Probability that 2 of the 10 chargers will be defective =0.35
Number of ways of selecting 10 chargers from 20 chargers is 20C10
20C10 = 184756
Number of ways of selecting 10 chargers from 20 = 184756
Number of ways of selecting 2 defective chargers from 5 defective chargers = 5C2
5C2 = 10
Since 2 defective chargers have been chosen, there remains 8 to choose
Number of ways of selecting 8 good chargers from 15 remaining chargers = 15C8
Number of ways of selecting 8 good chargers from 15 remaining chargers = 6435
Probability that 2 of the 10 will be defective =
(10x6435)/184756
Probability that 2 of the 10 will be defective = 64350/184756
Probability that 2 of the 10 chargers will be defective =0.35
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How to solve the equation
Answer:
x = -26
Step-by-step explanation:
\((f-g)(x)=\frac{4}{x-3}-\frac{3}{x+5}=\frac{3}{x^2 +2x-15} \\ \\ \frac{4(x+5)-3(x-3)}{x^2 +2x-15} \\ \\ =\frac{4x+20-3x+9}{x^2 +2x-15}=\frac{3}{x^2 +2x-15} \\ \\ \frac{x+29}{x^2 +2x-15}=\frac{3}{x^2+2x-15} \\ \\ x+29=3 \\ \\ x=-26\)
This is in the domain of the equation, and is thus a solution.
Determine the value of x.
Question 19 options:
x = 3.5
x = 4
x = 36
x = 5
(197−−−√)units
(221−−−√)units
(5–√)units
(41−−√)units
Answer:
4
Step-by-step explanation:
The angle bisector divides the sides of the triangle proportionally:
AD/CD = AB/CB
x/3 = 12/9
x = 3(12/9) . . . . multiply by 3
x = 4
Find the length of side X in simple radical form with a rational denominator
The length of side X in simple radical form with a rational denominator is 25/√3.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):
Adjacent side = 5/√3
Hypotenuse, x = 5 × 5/√3
Hypotenuse, x = 25/√3.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
what are the steps to solve this
Answer:
The equation of this line is y = -4.
Answer:
y=-4
Step-by-step explanation:
zero slope m=0
y-y1=m(x-x1)
y-(-4)=0(x-(-9))
y+4=0
y=-4
there exist two complex numbers $c$, say $c 1$ and $c 2$, so that $3 2i$, $6 i$, and $c$ form the vertices of an equilateral triangle. find the product $c 1 c 2$ in rectangular form.
(200 - 100√2) / 16 is the rectangular form of the product c1*c2 for an equilateral triangle's vertices.
What is triangle?A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.
Here,
An equilateral triangle is a triangle with three equal sides. If 3-2i, 6-i, and c form the vertices of an equilateral triangle, then the distance between 3-2i and 6-i is equal to the distance between 3-2i and c.
The distance between two complex numbers a + bi and c + di can be found using the formula:
√((c - a)² + (d - b)²)
So, the distance between 3-2i and 6-i is:
√((6 - 3)² + (-1 - (-2))²) = √((3)² + (1)²) = √(9 + 1) = √10
And the distance between 3-2i and c is:
√((c - 3)² + (c - (-2))²) = √((c - 3)² + (c + 2)²)
Since these distances must be equal, we have:
√((c - 3)² + (c + 2)²) = √10
Squaring both sides:
(c - 3)² + (c + 2)² = 10
Expanding both sides:
c² - 6c + 9 + c² + 4c + 4 = 10
Combining like terms:
2c² + 10c + 5 = 10
Subtracting 10 from both sides:
2c² + 10c - 5 = 0
This is a quadratic equation, which can be solved using the quadratic formula:
c = (-b ± √(b² - 4ac)) / 2a
Where a = 2, b = 10, and c = -5. Plugging these values into the formula:
c = (-10 ± √(10² - 4 * 2 * -5)) / 2 * 2
c = (-10 ± √(100 + 40)) / 4
c = (-10 ± √(140)) / 4
c = (-10 ± 10√2) / 4
So there are two complex solutions, c1 = (-10 + 10√2) / 4 and c2 = (-10 - 10√2) / 4.
The product of these two solutions is:
c1 * c2 = ((-10 + 10√2) / 4) * ((-10 - 10√2) / 4)
= (100 - 100√2 + 100) / 16
= (200 - 100√2) / 16
(200 - 100√2) / 16 is the answer in rectangular form for the product c1*c2 for the vertices of an equilateral triangle.
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what type of object around in locality
Objects commonly found in a locality include residential buildings, commercial establishments, public facilities, transportation infrastructure, landmarks, natural features, utilities, street furniture, and vehicles.
The type of objects that can be found in a locality can vary greatly depending on the specific location and its surroundings. Here are some common types of objects that can be found in a locality:
Residential Buildings: Houses, apartments, condominiums, and other types of residential structures are commonly found in localities where people live.
Commercial Establishments: Localities often have various types of commercial establishments such as stores, shops, restaurants, cafes, banks, offices, and shopping centers.
Public Facilities: Localities typically have public facilities such as schools, libraries, hospitals, community centers, parks, playgrounds, and sports facilities.
Transportation Infrastructure: Localities usually have roads, sidewalks, bridges, and public transportation systems like bus stops or train stations.
Landmarks and Monuments: Some localities may have landmarks, historical sites, monuments, or cultural attractions that represent the area's heritage or significance.
Natural Features: Depending on the locality's geographical characteristics, natural features like parks, lakes, rivers, mountains, forests, or beaches can be present.
Utilities: Localities have infrastructure for utilities such as water supply systems, electrical grids, sewage systems, and telecommunications networks.
Street Furniture: Localities often have street furniture like benches, streetlights, waste bins, traffic signs, and public art installations.
Vehicles: Various types of vehicles can be found in a locality, including cars, bicycles, motorcycles, buses, trucks, and possibly other modes of transportation.
It's important to note that the objects present in a locality can significantly differ based on factors such as urban or rural setting, cultural context, economic development, and geographical location.
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Solve for the AREA of the SMALL rectangle if the length is (x) and width is (x+7)
Answer:
Area = x² + 7x
Step-by-step explanation: 5 15 8 19
Area = LW
Area = x(x+7)
Area = x² + 7x
38. Which of the following describes a median of a triangle? (1 point)
a segment drawn from a vertex to the midpoint of the opposite side
a segment drawn from the vertex perpendicular to the line containing the opposite side
a segment drawn through the midpoint of a side and at a right angle to the side.
segment drawn from the center of an angle to the side opposite.
A statement that describes the median of a triangle include the following: A. a segment drawn from a vertex to the midpoint of the opposite side.
What is a triangle?In Mathematics and Geometry, a triangle is a two-dimensional geometric shape that comprises three sides, three vertices and three angles only.
In Mathematics and Geometry, the median of a triangle can be defined as a line segment with end points that is typically drawn from a vertex to the midpoint of the opposite side of the triangle.
In this context, we can logically deduce that a line segment with end points at the vertex and the midpoint of the triangle's opposite side simply refers to the median of a triangle.
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There is a ratio of 5 apples to 3 pears in a basket. There are 24 pears in the basket. How many apples are in the basker?
Answer:
There are 40 apples in the basket.
This is because 5 apples to 3 pears have a difference of 1.66666667 when dividing 5 by 3 to show the ratio difference. Then, all you do is multiply this number by the number of total pears which would look like 24 x 1.66666667 = 40.
I hope this helped you, have an amazing day! :)
how can u spot fake news through camerawork, audio, and lighting? pls answer asap
if u see someone is talking quickly if they dont have evidence and more!
I need Help please!!!
Step-by-step explanation:
it seems you solved the tricky part yourself already.
just to be sure, let's do the first derivative here again.
the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...
f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =
= 3t⁴ + 18t³ + 24t² + 18t + 21
f'(t) = 12t³ + 54t² + 48t + 18
and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).
we simply put the input number (2) at every place of the input variable (t).
so,
f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =
= 426
You have saved $14,000 for a down payment on a house. Your bank requires a minimum down payment of 17%. What is the maximum price you can offer for a home in order to have enough money for the down payment? (Round your answer to two decimal places.)
The maximum price you can offer for a home is approximately $82,352.94 for a 17% down payment.
To determine the maximum price you can offer for a home, you need to calculate 17% of the total price, which will be your down payment of $14,000.
Let's assume the maximum price you can offer for the home is P dollars.
According to the given information, the down payment requirement is 17% of the total price. So, we can set up the following equation:
\(0.17P = $14,000\)
To solve for P, divide both sides of the equation by 0.17:
P = $14,000 / 0.17
Calculating this expression, we find:
P ≈ $82,352.94
Therefore, the maximum price you can offer for a home in order to have enough money for the 17% down payment is approximately $82,352.94.
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Ulcers are sores on the lining of the digestive tract, caused by the bacteria Helicobacter pylori. You want to test the effectiveness of two new treatments for stomach ulcers. Out of 750 people with stomach ulcers, who are willing to serve as subjects, the researchers record various response variables and a number of demographic variables. For example, it was found that 100 subjects are under 18 years old, 250 subjects are 18-35 years old, 250 subjects are 35-55 years old, and 150 subjects are older than 55 years. Researchers speculated that people of different age groups would not react differently to the treatments.
a. completely randomized design.b. randomized block design.c. matched pairs design.
Answer:
c. matched pairs design.
Step-by-step explanation:
For an experimental design to be classified as matched pairs, it must have two treatment options and the grouping of participants with common demographics. The participants can be either grouped in pairs or within ranges. Grouping participants within ranges makes the assignment to groups less tedious compared to when they are in pairs. The test above employs this design because,
1. It tests the effectiveness of two new treatments for stomach ulcers
2. The subjects are grouped within ranges based on the age demographic factor.
Rotation 90° clockwise about the origin
N
O
G
An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.
What is a rotation?In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;
(x, y) → (y, -x)
Point N = (-4, -1) → Point N' (-1, 4)
Point O = (-4, -3) → Point O' (-3, 4)
Point G = (0, -1) → Point G' (-1, 0)
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Find the function f (x) = 3x - 4 find each of the following values.
1) Find f (10).
2) Find x when f (x) = 17
Answer:
1) 26
2) 7
Step-by-step explanation:
1) f(10)= (3*10)-4 = 26
2) f(x) = 3x-4
=> 17= 3x-4
=> 17+4= 3x
=> 21= 3x
=> x= 21÷3
so, x= 7
An object attached to a coiled spring is pulled down 5 centimeters from its rest position and released. If the motion is simple harmonic in nature, with a period of pi seconds, answer the following questions.
A. what is the maximum displacement form equilibrium of the object?
B. what is the time required for one oscillation?
C. what is the frequency?
D.write an equation to model the motion of the object.
The maximum displacement is 5 centimeters.
The time required for one oscillation is π seconds.
The frequency is 1 / π Hz.
Equation to model the motion of the object is x(t) = 5 × cos(2t)
The maximum displacement from equilibrium can be determined by observing that the object is pulled down 5 centimeters from its rest position.
In simple harmonic motion, the amplitude represents the maximum displacement from equilibrium.
The period of oscillation is given as π seconds.
The period (T) is the time required for one complete oscillation.
The frequency (f) is the reciprocal of the period and represents the number of oscillations per unit time.
Thus, the frequency is the inverse of the period: f = 1 / T.
To model the motion of the object, we can use the equation for simple harmonic motion:
x(t) = A×cos(ωt + φ)
A = 5 centimeters (maximum displacement),
T = π seconds (period),
f = 1 / π Hz (frequency).
To find ω, we can use the relation ω = 2π / T:
ω = 2π / π = 2 radians/second.
The equation to model the motion of the object is:
x(t) = 5 × cos(2t)
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Pls help extra points and mark brain-list
Answer:
29 - 8(3)
Step-by-step explanation:
Answer:
29 - 3q
put the value of q
29-3×8
29-24
5
I need help fast smart people I need your answer
Answer:
The angle D is 64 degrees.
Step-by-step explanation:
This is because they are vertical
Answer:
i think its the yellow square
Step-by-step explanation:
What is 4 & 1/2+1/8? *
Answer:
4 5/8
Step-by-step explanation:
Rewriting our equation with parts separated
=4+12+18
Solving the fraction parts
12+18=?
Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.
LCD = 8
48+18=58
Combining the whole and fraction parts
4+58=458
Simplify the following expression:
√-36+√-100+ 7
O A. 7+ 16i
OB. 7+√136i
O C. 16
C. 16 - 7i
O D. 23 + 0i
Prove whether each argument is valid or invalid. First find the form of the argument by defining predicates and expressing the hypotheses and the conclusion using the predicates. If the argument is valid, then use the rules of inference to prove that the form is valid. If the argument is invalid, give values for the predicates you defined for a small domain that demonstrate the argument is invalid.
The domain for each problem is the set of students in a class.
(c)Every student who missed class got a detention.
Penelope is a student in the class.
Penelope got a detention.
Penelope missed class.
(e)Every student who missed class or got a detention did not get an A.
Penelope is a student in the class.
Penelope got an A.
Penelope did not get a detention.
(c) The argument is valid, and we can conclude that Penelope missed class because she got a detention.
(e) The argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.
(c) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:
Let "M(x)" be the predicate "x missed class", and "D(x)" be the predicate "x got a detention".
Hypotheses: M(Penelope), D(Penelope)
Conclusion: M(Penelope)
Using modus ponens, which states that if P implies Q and P is true, then Q must be true, we can conclude that M(Penelope) is true:
From M(Penelope) and "Every student who missed class got a detention", we have D(Penelope)
From D(Penelope), we have M(Penelope)
So, the argument is valid, and we can conclude that Penelope missed class because she got a detention.
(e) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:
Let "M(x)" be the predicate "x missed class", "D(x)" be the predicate "x got a detention", and "A(x)" be the predicate "x got an A".
Hypotheses: A(Penelope), ~D(Penelope)
Conclusion: ~M(Penelope)
Using modus tollens, which states that if P implies Q and Q is false, then P must be false,
we can conclude that M(Penelope) is false:
From A(Penelope) and "Every student who missed class or got a detention did not get an A",
we have ~M(Penelope) & ~D(Penelope)
From ~D(Penelope), we have ~M(Penelope)
So, the argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.
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derivate (cos(3x^2). (5x^3 -1)^1/3 +sin 4x^3)^4
\( \: \: \: \: find \: first \: derivative \\ ( cos(3x {}^{2} ) \times ( \sqrt[3]{5x {}^{3} - 1} ) + \sin(4x {}^{3} ) {}^{4} \)
Answer:
Step-by-step explanation:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)
Lets look at the derivative part:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)
\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)
Substituting in eq(1), we have:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)
I NEED HELP PLS HURRY
1. Write each expression with a single exponent:
a. (10^7)²
b. (10^9)³
c. (10^6)³
d. (10^2)³
e. (10³)²
f. (10^5)^7
Answer:
We use the rule,
\((a^b)^c = a^{bc}\)
a. (10^7)²
\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)
10^14
b. (10^9)³
\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)
10^27
c. (10^6)³
\(10^{(6)(3)}= 10^{18}\)
10^18
d. (10^2)³
\(10^{(2)(3)} = 10^{6}\)
10^6
e. (10³)²
\(10^{(3)(2)}=10^{6}\)
10^6
f. (10^5)^7
\(10^{(5)(7)} = 10^{35}\)
10^35
Step-by-step explanation:
Suppose a scale model has a scale of 2 inches = 3 feet. What is the scale factor?
The required scale factor for the scale model is 3 / 2 feet/inches.
Given that,
a scale model has a scale of 2 inches = 3 feet, to determine the scale factor.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What is the scale factor?The scale factor is defined as the ratio of modified change in length to length.
Here,
2 inches = 3 feet,
express that in the plan of the 3 feet of the original scale is 2 inches on the plan. So,
scale factor = 3 feet / 2 inches
Scale factor = 3 / 2 feet / inches
Thus, the required scale factor for the scale model is 3 / 2 feet/inches.
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How many paths are there from $A$ to $B,$ if you travel along the edges? You can travel along each edge at most once, but you can pass through the same point more than once. (You can pass through $B,$ as long as you end up at the point $B.$)
Answer:
9
Step-by-step explanation:
You don't need to pass through each edge once.
If we name the top vertex 1 and the bottom vertex 2 then here are the possible combinations:
A-1-B
A-B
A-2-B
A-1-B-A-2-B
A-2-B-A-1-B
A-B-1-A-2-B
A-B-2-A-1-B
A-1-B-2-A-B
A-2-B-1-A-B
Some people say 6 because they think you need to pass through all the edges. But the only restriction with travelling on the edges is you can't pass one twice. The point is read the wording and it becomes easy.
Hope this helps!
Explain how you know that (3, 5) is not a solution to the given inequality by looking at the graph.
The reason that the point (3, 5) is not a solution to the given inequality is given below.
We are given that;
y > 2x + 1
Now,
The inequality y > 2x + 1 can be graphed by first graphing the boundary line y = 2x + 1. Since the inequality is strict (y >), we draw a dashed line to indicate that points on the line are not solutions to the inequality. Then, we shade the region above the line to indicate all points that satisfy the inequality.
If we have (3,5) as a point, we can see that it lies on the boundary line
y = 2x + 1.
Since the inequality is strict (y >), points on this line are not solutions to the inequality
Therefore, by the inequality the answer will be given above.
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361,354,347, ...
Find the 47th term.
This is an arithmetic sequence with a common difference given by d= -7
I will start by defining my first term as u⁰=361
Now we have to think, if u⁰ is my 1st term than my 47th term would be u⁴⁶ not u⁴⁷ since i start counting from 0 and not 1.
Using the relation that describes the implicit relation of an arithmetic sequence, i can say:
u(n)=u⁰+nd where n is any number
u⁴⁶=u⁰+46d
u⁴⁶=361+46(-7)
u⁴⁶=361-322
u⁴⁶=39
Answer:
39.
Step-by-step explanation:
This is an arithmetic sequence with common difference -7
47th term = a + d(n - 1)
= 361 - 7(47-1)
= 39.
what steps are needed to find the equation of a line given the graph?
The equation of the line is y = x.
To find the equation of a line given its graph, you need to follow the steps below.
Step 1: Determine the slope of the line.The slope of the line can be determined using the formula: slope = rise/run or m = Δy/Δx. Rise is the change in the y-coordinates and run is the change in the x-coordinates.
Step 2: Determine the y-intercept of the line.The y-intercept is the point where the line intersects the y-axis. You can determine the y-intercept by looking at the point where the line crosses the y-axis on the graph. The y-intercept is denoted by the letter b.
Step 3: Write the equation of the lineThe equation of the line can be written in slope-intercept form, which is y = mx + b. The slope (m) and y-intercept (b) that were determined in steps 1 and 2 are used to substitute into this equation. Thus, the equation of the line becomes y = slope(x) + y-intercept.
Example:Let's say you are given the graph of a line below: .
Step 1: Determine the slope of the line.To determine the slope of the line, you need to choose two points on the line and calculate the rise and run. Let's choose the points (2, 1) and (4, 3). The rise is 2 (3 - 1) and the run is 2 (4 - 2). Therefore, the slope of the line is: m = 2/2 = 1.
Step 2: Determine the y-intercept of the lineThe line crosses the y-axis at the point (0, 0). Therefore, the y-intercept of the line is b = 0.
Step 3: Write the equation of the line.The equation of the line in slope-intercept form is y = mx + b. Substituting the slope and y-intercept into this equation gives: y = 1x + 0 or y = x.
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Simplify each side of 4a+ 5a-2=5+3-1
Answer:
9a-2=7
Step-by-step explanation:
4a+ 5a-2=5+3-1
To simplify each side, combine like terms.
4a+5a = 9a
5+3-1 = 7
The equation becomes:
9a-2=7
What is the volume of this object?
Answer:
The volume is 45 cubic units.
So enter "45" into the box.
Step-by-step explanation:
Multiply the dimensions to get the volume. (Length times width times height)
The box is 5 units by 3 units by 3 units.
Solve 5x3x3 (LxWxH) using a calculator...
And you get 45 cubic units.
Answer:
45
Step-by-step explanation:
L= 3
W= 5
H= 3
V=LxWxH
3 x 3 x 5