Answer:
[tex]8\frac23\ cm^2[/tex]
Step-by-step explanation:
sector of the circle if the angle at the center is 150° means [tex]\frac{150^o}{360^o}[/tex] of full circle of given radius
area of a circle of given radius R is: πR²
so area of given sector:
[tex]A=\dfrac{150^o}{360^o}\cdot \pi\cdot8^2=\dfrac5{12}\cdot3.1\cdot64=82,(6)=8\frac23\ cm^2[/tex]
The area of a sector of the circle if the angle at the center is 150° is 82.67 square centimeter.
What is a circle?
A circle is a locus of a point whose distance always remains constant from a given specific point. The general equation is -
x² + y² = r² (for circle centered at origin)
Given is a circle has a radius of 8 cm.
The area of the sector subtending the angle 150° at center is -
A = (150/360) x 3.1 x 8 x 8
A = 82.67 square centimeter.
Therefore, the area of a sector of the circle if the angle at the center is 150° is 82.67 square centimeter.
To solve more questions on circles, visit the link below-
https://brainly.com/question/17006280
#SPJ5
The city park department is planning to enclose a play area with fencing. One side of the area will be against an existing building, so no fence is needed there. Find the dimensions of the maximum rectangular area that can be enclosed with 800 meters of fence. Include the units.
Answer:
The maximum rectangular area will have the length 400 meters and width 200 meters with one side of the length against an existing building.
Step-by-step explanation:
From the given information;
The perimeter of a rectangle = 2 (L+B)
here;
L = the length of the side of the fence
B = the width of the fence
So; The perimeter of a rectangle = 2L+2B
we are also being told that;
One side of the area will be against an existing building
i.e
The perimeter of a rectangle is now = L + 2B = 800 meters
L = 800 - 2B
Similarly; Area of a rectangle = L × B
Area of a rectangle = ( 800 - 2B) × B
Area of a rectangle = 800B - 2B²
assuming A(B) to represent the Area;
Then the maximum area A'(B) = 0 ;
Thus,
A'(B) = 800 - 4B = 0
-4B = - 800
4B = 800
B = 200
Therefore; the maximum area have a width = 200 meters and a length 800 - 2(200) = 800 - 400 = 400 meters
The graph of h(x) is a translation of f (x) = RootIndex 3 StartRoot x EndRoot. On a coordinate plane, a cube root function goes through (negative 3, negative 1), has an inflection point at (negative 2, 0), and goes through (negative 1, 1). Which equation represents h(x)?
Answer:
The correct option is;
[tex]h(x) = \sqrt[3]{x + 2}[/tex]
Step-by-step explanation:
Given that h(x) is a translation of f(x) = ∛x
From the points on the graph, given that the function goes through (-1, 1) and (-3, -1) we have;
When x = -1, h(x) = 1
When x = -3, h(x) = -1
h''(x) = (-2, 0)
Which gives
d²(∛(x + a))/dx²= [tex]-\left ( \dfrac{2}{9} \cdot \left (x + a \right )^{\dfrac{-5}{3}}\right )[/tex], have coordinates (-2, 0)
When h(x) = 0, x = -2 which gives;
[tex]-\left ( \dfrac{2}{9} \cdot \left (-2 + a \right )^{\dfrac{-5}{3}}\right ) = 0[/tex]
Therefore, a = (0/(-2/9))^(-3/5) + 2
a = 2
The translation is h(x) = [tex]\sqrt[3]{x + 2}[/tex]
We check, that when, x = -1, y = 1 which gives;
h(x) = [tex]\sqrt[3]{-1 + 2} = \sqrt[3]{1} = 1[/tex] which satisfies the condition that h(x) passes through the point (-1, 1)
For the point (-3, -1), we have;
h(x) = [tex]\sqrt[3]{-3 + 2} = \sqrt[3]{-1} = -1[/tex]
Therefore, the equation, h(x) = [tex]\sqrt[3]{x + 2}[/tex] passes through the points (-1, 1) and (-3, -1) and has an inflection point at (-2, 0).
Answer: B
Step-by-step explanation:
Please help me it will mean a lot
Answer:
A) a=25
B) b=14
Step-by-step explanation:
A) a/5+3=8
First you need to subtract 3 from both sides.
(a/5+3)-3=(8)-3
Then simplify
a/5=5
Multiply both sides by 5
(a/5)*5=(5)*5
Then simplify
a= 25
B )3b/7-1=5
First you need to add 1 to both sides
(3b/7-1)+1=(5)+1
Simplify
3b/7=6
Multiply both sides by 7
(3b/7)*7=(6)*7
Simplify
3b=42
Divide both sides by 3
(3b)/3=(42/3)/3
Simplify
b= 14
(Brainliest???) :P
solve the equation 2p square + 11p=30
Answer:
[tex]p=- \frac{15}{2}[/tex]
[tex]p=2[/tex]
Step-by-step explanation:
[tex]2p^2+11p=30[/tex]
Subtract 30 on both sides.
[tex]2p^2+11p-30=30-30[/tex]
[tex]2p^2+11p-30=0[/tex]
Factor left side of the equation.
[tex](2p + 15)(p-2)=0[/tex]
Set factors equal to 0.
[tex]2p+15=0[/tex]
[tex]2p=-15[/tex]
[tex]p=\frac{-15}{2}[/tex]
[tex]p-2=0[/tex]
[tex]p=2[/tex]
values of r and h, what do you notice about the proportions of the cylinders?
Answer:
Below
Step-by-step explanation:
r us the radius of the base and h is the heigth of the cylinder.
The volume of a cylinder is given by the formula:
V = Pi*r^2*h
V/Pi*r^2 = h
We can write a function that relates h and r
Answer:
One of the cylinders is short and wide, while the other is tall and thin.
Step-by-step explanation:
sample answer given on edmentum
What is the sum of 3x to the second power +2x-1
Answer:
[tex]3x^2+2x+1[/tex]
Step-by-step explanation:
Sum means to add and second power means that the exponent is "2". So, the expression is:
=> [tex]3x^2+2x+1[/tex]
It cannot be simplified further.
A total of $10,000 is invested in two mutual funds. The first account yields 5% and the second account yields 6%. How much was invested in each account if the total interest earned in a year is $575?
Answer:
$2,500 was invested in the first account while $7,500 was invested in the second account
Step-by-step explanation:
Here in this question, we want to find the amount which was invested in each of the accounts, given their individual interest rates and the total amount that was accorded as interest from the two investments
Now, since we do not know the amount invested , we shall be representing them with variables.
Let the amount invested in the first account be $x and the amount invested in the second account be $y
Since the total amount invested is $10,000, this means that the summation of both gives $10,000
Mathematically;
x + y = 10,000 ••••••(i)
now for the $x, we have an interest rate of 5%
This mathematically translates to an interest value of 5/100 * x = 5x/100
For the $y, we have an interest rate of 6% and this mathematically translates to a value of 6/100 * y= 6y/100
The addition of both interests, gives 575
Thus mathematically;
5x/100 + 6y/100 = 575
Multiplying through by 100, we have
5x + 6y = 57500 •••••••••(ii)
From 1, we can have x = 10,000-y
let’s substitute this into equation ii
5(10,000-y) + 6y = 57500
50,000-5y + 6y = 57500
50,000 + y = 57500
y = 57500-50,000
y = 7,500
Recall;
x = 10,000-y
so we have;
x = 10,000-7500 = 2,500
Grace starts with 100 milligrams of a radioactive substance. The amount of the substance decreases by 14 each week for a number of weeks, w. She writes the expression 100(14)w to find the amount of radioactive substance remaining after w weeks. Ryan starts with 1 milligram of a radioactive substance. The amount of the substance decreases by 40% each week for a number of weeks, w. He writes the expression (1 – 0.4)w to find the amount of radioactive substance remaining after w weeks. Use the drop-down menus to explain what each part of Grace’s and Ryan’s expressions mean.
Answer:
100= Initial Amount
1/4= decay factor for each week
w= number of weeks
1/4w= decay factor after w weeks
1 - 0.4= decay factor for each week
w= number of weeks
0.4= percent decrease
Step-by-step explanation:
Una estudiante gráfica muestras de mayolicas que desea comprar su papa para poner en el piso de la ducha. Las representaciones gráficas de 3/4 corresponde a la parte coloreada en cada una de las mayolicas ¿Son equivalentes las fracciones que representan la parte coloreada de cada muestra? ¿Cómo verifico que 2 fracciones son equivale?
Help plz down below with the question
Answer:
The SAS Postulate
Step-by-step explanation:
SAS means Side-Angle-Side; that is, two sides are equal and an angle between those sides are equal. We're given two sides: TK and TL, and we're given that 1 is congruent to 2. Knowing the latter, we can conclude that the angle between them (let's call it 1.5 for our purposes) will be congruent to itself. Since 1.5 is the angle right in the middle of two congruent sides, our answer is SAS.
plz help me .................
the price of a jacket was slashed from RS 960 to RS 816 .then the rate of discount offered is 10 percentage
Answer:
15%
Step-by-step explanation:
Question:
The price of a jacket was slashed from Rs.960 to Rs.816.Then the rate of discount offered is
Solution
Original price= Rs.960
Discount price= Rs.816
Difference in price=Original price - discount price
=Rs. 960 - Rs. 816
=Rs. 144
Percentage discount= Difference in price / Original price × 100
=Rs. 144 / Rs. 960 × 100
=0.15 × 100
=15%
The percentage discount =15% NOT 10% as you have written
The mean one-way commute to work in Chowchilla is 7 minutes. The standard deviation is 2.4 minutes, and the population is normally distributed. What is the probability of randomly selecting one commute time and finding that: a). P (x < 2 mins) _____________________________ b). P (2 < x < 11 mins) _____________________________ c). P (x < 11 mins) ________________________________ d). P (2 < x < 5 mins) _______________________________ e). P (x > 5 mins)
Answer:
The answer is below
Step-by-step explanation:
Given that:
The mean (μ) one-way commute to work in Chowchilla is 7 minutes. The standard deviation (σ) is 2.4 minutes.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
a) For x < 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
From normal distribution table, P(x < 2) = P(z < -2.08) = 0.0188 = 1.88%
b) For x = 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
For x = 11:
[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]
From normal distribution table, P(2 < x < 11) = P(-2.08 < z < 1.67 ) = P(z < 1.67) - P(z < -2.08) = 0.9525 - 0.0188 = 0.9337
c) For x = 11:
[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]
From normal distribution table, P(x < 11) = P(z < 1.67) = 0.9525
d) For x = 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
For x = 5:
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]
From normal distribution table, P(2 < x < 5) = P(-2.08 < z < -0.83 ) = P(z < -0.83) - P(z < -2.08) = 0.2033- 0.0188 = 0.1845
e) For x = 5:
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]
From normal distribution table, P(x < 5) = P(z < -0.83) = 0.2033
Evaluate the following expression using the given values: (1 point) Find x − 3y if x = 3 and y = −2.
Answer:
9
Step-by-step explanation:
x − 3y
Let x =3 and y = -2
3 -3(-2)
3 + 6
9
Lyla i am not cheating Guys please helps.
Answer:
C. 6√5
Step-by-step explanation:
√20 +√80= √4*5 + √16*5 = 2√5 + 4√5 = 6√5
1. What number comes next in this sequence?
483, 759, 264, 837,?
A) 487
B) 592
C) 375
D) 936
Answer:
C 375 this your answer
Hope it will help
Answer:
B) 592
Step-by-step explanation:
483, 759, 264, 837,?
Erase commas.
483759264837
Separate into two-digit groups:
48, 37, 59, 26, 48, 37
There is a common pattern:
48 - 11 = 37 + 22 = 59 - 33 = 26 + 22 = 48 - 11 = 37
The next term:
37 + 22 = 59 (add 22)
59 - 33 = 26 (subtract 33)
5926
State if the gives angles are coterminal.
Answer:
Below
Step-by-step explanation:
Coterminal angles are angles with same terminal angles
Mathematically speaking these angles should have the same coordinates in a trigonomitrical circle
●●●●●●●●●●●●●●●●●●●●●●●●
Angles like 0° and 360° are coterminal since to we made a spin from 0° to 360°
For two angles A and B to be coterminal they should verify this relation :
A = B + k*360° with k an integer
So A-B = k*360°
●●●●●●●●●●●●●●●●●●●●●●●●
7) :
35° and 395°
395° -35° = 360°
360° is a multiple of 360° so these angles are coterminal
8) :
140° and 860°
860° - 140° = 720°
720° is a multiple of 360°
720 = 360° × 2
9) :
350° and -710°
350 -(-710) = 350+ 710 = 1060°
1060° isn't a multiple of 360°
So these angles aren't coterminal
10) :
130° and -230°
130 -(-230) = 130+230 = 360°
So these angles are coterminal
11) :
30° and -690°
30 -(-690) = 30+ 690 = 720°
720 is a multiple of 360 so these angles are coterminal
12) :
210° and 10°
210-10 = 200
200 isn't a multiple of 360 so these angles aren't coterminal
Suppose a firm in a competitive market earned $1,000 in total revenue and had a marginal revenue of $10 for the last unit produced and sold. What is the average revenue per unit, and how many units were sold?
Answer:
$5 and 50 units
Step-by-step explanation:
Which of the following is the function of f(x)?
Answer:
f(x) = 8(x-3)
Step-by-step explanation:
F^ -1 ( x) = x/8 +3
Let y = x/8+3
To find the inverse
Exchange x and y
x = y/8+3
Solve for y
x-3 = y/8+3-3
x-3 = y/8
Multiply each side by 8
8(x-3) = y/8 * 8
8(x-3) = y
The inverse of the inverse is the function so
f(x) = 8(x-3)
Answer:
[tex]\boxed{f(x) = 8(x-3)}[/tex]
Step-by-step explanation:
[tex]y=\frac{x}{8} +3[/tex]
Switch variables.
[tex]x=\frac{y}{8} +3[/tex]
Make y as subject.
Subtract 3 from both sides.
[tex]x-3=\frac{y}{8}[/tex]
Multiply both sides by 8.
[tex]8(x-3)=y[/tex]
Steve paid $3.29 for a pizza. He now has $35.86. With how much money did he start?
Answer:
$39.15
Step-by-step explanation:
We can find that Steve started with $39.15, by adding the price he has now and the price he paid for the pizza.
35.86+3.29=$39.15
Answer:
$39.15
Step-by-step explanation:
$35.86 + $3.29 = $39.15
hOpEfUlLy ThIs HeLpEd!! :33
write a compound inequality that the graph could represent
Answer:
second option
Step-by-step explanation:
im stuck on this question helm me out I will mark you as brainliest
Answer: it is =4176000000000000
Step-by-step explanation:
(2.9)(100000)(7.2)(10^2)
5(10^−8)
=
(290000)(7.2)(10^2)
5(10^−8)
=
2088000(10^2)
5(10^−8)
=
(2088000)(100)
5(10^−8)
=
208800000
5(10^−8)
=
208800000
5(1/100000000)=
208800000/1
20000000
=4176000000000000
hope i helped
-lvr
first answer gets best marks
Answer:
A, B, E
Step-by-step explanation:
I attached everything that I thought it would help you.
Hope this helps ;) ❤❤❤
Question 4. In the graph, lines f and g intersect at P(6,6). What is the area, in square units, of the shaded region? * E. 15 F. 21 G. 27 H. 30
Answer:
E
Step-by-step explanation:
i guess the dotted lines outline a square
so get the area of the square which is 6×6=36
then don't focus on the shaded part but unshaded you'll see two right angled triangles
[tex]a = 1 \div2b \times h[/tex]
you will get a total for both as 21
then get the area of the square 36-21=15
so the area becomes 15
Consider the function represented by the table.
What is f(0)?
04
O 5
06
O 7
Answer:
6
Step-by-step explanation:
From the table given defining a function, the values of "x" on the table represents the input of the function, which gives us an output, f(x), which can be labelled as "y" in some instances.
Thus, the value of f(0), is simply the output value we would get, given an input value of "0".
So therefore, f(0) = 6. That is, at x = 0, f(x) = 6.
Answer: 6
Step-by-step explanation:
Instructions: Given the preimage reflect over the x-axis then they axis. Find
the new coordinates.
10
8
6
1012
А
-12 -10 8 6 4-2
-2
B
-4
D
-6
С
-12
The coordinates of the preimage are:
A(-8, -2)
B(-4, -3)
C(-2,-8)
D(-10, -6)
Now let's find the coordinates after the reflection over the x-axis.
A'(-8,
B' (-4,
C'(-2,
D' (-10,
Answer:
The coordinates are;
For reflection over the x-axis
A'(-8, 2)
B'(-4, 3)
C'(-2, 8)
D'(-10, 6)
For reflection over the y-axis;
A''(8, 2)
B''(4, 3)
C''(2, 8)
D''(10, 6)
Step-by-step explanation:
When a point (x, y) is reflected over the x, axis, we have;
Coordinates of the pre-image = (x, y)
Coordinates of the image after reflection = (x, -y)
Therefore, for the points A, B, C, D we have;
Pre-image A(-8, -2), Image A'(-8, 2)
Pre-image B(-4, -3), Image B'(-4, 3)
Pre-image C(-2, -8), Image C'(-2, 8)
Pre-image D(-10, -6), Image D'(-10, 6)
When a point (x, y) is reflected over the y, axis, we have;
Coordinates of the pre-image = (x, y)
Coordinates of the image after reflection = (-x, y)
Therefore, for the points A', B', C', D' we have;
Pre-image A'(-8, 2), Image A''(8, 2)
Pre-image B'(-4, 3), Image B''(4, 3)
Pre-image C'(-2, 8), Image C''(2, 8)
Pre-image D'(-10, 6), Image D''(10, 6).
Plzzzz Help
In Main City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as shown. Choose True or False for each statement
a. true
b. false ( angles should equal 180 125+65=190)
c. true
d. true
e. true
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
a. True (vertically opposite angles are equal)
b. False (angles on a straight line add up to 180 degrees)
c. True (corresponding angles are equal)
d. True (supplementary angles are angles that add up to 180 degrees)
e. True (alternating interior angles are equal)
An inverse variation includes the point (4,17). Which point would also belong in this inverse variation?
Answer:
(2, 34 )
Step-by-step explanation:
Since the points vary inversely then half the x, means double the y, thus
(2, 34) or (1, 68 ) would also belong in this inverse variation
WILL MARK BRAINLIEST
PLEASE HELP
Please help me answer 1 and 2 and explain how you did it so I can understand x
Answer:
poop
Step-by-step explanation:
Hey loves!!! Can any of you lovely people help me with my math?
Answer:
SAA or AAS
Step-by-step explanation:
∠BAC = ∠BCA Given
∠BDA = 90° and ∠BDC = 90° Given
∠BDA = ∠BDC All 90° angles are congruent
BD = DB Reflexive property
ΔADB = ΔCDB SAA
a previous analysis of paper boxes showed that the standard deviation of their lengths is 15 millimeters. A packers wishes to find the 95% confidense interval for the average length of a box. How many boxes do he need to measure to be accurate within 1 millimeters
Answer:
864.36 boxes
Step-by-step explanation:
In the question above, we are given the following values,
Confidence interval 95%
Since we know the confidence interval, we can find the score.
Z score = 1.96
σ , Standards deviation = 15mm
Margin of error = 1 mm
The formula to use to solve the above question is given as:
No of boxes =[ (z score × standard deviation)/ margin of error]²
No of boxes = [(1.96 × 15)/1]²
= 864.36 boxes
Based on the options above, we can round it up to 97 boxes.