Using the simple interest system, the interest rate for which Gary deposited $9,000 and earned $180 in interest after four months is 6%.
What is the simple interest system?The simple interest system is based on the process of computing interest on the principal only for each period.
This contrasts with the compound interest system that charges interest on both accumulated interest and the principal.
The simple interest formula is given as SI = (P × R × T)/100, where SI = simple interest, P = Principal, R = Rate of Interest in % per annum, and T = Time.
The principal amount invested by Gary = $9,000
Time = 4 months = 4/12 years
Interest = $180
Therefore, 180 = ($9,000 x R x 4/12)/100
R = 180/($9,000 x 4/12)/100
R = 6%
Thus, the interest rate is 6%.
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URGENT ANSWER QUICKLY PLEASE A manufacturer wants to design a cone-shaped container that has a volume of 175 cubic centimeters. Their old container is shown.
Hence,0.72 rather than to increase the radius to meet their requirements.
What is the cone ?A cone is a three-dimensional geometric form with a plane base and a smooth tapering vertex. A cone is made up of a collection of line segments, half-lines, its lines that connect the apex of the common point at to every point on a base that is in a flat other than the apex.
What is the volume ?A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using US-standard units ,SI-derived units, as well as several imperial Volume and the notion of length are connected.
Let the new radius x and the old radius as r. The formed volume was 175 cubic cm, and the new container height is 5 cm,
V = [tex]\frac{1}{3}\pi r^2h[/tex], where V is the volume, r is the radius, and h is the height, is the formula for a cone volume.
We can construct an equation using the previous volume:
175 = [tex]\frac{1}{3}\pi r^2h[/tex]
the height is same for new and old container , so,:
175 =[tex]\frac{1}{3}\pi r^2*5[/tex]
175 = [tex]\frac{5}{3}\pi r^2[/tex]
By multiplying both sides by (5/3)
[tex]r^2 = \frac{175*3}{5*\pi}[/tex] ≈ 22.3 use [tex]\pi[/tex]=3.14
When both sides are square root
r ≈ 4.72
Therefore, the old container radius is 4.72 cm.
now,We subtract the old radius from the new radius for determine how much the radius must increase to s the new container:
x - r ≈ 4 - 4.72 ≈ -0.72
Because the new radius is lower than the old radius, the outcome is negative.
We would need to reduce the radius by roughly 0.72 cm rather than expand it to satisfy the needs of the new container.
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For a population with a proportion equal to 0.32, calculate the standard error of the proportion for the following sample sizes of 40,80,120. round to 4 decimal places
The standard errors of the proportion for sample sizes of 40, 80, and 120 are 0.0733, 0.0518, and 0.0422, respectively,
How to calculate the standard error of the proportion?
To calculate the standard error of the proportion for a population with a proportion equal to 0.32 and sample sizes of 40, 80, and 120, we can use the formula:
Standard Error (SE) = √[(p * (1 - p)) / n]
where p is the proportion (0.32), and n is the sample size.
For a sample size of 40:
SE = √[(0.32 * (1 - 0.32)) / 40]
SE ≈ 0.0733 (rounded to 4 decimal places)
For a sample size of 80:
SE = √[(0.32 * (1 - 0.32)) / 80]
SE ≈ 0.0518 (rounded to 4 decimal places)
For a sample size of 120:
SE = √[(0.32 * (1 - 0.32)) / 120]
SE ≈ 0.0422 (rounded to 4 decimal places)
So, for a population with a proportion equal to 0.32, the standard errors of the proportion for sample sizes of 40, 80, and 120 are approximately 0.0733, 0.0518, and 0.0422, respectively, when rounded to 4 decimal places.
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The following linear differential equation models the charge on the capacitor, q(t), at time t in an RLC series circuit. L d^2q/dt^2 + R dq/dt + 1/C q = E(t) Find the charge on the capacitor when L = 10 henry, R = 20 ohms, C = (6260)^-1 farad, and E(t) = 100 volts, with the initial conditions q(0) = 0 coulombs and i(0) = 0 amperes.
The charge on the capacitor at time t is given by q(t) = -21292.5e^(-0.00878t) + 21292.5e^(-314.53t) + 626000 coulombs.
How to find the charge on the capacitor?To find the charge on the capacitor, with the initial conditions q(0) = 0 coulombs and i(0) = 0 amperes, we use the given linear differential equation:
L d^2q/dt^2 + R dq/dt + 1/C q = E(t)
We can solve for q(t) by finding the roots of the characteristic equation, and assuming a particular solution. Then we use the initial conditions to solve for the constants in the general solution.
The solution to the differential equation is:
q(t) = -21292.5e^(-0.00878t) + 21292.5e^(-314.53t) + 626000
Therefore, the charge on the capacitor at time t is given by q(t) = -21292.5e^(-0.00878t) + 21292.5e^(-314.53t) + 626000 coulombs.
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Factor each completely if possible
(1) x^2 - 11x + 28
(2) 2x^2 + 8x + 6
(3) k^2 - 25
(4) a^2 - 9a + 20
(5) 7x^2 - 11x - 6
(6) 14x^2 - 52x + 30
(7) 6n^3 - 8n^2 + 3n - 4
(8) 15y^3 - 3v^2 + 20v - 4
Factors (1) x² - 11x + 28 = (x-4)(x-7), (2) 2x² + 8x + 6 = 2(x+1)(x+3), (3) k² - 25 = (k+5)(k-5), (4) a² - 9a + 20 = (a-5)(a-4), (5) 7x² - 11x - 6 = (7x+2)(x-3) , (6) 14x² - 52x + 30 = 2(7x-3)(x-5), (7) 6n³ - 8n² + 3n - 4 = (2n-1)(3n²-2n+4), (8) 15y³ - 3v² + 20v - 4 = (5y-1)(3y²+1)(4-v)
Describe Factorization?Factorization is a process of finding the factors of a given mathematical expression, which can be a number, polynomial, or algebraic expression. In other words, factorization involves breaking down a mathematical expression into simpler terms that multiply together to give the original expression. For example, the factors of the expression x^2 - 4 are (x + 2)(x - 2).
In algebra, factorization is an important tool for solving equations and simplifying expressions. By factoring, we can often simplify complex expressions, making them easier to work with and understand. In addition, factorization plays an important role in number theory, where it is used to find prime factors and calculate the greatest common divisor and least common multiple of numbers.
(1) x² - 11x + 28 = (x-4)(x-7)
(2) 2x² + 8x + 6 = 2(x+1)(x+3)
(3) k² - 25 = (k+5)(k-5)
(4) a² - 9a + 20 = (a-5)(a-4)
(5) 7x² - 11x - 6 = (7x+2)(x-3)
(6) 14x² - 52x + 30 = 2(7x-3)(x-5)
(7) 6n³ - 8n² + 3n - 4 = (2n-1)(3n²-2n+4)
(8) 15y³ - 3v² + 20v - 4 = (5y-1)(3y²+1)(4-v)
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A coat that costs $131 is $18 less than twice the cost of a jacket, j. Write
an equation that represents the relationship between the cost of the coat
and the cost of the jacket
Answer:
2j - c
Step-by-step explanation:
If h(2) = 9 and h'(2) = −2, find
d/dx(h(x)/x)) at x=2
The derivative of x = 2 of the given function its value is -13/4.
To query the result of a function at x = 2, we must first use the division rule. The quotient law is a formula that calculates the derivative of a function that can be expressed as the quotient of two functions. Let
f(x) = h(x) and g(x) = x. We can express the function h(x)/x as f(x)/g(x). Now we can use the quotient rule like this:
d/dx(h(x)/x)) = d/dx(f(x)/g(x))
= [( g(x) * f '(x) )) - (f(x) * g'(x))] / (g(x))^2
= [(x * h'(x)) - (h (x) * 1) ] / x ^2
Now we can put the values given as x = 2 and h(2) = 9 and h'(2) = -2 into the formula:
d /dx(h(x)/ x) ) x = 2 = [ (2 * (-2)) - (9 * 1)] / 2^2
= (-4 - 9) / 4
= -13/4
Therefore, the derivative of x = 2 of the given function its value is -13/4.
That is, the function h(x) / x has a change of -13/4 at x = 2, so if we make a small change in x around x = 2, the function h(x ) / x changes units at x for each of 13 There is a /4 unit reduction. The negative sign indicates that the function decreases at x = 2; this is based on the fact that the number h(x) decreases less than the number x as x approaches 2.
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Work out the area of this semicircle. Take to be 3.142 and give your answer to 2 decimal places. Diameter is 8cm.
Answer:
3.142 in 2 decimal is 3.100
Step-by-step explanation:
When we come to diameter of 8cm I don't know
At the city museum, child admission is $5.60. and adult admission is $9.40. On wensday, 177 tickets were sold for a total of $1352.20. how many adult tickets were sold that day?
Let's use variables to represent the number of child and adult tickets sold on Wednesday.
Let c be the number of child tickets sold, and let a be the number of adult tickets sold.
We know that the price of a child ticket is $5.60, and the price of an adult ticket is $9.40.
From the problem statement, we know that 177 tickets were sold in total, so:
c + a = 177
We also know that the total revenue from ticket sales was $1352.20, so:
5.60c + 9.40a = 1352.20
Now we have a system of two equations with two variables. We can solve for a by using the first equation to express c in terms of a, and then substituting into the second equation:
c + a = 177 --> c = 177 - a
5.60c + 9.40a = 1352.20
Substituting c = 177 - a into the second equation, we get:
5.60(177 - a) + 9.40a = 1352.20
Expanding and simplifying:
992.20 - 5.60a + 9.40a = 1352.20
3.80a = 360
a = 95
Therefore, 95 adult tickets were sold on Wednesday.
Its bugging out but I got 95 tickets I would add explanation if it didn't act out.
X=Adult tickets
Y=Child tickets
X+Y=117
Y=117-X
9.40X+5.60Y=1352.20
9.40X+5.60(117-X)=1352.20
9.40X+991.20-5.60x=1352.20
3.80X=361
X=95
Given m
|| n, find the value of x.
m
n
126°
(8x-10)
8 is the value of x in parallel lines.
With an example, what is a parallel line?
Two lines in the same plane that are equally spaced apart and never meet are known as parallel lines in geometry. They can be either vertical or horizontal.
Examples of parallel lines in our everyday lives include zebra crossings, notebook lines, and railway tracks all around us. No matter how far apart they are on either side, two lines on the same plane are considered parallel if they never cross.
given
m ║n
8x - 10 + 126 = 180°
8x + 116 = 180°
8x = 180° - 116
8x = 64
x = 64/8
x = 8
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A cartographer at point C sites a prominent rock feature, at point R, East from his location. There is a grassy peak, at point G, at a distance of “y” miles directly North of the cartographer. The angle formed by the cartographer, rock feature, and grassy peak is “x” degrees. See the diagram below. Using complete sentences, explain how the cartographer can use only these two measurements to calculate the distance from the grassy peak to the rock feature.
True: A Chorochromatic map is a type of cartographic map that represents features depending on how they are distributed across the surface in terms of quality.`
We have,
The art and science of cartography involves visually depicting a geographic location, typically on a flat surface like a map or chart. It could include superimposing a region's depiction with non-geographical distinctions like political, cultural, or other ones.
Making and utilizing maps is the theory and application of cartography. Cartography, which combines science, aesthetics, and method, is based on the idea that reality may be described in ways that effectively convey spatial information. The same basic components are included on most maps: the main body, the legend, the title, the scale and orientation indications, the inset map, and the source notes.
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complete question:
a cartographic map style that symbolizes features based on the qualitative surface distribution of a mapped feature is called a chorochromatic map.
Find the common difference of the arithmetic sequence 14 , 16 , 18
Answer:
The common difference is 2.
Answer:
The common difference of the arithmetic sequence 14, 16, 18 is **2**.
In any arithmetic sequence, each term is equal to the previous term plus the common difference. So, the second term is equal to the first term plus the common difference. In this case, the second term, 16, is 2 more than the first term, 14. Therefore, the common difference is 2.
We can also find the common difference by subtracting any two consecutive terms in the sequence. For example, we can subtract the second term from the third term to get 18 - 16 = 2.
The common difference of an arithmetic sequence is always constant. This means that the difference between any two consecutive terms in the sequence will always be the same. In this case, the difference between any two consecutive terms is 2.
Step-by-step explanation:
Given that cos2α-5 and α terminates in quadrant I, find the exact value of sino. sina- (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
The result cos²(α) = -2 is not possible, as the square of cosine must be between 0 and 1. It appears there might be an error in the given information. Please double-check the values and try again.
Given that cos(2α) = -5 and that it terminates in quadrant I, we need to find the exact value of sin(α).
First, let's recall the Pythagorean identity: sin²(α) + cos²(α) = 1.
Since cos(2α) = -5, we need to find the value of cos(α). In order to do this, we'll use the double-angle formula for cosine: cos(2α) = 2cos²(α) - 1.
Now, we can plug in the given value of cos(2α) and solve for cos(α):
-5 = 2cos²(α) - 1
-4 = 2cos²(α)
cos²(α) = -2
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A farmer builds a water though to fit in a corner. The water though is made of two rectangular prisms
A) Length A = 5 ft and width B= 4 ft
B) Volume of the water though = 88 [tex]ft^3[/tex]
What is volume?
The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.
Here consider the prism plane figure the dotted lines are equal to the width,
Then width B= 8-4 = 4 ft
Length A = 8-3 = 5 ft
B) Now volume of rectangular prism = lwh cubic unit.
Volume of big prism = 8*2*3=48 [tex]ft^3[/tex]
Volume of small prism = 5*4*2 = 40 [tex]ft^3[/tex]
Then Total volume = 48+40 = 88 [tex]ft^3[/tex]
Hence in the rectangular prisms,
A) Length A = 5 ft and width B= 4 ft
B) Volume of the water though = 88 [tex]ft^3[/tex]
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Attempt 2 Select the true statement(s). As the sample size n increases, the distribution of the sum of the observations approaches a normal distribution. The sample mean varies from sample to sample. As the sample size n increases, the variance of the sample mean X also increases. The distribution of the mean X is never exactly normal. If the underlying population is not normal, the CLT says the distribution of the mean X approaches a normal distribution as the sample size n increases. Incorrect
Based on the terms you provided, I can help you identify the true statement(s):
1. As the sample size n increases, the distribution of the sum of the observations approaches a normal distribution.
2. The sample mean varies from sample to sample.
3. If the underlying population is not normal, the Central Limit Theorem (CLT) states that the distribution of the sample mean X approaches a normal distribution as the sample size n increases.
These statements are true. Note that the statement "As the sample size n increases, the variance of the sample mean X also increases" is incorrect, as the variance of the sample mean actually decreases when the sample size increases. Additionally, the statement "The distribution of the mean X is never exactly normal" is not universally true, as the distribution of the mean can be exactly normal under specific circumstances.
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On a recent quiz, the class mean was 73 with a standard deviation of 3.1. Calculate the z-score (to at least 2 decimal places) for a person who received score of 71. Z-Score: ____Is this unusual? A. Unusual B. Not Unusual
The, a z-score of -0.65 is not unusual
To calculate the z-score, we use the formula:
[tex]z =\frac{ (x - μ)}{σ}[/tex]
where x is the individual score, μ is the mean, and σ is the standard deviation.
Plugging in the values given, we get:
[tex]z= \frac{71-73}{3.1}[/tex]
z = -0.65
Rounding to 2 decimal places, the z-score is -0.65.
To determine if this score is unusual or not, we need to compare it to the normal distribution. A z-score of -0.65 means that the individual's score is 0.65 standard deviations below the mean.
According to the empirical rule, about 68% of the data falls within 1 standard deviation of the mean. Therefore, a z-score of -0.65 is not unusual and falls within the normal range of scores.
So, the answer is B. Not Unusual.
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c×cxdxd×d divided by
cxcxcxdxd
Answer:
Please leave more information regarding the question thank you
-Where does typology come from
-how does it work
-Defines types and antitypes of typology
-what assumptions do we make about the bible for typology to work
which equations are true? Select the four correct answers. A. 3/4=6/8 B. 4/6=10/12 C. 2/3=8/12 D. 8/8=5/5 E. 2/5=4/10 F. 1/4=5/8
Answer:
The Correct answers are
A
C
D
E
Answer:
Correct Answers:
A 3/4=6/8
C 2/3=8/12
D 8/8=5/5
E 2/5=4/10
Step-by-step explanation:
Can someone pls help me out with this?
Answer:
Every day, 33% of locusts are added to the locust population
A formula that uses one or more previous terms to find the next term is an
Answer:
A formula that uses one or more previous terms to find the next term is a recursive formula.
Step-by-step explanation:
A recursive formula is a formula that defines any term of a sequence in terms of its preceding term(s).
Learn
Dotebook
1. Mario has 12 boxes of pizza He cut each pizza into eights. How mar
pieces of pizza will there be?
Answer: 96 slices
Step-by-step explanation:
United Bank offers a 15-year mortgage at an APR of 6.2%. Capitol Bank offers a 25-year mortgage at an APR of 6.5%. Marcy wants to borrow $120,000.
a. What would the monthly payment be from United Bank?
b. What would the total interest be from United Bank? Round to the nearest ten dollars.
c. What would the monthly payment be from Capitol Bank?
d. What would the total interest be from Capitol Bank? Round to the nearest ten dollars.
e. Which bank has the lower total interest, and by how much?
f. What is the difference in the monthly payments?
g. How many years of payments do you avoid if you decide to take out the shorter mortgage?
Unit 10: Circles
Homework 5: Inscribed Angles
** This is a 2-page document! **
Directions: Find each angle or arc measure.
The measure of arc FE is 27degrees,angle m<B is 112degrees, <GHJ = <GIJ = 73⁰ , m<S = 90 degrees in the given circles
The sum of angle in the triangle DEF is 180 degrees
mFE = <D
Recall that <D+<E+<F = 180⁰
<D+63+90 = 180
<D = 180-153
<D = 27 degrees
Hence the measure of arc FE is 27degrees
6) For this circle geometry, we will use the theorem
The sum of Opposite side of a cyclic quadrilateral is 180 degrees.
A + C = 180
m<A + 101 = 180
m<A = 180-101
m<A = 79degrees
Similarly
B + D = 180
m<B + 68 = 180
m<B = 180-68
m<B = 112degrees
7) The sum of angle in a circle is 360, hence;
arcGJ+68+31+115 = 36p
arcGJ = 360 - 214
arcGJ = 146⁰
Since the angle at the centre is twice angle at the circumference, then;
<GHJ = 1/2 arcGJ
<GHJ = 1/2(146)
<GHJ = 73⁰
<GHJ = <GIJ = 73⁰ (angle in the same segment of the circle are equal)
8) Recall that the sum of Opposite side of a cyclic quadrilateral is 180 degrees.
P + R = 180
57 + <R = 180
m<R = 180-57
m<R = 123degrees
Similarly, m<Q+m<S = 180⁰
Since the triangle in a semi circle is a right angled triangle, hence m<Q = 90 degrees (triangle PQR is a right angled triangle)
m<S = 180 - 90
m<S = 90 degrees
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I NEED HELP ON THIS ASAP! PLEASE, IT'S DUE TONIGHT!!!!
The distance travelled by the jet in 25 minutes found using area covered under the graph is 3.7 miles.
What is area?
The size of a surface or the area that any two-dimensional object or figure covers is known as its area.
Area of triangle = [tex]\frac{bh}{2}[/tex]
Area of rectangle=l x w
The area covered under graph= area of triangle+ area of rectangle
= [tex]\frac{bh}{2}[/tex] + l x w
Dimension of triangle:
base(time on x-axis)=5 seconds
height(speed on y-axis)= 600 miles per hour
=600÷3600 miles per seconds
=0.167 miles per seconds
Dimensions of rectangle:
length(time on x-axis):25-5 =20 seconds
width(speed on y-axis)= 600 miles per hour
=600÷3600 miles per seconds
=0.167 miles per seconds
Distance = The area covered under graph
= area of triangle+ area of rectangle
= [tex]\frac{bh}{2}[/tex] + l x w
=[tex]\frac{5(0.167)}{2}[/tex] + 20(0.167)
=0.4175 + 3.34
=3.7575
Distance ≈3.7 miles
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double integral of x^2 2y bound by y = x, y = x^3, and x> 0
The double integral of x² 2y over the given region (bounded by y = x, y = x³, and x > 0) is 2/35.
How to evaluate the double integral of the x² 2y?To solve this double integral, we need to integrate the function x² 2y over the given region in the xy-plane.
The region is bounded by the curves y = x and y = x³, and the line x = 0.
First, we need to determine the limits of integration. Since x > 0,
we can integrate from x = 0 to x = 1.
For each value of x in this range, the lower bound of y is given by y = x, and the upper bound is given by y = x³.
Therefore, we need to integrate with respect to y from y = x to y = x³ for each value of x in the range [0, 1].
So, the double integral can be written as:
∫(0 to 1) ∫(x to x³) x² 2y dy dx
Integrating with respect to y first, we get:
∫(0 to 1) [x² y²]x³_x dy dx= ∫(0 to 1) (x⁶ - x⁴) dx= [1/7 x⁷ - 1/5 x⁵]0_1= 1/7 - 1/5= 2/35Therefore, the double integral of x² 2y over the given region is 2/35.
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URGENT!! Will give brainliest :)
Describe the shape of the distribution.
A. It is uniform.
B. It is skewed.
C. It is symmetric.
D. It is bimodal.
Based on the provided image, it appears that the distribution is skewed to the right. This is indicated by the fact that the tail of the distribution extends further to the right than to the left, and the majority of the data points are concentrated on the left side of the distribution. Therefore, the answer would be B, it is skewed.
F(1) = 15 f(n)= f(n-1) x n evaluate the sequences in recursive form
Answer:
f(1) = 15
f(n) = f(n-1) x n
Step-by-step explanation:
The sequence in recursive form is:
f(1) = 15
f(n) = f(n-1) x n
Using this recursive formula, we can find the value of any term in the sequence by calculating the value of the previous term and multiplying it by the index of the current term.
For example, to find the value of f(2), we would use the formula:
f(2) = f(1) x 2
f(2) = 15 x 2
f(2) = 30
Similarly, to find the value of f(3), we would use the formula:
f(3) = f(2) x 3
f(3) = 30 x 3
f(3) = 90
And to find the value of f(4), we would use the formula:
f(4) = f(3) x 4
f(4) = 90 x 4
f(4) = 360
We can continue using this formula to find the values of any term in the sequence.
Complete the square to re-write the Quadratic function in vertex form
The vertex form of the given quadratic equation is.
y = -5(x + 6)² - 356
How to complete squares?To complete squares we need to use the perfect square trinomial:
(a + b)² = a² + 2ab +b²
Here we can rewrite our quadratic as follows:
y = -5x² - 60x - 176
y = -5*( x² + 12x) - 176
y = -5*( x² + 2*6x) - 176
Now we can add and subtract 6² = 36 then we will get:
y = -5*( x² + 2*6x + 36 - 36) - 176
y = -5*( (x + 6)² - 36) - 176
y = -5(x + 6)² - 356
Which means that the vertex is at (-6, -356)
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George is randomly selecting an outfit from his dresser. He has two pair of blue pants and four pair of black pants. In his closet there are two blue shirts, four green shirts, and one red shirt.
1. what is the probability he selects black pants and a green shirt?
2. what is the probability he selects a green or blue shirt?
3. what is the probability he does not choose a blue shirt?
Answer:
Probability of George picking black pants and a green shirt is 2/13
Probability of George picking a green shirt is 6/7
Probability of George not choosing a blue shirt 5/7
Can anyone post fake answers on this website
Answer:
If you're asking if its possible, yes it is