food stores, and big box stores. The results are
summarized in the bar graph below, with the number of times each location
was chosen noted above the corresponding bar.
Where should we sell our organic coffee?
20
16
14
10
Grocery
Stores
Drugstores Health
Food Stores
Stores
What was the average number of locations chosen per potential customer?
Answers
Answer:
1.5
Step-by-step explanation:
The average number of locations chosen per potential customer in the coffee company's survey was 1.5.
Explanation:To calculate the average number of locations chosen per potential customer, we need to know the total number of preferences selected by all 40 potential customers. The numbers given for each location are: 20 for grocery stores, 16 for drugstores, 14 for health food stores, and 10 for big box stores.
Adding these together gives a total of 60 preferences for the four locations (20+16+14+10). This total is then divided by the 40 potential customers to produce the average. Therefore, the average number of locations chosen per potential customer is 1.5 (60 ÷ 40 = 1.5).
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I dont understand how to answer this. I tried to find the second derivative.
Answers
Answer:
(B) π/12 + π/6 k
Step-by-step explanation:
Points of inflection are where f"(x) = 0 and changes signs.
f(x) = cos²(3x)
f(x) = (cos(3x))²
f'(x) = 2 (cos(3x))¹ × -sin(3x) × 3
f'(x) = -6 sin(3x) cos(3x)
Using double angle formula:
f'(x) = -3 sin(6x)
f"(x) = -3 cos(6x) × 6
f"(x) = -18 cos(6x)
0 = -18 cos(6x)
0 = cos(6x)
6x = π/2 + 2πk or 6x = 3π/2 + 2πk
We can simplify this to:
6x = π/2 + πk
x = π/12 + π/6 k
what does 2+2 equal to
Answers
Answer:
Step-by-step explanation:
1
2+2=4 because you add it ok well bye :)
Simplify 143.87x34.65x87.78+12.63-19.63 to the nearest tenth.
Answers
Answer:
437584.68
Step-by-step explanation:
Answer:
Step-by-step explanation:
437584.7
12. For triangle MNP shown, find the value of x
and the measure of each of the three angles
M
/(2x – 1)º (2x + 1))
Answers
Answer:
[tex]x=36\°\\\angle P=71 \°,\angle N=73 \°,\angle M=36 \°[/tex]
Step-by-step explanation:
Given:
The triangle is shown below.
We know that the sum of all interior angles of a triangle is equal to 180°.
Therefore,
[tex]\angle M+\angle N+\angle P=180 \°\\\\x+2x+1+2x-1=180\°\\\\5x=180\°\\\\x=\frac{180}{5}\\\\x=36\°[/tex]
Now, plugging the value of 'x' in each angle measure and determining its values. We get:
[tex]\angle M=x=36\°\\\angle P=2x-1=2(36)-1=72-1=71\°\\\angle N=2x+1=2(36)+1=72+1=73\°[/tex]
Therefore, the value of 'x' is 36° and the measure of the three angles are 36°, 71° and 73°.
Solve for n: 5/6n+17=72
Answers
Answer:
n=66
Step-by-step explanation:
5/6n=72-17
5/6n=55
n=55/(5/6)
n=(55/1)(6/5)
n=(11*6)/1
n=66/1
n=66
Answer:
66
Step-by-step explanation:
The percents of students who travel to school by car, bus, and bicycle are shown for a school of 825 students. 20% by car 48% by bus and 8% by bike. What would be the other method present of going to school?
Plz give clear answer
Answers
Answer:
24% could be going to school by walking
Step-by-step explanation:
By adding the given percentages of students traveling by car, bus, and bike, and subtracting from 100%, we find that 24% of students use other methods to travel to school.
Explanation:To find the other method of traveling to school not mentioned among car, bus, and bicycle, we first need to add up the provided percentages for these modes of transportation: 20% (car) + 48% (bus) + 8% (bike) = 76%. Since all the percentages must add up to 100%, we subtract the sum of these percentages from 100% to determine the remaining percentage. Therefore, 100% - 76% = 24%. So, 24% of students travel to school by other methods that are not specified (walking, skateboarding, etc.).
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Given C is the midpoint of Ad and be
Answers
Answer:
By SAS rule
Step-by-step explanation:
Required to Prove
ABC is congruent to DEC
Given
C is midpoint of AD and BE
As C is the midpoint of both line segments
AC=CD
BC=CE
and ∠ACB=∠DCE(Vertically opposite angles)
⇒By SAS(side-AC and DC, angle-∠ACB,∠DCE,side-BC and EC) congruency rule
triangle ABC is congruent to triangle DEC
The table shows the distance a runner covers during a race:
Time, x
(minutes)
Distance, y
(miles)
5 0.5
10 1
15 1.5
20 2
25 2.5
Which equation represents the relationship between x and y?
a. y = 0.5x
b. y = 10x
c. y = x + 10
d. y = 110x
win brainliest
Answers
Answer:
b. y=10x
Step-by-step explanation:
here, x represents time(minutes) : 0.51
1.5
2
2.5
y represents distance (miles): 5
10
15
20
25
to write any equation(linear) basically we need 2 points lying on itlet the 2 points be: (1,10) and (2,20) [from the given information]
now, let (A,B) and (C,D) are two points on a linethen the equation of it can be given as :
[tex]y-B=(\frac{D-B}{C-A} )*(x-A)[/tex]
so, here the required equation will be,[tex]y-10=(\frac{20-10}{2-1} )*(x-1)\\[/tex]
this is also equal to, [tex]y-10=10*(x-1)\\y-10=10x-10\\y =10x-10+10\\y=10x[/tex]
therefore, option c represents the relationship between x and y.[trick: when you have options, you can directly substitute x and respective y values and check if the equation satisfies it. the equation which satisfies all the x and respective y values will be the correct equation.]Carolina paid $15.80 for 4 hamburgers.
What is the unit rate representing the cost of 1 hamburger? PLEASE HELP!!!!!!!!!!!!!!!1
Answers
Answer:
The cost of one hamburger is $3.95.
Step-by-step explanation:
15.80/4=3.95
Answer:
$ 3.95
Step-by-step explanation:
it is 3.95 because you divide 15.80 by 4
Subtract 11b2 - 4b +7 from b2 + 8b -9
Answers
Answer:
2(4b-1)
Step-by-step explanation:
If f (x) = -3x-5 and g(x) =4x-2 find (f+g)(x)
Answers
Answer:
C. (f + g)(x) = x - 7Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\\text{Substitute}\ f(x)=-3x-5\ \text{and}\ g(x)=4x-2:\\\\(f+g)(x)=(-3x-5)+(4x-2)\qquad\text{combine like terms}\\\\(f+g)(x)=(-3x+4x)+(-5-2)\\\\(f+g)(x)=x-7[/tex]
Jadon rode in the car 42 miles. This represents 70% of his entire trip. What is the total number of miles in jadons trip?
Answers
There are 60 miles in Jadon's trip.
Step-by-step explanation:
Distance covered by Jadon = 42 miles
This is 70% of his entire trip.
Let,
x be the total number of miles in Jadon's trip.
We know that,
70% of x = 42 miles
[tex]\frac{70}{100}*x=42\\0.7x=42[/tex]
Dividing both sides by 0.07;
[tex]\frac{0.7x}{0.7}=\frac{42}{0.7}\\x=60\ miles[/tex]
There are 60 miles in Jadon's trip.
Keywords: distance, percentage
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