B. Solve the following. Write your solutions and final answers in your notebook.
1. To relieve her stress from work. Tina would always watch the fishes moves around her 90 cm wide, 70 cm high, and 45 cm long aquarium. If the aquarium is filled halfway through its height; how much volume of water is in it?
2. Elisha has a swimming pool in their house that measures 10 m long, 5 m wide and 1 m high. Approximately, how much will she be paying for the water supply of her swimming pool, if the water costs P27.25 per cubic liter?
3. Myla bought a jar shaped like a rectangular prism having a length of 130 cm, a width of 70 cm, and a height of 110 cm. How much water is needed to fill the jar?
4. A truck with dimensions 9 feet long, 7 feet wide, and 5 feet high is delivering sand for a sand sculpture competition. How many trips must the truck make to deliver 945 cubic feet of sand?
5. Create a problem on volume and prepare a solution to your problem based on the figure below:
I need best answer please
Answers
The volume of water contained in this aquarium that is filled halfway through its height is equal to 141,750 cm³.
The volume of a right prism.Mathematically, the volume of a right prism is calculated by using this formula:
Volume = length × width × height
Given the following data:
Length = 45 cm.Width = 90 cm.Height = 70 cm.Based on the information, the aquarium is filled halfway through its height. Thus, the height of water is given by:
H = 70 × 0.5
H = 35 cm.
Substituting the parameters into the formula, we have;
Volume = 45 × 90 × 35
Volume = 141,750 cm³.
How to calculate the volume?Mathematically, the volume of Elisha's swimming pool is given by:
Volume = length × width × height
Volume = 10 × 5 × 1
Volume = 50 m³.
Now, we can calculate the cost of water supply:
Cost = 27.25 × 50 × 10³
Cost = P1,362,500.
How to calculate the volume of water.Mathematically, the volume of a rectangular prism is given by this formula:
Volume = length × width × height
Volume = 130 × 70 × 110
Volume = 1,001,000 cm³.
How to calculate the number of trips.Firs of all, we would determine the volume of this truck:
Volume = length × width × height
Volume = 9 × 7 × 5
Volume = 315 ft³.
Now, we can calculate the number of trips:
Number of trips = 945/315
Number of trips = 3 trips.
Read more on rectangular prism here: brainly.com/question/3867601
Related Questions
3(2x + 1) = 7x-2
What is x
Answers
Answer:
x=-5
Step-by-step explanation:
3(2x+1)=7x-2
6x+3=7x-2
6x-7x=-2-3
x=-5
3(2x + 1) = 7x-2
3*2x+3*1=7x-2
6x+3=7x-2
6x-7x=-3-2
-1x=-5
x=5
What is the factorization of the trinomial below?
x^3 - 12x^2 + 35x
A. (x - 7)(x + 5)
B. x(x - 7)(x - 5)
C. (x^2 - 7)(x + 5)
D. x(x - 7)(x + 5)
Answers
how many one third cup servings are in 16 cups
Answers
Part A: Given sine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,∞).
Part B: Given θ = 675°, convert the value of θ to radians and find sec θ.
(Picture below is equation stated in Part A)
Answers
Answer:
A. {60°, 120°, 420°}
B. θ = 15π/4; sec(θ) = √2
Step-by-step explanation:
A.The sine function is periodic with period 360°, and it is symmetrical about the line θ = 90°. The reference angle for the given value of sin(θ) is ...
θ = arcsin(√3/2) = 60°
The next larger angle with the same sine is (2×90°) -60° = 120°. Any multiple of 360° added to either one of these angles will give an angle with the same sine. A possible set of 3 angles is ...
{60°, 120°, 420°}
__
B.One degree is π/180 radians, so the given angle in radians is ...
θ = 675° = 675(π/180) radians = 15π/4 radians
This angle has the same trig function values as 7π4, a 4th-quadrant angle with a reference angle of π/4, or 45° The secant of that angle is
sec(45°) = √2
The 4th-quadrant angle has the same sign, so ...
sec(675°) = sec(15π/4) = √2
need help with the questions below. screenshots are provided. need help asap
Answers
Answer:
Step-by-step explanation:
12g - 17 ≥ 17
12g ≥ 34
g ≥ [tex]\frac{34}{12}[/tex]
g ≥ [tex]\frac{17}{6}[/tex]
A rare species of insect was discovered in the rain forest. In order to protect the species,
environmentalists declare the insect endangered and transplant the insects into a protected area.
The population of the insect t months after being transplanted is given by P(t).
P(t) =
60(1+0.4)
0.01t+3
a. How many insects were discovered? In other words, what was the population when t = 0?
b. What will the population be after 5 years? Round to the nearest whole insect.
Answers
Using the given function, it is found that:
a) 20 insects were discovered.
b) The population after 5 years will be of 417 insects.
What is the function for the number of insects after t months?As stated in the exercise, it is given by:
[tex]P(t) = \frac{60(1 + 0.4t)}{0.01t + 3}[/tex]
Item a:
[tex]P(0) = \frac{60[1 + 0.4(0)]}{0.01(0) + 3} = \frac{60}{3} = 20[/tex]
20 insects were discovered.
Item b:
5 years = 60 months, hence:
[tex]P(60) = \frac{60[1 + 0.4(60)]}{0.01(60) + 3} \approx 417[/tex]
The population after 5 years will be of 417 insects.
More can be learned about functions at https://brainly.com/question/25537936
The cards below have a mean of 25. What is the missing number?: ? 19, 22, 31
Answers
Answer: Its 28.
Step-by-step explanation:
The missing number in the card s 28
How to determine the missing number?Represent the missing number with x.
So, we have:
x, 19, 22 and 31
The mean of a dataset is:
Mean = Sum/Count
So, we have:
25 = (x + 19 + 22 + 31)/4
Multiply both sides by 4
100 = x + 19 + 22 + 31
Evaluate the sum
100 = x + 72
Subtract 72 from both sides
x = 28
Hence, the missing number is 28
Read more about mean at:
https://brainly.com/question/14532771
LOTS OF POINTS + BRAINLIEST
Suppose p and q are both prime numbers with p > q. Prove that p-q and p+q cannot both be positive perfect squares.
FULL PROOF REQUIRED.
Answers
Answer:
The list od prime number is a quadratic sequence, each time going up by n + 2. for example, 1, 4, 9, 16, 25. they are going up by 3, then + 2 and add 2 every step. The sequence is always going up by an odd number. a negative number take away a negative number always gives you a positive number, likewise, adding does too. Therefore, you can not get both of them to fit into the sequence of increasing odd numbers.
Liam is a tyre fitter. it takes him 124 minuets to fit 4 tyre's to a lorry. how long would t take him to fit 6 tyre's to a lorry?
if he works for 93 minuets how many tyre's will he fit?
Answers
168 minutes or 2 hours 48 minutes
Step-by-step explanation:
Since 12 tyres is 3 times 4 tyres, it will take 3 times as long as 56 minutes.
3 * 56 minutes = 168 minutes
We can convert the answer to hours and minutes.
60 minutes = 1 hour
120 minutes = 2 hours
168 minutes – 120 minutes = 48 minutes
168 minutes = 2 hours 48 minutes
Answer: 168 minutes or 2 hours 48 minute
3 * 56 minutes = 168 minutes
We can convert the answer to hours and
minutes.
60 minutes = 1 hour
120 minutes = 2 hours
168 minutes - 120 minutes = 48 minutes
168 minutes = 2 hours 48 minutes
Answer: 168 minutes or 2 hours 48 minute
Evan walked 2 1/8 miles to his aunts house. He has already walked 6/8 mile. How much farther does Evan have to go?
Answers
Rewrite 2 1/8 as 17/8
Now subtract:
17/8 - 6/8 = 11/8 = 1 3/8
answer : 1 3/8 miles left
Determine the value of y, if x is -1. y= | x |-4
Answers
The absolute value of -1 is 1
y=1-4
y=-3
Find the distance between the two points (1, -4) and (5, 3). Give an exact answer in
terms of a square root.
Answers
Answer:
A lovely answer of : [tex]\sqrt{17}[/tex]
For those of you who use a dark theme : square root of (17)
And a short Explanation:
Use the Pythagorean theorem to find the result
Help me out please, should be easy
Answers
Answer:
I'm pretty sure the points are plotted at (-1,-2) but I'm not exactly sure. Correct me if I'm wrong! :D
Round to the nearest tenth, I will give brainlyest PLEASE
Answers
1. cos B= a/x
x= 11/cos 37°
x= 13.77
2. tan A= a/x
x= 4/tan 41°
x= 4.60
3. sin B = x/c
x= sin 37° × 10.3
x= 6.20
4. tan A= a/b
tan A= 4/13
A= tan-1(0.31)
A= 17°6'10"
5. cos A= b/c
cos A= 12/13
A= cos -¹(0.92)
A= 22°37'12"
6. tan B= a/b
tan B= 3/3
tan B= 1
B= tan‐¹(1)
B= 45°
Carrie uses her phone primarily to take a lot of selfies. The storage space on her phone is limited, so Carrie needs to keep track of how many selfies she takes.
There is a proportional relationship between the number of selfies Carrie takes, x, and the amount of storage (in megabytes) she uses taking selfies, y.
x (selfies) y (megabytes)
10 20
12 24
21 42
22 44
Write an equation for the relationship between x and y. Simplify any fractions.
y=
Answers
Explanation:
A direct proportion is of the form y = kx
To find k, pick any row to divide the y over x value
k = y/x = 20/10 = 2k = y/x = 24/12 = 2k = y/x = 42/21 = 2k = y/x = 44/22 = 2No matter which row you go for, the constant of proportionality is 2. Meaning that we double the x value to get to y.
Therefore, we go from y = kx to y = 2x
255, 250, 245, ...
Find the 40th term.
Answers
Answer:
so here we minus 5 from 255 to get to 250 and we do it again to get to 245. for reaching the 40th term we should do it 39 times.
so, 255+ (-5) (39) = 255 - 195 = 60
which is our 40th term.
The 40th term of (255, 250, 245...) is 60.
What is arithmetic progression ?The difference between any two successive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.There are three distinct progression kinds. As follows:Mathematical Progress (AP)Graphical Progress (GP)Rhythmic Progress (HP)It is feasible to find a formula for the nth term for a certain kind of sequence called a progression. The most popular mathematical progression, with simple formulas, is the arithmetic progression.Calculations :
The formula to find the nth term = [tex]a_{n}[/tex] = -5n + 260
= [tex]a_{40}[/tex] x 5n = 260
= 260 - 200 = 60
Learn more about Arithmetic progression refer :
https://brainly.com/question/24191546
#SPJ2
find measure of the missing angles and justify your answer with postulates and theorems.
Answers
Answer:
Step-by-step explanation:
Solve for x. Round all answers to the nearest tenth.
11
11.7
10.2
11.9
Answers
11.9 - last one
Step-by-step explanation:
Adjacent + hypotenuse = Cos / Cah
Cos32 = x/14
x14
11.87... = x
So, 11.9 to nearest tenth
Hope this helps!
can someone solve what is n/n^3
Answers
Answer:
Alex = No B.
Step-by-step explanation:
1) Use Quotient Rule: [tex]\frac{x^{a} }{x^{b} } =x^{a-b}[/tex]
[tex]n^{1-3}[/tex]
2) Simplify 1 - 3 = 2
[tex]n^{-2}[/tex]
3) Use Negative Power Rule: [tex]x^{-a} =\frac{1}{x^{a} }[/tex]
[tex]\frac{1}{n^{2} }[/tex]
which pair of pairs of polygons are congruent.
Answers
Answer:
bottom left. (arrow shaped)
Step-by-step explanation:
congruent shapes are the same size and shape
Answer both Question 11 and 12. I will make Brainelist + 50 points
Answers
Answer:
#11. i) 5, ii) 6, iii) - 4, iv) 6#12- see belowStep-by-step explanation:
#11Given equation for sum of the first n terms
[tex]S_n=7n-2n^2[/tex]Using the equation solve the following
i)The first term [tex]t_1[/tex], is same as the sum of the first 1 term, so n = 1
[tex]t_1=S_1=7(1)-2(1)^2=7-2=5[/tex]ii)Sum of the first 2 terms, when n = 2
[tex]S_2=7(2)-2(2)^2=14-8=6[/tex]iii)Common difference is the difference between two consequitive terms.
First, find the second term:
[tex]t_2=S_2-t_1=6-5=1[/tex]Now find the difference between the first two terms:
[tex]d=t_2-t_1=1-5=-4[/tex]iv)We need to find such n that [tex]S_n[/tex] = - 30
[tex]7n - 2n^2=-30[/tex][tex]2n^2 - 7n-30=0[/tex][tex]2n^2-12n+5n-30=0[/tex][tex]2n(n-6)+5(n-6)=0[/tex][tex](n-6)(2n+5)=0[/tex][tex]n=6[/tex] is the only positive rootSo the answer is 6
#12Simplifying in steps as below
a) i)[tex]\dfrac{5}{y-3} +\dfrac{2}{3-y}=[/tex][tex]\dfrac{5}{y-3}-\dfrac{2}{y-3}=[/tex][tex]\dfrac{5-2}{y-3}=[/tex][tex]\dfrac{3}{y-3}[/tex]ii)[tex]\cfrac{1}{m+3} +\cfrac{2m}{m^2-9} =[/tex][tex]\cfrac{1}{m+3} +\cfrac{2m}{(m-3)(m+3)} =[/tex][tex]\cfrac{m-3}{(m-3)(m+3)}+\cfrac{2m}{(m-3)(m+3)} =[/tex][tex]\cfrac{m-3+2m}{(m-3)(m+3)} =[/tex][tex]\cfrac{3m-3}{(m-3)(m+3)}[/tex]A number w minus 3 is less than or equals to 10
Answers
Answer:
Step-by-step explanation:
A number w minus 3 (w - 3) is less than or equal (≤) to 10
w - 3 ≤ 10
+ 3 + 3
w ≤ 13
Hope this helps!
SOMEONE PLSSSSSS HELP ME SOLVE THIS FAST
I WILL MARK BRAINLIEST
Answers
Answer:
D
Step-by-step explanation:
I calculated the area for 54 feet and then for 0.5 feet using the equation [tex]A=\sqrt{\frac{3}{4} }a^{2}[/tex] , where a is the size and then divided first area by second area
convert 5'5 into meters
Answers
It will be around 1.6metres
hope it helps
Answer:
1.65 meters
Step-by-step explanation:
1 ft = 0.3048 meters
just multiply
What is the Area of this shape?
Answers
14 * 12 = 168
(12*8) / 2 = 48
216 cm ^2
Answer:
1,344 cm counting the side shape or 168 cm counting only the rectangle.
Step-by-step explanation:
14 cm x 12 cm = 168cm
168 x 8 = 1,344 cm
Please help 300 points
Answers
Answer:
4x + 9 ≥ 0
Step-by-step explanation:
The inside of the square root, the radicand, cannot be negative.
It can only be zero or positive.
Zero or positive is also described as being greater than or equal to 0.
Set the radicand to be greater than or equal to zero.
4x + 9 ≥ 0
Answer:
4x+9>=0
Step-by-step explanation:
The domain of a square root is that it can’t be less than 0. So we have the equation 4x+9>=0.
The graph of f(x) = 8 - x and line l which is tangent to f at x =1 is
shown in the figure to the right. The equation for line l is y =-3x +10.
Region R is the shaded region between line l, the graph off and the
y-axis while S is the shaded region between line l, the graph off and
the x-axis.
(a) Find the area of the shaded region R.
Answers
By taking the integral of the difference between the two given lines, we will see that R = 0.75.
How to find the area of the region R?Notice that the area will be given by the integral of the difference between the line L and our function on the interval [0, 1]
Then we just need to compute:
[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx[/tex]
Solving that we will get:
[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx = \int\limits^1_0 ({-3x + 10 - 8 + x^3} )dx\\\\\R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\\\[/tex]
[tex]R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\R = \frac{-3}{2}*(1)^2 + 2*1 + \frac{1^4}{4} = 0.75[/tex]
So the area of region R is 0.75 square units.
If you want to learn more about integrals, you can read:
https://brainly.com/question/14502499
How many sides does a regular polygon have if each interior angle measures 150°?
Answers
Answer:
12
Step-by-step explanation:
Its interior angle has measure 150∘. Therefore, the exterior angle has measure 180∘−150∘=30∘. Therefore, the number of sides of the regular polygon with interior angle 150∘ is 12.
Rewrite the following without an exponent. (9/5)^-1
Answers
Answer:
5/9
Step-by-step explanation:
What we have here is the reciprocal of (9/5). Inverting (9/5) results in (5/9), which is the desired result.
Please help me with this!!
Answers
Answer:
A, B, D, F
Step-by-step explanation:
Given expression: [tex]8^{\frac23}[/tex]
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^2)^{\frac13}[/tex]
Apply exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex]
[tex]\implies (8^2)^{\frac13}=\sqrt[3]{8^2}[/tex]
Therefore, option A
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]
Apply exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex]
[tex]\implies (8^{\frac13})^2=(\sqrt[3]{8})^2[/tex]
Therefore, option B
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]
As [tex]8^{\frac13}=2[/tex]
[tex]\implies (8^{\frac13})^2=2^2[/tex]
Therefore, option D
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]
As [tex]8^{\frac13}=2[/tex]
[tex]\implies (8^{\frac13})^2=2^2[/tex]
[tex]\implies 2^2=4[/tex]
Therefore, option F