1. Ewa has 20 balls of four colors: yellow, green, blue, and black. 17 of them are not green, 5 are black, and 12 are not yellow. How many blue balls does Ewa have? (Use Gaussian elimination method).
Answer:
In a bag of balls, 1/4th are green, 1/8th are blue, 1/12th are yellow and the remaining 26 are white. How many balls are blue?
There are 4 colours of balls - green, blue, yellow and white.
Add (1/4)+(1/8)+(1/12) = (6/24)+(3/24)+(2/24) = 11/24 so the balance or (24–11)/24 = 13/24 = 26 white. Hence the total number of balls are 2*24 = 48.
Of the 48 balls, green are (1/4)*48 = 12, blue are (1/8)*48 = 6, yellow are (1/12)*48 = 4 and the rest, white are 26.
Check: Total number of balls = 12+6+4+26 = 48
Answer: 6 balls are blue....
If a= 3 and b= 5; find
(a+b)
Answer: 3/8
Step-by-step explanation:
A=3
B=5
3/3+5=3/8
please help! thanks!
find y.
Answer:
y = 4
Step-by-step explanation:
The ratio of the lengths of the sides of a 30-60-90 triangle is
1 : √3 : 2
The sides in this triangle are in the order:
y : 4√3 : x
y/1 = 4√3/√3
y = 4
A. The interquartile range is 55
B.Three fourths of the data is less than 65
C. The median of the upper half of the data is 65
D. The median if the data is 55.
Answer:
d the median if the data is 55
Find the length of FT
Step-by-step explanation:
Hey there!
From the given figure;
Angle FVT = 43°
VT = 53
Taking Angle FVT as reference angle we get;
Perpendicular (p) = FT = ?
Base (b) = VT = 53
Taking the of tan;
[tex] \tan( \alpha ) = \frac{p}{b} [/tex]
Keep all values and simplify it;
[tex] \tan(43) = \frac{ft}{53} [/tex]
0.932515*53 = FT
Therefore, FT= 49.423.
Hope it helps!
Answer:
A. 49.42
Step-by-step explanation:
tan 43 = FT ÷ VT
0.932515086 = FT ÷ 53
49.42 = FT
3. Solve the system of equations using the elimination method.
5x + 2y = 9
-5x + 4y = 3
please give detailed steps!!
Answer:
x = 1
y = 2
Step-by-step explanation:
5x + 2y = 9
-5x + 4y = 3
==> 6y = 12 ==> y = 12/6 ==> y = 2.
we replace y by its value in the first or the second equation, so will have:
5x + 2×2 = 9
5x + 4 = 9
5x = 5
x = 1
In a high school graduating class of 300, 200 students are going to college, 40 are planning to work full-time, and 80 are taking a gap year.
a. These are mutually exclusive events.
b. These are not mutually exclusive events.
c. You should add their individual probabilities.
d. None of the above are true.
if f(x)=x+7 and 9(x)=1/x-13 what is the domain of (f•g)(x)
Answer:
The only limitation is x≠0
The interval notation is (-∞,0)∪(0,∞)
Step-by-step explanation:
Set up the expression.
[tex](x+7)*(\frac{1}{x}-13)[/tex]
Multiply using FOIL.
[tex](x*\frac{1}{x})+(x*-13)+(7*\frac{1}{x})+(7*-13)[/tex]
[tex]1-13x+\frac{7}{x}-91[/tex]
[tex]-13x+\frac{7}{x}-91[/tex]
Find the Domain.
The only limitation is x≠0
The interval notation is (-∞,0)∪(0,∞)
A right triangle has sides 20 and 48. Use the Pythagorean Theorem to find the length of the hypotenuse
Answer: Let the length of the hypotenuse be x
Applying the Pythagorean theorem we have :
x²=20²+48²
⇒x²=2704
⇒x=52( ∀ x >= 0 )
Step-by-step explanation:
Let assume the hypotenuse(longest side of right triangle) be x
By Pythagoras theorem
[tex] \bf \large \longrightarrow \: {c}^{2} \: = \: {a}^{2} \: + \: {b}^{2} [/tex]
c = xa = 20b = 48Applying Pythagoras theorem
[tex] \bf \large \implies \: {x}^{2} \: = \: {20}^{2} \: + \: {48}^{2} [/tex]
[tex]\bf \large \implies \: {x}^{2} \: = \:400 \: + \: 2304[/tex]
[tex]\bf \large \implies \: {x}^{2} \: = \:2704[/tex]
[tex]\bf \large \implies \: \sqrt{x} \: = \: \sqrt{2704} [/tex]
[tex]\bf \large \implies \: \: x \: = \: 52[/tex]
Hence , the length of hypotenuse is 52.
Find the quotient of 90 over -10
90/-10
= 9/-1
= -9
So, -9 is the quotient.
answer no explantion pls i need asap
Answer:
Below.
Step-by-step explanation:
Area = 5(x + 3)
= 5x + 15
Perimeter = 2(x + 3) + 2(5)
= 2x + 6 + 10
= 2x + 16.
Payton took a friend for a birthday dinner. The total bill for dinner was $44.85 (including tax and a tip). If Payton paid a 19.5% tip, what was his bill before adding the tip?
(Round your answer to the nearest cent.)
$
Number
Answer:
The answer closest to 36.10425. So 36.10 or 36.1
Step-by-step explanation:
x = 44.85 ( 1 - 0.195) = 36.10425
If this helps, it would be nice if 5 stars are given, and a brainliest :)
The amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
For this case, we can assume the amount of bill without tip being A.
Then, as given, Payton gave 19.5% tip (tip is given assumingly on A), then:
Total price of the bill = Bill amount before tip + Tip
44.85 = A + (19.5 % of A)
(we don't write symbols like of currency generally in equations, and understand it from context(which is dollars here))
44.85 = A + (19.5 % of A)
or
[tex]44.85 = A + \dfrac{A}{100} \times 19.5\\\\\text{Multiplying 100 on both the sides}\\\\4485 = 100A + 19.5A\\4485 = 119.5A\\\\\text{Dividing both the sides by 119.5}\\\\\dfrac{4485}{119.5} = A\\\\37.53 \approx A\\\\A \approx 37.53 \: \rm \text{(in dollars)}[/tex]
Thus, the amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.
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If the white rod is 1/3, what color is the whole??
Answer:
brown
Step-by-step explanation:
it might be brown because it compelled
8 thousand+7tens=6thiusand+. tens
Answer:
207 tens
Step-by-step explanation:
If you mean
8,000 + 70 = 6000 + X tens
then it should be 207 tens
If x = 1, y = 7, and z = 15, determine a number that when added to x, y, and z yields
consecutive terms of a geometric sequence. What are the first three terms in the
geometric sequence?
You're looking for a number w such that the numbers
{1 + w, 7 + w, 15 + w}
form a geometric sequence, which in turn means there is a constant r for which
7 + w = r (1 + w)
15 + w = r (7 + w)
Solving for r, we get
r = (7 + w) / (1 + w) = (15 + w) / (7 + w)
Solve this for w :
(7 + w)² = (15 + w) (1 + w)
49 + 14w + w ² = 15 + 16w + w ²
2w = 34
w = 17
Then the three terms in the sequence are
{18, 24, 32}
and indeed we have 24/18 = 4/3 and 32/24 = 4/3.
4) Daily tickets to Six Flags cost $50 each.
Variable #1:
What is the variable
Answer:
Amount of tickets
Step-by-step explanation:
The variable is the amount of tickets purchased because that is the only thing that changes, according to the statement that says that daily tickets are $50.
What is the probability of randomly picking a red marble from a bag of 10 green marbles, 10 yellow marbles, and 5 red marbles?
Answer
20%
Step-by-step explanation:
Jane and her two friends will rent an apartment for S550 a month, but Jane will pay double what each friend does because she will have her own bedroom.
How much will Jane pay a month?
Answer:
$275 a month
Step-by-step explanation:
Let x represent how much each friend is paying.
The amount Jane pays can be represented by 2x, since she is paying double than her friends.
Add together these terms and set them equal to 550. Then, solve for x:
x + x + 2x = 550
4x = 550
x = 137.5
So, each friend is paying $137.50. Double this to find how much Jane is paying:
137.5(2)
= 275
So, Jane is paying $275 a month
Which point on the number line shows the graph of
Answer:
the correct answer is point b
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis.
Using the shell method, the volume integral would be
[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx[/tex]
That is, each shell has a radius of x (the distance from a given x in the interval [0, 2] to the axis of revolution, x = 0) and a height equal to the difference between the boundary curves y = x ⁸ and y = 256. Each shell contributes an infinitesimal volume of 2π (radius) (height) (thickness), so the total volume of the overall solid would be obtained by integrating over [0, 2].
The volume itself would be
[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx = 2\pi \left(128x^2-\frac1{10}x^{10}\right)\bigg|_{x=0}^{x=2} = \boxed{\frac{4096\pi}5}[/tex]
Using the disk method, the integral for volume would be
[tex]\displaystyle \pi \int_0^{256} \left(\sqrt[8]{y}\right)^2\,\mathrm dy = \pi \int_0^{256} \sqrt[4]{y}\,\mathrm dy[/tex]
where each disk would have a radius of x = ⁸√y (which comes from solving y = x ⁸ for x) and an infinitesimal height, such that each disk contributes an infinitesimal volume of π (radius)² (height). You would end up with the same volume, 4096π/5.
The volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have a function:
[tex]\rm y = x^8[/tex] or
[tex]x = \sqrt[8]{y}[/tex]
And y = 256
By using the vertical axis of rotation method to evaluate the volume of the solid formed by revolving the region bounded by the curves.
[tex]\rm V = \pi \int\limits^a_b {x^2} \, dy[/tex]
Here a = 256, b = 0, and [tex]x = \sqrt[8]{y}[/tex]
[tex]\rm V = \pi \int\limits^{256}_0 {(\sqrt[8]{y}^2) } \, dy[/tex]
After solving definite integration, we will get:
[tex]\rm V = \pi(\frac{4096}{5} )[/tex] or
[tex]\rm V =\frac{4096}{5}\pi[/tex] cubic unit
Thus, the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.
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Which of the following is a monomial?
A. 8x^2 +7x+3
B. √x-1
C. 9/x
D. 7x
Answer:
7x is monomial according to question.
Find the area (in square feet) of a rectangle that measures 17" × 3'10".
Answer:
65 feet and 2 inches
Step-by-step explanation:
to find the area of a rectangle you need to multiply length times width in this case 17" times 3'10". But first you must convert everything into the same form(in this case feet) so first you can convert everything to inches by multiplying 3 times 12 which gives you 36 then add the 10, so it is now 46 inches then multiply that by 17 and altogether it is 782 inches, then divide by 12 (to convert it back to feet) and the answer is 65.1666666667. After you can round and get 65 feet and 2 inches.
purchased a book rs 500 sold 20%profit find its actual profit and sel
ling price
Answer:
Selling price=rs.600.
Profit of rs=100.
Step-by-step explanation:
C.P=500; profit%=20%
S.P.=100+profit%×C.P/100
S.P=120×500/100
=rs.600
S.P>C.P
Profit S.P-C.P
600-500=100
he gained for rs.100.
How would A = L + O be rewritten to solve for O?
Answer:
A - L = O
Step-by-step explanation:
A = L + O
Subtract L from each side
A-L = L + O - L
A - L = O
The way that the given formula A = L + O can be rewritten to solve for O is; O = A - L
How to change subject of formula?We are given the formula to find A as;
A = L + O
Now, to make O the subject of the formula, let us use subtraction property of equality to subtract L from both sides to get;
A - L = L + O - L
O = A - L
Thus, the way the formula can be rewritten to solve for O is;
O = A - L
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Please helps fill in the charts
A and b
With order of pairs
Answer:
...
Step-by-step explanation:
seeee the above picture
What is the smallest number that has both 6 and 9 as a
factor?
A 54
B 12
C 36
D 18
Answer:
yep it's D
Step-by-step explanation:
work out missing angle following polygons
Answer:
x = 150°
Step-by-step explanation:
Interior angle of a hexagon = 120° and interior angle of a square = 90°
so remaining angle, 360-120-90 = 150°
A bicycle with 24-inch diameter wheels is traveling at 12 mi/h.
What is the exact angular speed of the wheels in rad/min?
Number rad/min:
How many revolutions per minute do the wheels make?
The answer must be rounded to three decimal places by the way.
9514 1404 393
Answer:
1056.000 radians per minute168.068 revolutions per minuteStep-by-step explanation:
The linear speed 12 mi/h translates to inches per minute as follows:
(12 mi/h) × (5820 ft/mi) × (12 in/ft) ÷ (60 min/h) = 12,672 in/min
The relationship between arc length and angle is ...
s = rθ
For a constant radius, the relationship between linear speed and angular speed is ...
s' = rθ'
θ' = s'/r = (12,672 in/min)/(12 in) = 1056 rad/min
There are 2π radians in one revolution, so this is ...
(1056 rad/min) ÷ (2π rad/rev) = 168.068 rev/min
A whitetail deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour? There are 5,280 feet in one mile.
Answer:
The Bison is faster by 10 miles per hour.
Step-by-step explanation:
The Bison runs at 3520 ft / min
= 3520/ 5280 miles / minute
= (3520/ 5280) * 60 miles per hour
= 40 miles per hour
please help me with this
Given:
d = 2
f = 4
To find:
Value of [tex]\frac{14(7)-d}{2f}[/tex]
Steps:
we need to substitute and then find the value,
[tex]= \frac{14(7)-2}{2(4)}\\ \\=\frac{98-2}{8} \\\\=\frac{96}{8}\\\\=12[/tex]
Therefore, the answer is option C) 12
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