The probability that the exactly 5 are white and 2 are red is126/1716 and,
the probability that at least 5 of the balls are white is 133/1716
Given that:-
Total number of balls in the urn = 13
Number of white balls = 6
Number of red balls = 7
Number of randomly selected balls = 7
We have to find the probability that the exactly 5 are white and 2 are red and the probability that at least 5 of the balls are white.
Probability that exactly 5 balls are white and 2 are red, P(x = 5) = [tex]\frac{^6C_5*^7C_2}{^{13}C_7}[/tex] = 126/1716 = 21/286
We know that,
Probability that atleast 5 balls are white = P(x = 5) + P(x = 6)
We know that,
P(x = 6) = [tex]\frac{^6C_6*^7C_1}{^{13}C_7}[/tex] = 7/1716
Hence,
Probability that atleast 5 balls are white = 126/1716 + 7/1716 = 133/1716.
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Solve 3(x + 2) > x.
A. {x | x < -3}
B. {x | x > -3}
C. {x | x > -1}
D. {x | x < -1}
The solution for the inequality 3(x + 2) > x is given by:
B. {x | x > -3}.
How to solve an inequality?An inequality is solved similarly to an equality, in which we isolate the desired variable.
The biggest difference is the fact that the solution for the inequality won't be a single value like the solution for the equality, it will be a range containing infinity real values.
For this problem, the inequality is given as follows:
3(x + 2) > x.
Applying the distributive property, we have that:
3x + 6 > x.
Now we move x to the left side and 6 to the right side, both with inverse signals, hence:
3x - x > -6.
2x > -6
x > -6/2
x > -3.
Hence the correct option for the inequality in this problem is given by option B.
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Can i get some help
Answer:
Explanation:
iven the function:
can someone help me with this
If each of the 4 sloping side ahs length 10 cm
This implies they have length 40 cm altogether
To find the base length, simply subract the 40 cm from the total length of 68cm
68 - 40 = 28
each base length = 28/4 = 7cm
Area of the square base is = l x l = 7 x 7 = 49 cm²
You are the diving officer on a submarine conducting diving operations. As you conduct your operations, you realize that you can relate the submarine’s changes in depth over time to some linear equations. The submarine descends at different rates over different time intervals.
1. The depth of the submarine is 50 ft below sea level when it starts to descend at a rate of 10.5 ft/s. It dives at that rate for 5 s.
Part A
Using a linear function, the constraints for the values of x and of y, respectively, are given as follows:
x: 0 ≤ x ≤ 5.y: -102.5 ≤ y ≤ -50.What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the constant rate of change.The coefficient b is the y-intercept of the function, which is the initial value of the function.In the context of this problem, we have that:
The initial depth is of 50 ft, hence the intercept is of -50.The submarine descends at a rate of 10.5 ft/s, hence the slope is of -10.5.Thus the linear function that models the depth of the submarine after x seconds is given by:
f(x) = -50 - 10.5x.
This rate is for 5 seconds, hence the constraint for x is 0 ≤ x ≤ 5, and the minimum depth attained by the submarine is:
f(5) = -50 - 10.5(5) = -102.5 ft.
Hence the constraint for y is given as follows:
-102.5 ≤ y ≤ -50.
What is the missing information?The complete problem is given by the image at the end of the answer.
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in a triangle, the first angle is three times the measure of the second angle. the measure of the third angle is 70° more than the measure of the second angle. use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle
Answer:
Step-by-step explanation:
[tex]3x+x+(x+70)=180[/tex]
[tex]5x+70=180[/tex]
[tex]5x=180-70[/tex]
[tex]5x=110[/tex]
[tex]x=110/5[/tex]
x = 22°
"x" is the second angle: 22°
"3x" is the first angle: 3(22) = 66°
"x + 70" is the third angle: 22 + 70 = 92°
22 + 66 + 92 = 180
Hope this helps
What are the dimensions of a right triangle with an eight-inch hypotenuse and an area of 16 square inches?
The dimensions of the given right triangle would be 5.66 inches and 11.31 inches.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
Let the legs of the triangle be x and y
Using the Pythagorean theorem:
c² = a²+b²
So the hypotenuse will be:
x² + y² = 8²
x² + y² = 64
x² = 64 - y²
So the area of the triangle is:
A = 1/2bh
A = 1/2xy
⇒16 = 1/2xy
32 = xy
x = 32/y
x² = 1024/y²
Substitute the above value in x² = 64 - y² and solving for y we get:
1024/y² = 64 - y²
1024 = 64y²- y⁴
This can be written as:
y⁴ - 64y² + 1024 = 0
Thus y = 4√2 = 5.66
x = 64/(4√2)= 16/√2 = 8√2 = 11.31
Therefore, the dimensions of the given right triangle would be 5.66 inches and 11.31 inches.
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Use the graph to write the factorization of x2 + 4x - 5.10+y = x2 + 4x-5-1010-10O A. (x + 1)(x - 5)B. (x + 5)(x-1)C. (x-3)(x-2)D. (X+6)(x-2)
Solution
From the given graph
The zeros of the given graph are
[tex]x=-5,1[/tex]Converting the zeros to roots gives
[tex]\begin{gathered} x=-5,1 \\ x=-5 \\ x+5=0 \\ x=1 \\ x-1=0 \end{gathered}[/tex]The factorized form of the equation of the given graph is
[tex](x+5)(x-1)[/tex]Hence, the answer is option B
How is the graph of the parent function of y=3√x transformed to produce the graph Y=2
-√√√x₂
OIt is horizontally stretched by a factor of 2.
OIt is vertically stretched by a factor of 2.
of 1/1.
1
OIt is translated left by unit.
2
10
1
OIt is translated right by 2 unit.
Using transformations, it is found that the transformation from [tex]y = \sqrt[3]{x}[/tex] to [tex]y = \sqrt[3]{0.5x}[/tex] is:
It is horizontally stretched by a factor of 1/2.
What are transformations on the graph of a function?Transformations in the graph of a function happens when operations such as multiplication/division or sum/subtraction are applied in the definition of the function.
They can be either in the domain of the function, involving values of x, or the range, involving values of y.
For this problem, the change was that x -> x/2, that is, there was a multiplication in the domain, meaning that there was an horizontal stretch to the function.
The fact that the number was multiplied by 1/2 means that the factor of the stretch is of 1/2.
What is the missing information?The transformation is from [tex]y = \sqrt[3]{x}[/tex] to [tex]y = \sqrt[3]{0.5x}[/tex].
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Maddox has $100 and plans to spend $20 each time he goes to the movies. At this rate,how many times can Maddox go to the movies?O $5O 5 timesО 4 timesO $120
ANSWER
EXPLANATION
addox has $100.
He plans to spend $20 each time he goes to the movies.
To find out how many times he can go to the movies,
Find the equation of the graph given below. Notice that the cosine function is used in the answer template, representing a
cosine function that is shifted and/or reflected.
When entering in your answer, use the letter a rather than the multiplication symbol.
Provide your answer below:
Answer:
y = 1/2cos(x/2 -5π/4) -1
Step-by-step explanation:
You want the equation of the shifted and scaled cosine function shown in the graph.
TranslationA point on a function f(x) will be translated (right, up) = (h, k) by the transformation ...
g(x) = f(x -h) +k
ScalingA function will be vertically expanded by a factor of p and horizontally expanded by a factor of q by the transformation ...
g(x) = p·f(x/q)
Graphed functionThe graph shows a cosine function with a peak-to-peak amplitude of 1, which is 1/2 the parent function's amplitude, so p=1/2.
The period is (9π/2 -π/2) = 4π, which is twice the period of the parent cosine function, so q=2.
The first peak of the graphed waveform is at x=5π/2, and the midline of the graphed waveform is y=-1, so we have (h, k) = (5π/2, -1).
Putting these transformations together, we find the equation of the graph to be ...
y = 1/2cos((x - 5π/2)/2) -1 . . . . . . scaling applied before translation
y = 1/2cos(x/2 -5π/4) -1
Claudia is considering taking a vacation but she's not sure if she wants to drive or fly somewhere. She realized that it would take her the same amount of time to drive 150 miles as it would take a plane to fly 1350 miles. If the plane is flying 400 mph faster than the car, how fast is each traveling?
Solution
For this case we know that the distance covered by the plane is 1350 mi and the velocity 400 mph
We also know that the distance is given by:
D= vt
Let D= Distance travelled by the car and airplane
Vp= Vc+ 400 (Velocity of the plane)
1350 = (Vc +400)*t
150 = Vc * t
We can solve for t and we got:
t= 150/Vc
Replacing in the first equation we got:
1350= (Vc+400)* (150/Vc)
Solving for Vc we got:
1350= 150 + 60000/Vc
1200 = 60000/Vc
Vc= 60000/1200= 50 mph
Then the velocity of the car is Vc= 50mph and for the plane
Vp= 50+ 400= 450 mph
(02.01, 02.02 HC)Vanessa and William are stuck simplifying radical expressions. Vanessa has to simplifyx3William has to simplify 15xx.x4. Usingx6full sentences, describe how to fully simplify Vanessa and William's expressions. Describe if Vanessa and William started with equivalentexpressions or if they started with expressions that are not
ANSWER:
[tex]\begin{gathered} \text{ The Vanness expression is simplified by subtracting the exponents, and we obtain the following:} \\ \\ \frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}=x^{\frac{1}{2}} \\ \\ \text{ The Williams expression is simplified by adding the exponents, and we obtain the following:} \\ \\ \sqrt[16]{x\cdot\:x^3\cdot\:x^4}=x^{\frac{1}{2}} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have that the given expression is the following:
[tex]\frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}[/tex]The other expression is the following:
[tex]\sqrt[16]{x\cdot \:x^3\cdot \:x^4}[/tex]We simplify in each case:
[tex]\begin{gathered} \text{ The Vanness expression is simplified by subtracting the exponents, and we obtain the following:} \\ \\ \frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}=x^{\frac{4}{3}-\frac{5}{6}}=x^{\frac{1}{2}} \\ \\ \text{ The Williams expression is simplified by adding the exponents, and we obtain the following:} \\ \\ \sqrt[16]{x\cdot\:x^3\cdot\:x^4}=\sqrt[16]{x^{1+3+4}}=\sqrt[16]{x^8}=x^{\frac{8}{16}}=x^{\frac{1}{2}} \end{gathered}[/tex]This means that the expressions are equal
Write the quadratic equation whose roots are -6 and 5, and whose leading coefficient is 2 .
Answer: y = 2x² + 2x - 60
Step-by-step explanation:
We will write this in factored form since we are given the roots and leading coefficient. This will be written in the form y = c(x - a)(x - b) where c is the coefficient and a & b are the roots.
y = c(x - a)(x - b)
y = 2(x + 6)(x - 5)
Now, we will distribute so we end up with the standard quadratic equation form.
y = 2(x + 6)(x - 5)
y = 2x² + 2x - 60
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HELP! ALgebra 2
A soccer ball is kicked into the air so that its height, h, in feet, after t seconds is given by the function:
h(t)= -16t^2+96
What is the maximum height the ball reaches?
How long is the ball in the air?
The maximum height reached by the ball in discuss as described is; 96 while the time spent by the ball in the air is; 0 seconds.
What is the maximum height the ball reaches and how long was the ball in the air?It follows from the task content that the maximum height of the ball in the air is to be determined and so.is the time spent by the ball in the air.
Therefore, since the correct form of the function given is;
h(t) = -16t² + 96
By expressing the function above in vertex form; it follows that we have;
h(t) = -16 (t - 0)² + 96.
This vertex form function above therefore translates to the fact that the point, (0, 96) represents the vertex of the balls motion curve.
Ultimately, the maximum height reached by the ball is; 96 and the time it takes to reach this height is; 0 seconds.
PS; The scenario above in real life situation would translate to dropping a ball from the top.
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(−2, 5), slope = -4 slope intercept form
____________________________________________
Slope-Intercept Form - Solution and Explanation
____________________________________________
Hello! So...
We are given the following to convert:
Convert into Slope-Intercept Form
(-2, 5), slope = -4
____________________________
1. Compute the line equation y = mx + b for slope. In this case, our slope (m) equals -4, and passes through (-2, 5).
____________________________
2. Determine the y-intercept. In this case, b = -3.
____________________________
3. Now, construct the line equation (y = mx + b), where m = -4 and b = -3. Then, you will have your converted solution in Slope-Intercept Form.
Slope-Intercept Form:
[tex]y=-4x-3[/tex]
___________________________________________
Hope this helps! If not, feel free to comment on the matter and I will see what else I can do to assist your further. However, if this does help, lmk! Thanks and good luck!
true or false: when you find the area of a scaled copy, you cube the scale factor.
True, cube the scale factor while finding the area of a scaled copy.
The scale factor is the ratio of two equal lengths in two similar geometric objects. The fundamental formula for calculating the scale factor is the size of the former shape is Scale factor = Dimension of the new shape ÷ Dimension of the original shape. The area of a scaled element is equal to the squared scaling factor. If the scale factor is three, the area of the new item will be nine times, or three times, that of the original object. The area scale factor is equal to the square of the length scale factor. As a result, s2 is the surface scaling factor. If this is reversed, a solution to the situation at hand will be offered. The area has a scale factor of 2.
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Mateo fills a 20L jerrycan with gasoline, a volume of gasoline of 1L has a mass of 690 g and the empty jerrycan weighs 2.5 kg
a. calculate the density of gasoline
b. how much will the jerrycan weigh when it is full?
The density of the gasoline is 690 grams per litre.
The mass of the jerrycan when fully filled is 16.3 kg
How to find the density of the gasoline and mass of the jerrycan?He fills a 20 litre jerrycan with gasoline.
A volume of gasoline of 1 litre has a mass of 690 grams and the empty jerrycan weighs 2.5 kg.
Therefore, the density of the gasoline can be calculated as follows:
density = mass / volume
Hence,
mass of the gasoline = 690 grams
volume of the gasoline = 1 litres
density of the gasoline = 690 / 1
density of the gasoline = 690 grams per litre.
The weight of the jerrycan when filled with gas can be calculated as follows:
1 litre of gas = 690 grams
20 litres gas = 13800 grams
Hence,
1000 grams = 1kg
13800 grams = 13.8 kg
Therefore,
weight of the jerry can when filled with gas = 13.8 + 2.5 = 16.3 kg
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K is the midpoint of JL. If JK = 6x and JL = 13x − 7, what is JK?
The length of JK is 42.
JL is a line and K is the mid-point of that line.
J____________.___________L
K
From this we get:
JK = KL
JL = JK + KL
JL= 2JK = 2KL
Here it is given that,
JK = 6x and JL = 13x - 7
JL = 2JK
13x - 7 = 2× 6x
13x - 7 = 12x
x = 7
We have to find the length of JK
JK = 6x
=6× 7
= 42
Therefore the length of JK is 42.
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Element X is a radioactive isotope such that every 70 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 610 grams, how much of
the element would remain after 17 years, to the nearest whole number?
The element would remain 515 grams after 17 years.
What is isotope?Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.
Given Data
the initial mass of a sample of Element X is 610 grams
Element X is a radioactive isotope such that every 70 years, its mass decreases by half.
Since the half-life, or the number of years after which an isotope decays to half its original level, is stated to be 70 years.
k = [tex]\frac{2}{70}[/tex]
k= 0.0099
Equation-
N = 610e⁻⁰°⁰⁰⁹⁹ˣ
x = time
time = 17
N = 610 e⁻⁰°⁰⁰⁹⁹⁽¹⁷⁾
N = 610(0.845)
N = 515.49
The element would remain 515 grams after 17 years.
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Select the three pairs of numbers that 403 is between.
Answer:
1 and 403 13 and 31 13 and 31
Step-by-step explanation:
ƏR Ər Find for the following set of equations: R = ln(u² + v² + w²) with u = x + 2y, v = 2x ADSER y, w = 2xy
The chain rule tells us how to find derivative of a composite function., The following set of equations: R = ln(u² + v² + w²) with u = x + 2y, v = 2x-y, w = 2xy ƏR/Əx= 9/7 and ƏR/Əy = 9/7.
What is chain rule?The Chain Rule is a mathematical method to differentiate a composition of the functions. From this composition of the functions, we can discern the functions' derivatives and their relationships.
In other words, the derivative of composite function = derivative of the outside function × derivative of the inside function.
The Chain Rule gives:
ƏR/Əx= ƏR/Əu × Əu/Əx + ƏR/Əv × Əv/Əx + ƏR/Əw × Əw/Əx
= [tex]\frac{2u}{u^{2}+v^{2}+w^{2} } *1 + \frac{2v}{u^{2}+v^{2}+w^{2} } *2+ \frac{2w}{u^{2}+ v^{2}+w^{2} } *2y[/tex]
When from given information we have, x = y = 1, we have u = 3, v = 1, and w = 2, so
ƏR/Əx = 6/14 × 1+ 2/14 ×2+ 4/14×2 = 18/17 = 9/7
ƏR/Əy= ƏR/Əu × Əu/Əy + ƏR/Əv × Əv/Əy + ƏR/Əw × Əw/Əy
= [tex]\frac{2u}{u^{2}+v^{2}+w^{2} } *2 + \frac{2v}{u^{2}+v^{2}+w^{2} } *(-1)+ \frac{2w}{u^{2}+ v^{2}+w^{2} } *2x[/tex]
When from given information we have, x = y = 1, we have u = 3, v = 1, and w = 2, so
ƏR/Əy = 6/14 × 2 + 2/14 × (-1) + 1/14 × 2= 18/14 = 9/7
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4th grade elementary question… What is 2,746 divided by 517 =?
Answer:
It's 5.31
Explanation:
At one university, the mean distance commuted to campus by students is 19.0 miles, with a standard deviation of 4.2 miles. Suppose that the commutedistances are normally distributed. Complete the following statements.(a) Approximately 95% of the students have commute distances between ? milesand ? miles(b) Approximately ? of the students have commute distances between 6.4 miles and 31.6 miles.
From the given information, we know that the mean and standard deviation are, respectively,
[tex]\begin{gathered} \mu=19 \\ \sigma=4.2 \end{gathered}[/tex]From the 68-95-99 rule, we know that approximately 95% falls between 2 standard deviation of the mean, that is,
[tex]-2=\frac{x-19}{4.2}...(A)[/tex]and
[tex]2=\frac{x-19}{4.2}...(B)[/tex]From equation (A), we have
[tex]x-19=-8.4[/tex]then
[tex]x=10.6[/tex]Now, from equation (B), we get
[tex]\begin{gathered} x-19=8.4 \\ then \\ x=27.4 \end{gathered}[/tex]Therefore, the answer for part a is: Approximately 95% of the students have commute between 10.6 and 27.4 miles
Part b.In this case, we need to find the z score value for 6.4 miles and 31.6 miles and then obtain the corresponding probabilty from the z-table.
For 6.4 miles, the z score is
[tex]z=\frac{6.4-19}{4.2}=-3[/tex]and for 31.6 miles, the z score is
[tex]z=\frac{31.6-19}{4.2}=3[/tex]Now, we need to find the corresponding probability between z=-3 and z=3, which is 0.9973
Therefore, the answer for part b is: Approximately. 0.9973 of the students have commute distances between 6.4 miles and 31.6 miles
In the box below, explain why this is an error. What should he have done?
He should have divided both sides by -10.
i need help with this asap Consider the following equations.Approximate the solution to the equation f(x) = g(x) using three iterations of successive approximation. Use the graph below as a starting point.
we have the equations
[tex]\begin{gathered} f(x)=\frac{x+1}{x^2} \\ \\ g(x)=\frac{x-1}{x+1}+1 \end{gathered}[/tex]equate both equations
[tex]\frac{x+1}{x^2}=\frac{x-1}{x+1}+1[/tex]First iteration
For x=1
[tex]\begin{gathered} \frac{1+1}{1^2}=\frac{1-1}{1+1}+1 \\ \\ 2=1 \end{gathered}[/tex]For x=2
[tex]\begin{gathered} \frac{2+1}{2^2}=\frac{2-1}{2+1}+1 \\ \\ \frac{3}{4}=\frac{1}{3}+1 \\ \\ \frac{3}{4}=\frac{4}{3} \\ 0.75=1.33 \end{gathered}[/tex]For x=1.5
[tex]\begin{gathered} \frac{1.5+1}{1.5^2}=\frac{1.5-1}{1.5+1}+1 \\ \\ \frac{\frac{5}{2}}{\frac{9}{4}}=\frac{\frac{1}{2}}{\frac{5}{2}}+1 \\ \\ \frac{20}{18}=\frac{1}{5}+1 \\ \frac{10}{9}=\frac{6}{5} \\ 1.11=1.2 \end{gathered}[/tex]the answer must be less than 1.5 and greater than 1
so
Verify each option
A ----> 13/8=1.625 -----> is not a solution
B ----> 23/16=1.4375 ---> could be an approximate solution
C ---> 25/16=1.5625 ----> is not a solution
D ---> 7/4=1.75 ----> is not a solution
therefore
The answer is option Bwhich equation are correct select each other answers
Answer:
they all are correct asu know first expression is multiple by other one so u can check
How do I use the unit circle
Solution
For this case the unitary circle is given by:
[tex]x^2+y^2=1[/tex]this unitary circle is important for the trigonometric identities
Can be used also to solve inequalities
Can be used also in physics applications and in linear algebra
The midpoint of AB is M (−6, 2). If the coordinates of A are (-5, -2), what are
the coordinates of B?
Answer:
(-7,6)
Step-by-step explanation:
Midpoints
x = (x1 + x2)/2
y = (y1 + y2)/2
-6 = (-5 + x2)/2
x2 - 5 = -12
x2 = -7
2 = (-2 + y2)/2
y2 - 2 = 4
y2 = 6
The sun is shining on a house and fence. The roof of the house is 16 feet from the ground and makes a shadow 24 feet long. The fence is 4 feet tall. How long is the fence's shadow?
The length of the shadow of fence will be equal to 6 feet.
Proportionality may be defined as the term which can be used to describe or denote a relationship between two entities which are always in the same ratio. For example, the number of bananas is proportional to the number of trees with the proportionality being average number of bananas per number of trees. Here, we are given the height of house = 16 feet and length of its shadow = 24 feet and also the height of fence = 4 feet. Since, both house and fence lie in the same area they both are proportional. Let the length of shadow be x. Since, they are proportional
16/24 = 4/x
2/3 = 4/x
=> x = 12/2
=> x = 6 feet.
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Evaluate: - 2 to the third power - 45(15+10-23)
1. Remember
[tex]2^3[/tex]Means
[tex]2\times2\times2[/tex]Therefore,
[tex]2^3=2\times2\times2=8[/tex]2. Remember that we have to solve what's inside the parenthesis first. Therefore,
[tex]45(15+10-23)=45(2)=90[/tex]