Considering it's volume of 113 cm³, the approximate radius of the sphere is given by:
A. 3 cm
What is the volume of an sphere?
The volume of an sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In this problem, we have that V = 113 cm³, hence the radius in cm is given as follows:
[tex]V = \frac{4\pi r^3}{3}[/tex]
[tex]113 = \frac{4\pi r^3}{3}[/tex]
[tex]r^3 = \frac{113 \times 3}{4\pi}[/tex]
[tex]r = \sqrt[3]{\frac{113 \times 3}{4\pi}}[/tex]
r = 3 cm.
Hence option A is correct.
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Answer:
is 3 cm
Step-by-step explanation:
Solve for x. Write both solutions, separated by a
comma.
6x² + 5x - 6= 0
Answer:
[tex]x=\dfrac{2}{3},-\dfrac{3}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]6x^2+5x-6=0[/tex]
First, factor the left side of the given equation.
To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:
[tex]\implies ac=6\cdot-6=-36[/tex]
[tex]\implies b=5[/tex]
So the two numbers are: 9 and -4
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies 6x^2+9x-4x-6=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 3x(2x+3)-2(2x+3)=0[/tex]
Factor out the common term [tex](2x+3)[/tex]:
[tex]\implies (3x-2)(2x+3)=0[/tex]
To solve for x:
[tex]\begin{aligned}\implies (3x-2) & =0 & \implies (2x+3) & = 0\\3x & = 2 & 2x & = -3\\x & = \dfrac{2}{3} & x & = -\dfrac{3}{2}\end{aligned}[/tex]
Therefore:
[tex]x=\dfrac{2}{3},-\dfrac{3}{2}[/tex]
Find the area of the trapezoid.
The image is of a trapezoid with the lengths of lower and upper parallel sides marked as 12 in. and 8 in. respectively. The length of left side of the trapezoid which is perpendicular to the base is 7 in. and the fourth side is 8 in.
A. 140 in.2
B. 35 in.2
C. 75 in.2
D. 70 in.2
Answer:
Its a for me
Step-by-step explanation:
trust me fuys
Write this number in standard notation.
Answer:
12345678910
Step-by-step explanation:
TANQR
The standard notation of 7,250,000 is [tex]7.25 \times 10^6[/tex]
The standard notation of 0.000045 is [tex]4.5 \times 10^{-5}[/tex]
What is scientific notation?It is the way of writing a large number between 1 to 10 with a power of 10.
We have,
7,250,000
To write this number in standard notation, we can use powers of 10.
We start by counting the number of digits to the left of the decimal point.
In this case, there are 7 digits to the left of the decimal point.
We can then express this number in scientific notation as:
[tex]7.25 \times 10^6[/tex]
This means that we have 7.25 times 10 raised to the power of 6.
Now,
0.000045
To write this number in standard notation, we can again use powers of 10. We start by counting the number of digits to the right of the decimal point. In this case, there are 5 digits to the right of the decimal point.
We can then express this number in scientific notation as:
[tex]4.5 \times 10^{-5}[/tex]
This means that we have 4.5 times 10 raised to the power of -5.
Thus,
The standard notation of 7,250,000 is [tex]7.25 \times 10^6[/tex]
The standard notation of 0.000045 is [tex]4.5 \times 10^{-5}[/tex]
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The complete question.
Write this number in standard notation.
7,250,000
0.000045
Directions: Solve the following by multiplying by the inverse of the fractional coefficient. 1. \frac{2}{5} t = 20 2. \frac{7}{8} p = 56 3. \frac{5}{6} x = 30 4. \frac{1}{2} x = 20 5. \frac{3}{5} s = 60 6. \frac{1}{3} t = 3 7. \frac{3}{4} x = 9 8. \frac{11}{12} x = 11 9. \frac{8}{10} t = 80 10. \frac{p}{3} = 9 11. \frac{n}{5} = 30 12. \frac{6a}{7} = 36 13. \frac{1}{2} t + 3 = 28 14. \frac{1}{6} r = 12 15. \frac{11}{12} b = 32
The answer of the following options are as 50, 64, 36, 40, 100, 9, 12, 12 100, 27, 150 42, 50 72, 28.3.
How to interpret the fraction?Suppose the fraction is proper (the numerator is smaller than the denominator).
Let it be
[tex]\dfrac{a}{b}[/tex]
Then, we can interpret it as:
a parts out of b parts of a thing.
[tex]1. \dfrac{2}{5} t = 20\\\\t = 20 \times \dfrac{5}{2}\\\\t= 50[/tex]
[tex]2. \frac{7}{8} p = 56\\\\p = 56 \times \frac{8}{7} \\\\ p= 64[/tex]
[tex]3. \frac{5}{6} x = 30 \\\\x = 30 \times \frac{6}{5} = 36[/tex]
[tex]4. \frac{1}{2} x = 20\\\\x = 20 \times 2 = 40[/tex]
[tex]5. \frac{3}{5} s = 60\\\\s = 60 \times \frac{5}{3} = 100[/tex]
[tex]6. \frac{1}{3} t = 3 \\\\t = 3\times 3 = 9[/tex]
[tex]7. \frac{3}{4} x = 9\\\\x = 12[/tex]
[tex]8. \frac{11}{12} x = 11\\\\x = 11 \times 12/11 = 12[/tex]
[tex]9. \frac{8}{10} t = 80\\\\t = 80 \times 10/8 = 100[/tex]
[tex]10. \frac{p}{3} = 9 \\\\p = 9 \times 3 = 27[/tex]
[tex]11. \frac{n}{5} = 30\\\\n = 30 \times 5 = 150[/tex]
[tex]12. \frac{6a}{7} = 36 \\\\a = 36 \times 7/6 = 42[/tex]
[tex]13. \frac{1}{2} t + 3 = 28\\\\t = (28 - 3)2 = 50[/tex]
[tex]14. \frac{1}{6} r = 12\\\\r = 12\times 6 = 72[/tex]
[tex]15. \frac{11}{12} b = 32\\ \\b = 32 \times 11/12 = 29.33[/tex]
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Consider the sets A = {4,6,8} and B = {4,5,6} Find Ax B (b) Find the power set AB)
a) A × B is the Cartesian product of A and B, given by the set
A × B = {(a, b) | a ∈ A and b ∈ B}
Then for A = {4, 6, 8} and {4, 5, 6}, we have the product
A × B = {(4, 4), (4, 5), (4, 6), (6, 4), (6, 5), (6, 6), (8, 4), (8, 5), (8, 6)}
b) The power set of a set X is the set containing all subsets of X. I'm not sure what you're asking to find the power set of, though. Hopefully it's not of A × B, since that would contain 2⁹ = 512 elements...
Instead I'll assume you mean a simpler set, such as A ∩ B. The intersection of A and B is
A ∩ B = {4, 6, 8} ∩ {4, 5, 6} = {4, 6}
and has only 2 elements, so its power set has 2² = 4 elements (much more manageable!) and is the set
Pow(A ∩ B) = {{}, {4}, {6}, {4, 6}}
Pls need helppp in this question
Show all work. Find the measure of <1. Show all work.
Its in the picture below.
The value of x is 7 and the measure of ∠1 is 99
How to solve for x?The given parameters are:
∠NMQ = 5x + 19∠MQN = 8x - 11∠QNM = 11x + 4The sum of angles in a triangle is 180.
So, we have:
5x + 19 + 8x - 11 + 11x + 4 = 180
Evaluate the like terms
24x = 168
Divide both sides by 24
x = 7
Hence, the value of x is 7
How to determine the measure of ∠1?The angles on a straight line add up to 180.
This means that:
∠1 + ∠QNM = 180
Subtract ∠QNM from both sides
∠1 = 180 - ∠QNM
Substitute ∠QNM = 11x + 4
∠1 = 180 - 11x - 4
Substitute x = 7
∠1 = 180 - 11 * 7- 4
Evaluate
∠1 = 99
Hence, the measure of ∠1 is 99
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G(F(x)) = 7√√x+1
A. F(x)=√x and G(x) = 7
B. F(x)= x and G(x) = √√7
C. F(x) = 7x and G(x)=√x+1
D. F(x)=√x+1 and G(x) = 7x
Answer:
D)
Step-by-step explanation:
[tex]\sf f(x) = \sqrt{x+1}\\\\\\g(x) = 7x\\\\ g(f(x)) = g(\sqrt{x+1}) = 7*\sqrt{x+1}[/tex]
HELP PLEASE! THIS IS DUE SOON! HELP ME! QUESTION BELOW!
Answer:
A) x = 113°
Explanation:
Given three sides: 6.4 cm, 5.8 cm, 10.2 cm
Use the cosine rule:
c² = a² + b² - 2ab cos(C)
Insert/put variables:
[tex]\rightarrow \sf 10.2^2 = 5.8^2 + 6.4^2 - 2(5.8)(6.4) cos(x)[/tex]
[tex]\rightarrow \sf -74.24 cos(x) = 10.2^2 - 5.8^2 - 6.4^2[/tex]
[tex]\sf \rightarrow -74.24 cos(x) = 29.44[/tex]
[tex]\rightarrow \sf cos(x) = \dfrac{29.44}{-74.24}[/tex]
[tex]\rightarrow \sf x = cos^{-1}(-\dfrac{23}{58})[/tex] = 113.36° ≈ 113° (rounded to nearest degree)
Answer and EXplanatrion please
Answer:
whats nine + 10
Step-by-step explanation:
21
pencil is .10
pen is .90
Step-by-step explanation:
x = pencil y = pen
3x + y = 1.20
7x + 2y = 2.50
try make x or y cancelable
-2 times (3x + y = 1.20) = -6x - 2y = - 2.40
7x + 2y = 2.50
-6x - 2y = - 2.40
x = .10
plug .10 back into one of the equations
3(.10) + y = 1.20
.30 + y = 1.20
y = .90
X^2-4x+6=0 solve by completing square
Complete the square:
x² - 4x + 6 = 0
x² - 4x = -6
x² - 4x + 4 = -6 + 4
(x - 2)² = -2
But the left side is positive for any real number x, so there are no real solutions.
If you're solving over the complex numbers, we can go on to say
x - 2 = ± √(-2)
x - 2 = ± 2i
x = 2 ± 2i
where i = √(-1).
solve 2(r+6) =(6+1/3r)
Answer:
r = - 18/5
I hope this helps! ^^
( This problem has 13 steps, so it would take a lot of time to type them in ^^)
find the exact value of sin 15 degrees
Answer:
Hi,
Step-by-step explanation:
sin(a-b)=sin(a) cos(b)+ cos(a) sin(b)
a=45° and b=30°
[tex]sin(45^o-30^o)=sin(45^o)*cos(30^o)+cos(45^o)*sin(30^o)\\\\=\dfrac{\sqrt{2}}{2}* \dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{2}}{2}*\dfrac{1}{2}\\\\\\\boxed{sin(15^o)=\dfrac{\sqrt{2}}{4}*(1+\sqrt{3} )}\\[/tex]
What is the volume, in cubic meters, if the prism below?
=================================================================
Explanation:
Imagine rotating the figure so that the triangular face is flat on the ground. This makes the triangular faces to be the floor and ceiling of this room.
The floor is a triangle with base 24 meters and height 7 meters. The floor area is base*height/2 = 24*7/2 = 84 square meters.
Multiply this floor area with the height of the room (22 m) to get the volume of the room.
volume = (floor area)*(height) = 84*22 = 1848 cubic meters
Consider the function.
Which conclusions can be drawn about f–1(x)? Select two options.
f–1(x) has a slope of .
f–1(x) has a restricted domain.
f–1(x) has a y-intercept of (0, –36).
f–1(x) has an x-intercept of (–36, 0).
f–1(x) has a range of all real numbers.
The statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The question is: Consider the function f(x) = (-2/3)x - 24 Which conclusions can be drawn about f⁻¹(x) Select two options:
f⁻¹(x) has a slope of -2/3
f⁻¹(x) has a restricted domain.
f⁻¹(x) has a y-intercept of (0, –36).
f⁻¹(x) has an x-intercept of (–36, 0).
f⁻¹(x) has a range of all real numbers.
f(x) = (-2/3)x - 24
To find the inverse of a function:
interchange the x and y
x = (-2/3)y - 24
y = (-3/2)(x + 24)
y = (-3/2)x - 36
The slope of a function f⁻¹(x) is -3/2
From the graph, we can see the y-intercept is (0, -36) and the range will be all real numbers.
Thus, the statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.
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Answer:
D and E
Step-by-step explanation:
did the test
One block is needed to make an up-down-up staircase with one step up and one step down.
Four blocks are need to build and up-down-up staircase with 2 steps up and 2 steps down.
Complete parts (a) and (b) below.
***
a. How many blocks are needed to build an up-down-up staircase with 5 steps up and 5 steps down?
25 blocks are needed to build an up-down-up staircase with 5 steps up and 5 steps down.
(Type a whole number.)
b. How many blocks are needed to build an up-down-up staircase with n steps up and n steps down?
blocks are needed to build an up-down-up staircase with n steps up and n steps down.
Answer:
n² blocks are needed to build a staircase with n steps.
Step-by-step explanation:
Draw the line of reflection that reflects quadrilateral ABCD onto quadrilateral A'B'C'D'
What are the two points?
The two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have a quadrilateral ABCD which is reflected over a line and formed a mirror image A'B'C'D' of the quadrilateral.
From the graph:
The two points are (-4, -2) and (4, 5)
The line equation passing through two points:
[y - 5] = (5+2)/(4+4)[x - 4]
y - 5 = 7/8[x - 4]
8y - 40 = 7x - 28
8y = 7x + 12
Thus, the two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.
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The diameter of a circle is 5 meters. What is the circumference?
Answer:
15.71 m
Step-by-step explanation:
C = πd
d= diameter
C = π (3.14) * 5
= about 15.71 m
A. 15.71 m
Answer:[tex]5\pi[/tex]
Step-by-step explanation:The circumference is pi times the diameter. If you want a proof you can find it online with a quick search. This applied here means that since the diameter is 5, the circumference is 5*pi or rather 5pi.
A sample of 4 different calculators is randomly selected from a group
containing 46 that are defective and 26 that have no defects. What is the
probability that all four of the calculators selected are defective? Round to four
decimal places.
A) 0.1021 B) 0.1586 C) 0.1666 D) 10.9154
[tex]\displaystyle\\|\Omega|=\binom{72}{4}=\dfrac{72!}{4!68!}=\dfrac{69\cdot70\cdot71\cdot72}{2\cdot3\cdot4}=1028790\\|A|=\binom{46}{4}=\dfrac{46!}{4!42!}=\dfrac{43\cdot44\cdot45\cdot46}{2\cdot3\cdot4}=163185\\\\P(A)=\dfrac{163185}{1028790}=\dfrac{473}{2982}\approx0.1586[/tex]
what is the mean of 7,5,6,5,4,4,,8,6,6,7,4,5,5,6,6
Answer:
5.6 is the mean
Step-by-step explanation:
add up everything and then divide it over how many numbers are in the set to find the mean.
give brainliest, please!
hope this helps :)
Simplyfy 56 64 I want to simplify
Answer:
56/64 simplified is 0.875 or 7/8 as a fraction
ILL GIVE BRAINLYEST TO RIGHT ANSWER! The graph of a line has a positive slope if if is:
A. increasing/going up
B. horizontal
C. decreasing/going down
D. vertical
Answer: The correct answer is A.
Step-by-step explanation: A line with a positive slope always increases and goes up.
Which graph represents the following system of inequalities?
y>2x-5
y<-3x
give an answer with graph
The graph of the two given system of inequalities y > 2x - 5
y < -3x is; Attached below
How to graph Inequalities?We are given two inequalities;
y > 2x - 5
y < -3x
The graph that represents the 2 inequalities has been attached and from the graph, we see that;
The slope of the dotted line is negativeThe x- intercept of the dotted line is the point (0,0)The y- intercept of the dotted line is the point (0,0)The solution of the system of inequalities is the shaded pink area between the two dotted lines.
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AD are tangent to OC. Find the value of x.
NEED HELP WITH THIS QUESTION QUICK!!!
Answer:
x=5
Step-by-step explanation:
The two lines are the same length
2x+7 = 5x-8
15 = 3x
x = 5
how many terms are in 10y2-3y+8
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find how many terms are in [tex]\pmb{10y^2-3y+8}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
A term is a thing that's added or subtracted.So let's compute the number of terms in this expression.
The first term is [tex]\pmb{10y^2}[/tex].
Is anything added or subtracted from 10y²?
Sure! [tex]\pmb{-3y}[/tex] is subtracted from 10y².
Also, 8 is added to -3y.
Thus, this expression has 3 terms.
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
WHAT ARE THE ANSWERS TO 1,2,3,4 SOMEONE HELP!!!!!
Answer:
1) Ans; C .
2) Ans; D.
3) Ans; A.
4) Ans; C.
The methods of solving quadratic equations
There are three main ways of solving quadratic equations. The quadratic formula, factoring, and completing the square.
[1] using the quadratic formula
When the equation is in the form of ax² + bx + c = 0.
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
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[2] factoring
Read more about how to solve with factoring here:
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[3] completing the square
To start out with completing the square, make sure your constant is isolated on one side. The equation will be as ax² + bx = -c
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12.simplify the following expression
21q + 5/2(3/2) + 4q -5
Answer:
i think the answer is 25q - 5 / 4
3/y-3=12/y+3, what is y?
Answer:
i am not sure about your question but if it is 3 divided by y-3 =12 divide by y+3 you can use this
Step-by-step explanation:
3÷y-3=12÷y+3
cross multiply
12(y-3)=3(y+3)............brackets off
12y-36=3y+9..............group the same
12y-3y=9+36
9y=45.......duved by 9 both sides
y=5
Can someone help it’s a little confusing
Orange traffic cones comes in a variety of sizes. Approximate the volume, in cubic inches, of a traffic cone
that has a height of 2 feet and a diameter of 16 inches. Round your answer to the nearest tenth. Use 3.14
for a.
Answer:
V = 1607.7 in^3
V = 0.94 ft^3
Step-by-step explanation:
To find the volume of a traffic cone, use the formula for the volume of a cone: (1/3)*π*h*r^2
h = height
r = radius of cone
Step 1: determine variables and units
2 feet = 24 inches
diameter = 2 * radius
radius = (1/2) * diameter = (1/2)*16 in = 8 inches
Step 2: determine volume
V = (1/3)*π*h*r^2
V = (1/3)*3.14*24*(8)^2
V = 1607.7 in^3
Optional step 3: determine volume in ft^3
h = 2 ft
r = 0.67 ft
V = (1/3)*π*h*r^2 = (1/3)*3.14*2*(0.67)^2
V = 0.94 ft^3
Help me out, please!
Answer:
a = 63
b = 117
c = 63
Step-by-step explanation:
The sum of interior angles in a triangle is = 180
so the measure of a:
85 + 32 + a = 180 add like terms
117 + a = 180 subtract 117 from both sides
a = 63
a and be are supplementary angles so their sum is equal to 180
180 - 63 = 117 is the b's value
since a and c are on a pair of parallel lines, their value must be equal therefore the value of c is also 63