The rectangular prism is 187.5 - 125 = 62.5 cu.inches greater than the volume of cube.
What is Volume?Volume is defined as the space occupied by a three dimensional figure.
It is given that
A cube's edge lengths are each 5 inches
A rectangular prism's length and width are also 5 inches, but its height is [tex]\rm 7\dfrac{1}{2}[/tex]
The volume of the cube is given by side * side * side
Volume of cube = 5 *5 * 5 = 125 cu. inches
The volume of cuboid = length * width * height
Volume of Cuboid = 5 * 5 * 15/2Volume of Cuboid = 187.5 cu.inches.
Therefore the rectangular prism is 187.5 - 125 = 62.5 cu.inches greater than the volume of cube.
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ZA and B are supplementary and vertical angles. What is m<B
A.180
B.135
C.45
D.90
Reason:
Vertical angles are equal to each other. Call them x. They must add to 180 degrees because they are supplementary (they are able to form a straight line).
x+x = 180
2x = 180
x = 180/2
x = 90
(01.06 LC)
Which number is not in scientific notation?
Answer:
[tex]0.95*10^8[/tex]
Step-by-step explanation:
Hello!
Rules for scientific notation format:
Has to be multiplied to a power of 10One factor has to be greater than 1 but less than 10[tex]\bold{0.95*10^8}[/tex]
There is a multiplication to a power of 10, but the other factor is less than 1.
This is NOT in Scientific Notation.
All the other options have a multiplication operation to a power of 10, and all the other factors are above 1 and less than 10.
Find the length of the curve.
x=3t² +5₁y = 2t³ +5,0 ≤t≤1
The length of the curve will be given by the definite integral
[tex]\displaystyle \int_0^1 \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt[/tex]
From the given parametric equations, we get derivatives
[tex]x(t) = 3t^2 + 5 \implies \dfrac{dx}{dt} = 6t[/tex]
[tex]y(t) = 2t^3 + 5 \implies \dfrac{dy}{dt} = 6t^2[/tex]
Then the arc length integral becomes
[tex]\displaystyle \int_0^1 \sqrt{\left(6t\right)^2 + \left(6t^2\right)^2} \, dt = \int_0^1 \sqrt{36t^2 + 36t^4} \, dt \\\\ = \int_0^1 6|t| \sqrt{1 + t^2} \, dt[/tex]
Since 0 ≤ t ≤ 1, we have |t| = t, so
[tex]\displaystyle \int_0^1 6|t| \sqrt{1 + t^2} \, dt = 6 \int_0^1 t \sqrt{1 + t^2} \, dt[/tex]
For the remaining integral, substitute [tex]u = 1 + t^2[/tex] and [tex]du = 2t \, dt[/tex]. Then
[tex]\displaystyle 6 \int_0^1 t \sqrt{1 + t^2} \, dt = 3 \int_1^2 \sqrt{u} \, du \\\\ = 3\times \frac23 u^{3/2} \bigg|_{u=1}^2 \\\\ = 2 \left(2^{3/2} - 1^{3/2}\right) = 2^{5/2} - 2 = \boxed{4\sqrt2-2}[/tex]
A bag has 9 blue cubes, 11 red cubes, and 5 green cubes. If you
draw a cube and replace it in the bag 250 times, which of the
following amounts would you expect to pull?
The numbers that can be pulled based on the probability of the calls will be 90, 110, and 50.
How to depict the probability?From the information given, the bag has 9 blue cubes, 11 red cubes, and 5 green cubes and when one draws a cube and replace it in the bag 250 times, the number of blue balls that can be gotten will be:
= 9/(9+ 11 + 5) × 250
= 9/25 × 250
= 90
The number of red balls that can be gotten will be:
= 11/25 × 250
= 110
The number of green balls that can be gotten will be:
= 5/25 × 250
= 50
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How might an architect use geometry in their work?
Answer:
Architects use geometry to study and divide space as well as draft detailed building plans. Builders and engineers rely on geometric principles to create structures safely. Designers apply geometry (along with color and scale) to make the aesthetically pleasing spaces inside. Applying geometry in design is unavoidable.
Joan has some dimes and quarters. If she has 19 coins worth a total of $2.35, how many of each type of coin does she have?
The number of each type of coin that Joan has are; 16 dimes and 3 quarters
How to convert currencies?
We are told that Joan has a total of 19 coins.
Now, the worth of the coins is $2.35
Let dimes be d and let quarters be q. Thus;
10d + 25q = 235
d + q = 19
Substitute d = 19 - q in the 1st equation to get;
10(19 - q) + 25q = 235
190 - 10q + 25q = 235
15q = 45
q = 45/15
q = 3
Thus;
d = 19 - 3
d = 16
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jackson bought 3 pounds of candy for $9.60.
What was the price of this candy in cents per pound ?
PLS HELP ITS DU IN 5 MIN !!!!!!!!!!!!!!!!!!!!!!
Answer:
320 cents per pound
Step-by-step explanation:
so we do 9.60 divided by 3, which is 3.20. So, 3.20 for each pound. Now we need in cents. 3 dollars is 300 cents, plus another 20, so 320 cents. I hope this helped.
Donovan is paying for gym classes. Each type of class has its own weekly fee. He signed up for x weeks of yoga classes and y
weeks of kickboxing classes. He paid a total of $136. The equation below describes the relationship between the number of weeks
of yoga classes and the number of weeks of kickboxing classes Donovan signed up for.
8x + 12y
-
136
The ordered pair (5,8) is a solution of the equation. What does the solution (5.8)
Considering the given function, the ordered pair (5,8) means that the signed up for 5 weeks of yoga classes and 8 weeks of kickboxing classes.
What does the function represent?
The function that represents the relationship between the number x of yoga classes that Donovan signs up for and the number y of kickboxing classes is given by:
8x + 12y = 136.
Hence the ordered pair (5,8) means that the signed up for 5 weeks of yoga classes and 8 weeks of kickboxing classes.
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The incorrect work of a student to solve an equation 2(y + 6) = 4y is shown below: Step 1: 2(y + 6) = 4y Step 2: 2y + 8 = 4y Step 3: 2y = 8 Step 4: y = 4 Which of the following explains how to correct Step 2 and shows the correct value of y? (5 points) a 2 should be distributed as 2y + 12; y = 6 b 2 should be distributed as 2y + 12; y = 3 c The equation should be y + 6 = 4y after division by 2; y = 2 d The equation should be y + 6 = 4y after division by 2; y = 1
Step-by-step explanation:
The wording is slightly confusing so I will just solve the equation.
2 (y + 6) = 4y
We expand the bracket
2y + 12 = 4y
We subtract 2y from both sides
12 = 2y
We divide both sides by 2
6 = y
Question 6(Multiple Choice Worth 1 points)
(02.02 MC)
Given the function f(x) = -5x² + 2x + 9, find f(1) and f(2). Choose the statement that is true concerning these two values.
O The value of f(1) cannot be compared to the value of f(2).
O The value of f(2) is larger than the value of f(1).
O The value of f(2) is smaller than the value of f(1).
O The value of f(1) is the same as the value of f(2). help
Answer:
O The value of f(2) is smaller than the value of f(1).
Step-by-step explanation:
First, let's solve for both. When the problem says f(1) or f(2), this just means that the x value is equal to that. So:
f(1) = -5(1)^2 + 2(1) + 9 = 6
f(2) = -5(2)^2 + 2(2) + 9 = -7
Since f(1) = 6 and f(2) = -7, we know that f(1) is greater than f(2). Therefore, the value of f(2) is smaller than the value of f(1)
what is a factor of 84 but not a multiple of 3
Answer:
2
Step-by-step explanation:
Which of the following is equal to this expression?
(256·64)^1/4
A) 4·[tex]\sqrt[4]{4}[/tex]
B) 8·[tex]\sqrt[4]{4}[/tex]
C) 8·[tex]\sqrt[4]{2}[/tex]
D) 2·[tex]\sqrt[4]{2}[/tex]
Answer:
B) [tex]8\sqrt[4]{4}[/tex]
Step-by-step explanation:
[tex](2^{8} *2^{6} )^\frac{1}{4} = (2^{8+6} )^\frac{1}{4} =(2^{14} )^\frac{1}{4} =2^{\frac{7}{2} }=\sqrt{2^{7} } =2^{3} \sqrt{2} =8\sqrt{2} = 8\sqrt[4]{2^{2} } = 8\sqrt[4]{4}[/tex]
Triangle
ABC
GHI
DEF
S
NU
H"
Dimensions
2, 4, 5
5,5,9
4,4,4
Classify by
Sides
E
Classify by
Angles
Answer:
See below ~
Step-by-step explanation:
Classifying the triangles by sides and angles :
Triangle ABC
⇒ By Sides : Scalene (All sides are unequal)
⇒ By Angles : Right (There is a right angle = 90°)
============================================================
Triangle GHI
⇒ By Sides : Isosceles (2 sides are equal)
⇒ By Angles : Obtuse (One angle is greater than 90°)
============================================================
Triangle DEF
⇒ By Sides : Equilateral (All sides are equal)
⇒ By Angles : Acute (All angles are less than 90°)
Find the average value of f over the region D. f(x, y) = 3xy, D is the triangle with vertices (0, 0), (1, 0), and (1, 9)
The average value of f over the region D is 243/4
To answer the question, we need to know what the average value of a function is
What is the average value of a function?The average value of a function f(x) over an interval [a,b] is given by
[tex]\frac{1}{b - a} \int\limits^b_a {f(x)} \, dx[/tex]
Now, given that we require the average value of f(x,y) = 3xy over the region D where D is the triangle with vertices (0, 0), (1, 0), and (1, 9).
x is intergrated from x = 0 to 1 and the interval is [0,1] and y is integrated from y = 0 to y = 9
So, [tex]\frac{1}{b - a} \int\limits^b_a {f(x,y)} \, dA = \frac{1}{1 - 0} \int\limits^1_0 \int\limits^9_0 {3xy} \, dxdy \\= \frac{3}{1} \int\limits^1_0 {x} \,dx\int\limits^9_0 {y} \,dy\\ = \frac{3}{1} [\frac{x^{2} }{2} ]^{1}_{0}[\frac{y^{2} }{2} ]^{9}_{0} \\= 3[\frac{1^{2} }{2} - \frac{0^{2}}{2} ] [\frac{9^{2} }{2} - \frac{0^{2}}{2} ] \\= 3[\frac{1}{2} - 0 ][\frac{81}{2} - 0 ]\\= \frac{81}{2} X3 X \frac{1}{2} \\= \frac{243}{4}[/tex]
So, the average value of f over the region D is 243/4
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Based on the measures
provided in the diagram,
determine the measure of
BC.
(You may assume that point A is the
center of the circle.)
O 130⁰
O 25⁰
O 50⁰
O 100⁰
The measures of BC will be 100°. Option D is correct.
What exactly is a circle?It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.
The angle at the center is twice as large as the angle at the perimeter.
BC = 2 ×∠CDB
BC=2×50°
BC= 100°
Hence option D is correct.
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How many liters each of a 24% iodine solution in a 40% iodine solution must be used to produce a total make sure of 100 L of 28% iodine solution
By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.
How to determine the volume associated with a given concentrationPhysically speaking, concentration is equal to the amount of solute divided by the volume of solution. We have two solutions with same solute and different concentration and can find the right proportion between the 24 % solution and the 40 % solution by concept of weighted average:
x · 24 + (1 - x) · 40 = 28
40 - 16 · x = 28
16 · x = 40 - 28
16 · x = 12
x = 3/4
By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.
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Every day sandra eats 1/8 pound of a blueberries. If she does this for 9 days, how many pounds of blueberries did she eat?
Answer: 1.125 pounds of blueberries or [tex]1 \frac{1}{8}[/tex] or [tex]\frac{9}{8}[/tex]
Step-by-step explanation:
Since she will eat it for 9 days, just multiply or add the pounds.
Solve the system of equations
−5x−3y=−28 and x+2y=0 by combining the equations
Answer: (8, -4)
Step-by-step explanation:
-5x - 3y = -28
x + 2y = 0
1. Multiply both sides of the bottom system by 5 to cancel the x out
5(x+2y=0)
5x + 10y = 0
2. rewrite
-5x - 3y = -28
5x + 10y = 0
3. add
0x + 7y = -28
4. divide by 7
7y = -28
5. y = -4
6. plug in -4 for y in one of the original equations
x + 2(-4) = 0
7. simplify
x = 8
9. solution is
(8, -4)
can you help me with this question
PLEASE HELP! YOU WILL GET 100 POINTS! SUPER CONFUSED NEED HELP AS SOON AS POSSIBLE THIS IS DUE SOON!!! QUESTION IN PICTURE BELOW!
Answer:
Q = 40.6°
Explanation:
Given three sides: 9.6, 8.1, 6.3
Use the cosine rule:
c² = a² + b² - 2ab cos(C)
Insert following variables:
6.3² = 9.6² + 8.1² - 2(9.6)(8.1) cos(Q)
39.69 = 157.77 - 155.52 cos(Q)
cos(Q) = -118.08/-155.52
cos(Q) = 41/54
Q = cos⁻¹(41/54) = 40.6°
Question 4 of 10
If ƒ(x) = 3(x+5) +−, what is f(a+2)?
[tex]f(x) = 3(x+5)\\\\f(a+2) = 3(a+2 +5) \\\\~~~~~~~~~~~~=3(a+7)\\\\~~~~~~~~~~~~=3a+21[/tex]
Determine the area, in square centimeters, of
this quarter circle with a radius of 8 cm. Use 3.14
for π and round your answer to the nearest
hundredth.
Step-by-step explanation:
quarter circle means that you just find the are and then divide it by 4.
hence,
(3.14 × 8²) ÷ 4 = answer
the answer is 50.24 cm²
hope this helps.
Answer: 6.28
Step-by-step explanation: In order to get your answer, the equation that you need to do is 8 X 3.14 / 4 to get your answer.
One number is 2 less than a second number. Twice the second number is 7 less than 3 times the first. Find the two numbers.
Answer : 11 and 13
Step-by-step explanation:
Let the numbers be X and Y then,
By question
X= Y - 2 .....................(i)
2Y = 3X - 7 ...............(ii)
putting the value of X from (i) on equation (ii) we get,
2Y = 3(Y - 2) - 7
2Y = 3Y - 6 - 7
2Y - 3y = - 13
-Y = - 13
Y = 13
now putting value of Y in equation (i)
X = 13 - 2= 11
hence those numbers are 11 and 13 respectively
The solution to an absolute value inequality is shown on the graph below.
-5-4-3-2-1 0 1 2 3 4 5
What is another way to show the solution?
O x>-3 or x < 2
O {x|x <-3 orx <2}
O [-3, 2]
O (-3,2)
The solution to the absolute value inequality is (-3,-2)
How to determine the absolute inequality?On the absolute value inequality, we have:
Interval = -3 to 2
The intervals are represented with open circles.
This means that -3 and 2 are exclusive of the values of the inequality.
So, we have:
-3 < x < 2
As an interval notation, we have:
(-3,-2)
Hence, the solution to the absolute value inequality is (-3,-2)
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A group of people were asked if they had run a red light in the last year. 218 responded "yes", and 270 responded "no". Find the probability that if a person is chosen at random, they have run a red light in the last year.
an angle measures 122 degrees more than the measure of a supplementary angle. What is the measure of each angle?
Answer:
the measure of each angle is 75degrees
Match the average rates of change of f(x) to the corresponding intervals.
-3
-8
-7
[-5, -1]
[-4,-1]
[-3, 1]
[-2, 1]
The average rates of change of f(x) and their corresponding intervals are given as:
Interval Rate of Change
[-5, -1] -8
[-4, -1] -7
[-3, 1] -4
[-2, 1] -3.
What is the explanation for the above?Step 1 - See Table Attached
Step 2 - State the formula for rate of change
The formula for rate of change is given as:
= [change in f(x)] / [change in x]
a) For interval [5, -1] ⇒
Rate of Change - [ f(1) - f(-5) ] / [-1 - (-5)]
= [-1 - 35] / [-1+5]
= -36 / 4
= - 8
b) For interval [-4, -1] ⇒
rate of change = [ f(-1) - f(-4) ] / [ -1 - (-4) ]
= [3 - 24] / [-1 + 4]
= -21/3
= - 7
c) interval [-3,1] ⇒
rate of change = [ f(1) - f(-3) ] / [ 1 - (-3) ]
= [-1 - 15] / [1 + 3]
= -16/4
= - 4
d) interval [-2,1] ⇒
rate of change = [f (1) - f(-2)] / [1 - (-2)]
= [ -1 - 8] / [1 + 2]
= -9/3
= -3
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1+ cos^4 x-sin^4 x = 2 cos² x
[tex]\text{L.H.S}\\\\=1+ \cos^4 x - \sin^4 x\\\\=1+ (\cos^2 x)^2 - (\sin^2 x)^2\\\\=1+(\cos^2 x + \sin^2 x)(\cos^2 x- \sin^2 x)\\\\=1+1\cdot(\cos 2x)\\\\=1+\cos 2x\\\\=2\cos^2 x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
Use four unit multipliers to convert 120 square inches to square yards.
The conversion of 120 sq. inches is equivalent to 0.09264 sq. yd.
What is Conversion?Conversion is the process of changing the value of one form to another for example inches to millimeters, or liters to gallons.
Here, we know that,
1 square inches = 0.000772 sq yd
we have 120 sq. inches
so, 120 sq. inches = 120 X 0.000772 sq yd
= 0.09264 sq. yd.
Thus, the conversion of 120 sq. inches is equivalent to 0.09264 sq. yd.
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3/4(2x-3) = 2/3 x+5 with detailed explanation
Answer:
x = 11
Step-by-step explanation:
3/(3(2x-3)) = 2/(3x+5)
3(2x-3) = 6x - 9
3/(6x-9) = 2/(3x+5)
3(3x+5) = 2(6x-9)
9x + 15 = 12x - 18
12x - 9x = 15 + 18
3x = 33
x = 11
Answer:
[tex]\mathrm x= \dfrac{87}{10} \quad or \quad 8.7[/tex]
Explanation:
[tex]\longrightarrow \sf \dfrac{3}{4} (2x-3)=\:\dfrac{2}{3}\:x+5[/tex]
Distribute inside parenthesis[tex]\longrightarrow \sf \dfrac{3}{2} x-\dfrac{9}{4} =\:\dfrac{2}{3}\:x+5[/tex]
Group the variables[tex]\longrightarrow \sf \dfrac{3}{2} x-\dfrac{2}{3}x=5+\dfrac{9}{4}[/tex]
Add or Subtract[tex]\longrightarrow \sf \dfrac{5}{6} x=\dfrac{29}{4}[/tex]
Cross Multiply[tex]\longrightarrow \sf x=\dfrac{29(6)}{4(5)}[/tex]
Simplify the following[tex]\longrightarrow \sf x=\dfrac{87}{10} \quad or \quad 8.7[/tex]