Answer:
If you've more doubts you can ask :)
Step-by-step explanation:
If the centre of a circle is (a, b) and radius r, then the equation of the circle is :
[tex](x - x)^2 + (y-b)^2 = r^2[/tex]
First we will find the centre, (a , b):
[tex]a = \frac{3+(-1)}{2} = \frac{2}{2} = 1\\\\b = \frac{-2 + 4}{2} = \frac{2}{2} = 1[/tex]
Find radius:
[tex]Radius, r = \frac{Diameter}{2}[/tex]
Diameter is the distance between (-1, 4) and (3, -2)
[tex]diameter = \sqrt{(x_2 - x_1)^2 +(y_2-y_1)^2} \\\\[/tex]
[tex]= \sqrt{(3-(-1)^2 + (-2-4)^2} \\\\=\sqrt{16 + 36}\\\\=\sqrt{52}\\\\=\sqrt{4 \times 13}\\\\=2\sqrt{13} \ units[/tex]
Therefore , [tex]r = \frac{2 \times \sqrt{13} }{2} = \sqrt{13} \ units[/tex]
Equation of the circle is :
[tex](x - 1)^2 +(y-1)^2 = 13[/tex]
Question 2
Find the volume.
Answer:
Volume of cone = 686π/3 or 718.67 in³
Step-by-step explanation:
Given the following data;
Radius, r = 7 in
Height, h = 14 inches
From the diagram, we can see that the object is a cone
To find the volume of a cone;
Mathematically, the volume of a cone is given by the formula;
[tex] V = \frac{1}{3} \pi r^{2}h[/tex]
Where;
V is the volume of the cone.
r is the radius of the base of the cone.
h is the height of the cone.
Substituting into the equation, we have;
[tex] Volume = \frac{1}{3} * \frac {22}{7} *7^{2}*14 [/tex]
[tex] Volume = \frac{1}{3} * 22 * 7 * 14 [/tex]
[tex] Volume = \frac{1}{3} * 2156 [/tex]
[tex] Volume = 718.67 [/tex]
Volume of cone = 718.67 in³ or 686π/3 in³
help please anyone ??
Austin was budgeted $ 825 to spend on chairs for his upcoming event. If each chair costs $ 15 , how many chairs can he purchase?
Answer:
55 chairs
Step-by-step explanation:
825/15=55
Find the particular solution of the differential equation passing through the given point.
(1+x2)dy=(x+1)ydx,(2,2)
Try this option, the answer is marked with red colour.
Can y’all help me please?
Answer:
(A) [tex]5\frac{1}{4}*4\frac{1}{5}[/tex]
Step-by-step explanation:
The area of a parallelogram is the same as the area of a rectangle which is A=bh where b is the base and h is the height. Therefore, Erica can use the expression [tex]5\frac{1}{4}*4\frac{1}{5}[/tex] to find the area of the parallelogram.
If M is the midpoint of AB, find the coordinates of A if M(-3, 5) and B(6, -11)
midpoint= (x, y)
where x=(x1 + x2)/2
y=(y1 + y2)/2
x1=-3, x2=6, y1=5, y2=-11
so x=(-3 + 6)/2= 3/2
y=(5 + -11)/2= (5-11)/2= -6/2= -3
so mid point =(3/2, -3)
hope this helps
The hypotenuse of a right triangle is 13 ft long. The longer leg is 7 ft longer than the shorter leg. Find the side lengths of the triangle.
Answer:
The shorter leg is five feet, the longer leg is 12 feet, and the hypotenuse is 13 feet.
Step-by-step explanation:
Let the shorter leg be x.
Since the longer leg is seven feet longer than the shorter leg, the length of the longer leg can be modeled by (x + 7).
Since the triangle is a right triangle, we can use the Pythagorean Theorem, given by:
[tex]a^2+b^2=c^2[/tex]
Where a and b are the side lengths and c is the hypotenuse.
The hypotenuse is 13 and the legs are x and (x + 7). Substitute:
[tex](x)^2+(x+7)^2=(13)^2[/tex]
Square:
[tex]x^2+x^2+14x+49=169[/tex]
Simplify:
[tex]2x^2+14x-120=0[/tex]
We can divide both sides by two:
[tex]x^2+7x-60=0[/tex]
Factor:
[tex](x-5)(x+12)=0[/tex]
Zero Product Property:
[tex]x-5=0\text{ or }x+12=0[/tex]
Solve for each case:
[tex]x=5\text{ or } x=-12[/tex]
Since lengths cannot be negative, we can ignore the negative answer. So, our only solution is:
[tex]x=5[/tex]
The shorter leg is five feet, the longer leg will be (5 + 7) or 12 feet. And the hypotenuse is 13 feet as given.
Given the circle, find the arc measure.
Please help I’ll mark brainliest
Answer:
arc KLJ = 205°
Step-by-step explanation:
Recall: measure of arc equals measure of central angle
Therefore:
measure of arc LJ = 56°
measure of arc KL = 149°
arc LJ + arc KL = arc KLJ
Substitute
56° + 149° = arc KLJ
205 = arc KLJ
arc KLJ = 205°
I need help with this problem-
Answer:
wat
Step-by-step explanation:
6x+2y=
6x+2y=
\,\,16
16
2x-2y=
2x−2y=
\,\,32
32
Answer:
x = 6, y = -8
Step-by-step explanation:
First we take the equations side by side and put them like this:
6x + 2y = 16
+ 2x - 2y = 32
8x = 48
Then solve for x.
x = 6
Then insert x back into either equation
2(5) - 2y = 32
10 - 2y = 32
solve for y,
y = -10
Why is this graph proportional?
Answer:
The graph represents a linear function that passes through the origin.
Step-by-step explanation:
Proportional functions can be represented by [tex]y=kx[/tex], where [tex]k[/tex] is some constant. They form a straight line that always pass through the origin (0,0). We can see all these characteristics in the graph, thus the graph is proportional.
Which function has a greater Y intercept
A Driver’s Ed program is curious if the time of year has an impact on number of car accidents in the U.S. They assumethat weather may have a significant impact on the ability of drivers to control their vehicles. They take a randomsample of 150 car accidents and record the season each occurred in. They found that 27 occurred in the Spring, 39 inthe Summer, 31 in the Fall, and 53 in the Winter.
Required:
Can it be concluded at the 0.05 level of significance that caraccidents are not equally distributed throughout the year?
Answer:
p-value = 0.0145
Hence, Since p-value ( 0.0145 ) is less than significance level ( 0.05 )
we reject null hypothesis.
Therefore, there is sufficient evidence to conclude that Car accidents are NOT equally distributed throughout the year
Step-by-step explanation:
Given the data in the question;
Hypothesis;
Null hypothesis : H₀ : Car accidents are equally distributed throughout the year
Alternative hypothesis : Hₐ : Car accidents are NOT equally distributed throughout the year
significance level ∝ = 0.05
x ;
Spring = 27
Summer = 39
Fall = 31
Winter = 53
Test Statistics;
Chi Square = ∑[ (O – E)²/E ]
O E (O – E)²/E
Spring 27 37.4 2.94
Summer 39 37.4 0.06
Fall 31 37.4 1.1267
Winter 53 37.4 6.4067
Total 150 150 10.5334
so; z = ∑[ (O – E)²/E ] = 10.5334
{from table}
p-value = 0.0145
Hence, Since p-value ( 0.0145 ) is less than significance level ( 0.05 )
we reject null hypothesis.
Therefore, there is sufficient evidence to conclude that Car accidents are NOT equally distributed throughout the year
In this exercise we have to use probability knowledge to calculate the distribution during the year, so we find that:
There is sufficient evidence to conclude that car accidents are not equally distributed throughout the year.
Given the data in the question;
[tex]Null \ hypothesis: H_0[/tex][tex]Alternative \ hypothesis : H_a[/tex] [tex]Significance\ level = 0.05[/tex]Now the values given in the statement can be exemplified below as:
[tex]Spring = 27[/tex][tex]Summer = 39[/tex][tex]Fall = 31[/tex][tex]Winter = 53[/tex]In this way, we can assemble a table of values with the statistical data previously informed and using the formula given below:
[tex]Z=\sum[\frac{(O-E)^2}{E}][/tex]
[tex]Z = 10.5334[/tex]
So:
[tex]\ \ \ \ \ \ \ \ \ \ \ O \ \ \ \ \ E \ \ \ \ (O - E)^2/E\\Spring \ \ 27 \ \ 37.4 \ \ \ \ 2.94\\Summer \ 39 \ 37.4 \ \ \ \ 0.06\\Fall \ \ \ \ \ \ 31 \ 37.4 \ \ \ \ 1.1267\\Winter \ \ \ 53 \ 37.4 \ \ \ 6.4067\\Total \ 150 150 \ 10.5334[/tex]
Hence, Since pvalue ( 0.0145 ) is less than significance level ( 0.05 ), so we reject null hypothesis.
See more about probability at brainly.com/question/795909
What is the greatest common
factor of the expression?
2x^2y^3+4x^2y^5
Answer:
[tex]2x^2y^3[/tex]
Step-by-step explanation:
The given expression is :
[tex]2x^2y^3+4x^2y^5[/tex]
We need to find the greatest common factor of the expression.
The first term is [tex]2x^2y^3[/tex]
The other term is [tex]4x^2y^5[/tex]
[tex]2x^2y^3[/tex] is common in both terms. So,
[tex]2x^2y^3(1+2y^2)[/tex]
Hence, the greatest common factor of the expression is equal to [tex]2x^2y^3[/tex].
What is the slope of a line perpendicular to the line containing the points (4,-7) and (-5,-1)? Express your answer as a common fraction.
40 POINTS!!!!!!
if not right i report
Answer:
3/2
Step-by-step explanation:
Slope 1 = (-1+7)/(-5-4) = 6/(-9) = -2/3
Slope 2 perpendicular to Slope 1 :
-1 ÷ -⅔ = 3/2
Answer to the question
Answer:
x = 4
Step-by-step explanation:
180 = 102 + 24x - 18
102 - 18 = 84subtract 84 from both sides96 = 24xdivide both sides by 44 = xA news report suggested that an adult should drink a minimum of 4 pints of water per day.
Based on this report, determine the minimum amount of water an adult should drink,
in fluid ounces, per week.
9514 1404 393
Answer:
448
Step-by-step explanation:
(4 pt/da)×(7 da/wk)×(16 oz/pt) = 448 oz/wk
That would be 448 fluid ounces per week.
the volume of a cone with a radius of 6 and slant height of 10
Answer:
21.161
Step-by-step explanation:
use Pythagoras theorem ti find your slant height
then you use your formula which
[tex]1 \3\pi {r }^{2} h[/tex]
4x – 26 = 18 pls answer fast
Answer:
X = 11
Step-by-step explanation:
4x - 26 = 18
Add 26 on both sides to get 4x alone.
4x - 26 + 26 = 18 + 26
4x = 44
44 divided by 4 is 11.
Therefore X is 11.
Answer: x=11
Step-by-step explanation:
Add 26 to both sides
4x-26+26=18+26
4x=44
Divide by 4 and get 11
x=11
Bill makes $240 per hour for a standard 40 hour work week. He earns time- and - a - half for every overtime hour he works. Bill earned a total of$11,400 in one week,how many overtime hours did her work?
Answer:
5 overtime hours
Step-by-step explanation:
Given that :
Pay per hour = 240
Overtime pay = 1 1/2 * pay per hour = 1 1/2 * 240 = 360 per hour
Amount earned for the week = 11400
Let overtime hours = x
Total hours worked = 40 + x
Earning for the week based on hours worked :
240(40) + 360x = 11400
9600 + 360x = 11400
360x = 1800
x = 1800 / 360
x = 5 hours
You purchase a painting for 9,000 that has an appreciation rate of 12%. What is the growth
factor?
Answer:
Step-by-step explanation:
Answer:
$1080
Step-by-step explanation:
I think I am not sure
In 42 - 15 = 27, the number 42 is called the
the number 15 is called the
and the number 27 is called
Answer:
The Answer to the Ultimate Question of Life, the Universe, and Everything is 42
Step-by-step explanation:
In this equation, the number 42 is called a minuend.
15 is a subtrahend because it is being subtracted from another number.
The number 27 would be called the difference.
Becoming a member at fitness club costs $50 plus a monthly fee of $25. Using the graph, estimate how many months a person has been a member if he has paid a total of $250.
Answer:
0.3
Step-by-step explanation:
Surface Area of a Triangular Pyramid, please help!
Answer:
surface area of the triangular pyramid
=(1/2×9×7.8)+(3×1/2×9×12.3)
=35.1+166.05
=201.15 inch²
Help troll or report Help plsssss
Answer:
11. (a) 3/4+1/2=5/4
(b) 4/5= 8/10 , 16/20
12. 8 children don't like choc ice cream
Step-by-step explanation:
11. 3/4 +2/4=5/4(change 1/2 by making it the same as the one next to it)
12. 3/5 of 20 = 12
20-12=8
Could anyone help me please?
9514 1404 393
Answer:
4
Step-by-step explanation:
In order to evaluate f(g(-1)), you first need to find g(-1).
The graph of g(x) crosses the line x = -1 at y = 1, so g(-1) = 1.
The second step is evaluating f(1). The graph of f(x) crosses the line x=1 at y=4, so f(1) = 4.
f(g(-1)) = f(1) = 4
you sight a rock climber on a cliff at a 32° angle of elevation. your eye level is 5.5 feet above the ground and you are 1000 feet from the base of the cliff. what is the approximate height of the rock climber from the ground?
Answer:
630 feets
Step-by-step explanation:
From the triangle attached :
Using trigonometry, the height h, which is the height of climber to your eye level :
Tan θ = opposite / Adjacent
Tan 32 = h / 1000
h = tan 32 * 1000
h = 0.6248693 * 1000
h = 624.86935
Height from the ground :
624.86935 + 5.5
= 630.369 feets
= 630 feet
A bag of candy has equal numbers of candies in eight colors: blue, red,
brown, green, yellow, orange, pink, and black. If you eat them one by one,
what's the probability of getting your first red candy on or before the fifth
pick?
Answer:
the answer would be b I'm pretty sure
Can someone please answer and explain this.
Answer:
x =74
Step-by-step explanation:
540 degrees is the sum of all the angles
90 +90 + 2x+10 + x + 2x-20 = 540
Combine like terms
5x+170=540
Subtract 170 from each side
5x = 370
Divide by 5
5x/5 = 370/5
x =74
Find the area of a regular
polygon with 5 sides that has a
side length of 6 inches and an
apothem of 9 inches.
Answer:
area of polygon : 120in²
