Answer:
Area = 150 m²
Volume = 125 m³
Step-by-step explanation:
• The surface area of a cube is given by the formula:
[tex]Area = 6r^2[/tex]
where r is the length of an edge of the cube = 5 m.
∴ Area = 6(5)²
= 6(25)
= 150 m²
• The volume of a cube is given by the formula:
[tex]Volume = r^3[/tex]
∴ Volume = (5)³
= 125 m³
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\textsf{\textbf{\underline{\underline{Answer :}}}}}}[/tex]
We use the formulas for the area and volume of the cube, assuming that the length [tex] \bold{A=5m}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold\red \: \bold \red A \purple = \bold \blue6 \bold \blue a {}^{ \bold \orange2} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold \red A \purple= \bold \blue6 \bold \blue \: \: \blue • \: \: \bold \blue5 {}^{ \bold\orange{ 2}} [/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold \red A \purple= \bold \blue 1 \bold \blue5 \bold \blue0 \bold \blue m {}^{ \bold \orange2} [/tex]
Now we will find the volume of the cube :-
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\bold \red V \purple = \bold\blue a {}^{ \bold \orange3} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold \red V \purple = \bold \blue 5 {}^{ \bold \orange3} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold \red V \purple = \blue{ \bold{125m}} {}^{ \bold \orange3} [/tex]
Answer: The area of the cube is 150 m² and the volume it Equal a 125 m³
I hope I've helped : )
Question 9 of 10
Which of the following lists of ordered pairs is a function?
OA. (2, 5), (3, 6), (6,9)
OB. (2, 5), (3, 6), (2, 1)
C. (-1, 2), (2, 3), (3, 1), (2, 5)
O D. (1, 2), (4, 0), (3, 5), (4,3)
Answer: A. (2, 5), (3, 6), (6,9)
Step-by-step explanation:
Each value of x maps onto only one value of y.
Point Z (-3, 4) is translated using the (x, y) (x + 2, y-1). It is then reflected across the x-axis
Determine the point location of the image.
This is the new coordinate for Z (-1, 3)
What is graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
The point Z is (-3, 4) is translated using the rule
x,y → (x+2),(y-1)
Then simply plug-in the values of x and y which are x = -3 and y = 4
x,y → ((-3) +2), (4 -1) which is (-1, 3)
Hence, this is the new coordinate for Z (-1, 3)
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Answer two questions about Systems AAA and BBB:
System AAA \text{\quad}start text, end text System BBB
\begin{cases}6x-5y=1\\\\-2x+2y=-1\end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
6x−5y=1
−2x+2y=−1
\begin{cases}4x-3y=0\\\\-2x+2y=-1\end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
4x−3y=0
−2x+2y=−1
1) How can we get System BBB from System AAA?
Choose 1 answer:
(Choice A, Checked, Correct)
CORRECT (SELECTED)
Replace one equation with the sum/difference of both equations
(Choice B, Incorrect)
INCORRECT
Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations
(Choice C, Incorrect)
INCORRECT
Replace one equation with a multiple of itself
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
CORRECT (SELECTED)
Yes
For the given systems A and B:
1) Replace the first equation of A by the sum between the two equations of A.
2) Yes, the systems are equivalent.
How to get system B from system A?
Here we have the two systems of equations:
A:
6x - 5y = 1
-2x + 2y = -1
B:
4x - 3y = 0
-2x + 2y = -1
The second equation is the same in both systems, so we only look at the first equations.
In A we have:
6x - 5y = 1
If we add the second equation of A, then we get:
(6x - 5y) + (-2x + 2y) = 1 + (-1)
4x - 3y = 0
This is the first equation of B.
Then we need to replace the first equation by the sum between the first and second equations.
2) Are the systems equivalent?
Yes, because we did not "modify" system A, we just rewrite it and we got system B, then both systems have the same solutions.
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Answer: A) , Yes
Step-by-step explanation:
When a numberis decreased by 20% of itself the result is 64
Answer:
80Step-by-step explanation:
100% - 20% = 80% = 64
so
64 : 80 * 100 = 80
check
80 - 20% = 64
Describe how to transform the graph of g(x) - Inx in the graph of f(x) - In (-x)-9.
a. Reflect across the y-axis and translate 9 units to the left
b. Reflect across the x-axis and translate 9 units to the left
c. Reflect across the x-axis and translate 9 units to down
d. Reflect across the y-axis and translate 9 units to down
Answer:
d. Reflect across the y-axis and translate 9 units to down
Step-by-step explanation:
Reflection of the graph of a function across the y-axis is accomplished by replacing x with -x in the function definition.
Translation of the graph of a function by k units upward is accomplished by adding k to the function value.
ApplicationHere, we observe that f(x) is g(x) with x replaced by -x. That means the graph of f(x) will be the graph of g(x) reflected across the y-axis.
The function f(x) is the function g(x) with -9 added to it. That translates the graph downward by 9 units.
These transformations, reflection across the y-axis and translation 9 units downward, can be seen in the attached graphs. Corresponding points are marked.
a line of best fit was drawn for 15 data points. what is the maximum number of these data points that may not actually be on the line?
The maximum number of the data points that may not actually be on the line is 15
How to determine the number of data points?The number of points is given as:
Points = 15
A line of best fit implies that the model is a regression model
In a regression model, all the data points may not pass through the line of best fit.
This means that the maximum number of the data points that may not actually be on the line is 15
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I am a 3-digit odd number.
The sum of my digits is 9.
My tens digit is twice that if my hundreds digit.
What am I?
Answer:
Step-by-step explanation:
let the number at unit place=x
ten's place=y
hundred's place=z
x,y,z are integers.
x+y+z=9
also digit=100z+10y+x
y=2z
x+2z+z=9
x+3z=9
x=1,3,5,7,9
for x=1
1+3z=9
3z=9-1=8
z=8/3 (rejected as z is an integer.)
when x=3
3+3z=9
3z=9-3=6
z=6/3=2
z=2
y=2z=2×2=4
so number=100×2+10×4+3=200+40+3=243
Suppose you have 7 red cards, 9 green cards, and 12 blue cards. The cards are well shuffled, and you randomly draw one card How many elements are there in the sample space?
Find the probability of drawing a green card
How many elements are there in the sample space?
There are 28 elements in the sample space and the probability of a green card is 9/28
The elements in the sample space?The given parameters are:
Red = 7
Green = 9
Blue = 12
The elements in the sample space is:
Elements =7 + 9 + 12
Evaluate
Elements = 28
Hence, there are 28 elements in the sample space
The probability of green?This is calculated as
P =Green/Elements
So, we have:
P = 9/28
Hence, the probability of a green card is 9/28
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How to solve exercise 1
Answer:
[tex]period \: of \: sin(2x) = \pi \\ period \: of \: cos \frac{x}{4} = 8\pi \\ period \: of \: tan \frac{x}{3} = 3\pi[/tex]
Step-by-step explanation:
Hello !
[tex]periodicity \: of \: a.sin(bx + c) + d = \\ \frac{periodicity \: of \: sin(x)}{ |b| } \\ periodicit \: of \: sin \: (x) \: is \: 2\pi = \\ \frac{2\pi}{2} \: simplify = \pi \\ periodicity \: of \: a.cos(bx + c) = \\ \frac{periodicity \: of \: cos(x)}{ |b| } \\ periodicit \: of \: cos \: (x)is \: 2\pi = \\ \frac{2\pi}{1\frac{1}{4} } \: simplify \: = 8\pi \\ periodicity \: of \: a.tan(bx + c) = \\ \frac{periodicity \: of \: tan(x)}{ |b| } \\ periodicity \: of \: tan(x) \: is \: \pi \\ \frac{\pi}{} \frac{1}{3} [/tex]
Brainliest to whoever answers accurately
Answer: [tex]a_{n}=5000(1.02)^{n-1}[/tex]
Step-by-step explanation:
to get the rate do:
5100/5000 to get 1.02
Also for geometric sequence, the exponent 'n' is always subtracted by 1
Therefore, your answer is:
[tex]a_{n}=5000(1.02)^{n-1}[/tex]
(a) Using the digits 0 to 7 exactly once each, form a collection of positive integers whose sum is 100.
(b) Find a second solution to (a) which has a different number of integers in the sum.
(c)Show that in any solution (a), the sum of the digits in the units places is 20.
(d)Find, with reasons, the smallest possible value of the largest integer in a solution to (a).
A) The collection of positive integers whose sum is 100 are: 23, 17, 6, 54, 0.
B) Another collection of positive integers whose sum is 100 are: 13, 27, 4, 56, 0.
C) Due to the fact that the units can be commuted, their sum is always equal to 20.
D) The smallest possible value is 0 and the largest is 57.
What is the sequence of positive integers?A) The formation of a collection of positive integers can be done by trial and error. For example, only using the digits {0, 1, 2, 3, 4, 5, 6, 7}.
For example, we can have;
23 + 17 + 6 + 54 + 0 = 100
Where the numbers used are: 23, 17, 6, 54, 0.
B) Another example is;
13 + 27 + 4 + 56 + 0 = 100
C) If we add the units digits of these 5 numbers, we get:
3 + 7 + 6 + 4 + 0 = 20
Now, if we compute the units digits between the different numbers, to get for example: 27, 13, 6, 54, 0
The sum is still equal to 100, and the units digits are the same ones, so we still have that the sum of the units digits is equal to 20.
d) The smallest integer that we use is 0.
For the largest we just commute the tens and units digits so we make the larger integer possible, which is:57.
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A printer designs a tag in the shape of a circle with a smaller circle cut out. She cuts her prototype from a 5 in. by a 7 in. index card. The cut edges of the tag will be printed with gold leaf. What is the approximate amount of gold leaf on a tag?
The circumference of the larger circle is about ____ inches. The circumference of the smaller circle is about ____ inches. So, the total length of gold leaf on a tag is approximately
____ inches.
The circumference of the larger circle is about 12.57 inches. The circumference of the smaller circle is about 3.14 inches. So, the total length of gold leaf on a tag is approximately 15.71 inches.
How to illustrate the circle?The circumference will be:
= 2πr
= 2 × 3.14 × 2
= 12.57 inches.
The circumference of the smaller circle will be:
= 2πr
= 2 × 3.14 × 0.5
= 3.14
The total length will be:
= 12.57 + 3.14
= 15.71 inches.
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6. The product of two numbers is 18.576. If one of them is 5.4, find the other .
Answer:
3.44
Step-by-step explanation:
Another way to rewrite this question is 18.576/5.4. (18.576 divided by 5.4), and the answer to that is 3.44.
Type the correct answer in each box. Use numerals instead of words.
Functions f and g are represented in the table and the graph.
The values of the functions from the graph and table are; (f ° g)(4) = 4 and x = 0 at (g ° f)(x) = 1
How to solve function inputs?1) We want to find the value of (f ° g)(4). This can also be expressed as;
f(g(4))
Now, from the given graph, g(4) = 2. Thus;
f(g(4)) = f(2)
From the table, f(2) = 4. Thus;
(f ° g)(4) = 4
2) We are given; (g ° f)(x) = 1
This is also expressed as;
g(f(x)) = 1
From the graph g(x) = 1 is at x = 1. Thus;
f(x) = 1 and from the tabe;
x = 0 at f(x) = 1
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30 245x-1) (x³+3) 30 245x - 1 ) ( x³ + 3 )
Answer:
30245x⁴ - x³ + 90735x - 3
Step-by-step explanation:
1. Expand the expression
(30245x - 1)(x³ + 3)
2. Multiply
30245x x x³ + 30245x x 3-(x³ + 3)
3. Determine the sign
304245x⁴ + 90735x - (x³ + 3)
4. Rewrite the expression
30425x⁴ + 90735x - x³ - 3
= 30245x⁴ - x³ + 90735x - 3
(brainliest will be appreciated :)
find x and y.
please help !
Using linear pairs,
[tex]115+5x=180\\\\5x=65\\\\x=\boxed{13}[/tex]
By the exterior angle theorem,
[tex]2y=45+5(13)\\\\2y=45+65\\\\2y=110\\\\y=\boxed{55}[/tex]
f(x) = x/2 - 3 and g(x) = 3x² + x − 6, find (f+ g)(x)
Answer:
3x^2+3x/2-9
Step-by-step explanation:
collect like term
Which equation represents a line that passes through (-2, 4) and has a slope of 2/5
An equation represents a line that passes through (-2, 4) and has a slope of 2/5 is y-4 = 2/5(x+2)
Equation of a lineThe equation of a line in point-slope form is expressed as;
y-y1 = m(x - x1)
where
m is the slope
(x1, y1) is any pint on the line
Substitute the given parameter
y - 4 = 2/5(x-(-2))
y-4 = 2/5(x+2)
Hence an equation represents a line that passes through (-2, 4) and has a slope of 2/5 is y-4 = 2/5(x+2)
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What is the value of f(x) when x = 4 in the piecewise function f(x) =
2x² when x>4 …….. 4x when x < 4
The question asks the value of f(x) when x = 4 in the equation
x = 4 is less than or equal to 4, so we use the first equation in the piecewise functions => {4x when x≤4}
Solving for f(x):
4(4)=16
16 is the answer!
Hope it helps!
Sam ran 3 1/4 miles on Tuesday and then ran 2 5/6 miles on Wednesday. How many total miles did Sam run?
Sam run for total 6.08 miles.
Sam run 3 1/4 miles on Tuesday and then ran 2 5/6 miles on Wednesday.
What is fraction?Fraction is ratio of integers. example- 7/8.
Sam run [tex]3\frac{1}{4}[/tex] miles on Tuesday.
on [tex]2\frac{5}{6}[/tex] on Wednesday
Total run =Run on tuesday + Run on wednesday
Total run = [tex](3\frac{1}{4} )+(2\frac{5}{6} )[/tex]
= 13/4 + 17/6
Total run = 6.08
Thus Sam run for total 6.08 miles
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Type your answer into the box. 7.3 m 6 m cm³ Q The width of a cuboid is 6 metres, the length is 7.3 metres and the height is 4.2 metres. Dulce Livramento 4.2 m What is the volume of the cuboid? Type your answer into the box . 7.3 m 6 m cm³ Q The width of a cuboid is 6 metres , the length is 7.3 metres and the height is 4.2 metres . Dulce Livramento 4.2 m What is the volume of the cuboid ?
The volume of the cuboid is 183.96 m³
What is the volume of a cuboid?A cuboid is a plane shape with a six-faced solid called a hexahedron. The volume of a cuboid is Length × width × height
From the information given:
The length of a cuboid is = 7.3 metresThe width = 6 metresThe height = 4.2 metresThe volume of the cuboid is;
= (7.3 × 6 × 4.2) m³
= 183.96 m³
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what is the constant of variation?
Answer:
constant (unchanged) ratio of two variable quantities
Step-by-step explanation:
y = k x ( or y = k x )
y = 15 when x = 24, find x when y = 25. find the constant of variation.
factor equation. answer is -47, just puzzled on how to get it. step by step
Answer:
-47
Step-by-step explanation:
First you use PEMDAS, so you start with the exponent.
-5^2 = 25
Then you multiply the -2!!! Not the 2 with the 25, multiplying the 2 is a common mistake.
When you multiply the -2, it results in:
3 - 50
= -47
Answer:
-47
Step-by-step explanation:
Original Equation:
[tex]f(-5)=3-2(-5)^2[/tex]
Square the -5 (this cancels out the negative sign
[tex]f(-5)=3-2(25)[/tex]
Multiply 2 and 25
[tex]f(-5) = 3-50[/tex]
Subtract 50 from 3
[tex]f(-3) = -47[/tex]
I'm a bit confused by what you mean factor the equation? Given the context. But I'm going to assume the equation is: [tex]f(x)=3-2x^2[/tex]. Which isn't exactly factorable.
Will give brainliest!
2. The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the expected population of each country in 2025, assuming their annual growth rates remain steady
The expected population of each country in 2025 are 22261221, 1465382683, 116537821 and 60347662
The expected population in 2025The expected population of each country is calculated as:
P(n) = a *(1 + r)^n
Where:
a represents the initial populationr represents the growth raten represents the number of years since 20002025 is 25 years since 2000.
This means that:
n = 25
So, we have:
Australia
P(25)= 19169000 * (1 + 0.6%)^25
P(25)= 22261221
China
P(25)= 1261832000* (1 + 0.6%)^25
P(25)= 1465382683
Mexico
P(25)= 100350000 * (1 + 0.6%)^25
P(25)= 116537821
Zaire
P(25)= 51965000* (1 + 0.6%)^25
P(25)= 60347662
Hence, the expected population of each country in 2025 are 22261221, 1465382683, 116537821 and 60347662
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3: Morgan Cruise earns net self-employment income of $221,600. She works a second job from which she receives FICA taxable earnings of $111,300.00.
Self-Employment tax =
137,700 cap
Based on the amounts that Morgan Cruise is getting paid, her self-employment tax will be $22,916.63.
How much does Morgan pay in self-employment tax?taxable earnings from self-employment:
= 92.35% x 221,600
= $204,647.60
Self-employment tax is:
= (12.4% x 137,700 limit) + (2.9% x 200,000 limit) + (0.9% x (204,647.60 - 200,000)
= 17,074.80 + 5,800 + 41.83
= $22,916.63
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in a class of 28 students everyone like math, english, or both. if 17 like math and 19 like english how many like both?
A) 2
B) 8
C) 16
D) 20
E) 28
Answer:
B) 8 students like both
===========================
Let the numbers be:
M - likes math, M = 17;E - likes English, E = 19;B - likes both, B is unknown;T- total number, T = 28.Since both M and E include B, we can show the total as:
Math only + English only + Both = Totaland
Math only = M - BEnglish only = E - BThe total can be expressed as:
M - B + E - B + B = T M + E - B = TSubstitute values and solve for B:
17 + 19 - B = 2836 - B = 28B = 36 - 28B = 8This is matching the answer choice B)
Maths be A and English be B
A+B-A[tex]\cap[/tex] B=AUBA intersection B be X
(A-X)+(B-X)+X=AUBA+B-X=2817+18-X=1835-X=28X=8Option B
Geometry question Help please! Thanks!
Answer:
[tex]theta=47.33 degrees[/tex]
Step-by-step explanation:
sin theta=opposite/hyp
sin theta=500/680
theta in degrees=47.33
Answer:
The angle is 47.33°
Step-by-step explanation:
We have the hypotenuse as 680 ft and the opposite side as 500 ft, so we can use sin as a way to find the angle:
sin θ = opposite side / hypotenuse
sin θ = 500 ft / 680 ft
sin θ = 0.7353
θ = sin^-1 (0.7353) [this is called inverse of sine]
θ = 47.33°
here is a gauge for the fuel tank of a car the fuel tank hols 52 litres of fuel when the tank is full the tank is 1/4 full of fuel
work out how many more litres of fuel are needed to fill the tank
help me help me help help help me
Answer:
b. 0
c. 4
d. 2
e. [tex]\frac{76}{35}[/tex]
Step-by-step explanation:
b.) When translated it will become this expression 10 - [(2x15)/3] = 0
c.) It will become [tex]\frac{4(12-7)}{5}[/tex]
d.) This will transform to [tex]\frac{(\frac{78-13}{5}) + 5}{9}[/tex]
e.) The first eq is [tex]\frac{4(7+3)}{8}[/tex], then after the changes it becomes [tex]\frac{4[\frac{(7+3)+9}{7}]}{5}[/tex]
Algebra
Help me with this question
Answer:
SORRY I CAN NOT HELP YOU