Answers
Answer:
a) 19.63 mm (2 dp)
b) 245.44 mm² (2 dp)
Step-by-step explanation:
Formula
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]
[tex]\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}[/tex]
Calculation
Given:
[tex]\theta[/tex] = 45°r = 25 mm[tex]\begin{aligned}\implies \textsf{Arc length} &=2 \pi (25)\left(\dfrac{45^{\circ}}{360^{\circ}}\right)\\ & = 50 \pi \left(\dfrac{1}{8}\right)\\ & = \dfrac{25}{4} \pi \\ & = 19.63\: \sf mm \:(2\:dp)\end{aligned}[/tex]
[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{45^{\circ}}{360^{\circ}}\right) \pi (25)^2\\& = \left(\dfrac{1}{8}\right)\pi \cdot 625\\& = \dfrac{625}{8} \pi\\& = 245.44\: \sf mm^2 \:(2\:dp)\end{aligned}[/tex]
Please note: As you have not specified if π should be approximated, I have not used an approximation for π.
Related Questions
Calculate the value of p in the diagram below
Answers
Answer:
40.5
Step-by-step explanation:
(n-2)*180
(7-2)*180=5*180=900
10p+135+149+121+90=900
10p=-495+900=405
p=40.5
Bob bikes to work 8 miles each day. The trip takes him 0.5 hours. If Bob bikes at a constant rate, what is his biking speed? A. 5 mph B. 8 mph C. 16 mph D. 40 mph
Answers
Given the distance covered and the time elapsed, if the bike is at a constant rate, the speed of Bob's bikes is 16 mph.
Option C) is the correct answer.
What is Speed?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given the data in the question;
Distance covered d = 8milesTime elapsed t = 0.5hrsSpeed of the bike S = ?Speed = Distance ÷ time
Speed = 8miles / 0.5hrs
Speed = 16 mph
Therefore, Given the distance covered and the time elapsed, if the bike is at a constant rate, the speed of Bob's bikes is 16 mph.
Option C) is the correct answer.
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Indigo needs to order some new supplies for the restaurant where she works. The restaurant needs at least 430 knives. There are currently 269 knives. If each set on sale contains 18 knives, what is the minimum number of sets of knives Indigo should buy?
Answers
The minimum number of sets of knives Indigo should buy is 9.
What is Inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Here, Let the minimum number of sets be x.
restaurant needs at least 430 knives
currently restaurant have 269 knives
each set contains 18 knives.
According to question,
18x + 269 ≥ 430
18x ≥ 161
x ≥ 161/18
x ≥ 8.94
Thus, the minimum number of sets of knives Indigo should buy is 9.
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1. You and your friends receive a lunch bill for $22.50 before tax is included. The sales tax in your state
is 8%. What is the total cost when the tax is included?
Answers
Answer:
$24.30
Step-by-step explanation:
8% of 22.50 = $1.8
$22.50 + $1.8 = $24.30
Give brainliest, please!
Hope this helps :)
The measurement of an angle is 40°, and the length of a line segment is 8 centimeters.
Answers
Answer:
I'm assuming it's a triangle of some sort. I'll assume it's a right triangle. All the angles and sides are there. I would need 2 angles and 1 side or 2 sides and 1 angle to get a specific triangle.
Step-by-step explanation:
If a right circular cylinder and oblique cylinder both have a height of 12 inches and diameter of 6 inches, do they have the same volume? (Use straight pi equals 3.14)
Group of answer choices
Yes, they both have a volume of 339.12 inches cubed.
No, the right circular cylinder has a volume of 339.12 inches cubed and the oblique cylinder has a volume of 1 comma 356.48 inches cubed.
No, the right circular cylinder has a volume of 1 comma 356.48 inches cubedand the oblique cylinder has a volume of 339.12 inches cubed.
Yes, they both have a volume of 1 comma 356.48 inches cubed.
Answers
Answer:
Yes, they both have a volume of 339.12 inches cubed.
Step-by-step explanation:
To calculate the volume of an oblique cylinder is very simple, we must multiply π (Pi = ~ 3.14) by the radius to the power of two and then multiply by the height. In this case the height forms a 90 degree angle from the opposite base to the position of the base, but outside of it.
Volume = π × Radius² × Height
The formula for the volume of a regular cylinder or an oblique cylinder is the same, if we imagine a stack of poker chips (forming a cylinder), even when we tilt the chips to one side (forming an oblique cylinder) the volume remains the same.
Now using this information, we must find the volumes of both cylinders.
For the oblique cylinder:
Given
Using the formula,
The volume would be 339.29 m³
Now solving for the other cylinder:
V=πr²h=π·32·12≈339.29201
Rounded, the answer would be 33.29 m³
This therefore proves that they both have the same volume.
find the value of x
50°
6
X
Not drawn to scale
Answers
Answer:
Hence option C is correct...hope this helps you:)
A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the
students, Sandra, Marta, and Jane, are girls. The fourth student, Franklin, is a boy.
Using the sample space of possible outcomes listed below, where each student is represented by the first letter
of his or her name, answer each of the following questions.
What is P(A), the probability that the first student is a girl?
What is P(B), the probability that the second student is a girl?
What is P(A and B), the probability that the first student is a girl and the second student is a girl?
Answers
Answer:
what is P(A), the probability that the first student is a boy? 3/5
what is P(B), the probability that the second student is a girl? 3/4
what is P(A and B), the probability that the first student is a boy and the second student is a girl? 1/2
No, évents A and B are not independent events
Step-by-step explanation:
The probability that the first student is a girl P(A)= 3/4.
The probability that the second student is a girl P(B)= 3/4.
The probability that the first student is a girl and the second student is a girl P(A and B)=9/16.
Given that there are three girls (Sandra, Marta, Jane) and one boy (Franklin), and the sample space of possible outcomes is:
{SA, SM, SJ, SF, MA, MS, MJ, MF, JA, JS, JM, JF, FA, FS, FM, FJ}
P(A): Probability that the first student is a girl (Sandra, Marta, or Jane).
Number of favorable outcomes where the first student is a girl: 3 (Sandra, Marta, Jane)
Total outcomes: 4 (total number of students)
P(A) = Number of favorable outcomes / Total outcomes = 3 / 4
P(B):
Probability that the second student is a girl (Sandra, Marta, or Jane).
Number of favorable outcomes where the second student is a girl: 3 (Sandra, Marta, Jane)
Total outcomes: 4 (total number of students)
P(B) = Number of favorable outcomes / Total outcomes = 3 / 4
P(A and B):
Probability that the first student is a girl and the second student is a girl.
Number of favorable outcomes where both students are girls: 3 (Sandra, Marta, Jane)
Total outcomes: 4 (total number of students)
P(A and B) = P(A).P(B)
= 3/4 × 3/4
=9/16
Hence, P(A)=3/4
P(B)=3/4
P(A and B)=9/16
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What is the length of segment
Answers
Answer: square root of 53
Step-by-step explanation:
did the math
Find the value of x in the parallelogram below.
Answers
Answer:
102
Step-by-step explanation:
78 and x are adjacent angles.
Sum of adjacent angles is 180 in a parallelogram.
78 + x = 180
x = 180 - 78
x = 102
Answer:
102°
Step-by-step explanation:
A parallelogram is a special type of quadrilateral that has both the pair of opposite sides parallel and equal.78+x= 180( adjacent angles in a parallelogram)
x=180-78=102°
Find the area of a triangle whose sides are 35 cm, 45 cm and 50 cm.
Answers
Answer:To find out the Area of a scalene triangle whose three sides are given, first find out the half perimeter
s = (a+b+c)/2
where a, b, and c are the length of the three sides of a triangle
s = (35 + 45 + 50) / 2
= 130 / 2
= 65 cm
Area of scalene triangle is given by
A = sqrt (s (s - a) (s - b) (s - c))
= sqrt (65 * (65 - 35) ( 65 - 45) (65 - 50))
= sqrt (65 * 30 * 20 * 15)
= sqrt (585000)
= 764.853 sq cm
Step-by-step explanation:
What is the volume of a rectangular sandbox that is 3 feet by 4 feet by 1 foot?
13 ft 3
8 ft 3
12 ft 3
7 ft 3
Answers
Answer:
Volume = 12 ft^3
Step-by-step explanation:
Vol = length×width×height
= 3×4×1
= 12
The volume is 12 cubic feet.
Help me i am on iready math
Answers
Answer:
14
Step-by-step explanation:
Because your total is 182 desserts and you want to arrange them into 13 rows you will divide the two numbers. So, 182/13 is 14. so 14 is your answer.
Hope that helped
Answer:
14 Tropical cupcakes per row
Hope this helped :)
Step-by-step explanation:
182 ÷ 13 = 14
Check:
14 × 13 = 182 ✓
A municipal trash facility allows a person to throw away a maximum of 40 pounds of trash per week. Last week, 195 people threw away the maximum allowable trash. How many tons of trash did this equal
Answers
The total tons of trash that was thrown away by the people is 3.9 tons.
How many tons of thrash was thrown away?The first step is to convert pounds to tons
1 pound = 0.0005 tons
40 x 0.0005 = 0.02 tons
The second step is to multiply 0.02 by 195
0.02 x 195 = 3.9 tons
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Solve the following:
4x3 = 2x + 7
Answers
Answer:
If you meant 4x to the third power, than x = 1.34
This makes zero sense give answer
Answers
Answer:
IQR for males: 3
IQR for females: 2
Q1 for males: 5
Q1 for females: 6
the number of females who spend over 6 hours exercising is greater(?) than the number of males who spent 6 hours exercising
Step-by-step explanation:
An equal amount of men and women were randomly selected and asked how many hours per week they spend excercising
How to find IQR?to find IQR you have to identify your median(middle value) of the lower and upper half of the data. These are called quartile 1(Q1) and quartile 3(Q3). You subtract these two (Q3 and Q1) and the IQR is the difference.
Males box plot:
Minimum: 1
Maximum: 10
Q1: 5
Q2: 7
Q3: 8
Subtract Q3 and Q1
8 - 5 = 3
This is the IQR
Females box plot:
Minimum: 4
Maximum: 10
Q1: 6
Q2: 7
Q3: 8
Subtract Q3 and Q1
8 - 6 = 2
IQR =2
the number of females who spend over 6 hours exercising is greater than the number of males who spent 6 hours exercising
the points at which a quadratic equation intersects the x-axis
Answers
The points at which a quadratic equation intersects the x-axis are referred to as x intercepts or zeros or roots of quadratic equation
Given :
The points at which a quadratic equation intersects the x-axis
The points at which the any quadratic equation crosses or touches the x axis are called as x intercepts.
At x intercepts the value of y is 0.
So , the points at which a quadratic equation intersects the x-axis is also called as zeros or roots of the quadratic equation .
The points at which a quadratic equation intersects the x-axis are referred to as x intercepts or zeros or roots of quadratic equation
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f(x) = x + 3
g(x) = 7x +4
What does (f+g) (x)equal?
To obtain credit, provide your answer with no spaces. Example answer: 42x+9
Answers
What is the factorization of the expression below?
x2-14x + 49
Answers
Answer:
The value of x = 7
Step-by-step explanation:
x²-14x + 49
=> x² - 7x - 7x + 49
=> x ( x - 7) - 7 ( x - 7 )
=> (x - 7) (x - 7)
=> x = 7
Given the points K(-2;5), L(1,3) and M(-5; 2p). Calculate the value
of p if KL ILM.
How do I solve this question?
Answers
The product of the perpendicular lines is a negative one. Then the value of p will be negative 3.75.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Given the points K(-2,5), L(1,3) and M(-5, 2p).
If KL is perpendicular to LM. Then we have
The slope of KL will be
KL = (1+2)/(3-5)
KL = -1.5
The slope of LM will be
LM = (1+6)/(3-2p)
LM = 7/(3-2p)
We know the product of the perpendicular lines is a negative one.
KL x ML = -1
-1.5 x 7/(3-2p) = -1
-10.5 = -3 + 2p
2p = -7.5
p = -3.75
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Patricia has a circular swimming pool. The diameter of the pool is 15 feet. What is the area of the swimming pool.
Answers
Answer:
The area of the pool is 176.71
Step-by-step explanation:
The formula for a triangle is Area= Pi r (radius) sq.
In this problem, you need to remember that radius is half the diameter.
STEP 1: Divide the diameter in half.
STEP 2: Multiply your answer by itself. (example: if your answer was 8, you would multiply by 8)
STEP 3: Multiply the answer by 3.14 (or Pi)
STEP 4: You just found the area of a circle, GREAT JOB!
diameter= 15 feet
to find:the area of the circular swimming pool.
solution:[tex]a = \frac{1}{4} \pi {d}^{2} [/tex]
[tex]a = \frac{1}{5} \times \pi \times {15}^{2} [/tex]
[tex]a = 176.71459 \: {ft}^{2} [/tex]
[tex]a = 176.71 \: {ft}^{2} [/tex]
therefore, the area of the circular swimming pool is 176.71 square feets.
help geometry ………ignore this i need 20 words
Answers
Answer:
The answer is 1
Step-by-step explanation:
What is the slope of the line segment?
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15
12
9
6
3
0
1 2 3 4 5
0-3
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3
0 1
3
3
Answers
The paddock in judy's ranch is 60 feet long and 20 feet wide. he also built a square corral adjacent to the paddock. if the side of the corral measures 16 feet, determine the total area of the paddock and corral.
Answers
Answer:
1456ft²
Step-by-step explanation:
A = lw
A = 60(20)
A = 1200ft²
A = 16(16)
A = 256ft²
1200 + 256 =
1456ft²
Find the area of triangle
Answers
Answer:
C- 17 cm
A- 9cm
Step-by-step explanation:
C - because plus 9 and 8 is 17 cm
A - because plus 4 and 5 is 9 cm
It's going 2 by 2 for the paper i couldn't get it all in at a time so the first 2 are one paper and its like that for the next 2 papers but the last paper is the whole paper
Answers
it took I'd :safalbista10 10
How do I solve this!! Quick and urgent (23. Is the number for the equation)
Answers
Answer:
Independent: Time
Dependent: Views
Step-by-step explanation:
Independent variables are the things that are purposefully altered.
Dependent variables are the things that change in response to the independent variables being changed.
As the hours increase, so do the views. The views will change as time goes by. A change in the number of views does not affect the time passed. Therefore, time is the independent variable and the number of views is the dependent variable.
Find the missing side
Answers
Answer:
5^2+7^2= 12^2 so your answer should be 12
− 4 + 1 2 x = 8 is it true
Answers
Answer:
12 -4x = 8
So "Yes" it is true
P is a rectangle with length 80 cm and width x cm.
q is a rectangle with width y cm.
p
the length of q is 25% more than the length of p.
the area of q is 20% less than the area of p.
work out the ratio x:y
give your answer in its simplest form.
x cm
80 cm
:
q
y cm
Answers
The ratio of x and y will be equal to x:y = 25:16
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
We know that
The length of Q is 25% more than the length of p
length Q=1.25 x 80--------> 100 cm
The area of Q is 20% less than the area of p
Area Q=100 x y
Area P=80 x x
100 x y=0.80 x [80 x x]---------> 100 x y = 64 x x-------> x/y=100/64--> 25/16
Therefore the ratio of x and y will be equal to x:y = 25:16
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Answer:
25:16
Step-by-step explanation: