The area of the shaded region is 4π/3 square units.
We have given that x= center diameter =wz w and z end over line radius=2
Triangle XYZ is equilateral,
What is the central angle of equilateral ?
120 degrees
so the central angle of the sector is 120°,
In radian
=120×[tex]\pi[/tex]/180
=2π/3 radians.
The area of a sector of central angle β is given by,
[tex]A = (1/2)r^2(\beta )[/tex] . . . . . . β in radians
[tex]A = (1/2)*2^2*(2\pi /3)[/tex]
= 4π/3 . . . . square units
Therefore the area of the shaded region is 4π/3 square units.
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Which interval is the solution set to 0.35x – 4.8 < 5.2 – 0.9x?
The solution to the mathematical inequality equation 0.35x - 4.8 < 5.2 - 0.9x is the interval x < 8.
Explanation:In order to find the solution to the equation 0.35x - 4.8 < 5.2 - 0.9x, you first need to rearrange the terms in the equation such that all terms involving x are on one side of the inequality and the other terms are on the other side. Starting with: 0.35x - 4.8 < 5.2 - 0.9x, if we add 0.9x to both sides we get 0.35x + 0.9x < 5.2 - 4.8, which simplifies to 1.25x < 10.
Next, to isolate 'x' we divide through by 1.25, which gives us: x < 10/1.25 which simplifies to x < 8. Therefore the answer to the equation 0.35x - 4.8 < 5.2 - 0.9x is the interval x < 8.
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the basketball court in the park is rectangle two of the sides are 84 feet long and the other two sides are 50 ft long what is the perimeter of the basketball court
Explain what a polynomials is and identify the different parts of a polynomial.
Explain the different labels used to categorize polynomials
Explain how addition and subtraction of polynomials is accomplished
When multiplying polynomials, we are taking every term of one polynomial and multiplying them by every term of the second polynomial, then collecting like terms explain how foil helps us to accomplish this and what category of polynomials foil applies to.
There are tow special case products where the product takes on special patterns explain these two cases and when they occur.
For each of the two special cases, illustrate your explanation with an appropriate exercise from the ( a+b)2=a2+2ab+b2 )(a-b)2=a2-2ab+b2 ) showing how the multiplication is performed using the special pattern formula then also showing the same result using foil.
Jack is in hospital and his temperature is recorded every hour one morning. Time Temperature 06:00 40.0 07:00 40.0 08:00 39.5 09:00 39.0 10:00 38.5 11:00 38.0 12:00 38.0 Which is the best type of chart to use to represent this information? scatter diagram, pictogram, pie chart, line graph, tally chart, bar chart?
Here we are given two types of data : Time and Temperature.
We can plot one of these on x axis and the other on y axis.
So we can use a line graph here.
What methods can be used to solve quadratic equations?
What is the sum of the series?
write an inequality in slope intercept form for the graph below. if necessary use <= or >=
The correct options are:
1. The equation of a given line is y=-x-3 (it is easy to find it using points (0;-3)&(-3;0)).
2. According to the equation of a line: y≥-x-3
What is the inequality in slope-intercept form?You may use the slope-intercept form to graph inequalities. The slope-intercept form is expressed as y = mx + b, where the variable m stands for the slope of the line, and b stands for the y-intercept (or in which the line crosses the y-axis).
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1. James buys a video game for his Xbox for $49.99, a controller for $34.95, and a walk through manual for $19.99. The sales tax in his area is 8.25%. What will be the total cost of his purchase?
You process paychecks for your company. Paydays are 2 weeks apart, on Fridays. The first payday in one month is on the 12th. The next payday is on the:
Answer:
The next payday is on the: 26th of that month.
Step-by-step explanation:
You process paychecks for your company.
Paydays are 2 weeks apart, on Fridays.
2 weeks apart means 14 days apart.
The first payday in one month is on the 12th.
Therefore, The next payday is on the: [tex]12+14=26[/tex]
26th of that month.
Ling lives 2 miles from school. It took him 15 minutes to bike from school to home. The first half of the distance he biked at a speed of 12 mph. What was his speed for the remaining distance? What was his average speed?
Answer:
First Part: 6 mphSecond Part: 8 mphy=-2x+1
y=-2x-3
solve and graph
Melvin has 1/2 of a cake. He shares the cake equally with each of 2 friends and himself. Show me how u got your answer
Melvin and each of his 2 friends get [tex]\( \frac{1}{6} \)[/tex] of the cake each.
Sure! If Melvin has [tex]\( \frac{1}{2} \)[/tex] of a cake and he wants to share it equally with each of his 2 friends and himself, we need to find out how much each person gets.
First, we need to find out how many people are sharing the cake. Melvin himself plus his 2 friends make a total of 3 people.
Now, to divide [tex]\( \frac{1}{2} \)[/tex] of the cake equally among 3 people, we divide [tex]\( \frac{1}{2} \)[/tex] by 3:
[tex]\[ \frac{1/2}{3} = \frac{1}{2} \times \frac{1}{3} \][/tex]
To multiply fractions, we multiply the numerators together and the denominators together:
[tex]\[ = \frac{1 \times 1}{2 \times 3} \][/tex]
[tex]\[ = \frac{1}{6} \][/tex]
So, each person gets [tex]\( \frac{1}{6} \)[/tex] of the cake.
Therefore, Melvin and each of his 2 friends get [tex]\( \frac{1}{6} \)[/tex] of the cake each.
Find all the second partial derivatives. w = u9 + v7
Answer:
[tex]w_{uu} = 72u^{7}[/tex]
[tex]w_{uv} = w_{vu} = 0[/tex]
[tex]w_{vv} = 42v^{5}[/tex]
Step-by-step explanation:
We can have the second partial derivatives of w in relation to u, v and uv. So
[tex]w = u^{9} + v^{7}[/tex]
[tex]w_{u} = 9u^{8}[/tex]
[tex]w_{uu} = 72u^{7}[/tex]
[tex]w_{uv} = w_{vu} = 0[/tex]
[tex]w_{v} = 7v^{6}[/tex]
[tex]w_{vv} = 42v^{5}[/tex]
Final answer:
The second partial derivatives of w = u^9 + v^7 are w_uu = 72u^7, w_uv = 0, and w_vv = 42v^5.
Explanation:
To find all the second partial derivatives of w = u^9 + v^7, we need to differentiate twice with respect to each variable. Let's start:
First, find the first partial derivatives:
wu = 9u^8 (differentiating with respect to u)
wv = 7v^6 (differentiating with respect to v)
Now, take the second partial derivatives:
wuu = 72u^7 (differentiating wu with respect to u)
wuv = 0 (differentiating wu with respect to v)
wvv = 42v^5 (differentiating wv with respect to v)
So, the second partial derivatives of w = u^9 + v^7 are wuu = 72u^7, wuv = 0, and wvv = 42v^5.
Find all real numbers X such that 18x-9>9 or 2x-4>-10
The fountain is made up of two semicircles and a quarter circle. Find the perimeter and the area of the fountain. Round the perimeter to the nearest tenth of a foot and the area to the nearest square foot.
The perimeter and area of the fountain comprising two semicircles and a quarter circle can be calculated using principles of circle geometry, adding respective perimeter parts for the total perimeter and summing up the areas of each part for the total area. The perimeter calculation includes the semicircles' straight edges, while the area computation combines semicircle and quarter circle areas.
Explanation:To calculate the perimeter and area of a fountain composed of two semicircles and a quarter circle, we first need to acknowledge that all parts of this shape are derived from circles. Therefore, understanding the properties of a circle is crucial. The formula for the perimeter (circumference) of a whole circle is 2πr, and the formula for the area is πr², where r is the radius of the circle.
To find the perimeter of the given shape, add the perimeters of the two semicircles and a quarter circle. Since the perimeter of a semicircle is πr and there are two, their combined perimeter is 2πr. The perimeter of a quarter circle is πr/2. Therefore, the total perimeter of the shape would be 2πr + πr/2. The straight edges that close the semicircles also contribute to the perimeter, which are diameters of the circles (ϐ2r for each semicircle), resulting in an additional 2r + 2r = 4r to the total perimeter.
For the area, sum the areas of two semicircles and a quarter circle. The area of a semicircle is πr²/2, so together, two semicircles have an area of πr². The area of a quarter circle is πr²/4. Thus, the total area of the shape is πr² + πr²/4 = 5πr²/4.
To find the exact values, you would substitute the specific radius (r) of the circles that constitute the fountain, and calculate using π ≈ 3.14. Make sure to round the perimeter to the nearest tenth of a foot and the area to the nearest square foot as instructed.
which graph represent the equation y - 2 = 3x?
Tom is going to build a fence around his garden which is a rectangle measuring 8 m by 20 m. He will first put in posts which will be 4 m apart. If the posts cost $5.50 each, what will be the total cost for all the posts?
Write a Multiplication expression that shows 10 sixths
Jatonia sold n cups of lemonade at her stand for $0.75 each. She made a total of $18.00. Write an expression to express how many cups of lemonade she sold.
A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.1%, 3.4%). what is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?
What is the value of the expression shown below?
7 + (10 − 4)2 ÷ 4 × 1 over 2 to the power of 3
A. 8
B. 8 and 1 over 6
C. 8 and 1 over 8
D. 79
In playing Monopoly, rolling doubles three times in a row sends you to jail. What is the probability of rolling three consecutive doubles? a. 0.167 b. 0.5 c. 0.00463 d. 18.0
What is the truth value for the following conditional statement? If the snow is white, then the grass is red.
Final answer:
The truth value of the conditional statement 'If the snow is white, then the grass is red' cannot be determined to be true or false without context, as it is a statement that requires evaluation of its antecedent and consequent. In logic, a conditional statement is true unless the antecedent is true and the consequent is false.
Explanation:
The truth value for the conditional statement "If the snow is white, then the grass is red," cannot be evaluated as true or false based solely on the content of the statement. In logic, a conditional statement is considered to be true unless a situation occurs where the first part (the antecedent) is true and the second part (the consequent) is false.
Here, the statement "the snow is white" is true, but the statement "the grass is red" can be false, as grass is typically green. This illustrates an important logical principle where the truthfulness of a conditional does not require that the consequent actually follows from the antecedent. To evaluate the truth of a conditional statement, it would be more appropriate to look for a counterexample that disproves it or involves a scenario where the antecedent is true and the consequent is false.
Which of the points listed is the same distance from the x-axis as the point (8, 3.25)?
A- (-8, 4.75) B- (7, -3.25) C- (3.25, 7) D- None of these are correct.
The points listed which has the same distance from the x axis as the point (8, 3.25) is B- (7, -3.25).
What are the Coordinates?Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.
Given is a point in the XY plane with the coordinates (8, 3.25).
We have to find the point in the options which are at a same distance as the given point.
In order for two points to be at a same distance from the x axis, their y coordinates must be same with either same sign or of the opposite sign.
Here the point with the same y coordinate as the given point is B- (7, -3.25)
Hence option B is correct.
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It is estimated that approximately one-half of all aluminum cans will be recycled each year. If a soft drink company produces 350,000 cans one year, how many cans are still in use after 4 years of recycling and re-using, using this function?
Nt = 350,000(0.52)t
A 87,500
B 25,591
C 175,000
D 21,875
Answer: B
Step-by-step explanation:
plato
Which of the following criteria are necessary conditions for making a statistical inference?
sample size greater than 30, or an approximately normal data set
sample size greater than 100
convenience sample
simple random sample
systematic sample
Answer:
1 and 4 are correct
Step-by-step explanation:
Find the perimeter of a polygon with sides 11ft, 7ft, 18ft, 22ft, 14ft, and 23.5ft
Find the number, if 5/7 of it is 15
The number is 21.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number = M
5/7 of M = 15
This can be written as,
(5/7)M = 15
M = 15 x 7/5
M = 3 x 7
M = 21
Thus,
The number is 21.
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el area de un rectangulo de lados 0,0005m y 0,003m es
Suppose that with a budget of $100, Deborah spends $60 on sushi and $40 on bagels when sushi costs $2 per piece and bagels cost $2 per bagel. But then, the price of bagels falls to $1 per bagel.
b. At the new prices, how much money would it have cost Deborah to buy those same quantities (the ones that she consumed before the price change)?
c. Given that it used to take Deborah’s entire $100 to buy those quantities, how big is the income effect caused by the reduction in the price of bagels?
Answer:
Part A) The quantities are [tex]30\ piece\ of\ sushi[/tex] and [tex]20\ bagels[/tex]
Part B) [tex]\$80[/tex]
Part C) The income effect is a loss of [tex]\$20[/tex]
Step-by-step explanation:
Part A)
Let
x-----> the number of piece of sushi
y----> the original number of bagels
we know that
[tex]2x=60[/tex] ------> [tex]x=30\ piece\ of\ sushi[/tex]
[tex]2y=40[/tex] ------> [tex]y=20\ bagels[/tex]
Part B) At the new prices, how much money would it have cost Deborah to buy those same quantities (the ones that she consumed before the price change)?
Bagels
[tex]20(1)=\$20[/tex]
Sushi
[tex]30(2)=\$60[/tex] -----> is the same
The total cost is
[tex]\$20+\$60=\$80[/tex]
so
The same quantities would have cost [tex]\$80[/tex]
Part C) Given that it used to take Deborah’s entire $100 to buy those quantities, how big is the income effect caused by the reduction in the price of bagels?
Find the difference
[tex]\$100-\$80=\$20[/tex]
therefore
The income effect is a loss of [tex]\$20[/tex]