Answer: 4/7
Step-by-step explanation:
You pick one black sock, meaning there are 14 socks remaining in the drawer, 8 of which are black. Thus, the probability is 8/14, which simplifies to 4/7.
In a mathematics test, Jack scored 17 marks more than Yazid while Susan scored twice Yazid's score. If their total score is 161, what is Jack's score?
Answer:
53
Step-by-step explanation:
Let yazid's score be x
x + x + 17 + 2x = 161
4x + 17 = 161
4x = 144
x = 36
jack = x + 17
jack = 53
Answer:
Jack: 36
Bonus: Yazid: 53 and Susan: 72
Step-by-step explanation:
Let J, Y, and K stand for Jack, Yazin, Susan's scores.
We are told that:
J = Y + 17 [Jack scored 17 marks more than Yazid]
S = 2Y [Susan scored twice Yazid's score]
J + Y + S = 161 [total score is 161]
Substitute the first two expressions into the last equation:
J + Y + S = 161
(Y+17) + Y + (2Y) = 161
4Y = 144
Y = 36
Use Y = 36 to find the other scores:
J = Y + 17
J = 36 + 17
J = 53
S = 2Y
S = 2*(36)
S = 72
CHECK:
Does 36+53+72 = 161?
YES
What is the domain of f(x) = 5x – 7?
{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}
Answer:
{x:x is a real number}
Since any value can replace x to give an integer.
{x:x is a real number}
Please please please help with b
The diameters of two circular pulleys are 6cm and 12 cm, and their centres
are 10cm apart.
a. Angle a = 72.54 degrees
b. Hence find, in centimetres correct to one decimal place, the length of a
taut belt around the two pulleys
The length of the belt around the two pulleys is approximately 49.2 centimeters.
How to determine the length of the belt around the two pulleys?
In this question we must determine the perimeter of a belt around two pulleys, whose centers are 10 centimeters apart. This perimeter is the sum of part of the circumference of small pulley, part of the circumference of the big pulley and two times the segment tangent to the two pulleys.
Now we proceed to determine the parts of the perimeter of the belt:
Big pulley
s' = (214.92° / 180°) · π · (6 cm)
s' ≈ 22.506 cm
Small pulley
s'' = (145.08° / 180°) · π · (3 cm)
s'' ≈ 7.596 cm
Tangent segments
l = (10 cm) · sin 72.54°
l ≈ 9.539 cm
Lastly, the perimeter of the belt is:
L = s' + s'' + 2 · l (1)
L = 22.506 cm + 7.596 cm + 2 · (9.539 cm)
L = 49.180 cm
The length of the belt around the two pulleys is approximately 49.2 centimeters.
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What is the area of the triangle?
Enter your answer in the box.
in²
Right triangle with sides forming the right traingle labeled 25 inches and 60 inches and the side across from the right angle labeled 65 inches.
Using it's formula, the area of the right triangle is of 750 inches squared.
What is the area of a right triangle?The area of a right triangle is given by half the multiplication of the two legs, which are the two smaller sides.
In this problem, the two legs are 25 inches and 60 inches, hence the area of the triangle is:
A = 0.5 x 25 x 60 = 750 inches².
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For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1? f (x) = startfraction 2 x superscript m baseline over x a endfraction
Using the concept of vertical and horizontal asymptotes, it is found that the function will have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1 for a = -1 and m = 1.
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.In this problem, the function is:
[tex]f(x) = \frac{2x^m}{x + a}[/tex]
It has a vertical asymptote at x = 1, hence:
x + a = 0
1 + a = 0
a = -1
It has a horizontal asymptote at y = 2, hence:
[tex]\lim_{x \rightarrow \infty} f(x) = 2[/tex]
[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x + a} = 2[/tex]
[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x} = 2[/tex]
[tex]2^{m-1} = 2[/tex]
Then, since we want to simplify, the exponents at the numerator and the denominator have to be equal, hence m = 1.
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When preparing a representative sample from a list of 200 customers who complained about errors in their statements, a _____ might select every tenth customer for review. a. stratified sample b. comprehensive sample c. random sample
When preparing a representative sample from a list of 200 customers who complained about errors in their statements, a systematic sample might select every tenth customer for review.
What is systematic random sampling?Systematic random sampling is known to be a form of a random sampling method that needs one to select samples using a system of intervals where one has ranges of numbered population.
Note that When preparing a representative sample from a list of 200 customers who complained about errors in their statements, a systematic sample might select every tenth customer for review.
See options below
a. stratified sample
b. comprehensive sample
c. random sample
d. Systematic sample
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let n be a natural number such that GCF(n, 70)= 10, and LCM(n, 70)=210. Find N. (Hint: Do you remember that LCM(A,B) x GCF(A, B)= A x B?)
The natural number , n is 30
How to determine the value
Given;
GCF(n, 70) = 10
LCM(n, 70) = 210
We have that;
LCM(A,B) x GCF(A, B)= A x B
Then,
(n, 70) = n × 70 = 70n
10 × 210 = 2100
Equate the two expressions
70n = 2100
n = [tex]\frac{2100}{70}[/tex]
n = [tex]30[/tex]
Thus, the natural number , n is 30
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Olympia ate lunch at a restaurant the amount of her check was $6.89 she left eight dollars on the table which included the amount she owed plus a tip for the waiter which equation shows t and the amount of her tip in dollars
The equation will be like this,
6.89 + t = 8.00
t = 8 - 6.89
t = 1.11
tips = $1.11
6.89 + t = 8.00
To sum up the total amount of cash and coins you have, first, sort each invoice and coin by denomination. Create a separate stack for each denomination and count how many denominations or coins you have.
For each denomination of banknotes and coins, multiply the number you have by the denomination. For example, if you have 4 out of $ 10, multiply by 4x10 to get $ 40. If you have three $ 5 bills, multiply by 3x5 to get $ 15.
Sum the totals to calculate the total amount.
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Write the standard equation of a circle that passes through(-4,0) with center (-1,-4)
The standard equation of the circle is x² + y² + 8x - 9 = 0 if the circle with center at (-1,-4) that passes through the point (-4,0).
According to the question,
The circle with center at (-1,-4) that passes through the point (-4,0).
To find the radius of the circle:
Radius r = √[(-4 - (-1))² + (0- (-4))²]
=√(-4+1)² + (4)²
=√9+16
=√25
=5.
In order to find the standard equation of the circle is
(x - (-4))² + (y - (0))² = (5)²
(x + 4)² + (y )² = 25
x² + 8x + 16 + y² = 25
x² + y² + 8x + 16 = 25
x² + y² + 8x = 25 - 16
x² + y² + 8x = 9
x² + y² + 8x - 9 = 0
Hence, the standard equation of the circle is x² + y² + 8x - 9 = 0.
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1. Prove the following identities
Answer:
Step-by-step explanation:
[tex]\sf 1.1)\dfrac{Sin \ \theta-Cos \ \theta}{Sin \ \theta + Cos \ \theta}=\dfrac{(Sin \ \theta-Cos \ \theta)}{((Sin \ \theta + Cos \ \theta)}*\dfrac{(Sin \ \theta-Cos \ \theta)}{(Sin \ \theta-Cos \ \theta)}[/tex]
[tex]\sf = \dfrac{(Sin \ \theta-Cos \ \theta)^2}{Sin^2 \ \theta-Cos^2 \ \theta}\\\\=\dfrac{Sin^2 \ \theta+Cos^2 \ \theta-2Sin \ \theta \ Cos\ \theta}{(Sin \ \theta-Cos \ \theta)}\\\\\\\bf Identity: \ (a +b)^2= a^2 + b^2 - 2ab\\\\\\=\dfrac{1-2Sin \ \theta \ Cos \ \theta}{(Sin \ \theta-Cos \ \theta)} = LHS[/tex]
[tex]\sf 1.2) LHS = tan^2 \ x - Sin^2 \ x = \dfrac{Sin^2 \ x}{Cos^2 \ x}-Sin^2 \ x[/tex]
[tex]\sf =\dfrac{Sin^2 \ x}{Cos^2 \ x}-\dfrac{Sin^2 \ x*Cos^2 \ x}{1*Cos^2 \ x}\\\\\\ = \dfrac{Sin^2 \ x - Sin^2 \ x*Cos^2 \ x}{Cos^2 \ x}\\\\\\= \dfrac{Sin^2 \ x *(1 -Cos^2 \ x)}{Cos^2 \ x}\\\\=\dfrac{Sin^2 \ x*Sin^2 \ x}{Cos^2 \ x} \\\\ \bf 1 - Cos^2 \ x = Sin^2 \ x\\\\= \dfrac{Sin^2 \ x}{Cos^2 \ x}*Sin^2 \ x\\\\=tan^2 \ x * Sin^2 \ x = RHS[/tex]
[tex]\sf 1.3) LHS = \dfrac{1-Cos \ x}{Sin \ x}-\dfrac{Sin \ x}{1+Cos \ x} =\dfrac{(1-Cos \ x)(1+Cos \ x)}{Sin \ x*(1+Cos \ x)}-\dfrac{Sin \ x*Sin \ x}{(1+Cos \ x)*Sin \ x}\\[/tex]
[tex]\sf =\dfrac{1 - Cos^2 \ x}{Sin \ x*(1+Cos \ x)}-\dfrac{Sin^2 \ x}{Sin \ x*(1+Cos \ x)}\\\\=\dfrac{Sin^2 \ x}{Sin \ x*(1+Cos \ x)} - \dfrac{Sin^2 \ x}{Sin \ x*(1+Cos \ x)}\\\\=\dfrac{Sin^2 x - Sin^2 \ x}{Sin \ x*(1+Cos \ x)} \\\\= 0 = RHS[/tex]
[tex]\sf 1.4) LHS = Sin x - \dfrac{1}{Sin \ x + Cos \ x}+Cos \ x \\[/tex]
[tex]\sf = \dfrac{Sin \ x *(Sin \ x + Cos \ x) - 1 + Cos \ x * (Sin \ x + Cos \ x)}{Sin \ x + Cos \ x }\\\\\\= \dfrac{Sin \ x * Sin \ x + Sin \ x*Cos \ x -1 + Cos \ x*Sin \ x + Cos \ x*Cos \ x}{Sin \ x + Cos \ x}\\\\\\=\dfrac{Sin^2 \x + Sin \ x \ Cos \ x - 1 + Cos \ x \ Sin \ x + Cos^2 \x}{Sin \ x + Cos \ x}\\\\=\dfrac{Sin^2 \ x + Cos^2 \ x - 1 + Sin \ xCos \x +Sin \ x Cos \ x}{Sin \ x + Cos \ x}\\\\= \dfrac{1 - 1 +2Sin \ x Cos \ x}{Sin \ x + Cos \ x}\\\\= \dfrac{2Sin \ x Cos \ x}{Sin \ x + Cos \ x}[/tex]
A rectangle is 2 feet long and
x+10) feet wide. What is the area?
A. (2x + 10) ft²
C. (22x) ft²
B. (2x + 20) ft²
D. (20x) ft²
Answer:
(2x + 20) ft^2.
Step-by-step explanation:
Area = length * width
= 2 * (x + 10)
= (2x + 20) ft^2.
Find the volume of the solid to the nearest whole cubic unit. use a calculator, if needed. yellow solid v = ______
The volume of the cuboid is 132 cubic inches.
Given length of cuboid 7 1/3 inches, breadth being 6 2/3 inches , height being 2 7/10 inches.
Volume is amount of liquid a container can hold in its capacity. Cuboid is a 3 dimensional figure having length , breadth and height.Volume of cuboid is the product of length, breadth and height of cuboid.
We have to calculate volume of cuboid.
We have to make a simple fraction showing length , breadth and height.
Length=(3*7+1)/3=22/3
Breadth=(3*6+2)/3=20/3
Height=(10*2+7)/10=27/10
Volume=22/3*20/3*27/10
=11880/90
=132 cubic inches.
Hence the volume of cuboid having length of 22/3 inches, breadth of 20/3 inches and height of 27/10 is 132 cubic inches.
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Question is incomplete as it should include figure.
Tristen is packing lunch boxes for the school trip. Each lunch box consists of 1 sandwich, 1 fruit, and 1 drink. Tristen can choose from 3 types of sandwiches, 4 types of fruit, and 2 types of drinks. How many different lunch boxes can Tristen pack
Answer:
24
Step-by-step explanation:
3x4x2=24
When finding the answer to this problem, you times all of the options by each other.
In a year of 365 days Paul skipped school for the months of January and February.
He had summer vacations for the months June to August. How many days of the
year (excluding Sundays) did he attend school?
The days of the year (excluding Sundays) paul attends school is 183 days
CalendarTotal days in a year = 365
Months Paul skipped school = January, February, June, July August
= 31 + 28 + 30 + 31 + 31
= 151 days
Days he attend school excluding Sunday = Total days in a year - (Months Paul skipped school + Sundays)
= 365 - (151 + 31)
= 365 - 182
= 183 days
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Putting the other player's king in check is always a good move. true or false subject: chess
Putting the other player's king in check is always a good move. true
What is chess?The policies of chess allow a king to take an opponent's piece whilst in check, so long as that piece isn't always being defended. At the equal time, a king in the test is usually forced to move.The standard regulations of chess, a participant may not make any pass that places or leaves their king in the test. A player may additionally pass the king, seize the threatening piece, or block the check with some other piece. A king cannot look at the opposing king, considering this will vicinity the first king in check as well.
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HELP MEEEEEEEEEEEEEEEE
Step-by-step explanation:
Well first let's find the derivative in using the power rule
h'(t) = (-4.9)t + 157
h'(t) = -9.8t + 157
we can see from the image above that the maximum height is 1452.602 so that is the answer to the second question.
h'(1452.602) = -9.8(1452.602) + 157
h' = 14,078.500
A rectangular piece of land measures 4.5 km long and 2.5 km wide
Calculate the ratio of
1.It's width to its length
2.Its length to its perimeter
The ratio of its width to its length is; 5 :9.
The ratio of its length to its perimeter is; 9: 28.
What is the ratio of its width to its length?1). From the task content, the land measures 4.5 km long and 2.5 km wide. Hence, the ratios is; 2.5: 4.5.
Therefore, we have; 5: 9 by expression as whole number ratios.
2) Since the perimeter of the rectangle is; 2(2.5+4.5) = 14.
The ratio of length to perimeter expressed simply is therefore; 9: 28.
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Simplify :-
(3x-2y) (3x+2y) (9x²+4y²)
Answer:
[tex]\huge\boxed{\sf 81x^4 - 16y^4}[/tex]
Step-by-step explanation:
Given expression:= (3x - 2y)(3x + 2y)(9x² + 4y²)
Using formula:[tex](a+b)(a-b)=a^2-b^2[/tex]= [(3x)² - (2y)²] (9x² + 4y²)
= (9x² - 4y²)(9x² + 4y²)
Using the above formula again
= (9x²)² - (4y²)²
= 81x⁴ - 16y⁴[tex]\rule[225]{225}{2}[/tex]
Sandy rakes and bags the leaves on her front lawn in 30 mins. Randy does the same job in 20 mins. How many fewer minutes will it take to complete the same job if sandy and randy work together than if sandy works alone?
The number of minutes it take to complete the same job if sandy and randy work together than if sandy works alone is 18mins.
How to calculate time?According to this question, Sandy rakes and bags the leaves on her front lawn in 30 mins while Randy does the same job in 20 mins.
To calculate the time it will take both of them to work together, we use the following expression;
1/30 + 1/20 = 1/x
x = 12mins
Therefore, it will take 30 - 12 = 18 mins, to complete the same job if sandy and randy work together than if sandy works alone.
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How can you do mental math and solve 2.22 divided by 2 without writing anything down? explain.
Answer:
1.11
Step-by-step explanation:
The density of a certain material is such that it weighs 5 ounces per gallon of volume what is the density in pounds per cubic meter
The density in pounds per cubic meter is 83 pounds per cubic metre.
How to find density?The density is mass of a unit volume of a material substance.
In other words, density is the ratio between mass and volume or mass per unit .
Therefore, density can be represented mathematically as follows:
density = mass / volume
Hence,
mass = 5 ounces
5 ounces = 0.3125 pounds
1 gallon = 0.00378541 pounds
Therefore,
density = 0.3125 / 0.00378541
density = 82.5538052681
density = 83 pounds per cubic metre.
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Find a linear differential operator that annihilates the given function. (Use D for the differential operator.) cos 2x
Let [tex]y=\cos(2x)[/tex], with first two derivatives
[tex]Dy = -2\sin(2x)[/tex]
[tex]D^2y = -4\cos(2x)[/tex]
Consider the linear ODE
[tex]aD^2y + bDy + cy = 0[/tex]
Substitute [tex]y[/tex] and its derivatives and solve for the unknown coefficients [tex]a,b,c[/tex].
[tex]-4a\cos(2x) - 2b\sin(2x) + c\cos(2x) = 0[/tex]
[tex]\implies \begin{cases}-4a+c=0 \\ -2b=0 \end{cases}[/tex]
[tex]\implies b=0 \text{ and } c= 4a[/tex]
Then the minimal ODE with this solution is
[tex]aD^2y + 4ay = 0 \implies \boxed{D^2y + 4y = 0}[/tex]
What are the domain and range ofWhat are the domain and range of ?
D: [3, ∞) and R: [0, ∞)
D: [4, ∞) and R: (–∞, 0)
D: [–4, ∞) and R: [0, ∞)
D: (3, ∞) and R: (–∞, 0)
Answer:
Domain:[-4,∞)
Range:[0, ∞)
Thus, choice C is the exact answer
What is the following sum?
3/125x10,13 +3/27x10,13
O
○ 8x³y² (¹³√xy)
15x³y³ (³√xy )
O 15x5
O
15x³y² (2√xy)
O
○ 8x³y³ (³√xy)
[tex]\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }[/tex]=[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }[/tex]
How to solve an expression?[tex]\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }[/tex]
Therefore,
125 = 5³
27 = 3³
Hence,
[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} }[/tex]
Hence,
Both cube root are the same now,
Therefore, we have to add them together.
[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }[/tex]
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
The number of songs that Deante' would have downloaded during month 9 is 58 songs.
What is a regression line?A regression line is a statistical line that best describes the behavior of a data set and such, it is a line that best fits a set of data.
By using Microsoft excel to plot the data on a scatter plot, we can logically deduce that line of best fit for the songs downloaded is given by:
y = 2.03x + 39.7
Thus, the number of songs that Deante' would have downloaded during month 9 is:
y = 2.03(9) + 39.7
y = 18.27 + 39.7
y = 57.97 ≈ 58 songs.
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Answer:
A) ŷ = 2.03X + 39.73
B) 58
Step-by-step explanation:
A line of best fit is a line drawn on a scatter plot that shows the trend and the best estimation of the relationship between x and y.
After graphing it, it's easy to find the point at which x and why intersect along the line where x is nine.
Using the equation, just replace x with nine and solve.
How many triangles are there?
Answer:
20
Steps-by-step explanation:
sorry mistake
Answer:
12
Explanation: I just counted them! :) and there was 6 in the middle and on the outside so 6 + 6 = 12! :)
In a two digit number, t = the tens digit and u = the ones digit. Which of the expressions below shows the value of its reversal?
10u + t is the expressions shows the value of the reversal of digits in a two digit number, t = the tens digit and u = the ones digit. This can be obtained by multiplying 10 with the tens digit and adding unit digit.
Which is the required expressions?
Given that, in a two digit number,
t = the tens digit
u = the ones digit
The expression for the digit will be ,
10×t + u = 10t + u
The value of its reversal,
u = the tens digit
t = the ones digit
10×u + t = 10u + t is the required expression
For example,
37 = 10×3 + 7 = 30 + 7 and its reverse 73 = 10×7 + 3 = 70 + 3
Hence 10u + t is the expressions shows the value of the reversal of digits in a two digit number, t = the tens digit and u = the ones digit.
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An owner of a large car lot believes that fuel prices are going to rise significantly and wonders how this rise might affect demand for the high performance vehicles. Specifically, the owner is investigating a link between how fast a car can go from 0 to 60 miles per hour (measured in seconds) and the car's economy as measured in miles traveled per gallon used (mpg). If fast cars, which are normally high in demand, are associated with higher mpg then there will be much less demand if gas prices rise as predicted. The owner gathers data on 20 vehicles. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places. "mpg" 0 to 60 time (seconds) 28 7.7 25 8.2 25 8.6 22 7.4 22 8 21 6.9 21 7.5 21 7.4 21 7.8 21 8.8 20 6.1 20 6.9 20 7.2 20 7.5 20 7.5 20 7.5 20 7.7 19 6.7 19 7.9 19 8.5
The correlation coefficient r between the two data sets is 0.33
How to determine the correlation coefficient r?From the table of values, we make use of the following representations:
Represent the mpg on the x axisRepresent the time on the y axisUsing the above representations, we can now plot our data values in the Excel software
From the Excel application, we have the following summary:
X Values
∑ = 424
Mean = 21.2
∑(X - Mx)2 = SSx = 101.2
Y Values
∑ = 151.8
Mean = 7.59
∑(Y - My)2 = SSy = 8.238
X and Y Combined
N = 20
∑(X - Mx)(Y - My) = 9.54
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
This gives
r = 9.54 / √((101.2)(8.238))
Evaluate
r = 0.3304
Approximate
r = 0.33
Hence, the correlation coefficient r between the two data sets is 0.33
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find the equation of the straight line with ng gradient and points. b) - 1/2, (2,3)
Answer:
[tex]y = -\frac{1}{2} x+4[/tex]
Step-by-step explanation:
Standard form for equation of line: y = mx + c
where m = gradient or slope
c = y-intercept
From the question we know that,
x = 2
y = 3
m = - 0.5
We will substitute these values into the equation to find c.
3 = (-0.5)(2) + c
3 = - 1 + c
c = 3 + 1 = 4
Therefore the equation of this line is [tex]y = -\frac{1}{2} x+4[/tex]
24 feet in 10 seconds
Answer:Divide your speed in feet per minute by 60
Step-by-step explanation: