What is the surface area of a sphere with a radius of 13 units?
A. 6767 units2
B. 10147 units
C. 8451 units2
D. 5077 units2
I hope this helps you
Sphere Surface Area Formula is
4.pi.r^2
4.pi.13^2
4.pi.169
676.pi
The surface area of the sphere with radius 13 units is S = 676π units²
What do you mean by a Sphere?A sphere is a three-dimensional geometrical object that is perfectly round in shape. A sphere is a fully spherical, three-dimensional geometrical object. Every point on its closed surface is equally spaced from the centre, which is the only point on the surface.The distance from the center to any point on the surface of the sphere is known as the radius of the sphere..
Surface Area of a Sphere = 4πr²
Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
They are used to represent many natural and man-made objects such as planets, basketballs, and molecules.
Let the data be ,
Let r = 13 units be the sphere's radius.
Let S be the sphere's surface area.
And , Surface Area of a Sphere = 4πr²
On simplifying , we get
S = 4π ( 13 )²
S = 4π ( 169 )
S = 676π units²
Thus, the sphere's surface area is S = 676 units2.
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One positive integer is 1 greater than 3 times another positive integer. If the product of the two integers is 154, then what is the sum of the two integers?
Answer:
29
Step-by-step explanation:
Let the smaller integer be x.
The other integer is 1 greater than 3 times x, or 3x + 1.
The product is 154.
x(3x + 1) = 154
3x^2 + x - 154 = 0
157 = 2 * 7 * 11
14 * 11 = 154
22 * 7 = 154
(3x + 22)(x - 7) = 0
3x + 22 = 0 or x - 7 = 0
3x = -22 or x = 7
x = -22/3 or x = 7
-22/3 is not a positive integer, so we discard that solution.
The smaller integer is 7.
3x + 1 = 3(7) + 1 = 22
The greater integer is 22.
The sum of the integers is 7 + 22 = 29
Answer: 29
Step-by-step explanation:
Which point of intersection is the solution to the system that of equations y= 2/5x-1/2 and y=-1/3x+2/3
Answer:
x = 35/22
y = 3/22
Step-by-step explanation:
y= 2/5x-1/2 ................(1)
y=-1/3x+2/3 ...............(2)
10*(1)
10y = 4x -5 ...................(1A)
3*(2)
3y = -x +2 ....................(2A)
To find intersection, solve for y & x
4(2A) + (1A)
12y+10y = -4x+4x +8-5
22y = 3
y = 3/22
Substitute in (1)
3/22 = 2/5x -1/2
multiply by 110
15 = 44x - 55
70 = 44x
x = 70/44 = 35/22
Please help i will give out brainliest
Answer:
A
Step-by-step explanation:
To determine if a point lies on the curve, substitute the x- coordinate into the equation. If the value obtained is equal to the y- coordinate then the point lies on the curve, that is
A
y = ([tex]\frac{3}{2}[/tex] )² = [tex]\frac{9}{4}[/tex] ≠ [tex]\frac{9}{2}[/tex] ← not on line
B
y = (- 1)² = 1 ← lies on line
C
y = 4² = 16 ← lies on line
D
y = ([tex]\frac{1}{2}[/tex] )² = [tex]\frac{1}{4}[/tex] ← lies on line
Which graph represents the scenario? PLEASE HELP VERY EASY
Answer:
The answer is option B.
The second graph.
Hope this helps you
Hey everyone, can you please help me with this question? THANKS!
Answer:
6 granite, 3 marble, 14 sandstone, 1 slate
ratio of sandstone to marble
how many sandstone does she have .....14
how many marble does she have......3
so the ratio would be 14:3
Answer:
C. 14:3
Step-by-step explanation:
Dana has 14 pieces of sandstone.
Dana has 3 pieces of marble.
The ratio of pieces of sandstone to pieces of marble is 14:3.
The ratio cannot be simplified further.
(ANSWER ASAP) Which table represents a linear function? graph 1 graph 2 graph 3 graph 4
Answer:
D)
Step-by-step explanation:
Use desmos in the future to help you determine if all of those coordinate make a straight line.
Which best describes how the graph of g(x) =1/9sqrt(x) relates to the graph of the parent function, f(x) =sqrt(x) ? The graph of g(x) is shrunk vertically by a factor of 1/9. The graph of g(x) is stretched vertically by a factor of 1/9. The graph of g(x) is shrunk vertically by a factor of 1/3. The graph of g(x) is stretched vertically by a factor of 1/3.
Answer:
The graph g(x) is vertically shrunk by a factor of 1/9.
Step-by-step explanation:
Parent Graph: f(x) = a√(bx - c) + d
Since we are only modifying a, we are dealing with vertical shrink (a < 1) and stretch (a > 1). Since 1/9 < 1, we have a vertical shrink by a factor of 1/9.
The correct description is:
"The graph of g(x) is shrunk vertically by a factor of 1/9"
How do dilations work?
There are two types of dilations.
Vertical dilation:
For a function f(x), a vertical dilation of scale factor k is written as:
g(x) = k*f(x).
Where if k > 1, we have a dilation, if 0 < k < 1, we have a contraction.
Horizontal dilation:
For a function f(x), a horizontal dilation of scale factor k is wrtten as:
g(x) = f(x/k).
Where if k > 1, we have a dilation, if 0 < k < 1, we have a contraction.
Here we have:
f(x) = √xg(x) = (1/9)*√xSo we can see that g(x) is a vertical contraction of scale factor 1/9.
Then the correct option is:
"The graph of g(x) is shrunk vertically by a factor of 1/9"
If you want to learn more about dilations, you can read:
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root( x-1 ) = 2 - root (x+3)
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
[tex]\sqrt{x-1} =2-\sqrt{x+3}[/tex]
Square both sides.
[tex]\left(\sqrt{x-1}\right)^2=\left(2-\sqrt{x+3}\right)^2[/tex]
[tex]x-1=x+7-4\sqrt{x+3}[/tex]
Subtract x on both sides.
[tex]x-1-x=x+7-4\sqrt{x+3}-x[/tex]
[tex]-1=-4\sqrt{x+3}+7[/tex]
Subtract 7 on both sides.
[tex]-1-7=-4\sqrt{x+3}+7-7[/tex]
[tex]-8=-4\sqrt{x+3}[/tex]
Square both sides.
[tex]\left(-8\right)^2=\left(-4\sqrt{x+3}\right)^2[/tex]
[tex]64=16x+48[/tex]
Subtract 48 on both sides.
[tex]64-48=16x+48-48[/tex]
[tex]16=16x[/tex]
Divide both sides by 16.
[tex]\frac{16}{16} =\frac{16x}{16}[/tex]
[tex]1=x[/tex]
Switch sides.
[tex]x=1[/tex]
A chef planning for a large banquet thinks that 2 out of every 5 dinner guesis will order his soup appetizer he excepts 800 guests at the banquet
Answer:
320 people
Step-by-step explanation:
[tex]\frac{2 people}{5 people}[/tex]=[tex]\frac{x}{800 people}[/tex]
solve for x by using cross multiplication
-multiply 2 by 800 to get 1,600
-divide 1,600 by 5 people to get 320
your answer is 320 people
PLZZZZZZZZZZ HLPPPPPPPPP MEEEEEEEEEE what is the factorization of the polynomial graphed below? assume it has no constant factor. write each factor as a polynomial in descending order.
Answer:
(x-5)(x-8)(x+2)=0
Step-by-step explanation:
first look at the x intercept to find the factor
x:-2,5,8
x=-2 then x+2=0
x=5 then x-5=0
x=8 then x-8=0
(x-5)(x-8)(x+2)=0
check for y in the polynomial when x=0
x^3-11x^2+14x+80
x=0 y=80 ( correct according to the graph
Write the slope-intercept form (y=mx + b) of the blue line. Explain or show your work. Write a one sentence summary comparing the blue line to the black line. Hint: Find the y-intercept. Then count up and over (y/x) to the next point on the line to determine the slope.
Answer:
y=1/2x+2(2 is the y-intercept)
The blue line and black line have the same y-intercept, but the black line has a slope 1/6 greater than the blue line.
Hope it helps <3
Answer:
[tex]\boxed{y=\frac{1}{2} x+2}[/tex]
Step-by-step explanation:
Let's take any of the coordinates of blue line to find the slope
The coordinates are (4,4) and (0,2)
Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]
Slope = [tex]\frac{2-4}{0-4}[/tex]
Slope = [tex]\frac{-2}{-4}[/tex]
Slope = m = 1/2
Y-intercept = b = 2 (Because here x= 0)
So, the slope intercept equation becomes:
=> [tex]y = mx+b[/tex]
=> [tex]y = \frac{1}{2} x+2[/tex]
It costs $1.58 to buy a bag of popcorn. Which of the following equations shows the amount of money needed, z, to buy n bags of popcorn? z = 1.58 + n n = 1.58 + z z = 1.58n n = 1.58z
Answer:
z = 1.58n
Step-by-step explanation:
To find the total amount (z), the cost of a bag (1.58) must be multiplied by the number of bags (n).
z = 1.58n
Answer:
1.58 times the number of bags you're buying will give you how much money it all is: z=1.58n
Rowan is taking his siblings to get ice cream. They can't decide whether to get a cone or a cup because they want to get the most ice cream for their money. If w = 2.5 in, x = 5 in, y = 5 in, z = 3 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? Use 3.14 for π, and round your answer to the nearest tenth.
Answer:
The cup holds 26.2 in3 more ice cream than the cone.
Step-by-step explanation:
1. Let's find the volume of ice cream that the cone holds, this way:
Volume = π * r² * h/3
Replacing with the real values, we have:
Volume = 3.14 * 2.5² * 5/3
Volume =32.7 inches³
2. Let's find the volume of ice cream that the cup holds, this way:
Volume = π * r² * h
Diameter = 5 inches ⇒ Radius = 2.5 inches
Replacing with the real values, we have:
Volume = 3.14 * 2.5² * 3
Volume =58.9 inches³
3. Let's find the difference, this way:
Volume of the cup - volume of the cone = 58.9 - 32.7 = 26.2 inches³
The cup holds 26.2 in³ more ice cream than the cone.
I need help please! The sequence 6,18,54,162, ... shows the number of pushups Kendall did each week, starting with her first week of exercising (a) What is the recursive rule for the sequence (b) What is the iterative rule for the sequence
Answer:
a: 3
b. 6973568802
Step-by-step explanation:
a₁ = 6 , r = 3 , a₂₀ =?
Result:
a₂₀ = 6973568802
Explanation:
To find a₂₀ we use the formula
aₙ = a₁ · r ^ⁿ⁻¹
In this example we have a₁ = 6 , r = 3 , n = 20. After substituting these values to above
formula, we obtain:
aₙ = a₁ · r ^ⁿ⁻¹
a₂₀ = 6 · 3 ^²⁰⁻¹
a₂₀ = 6 · 1162261467
a₂₀ = 6973568802
Evan, Claire, Jaya and Tim are running a 3km relay race.
Evan ran 9/10 of a km
Claire ran 7/9 of a km
Jaya ran 2/3 of a km
What fraction of a km does Tim need to run to finish the race?
Try to answer ASAP please, thank you.
Answer:
Tim needs to finish 59/90
Step-by-step explanation:
Add together what Evan Claire and Jaya ran
9/10 + 7/9+ 2/3
The common denominator is 90
9/10 (9/9) +7/9 *10/10 + 2/3 *30/30
81/90 + 70/90 + 60/90
211/90
We need 3 km = 3 *90/90 = 270 /90
270/90 - 211/90 = 59/90
What is the area of the triangle in the diagram?
Answer:
[tex]\frac{(a-b)^2+b^2}{a^2}[/tex]
which agrees with the first choice (A) in your list of possible answers
Step-by-step explanation:
Notice that the area of the outer square is given by the square of it side [tex](a)[/tex].Then the outer area is given by: [tex]a^2[/tex]
Now, the inner square's area we calculate by subtracting from the outer area four equal right angle triangles (those shaded in grey in the figure provided). Each of such right angle triangles have an area given by the general formula of a triangle's area:
[tex]Area_{triangle}= \frac{base\,*\,height}{2} =\frac{(a-b)\,b}{2} =\frac{ab-b^2}{2}[/tex]
Therefore the internal square's area is:
[tex]a^2-4\frac{ab-b^2}{2} =a^2-2ab+2b^2[/tex]
And then the quotient of this are over the larger square area becomes:
[tex]\frac{a^2-2ab+2b^2}{a^2} =\frac{a^2-2ab+b^2+b^2}{a^2}=\frac{(a-b)^2+b^2}{a^2}[/tex]
There are three cards. One is green on both sides, the second is red on both sides and the third is red on one side and green on the other. We choose a card at random and we see one side (also chosen at random). If the side we see is green, what is the probability that the other side is also green
Answer:
0.667
Step-by-step explanation:
According to Bayes theorem:
Since there are three cards, the probability that the side is green = 1/3
For the first card, if one side is green, the probability that the other side is also green = 1 (both sides are green)
For the second card, if one side is green, the probability that the other side is also green = 0 (both sides are red)
For the third card, if one side is green, the probability that the other side is also green = 1/2 (one side is green and the other side is red)
[tex]P(G_k/A)=\frac{P(G_k)P(A/G_k)}{\Sigma_{i=1\ to\ m} P(G_i)P(A/G_i)} \\P(B_1/A)=\frac{P(G_1)P(A/G_1)}{P(G_1)P(A/G_1)+P(G_2)P(A/B_2)+P(G_3)P(A/G_3)}\\ P(B_1/A)=\frac{1/3*1}{(1/3*1)+(1/3*0)+(1/3*1/2)=\frac{1/3}{1/2} }=0.667[/tex]
What conclusion can you make from the information below?
Three people (Jack, Karen, and Louis) drive three different types of cars
(Ford, Chevrolet, Honda).
• Jack does not drive a Chevrolet.
• Karen does not drive a Chevrolet,
A. Louis drives a Chevrolet
B. Jack drives a Honda
C. Karen does not drive a Ford.
D. Louis does not drive a Chedly let.
M
Answer:
A.louis drive a chevolet
Step-by-step explanation:
from the question three different people drive different cars . since two out of the three people has been excluded from driving a particular car i.e the third person is the one driving Chevrolet
Nine less than the quotient of two and a number x.
Answer:
Hey there!
Your answer would be x/2 - 9
Answer:
2 ÷ x - 9
Step-by-step explanation:
Quotient of two is written as = 2 ÷ x
Nine less is written as = -9
Final answer = 2 ÷ x - 9
Hope this helped! :)
Joe takes out a 30-year fixed rate amortized loan for 220,000, and makes equal size payments at the end of each month. The rate is quoted as being an annual nominal interest rate of 5.25% compounded monthly and Joe also has to pay closing fees equal to 5% of the value of the loan. Based on this information, find the actual interest rate realized by Joe (i.E. Taking into account the loan given to Joe and the 5% that he pays for the closing fees). Give the value as an annual nominal rate compounded monthly, and round your percent answer to two decimal places.
Answer:
Annual Interest Rate, r = 5.69%
Step-by-step explanation:
Amount of loan taken = 220,000
Closing fee is 5% of the loan value
Closing fee = 5% of 222,000 = 0.05 * 220000 = 11000
Therefore, Principal, P = Loan amount + closing fee
P = 220000 + 11000
P = 231, 000
Annual rate, r= 5.25% = 0.0525
Monthly rate, i = 0.0525/12 = 0.004375
Time, n = 30 years = 30*12 = 360 months
The monthly payment will be calculated by:
[tex]PMT = \frac{P*i}{1 - (1 + i)^{-n}} \\\\PMT = \frac{231000 * 0.004375}{1 - (1 + 0.004375)^{-360}} \\\\PMT = 1275.59[/tex]
Assuming payments are made based on 220,000, let us calculate the monthly interest rate.
[tex]PMT = \frac{P*i}{1 - (1 + i)^{-n}} \\\\1275.59 = \frac{220000 * i}{1 - (1 + i)^{-360}} \\\\i = 0.00474229[/tex]
Annual rate, r = 12 * 0.0047429
r = 0.0569 = 5.69%
Find the equation of the line passing
through the points (3, 3) and (4, 5).
y = [? ]x + [
Hi everyone please help me with two questions,THX...this is for 6th grade
Answer:
A. 12 for every 7
Step-by-step explanation:
There are 12 peas in her bowl.
There are 7 peas in her hair.
The ratio of peas in her bowl to peas in her hair is 12 for every 7.
Factorize: 9(2a – b)^2 – 4(2a – b)
Answer:
(2 a - b) (18 a - 9 b - 4)
Step-by-step explanation:
Factor the following:
9 (2 a - b)^2 - 4 (2 a - b)
Factor 2 a - b out of 9 (2 a - b)^2 - 4 (2 a - b):
(2 a - b) (9 (2 a - b) - 4)
9 (2 a - b) = 18 a - 9 b:
Answer: (2 a - b) (18 a - 9 b - 4)
Helppp!!!! please!!!
Answer:
I. (x - 6)² + (y + 7)² = 121
Step-by-step explanation:
Given a circle with coordinates of the center as (6, -7), and with a diameter of 22, equation of the circle is given below using the standard equation formula of a circle:
Formula => (x - a)² + (y - b)² = r²
Where,
a = 6
b = -7
r = radius of circle = ½ of diameter = ½ of 22 = 11
Thus, plug in the above values into the standard equation formula:
(x - 6)² + (y - (-7))² = 11²
(x - 6)² + (y + 7)² = 121
Our answer, which is the equation of the circle is I. (x - 6)² + (y + 7)² = 121
in the given figure angle 1 is equal to angle 2 then the measurements of angle 3 and angle 4 are
Answer:
(3) = 119
(4) = 119
Step-by-step explanation:
Given isosceles triangle with vertex angle 58.
Need exterior angles of base angles 1 & 2.
Solution:
Vertex angle = 58.
Base angle = x
Sum of triangles = 180 =>
x + x + 58 = 180
Solve for x
x = (180-58)/2 = 122/2 = 61
Exterior angles are supplementary to interior (base) angles, so
(3) = 180-(1) = 180 - 61 = 119
(4) = 180-(2) = 180 - 61 = 119
* note: supplementary means sum of two angles = 180.
The measurements of angle 3 and angle 4 are 119degrees and 119degrees respectively.
The sum of the interior angle of the triangle is 180degrees.
According to the diagram shown:
m<1 + m<2 + 58 = 180
Since <1 = <2, hencce:
m<1 + m<1 + 58 = 180
2m<1 = 180 - 58
2m<1 = 122
m<1 = 122/2
m<1 = 61 degrees
Since <1 = <2, thereofore m<3 = m<4
Get the measure of m<3
m<1 + m<3 = 180 (supplementary angles)
61 + m<3 = 180
m<3 = 180 - 61
m<3 = 119 degrees
Recall that m<3 = m<4, hence m<4 = 119degrees
The measurements of angle 3 and angle 4 are 119degrees and 119degrees respectively.
Learn more here: https://brainly.com/question/21680544
State whether the data described below are discrete or continuous, and explain why The durations of movies in minutes A Choose the correct answer below OA. The data are continuous because the data can take on any value in an interval. St O B. The data are continuous because the data can only take on specific values OC. The data are discrete because the data can take on any value in an interval. O D. The data are discrete because the data can only take on specific values. G D
Answer:
D. The data are discrete because the data can only take on specific values.
Step-by-step explanation:
Continuous variables are variables that can take on any value in an interval. Examples of continuous variables are length, time, etc.
Discrete variables on the other hand are variables that can only take on specific values.
The durations of movies in minutes can only take on integer values from 0 to 60. Therefore, it is a discrete data.
The correct option is D.
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
D.
Step-by-step explanation:
As long as the function's largest power is two, it is a quadratic function.
a. (3x - 2)(4x + 7)
= 12x^2 - 8x + 21x - 14
The largest power is 2. This is a quadratic function.
b. 7x^2 + 8x
The largest power is 2. Quadratic function.
c. (2x - 1)^2
= 4x^2 - 4x + 1
Largest power is 2. Quadratic function.
d. 8x^4- 3x^3 + 5x^2
Largest power is 4. Non-quadratic function.
Hope this helps!
A central angle of a circle intercepts an arc of length 18 centimeters. The radius of the circle is 9 centimeters. What is the measure of the central angle in radians?
Answer:
.44444444
Step-by-step explanation:
πr²=full circumference
18/π(9)²=x/2π
What is the sum of the fractions? Use the number line and equivalent fractions to help find the answer. Negative 1 and one-fourth + one-half A number line going from negative 3 to 0 in increments of one-fourth. Negative 1 and three-fourths Negative 1 and one-half Negative three-fourths Negative one-half
Answer:
C. Negative three-fourths
Step-by-step explanation:
Given two fractions -1 1/4 and 1/2, the sum of the fractions is expressed as shown below:
-1 1/4 + 1/2
Converting the improper fraction -1 1/4 to mixed fraction will give -5/4. The expression will now become:
-5/4 + 1/2
Taking the LCM of the expression
= (-5+2)/4
= -3/4
Hence the sum of fraction Negative 1 and one-fourth and one-half is negative three-fourths
Answer:
-3/4
Step-by-step explanation:
-1 1/4 +1/2
-5/4 + 2/4
-3/4