Answer:
B. because A and B cannot occur at the same time.
Step-by-step explanation:
If two events are mutually exclusive, why is ? Choose the correct answer below.
A. because A and B each have the same probability.
B. because A and B cannot occur at the same time.
C. because A and B are independent.
D. because A and B are complements of each other.
The mean height of women in a country (ages 20-29) is 63.5 inches. A random sample of 50 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume the standard deviation equals 2.96.
Answer:
11.70% probability that the mean height for the sample is greater than 64 inches
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 63.5, \sigma = 2.96, n = 50, s = \frac{2.96}{\sqrt{50}} = 0.4186[/tex]
What is the probability that the mean height for the sample is greater than 64 inches?
This is 1 subtracted by the pvalue of Z when X = 64.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64 - 63.5}{0.4186}[/tex]
[tex]Z = 1.19[/tex]
[tex]Z = 1.19[/tex] has a pvalue of 0.8830
1 - 0.8830 = 0.1170
11.70% probability that the mean height for the sample is greater than 64 inches
Plz help ASAP I’ll give lots of points
Answer:
8
Step-by-step explanation:
Because it is equal to the 4 side
Given the equation 4x - 3y = 12
1. Write the equation in slope-intercept form.
2. Identify the slope and y-intercept.
3. Graph the line.
4. Identify if it is a positive or negative slope.
Answer:
see below
Step-by-step explanation:
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
4x - 3y = 12
Solve for y
Subtract 4x from each side
4x-4x - 3y =-4x+ 12
-3y = -4x+12
Divide by -3
-3y/-3 = -4x/-3 + 12/-3
y = 4/3x -4
The slope is 4/3 and the y intercept is -4
The slope is Positive
What is the equation of the line which passes through (-0.5,-5) and (2,5)
Answer:
by using distance formula
d=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
by putting the values of coordinates
[tex]d=\sqrt{(2-(-0.5))^2+(5-(-5))^2}[/tex]
[tex]d=\sqrt{(2+0.5)^2+(5+5)^2}[/tex]
[tex]d=\sqrt{(2.5)^2+(10)^2}[/tex]
[tex]d=\sqrt{6.25+100}[/tex]
[tex]d=\sqrt{106.25}[/tex]
[tex]d=10.3[/tex]
Step-by-step explanation:
i hope this will help you :)
About ____% of the area is between z= -2 and z= 2 (or within 2 standard deviations of the mean)
Answer:
The percentage of area is between Z =-2 and Z=2
P( -2 ≤Z ≤2) = 0.9544 or 95%
Step-by-step explanation:
Explanation:-
Given data Z = -2 and Z =2
The probability that
P( -2 ≤Z ≤2) = P( Z≤2) - P(Z≤-2)
= 0.5 + A(2) - ( 0.5 - A(-2))
= A (2) + A(-2)
= 2 × A(2) (∵ A(-2) = A(2)
= 2×0.4772
= 0.9544
The percentage of area is between Z =-2 and Z=2
P( -2 ≤Z ≤2) = 0.9544 or 95%
A veterinarian is enclosing a rectangular outdoor running area against his building for the dogs he cares for. He needs to maximize the area using 100 feet of fencing. The quadratic function A(x)=x(100−2x) gives the area, A, of the dog run for the length, x, of the building that will border the dog run. Find the length of the building that should border the dog run to give the maximum area, and then find the maximum area of the dog run.
Answer:
a) The length of the building that should border the dog run to give the maximum area = 25feet
b) The maximum area of the dog run = 1250 s q feet²
Step-by-step explanation:
Step(i):-
Given function
A(x) = x (100-2x)
A (x) = 100x - 2x²...(i)
Differentiating equation (i) with respective to 'x'
[tex]\frac{dA}{dx} = 100 (1) - 2 (2x)[/tex]
⇒ [tex]\frac{dA}{dx} = 100 - 4 x[/tex] ...(ii)
Equating zero
⇒ 100 - 4x =0
⇒ 100 = 4x
Dividing '4' on both sides , we get
x = 25
Step(ii):-
Again differentiating equation (ii) with respective to 'x' , we get
[tex]\frac{d^{2} A}{dx^{2} } = -4 (1) < 0[/tex]
Therefore The maximum value at x = 25
The length of the building that should border the dog run to give the maximum area = 25
Step(iii)
Given A (x) = x ( 100 -2 x)
substitute 'x' = 25 feet
A(x) = 25 ( 100 - 2(25))
= 25(50)
= 1250
Conclusion:-
The maximum area of the dog run = 12 50 s q feet²
Question 15 A party rental company has chairs and tables for rent. The total cost to rent 8 chairs and 3 tables is $38 . The total cost to rent 2 chairs and 5 tables is $35 . What is the cost to rent each chair and each table?
Answer:
Each table is $6 and each chair is $2.50
Step-by-step explanation:
what is the solution for the inequality l2x-6l<4
Answer:
x < 5 or x > 1
Step-by-step explanation:
2x - 6 < 4
2x < 4 + 6
2x < 10
x < 10/2
x < 5
2x - 6 > - 4
2x > - 4 + 6
2x > 2
x > 2/2
x > 1
7
х
45
Find x.
x=
V(14)
7
07/2
Answer:
7
Step-by-step explanation:
This a special 90° 45° 45° triangle and is an Isosceles triangle at the same time
Of one of the equal side is 7 than the other one too must be 7
the required condition for using an anova procedure on data from several populations for mean comparison is that the
Answer:
The sampled populations have equal variances
Step-by-step explanation:
ANOVA which is fully known as Analysis of variances can be defined as the collection of statistical models as well as their associated estimation procedures which enables easily and effectively analyzis of the differences among various group means in a sample reason been that ANOVA is a total variance in which the observed variance in a specific variable is been separated into components which are attributable to various sources of variation which is why ANOVA help to provides a statistical test to check whether two or more population means are equal.
Therefore the required condition for using an ANOVA procedure on data from several populations for mean comparison is that THE SAMPLED POPULATION HAVE EQUAL VARIANCE.
For the functions f(x)=3x−1 and g(x)=4x−3, find (f∘g)(x) and (g∘f)(x)
The weight of a chocolate bar is 4.4 ounces, but can vary. Let W be a random variable that represents the weight of a chocolate bar. The probability density function of Wis given below. If the shaded portion of the graph of the continuous probability density function below is 0.42739, what is the probability that a chocolate bar is at least 4 ounces, but no more than 7 ounces?
Answer:
Ans) 42.7%
Step-by-step explanation:
For a continuous probability distribution, a curve known as probability density function contains information about these probabilities.
in the given range -
The probability that a continuous random variable = equal to the area under the probability density function curve
The probability that the value of a random variable is equal to 'something' is 1.
As per the diagram,
Weight of chocolate bar between 4 ounces and 7 ounces is highlighted in the blue part. That area is said to be 0.42739 and the total area under the curve is 1.
Hence required probability
=0.42739/1=0.42739
Ans) 42.7%
Round to nearest tenth of a percent
WWW
3.
The expression "5 FACTORIAL" equals
3-A
125
3-B
120
3-C
25
3-D
10
* Select Answer Below
Answer:
5! = 120
Step-by-step explanation:
5! is basically 5(4)(3)(2)(1).
find the solution set x^2+2x-15=0
Answer:
x = 3 or x = -5
Step-by-step explanation:
x² + 2x - 15 = 0
Factor left side of equation.
(x - 3)(x + 5) = 0
Set factors equal to 0
x - 3 = 0
x = 3
x + 5 = 0
x = -5
One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, 1 point to a D, and 0 points to an F. What is the GPA of a student who gets an A in a -credit course, a B in each of -credit courses, a C in a -credit course, and a D in a -credit course?
Question Correction
One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, 1 point to a D, and 0 points to an F. What is the GPA of a student who gets an A in a 3-credit course, a B in each of three 4-credit courses, a C in a 2-credit course, and a D in a 3-credit course?
Answer:
2.75
Step-by-step explanation:
We present the information in the table below.
[tex]\left|\begin{array}{c|c|c|c}$Course Grade&$Grade Point(x)&$Course Credit(y)&$Product(xy)\\---&---&---&---\\A&4&3&12\\B&3&4&12\\B&3&4&12\\B&3&4&12\\C&2&2&4\\D&1&3&3\\---&---&---&---\\$Total&&20&55\end{array}\right|[/tex]
Therefore, the GPA of the student is:
[tex]GPA=\dfrac{55}{20}\\\\ =2.75[/tex]
One of the solutions to x2 − 2x − 15 = 0 is x = −3. What is the other solution?
20 points if you can answer in under 30 minuets
Answer:
x=5 x=-3
Step-by-step explanation:
x^2 − 2x − 15 =0
Factor
What two numbers multiply to -15 and add to -2
-5*3 = -15
-5+3 =-2
(x-5) (x+3)=0
Using the zero product property
x-5 =0 x+3 =0
x=5 x=-3
Answer:
x^2 - 2x - 15 = 0
(x - 5) (x + 3) = 0
x - 5 = 0
x = 5
x + 3 = 0
x = -3
Don’t understand this, if anyone can help that would be awesome. :)
Answer:
look up the basic rules for sin and cos
Step-by-step explanation:
When a frequency distribution is exhaustive, each individual, object, or measurement from a sample or population must appear in at least one category.
a. True
b. False
Answer:
a. True
Step-by-step explanation:
The frequency distribution is a summary of the gathered data set, in which the interval of values is divided into classes.
A requirement for a frequency distribution is for the classes to be mutually exclusive and exhaustive. That is, each individual, object, or measurement in the data set must belong to one and only one class.
Then, we can conclude that each individual, object, or measurement must appear in at least one (in fact, only in one) category or class.
The smaller of two numbers is one-half the larger, and their sum is 27. Find the
numbers.
Answer:
9 and 18
Step-by-step explanation:
The numbers are in the ratio 1 : 2, so the ratio of the smaller to the total is ...
1 : (1+2) = 1 : 3
1/3 of 27 is 9, the value of the smaller number. The larger number is double this, so is 18.
The numbers are 9 and 18.
Answer:
9 and 18
Step-by-step explanation:
you know the explanation since another guy put it
Create a transformation that is not a similarity transformation. Use coordinate notation .
Answer:
(x, y) ⇒ (2x, y)
Step-by-step explanation:
Any rigid transformation or dilation will be a similarity transformation. A transformation that doesn't preserve similarity will be none of those, so may be non-linear or different in one direction than another.
Several possibilities come to mind:
(x, y) ⇒ (2x, y) . . . . . . stretches x, but not y
(x, y) ⇒ (x+y, y) . . . . . a "shear" transformation
(x, y) ⇒ (x, y^(3/2)) . . . . . a non-linear transformation
These only transform one coordinate. Of course, different transforms or combinations can be used on the different coordinates.
__
The attachment shows the effect of each of these. The red figure is the original icosagon (20-gon). The blue figure shows the horizontal stretch of the first transformation. The green figure shows the diagonal stretch of the shear transformation. The purple figure shows the effect of a non-linear transformation.
A child is 2 -1/2 feet tall. The child’s mother is twice as tall as the child. How tall is the child’s mother
Answer:
5 feet
Step-by-step explanation:
"Twice as tall" means "2 times as tall".
2 × (2 1/2 ft) = (2 × 2 ft) +(2 × (1/2 ft)) = 4 ft + 1 ft = 5 ft
The child's mother is 5 feet tall.
Answer:
The mother is 5ft tall
Step-by-step explanation:
2 1/2 + 2 1/2 = 5ft
2ft+2ft = 4ft
1/2+1/2= 1ft
4ft+1ft = 5ft
Will give brainliest answer
Answer:
[tex]153.86 \: {units}^{2} [/tex]
Step-by-step explanation:
[tex]area = \pi {r}^{2} \\ = 3.14 \times 7 \times 7 \\ = 3.14 \times 49 \\ = 153.86 \: {units}^{2} [/tex]
Answer:
153.86 [tex]units^{2}[/tex]
Step-by-step explanation:
Areaof a circle = πr^2
[tex]\pi = 3.14[/tex](in this case)
[tex]r^{2} =7[/tex]
A = πr^2
= 49(3.14)
= 153.86
Find the 61st term of the following arithmetic sequence.
15, 24, 33, 42,
Answer:
The answer is
555Step-by-step explanation:
For an nth term in an arithmetic sequence
[tex]U(n) = a + (n - 1)d[/tex]
where n is the number of terms
a is the first term
d is the common difference
From the question
a = 15
d = 24 - 15 = 9
n = 61
So the 61st term of the arithmetic sequence is
U(61) = 15 + (61-1)9
= 15 + 9(60)
= 15 + 540
= 555
Hope this helps you.
Please answer this correctly
Answer:
2/3
Step-by-step explanation:
There are 2 numbers out of 3 that fit the rule, 1 and 3. There is a 2/3 chance picking one of them.
Answer:
2/3Step-by-step explanation:
This is the answer because one number that is select is one. A number greater than 2 is 3. SO it is 2/3.
which of the following has a value less than 0?
A.4
B. |4|
C. |-4|
D. -4
Answer:
D
Step-by-step explanation:
The numbers that are less than 0 are negative. Negative numbers have the "-" sign in front of them so the answer is D.
Answer:
d
Step-by-step explanation:
The other ones will always be positive four
I NEED HELP PLEASE, THANKS! :)
Consider the standard form of each of the following options given, and note the hyperbola properties through that derivation -
[tex]Standard Form - \frac{\left(x-5\right)^2}{\left(\sqrt{7}\right)^2}-\frac{\left(y-\left(-5\right)\right)^2}{3^2}=1,\\Properties - \left(h,\:k\right)=\left(5,\:-5\right),\:a=\sqrt{7},\:b=3\\[/tex]
Similarly we can note the properties of each of the other hyperbolas. They are all similar to one another, but only option C is correct. Almost all options are present with a conjugate axis of length 6, but only option c is broad enough to include the point ( 1, - 5 ) and ( 9, - 5 ) in a given radius.
Solution = Option C!
Solve the triangles with the given parts: a=103, c=159, m∠C=104º
Answer:
Sides:
[tex]a= 103[/tex].[tex]b \approx 99[/tex].[tex]c - 159[/tex].Angles:
[tex]\angle A \approx 39^\circ[/tex].[tex]\angle B \approx 37^\circ[/tex].[tex]\angle C = 104^\circ[/tex].Step-by-step explanation:
Angle AApply the law of sines to find the sine of [tex]\angle A[/tex]:
[tex]\displaystyle \frac{\sin{A}}{\sin{C}} = \frac{a}{c}[/tex].
[tex]\displaystyle\sin A = \frac{a}{c} \cdot \sin{C} = \frac{103}{159} \times \left(\sin{104^{\circ}}\right) \approx 0.628556[/tex].
Therefore:
[tex]\angle A = \displaystyle\arcsin (\sin A) \approx \arcsin(0.628556) \approx 38.9^\circ[/tex].
Angle BThe three internal angles of a triangle should add up to [tex]180^\circ[/tex]. In other words:
[tex]\angle A + \angle B + \angle C = 180^\circ[/tex].
The measures of both [tex]\angle A[/tex] and [tex]\angle C[/tex] are now available. Therefore:
[tex]\angle B = 180^\circ - \angle A - \angle C \approx 37.1^\circ[/tex].
Side bApply the law of sines (again) to find the length of side [tex]b[/tex]:
[tex]\displaystyle\frac{b}{c} = \frac{\sin \angle B}{\sin \angle C}[/tex].
[tex]\displaystyle b = c \cdot \left(\frac{\sin \angle B}{\sin \angle C}\right) \approx 159\times \frac{\sin \left(37.1^\circ\right)}{\sin\left(104^\circ\right)} \approx 98.8[/tex].
x = ? ? ? ? ? ? ? ? ?
Answer:
7
Step-by-step explanation:
Answer:
x = 3
Step-by-step explanation:
Two secants drawn to a circle from an external point, then
The product of the measures of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant.
Thus
x × 12 = 4 × 9
12x = 36 ( divide both sides by 12 )
x = 3
After scoring a touchdown, a football team may elect to attempt a two-point conversion, by running or passing the ball into the end zone. If successful, the team scores two points. For a certain football team, the probability that this play is successful is 0.40.
a.â Let X =1 if successful, X= 0 if not. Find the mean and variance of X.
b.â If the conversion is successful, the team scores 2 points; if not the team scores 0 points. Let Y be the number of points scored. Does Y have a Bernoulli distribution? If so, find the success probability. If not, explain why not.
c.â Find the mean and variance of Y.
Answer:
a) Mean of X = 0.40
Variance of X = 0.24
b) Y is a Bernoulli's distribution. Check Explanation for reasons.
c) Mean of Y = 0.80 points
Variance of Y = 0.96
Step-by-step explanation:
a) The probability that play is successful is 0.40. Hence, the probability that play isn't successful is then 1 - 0.40 = 0.60.
Random variable X represents when play is successful or not, X = 1 when play is successful and X = 0 when play isn't successful.
The probability mass function of X is then
X | Probability of X
0 | 0.60
1 | 0.40
The mean is given in terms of the expected value, which is expressed as
E(X) = Σ xᵢpᵢ
xᵢ = each variable
pᵢ = probability of each variable
Mean = E(X) = (0 × 0.60) + (1 × 0.40) = 0.40
Variance = Var(X) = Σx²p − μ²
μ = mean = E(X) = 0.40
Σx²p = (0² × 0.60) + (1² × 0.40) = 0.40
Variance = Var(X) = 0.40 - 0.40² = 0.24
b) If the conversion is successful, the team scores 2 points; if not the team scores 0 points. If Y ia the number of points that team scores.Y can take on values of 2 and 0 only.
A Bernoulli distribution is a discrete distribution with only two possible outcomes in which success occurs with probability of p and failure occurs with probability of (1 - p).
Since the probability of a successful conversion and subsequent 2 points is 0.40 and the probability of failure and subsequent 0 point is 0.60, it is evident that Y is a Bernoulli's distribution.
The probability mass function for Y is then
Y | Probability of Y
0 | 0.60
2 | 0.40
c) Mean and Variance of Y
Mean = E(Y)
E(Y) = Σ yᵢpᵢ
yᵢ = each variable
pᵢ = probability of each variable
E(Y) = (0 × 0.60) + (2 × 0.40) = 0.80 points
Variance = Var(Y) = Σy²p − μ²
μ = mean = E(Y) = 0.80
Σy²p = (0² × 0.60) + (2² × 0.40) = 1.60
Variance = Var(Y) = 1.60 - 0.80² = 0.96
Hope this Helps!!!
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.050.05. If 212212 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.030.03
Answer:
95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.05, n = 212, \mu = 0.05, s = \sqrt{\frac{0.05*0.95}{212}} = 0.015[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 0.03?
This is the pvalue of Z when X = 0.03 + 0.05 = 0.08 subtracted by the pvalue of Z when X = 0.05 - 0.03 = 0.02. So
X = 0.08
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.08 - 0.05}{0.015}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 0.02
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.02 - 0.05}{0.015}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.