Answer:
The probability that, in successive drawing of chips, the colors of the first four chips alternate = 0.0751
Step-by-step explanation:
Step 1:
The probability that, in successive drawing of chips, the colors of the first four chips alternate, can occur in two ways: RED-WHITE-RED-WHITE (RWRW) or WHITE-RED-WHITE-RED (WRWR).
Step 2:
Given that an urn contains three white and four red chips and that each time we draw a chip, we look at its color. If it is red, we replace it along with two new red chips, and if it is white, we replace it along with three new white chips.
Probability of RWRW is given as follows:
Probabilty of the first being a red = 4/7
Probability of the next being a white = 3/9 = 1/3
Probability of the next being a red = 6/12 = 1/2
Probability of the next being a white = 6/14 = 3/7
Thus, probability of RWRW = 4/7 × 1/3 × 1/2 × 3/7 = 0.0408
Probability of WRWR is given as follows:
Probabilty of the first being a white = 3/7
Probability of the next being a white = 4/10 =2/5
Probability of the next being a red = 6/12 = 1/2
Probability of the next being a white = 6/15 = 2/5
Thus, probability of WRWR = 3/7 × 2/5 × 1/2 × 2/5 = 0.0343
Step 3:
Probability of RWRW or WRWR = 0.0408 + 0.0343 = 0.0751
Therefore, the probability that, in successive drawing of chips, the colors of the first four chips alternate = 0.0751
A local police chief claims that about 51% of all drug related arrests are ever prosecuted. A sample of 900 arrests shows that 47% of the arrests were prosecuted. Is there sufficient evidence at the 0.01 level to refute the chief's claim? State the null and alternative hypotheses for the above scenario.
Answer:
The null hypothesis is [tex]H_0: p = 0.51[/tex].
The alternate hypothesis is [tex]H_1: p \neq 0.51[/tex].
The p-value of the test is 0.0164 > 0.01, which means that there is not sufficient evidence at the 0.01 level to refute the chief's claim.
Step-by-step explanation:
A local police chief claims that about 51% of all drug related arrests are ever prosecuted
At the null hypothesis, we test if the proportion is of 51%, that is:
[tex]H_0: p = 0.51[/tex]
At the alternate hypothesis, we test if the proportion is different from 51%, that is:
[tex]H_1: p \neq 0.51[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.51 is tested at the null hypothesis:
This means that [tex]\mu = 0.51, \sigma = \sqrt{0.51*0.49}[/tex]
A sample of 900 arrests shows that 47% of the arrests were prosecuted.
This means that [tex]n = 900, X = 0.47[/tex]
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.47 - 0.51}{\frac{\sqrt{0.51*0.49}}{\sqrt{900}}}[/tex]
[tex]z = -2.4[/tex]
P-value of the test:
Probability that the sample proportion differs from 0.51 by at least 0.04, which is P(|z|>2.4), which is 2 multiplied by the p-value of Z = -2.4.
Looking at the z-table, the Z = -2.4 has a p-value of 0.0082.
2*0.0082 = 0.0164.
The p-value of the test is 0.0164 > 0.01, which means that there is not sufficient evidence at the 0.01 level to refute the chief's claim.
A rectangle’s length is two feet less than three times it’s width. If it’s width is 7 feet, then which of the following is its area?
1. 19 square feet
2. 57 square feet
3. 114 square feet
4. 133 square feet
The area of a rectangle is 28 m', and the length of the rectangle is 1 m more than twice the width. Find the dimensions of the rectangle.
Answer:
8m ×3.5m
Step-by-step explanation:
Area of rectangle= length ×width
Let the length and width of the rectangle be L and W meters respectively.
Area of rectangle= LW
LW= 28 -----(1)
L= 2W +1 -----(2)
Subst. (2) into (1):
(2W +1)(W)= 28
Expand:
2W² +W= 28
-28 on both sides:
2W² +W -28= 0
Factorise:
(W +4)(2W -7)= 0
W +4=0 or 2W -7=0
W= -4 (reject) or W= 3.5
Substitute W= 3.5 into (2):
L= 2(3.5) +1
L= 7 +1
L= 8
∴ The dimensions of the rectangle is 8m ×3.5m.
Solve the inequality and write the solution set using both set-builder notation and interval notation. -3a-15≤-2a+6
Answer:
Set builder notation: {a | a ≥ -21}
Interval notation: [-21, ∞)
Step-by-step explanation:
A set represents a collection of things, objects, or numbers. A set builder notation is in the form y = {x | x is an odd number between 8 and 10}, which means y contains all the odd numbers between 8 and 10.
Interval notation is a way to define a set of numbers between a lower limit and an upper limit using end-point values. for example (8, 20) means numbers between 8 and 20.
Given -3a-15≤-2a+6; solving :
-3a - 15 ≤ -2a + 6
-3a + 2a ≤ 6 + 15
-a ≤ 21
dividing through by -1:
a ≥ -21
The solution is:
Set builder notation: {a | a ≥ -21}
Interval notation: [-21, ∞)
Jane needs to buy mulch to cover a circular garden
whose dimensions are shown in the figure. The cost of
the mulch is $32.52 per square yard. Find the amount
of mulch she will need to the nearest square yard and
find the cost of the mulch.
Answer:
$3089.4
Step-by-step explanation:
A circle is a locus of a point such that its distance from a point known as the center is always constant.
The area of a circle is given by the formula:
Area = πr²; where r is the radius of the circle.
From the image attached, we can see that the garden is circular with a radius of 5.5 yard. Hence:
Amount of mulch needed to cover garden = area of garden = πr² = π(5.5)² = 95 yd²
Since mulch cost $32.52 per square yard, hence:
Cost of mulch needed = $32.52 per yd² * 95 yd² = $3089.4
what is the value of the x in the given diagram?
Answer:
x = 79
Step-by-step explanation:
All triangles have a sum of 180°. Knowing this, we can solve for the unknown angle.
56 + 23 + ? = 180
79 + ? = 180
? = 101
The variable x is known as an exterior angle. That and the angle we just solved for are supplementary meaning they add up to 180°.
101 + x = 180
x = 79
Answer:
79 degrees
Step-by-step explanation:
56 + 23 = 79
plz help me i am trying to get this done
Answer:
2700
Step-by-step explanation:
108*25=2700
100*25=2500
+
8*25=200
-------------------------------
2700
(4-2)^2x5+9
Answer+step by step
Answer:
4-2 = 2
2x5+9 = 19
2^19 = 2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2 = 524288
Answer:
29
Step-by-step explanation:
Use PEMDAS
P- Parenthesis
E- Exponents
M- Multiply
D- Divide
A- Add
S- Subtract
(4-2)^2×5+9 first you do parenthesis which is (4-2)=2
(2)^2×5+9 next the exponents (2)^2=4
4×5+9 now the multiplication, 4×5=20
20+9 And now finish it off with the addition
So the answer ends up being 29.
You roll two fair dice. Find the probability that the first die is a 6 given that the minimum of the two numbers is a 2.
Answer:
1/9 = 0.1111 = 11.11% probability that the first die is a 6 given that the minimum of the two numbers is a 2.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Minimum of the two numbers is 2.
Event B: First die in a 6.
Fair dice:
Each throw has 6 equally likely outcomes. Thus, in total, there are [tex]6^2 = 36[/tex] possible outcomes.
Minimum of the two numbers is a 2.
(2,2), (2,3), (3,2), (2,4), (4,2), (2,5), (5,2), (2,6), (6,2).
9 total outcomes in which the minumum of the two numbers is a two, which means that:
[tex]P(A) = \frac{9}{36}[/tex]
Minimum of the two numbers is a 2, and the first die is a 6.
Only one possible outcome, (6,2). So
[tex]P(A \cap B) = \frac{1}{36}[/tex]
Probability that the first die is a 6 given that the minimum of the two numbers is a 2.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{1}{36}}{\frac{9}{36}} = \frac{1}{9} 0.1111[/tex]
1/9 = 0.1111 = 11.11% probability that the first die is a 6 given that the minimum of the two numbers is a 2.
A density curve for all the possible weights between 0 pounds and 10 pounds is in the shape of a rectangle. What is the height of the rectangle in this density curve? O A. 0.01 OB. 0.001 C. 0.1 O D. 0.0001 SUBMIT
Answer:
0.1
Step-by-step explanation:
For a density curve, total area = 1
Probability lies in between 0 and 1
The Area of rectangle :
Area = Length * width
Length = 0 - 10 = 10
Area = 1
Hence,
Area = Length * width
1 = 10 * w
1 = 10w
w = 1 /10
w = 0.1
What is the equation of the line graphed below?
Answer: [tex]y=-\frac{1}{3}x[/tex]
Step-by-step explanation:
From the origin we can see to get to the point plotted we have to go down 1 and right three giving us the slope [tex]\frac{-1}{3}[/tex]
These are in the form of y=mx+b
b is the y-intercept and m is the slope
since the y-intercept is 0 b is 0 and isn't need leaving us with y=mx
We can put our slope into the equation giving us the answer in C
The required equation of the line is that passing through the point (3, -1) is y = -x/3.
Given that,
To determine the equation of the line that passes through the origin and a point (3, -1).
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
Since the line passes from the origin and a point (3, -1)
So, the slope of the line is given by,
m = (y₂ - y₁) / (x₂ - x₁)
Substitute the respective values in the above equation,
m = -1 + 0 / 3 - 0
m = -1/3,
Now the point-slope form of the equation of a line is,
y - y₁ = m (x - x₁)
Substitute the respective values in the above equation,
y + 1 = -1/3 (x - 3)
y = -x/3
Thus, the required equation of the line is that passing through the point (3, -1) is y = -x/3.
Learn more about slopes here:
https://brainly.com/question/3605446
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Find the value of x if the angles below are vertical.
Answer:
x = 19
Step-by-step explanation:
Since the angles are vertical, that means these angles are equal to each other:
7x + 34 = 10x - 23
7x - 10x = -23 - 34
-3x = -57
x = 19
Answer:
Step-by-step explanation:
7x+34=10x-23 (being vertically opposite angles)
34+23=10x-7x
57=3x
57/3=x
19=x
What is the mode for the set of data shown below?
14, 28, 33, 97, 53, 81, 42, 28, 32, 35, 75, 38, 69, 95, 49, 90
A. 14
B. 28
C. 95
D. 32
Answer:
28
Step-by-step explanation:
4, 28, 33, 97, 53, 81, 42, 28, 32, 35, 75, 38, 69, 95, 49, 90
Mode is the number that appears most often
4, 28, 28, 32, 33,35, 38, 42, 49,53,69, 75, 81, 90, 95, 97
28 appears twice
is y= 2^x + 3x - 4 a quadratic function
Answer:
No
Step-by-step explanation:
Due to the absence of the squared coefficient, we can automatically strike this as not a quadratic.
And, judging by the terms of the function, this is a trinomial.
Please help i’ll rate brainliest too
Answer:
- 4
Step-by-step explanation:
h(x) = sin x
f(x) = | 3x - 4 |
g(x) = 2x² - 6
h( [tex]\frac{\pi }{2}[/tex] ) = sin ( [tex]\frac{\pi }{2}[/tex] ) = 1
f ( 1 ) = | 3 × 1 - 4 | = 1
g ( 1 ) = 2( 1² ) - 6 = - 4
g ( f ( h ( [tex]\frac{\pi }{2}[/tex] ) ) ) = - 4
How many liters of a 20% alcohol solution must be mixed with 50 liters of a 70% alcohol solution to get a 40% alcohol solution?
What’s the answer to this? I need to do this for extra credit and I have no idea what this is
9514 1404 393
Answer:
20
Step-by-step explanation:
As with any evaluation problem, take it step by step according to the order of operations.
The first thing you need to do here is compute a#b.
The given definition can be simplified a bit for evaluation purposes:
a#b = a²b -ab² = ab(a -b)
Then for a=3 and b=-2, you have ...
(3)#(-2) = (3)(-2)(3 -(-2)) = -6(5) = -30
Now, you are in a position to evaluate the expression you're asked for.
[tex]\dfrac{(a\#b)^2}{15-(a\#b)}=\dfrac{(-30)^2}{15-(-30)}=\dfrac{900}{45}=\boxed{20}[/tex]
Two cyclists, 68 miles apart, start riding toward each other at the same time. One cycles 3 miles per hour faster than the other, and they meet after 4 hours of riding.
a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist. __________________
b. What are the speeds of the two cyclists? __________________
9514 1404 393
Answer:
a) r + (r+3) = 68/4 . . . . equation to answer the question
b) r = 7, r+3 = 10 . . . miles per hour
Step-by-step explanation:
a. The combined speed of the two cyclists is found from the time it takes for them to close the distance between them. The faster cyclist is traveling at (r+3) miles per hour.
speed = distance/time
r + (r+3) = 68/4 . . . . an equation to answer the problem
__
b. Solving the above equation helps us answer the question
2r +3 = 17 . . . simplify
2r = 14 . . . . . subtract 3
r = 7 . . . . . . divide by 2
r+3 = 10
The speeds of the two cyclists are 7 miles per hour and 10 miles per hour.
(8+3)(-1) Distributive Property
Answer:
-11
Step-by-step explanation:
(8+3)(-1) Add 8 + 3
(11)(-1) Multiply
-11 Final Answer
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{(8 + 3)(-1)}\\\\\large\textsf{(8 + 3) = \bf 11}\\\\\large\textsf{11(-1)}\\\\\large\textsf{= \bf -11}\\\\\boxed{\boxed{\large\textsf{\large\textsf{Answer: \huge \bf -11}}}}\huge\checkmark\\\\\\\\\\\large\text{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\\\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]
Suppose aggressive behavior is the dependent variable in a regression model and the other variables are independent variables. Is there evidence of extreme Multicollinearity
Answer and explanation:
Multicollinearity happens when multiple independent variables are correlated and therefore it is hard to determine which independent variable has the most impact or is most significantly affecting the dependent variable. This could be a source of confusion as the coefficients become less reliable.
Extreme multicollinearity occurs when there is exaggerated standard errors or increased variance of coefficient estimates.
Brainliest to who gets it right no links
A. t(x)=450-0.06x
hope this helps
$250 is invested in an account earning 6.8% interest (APR), compounded monthly. Write a function showing the value of the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
Answer:
36123.5994797
whats the missing number
Answer:
5Step-by-step explanation:
X * 3^2 +2 = 47
X * 9 + 2 = 47
9X = 47 - 2
9x = 45
x = 45 : 9
X = 5
The cost of 5 diesels is $1025. Calculate the cost of 17diesels
Write a cosine function that has an amplitude of 3, a midline of 2 and a period
Answer:
f(x) = 3 cos (2Pi / period value ; x )+ 2
or see answer using 2 as the period see answer in bold below.
Step-by-step explanation:
cosine function amplitude of 3 is A = 3
The period is used to find B
You need to show period value as the denominator and work out from there with 2PI as a function numerator to show as 2pi / period can be a data angle
C is the adding value.
Acos (Bx) + C
A = 3
Bx = 2 pi / period
C = + 2
However f 2 is also the period found
then we just plug in 2 to above formula
f(x) = 3 cos (2Pi / 2 ; x )+ 2
f(x) = 3cos (x pi) + 2
4x2-36x+80=0
Soma e Produto
Suppose x is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that x equals 19.62 is _____.
Answer:
The probability that x equals 19.62 is 0
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In the normal probability distribution, the probability of an exact value, that is, P(X = x) is 0. Thus, the probability that x equals 19.62 is 0
Solve the inequality:
4 +5t < 19
Answer:
t < 3 is the answer
Step-by-step explanation:
source: https://www.tiger-algebra.com/drill/4_5t%3C19/
^ (it has an explanation too)
In the triangle below, which of the following is equivalent to the tangent of
62°?
Answer:
tan62= 7/25
Step-by-step explanation:
tan = opposite/adjacent
Option A is the correct answer.
We need to find, from the given option which is equivalent to the tangent of 62°.
What is the ratio of trigonometric function tangent?The ratio of trigonometric function tangent is tanθ=Opposit/Adjacent.
Now, tan62°=24/7.
Therefore, option A is the correct answer.
To learn more about trigonometric ratios visit:
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HELP PLEASEEEEEEEE !!!