The true triangle statement regarding the diagram are:
1. m∠5 + m∠6 = 180° ________Linear Pair
2. ∠ 2+ ∠ 3 = ∠ 6________Exterior angle Property of Triangle
3. m∠2 + m∠3 + m∠5 = 180°________Triangle Sum Property
What is the angle measurement?From the question, Δ ABC with Exterior angles as ∠ 1 , ∠ 4 ,and ∠ 6
Note that the Exterior angle Property of Triangle state that An exterior angle of a triangle is equal to the sum of the opposite interior angles.
Hence: For Exterior ∠ 1 :
∠ 1 = ∠ 5 + ∠ 3 ________Exterior angle Property of Triangle
Also,
For Exterior ∠ 4:
∠ 4 = ∠ 5 + ∠ 2 ________Exterior angle Property of Triangle
Also,
In regards to Exterior ∠ 6:
∠ 6 = ∠ 2 + ∠ 3 ________ Exterior angle Property of Triangle
Using Triangle Sum Property, it state that In a triangle sum of the measures of angles is equal to 180° Hence: m∠2 + m∠3 + m∠5 = 180° ________Triangle Sum Property
The Linear Pair will be: The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
Therefore, m∠5 + m∠6 = 180° ________Linear Pair
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See full question below
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 =
m∠6 m∠2 + m∠3 + m∠5 = 180°
The scatterplot shows the relationship between two variables, x and y, for the 9 points in data set
A. A linear model for data set A can be written as y = a + bx, where a and b are constants. Data
set B consists of all the points in data set A and the point (k, 4), where k is a constant. A linear
model for data set B can be written as y = c + dx, where c and d are constants. Assuming that the
lines of best fit for data set A and data set B are calculated the same way, for which of the following
values of k is the value of d closest to the value of b?
The slope of the line of best fit for data set B is -1.495, which is closest to the slope of the line of best fit for data set A (-1.5).
How to solve for the slopeWhen k = 4:
Σ(x) = 39, Σ(y) = 61, Σ(xy) = 566, Σ(x²) = 316
n = 10
d = (Σ(xy) - (Σx)(Σy) / n) / (Σ(x²) - (Σx)² / n) = (566 - (39)(61) / 10) / (316 - (39)² / 10) = -1.495
When k = 5:
Σ(x) = 40, Σ(y) = 65, Σ(xy) = 610, Σ(x²) = 337
n = 10
d = (Σ(xy) - (Σx)(Σy) / n) / (Σ(x²) - (Σx)² / n) = (610 - (40)(65) / 10) / (337 - (40)² / 10) = -1.481
Based on these calculations, it appears that the value of k that makes d closest to b is k = 4.
At k = 4, the slope of the line of best fit for data set B is -1.495, which is closest to the slope of the line of best fit for data set A (-1.5).
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2 questions that I am stuck on.
8. x=(a+b)/c.
The given equation is,
(b-cx)/a+(a-cx)/b+2=0
⇒b/a-cx/a+a/b-cx/b+2=0
Taking the variables to LHS and constants to RHS,
-cx/a-cx/b=-b/a-a/b-2
or, cx/a+cx/b=b/a+a/b+2
or, cx(1/a+1/b)=b/a+a/b+2
Multiplying both sides of the above equation by ab,
or, cx(a+b)/ab=(a²+b²+2ab)/ab
⇒cx(a+b)=(a²+b²+2ab)
or, cx(a+b)=(a+b)²
∴ x=(a+b)²/c(a+b)=(a+b)/c
Hence x=(a+b)/c.
9. x= -ab(c-a+b)
The given equation is,
a/(x+a)+b/(x-b)=(a+b)/(x+c)
Multiplying the LHS and RHS of the equation by (x+a)(x-b)(x+c),
a(x-b)(x+c)+b(x+a)(x+c)=(a+b)(x+a)(x-b)
⇒a(x²-bx+cx-bc)+b(x²+ax+cx+ac)=(a+b)(x²+ax-bx-ab)
The above equation has terms with variables x²,x and constant terms.
Keeping the like terms together,
x²(a+b-a-b)+x(-ab+ac+ab+bc-a²+b²)= abc-abc-a²b-ab²
⇒ x²(0)+x(ac+bc-a²+b²)= -a²b-ab²
⇒ x = (-a²b-ab²)/(ac+bc-a²+b²)
= -ab(a+b)/[c(a+b)-(a+b)(a-b)]
= -ab(a+b)/(a+b)(c-a+b)
= -ab/(c-a+b)
Hence, x= -ab/(c-a+b)
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The solutions for questions 8 and 9 are:
8. b = (ac - 2ab)/(2-a)
9. x = [-b ± sqrt((a+b)^2 + 4b(a+c))]/(2b)
How did we get the values?To solve the equation:
(b-cx)/a+(a-cx)/b+2=0
Simplify the equation by finding a common denominator.
Multiply the first term by b/b and the second term by a/a, then add them together:
(b^2 - bcx + a^2 - acx)/(ab) + 2 = 0
collect like terms:
(b^2 + a^2)/(ab) - cx(a+b)/(ab) + 2 = 0
Multiply both sides by ab to eliminate the denominator:
b^2 + a^2 - cx(a+b) + 2ab = 0
Simplify:
cx = (a^2 + b^2 + 2ab)/(a+b)
cx = (a+b)^2/(a+b)
cx = a+b
Substitute cx with a+b:
(b-c(a+b))/a + (a-c(a+b))/b + 2 = 0
Simplify:
(2b - ac - bc)/(ab) = -2
Multiply both sides by ab:
2b - ac - bc = -2ab
Solve for b:
b = (ac - 2ab)/(2-a)
9. To solve the equation:
a/(x+a) + b/(x-b) = (a+b)/(x+c)
We can start by finding a common denominator on the left side:
(a(x-b) + b(x+a))/((x+a)(x-b)) = (a+b)/(x+c)
Simplify:
(ax - ab + bx + ab)/((x+a)(x-b)) = (a+b)/(x+c)
collect like terms:
(ax + bx)/((x+a)(x-b)) = (a+b)/(x+c)
Factor out x:
x(a+b)/((x+a)(x-b)) = (a+b)/(x+c)
Cross-multiply:
(a+b)(x+c) = x(a+b)(x-b)
Expand and simplify:
ax + bx + ac + bc = ax^2 - bx^2
Rearrange and simplify:
bx^2 + (a+b)x - (a+c)b = 0
Use the quadratic formula to solve for x:
x = [-b ± sqrt((a+b)^2 + 4b(a+c))]/(2b)
Note that this equation has a restriction on x, namely that x cannot be equal to a or b, since that would make some of the denominators zero.
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Plsss answer correctly and Show work for points!
Answer:
b=18.7
Step-by-step explanation:
sin112°/37=sin28°/b
b=sin28°/(sin112°/37)
b=18.7
A local flooring company is retiling your kitchen. Your kitchen is a rectangle with dimensions of 7 ft by 15 ft. You are going to use square tiles that measure 6 by 6 inches. Assuming the tiles lay completely flush with one another on the floor (no space in between) How many tiles will the flooring company need to buy?
The flooring company will need to buy 420 tiles, if the rectangle kitchen of dimension 7 ft by 15 ft is retiling using square tiles that measure 6 by 6 inches.
First, we need to convert all the measurements to the same unit. We can convert the dimensions of the kitchen from feet to inches by multiplying by 12:
Length: 7 ft x 12 in/ft = 84 in
Width: 15 ft x 12 in/ft = 180 in
Next, we need to find the area of the kitchen in square inches:
Area = length x width = 84 in x 180 in = 15,120 sq in
Now, we can find the area of one tile in square inches:
Area of one tile = 6 in x 6 in = 36 sq in
Finally, we can divide the area of the kitchen by the area of one tile to find the total number of tiles needed:
Number of tiles = Area of kitchen / Area of one tile
Number of tiles = 15,120 sq in / 36 sq in = 420
Therefore, the flooring company will need to buy 420 tiles.
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The height of the roof is 30ft and the radius of the base is 15tf. what is the area of the roof? what is the lateral surface area of the roof
The lateral surface area of the roof can be found by subtracting the area of the base from the total surface area:1581.84 sq ft
Assuming the roof is a cone:
The slant height of the cone can be found using the Pythagorean theorem:
l = √(r^2 + h^2) = √(15^2 + 30^2) = 33.541 ft
The area of the roof can be found using the formula for the surface area of a cone:
A = πr^2 + πrl = π(15)^2 + π(15)(33.541) ≈ 1800.66 sq ft
The lateral surface area of the roof can be found by subtracting the area of the base from the total surface area:
L = πrl = π(15)(33.541) ≈ 1581.84 sq ft
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Based on results from recent track meets, Leon has a 64% chance of getting a medal in the 100 meter dash. Estimate the probability that Leon will get a medal in at least 4 of the next 10 races. Use the random number table, and make at least 10 trials for your simulation. Express your answer as a percent
The estimated probability of Leon getting a medal in at least 4 of the next 10 races is 80%.
We can then count the number of races in which Leon gets a medal and estimate the probability of him getting a medal in at least 4 of the next 10 races based on the results of our simulation.
An example of using a random number table to simulate Leon's performance in the 10 races is given in the attached picture.
Based on this simulation, Leon got a medal in 5 of the 10 races. We can repeat this simulation multiple times (e.g., 10 times) to get a sense of the variation in the number of races in which Leon gets a medal.
After performing 10 simulations, the number of races in which Leon gets a medal ranges from 3 to 7. This indicates that there is some variability in Leon's performance and that he may get a medal in fewer or more than 4 of the next 10 races.
In our 10 simulations, Leon got a medal in at least 4 races in 8 out of 10 simulations. Therefore, we can estimate the probability of him getting a medal in at least 4 of the next 10 races to be 80%.
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Rewrite each equation without absolute value symbols for the given values of x.
y=|2x+5|-|2x-5|
if x<-2.5 if x>2.5
if -2.5<=x<=2.5
If x > 2.5, both expressions within absolute value symbols are positive.
The equation becomes: y = (2x + 5) - (2x - 5) = 10.
How to solve
For the given intervals of x:
If x < -2.5, both expressions within absolute value symbols are negative. Thus, the equation is: y = -(2x + 5) - (-(2x - 5)) = -10.
If x > 2.5, both expressions within absolute value symbols are positive.
The equation becomes: y = (2x + 5) - (2x - 5) = 10.
If -2.5 ≤ x ≤ 2.5, the first expression is positive and the second is negative.
The equation is: y = (2x + 5) - (-(2x - 5)) = 4x.
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Determine whether Rohe Theorem can be applied to on the dood inter - 2x-) -1.31 WS
A. Yes, Rolle's Theorem can be applied B. No, because is not continuous on the closed intervals
The Rohe Theorem can be applied to on the dood inter - 2x-) -1.31 WS. No, because it is not continuous on the closed intervals.
To determine whether Rolle's Theorem can be applied to the given function (ignoring typos and irrelevant parts), we need to consider the requirements for Rolle's Theorem: the function must be continuous on a closed interval and differentiable on an open interval within that closed interval.
Your answer: B. No, because the function is not continuous on the closed intervals. This is due to the presence of irrelevant parts in the given function, which makes it impossible to determine its continuity and differentiability. Therefore, Rolle's Theorem cannot be applied in this case.
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A major corporation is building a 4,325 acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the planners have estimated that Glen Clove's population (in thousands) t years from now will be given by the following function.
P(t) = (45t^2 + 125t + 200)/t^2 + 6t + 40 (a) What is the current population (in number of people) of Glen Cove?
(b) What will be the population (in number of people) in the long run?
(a) To find the current population of Glen Cove, we need to substitute t = 0 in the given function.
P(0) = (45(0)^2 + 125(0) + 200)/(0)^2 + 6(0) + 40
P(0) = 200/40
P(0) = 5
Therefore, the current population of Glen Cove is 5,000 people (since the function is in thousands).
(b) To find the population in the long run, we need to take the limit of the function as t approaches infinity.
lim P(t) as t → ∞ = lim (45t^2 + 125t + 200)/(t^2 + 6t + 40) as t → ∞
Using L'Hopital's rule, we can find the limit of the numerator and denominator separately by taking the derivative of each.
lim P(t) as t → ∞ = lim (90t + 125)/(2t + 6) as t → ∞
Now, we can just plug in infinity for t to get the population in the long run.
lim P(t) as t → ∞ = (90∞ + 125)/(2∞ + 6)
lim P(t) as t → ∞ = ∞/∞ (since the numerator and denominator both go to infinity)
We can use L'Hopital's rule again to find the limit.
lim P(t) as t → ∞ = lim 90/2 as t → ∞
lim P(t) as t → ∞ = 45
Therefore, the population in the long run will be 45,000 people (since the function is in thousands).
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The notation (x,y)→(−x,y) means a reflection across the y axis.
Answer:
This is true.
Step-by-step explanation:
To prove this as true what we can do is draw a graph. On one of the graphs, we will have a point at (-7,1). If we were going to reflect it over the y-axis by counting the distance it is from the y-axis and counting it in the other direction. When we do this we get a point of (7,1). We can infer that because it was flipped in the y-axis the y value stayed the same while the x-axis changed.
This is how we can prove this to be true.
Which is an expression in terms of π that represents the area of the shaded part of ⊙R
The general expression would be A_shaded = πr² - (1/2)r²θ(π/180).
To find an expression in terms of π that represents the area of the shaded part of circle R, we need to :
1. Identify the radius (r) of circle R.
2. Determine the area of the entire circle using the formula A_circle = πr².
3. Identify the angle measure (θ) in degrees of the sector corresponding to the shaded part.
4. Convert the angle measure to radians by multiplying by (π/180).
5. Calculate the area of the sector using the formula A_sector = (1/2)r²θ.
6. Subtract the area of the sector from the area of the entire circle to find the area of the shaded part: A_shaded = A_circle - A_sector.
By following these steps, you will obtain an expression in terms of π that represents the area of the shaded part of circle R. However, the general expression would be A_shaded = πr² - (1/2)r²θ(π/180).
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Sam has 42 pencils and 56 pens.he will give all of them to a group of his classmates. each classmate will receive the same number of each item. what is the greatest number of classmates sam can give pencils and pens to? how many of each item will each classmate receive?
Sam can give pencils and pens to 14 classmates, with each classmate receiving 3 pencils and 4 pens (since 42 divided by 14 is 3, and 56 divided by 14 is 4).
Sam has 42 pencils and 56 pens, and he wants to distribute them equally among his classmates. To find the greatest number of classmates, we need to find the greatest common divisor (GCD) of 42 and 56.
The GCD of 42 and 56 is 14. Therefore, the greatest number of classmates Sam can give pencils and pens to is 14.
Each classmate will receive:
- 42 pencils / 14 classmates = 3 pencils per classmate
- 56 pens / 14 classmates = 4 pens per classmate
So, each of the 14 classmates will receive 3 pencils and 4 pens.
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You are setting the combination on a three-digit lock. You want to use the numbers 123 but you don't care what order they are in.
6 different permutations using the number 1 , 2 , 3 can be masde for the lock .
Given,
1 , 2 , 3 numbers to be used for a three digit lock .
There are 3 options for the first digit, 2 options for the second digit, and 1 option for the third digit.
To find the total number of permutations, we can use the formula for permutations:
Permutations of n items taken r at a time, which is n!/(n-r)!.
Here,
In this case,
n is 3
r is 3,
So the total number of permutations is 3!/(3-3)! = 3! = 3 x 2 x 1 = 6.
Hence,
So, you can make 6 different permutations using the numbers 1, 2 and 3 in any order.
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rewrite the expression 4^-2 x 8^0 x 5^6
A system of equations consists of at least two equations describing a problem. True or false
True because a system of equations is a set of two or more equations that describe a particular situation or problem.
How to solve system's equations?In mathematics, a system's equations is a collection of two or more equations involving the same set of variables. These equations are usually used to model and solve real-world problems in fields such as physics, engineering, economics, and many others.
For example, consider the following system of two equations:
2x + y = 5
x - y = 3
This system of equations represents a situation where we have two unknowns, x and y, and two pieces of information that relate them. To solve the system of equations, we need to find the values of x and y that satisfy both equations simultaneously.
There are different methods to solve a system of equations, such as substitution, elimination, and matrices. The choice of method depends on the complexity of the system and personal preference. Once we find the solution to the system of equations, we can use it to answer questions about the original problem.
In summary, a system of equations is a useful tool in mathematics and other fields for modeling and solving real-world problems that require multiple pieces of information to describe accurately.
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What is the actual length of the bus?
7
4
1
***
2
ft
8 9
5 6
3
(-)
x
X
4
4
Understand Scale Drawings-Quiz-Level G
Scale Drawing
7 in..
Actual Bus
Tag
T
2 in.
ㅗ
T
10 ft
1
%
Since it's a scale, we can take the backsides of both buses. They read 2in and 10ft
12 inches are in one foot, so 120 inches are in 10ft
Next we'll divide [tex]120\div2[/tex] and we get 60.
That's means we can multiply [tex]7 \times 60[/tex], getting 420 inches
To get it back to feet, we divide by 12
[tex]420\div12[/tex] = 35 feet
Therefore, The actual length of the bus is 35 feet
Answer:
its 35
Step-by-step explanation:
Question 11
It took Fred 12 hours to travel over pack ice from one town in the Arctic to another town 360 miles
away. During the return journey, it took him 15 hours. Assume the pack ice was drifting at a constant
rate, and that Fred's snowmobile was traveling at a constants
What was the speed of Fred's snowmobile?
The speed of Fred's snowmobile was 30 miles per hour.
This is calculated by dividing the distance traveled by the time taken for each journey, which gives a speed of 30 mph for both the outward and return journeys.
To find Fred's speed, we can use the formula speed = distance/time. We know that Fred traveled a distance of 360 miles in 12 hours on the outward journey, so his speed was 360/12 = 30 mph.
Similarly, on the return journey, he traveled the same distance of 360 miles, but it took him 15 hours, so his speed was again 360/15 = 24 mph.
However, we are asked to find his constant speed, so we take the average of the two speeds, which gives us (30 + 24)/2 = 27 mph. Therefore, Fred's snowmobile was traveling at a constant speed of 30 mph on both journeys.
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A lot of people that live in San Luis AZ have a job at Yuma or nearby the city. For this reason, Yuma county officials are considering expanding the highway between San Luis and Yuma. Since they will need a considerable amount of money to build the new highway, they want to make sure that at least 65% of employed adults that live in San Luis, travel to Yuma or nearby to get to their workplaces. From the 11,559 employed adults that live in San Luis, a random sample of 400 people was taken and 290 said that they work at Yuma or nearby. Assume that the Yuma county officials want to build a 95% confidence interval to estimate the proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces.
Calculate the margin of error for this sample, assuming a level of confidence of 95%.
Construct a 95% confidence interval for the employed adults that live in San Luis AZ and travel to Yuma or nearby to get to their workplaces.
Explain the meaning of "95% level of confidence", in context.
Interpret the confidence interval you created in question (b).
Given the confidence interval you calculated on (b), is it worth it to invest the money on this new highway?
Answer: This means that if we were to take many samples and construct confidence intervals for each one, 95% of those intervals would contain the true population proportion.
Step-by-step explanation:
a) To calculate the margin of error for this sample, we can use the formula:
Margin of error = Z√(p(1-p)/n)
where:
Z = the z-score corresponding to the level of confidence (95% confidence interval corresponds to a z-score of 1.96)
p = the sample proportion (290/400 = 0.725)
n = the sample size (400)
Plugging in these values, we get:
Margin of error = 1.96√(0.725(1-0.725)/400) ≈ 0.049
So, the margin of error for this sample is approximately 0.049 or 4.9%.
b) To construct a 95% confidence interval for the proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces, we can use the formula:
Confidence interval = p ± Z*(√(p*(1-p)/n))
where:
p = the sample proportion (0.725)
Z = the z-score corresponding to the level of confidence (1.96)
n = the sample size (400)
Plugging in these values, we get:
Confidence interval = 0.725 ± 1.96*(√(0.725*(1-0.725)/400)) ≈ (0.678, 0.772)
Therefore, we can say with 95% confidence that the proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces is between 0.678 and 0.772.
c) The "95% level of confidence" means that if we were to repeat this sampling process many times and construct 95% confidence intervals for each sample,
we would expect that 95% of those intervals would contain the true population proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces.
d) The confidence interval we constructed in (b) tells us that we can be 95% confident that the true population proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces is between 0.678 and 0.772.
This means that if we were to take many samples and construct confidence intervals for each one, 95% of those intervals would contain the true population proportion.
Based on this interval, we can conclude that it is likely that at least 65% of employed adults that live in San Luis travel to Yuma or nearby to get to their workplaces, as the lower bound of the interval is above 65%.
e) Whether or not it is worth it to invest in the new highway depends on many factors beyond just the proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces.
The decision to invest in the highway should be based on a careful cost-benefit analysis that takes into account factors such as the expected traffic volume, the expected economic benefits, and the cost of the project.
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The function f(x)=3^x-3 is an exponential function containing the points (0,-2) and (2,6).
the function g(x)=-1/2f(x)+3 containing points ____
a. (0,2)
b. (0,4)
c. (-2,3)
d. (-2,2)
and ____
a. (2,0)
b. (2,6)
c. (6,2)
d. (6,6)
The function g(x)=-1/2f(x)+3 containing points (a) (0, 4) and (a) (2, 0).
The function g(x) = -1/2f(x) + 3 is obtained by applying certain transformations to the original function f(x) = 3^x - 3.
To find the points on the graph of g(x), we need to substitute the x-values from the given points into the function g(x) and determine the corresponding y-values.
Given:
Original function f(x) = 3^x - 3
Points on f(x): (0, -2) and (2, 6)
To find the points for g(x), we substitute the x-values into g(x) = -1/2f(x) + 3:
1. For the point (0, -2):
g(0) = -1/2f(0) + 3
= -1/2(-2) + 3
= 1 + 3
= 4
2. For the point (2, 6):
g(2) = -1/2f(2) + 3
= -1/2(6) + 3
= -3 + 3
= 0
Therefore, the points for the function g(x) = -1/2f(x) + 3 are:
(a) (0, 4)
and
(a) (2, 0)
Hence, the correct answer is:
(a) (0, 4) and (a) (2, 0).
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Assuming the utility function of an individual is as follows. U= 18q+7q2-1/3q3
determine the utility maximizing units of consumption
The utility maximizing units of consumption are approximately 1 or 15 units, depending on other factors such as budget constraints and the specific preferences of the individual.
To find the utility maximizing units of consumption, we need to calculate the first derivative of the utility function (U) with respect to q and set it equal to zero. Here's the utility function:
U = 18q + 7q^2 - (1/3)q^3
Now, we'll find the first derivative (dU/dq):
dU/dq = 18 + 14q - q^2
To find the utility maximizing units, set dU/dq to zero and solve for q:
0 = 18 + 14q - q^2
Rearrange the equation:
q^2 - 14q + 18 = 0
Now, we'll solve for q using the quadratic formula:
q = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = -14, and c = 18. Plug these values into the formula:
q = (14 ± √((-14)^2 - 4 * 18)) / 2
q = (14 ± √(196 - 72)) / 2
q = (14 ± √124) / 2
The two possible solutions for q are:
q1 ≈ 1.27
q2 ≈ 14.73
Since the individual consumes discrete units, the utility maximizing consumption will be the whole number closest to these values.
Therefore, the utility maximizing units of consumption are approximately 1 or 15 units, depending on other factors such as budget constraints and the specific preferences of the individual.
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Please help I am giving a lot of points
A circle has been dissected into 16 congruent sectors. The base of one sector is 1. 56 units, and its height is 3. 92 units. Using the area of a triangle formula, what is the approximate area of the circle?
circle A is dissected into 16 congruent sectors, one sector is highlighted
27. 52 units2
48. 25 units2
48. 92 units2
76. 44 units2
The closest answer choice is [tex]27.52 units^2.[/tex]
The area of the circle, we need to find the area of one sector and then multiply it by 16 since there are 16 congruent sectors.
To find the area of one sector, we use the formula:
[tex]Area of sector = (angle/360) * \pi*r^2[/tex]
Since we know the base and height of the highlighted sector, we can use the Pythagorean theorem to find the radius of the circle:
[tex]r^2 = (1.56/2)^2 + (3.92)^2[/tex]
r ≈ 3.969 units
Now we can find the angle of one sector using the formula:
angle = (base/radius) x 180/π
angle ≈ 22.5 degrees
Plugging in the values for angle and radius in the area of sector formula, we get:
[tex]Area of sector =(22.5/360) *\pi (3.969)^2[/tex]
Area of sector ≈ 0.491π
Multiplying this by 16, we get the approximate area of the circle:
Approximate area of circle ≈ 16 x 0.491π
Approximate area of circle ≈ 7.8π
Using a calculator to approximate π as 3.14, we get:
Approximate area of circle ≈ [tex]24.46 units^2[/tex]
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Sneha’s mother is 12 years more than twice Sneha’s age. After 8 years, she will be 20 years
less than three times Sneha’s age. Find Sneha’s age and Sneha’s mother’s age.
Sneha's current age is 16 years old. Sneha's mother is 44 years old.
Let's assume Sneha's current age is x.
Sneha's mother's current age = 2x + 12
After 8 years, Sneha's age = x + 8
After 8 years, Sneha's mother's age = 2x + 12 + 8 = 2x + 20
After 8 years, Sneha's mother's age will be 20 less than three times Sneha's age: 2x + 20 = 3(x + 8) - 20
Now we can solve for x:
2x + 20 = 3(x + 8) - 20
2x + 20 = 3x + 24 - 20
2x + 20 = 3x + 4
x = 16
Therefore, Sneha's current age is 16 years old.
Sneha's mother's current age = 2x + 12
= 2(16) + 12 = 44
So, Sneha's mother is 44 years old.
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the Senators won 18 more games than they lost. they played 78 games. how many games did they win?
Answer:
let amount of games won and lost be x and y respectively
y+18=x
x+y=78
y+y+18=78
2y=78-18
2y=60
y=30
x=30+18
x=48
thus, games won is 48
Please help I need it ASAP
Answer:
BC= 47.424
I believe that’s correct, but if you really need an answer just get a triangle calculator
PLEASE HELP 30 POINTS
The volume of the oblique cylinder whose base and height is given would be = 9,646.08 m³. That is option B.
How to calculate the volume of a cylinder?To calculate the volume of a cylinder, the formula that should be used is given as follows:
Volume of a cylinder = πr²h
π = 3.14
R = diameter/2 = 16/2 = 8m
Height = 8²+48² (using the Pythagorean formula)
= 64+2304
=√ 2368
= 48.66cm³
The volume of the cylinder = 3.14 × 8×8×48.66
= 9,646.08 m³
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Daria performed an experiment in which she randomly pulled a marble from a bag, recorded its color, put it back, and then repeated. The following table represents the number of times each color of marble was pulled.
Color of Marble Frequency
Yellow 26
Green 34
Purple 18
Red 22
If Daria repeats the experiment 50
more times, how many of those times should she expect to pull a yellow marble?
The number of times she should expect to pull a yellow marble is 13
How many of those times should she expect to pull a yellow marble?From the question, we have the following parameters that can be used in our computation:
Color of Marble Frequency
Yellow 26
Green 34
Purple 18
Red 22
This means that
Times she should expect to pull a yellow marble is
Yellow = P(Yellow) * 50
So, we have
Yellow = 26/(26 + 34 + 18 + 22) * 50
Evaluate
Yellow = 13
Hence, the number of times she should expect to pull a yellow marble is 13
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Please help me with this math problem!! Will give brainliest!! :)
part a.
the percentage of eggs between 42 and 45mm is 48.48%
part b.
The median width is approximately (42+45)/2 = 43.5mm.
The median length is approximately (56+59)/2 = 57.5mm.
part c.
The width of grade A chicken eggs has a range of about 24mm.
part d.
I think its impossible to determine because we don't have the value for the standard deviation.
The second option should be correct.
What is a histogram?A histogram is described as an approximate representation of the distribution of numerical data.
part a.
From the histogram, we see that the frequency for the bin that ranges from 42 to 45mm is 4 and we have a total of 33 eggwe use this values and calculate the percentage of eggs between 42 and 45mm is 48.48%.
part b.
we have an estimation that the median of the width is 48mm and the median of the length is around 60mm.
part c.
Also from the histogram, we notice that the smallest value is around 36mm and the largest value is around 66mm, hence the width of grade A chicken eggs has a range of about 24mm.
In a histogram, the range is the width that the bars cover along the x-axis and these are approximate values because histograms display bin values rather than raw data values.
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The table shows transactions from a bank account. fill in the missing number for box a.
transaction amount
account balance
transaction 1
150 150
transaction 2
50 100
transaction 3
90 a
transaction 4
-200 b
transaction 5
c 0
btw this is integers
The missing number for box a transaction amount account balance are a = 10, b = 210, c = 210.
Using the information provided in the table, we can fill in the missing numbers as follows:
For transaction 3: The account balance after transaction 2 was $100, and transaction 3 had an amount of $90. Therefore, the account balance after transaction 3 is $190. Hence, the missing number in box a is 190.
For transaction 4: The account balance after transaction 3 was $190, and transaction 4 had an amount of -$200. Therefore, the account balance after transaction 4 is -$10. Hence, the missing number in box b is -10.
For transaction 5: The account balance after transaction 4 was -$10, and transaction 5 had an amount of $c. Therefore, the account balance after transaction 5 is 0. Hence, the missing number in box c is 10.
Therefore, the completed table is:
transaction amount account balance
1 150 150
2 50 100
3 90 190
4 -200-10
5 10 0
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Hugo rides the bus to work every day, a distance of 18 miles. The distance on the route map between the station by Hugos house and the station by his work is 3 inches. What is the maps scale? 1 inch = _____ miles.
The maps scale is 1 inch = 6 miles. This means that for every inch on the map, it represents 6 miles in real-life distance.
To determine the scale, we need to know the relationship between the distance on the map and the actual distance. In this case, the distance on the route map between Hugo's house and his work is 3 inches, and the actual distance he travels by bus is 18 miles.
To find the scale, we can set up a proportion using the given information:
(distance on the map in inches) / (actual distance in miles) = (1 inch) / (x miles)
Now, we can plug in the known values:
(3 inches) / (18 miles) = (1 inch) / (x miles)
To solve for x, we can cross-multiply:
3 inches * x miles = 18 miles * 1 inch
3x = 18
Now, divide both sides by 3:
x = 6
So, the scale of the map is 1 inch = 6 miles.
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The ratio of three numbers is 6 : 1 : 5. The sum of the numbers is 36. What are the three numbers?
Answer:3,15,18.
Step-by-step explanation:
6:1:5 total ratio =6+1+5=12 so you’ll take all the numbers at different times so 6 will be divided by 12 and multiplied by36 (6/12)36= 18so the first number is nine do the same thing for the next ratio (1/12)36=3 thirdly(5/12)36=15 now add the three numbers to check whether they sum up to36(18+3+15=36)