Rounded it is 11.7 cubic cm.
Week 3 Day 14 – POD
On Friday, Mica has $22.50 in her bank account. Mica goes to the market to get
groceries for the week and ends up spending more than planned. When Mica checks
her account, she now has a balance of $-48.15. How much money did Mica spend at
the market?
Show or explain your work in the space below:
Can u plz help me create a model to solve the math problem plz?
Answer: Mica spent $70.65
Step-by-step explanation:
Mica's bank balance before shopping = $22.50
Mica's bank balance after shopping = - $48.15
Mica's spending could be calculated by:
Difference between initial and final bank balance.
Hence,
[(Bank balance before shopping - (bank balance after shopping)]
[$22.50 - (-$48.15)]
= $22.50 + 48.15
= $70.65
PLSSSS HELPPP>> Show work solve the sysytem- y=1/2x^2+4x+4 y=-4x+12 1/2
Answer:
The solution is (-17,80.5) and (1,8.5)
Step-by-step explanation:
Equation 1 : [tex]y=\frac{1}{2}x^2+4x+4[/tex]
Equation 2: [tex]y = -4x+12.5[/tex]
Substitute the value of y from equation 2 in equation 1
Equation 1 : [tex]y=\frac{1}{2}x^2+4x+4[/tex]
After substitution :
[tex]-4x+12.5=\frac{1}{2}x^2+4x+4\\\frac{1}{2}x^2+8x+4-12.5=0\\\frac{1}{2}x^2+8x-8.5=0\\x^2+16x+17=0\\x=-17,2[/tex]
Substitute the value of x = -17
y = -4x+12.5
y = -4(-17)+12.5
y=80.5
Substitute the value of x = 1
y = -4(1)+12.5
y=8.5
Hence the solution is (-17,80.5) and (1,8.5)
Which inequality is equivalent to \-41 <9?
0-9 > X-4 < 9
-9 < x-4 < 9
O X-4<-9 or x – 4 < 9
hry 4 > -9 or x - 4<9
Find the volume of a pyramid with a square base, where the side length of the base is
15.3 m and the height of the pyramid is 19.6 m. Round your answer to the nearest
tenth of a cubic meter.
Answer:
1529.4 m^3
Step-by-step explanation:
We will use the formula V = 1/3*h*B for the volume of the pyramid, where V is volume, h is height, and B is are of the base.
First, since we know h and are looking for V, we need B. To find this, since it has a square base, we multiply b, the base length, by itself. 15.3m * 15.3m = 234.09m^2.
Next, we plug into the formula.
V = 1/3*19.6m*234.09m^2
And simplify:
V= 1/3 * 4,588.164m^3
V= 15.29.3879....
Last, round to the tenth
1529.4 m^3
Answer: 1529.4
Step-by-step explanation:
Use the following data set to find the sample statistics for the following data set. 1. (N) or (n) 2. (x-bar) or (μ) 3. (σ) or (s) Thanks!
Answer:
(1) N or n = 20
(2) [tex]\bar X \text{ or } \mu[/tex] = 43.4
(3) σ = 9.78 and s = 10.04.
Step-by-step explanation:
We are given with the following data set below;
{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}
(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.
(2) The formula for calculating Mean of the data, i.e. [tex]\bar X \text{ or } \mu[/tex] is given by;
Mean = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{51 +48+ 42+ 43+48+48+ 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42}{20}[/tex]
= [tex]\frac{868}{20}[/tex] = 43.4
So, the value of [tex]\bar X \text{ or } \mu[/tex] is 43.4.
(3) The formula for calculating population standard deviation ([tex]\sigma[/tex]) is given by;
Standard deviation, [tex]\sigma[/tex] = [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{N} }[/tex]
= [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20} }[/tex]
= 9.78
Similarly, the formula for calculating sample standard deviation (s) is given by;
Sample Standard deviation, s = [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20-1} }[/tex]
= 10.04
How is the graph of y = 2 (3)^x+1 -4 translated from the graph of y = 2(3)^x
Answer:
f(x - n) - shift the graph n units right
f(x + n) - shift the graph n units left
f(x) - n - shift the graph n units down
f(x) + n - shift the graph n units up ----------------------------------------------------------------------------
Answer: shift the graph of y = 2(3)ˣ one unit right and four units up.
PLEASE HELP GUYS ILL REWARD BRAINLIEST
Answer:
Step-by-step explanation:
(2,6)
Answer:
The solution of the two equations is where both lines intersect
From the graph they intersect at point
(6,2)
So the solution is x = 6 y = 2
Hope this helps you
On which number line do the points represent negative seven and one over two and +1? Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed in between the 6th and 7th tick marks to the left of 0. Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed on the 1st tick mark to the right of 0 Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed in between the 7th and 8th tick marks to the right of 0. Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed is placed on the 1st tick mark to the left of 0. A point labeled T is placed between the 6th and 7th tick marks to the right of 0.
Answer:
A number line is used in the mathematical positioning of real numbers that include the numbers from positive infinity to negative infinity. This includes rational, irrational, fractions, and whole numbers. In this case, we are given with an expression that we have to reduce to lowest terms: negative seven and one over two and +1. The first one is equal to -7.5 while the other one is equal to +1. Positive numbers lie on the right side of zero (center of the line) while negative numbers lie on the left on the other hand. -7.5 lies between -8 and -7 while +1 lies exactly between 0 and 2. Both of which are positive numbers
I hope that is what your asking...
Answer:
On which number line do the points represent negative seven and one over two and +1? The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed in between the 6th and 7th tick marks to the left of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed on the 1st tick mark to the right of 0 Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed in between the 7th and 8th tick marks to the right of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed between the 6th and 7th tick marks to the right of
Step-by-step explanation:
Solve the system of equations: y²-x²=16, x²-y²=16 (explain and show work) Will name most brainy
=====================================================
Explanation:
Rearrange the first equation into [tex]-x^2+y^2 = 16[/tex]
So we have this equivalent system
[tex]\begin{cases}-x^2+y^2 = 16\\\\x^2-y^2=16\end{cases}[/tex]
If you add the terms straight down, then you'll find that the x^2 and y^2 terms add to 0. The right hand side terms add to 16+16 = 32
We are left with the equation 0 = 32, which is a false equation or contradiction. Therefore, there are no solutions. We say the system is inconsistent. The two graphs do not intersect at all as shown in the diagram below. We have two hyperbolas in which the branches extend off to infinity to slowly approach the asymptotes. They never actually get to the asymptotes, but only get closer.
Translate into an algebraic expressions: x is increased by 50% and decreased by 30% . What is the result?
Answer: 1.05x
Step-by-step explanation:
From the question, we are informed to translate into an algebraic expressions: x is increased by 50% and decreased by 30%. This will be calculated thus:
Firstly, we'll increase x by 50%.
= x + (50% of x)
= x + (0.5 × x)
= x + 0.5x
= 1.5x
Then, we'll decrease 1.5x by 30%. This will be:
= 1.5x - (30% × 1.5x)
= 1.5x - (0.3 × 1.5x)
= 1.5x - 0.45x
= 1.05x
The answer is 1.05x.
Answer:
1.05x
Step-by-step explanation:
Miracle Maid Service charges a $30 house visit fee plus $5 per room to clean a house. What is the independent variable? A) The price per room B) The number of rooms C) The house visit fee D) The Miracle Maid Service
Answer:
B
Step-by-step explanation:
The independent variable is the variable who's variation doesn't depend on the other. Therefore the answer is B because the amount of rooms doesn't depend on the charge, the charge depends of the amount of rooms.
Lines AB and CD (if present in the picture) are straight lines. Find x. Give reasons to justify your solutions.
Answer:
WORDS: The value of x is 15.
EQUATION: x = 15
Step-by-step explanation:
1. AB is a straight line therefore angles AOF, FOG, and GOB total 180º
2. If ∠FOG = 90º, AOF + GOB = 90º by subtraction & substitution property
3. 5x - 15 + 2x = 90 (now solve) --> by substitution
4. 7x - 15 = 90 --> by C.L.T. or Combine Like Terms
5. 7x = 105 --> by C.L.T. or Combine Like Terms
6. x = 15 --> by inverse operations (division)
Hope this helps!
What are the units for the variable in the following scenario?
Sherry bought 6 apples at 43° per apple. She then bought 4 oranges at 51c
per orange. How much was her grocery bill?
Answer:
Her grocery bill is $4.62
Step-by-step explanation:
The first step is to multiply 6 and .43 to get how much it was for all of the apples.
Then the next step is to do the same thing with the oranges.
Then the last step is to add the two together.
Answer:
$4.62
Step-by-step explanation:
PLLLEASEEEEE!!!!!
Find the value of v and w.
Answer:
v=20, w=80
Step-by-step explanation:
First, we can find v by determining that angle 5v and angle 4v and supplementary to each other. This means that their sum adds up to 180 degrees.
5v + 4v=180
9v=180
v=20
We also know 4v is equivalent to w.
4(20)=w
w=80
Answer:
Step-by-step explanation:
5v + 4v = 180 {co-interior angles}
9v = 180
v = 180/9
v = 20
Angles opposite to equal sides are equal.
So, w = 4v
w = 4*20
w = 80
The least of 3 consecutive integers is a, and the greatest is z. What is the value of a + 2z/ 2 in terms of a?
Answer:
The value of a + 2z/ 2 in terms of a is (3a+4)/2
Step-by-step explanation:
least of 3 consecutive integers is a, and the greatest is z
if a is the least one
we know that integers differ by value of 1.
example -2, -1, 0, 1,2
they all differ by
then next consecutive integer will be a+1
third integer will be second integer +1 = a+1 + 1 = a+2
Thus, 3 consecutive integer
a , a+1, a+2
but given that greatest is z
thus, a+2 is greatest and hence
a+2 = z
we have to find value of a + 2z/ 2 in terms of a
a + 2z/ 2 = a + 2(a+2)/2 = (a+ 2a +4)/2 = (3a+4)/2.
The value of a + 2z/ 2 in terms of a is (3a+4)/2
h(t)=-16t^{2}+100t+10 find the domain and range. please
Answer:
Step-by-step explanation:
The graph of this function is that of a parabola that opens down (due to the negative coefficient of t^2). The axis of symmetry is
-b -100
x = --------- = ----------- = 50/16 = 25/8.
2a 2(-16)
The y value of the vertex is h(25/8) = -16(25/8)^2 + 100(25/8) + 10, or 166/25.
The largest value this function can take on is 166/25. Thus, the range is
(-infinity, 166/25).
Since the given function is a polynomial, the domain consists of all real numbers.
What is the surface area of a can that has radius of 9 ft. and height of 3 ft.? SA = __________ ft.2. Use 3.14 for pi. A. 678.2 B. 458.6 C. 354.3 D. 292.0
Answer:
678.2
Step-by-step explanation:
To find the surface area you need to use the expression [tex]2\pi rh + 2\pi r^2[/tex]
When you substitute the numbers in you get 678.24
The surface are of the can that has radius of 9 ft. and height of 3 ft is 678.2 ft².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The surface area of the can is the sum of the area of the bases of the can and the lateral surface area of the can. Therefore, the total surface area of the can is,
The surface area of can = 2(Area of base) + Lateral surface area of can
= 2(πr²) + 2πrh
= 2[π×(9 ft)²] + (2 × π × 9ft × 3ft)
= 508.8 ft² + 169.4 ft²
= 678.2 ft²
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How many solutions does this equation have?
x=y - 3
2x - 2y = - 6
1. NO SOLUTION
2. ONE SOLUTION
3. INFINITE NUMBER OF SOLUTIONS
Answer:
option 2 is correct ans. it can be solved by substitution method.
Which set of ordered pairs below is a function?
I.{(3,3),(6,1),(2,3)} .................. II.{(4,7),(2,8),(4,2)} .............. III.{(9,6),(3,1),(7,3)}
(((((((A I only )))))))) ((((( B II only ))))))) ((((((( C III only)))))) (((D I and III))))
Answer:
C
Step-by-step explanation:
if the first and third of three consecutive odd integers are added, the result is 75 less than five times the second integers. find the third integer. please show work
Answer:
The third integer is 27
Step-by-step explanation:
Given
Represent the consecutive odd numbers with [tex]T_1, T_2; and\ T_3[/tex]
Since they are consecutive odds, then
[tex]T_2 = 2 + T_1[/tex]
[tex]T_3 = 2 + T_2[/tex]
From the first statement in the question, we have that
[tex]T_1 + T_3 = 5 T_2 - 75[/tex]
Required
Find the third integer
Recall that
Substitute [tex]T_2 = 2 + T_1[/tex] in [tex]T_3 = 2 + T_2[/tex]
[tex]T_3 = 2 + 2 + T_1[/tex]
[tex]T_3 = 4 + T_1[/tex]
Substitute [tex]T_3 = 4 + T_1[/tex] and [tex]T_2 = 2 + T_1[/tex] in [tex]T_1 + T_3 = 5 T_2 - 75[/tex]
[tex]T_1 + 4 + T_1 = 5(2 + T_1) - 75[/tex]
Open Brackets
[tex]T_1 + 4 + T_1 = 10 + 5T_1 - 75[/tex]
Collect like terms
[tex]T_1 + T_1 + 4 = 5T_1 - 75 + 10[/tex]
[tex]2T_1 + 4 = 5T_1 - 65[/tex]
Collect like terms
[tex]2T_1 - 5T_1 = - 65 - 4[/tex]
[tex]-3T_1 = - 69[/tex]
Divide both sides by -3
[tex]\frac{-3T_1}{-3} = \frac{- 69}{-3}[/tex]
[tex]T_1 = 23[/tex]
Recall that [tex]T_3 = 4 + T_1[/tex]
[tex]T_3 = 4 + 23[/tex]
[tex]T_3 = 27[/tex]
The third integer is 27
You can buy shampoo in a 6 oz bottle for 2.79 or in a 14 oz bottle for 10.89
Answer:
Step-by-step explanation:
Find and compare the unit costs of the two different bottle sizes.
First:
$2.79/(6 oz) = $0.465/oz
Second:
$10.89/(14 oz) = $0.778/oz
Clearly, the larger (14 oz) bottle is a much better buy
Answer: 14oz bottle for 10.89
Step-by-step explanation:
Did it before
Simplify:$$\sqrt{2\sqrt{8^2+15^2}+\sqrt{9^2+40^2}}$$
Answer:
[tex]5\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{2\sqrt{8^2+15^2}+\sqrt{9^2+40^2}}=?\\\\1)\sqrt{8^2+15^2}=\sqrt{289}=17\\2)\sqrt{9^2+40^2}=\sqrt{1681}=41\\3)2\times17=34\\4)\sqrt{34+41}=5\sqrt{3}[/tex]
All Done!
Answer:
Your correct answer is 8.660254
Step-by-step explanation:
√2√82 + 152 + √92 + 402 = 8.660254
65.
Evaluate a-b+c for?
Answer:
From the problem, the answer to the equation is 5 1/10
Step-by-step explanation:
First, let's gather the information from the problem.
a = 4 1/5 (also can be turned into 21/5)
b = 2 7/20 (also can be turned into 47/20)
c = 3 1/4 (also can be turned into 13/4)
Now, plug in the numbers using the improper fractions.
21/5 - 47/20 + 13/4
Turn the denominators into the same number.
84/20 - 47/20 + 65/20
Subtract 84/20 and 47/20.
37/20 + 65/20
Add 37/20 and 65/20.
102/20 or 5 1/10
So, your answer to this equation is 5 1/10.
Compare the fractions.
Use <,=,or>. 1/3 4/6
Answer:
1/3 < 2/3
Step-by-step explanation:
1/3 compared to 4/6
Simplify 4/6 by dividing the top and bottom by 2
4/5 = 2/3
Since the denominators are the same we compare the numerators
1/3 < 2/3
The perpendicular bisector of the line segment connecting the points (-3,8) and (-5,4) has an equation of the form y = mx + b. Find m+b. BTW, the answer is not 16...
Answer:
Step-by-step explanation:
find the slope
[tex]\frac{4-8}{-5-(-3)} =\frac{-4}{-2} \\\\slope=2\\y=mx+b\\y=2x+b\\[/tex]
take a coordinate to fill in
[tex](-5,4)\\y=-5\\x=4\\-5=2(4)+b\\-5=8+b-8 -8\\-13=b\\[/tex]
this means that the equation is y=2x-13
and if you add m and b
you get :-11
I HOPE THIS HELPS
Answer:
7/2
Step-by-step explanation:
Let $A = (-3,8)$ and $B = (-5,4)$. The midpoint of $\overline{AB}$ is $\left( \frac{(-3) + (-5)}{2}, \frac{8 + 4}{2} \right) = (-4,6)$.
The slope of $\overline{AB}$ is $\frac{8 - 4}{(-3) - (-5)} = 2$, so the slope of the perpendicular bisector of $\overline{AB}$ is $-\frac{1}{2}$. Therefore, the equation of the perpendicular bisector is given by
\[y - 6 = -\frac{1}{2} (x + 4).\]Isolating $y,$ we find
\[y = -\frac{1}{2} x + 4.\]
Christina's family is building a house. On the blueprint, Christina's rectangular room measures 10cm by 12cm. The map has a scale of 1 cm=1.5 ft. What is the actual area of Christina's room?
Answer:
270 ft square
Step-by-step explanation:
10cm * 1.5ft = 15 ft
12cm * 1.5ft = 18ft
18ft * 15ft = 270ft square
Answer:
270 sq ft
Step-by-step explanation:
A principle of $2400 is invested at 7.5% interest, compounded annually. How many years will it take to accumulate $6000 or more in the account? Write the smallest possible whole number answer.
Step-by-step explanation:To find the interest accumulated over a period of time you use:
A = P [1 + (r/n)]^(nt)
with A = new amount in the account, P = principal, r = percent rate as a decimal, n = how many times you compound during one year, t = time in years.
A = 2000
P = 1500
r = 0.035
n=1
Thus you get:
2000 = 1500 (1+0.035)^t
Divide by 1500:
(4/3) = (1.035)^t
Apply "ln" on both sides:
ln(4/3) = t*ln(1.035)
Calculate the logarithms:
0.28768 = t*0.03440
Divide by 0.03440 on both sides:
t = 8.36 years
So after approximately 8 years and 5 month you will have $2000 or more in the account.
Need help ASAP the numbers are correct I just need to know the other missing numbers
Step-by-step explanation:
1.32:24
32/8:24/8
4:3
2.20:32
20/4:32/4
5:8
3.24:76
24/4:76/4
6:19
4.24:32:20
24/4:32/4:20/4
6:8:5
Which point is a solution of x + 2y ≤ 4?
Answer:
0 = x, y = 2.
Or x = 2 and y = 1.
Step-by-step explanation:
≤ means less than or equal to.
This rectangular frame is made from 5 straight pieces of metal.
5 m
12 m
The weight of the metal is 1.5 kg per metre.
Work out the total weight of the metal in the frame.
Answer:
Total weight = 70.5 kg
Step-by-step explanation:
Rectangular frame is made from 5 straight pieces of metal. One of them goes through the diagonal of the rectangle.
2 pieces form the length of the rectangular frame, hence, they have a length of 12 m each
2 pieces from the width of the rectangular frame, hence, they a length of 5 m each
To find the length of the diagonal, we can use Pythagoras Theorem:
Hypotenuse² = Base² + Perpendicular²
Hypotenuse² = 5² + 12²
Hypotenuse² = 169²
Hypotenuse = 13
Hence, the length of the piece of metal placed at the diagonal is 13cm
Find the sum of all lengths of the metal pieces.
Total length = 12 + 12 + 5 + 5 + 13
Total length = 47 m
Total weight = 1.5 × Total length
Total weight = 1.5 kg/m × 47m
Total weight = 70.5 kg
The total weight of the metal in the frame is 70.5 kg
If a rectangular frame is made from 5 straight pieces of metal, with a length of 5m and a width of 12m
Get the diagonal
[tex]d^2= 5^2 + 12^2\\d^2 = 25 + 144\\d^2 = 169\\d= 13m[/tex]
Get the perimeter of the rectangular frame:
Perimeter of the frame = 2(5 + 12) + 13
Perimeter of the frame = 2(17) + 13
Perimeter of the frame = 34 + 13
Perimeter of the frame = 47m
If the weight of the metal is 1.5 kg per metre, the total weight will be expressed as:
Total weight = 47 * 1.5
Total weight = 70.5kg
Hence the total weight of the metal in the frame is 70.5 kg
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