Final answer:
The surface area of the cargo box, which is a rectangular prism with dimensions of 3 meters wide, 5 meters long, and 6 meters tall, is calculated using the formula SA = 2lw + 2lh + 2wh. The correct answer is D. 126 meters squared.
Explanation:
To find the surface area of a rectangular prism, you need to calculate the area of all six faces and sum them up.
The formula for the surface area (SA) of a rectangular prism is SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism.
In this case, the dimensions of the cargo box are 3 meters wide (w), 5 meters long (l), and 6 meters tall (h). Using the formula:
SA = 2lw + 2lh + 2whSA = 2(5m × 3m) + 2(5m × 6m) + 2(3m × 6m)SA = 2(15m²) + 2(30m²) + 2(18m²)SA = 30m² + 60m² + 36m²SA = 126m²Therefore, the correct answer is D. 126 meters squared.
A system of equations is shown below.
Equation A: 5x +9y = 12
Equation B: 4x – 3y = 8
Which method eliminates one of the variables?
1) Multiply equation A by and add the result
to equation B.
2) Multiply equation B by 3 and add the result to
equation A.
3) Multiply equation A by 2 and equation B by - 6
and add the results together.
4) Multiply equation B by 5 and equation A by 4
and add the results together.
1on
Multiply equation B by 3 and add the result to
equation A.
Option 2 is correct
Multiply equation B by 3 and add the result to A
How to Solve linear equations?When we are given two equations we can solve them by eliminating one variable, and equating the value of one variable to another or by using a matrix.
How to Eliminate One Variable?Let us assume two-equation ax+by = c and px+qy = d, now suppose we want to eliminate x from this two-equation, then we cross-multiply the x coefficients and then subtract them or add them considering the final coefficients of x, we multiply the equation by a multiple of their LCM So multiplying equation ax+by= c by p we get: apx+bpy=pc similarly we mulitply (-a) in equation px+qy=d we get -apx-aqy= -ad If we add the new equation we get y(bp-aq) = pc-ad and we have eliminated x successfully. for eliminating y we would have used coefficients of y.Solving the questionIf we want to eliminate y in the given equation we will, LCM of (9,3) is 9 we can multiply B by 3 and add to A.
Hence Option 2 is correct.
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Solve the following system via substitution.
m = 2n + 30
2m - n = 39
Answer:
m=16
n=-7
Step-by-step explanation:
Answer: n=-7, m=16
Step-by-step explanation:
The partial factorization of x2 – 3x – 10 is modeled with algebra tiles.
Factoring out in algebra simplifies expressions such as quadratic equations into products of binomials or linear factors, sometimes using complex coefficients to achieve this if necessary.
The process of factoring out involves finding the numbers or expressions that divide evenly into the original expression. In the case of quadratic expressions like [tex]x^2 - 3x - 10[/tex], we look for two binomials that multiply together to give us the original quadratic. In algebra, a common method of factoring is looking for two numbers that multiply to give the constant term (in this case -10) and add up to the coefficient of the middle term (in this case -3). These two numbers are the factors of -10 that we use to split the middle term.
For example, the factors of -10 that add up to -3 are -5 and 2. Using these numbers, we can write [tex]x^2 - 3x - 10[/tex] as (x - 5)(x + 2). This is called factoring by grouping, wherein we factor common terms out of pairs of terms and then factor further if possible.
In the context of complex numbers, all second-order polynomials can be factored into linear factors. For instance, [tex]x^2 + 1[/tex] can be factored as (x - i)(x + i), utilizing complex roots i and -i. The fundamental theorem of algebra assures us that any polynomial can be factored completely into linear factors using the complex number system.
I need the answer ASAP !!!!
I hope this helps you
x^2+2.(-3).x+(-3)^2
(x-3).(x-3)
(x-3)^2
On January 1, 2010, Lucita bought a car for $25,000. If the car depreciates at a rate of 15% per year, which equation can be used to find the value of the car on January 1, 2018?
Answer:
[tex] a_9=25,00(0.85)^{9-1}[/tex]
Step-by-step explanation:
Let [tex]a_1=25,000[/tex]
After one year, in 2001, the price is $a_2$, where
$a_2= a_1-a_1\times (0.15)$
$\therefore a_2=a_1(1-0.15)=a_0(0.85)$
Now after two years, in 2002, let the price be $a_3$
The pattern is pretty clear. After $n$ years, in $200n$ the price will be:
$a_n= a_0(0.85)^{n-1}$
Answer:
A
Step-by-step explanation:
a1=25000(0.85)^ 9-1
The guy above is right. I just wanted to simplify the answer.
A bacterial culture starts with 400 bacteria and grows at a rate proportional to its size. After 2 hours there will be 800 bacteria.
1) Express the population, P(t) after t hours as a function of t
2) Using your equation from above, what will the population be after 8 hours?
3) Using your equation from above, after how many hours will the population reach 2270 bacteria?
Answer:
P(t) = 400×2^(t/2)64005.0Step-by-step explanation:
The wording "a rate proportional to its size" is an indication that growth (or decay) is exponential.
1) For many problems involving exponential growth, I like to use the numbers given in the problem statement as follows.
population = (initial population) × (growth factor)^(t/(growth period))
where the "growth period" is the period of time in which the population is multiplied by the "growth factor".
Here, we're given ...
(initial population) = 400
(growth factor) = 800/400 = 2
(growth period) = 2 . . . . hours
So, our population function can be written as ...
P(t) = 400×2^(t/2)
__
2) Putting t=8 into the formula, we get ...
P(8) = 400×2^(8/2) = 400×16 = 6400
After 8 hours, the population will be 6400.
__
3) Fill in the given number and solve for t.
2270 = 400×2^(t/2)
2270/400 = 2^(t/2)
Taking logs, we have ...
log(227/40) = (t/2)log(2)
t = 2×log(227/40)/log(2) ≈ 5.009
After 5.0 hours, the population will reach 2270.
Solve the system of equations below by graphing both equations with a
pencil and paper. What is the solution?
y = 2x - 3
y = -2x + 5
A.) (-2,5)
B.) (-2,-7)
C.) (2,1)
D.) (2,-3)
Answer:
4
Step-by-step explanation:
Answer:
The answer is C. (2,1)
Step-by-step explanation:
10
A person is selected randomly. What is the probability that the person was born on a
Sunday? *
14.3%
20%
80%
85.7%
Suppose that Marvin rolls a pair of fair six-sided dice. Let A be the event that the first die lands on a 4 and B be the event that rolls doubles
P(A), the probability that the first die lands on 4?
P(B), the probability that Marvin rolls doubles?
P(A and B) the probability that the first die lands on 4 and Marvinv rolls doubles?
DEPENDENT OR INDEPENDENT?
Answer:
1/6
1/6
1/36
Independent
Step-by-step explanation:
Make a chart with 36 outcomes of a pair of six sided dice.
Count the amount that starts with 4, which is 6. 6/36 = 1/6
Doubles. Count the pairs, basically both numbers are the same. 6 outcomes out of total is 1/6.
Last one.
(1/6)^2 = 1/36
These are independent, because the first die landing on 4 doesn't have anything to do with making the die becoming doubles.
please help will give brainliest and 80 points
Answer:
Start
A2
B2
B1
C1
C2
D2
D3
D4
C4
END
Step-by-step explanation:
Start (A3)
x is equal to 141 because they are alternate interior angles.
A2. x is equal to 39 because they are corresponding angles.
B2. x would be supplementary to 41 because the angle that x supplements is corresponding to 41.
41 + x = 180 due to the linear pair postulate. Therefore, x = 139.
B1. x would be supplementary to 82 because they are consecutive exterior angles.
82 + x = 180 due to the linear pair postulate. Therefore, x = 98.
C1. x = 102 due to the vertical angles theorem.
C2. x would be supplementary to 130 because the angle that x supplements is equal to 130 (Alternate Exterior Angles).
130 + x = 180, x = 50.
D2. x = 74, corresponding angles.
D3. x = 83, corresponding angles.
D4. x = 95, corresponding
C4. x is supplementary to 18 because of the consecutive interior angles theorem.
x = 162
END
pls help i’ll give u a brainlest
Answer:
(13×14×6)/3= 364 centimeter cube
I answered wrongly cuz forgot to divide by 3
my mistake
Answer:
4263m^3
Step-by-step explanation:
So for number 2, that is a right rectangular pyramid. The formula is lwh/3.
The length is 21, the width is 21, and the height is 29. So the volume is 4263.
What is the value of x 4 + 0:5y 3 when x = 2 and y = 4?
Answer:
Step-by-step explanation:
x^4+0.5y^3=2^4+0.5x4^3
=16+0.5x64
=16+32
=48
8 times the sum of 2 and 15
Answer:
136
Step-by-step explanation:
15 plus 2 is 17,then multiplied by 8
Mark, Chase, and Beatrice are running a 100-meter race. Which list represents the sample space of all the possible ways in which the three runners can win first, second, and third places? If there were four runners and three positions to be won, what would the sample size be?
A.
The sample space is {MBC, BCM, CMB}. If there were four runners, the sample size would be 4.
B.
The sample space is {MBC, MCB, BCM, BMC, CBM, CMB}. If there were four runners, the sample size would be 24.
C.
The sample space is {MBC, BCM, CMB}. If there were four runners, the sample size would be 4.
D.
The sample space is {MBC, MCB, BCM, BMC, CBM, CMB}. If there were four runners, the sample size would be 16.
the answer is B: 24
i know it
You miss 6 out of 25 questions on an science quiz 5 out of 20 questions on an math quiz. Which Quiz has an higher percent of correct answers.
The science quiz has a higher percentage of correct answers.
To determine which quiz has a higher percent of correct answers, we need to calculate the percentage of correct answers for each quiz.
Science Quiz:
You missed 6 out of 25 questions. Therefore, you answered 25 - 6 = 19 questions correctly.To find the percentage of correct answers, use the formula:Math Quiz:
You missed 5 out of 20 questions. Therefore, you answered 20 - 5 = 15 questions correctly.For the math quiz:[tex]Percentage = \frac{15}{20}*100 = 75\%[/tex]Comparison
The science quiz has a higher percentage of correct answers (76%) compared to the math quiz (75%).
what is the cost of a new trampoline cover that needs to cover a trampoline with a diameter of 8 feet if the material cost 6.75 per square foot?
Answer: The cost of the trampoline cover would be $339.12
Step-by-step explanation: The radius of the trampoline is 4 feet (Diameter divided by 2 equals radius).
The trampoline cover will effectively cover the entire area of the trampoline and the area is given as
Area of circle = πr²
Area of circle = 3.14 x 4²
Area of circle = 3.14 x 16
Area of circle = 50.24 square foot
However the material costs $6.75 per square foot, which means the total cost of the trampoline cover would be derived as
Total area x cost per square foot = cost of trampoline cover
50.24 x 6.75 = Cost of trampoline cover
$339.12 = Cost of trampoline cover
Answer: The cost of the new trampoline cover is $339.29
Step-by-step explanation:
Hi, we have to calculate the area of the trampoline cover.
Since it has a circle form with a 8 ft diameter.
Area of a circle = π r^2
Since the radius (r) is equal to the diameter (d) divided by 2
R = d/2 = 8/2 =4
Replacing in the formula:
A = π 4^2 = 50.26 square ft
Since the material cost 6.75 per square foot
Cost = 6.75 x 50.26 = $339.29
Ariel and her family are going to order one large circular pizza that has a diameter of
20 inches and one small circular pizza that has a diameter of 12 inches.
Which measurement is closest to the difference between the area of the large pizza and the
area of the small pizza in square inches?
The difference between the area of the large pizza (20-inch diameter) and the small pizza (12-inch diameter) is about 201.06 square inches. We calculated this by finding the area of each pizza using the formula for the area of a circle, and then subtracted the smaller area from the larger.
Explanation:The subject of this question is Mathematics, specifically the concept of area for circles. To calculate the difference between the areas of the two pizzas, we first have to find the area of each pizza individually.
The formula for the area of a circle is A = πr^2, where r is the radius of the circle. For the large pizza with a diameter of 20 inches, the radius is 20/2=10 inches, so its area would be A = π * (10^2) = 314.16 square inches.
For the smaller pizza with diameter of 12 inches, the radius is 12/2 = 6 inches. So, the area of the small pizza is A = π * (6^2) = 113.10 square inch.
Now, to get the difference between the two areas, we subtract the smaller area from the larger area: 314.16 square inches - 113.10 square inches = 201.06 square inches. This is the difference between the area of the large pizza and the small pizza.
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Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $136. Two adults and three children must pay $97. Find the price of the adult's
ticket and the price of a child's ticket
Answer:
all work pictured and shown
The price of the adult's ticket and the price of a child's ticket are $20 and $19 respectively.
What is a system of linear equations?A "system" of equations is a set or collection of equations that you deal with all together at once.
Given that, Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $136. Two adults and three children must pay $97.
Let the price for adult be a and for children be c,
Establishing the equations,
3a+4c = 136.......(i)
2a+3c = 97.........(ii)
Solving the equations,
Multiplying the equation 1 by 3 and equation 2 by 4 and subtracting,
(9a+12c = 408) - (8a+12c = 388)
a = 20
c = 19
Hence, the price of the adult's ticket and the price of a child's ticket are $20 and $19 respectively.
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Explain the differences between solids that are polyhedra and solids that aren’t polyhedra.
Answer:
A polyhedron is a solid shape with flat sides, while a non polyhedron is a solid shape which has curved sides.
Step-by-step explanation:
A polyhedron, can be seen as a solid shape with many plane figures, forming its sides. Examples of polyhedrons are cuboids, squares and pyramids. As you can see, these solid shapes have flat sides.
On the other hand, a non polyhedron is a solid shape that has curved surfaces. Examples include: cones, spheres and cylinders.
Hence polyhedron: No curved surface
Non polyhedron: curved surface
Final answer:
Polyhedral solids are composed of flat polygonal faces and have geometrically regular shapes, while non-polyhedral solids can have curved surfaces and irregular shapes, such as spheres and cylinders.
Explanation:
Differences Between Polyhedral and Non-Polyhedral Solids:
Solids that are polyhedra have flat faces, straight edges, and sharp vertices. Polyhedral solids are a category of solids composed of polygons that are joined together at their edges and vertices. The most common examples of polyhedra include cubes, pyramids, and prisms. These solids have a geometrically regular shape and are often symmetrical.
In contrast, solids that are not polyhedra may have curved surfaces, and irregular shapes, and do not consist exclusively of flat polygonal faces. Common examples of non-polyhedral solids include spheres, cylinders, and cones. These shapes are not limited by flat surfaces and can have continuous curved surfaces.
While polyhedral solids can be easily mathematically described by the polygons that comprise their faces, non-polyhedral solids often require more complex geometry, such as calculus, to describe their curved surfaces.
as of 2010, the new york yankees had one more world series championships than any other team. in fact, the yankees had won 3 fewer than 3 times the number of world series championships won by the second most winning team, the st. louis cardinals. the sum of the two teams' world series championships is 37. how many times has each team won the world series?
solve using a system of equations. please show work.
Answer:
Step-by-step explanation:
first you get your equations, because the game sums are based upon the st louis cardinals we will use them as x.
According to the problem the yankees won 3 fewer (-3) that 3 times (3x) the st louis cardinals which brings their equation to 3x-3
The sum of these to equations equals 37
37=x+3x-3
when you solve, you get x=10
then you plug it into the DIFERENT equations
3(10)-3=27 (yankees)
x=10
then check using your preffered method
Final answer:
Using a system of equations, it was determined that the New York Yankees had won 27 World Series championships, and the St. Louis Cardinals had won 10 by 2010.
Explanation:
Let Y represent the number of World Series championships won by the New York Yankees, and let C represent the number won by the St. Louis Cardinals. We have two facts from the question:
The sum of the World Series championships for both teams is 37: Y + C = 37.
The Yankees have won 3 fewer than 3 times the number won by the Cardinals, and one more than the Cardinals: Y = 3C - 3 and C = Y - 1.
Substituting the second equation into the first, we get (3C - 3) + C = 37. Solving this, we get 4C - 3 = 37, so 4C = 40, and C = 10. Substituting C into Y = 3C - 3, we get Y = 3(10) - 3 = 30 - 3 = 27.
Therefore, the Yankees had won 27 World Series championships, and the Cardinals had won 10 by 2010.
find the mode of the following data: 9,15,17,18,6,20,8,5,18,18,10,5,14,12,10,7
Answer:
18
Step-by-step explanation:
mode is the number that occurs the most
Answer:
18
Step-by-step explanation:
I just identified the numbers and saw 18 the most
A bag contains 5 blue marbles, 2 blavk marbles, and 3 red marbles. A marble is randomly drawn from the bag. The probability of not drawing a black marble is ___. The probability of drawing a red marble is ___.
Answer:
20% black marble 30% red marble
Final answer:
The probability of not drawing a black marble is 4/5. The probability of drawing a red marble is 3/10.
Explanation:
To find the probability of not drawing a black marble, we need to find the ratio of the number of marbles that are not black to the total number of marbles. In this case, there are 5 blue marbles and 3 red marbles, so the total number of marbles is 5 + 2 + 3 = 10. The number of marbles that are not black is 5 + 3 = 8. Therefore, the probability of not drawing a black marble is 8/10 or 4/5.
To find the probability of drawing a red marble, we need to find the ratio of the number of red marbles to the total number of marbles. In this case, there are 3 red marbles out of a total of 10 marbles. Therefore, the probability of drawing a red marble is 3/10.
2772, 3663, 2970,4275, 5841, 3564 which of the numbers has to be excluded?
Answer:4275
Step-by-step explanation:4275 will be removed because in the other numbers ,the numbers formed by the first two digits plus the number formed by the second two digits is 99 which does not happen in the case of 4275.
27=9 72=9
36=9 63=9
I need help please. Solve by the method of substitution, and could you please show/explain how? Im stumped. Thanks
Answer:
D x+9 = 2x+1
Step-by-step explanation:
y = x+9
y = 2x+1
Substitute x+9 for y in the second equation
y = 2x+1
x+9 = 2x+1
This answers the question
To finish the problem
Subtract x from each side
x+9-x =2x-x+1
9 = x+1
Subtract 1 from each side
9-1 =x+1-1
8=x
Now find y
y = x+9
y = 8+9
y=17
Let p be a prime number such that p>2. Use the proof by contradiction to show that at least one of numbers p−1 and p+1 is divisible by 4.
David is an enthusiastic cyclist. He uses an app on his phone to track each of his cycling sessions. What was the shortest he cycled
Answer:
There is no picture
Step-by-step explanation:
There is no picture but the answer would be the shortest amount of time.
The answers are as follows:
15.05 miles2 :09:125 hours 19 minutes 18 secondsWhat is unit Conversion?Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
Given :
28/4/18:Time : 1 :03 : 25
Fastest mile = 02 : 25
Distance = 15.05 miles
03/5/18:Time : 2:06: 41
Fastest mile = 02 : 53
Distance = 28.70 miles
08/5/18:Time : 2 :09:12
Fastest mile = 02 : 45
Distance = 26.39 miles2
1.)As, per the data
15.05 < 26.39 < 28.70
Shortest distance cycled = 15.05 miles
and, 1 :03 : 25 < 2:06: 41 < 2 :09:12
Longest = 2 :09:12
Total time, in hours
=1 :03 : 25 + 2:06: 41 + 2 :09:12
=(1 + 2 + 2)
= 5 hrs
In minutes
= 03 + 06+ 09
= 18 minutes
For seconds,
25 + 41 + 12
= 78 seconds
= 1 minute 18 seconds
Hence, Total time = 5 hours 19 minutes 18 seconds.
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Which of the following is a trinomial?
O A. 7+X
O B. v3x+1
O C. x+3
D. 3x2 + 4x+1
su
Answer:
D. 3x2 + 4x+1
Step-by-step explanation:
This answer is a trinomial because there are 3 terms being used, 3x2, 4x, and 1.
If this answer is correct, please make me Brainliest!
The tires on your bicycle have a diameter of 9 inches. How many rotations does each tire make when you travel 300 feet. Round your answer to the nearest whole number
Answer:
127
Step-by-step explanation:
The diameter in feet is ...
(9 in)·(1 ft)/(12 in) = 9/12 ft = 0.75 ft
Then the circumference is ...
C = πd = 3.14159·0.75 ft ≈ 2.3561925 ft
The number of rotations in 300 ft is ...
(300 ft)/(2.3561925 ft/rotation) ≈ 127.32 rotations
The tires make about 127 rotations when you travel 300 feet.
simplify 3 square root of 4/ 3 square root of 5
The final simplified expression is 2 over the square root of 5, represented as [tex]\( \frac{2}{\sqrt{5}} \).[/tex]
Let's break it down step by step:
1. Simplify the square roots:
[tex]- \(\sqrt{4}\) equals 2 because \(2 \times 2 = 4\). So, \(\sqrt{4} = 2\).[/tex]
- We have [tex]\(\sqrt{5}\)[/tex] in the denominator, which cannot be simplified further because 5 is a prime number and doesn't have any perfect square factors.
2. Substitute the simplified square roots:
- After simplifying [tex]\(\sqrt{4}\)[/tex] to 2, the expression becomes [tex]\(\frac{3 \times 2}{3\sqrt{5}}\).[/tex]
3. Cancel out the common factor:
- Both the numerator and the denominator have a factor of 3. So, we can cancel out 3 from both sides:
[tex]\[\frac{3 \times 2}{3\sqrt{5}} = \frac{2}{\sqrt{5}}\][/tex]
4. Final simplification:
- The expression [tex]\(\frac{2}{\sqrt{5}}\)[/tex] is simplified as far as it can go because the square root of 5 cannot be simplified further.
So, the simplified expression is [tex]\(\frac{2}{\sqrt{5}}\).[/tex]
In triangle ABC a=8. b=6, and angleC= 60°. Find the measure of angleA
16 degrees
46 degrees
74 degrees
106 degrees
Answer: The correct answer is 74˚