Step-by-step explanation:
Provide the values...........
a terrarium in the shape of a rectangular prism has a volume of 4608 cubic inches. its length is more than 10 inches. the dimensions of the terrarium in terms of width are shown. calculate the length width and height of the terrarium
Answer:
The width is 12 inches, the length is 24 inches, and the height is 16 inches
Step-by-step explanation:
Please see the attached photo, it provides full information we need to solve this problem
We know that:
volume = 4608 cubic Lenth = (36-w)With = wHight = w+4So the vomume fomula is = LWH = (36 -w)*w*(w+4)
<=> [tex]32w^{2}[/tex] + 114w - [tex]-w^{3}[/tex] - 4608
<=> w = 32 and w = 12 and w= -12
Disregard w= -12, because the width cannot be negative, and we also know that length is more than 10 inches so w = 12 is fit with the requirement.
=> Length = 36 -12 = 24
Width = 12 and Hight = 12 + 4 = 16
The length, width, and height of the terrarium that has a shape of a rectangular prism is:
Length = 24 inWidth = 12 in.Height = 16 in.What is the Volume of a Rectangular Prism?Volume of rectangular prism = length × width × height.
Given the dimensions of the terrarium in the shape of a rectangular prism as:
Volume = 4,608 cubic in.
Length = (36 - w) in
Width = w in.
Height = (w + 4) in.
Plug in the values:
4,608 = (36 - w)(w)(w + 4)
4,608 = (36 - w)(w² + 4w)
4,608 = 36(w² + 4w) -w(w² + 4w)
4,608 = 36w² + 144w - w³ - 4w²
36w² + 144w - w³ - 4w² - 4,608 = 0
-w³ + 32w² + 144w - 4,608 = 0
Factorize
w = −12 or w = 12 or w = 32
Since we know the length is more than 10 inches and cannot be negative, therefore, w = 12.
Plug in the value of w
Length = (36 - 12) = 24 in
Width = 12 in.
Height = (12 + 4) = 16 in.
Therefore, the length, width, and height of the terrarium that has a shape of a rectangular prism is:
Length = 24 inWidth = 12 in.Height = 16 in.Learn more about volume of rectangular prism on:
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(-w^3 + 8w^2 – 3w) + (-8w^2 + w + 3) =
Wich equation is the standard form of
-56+14^2=-51
Answer:
The answer should be [tex]14x^{2} - 56 x + 51 = 0[/tex]
Step-by-step explanation:
Step 1: First, you add 51 to both sides
−56x + [tex]14x^{2}[/tex]+ 51= 0
Step 2: then you fix the order.
[tex]14x^{2} - 56 x + 51 = 0[/tex]
Solve by using substitution. SHOW YOUR WORK. y=-2x – 1
y = 8x + 19
Answer: x= -2; y = 3
Step-by-step explanation:
y=-2x – 1
y = 8x + 19 -
replacing "y"
-2x – 1 = 8x + 19
-2x - 8x = 19 + 1
-10x = 20
x = 20/-10
x= -2
y=-2x – 1
y= -2.(-2) - 1
y= 4 - 1
y = 3
what is the inequality to 2w+5>45
Answer:
w > 20
Step-by-step explanation:
Perhaps you want the solution to the inequality 2w+5>45.
Subtract 5:
2w > 40
Divide by 2:
w > 20 . . . . this is the solution
_____
Comment on solving inequalities
An inequality is solved in virtually the same way that an equation is solved: undo what is done to the variable. The only difference is that when you perform an operation that reverses the ordering, you need to reverse the ordering symbol.
Multiplying or dividing by a negative number will reverse the ordering. Consider, for example, ...
2 > 1
Multiplying both sides by -1, we get ...
-2 < -1 . . . . . the > sign needs to be reversed to a < sign to keep the inequality true
johnny has 24 soap bottles he shares half of all the soap bottles with his friends how many soap bottles does johnny have left
Answer: Johnny will have 12 soap bottles left
Suppose that of 1400 students, 550 take Spanish, 700 take biology, and 400 take both
Spanish and biology. What is the probability that a student selected at random takes
Spanish or Biology? Simplify the fraction!
Answer:
17/28Explanation:
1. Call A the event of selecting a student who takes Spanish and P(A) the corresponding probability:
P(A) = number of students who take Spanish / number of studentsP(A) = 550 / 1400 = 11/282. Call B the event of selecting a student who takes biology and P(B) the corresponding probability:
P(B) = number of students who take biology / number of studentsP(B) = 700 / 1,400 = 1/23. The joint probability, P(A∩B), is the probability that a student takes Spanish and biology:
P(A∩B) = number of students that take both Spanish and biology / number of studentsP(A∩B) = 400/1400 = 2/74. By the properties of probabilities, the probability of the event A or B is:
P (A or B) = P (A∪B) = P(A) + P(B) - P(A∩B)P(A or B) = 11/28 + 1/2 - 2/7 = (11 + 14 - 8) / 28 = 17/28Final answer:
To find the probability of a student taking Spanish or Biology, you need to consider the students taking each subject and those taking both, applying the principle of inclusion-exclusion. The simplified probability is [tex]\frac{17}{28}[/tex].
Explanation:
The probability that a student selected at random takes Spanish or Biology can be calculated using the principle of inclusion-exclusion.
Find the total number of students taking Spanish or Biology: 550 + 700 - 400 (students taking both) = 850.
Calculate the probability: P(Spanish or Biology) = Number of students taking Spanish or Biology ÷ Total number of students = [tex]\frac{850 }{ 1400} = \frac{17}{28}[/tex].
What resources were brought from Europe to exchange for slaves
Answer:
Step-by-step explanation:
they were exchanged for iron, guns, gunpowder, mirrors, knives, cloth, and bead
Marcy’s breakfast table has a square table top with an area of 36 square feet. What is the diagonal length of the table top? how do you solve this i need help
Answer:
[tex]d=6\sqrt{2}\ ft[/tex]
Step-by-step explanation:
step 1
Find the length side of the square
we know that
The area of the square is given by the formula
[tex]A=b^2[/tex]
where
b is the length side of the square
we have
[tex]A=36\ ft^2[/tex]
substitute
[tex]36=b^2[/tex]
solve for b
[tex]b=6\ ft[/tex]
step 2
Find the diagonal length of the table top
Let
d ----> the diagonal length of the table top
Applying the Pythagorean Theorem
[tex]d^2=b^2+b^2[/tex]
substitute the value of b
[tex]d^2=6^2+6^2[/tex]
[tex]d^2=72[/tex]
[tex]d=6\sqrt{2}\ ft[/tex]
8 more than a number p is 17 equation
Answer:
17=p+8
Step-by-step explanation:
Start by setting the equation equal to 17 on either the right or left side. Now, on the opposite side of the equation read out what the question is saying.
"8 more than a number (p)" the variable would be p, and 8 more than p is 17. Now that you have that in mind, write 17 is equal to p plus 8.
17=p+8
If the question asks you to solve this equation for p, subtract 8 from both sides to get 9 for p.
I hope this is easy to understand.
In the diagram below,AB is parallel to CD. What is the value of x?
Answer: There is no diaphragm below
Step-by-step explanation: Please add picture
Each wheel of Gia's bicycle is 24 inches in diameter. Gia rides her bike 1,884 feet. To
the nearest whole number, how many times does her front bicycle wheel turn all the
way around?
The front wheel turns around approximately 300 times.
To determine how many times Gia's bicycle wheel turns around during her 1,884 feet ride, we need to calculate the circumference of the wheel and then divide the total distance traveled by the circumference.
The diameter of the wheel is 24 inches. To find the circumference (C), we use the formula C = pi x d, where d is the diameter, and (pi) is approximately 3.14159.
C = 3.14159 x 24 inches = 75.39816 inches.
Next, we need to convert the distance Gia rode her bike from feet to inches because the circumference is in inches. There are 12 inches in a foot, so
1,884 feet x 12 inches/foot = 22,608 inches.
Now we divide the total distance traveled in inches by the circumference of the wheel to find out how many full revolutions there are:
22,608 inches / 75.39816 inches/revolution ≈ 300 revolutions.
To the nearest whole number, Gia's front bicycle wheel turns all the way around 300 times.
Help me find the area pls
Answer: 49m
Step-by-step explanation:
4m, 1m and 2m add up to 7m on the right side. so, L x W= 7x7 which is 49
If a car travels 150km for 1hour and 30 minutes how long in hours will it take the car to travel 260km
Time taken by the car to cover 260 km is 2.6 hrs
Step-by-step explanation:
Step 1: Find the speed of the car given distance covered = 150 km and time = 1.5 hrs.Speed = Distance/Time = 150/1.5 = 100 km/hr
Step 2: Find the time taken by the car to cover 260 km.Time = Distance/Speed = 260/100 = 2.6 hrs
Scientists are studying a group of living cells under a microscope. They write down notes about the size, shape, and color of the cells as well as other traits.
Which best describes this type of investigation?
comparative, because the scientists will be making observations in order to form a hypothesis
comparative, because the scientists are measuring dependent and independent variables
descriptive, because the scientists are using independent variables to test a hypothesis
descriptive, because the scientists are writing down observations but not making comparisons
Answer: answer is D, descriptive, because the scientists are writing down observations but not making comparisons
Step-by-step explanation:
According to the question, the scientists were making individual notes on their observation about shape, colour, size and other characteristics of the living cells. We do not have enough information to show that they were making comparisons.
I hope this helps.
Answer:
anwser D
Step-by-step explanation:
discreptive because scientist are writing dow explanations
What is 3.15 trillion in scientific notation?
[tex]3.15*10^{12}[/tex] would be 3.15 trillion in scientific notation. When putting a number into scientific notation, move the decimal point until you have a number between 1 and 10.
To convert 3.15 trillion to scientific notation, express it as 3.15 × 10¹². This involves moving the decimal point 12 places to the left. Scientific notation helps manage very large or very small numbers efficiently.
To convert the number 3.15 trillion to scientific notation, follow these steps:
First, recognize that a trillion is equal to 1,000,000,000,000 or 10¹².Next, express 3.15 trillion as a numerical value: 3,150,000,000,000.To write this in scientific notation, move the decimal point so that there is only one non-zero digit to the left of the decimal point. In this case, 3.15 becomes 3.15.Count the number of places the decimal point has moved. Here, it moves 12 places to the left.Thus, 3.15 trillion in scientific notation is written as 3.15 × 10¹².Scientific notation is particularly useful in fields where dealing with extremely large or small numbers, such as astronomy and other sciences, is common.
if you buy a 10-inch pizza is that the diameter or the circumference
A class contains 13 girls and 15 boys.
What is the ratio of boys to girls?
How many students are there in all?
What fraction of the students are girls?
The ratio of boys to girls will be 15 : 13.
There are 28 students in all.
The fraction of the students are girls will be 13/28.
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.
Given that;
A class contains 13 girls and 15 boys.
Now,
Since, A class contains 13 girls and 15 boys.
Hence, Number of total students = 13 + 15
= 28
So, The ratio of boys to girls = Number of boys : Number of girls
= 15 : 13
Hence, Number of total students = 13 + 15
= 28
And, The fraction of the students are girls is;
= Number of girls / Number of students
= 13 / 28
Thus, The ratio of boys to girls = 15 : 13.
Total number of students = 28
And, The fraction of the students are girls = 13/28.
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change improper fraction to mixed number
10/7
Answer:
1 3/7
Step-by-step explanation:
10/7 is same as 7/7 + 3/7
7/7 equals to 1
Therefore, 1 + 3/7
Answer: 1 3/7
How many hundreds are in number 500
Answer:
5 hundreds
Step-by-step explanation:
5 is the hundreds place. So, there are 5 hundreds
Answer:
5 hundreds
Step-by-step explanation:
500 divided by 100 = 5
so, there are 5 hundreds in the number 5
At what time is the cake done
Here we know that at 3:17 pm you started to bake the cake. The total revolution the minute hand on the clock makes is:
[tex]\frac{5}{8}+\frac{13}{24}=\frac{7}{6} \ revolutions[/tex]
We know that:
[tex]1 \ revolution ----------- 60min \\ \\ 7/6 \ revolutions -----------x[/tex]
Solving for x:
[tex]x=\frac{7}{6}\times 60=70 minutes[/tex]
So it takes 70 minutes after you put the cake in the oven. But:
[tex]70minutes=1h \ 10min[/tex]
Adding this to the initial time:
[tex]3:17pm+1h \ 10min=4:27pm[/tex]
Finally, the cake is done at 4:27 pm, option C.
Drag the values to order them from least to greatest, with the least at the top.
Answer:
√143
4π
√79+√63
Step-by-step explanation:
√143 gives 11.958
4π = 4 times 22/7 = 12.57
√79+√63 gives 16.825
In ascending order, i.e from the least to the greatest, we have
11.958
12.57
16.825
Which is same as
√143
4π
√79+√63
I need help asap for this question
Answer:
1 5/6 is on the twelfth line/tick mark. 2 1/3 is on the 15 line/tick mark.
Step-by-step explanation:
Go to the 1 and count up five lines. (5/6) For the 2nd one convert the 1/3 into 6ths. You now have 2 2/6. go to the 2 and count up 2 lines.
A washer and dryer cost $652 combined. The washer cost $48 less than the dryer. What is the cost of the dryer?
Answer:
The dryer costs $350
Step-by-step explanation:
Step 1: Make a system of equations
w + d = 652
w = d - 48
Step 2: Plug in the know w into the first equation
d - 48 + d = 652
2d - 48 + 48 = 652 + 48
2d / 2 = 700 / 2
d = 350
Answer: The dryer costs $350
BRAINLIESt if u answer 10 to the 2nd power
10 to the second power = 100
Since powers of TEN is 10 multiplied by itself, multiply 10 by 10 TWO times, because its 10 to the SECOND power
10x10=100
By the way do not multiply 10 by 2 at ALL IT IS WRONG!!!
For example, 10 to the 3rd power is 10x10x10 not 10x3
Answer: +100
Explanation: 10 raised to the 2nd power means the same thing as 10 squared and any number squared is that number times itself.
So 10² is just 10 · 10 or +100.
The largest pyramid in Egypt, built almost 5,000 years ago, covers an area of about 63,300 square yards. Find the length of each side of the square base. Round to the nearest yard.
Answer:
15,825
Step-by-step explanation:
Because it is a square divide 63,300 by 4.
9. James wants to purchase a telescope for
$54. If he saves $3 per week, in how many
weeks will he have saved enough to purchase
the telescope?
Answer: James will save $3 for 18 weeks before he can buy the telescope
Step-by-step explanation:
Answer:18weeks
Step-by-step explanation:
54/3=18
He will save up for 18weeks to buy the telescope
Which of the following terms have a GCF of ? Select two options
Answer:
the answers are A) 18p^3r and D) 54p^3
Good luck! :)
Answer:
A) 18p³r
D) 54p³
Step-by-step explanation:
The term 6p³ multiplies into (or goes into) both 18p³r and 54p³.
Solve the two-step equation.
-0.45x + 0.33 = -0.66
What is the solution?
Answer:2.2
Step-by-step explanation:
Boo
x-5/50°
What is the measure of
ZQRT?
What is the value of x?
What is the measure of
ZQRS?
NEED HELP PLEASE FOR BRAINLEST
Answer:
<QRT = 130°
X = 135
<QRS = 180°
Step-by-step explanation:
1. A straight line is 180°.
180° - 50° = 130°
<QRT = 130°
2. x - 5 = 130°
130° + 5° = 135°
3. As stated before, a straight line is 180°.