The volume of the prism that is completely filled with 72 cubes that have edge lengths of 1/2 in. is 9 in³.
What is a prism?A prism is a 3-dimensional shape, with two identical shapes facing each other.
To calculate the volume of the prism, we use the formula below.
Formula:
The volume of the prism (V) = 72×volume of one cubeV = 72L³............. Equation 1Where:
V = Volume of the prismL = Length of the cubeFrom the question,
Given:
L = 1/2 inSubstitute these values into equation 1
V = 72(1/2)³V = 72(1/8)V = 9 in³Hence, the volume of the prism is 9 in³.
Learn more about prisms here: https://brainly.com/question/23741714
Each package of dog treats has 15 treats.
The equation d = 15t, where d represents the total number of dog treats and t represents number of packages, shows this relationship.
If Esther bought 45 dog treats total, how many packages did she buy?
Answer:
675 packages
Step-by-step explanation:
You multiply 15 x 45 to get 675
if 1 treat per 15 bags is correct
Destinee bought a tablet for $599 and enrolled in a data plan for $25 per month. The total amount y Destinee has paid towards the tablet after x months is found using an equation in the form y = mx + b. What is the value of m and b? m= -25 and b = 599 m= 599 and b = 25 Om = 25 and b = 599 = m= -599 and b = 25
Answer:
m = 25 and b = 599
Step-by-step explanation:
the m represents month while the B represent buy that means when he bought a tablet
=> m = 25 and b = 599
Our m will be 25 because every month she pays $25 for the data plan, increasing it by 25.
Our b will be 599 because the tablet started out at $599 dollars.
Answer:m = 25 and b = 599, the third option
A, B & C form the vertices of a triangle. ∠ CAB = 90°, ∠ ABC = 49° and AB = 9.2. Calculate the length of AC rounded to 3 SF.
Answer:
Step-by-step explanation:
20.3 Yw :)
Expand (2a^2+7a-10)(a-5) your answer should be a polynomial in standards form
Answer:
2a^3 -3a^2 -45a +50
Step-by-step explanation:
The expansion of the product of polynomials is an application of the distributive property. Usually, it needs to be applied several times.
(2a^2+7a-10)(a-5)
= 2a^2(a -5) +7a(a -5) -10(a -5)
= 2a^3 -10a^2 +7a^2 -35a -10a +50
= 2a^3 -3a^2 -45a +50
Two numbers are in the ratio 7:5. If 2 is subtracted from each of them, the ratio becomes 3:2. Find the numbers.
Answer:
Step-by-step explanation:
Ratio = 7 : 5
Numbers are 7x , 5x
[tex]\dfrac{7x-2}{5x-2}=\dfrac{3}{2}\\\\\\[/tex]
Cross multiply,
2*(7x - 2) = 3*(5x -2)
2*7x - 2*2 = 3*5x - 3*2
14x - 4 = 15x - 6
14x - 4 + 6 = 15x {Add 6 to both sides}
14x + 2 = 15x
2 = 15x - 14x {Subtract '4x' from both sides}
x = 2
7x = 7*2 = 14
5x = 5*2 = 10
Numbers are 14 , 10
You want to frame a 6 inch by 9-inch picture. The frame has a two-inch width. Calculate the area of the framed photo.
Answer:
It's either 108 or 54, the area is 54 in^2 and the volume of the frame is 108^3
Step-by-step explanation:
Volume (if that is what its asking) would be 54 in^2
Find two solutions to the linear equation x = 15 − y.
Answer:
(-1, 16), (3, 12)
These are my examples so if you want you can do different solutions, too!
Step-by-step explanation:
It may sound weird, but there are infinitely many solutions to a linear equation. It's basically all real numbers that are on the line.
So, just choose two random numbers for the x-value and substitute in into the equation. I'm going to use -1 and 3.
x = 15 - y
when x = -1
-1 = 15 - y
y = 16
(-1, 16)
when x = 3
3 = 15 - y
y = 12
(3, 12)
Answer:
Step-by-step explanation:
hello :
if y=0 so x= 15 and if : x=0 so y = 15
you have two solutions : (15;0) and (0;15)
The function g(x) is the height of a football x seconds after it is thrown in the air. The football reaches its maximum height of 30 feet in 4 seconds, and hits the ground at 10 seconds.
What is the practical domain for the function f(x)
Write your answer in interval notation.
Answer:
[0,10]
Step-by-step explanation:
The domain unit is seconds.
Time can't be negative so x is greater than or equal to zero.
The time here stops after 10 seconds. So our domain is
Since time will start at 0 and end at 10,we use a bracket.
[0,10]
Erica has \$30.00$30.00dollar sign, 30, point, 00 saved and receives an allowance of \$10.00$10.00dollar sign, 10, point, 00 each week.
Answer:
BB
Step-by-step explanation: Because I did it
Answer: A
Step-by-step explanation:
NO LINKS!!! Please help me with this problem. Part 2
Answer: approximately 7525 feet
A more accurate value is 7,524.6679636332 feet, but even that isn't fully exact.
==========================================================
Explanation:
The change in height, or delta height value, is 11200-9000 = 2200 which is the vertical component of the right triangle shown below. This side is opposite the reference angle, aka the angle of elevation 17°
The hypotenuse is x, which is the length of the trail. Assume we're dealing with a flat and straight surface. Of course realistically the ground is very likely going to be bumpy with various curved complexities; but we'll simplify things greatly.
We'll use the sine ratio to find x.
sin(angle) = opposite/hypotenuse
sin(17) = 2200/x
x*sin(17) = 2200
x = 2200/sin(17)
x = 7,524.6679636332
Assuming your teacher wants you to round to the nearest whole number, then we'd get to 7525 feet
We need Hypotenuse
[tex]\\ \rm\rightarrowtail sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
Hypotenuse be h[tex]\\ \rm\rightarrowtail sin17=dfrac{2200}{h}[/tex]
[tex]\\ \rm\rightarrowtail h=2200/sin17[/tex]
[tex]\\ \rm\rightarrowtail h=2200/0.2923[/tex]
[tex]\\ \rm\rightarrowtail h=7526.51ft[/tex]
Mr. Dean pays his employees after they have worked 40 hours. If each employee has worked 2 1/2 hours a day, after how many days will they get paid?
Answer:
They need to work 16 days before they get paid.
Step-by-step explanation:
40/2.5=16
15+6+5+8 please answer this
Answer:
34
Step-by-step explanation:
15+6=21
21+5=26
26+8=34
Write the following ratios 750 ml: 3L
Answer:
1:4
Step-by-step explanation: 750/3000 = 1/4 = 1:4
the volume of a cube is 528cm cubed. work out the length of its side rounded to 1DP
Answer:
8.1
Step-by-step explanation:
Formula for volume of cube. V = Volume and A = Edge.
[tex]V=a^{3}[/tex]
[tex]a=\sqrt[3]{v}[/tex]
Therefore we have.
[tex]528=a^{3}[/tex]
[tex]a=\sqrt[3]{528}[/tex]
We have to use the cube root function.
The cube root of (n) is the same as (n) raised to the 1/3 power.
n = a number
[tex]a=v^{\frac{1}{3} }[/tex]
So then we have.
[tex]528^{\frac{1}{3} } =a[/tex]
[tex]a=8.08248004[/tex]
Round to 1 decimal place.
[tex]a=8.1[/tex]
The diameter of a circle is 6 kilometers.
what is the circle's circumference?
d =6km
. Use 3.14 for Pi.
1b. Solve the differential equations
y''+ 4y' + 4y = 0, y(0) = 1 and y'(0) = 1
Note that each equation has right hand side zero. So, you don’t have to use the Laplace transform. You just use the characteristic equaiton.
Answer:
No solutions
Step-by-step explanation:
[tex]y''+4y'+4y=0,\:y(0)=1,\:y'(0)=1\\\\m^2+4m+4=0\\\\(m+2)(m+2)=0\\\\m=-2[/tex]
Thus, since we have equal real roots, we use the general solution [tex]y(x)=C_1e^{m_1x}+C_2e^{m_1x}[/tex] and our initial conditions to set up our system of equations:
[tex]y(x)=C_1e^{-2x}+C_2e^{-2x}\\\\y(0)=C_1e^{-2(0)}+C_2e^{-2(0)}\\\\1=C_1+C_2[/tex] <-- First one
[tex]y(x)=C_1e^{-2x}+C_2e^{-2x}\\\\y'(x)=-2C_1e^{-2x}-2C_2e^{-2x}\\\\y'(0)=-2C_1e^{-2(0)}-2C_2e^{-2(0)}\\\\1=-2C_1-2C_2[/tex] <-- Second one
Solve the system
[tex]C_1+C_2=-2C_1-2C_2\\\\3C_1+3C_2=0\\\\3C_1=-3C_2\\\\C_1=-C_2[/tex]
[tex]1=C_1+C_2\\\\1=-C_2+C_2\\\\1=0[/tex]
Therefore, there are no solutions to the differential equation given the initial conditions.
What is the future value of an account if $3,000 is invested at a rate of 8% compounded monthly
for 18 years? Round your answer to 2 decimal places.
Answer:
≈$12601.72
Step-by-step explanation:
Use the compounded interest formula:
[tex]A = P(1+\frac{r}{n})^{nt}[/tex]
In our case,
P = 3000
r = 8% = 0.08
n = 12 (months per year)
t = 18 (years in total)
Therefore, A ≈ $12601.72 (2.d.p.)
Need help asap pls :)
Answer:
See explanation below.
Step-by-step explanation:
First I'm going to find angle 2. Angle two plus 55 is equal to 115. 180-115=65. 65-55=10 Angle 2 = 10
Next, we can find angle 3. 55+10=65. 180-65=115. Angle 3 = 115
Angle 2 is equal to angle 5, angle 3 is equal to angle 6, and angle 4 is equal to 55.
Angle 5 = 10
Angle 4 = 55
Angle 6 = 115
Now we can find angle 8. 180-115=65. Angle 8 = 65
Angle 11 = 65
Angle 12 = 115
10+115=125 Angle 10 = 125
180-125 = 55 Angle 9 = 55
Angle 14 = 55
Angle 13 = 125
Answer:
<8, <5, <10 are 65 degrese
Step-by-step explanation:
oki, so, 55+m<2 must be 115 because 115 is a corresponding angel to 55+<2 meaning they are =, so m<2=115-55, m<2=60.
m<3 must then = 65 because line a phase a 180 angle (assuming a and b are parallel)
<3 is also corresponding to angle <10 so by the transitive property m<10=65.
m<8 must then = 65 because the angle of line b in 180, and the transversal cuts 115, 180-115=65.
whoops, then finally 5 is vertical from <2 so it is congruent, so <2 must be 65, so all angles are 65 degrees.
Daisy looked at the table shown and claimed that for every integer value, the expression -x < x is true.
Enter an integer value that proves Daisy's claim is not true.
Please help!!
Find the volume of the sphere
Answer:
Hi , your answer is V = 4/3 πr³.
Hope this helps
Find the slope of the line below . Enter your answer as a fraction or decimal. Use a slash mark ( / ) as the fraction bar if necessary
Answer:
Slope m = [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
[tex]x_{1}=-6\\ y_{1}=-4\\\\x_{2}=2\\y_{2}=1\\\\[/tex]
def. of slope = rise over run
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{2}}[/tex]
so:
[tex]\frac{1-(-4)}{2-(-6)} = \frac{1+4}{2+6} = \frac{5}{8}[/tex]
We get [tex]\frac{5}{8}[/tex] as our slope
The slope of the line in the graph is 5/8.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
As we observe the graph the line is passing from points (-6, -4) and (2, 1)
Slope = 1+4/2+6
=5/8
Hence, the slope of the line in the graph is 5/8.
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A premature baby needed to gain weight before being released from the hospital. She weighed 3 pounds 6
ounces. She needed to weigh 5 pounds 8 ounces. What is the percent of change?
Round to the nearest whole number.
Answer:
Step-by-step explanation:
When all the sides of a square is reduced by half, the new area is 108 cm square smaller than the old area. What is the new perimeter of the square?
Answer:
41.60
Step-by-step explanation:
[tex]\sqrt{108}[/tex]=10.39230485=10.40
10.40+10.40+10.40+10.40=41.60
10.40*2=20.80
[tex]20.80^{2}[/tex]=432.64
Brainliest if correct
Answer:
u⁷
Step-by-step explanation:
When multiply variables with exponents , all you do is add the exponents
so,
our powers are 3,3,1 (because no exponent means to the power of 1)
Adding the powers is 7
so u⁷
Answer:
[tex]u^{7}[/tex]
Step-by-step explanation:
In exponent multiplication, if bases are same just add the exponents.
[tex]a^{m}*a^{n}=a^{m+n}\\\\\\u^{3}*u^{3}*u = u^{3+3+1}=u^{7}[/tex]
In March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost $1382. They start with $125. At the
beginning of each month they plan to deposit 20% more than the previous month Will they have enough money for their trip? If not, how much more do they need?
Answer:
no and they need 936 more dollars
Step-by-step explanation:
Solve the inequality for z.
23 7-6
Simplify your answer as much as possible.
D>
DO
Answer:
[tex]z \leqslant 29[/tex]
Step-by-step explanation:
[tex] - z \geqslant - 6 - 23[/tex]
[tex] - z \geqslant - 29[/tex]
[tex]z \leqslant 29[/tex]
You please tell me if it’s A,B,C,D
The difference between two numbers is 108. Six times the smaller is equal to 7 more than the larger. What are the numbers?
Answer:
The smaller number is 23.
The bigger number is 131.
Step-by-step explanation:
"difference" means subtraction. In this question "more than" means adding. This can be done with one variable. And would take more reasoning with the meaning of the words, but less complicated algebra.
If you are learning systems of equations in high school or college, then you may want to use two variables. The set up is way more straight forward. But then you also need strategies to solve a system of equations.
There are two solutions attached. You only need one that matches the math you are studying. see images.
Terry rides his bicycle 4/5 mile in
6 minutes. If he continues at this rate,
how far will he travel in 21 minutes?
WILL MARK BRAINLIEST!!!
Based on the graph, which statement appears to be true?
A. The minimum point on the graph of k is (3, 16).
B. The graph of k has a y-intercept of 10.
C. The axis of symmetry of the graph of k is y = 3.
D. The graph of k has an x-intercept at (-1,0).
Answer:
C is right ಠ_ಠ