Therefore , the solution of the given problem of probability comes out to be probability that the second marble will be red = 0.5.
What exactly does the probability process entail?Calculating the likelihood that a statement is true or that an event will occur is the focus of the branch of mathematics known as probability theory. Any number from 0 to 1, where 1 represents certainty and 0 normally represents possibility, may be used to represent chance. The likelihood that a particular event will occur is depicted in a probability diagram. Probabilities can be represented by the numbers 0 and 1, percentages with a range of 0% to 100%, and a small number of extra characters. the proportion of incidents that occurred among a set of equally likely possibilities out of all potential outcomes
Here,
(p = 5/10) First Blue
Blue II (p = 4/9)
Red 2 (p = 5/9)
Primary Red (p = 5/10)
Blue II (p = 5/9)
Fourth Red (p = 4/9)
Interestingly, if you observe the first marble and then put it back in, the outcome will remain the same (sampling with replacement). The second draw doesn't depend on the first.
=> Pr(B, R) = Pr(B)*Pr(R)
=> (5/10), (5/10), (1/2), (1/2), and 1/4.
and
=>Pr(R, R) = Pr(R)*Pr(R)
=> (5/10), (5/10), and (1/2).
(1/2) = 1/4
Pr
R, R, or (B, R) = (1/4) + (1/4) = 1/2
Therefore , the solution of the given problem of probability comes out to be probability that the second marble will be red = 0.5.
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Melanie bought two different pieces of wire to make different types of jewelry. She bought a 16-gauge piece of wire and cut it into six 16.5-inch pieces. She also bought a 22-gauge piece of wire and cut it into eight 9.6-inch pieces. What is the difference in the total lengths of the two wires that Melanie bought?
Answer:
The length of the 16-gauge wire is 16.5 inches * 6 pieces = 99 inches.
The length of the 22-gauge wire is 9.6 inches * 8 pieces = 76.8 inches.
The difference in the total lengths is 99 inches - 76.8 inches = 22.2 inches.
Step-by-step explanation:
Which expressions can be used to find m∠BAC? Check all that apply. Cos−1 cos−1 sin−1 sin−1 tan−1 tan−1
The expressions that can be used to find the measure of angle BAC in triangle ABC are [tex]Cos^{-1} (\frac{6.9}{12} )[/tex] , [tex]Sin^{-1} (\frac{9.8}{12} )[/tex] and [tex]Tan^{-1} (\frac{9.8}{6.9} )[/tex] .
The trigonometric ratios involving the angle BAC (∠A) can be written as follows :
In triangle ABC ,
(i) Sine of A = [tex]\frac{BC}{AB}[/tex] ,
Substituting the value of BC and AB ,
we get ;
[tex]SinA = \frac{9.8}{12}[/tex] ;
⇒ [tex]\angle A = Sin^{-1} (\frac{9.8}{12} )[/tex] ;
(ii) Cos of A = [tex]\frac{AC}{AB}[/tex]
Substituting the value of AC and AB ,
we get ;
[tex]CosA = \frac{6.9}{12}[/tex]
⇒ [tex]\angle A = Cos^{-1} (\frac{6.9}{12} )[/tex] ;
(iii) Tan of A = [tex]\frac{BC}{AC}[/tex]
Substituting the value of BC and AC ,
we get ;
[tex]TanA = \frac{9.8}{6.9}[/tex]
⇒ [tex]\angle A = Tan^{-1} (\frac{9.8}{6.9} )[/tex] ;
Therefore , the only options that satisfy the triangle ABC are [tex]Cos^{-1} (\frac{6.9}{12} )[/tex] , [tex]Sin^{-1} (\frac{9.8}{12} )[/tex] and [tex]Tan^{-1} (\frac{9.8}{6.9} )[/tex] .
The given question is incomplete , the complete question is
Which expressions can be used to find m∠BAC in the triangle ABC ? Check all that apply.
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How do you know when a radical equation has an extraneous solution?
Extraneous solutions occur when we execute non-invertible operations on both sides of an equation.
Squaring (or raising any other even power) is a non-invertible operation. Solving equations applying square roots involves squaring both sides of an equation.
For example to show the idea:
The equations: x−1 = 4 and x = 5, have exactly the same set of solutions. Namely: {5}.
Square both sides of x = 5 to get the new equation: x² = 25. The solution set for this new equation is; {−5,5}. −5 is an extraneous solution raised by squaring the two expressions
Square both sides of x−1 = 4 to get x² − 2x + 1 = 16
which is equivalent to x² − 2x − 15 = 0.
and, rewriting the left, (x+3)(x−5) = 0.
So the solution set is {−3,5}.
This time, it is −3, which is the extra solution.
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8. Glen raised $275 for his softball team's fundraiser.
He wants to raise at least $715.
a. Write and solve an inequality to determine
how much more money Glen must raise to
reach his goal. Let d represent the amount of
money in dollars Glen must raise to reach his
goal.
b. If Glen raises $50 per week, what is the
minimum number of weeks it will take him to
reach his goal?
The money Glen must raise to reach his goal will be $440. And the minimum number of weeks it will take him to reach his goal will be 9 weeks.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Glen raised $275 for his softball team's fundraiser. He wants to raise at least $715. Let 'y' be the amount of money Glen must raise to reach his goal. Then the inequality is given as,
y + $275 ≥ $715
y ≥ $440
Let 'x' be the number of weeks, then we have
50x > $440
x > 8.8
x = 9 week
The minimum number of weeks it will take him to reach his goal will be 9 weeks.
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a fraction that has a numerator of one
Answer:1/4,1,8
Step-by-step explanation:anything with one on top
Alang drives 22. 5 miles in 30 minutes. If he drove two hours in total at the same rate, how far did he go?.
If Alang drove two hours in total at the same rate,( i.e., with 45 mph), he goes to ninty miles far away.
Distance is the measure of the space between two points or how far you travel. The rate is the measure of the speed that you travel and time is used to measure that how long you travel. When using the formula related to distance, rate, and time. If the rate in the problem gives miles per hour (mph), then time must be in hours. If time in minutes then divide the time by sixty. Distance in terms of rate is defined as the product of rate of object and time taken to cover the required distance. Use the formula:
Distance = rate × time
We have , distance drive by Alang in 30 minutes = 22.5 miles
So, rate/ speed with which Alang drives
= 22.5/30 /60 miles per hour
= 22.5 × 2 = 45 mph
Rate of driving = 45 mph
If he drove two hours in total at the same rate, we have to determine the distance travelled by him in these two hours. Time , t = 2 hours
Distance = 45 miles per hour × 2 hours
= 90 miles
Thus, required distance is 90 miles.
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Which expression is equivalent to
6
(√²) "?
A quadrilateral has two angles that measure 303° and 6°. The other two angles are in a ratio of 8:9. What are the measures of those two angles?
Answer: 24 and 27 degrees
Step-by-step explanation:
The 2 other angles add up to 360 - 303 - 6 = 51
51/(8+9) = 51/17 = 3
The 2 angles are 3*8 and 3*9, which are 24 degrees and 27 degrees
What is the equation please hurry
Answer:
Total Cost for Club Member = $15.00 + (n * $0.25)
Step-by-step explanation:
The equation for the total cost for a non-member to have n prints made is:
Total Cost for Non-Member = (n * $0.40)
This is because the club membership costs $15.00 initially, and each print for a club member costs $0.25 while each print for a non-member costs $0.40. So, the total cost is just the initial cost plus the cost of each print multiplied by the number of prints.
Tamela compared the rates of three cable companies.
TV Watchers—$30.80 for 70 channels
Tel-EVision—$46.40 for 145 channels
Channels Galore—$40.80 for 120 channels
Which cable company has the best rate of price per channel?
Answer:
round 3.62to the nearest kilogram
Step-by-step explanation:
Which model shows two equal expressions when the value of x is 4?
~~~~~
(Please answer asap!)
The given mathematical model that shows two equal expressions when the value of x is 4 is; Option A
How to interpret mathematical models?We want to find the mathematical models where the left hand and right hand sides are equal to 4.
Option A; We see that the left hand side has four number of x while the right hand side has 4 number of 1. Thus this option shows two equal expressions when the value of x is 4
Option B; This does not show two equal expressions when the value of x is 4 because there are 4 number of x on the left hand side and only one number on the right side.
Option C; This does not show two equal expressions when the value of x is 4 because there is a number of x and two 1's on the left hand side and five 1's on the right side.
Option D; This does not show two equal expressions when the value of x is 4 because both sides don't balance out.
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A circular cookie cake costs $15.70. If the diameter of the cookie cake is 10 inches, what is the approximate cost per square inch of the cookie cake? Use π = 3.14.
$0.05
$0.20
$0.50
$0.64
Answer: B: $0.20
Step-by-step explanation:
A plant measures x inches this week, and had grown 8 times as the height from last week.
The requried measure of the height of the plant this week is y = 9x.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
A plant measures x inches this week and had grown 8 times as the height from last week.
The height of the plant after a week is y,
According to the quesiton,
y = x + 8x
y = 9x
Thus, the requried measure of the height of the plant this week is y = 9x.
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Write the slope-intercept form of the equation of each line.
-5-4-3-2-1
=-3x+4
A) y =
4
C) y=x+4
5
8
B) y=-x+4
5
D) y = 4x-
85
The slope-intercept form of the equation of each line is y=-x+4.
How should a slope-intercept form equation be written?When you know the slope of the line to be investigated and the specified point is also the y intercept (0,), you may apply the slope intercept formula, y = mx + b. The y value of the y intercept point is represented by b in the equation.Simply said, the slope-intercept form is the technique to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.The slope-intercept form of the equation of each line is y=-x+4.To learn more about slope-intercept refer to:
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Question 4(Multiple Choice Worth 1 points)
(03.01 MC)
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.
√√8
√
58
Therefore , the solution of the given problem of equation comes out to be value of this equation is best describe by option C.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter.
Here,
Given :
we have equations as -
=> [tex]7^{1/3}[/tex] = ³√7
From option C
=> 7 = [tex]^{1/3}[/tex]* ³√7
=> 7 = ¹7
=> 7 = 7
so the value of this equation is best describe by option C.
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using traditional methods it takes 101 hours to receive an advanced flying license. a new training technique using computer aided instruction (cai) has been proposed. a researcher believes the new technique may lengthen training time and decides to perform a hypothesis test. after performing the test on 170 students, the researcher fails to reject the null hypothesis at a 0.05 level of significance. what is the conclusion?
The conclusion of the hypothesis test performed by the researcher is that there is not sufficient evidence to support the claim that the new computer-aided instruction (CAI) technique increases the time needed to receive an advanced flying license.
The failure to reject the null hypothesis at a 0.05 level of significance suggests that the difference in training time between the traditional method and the CAI method involves technology in teaching.
It includes mobiles and other devices and provides the students with different opportunities to study but it is not statistically significant, and therefore the null hypothesis that the training times are equal cannot be rejected.
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12
11
10
9
8
7
6
5
4
3
2
1
A(4,2)
B(9, 10)
1 2 3 4 5 6 7 8 9 10 11 12
OA. 13 units
OB. About 3.6 units
C. 89 units
OD. About 9.4 units
Answer:
D
Step-by-step explanation:
calculate the length of AB using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (4, 2 ) and (x₂, y₂ ) = B (9, 10 )
AB = [tex]\sqrt{(9-4)^2+(10-2)^2}[/tex]
= [tex]\sqrt{5^2+8^2}[/tex]
= [tex]\sqrt{25+64}[/tex]
= [tex]\sqrt{89}[/tex]
≈ 9.4 ( to 1 decimal place )
a salad dressing recipe calls for 3/4 cups of olive oil for every 1/2 cup of vinegar how many cups of vinegar are needed for 2 cups of olive oil
Answer: 4/3 or 1 & 1/3 cups of vinegar
Step-by-step explanation:
1. Set a proportion: 3/4 : 1/2
2. Divide 2 by 3/4 to get 2 & 2/3
3. Multiply 2 & 2/3 and 1/2 together to get 4/3 or 1 & 1/3
Which expression best describes ‘the difference of 7 and x
Answer: -7 times x
Step-by-step explanation:
The cost of soup, s, varies directly with the number of cans, c. When c is 4, the cost is $3. Which graph represents the
cost of the soup?
O
286
9
7
6-
5-
of s
10
1234567 89
This indicates that the cost of the soup varies directly with the number of cans
How to plot the points on graph?
To plot points on a graph, you need to have an ordered pair of coordinates that represent the point. An ordered pair is written as (x,y), where x is the value on the x-axis and y is the value on the y-axis.
To plot a point on the graph:
Locate the x-value on the horizontal (x) axis and the y-value on the vertical (y) axis.Draw a dot on the graph at the point where the x and y values intersect.The graph that represents the cost of the soup is the one with a straight line passing through the point (4,3). This indicates that the cost of the soup varies directly with the number of cans, and when there are 4 cans, the cost is $3.
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form
y/x = k or y = kx
In this problem
Let
x--------> the number of cans
y-------> the cost of a soup
so,
when
x = 4 cans
y = $3
substitute
y / x = k
3 / 4 = k
The equation is
y = 3 / 4 x
using a graph tool
see the attached figure
the answer in the attached figure
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David is going to invest $3,900 and leave it in an account for 10 years. Assuming the interest is compounded daily, what interest rate, to the nearest tenth of a percent, would be required in order for David to end up with $6,200?
David needs an interest rate of 4.363% to make a profit of $6,200, which is calculated to be the closest tenth of a percent.
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.
Given, David is going to invest $3,900 and leave it in an account for 10 years. Assuming the interest is compounded daily,
Compound interest formula for daily compounding
A = P(1+r/365)^(365t)
Where:
A = the future value of the investment
P = the principal investment amount
r = the annual interest rate (decimal)
t = the number of years the money is invested for
6200 = 3900((1+r/365)^(365*10)
1.58 = (1+r/365)^(365*10)
r = 4.636
therefore, an interest rate, to the nearest tenth of a percent, would be required in order for David to end up with $6,200 will be 4.363%.
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2(4x+3)=10-2x
please help.
Answer:
x=2/5
Step-by-step explanation:
did the equation
steve guesses randomly on a 15-question multiple choice test in which each problem has two choices, a correct one and an incorrect one. what is the probability that he gets at least half of the questions correct? express your answer as a common fraction.
"At least half" denotes a score of 8 or above.
Probability of getting 8 correct
C(15,8)(1/2)^8(1/2)^7 = 6435/32768
Probability of getting 9 correct
C(15,9)(1/2)^9(1/2)^6 = 5005/32768
Probability of getting 10 correct
C(15,10)(1/2)^10(1/2)^5 = 3003/32768
Probability of getting 11 correct
C(15,11)(1/2)^11(1/2)^4 = 1365/32768
Probability of getting 12 correct
C(15,12)(1/2)^12(1/2)^3 = 455/32768
Probability of getting 13 correct
C(15,13)(1/2)^13(1/2)^2 = 105/32768
Probability of getting 14 correct
C(15,14)(1/2)^14(1/2)^1 = 15/32768
Probability of getting 15 correct =
C(15,15)(1/2)^15(1/2)^0 = 1/32768
So....the total probability is = [6425 + 5005 + 3003 + 1365 + 455 + 105 + 15 + 1 ] / 32768 =
16374/32768 = 8187/16384
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please hurry!! Solve x² - 2x - 2 = 0
O no solutions
0 x = -2
Ox=2+2√3
O x=1+i
Answer:
Step-by-step explanation:
Solve for x over the real numbers:
x^2 - 2 x - 2 = 0
Add 2 to both sides:
x^2 - 2 x = 2
Add 1 to both sides:
x^2 - 2 x + 1 = 3
Write the left hand side as a square:
(x - 1)^2 = 3
Take the square root of both sides:
x - 1 = sqrt(3) or x - 1 = -sqrt(3)
Add 1 to both sides:
x = 1 + sqrt(3) or x - 1 = -sqrt(3)
Add 1 to both sides:
Answer: x = 1 + sqrt(3) or x = 1 - sqrt(3)
For which value of b is it true that b +7 < 12?
The number 24 has a place value of two due to the presence of two full sets of tens.
What is meant by value?The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value.The occurrence of two complete sets of tens gives the number 24 its place value of two. Due to 4 units that are missing from a complete set of 10, the number 24 has a place value of 4 in the ones because of this. Honesty, integrity, benevolence, kindness, courage, and self-assurance are a few examples of values. These values aid people in determining what they find desirable or unattractive.[tex]Solution:}\:&\:b < 5\:\\[/tex]
[tex]\:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:5\right)\end{bmatrix}[/tex]
b + 7 < 12
b < 5
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How do you find the measure of an unknown angle X?
There are several methods to find the measure of an unknown angle X in a triangle like angle sum property, Pythagorean theorem, trigonometric ratios, law of cosines and law of sines.
Using the Angle Sum Property: The sum of the measures of the angles in a triangle is always 180 degrees. If the measures of two angles in a triangle are known, then you can use the Angle Sum Property to find the measure of the third angle.
Using the Pythagorean Theorem: If a right triangle is given, we can use the Pythagorean theorem to find the measure of the right angle, which is 90 degrees.
Using the Sine, Cosine, and Tangent ratios: In a triangle, the measure of an angle can be found by using the ratios of the sides of the triangle. For example, the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Using the Law of Cosines or Law of Sines: The Law of Cosines and Law of Sines are two formulas that can be used to find the measure of an angle in a triangle if the measures of two angles and the lengths of two or three sides are known.
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if the radius of a balloon is increasing at a constant rate of 0.03 in/min, how fast is the volume of the balloon changing at the time when its radius is 5 inches?
9.4248 cu in/min volume of the balloon changing at the time when its radius is 5 inches
To solve this, you need to know how to find a derivative and use two equations.
The formula for a sphere's volume in terms of radius and chain rule is represented by the two equations. It will be useful to use the formula dV/dt = dV/dR x dR/dt.
V = (4/3)(Pi)r^3 ; dV/dr = 4(Pi)r^2 ;
dV/dt = ( dV/dr)(dr/dt)
DV/dr = 4(3.1416)(5)(5) = 314.16 ;
dr/dt = 0.03 in/min
DV/dt = ( 314.16 in sq)( 0.03 in/min) = 9.4248 cu in/min
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What is called product in maths?
In mathematics, a product is the result of multiplying two or more numbers together.In mathematics, a product is an operation where two or more numbers are multiplied together to get a single result.
In mathematics, a product is an operation where two or more numbers are multiplied together to get a single result. For example, if we multiply 3 and 4, the product would be 12. Similarly, if we multiply 5, 6 and 7 together the product would be 210. In algebra, products are written using the multiplication symbol which is an asterisk (*) or a dot (.).
In mathematics, a product is the result of multiplying two or more numbers together
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How do you calculate uniform motion speed?
By dividing the distance travelled by the time needed to cover that distance, uniform motion speed is found. Speed is calculated as follows:
Speed = Distance / Time
An object would move at a pace of 10 meters per second (100/10 = 10) if it covered 100 meters in 10 seconds.
It is crucial to remember that the distance and time must both be expressed in the same unit in order to compute speed. For instance, the time must be expressed in seconds if the distance is expressed in meters.
The motion in which an object moves in a straight line at a constant speed is often referred to as uniform motion. An object's speed is not constant and it is not thought to be moving uniformly if it is accelerating or decelerating.
Therefore ,By dividing the distance travelled by the time it took to cover that distance, uniform motion speed is the rate at which an object moves in a straight line at a constant speed.
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please help mee please
Answer:
x = 32
Step-by-step explanation:
The two angles form a straight line so they add to 180
The angles are colinear angles.
3x-4 + 3x-8 = 180
Combine like terms
6x -12 =180
Add 12 to each side
6x-12+12 =180+12
6x = 192
Divide each side by 6
6x/6 = 192/6
x = 32
Answer:
32°
Step-by-step explanation:
We know the measure of a straight line is 180° . And therefore the measure of the given two co linear angles would be 180° . So ,
[tex]\implies \rm 3x-4 +3x -8=180\\ [/tex]
[tex]\implies \rm 6x -12 =180\\ [/tex]
[tex]\implies \rm 6x = 180+12 = 192\\ [/tex]
[tex]\implies \rm x =\frac{192}{6}= 32^o[/tex]
And we are done!