Answer: I think In short, the interior angles are all the angles within the bounds of the triangle. ... If you think about it, you'll see that when you add any of the interior angles of a triangle to its neighboring exterior angle, you always get 180—a straight line, A square has 4 90 degree angles so it adds to 360, think about how triangles having half the area of a square, just like how 180 is half of 360
hope this helped
COMPUTE:
A) 40−5÷ 1/5 =
B) (4.8−1.8÷6)÷5=
Answer:
A) 15
B) 0.9
Step-by-step explanation:
Use the correct order of operations.
A) 40 − 5 ÷ 1/5 =
= 40 − 5 * 5
= 40 - 25
= 15
B) (4.8 − 1.8 ÷ 6) ÷ 5 =
= (4.8 − 0.3) ÷ 5
= 4.5 ÷ 5
= 0.9
A newborn baby whose Apgar score is over 6 is classified as normal and this happens in 80% of births. As a quality control check, an auditor examined the records of 100 births. He would be suspicious if the number of normal births in the sample of 100 births fell below the lower limit of "usual." What is that lower limit?
Answer:
The lower limit is 72.
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.
If X is more than 2 standard deviations from the mean, it is unusual.
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, we have that:
[tex]n = 100, p = 0.8[/tex]
So
[tex]\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04[/tex]
He would be suspicious if the number of normal births in the sample of 100 births fell below the lower limit of "usual." What is that lower limit?
2 standard deviations below the mean is the lower limit, so X when Z = -2.
Proportion:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2 = \frac{X - 0.8}{0.04}[/tex]
[tex]X - 0.8 = -2*0.04[/tex]
[tex]X = 0.72[/tex]
Out of 100:
0.72*100 = 72
The lower limit is 72.
The mean of the data set(9,5,y,2,x)is twice the data set (8,x, 4,1,3).What is (y-x)
Answer:
y - x = 16
Step-by-step explanation:
Explanation:-
Step(i):-
Given data set A is 9,5,y,2,x
Mean of the Data set A
= [tex]\frac{9 + 5 + y + 2 +x}{5}[/tex]
= [tex]\frac{16 +x+y}{5}[/tex]
Given data set B is 8, x, 4, 1, 3
Mean of the Data set B
= [tex]\frac{8+ x+4+1+3}{5}[/tex]
Step(ii):-
Mean of the Data set A = 2 X Mean of the Data set B
[tex]\frac{16 +x+y}{5} = 2 X \frac{16+x}{5}[/tex]
On simplification , we get
16 +x + y = 2( 16 +x)
16 + x + y = 32 + 2 x
16 + x + y - 32 - 2 x = 0
y - x -16 =0
y - x = 16
Simplify.
(8^3)7 = 8n
Answer:
448I think
Step-by-step explanation:
Answer:21
Step-by-step explanation:
in four lines determine how to find a perimeter and area of garden with specific dimensions
Answer:
[tex]Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]
[tex]Area\ of\ the\ garden\ =l1*b1[/tex]
Step-by-step explanation:
Let assume the l1 is the length of the garden and b1 is the breadth of garden then
[tex]Perimeter\ of\ the\ Garden\ = 2 ( L ength + Breadth )\\Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]
Now,
[tex]Area\ of\ Garden\ = Length * Breadth[/tex]
[tex]Area\ of\ the\ garden\ =l1*b1[/tex]
Anyone Can help me? Thanks
Answer:
9.8
Step-by-step explanation:
updated
9^2=x^2+4^2
9*9=x*x+4*4
81=x*x-16
+16. +16
97=x*x
√97=√x*x
√97=x
So the answer is √97, but the question wants it rounded so it's actually 9.8
if F (x) equals 4x + 7 which of the following is the inverse of F(x)
Answer:
[tex]F^{-1}(x)=\dfrac{x-7}{4}[/tex]
Step-by-step explanation:
To find the inverse function, solve for y the relation ...
F(y) = x
4y +7 = x
4y = x - 7
y = (x -7)/4 . . . . the inverse function
[tex]\boxed{F^{-1}(x)=\dfrac{x-7}{4}}[/tex]
Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles; the sample standard deviation was 1,412 miles.
a) To decide if the sample data support the company records that the spark plugs average 22,100 miles, state your decision in terms of the null hypothesis. Use a 0.05 level of significance.
b) What is the critical value for the test using a 0.05 level of significance?
c) What is the test statistic?
d) What is your decision?
Answer:
a) We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 22100[/tex]
Alternative hypothesis:[tex]\mu \neq 22100[/tex]
b) We need to find the degrees of freedom given by:
[tex] df =n-1 = 18-1=17[/tex]
And the critical values for this case are:
[tex] t_{\alpha/2}= 2.110[/tex]
c) [tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]
d) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi
Step-by-step explanation:
Information provided
[tex]\bar X=23400[/tex] represent the sample mean
[tex]s=1412[/tex] represent the sample standard deviation
[tex]n=18[/tex] sample size
[tex]\mu_o =22100[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Part a
We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 22100[/tex]
Alternative hypothesis:[tex]\mu \neq 22100[/tex]
Part b
We need to find the degrees of freedom given by:
[tex] df =n-1 = 18-1=17[/tex]
And the critical values for this case are:
[tex] t_{\alpha/2}= 2.110[/tex]
Part c
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]
Part d
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi
A local coffee house surveyed 317 customers regarding their preference of chocolate chip or cranberry walnut scones . 150 customers prefer the Cranberry Walnut Scones . 81 customers who responded were males and prefer the Chocolate Chip Scones . 172 female customers responded . Find the probability that a customer chosen at random will be a male or prefer the Chocolate Chip Scones .
1. 25.6%
2. 24.1%
3. 72.9%
4. 98.4%
Answer:
3. 72.9%
Step-by-step explanation:
Let's call M the event that the customer is male and C the event that the customer prefer chocolate chips Scones.
So, the probability P(M∪C) that a customer chosen at random will be a male or prefer the Chocolate Chip Scones is calculated as:
P(M∪C) = P(M) + P(C) - P(M∩C)
Then, there are 145 males (317 customer - 172 females = 145 males), so the probability that the customer is a males is:
P(M) = 145/317 = 0.4574
There are 167 customers that prefer chocolate chips Scones ( 317 customers - 150 customers that prefer the Cranberry Walnut Scones = 167), so the probability that a customer prefer chocolate chips Scones is:
P(C) = 167/317 = 0.5268
Finally, 81 customers were males and prefer the Chocolate Chip Scones, so the probability that a customer will be a male and prefer chocolate chip scones is:
P(M∩C) = 81/317 = 0.2555
Therefore, P(M∪C) is equal to:
P(M∪C) = 0.4574 + 0.5268 - 0.2555
P(M∪C) = 0.7287
P(M∪C) = 72.9%
Answer:
3. 72.9%
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Desired outcomes:
Male or prefers the Chocolate Chip Scones. That is, males and females who prefer the Chocolate Chip Scones.
There are 172 female customers and 317-172 = 145 male customers.
150 customers prefer the Cranberry Walnut Scones. So 317 - 150 = 167 customers prefer the Chocolate Chip Scones.
81 of those are male, so 167 - 81 = 86 are female.
So the total of desired outcomes is 86 + 145 = 231
Total outcomes:
317 total customers.
Probability:
231/317 = 0.729
So the correct answer is:
3. 72.9%
One side of a rectangle is 14 meters. The perimeter of the rectangle is 44 meters. What is the area of this rectangle?
HELP! the function f(x)=200/x+10 models the cost per student of a field trip when x students go on the trip. how is the parent function f(x)=1/x transformed to create the function f(x)=200/x+10
Answer:
stretch of 200 shift up 10 units
Step-by-step explanation:
f(x)=1/x to 200/x+10
Multiply by 200 means a stretch of 200
f(x) = 200/x
Now shift up 10 units
f(x) = 200/x + 10
Answer:
It moves up 10 units
Step-by-step explanation:
f(x) =1/x to 200/x + 10
= 200/x
If we shift up 10 units, we get:
f(x) = 200/x + 10
Hope this helps!
A study of consumer smoking habits includes A people in the 18-22 age bracket (B of whom smoke), C people in the 23-30 age bracket (D of whom smoke), and E people in the 31-40 age bracket (F of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes.
The correct question is:
A study of consumer smoking habits includes 167 people in the 18-22 age bracket (59 of whom smoke), 148 people in the 23-30 age bracket (31 of whom smoke), and 85 people in the 31-40 age bracket (23 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes
Answer:
The probability of getting someone who is age 23-30 or smokes = 0.575
Step-by-step explanation:
We are given;
Number consumers of age 18 - 22 = 167
Number of consumers of ages 22 - 30 = 148
Number of consumers of ages 31 - 40 = 85
Thus,total number of consumers in the survey = 167 + 148 + 85 = 400
We are also given;
Number consumers of age 18 - 22 who smoke = 59
Number of consumers of ages 22 - 30 who smoke = 31
Number of consumers of ages 31 - 40 who smoke = 23
Total number of people who smoke = 59 + 31 + 23 = 113
Let event A = someone of age 23-30 and event B = someone who smokes. Thus;
P(A) = 148/400
P(B) = 113/400
P(A & B) = 31/400
Now, from addition rule in sets which is given by;
P(A or B) = P (A) + P (B) – P (A and B)
We can now solve the question.
Thus;
P(A or B) = (148/400) + (113/400) - (31/400)
P(A or B) = 230/400 = 0.575
A mattress store sells only king, queen and twin-size mattresses. Sales records at the store indicate that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. Records also indicate that three times as many king-size mattresses are sold as twin-size mattresses. Calculate the probability that the next mattress sold is either king or queen-size.
Answer:
The probability that the next mattress sold is either king or queen-size is P=0.8.
Step-by-step explanation:
We have 3 types of matress: queen size (Q), king size (K) and twin size (T).
We will treat the probability as the proportion (or relative frequency) of sales of each type of matress.
We know that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. This can be expressed as:
[tex]P_Q=\dfrac{P_K+P_T}{4}\\\\\\4P_Q-P_K-P_T=0[/tex]
We also know that three times as many king-size mattresses are sold as twin-size mattresses. We can express that as:
[tex]P_K=3P_T\\\\P_K-3P_T=0[/tex]
Finally, we know that the sum of probablities has to be 1, or 100%.
[tex]P_Q+P_K+P_T=1[/tex]
We can solve this by sustitution:
[tex]P_K=3P_T\\\\4P_Q=P_K+P_T=3P_T+P_T=4P_T\\\\P_Q=P_T\\\\\\P_Q+P_K+P_T=1\\\\P_T+3P_T+P_T=1\\\\5P_T=1\\\\P_T=0.2\\\\\\P_Q=P_T=0.2\\\\P_K=3P_T=3\cdot0.2=0.6[/tex]
Now we know the probabilities of each of the matress types.
The probability that the next matress sold is either king or queen-size is:
[tex]P_K+P_Q=0.6+0.2=0.8[/tex]
What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places
Answer:
The probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.
Step-by-step explanation:
The complete question is:
There are 103 students in a physics class. The instructor must choose two students at random.
Students in a Physics Class
Academic Year Physics majors Non-Physics majors
Freshmen 17 15
Sophomores 20 14
Juniors 11 17
Seniors 5 4
What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.
Solution:
There are a total of N = 103 students present in a Physics class.
Some of the students are Physics Major and some are not.
The instructor has to select two students at random.
The instructor first selects a senior Physics major and then a sophomore Physics major.
Compute the probability of selecting a senior Physics major student as follows:
[tex]P(\text{Senior Physics Major})=\frac{n(\text{Senior Physics Major}) }{N}[/tex]
[tex]=\frac{5}{103}\\\\=0.04854369\\\\\approx 0.0485[/tex]
Now he two students are selected without replacement.
So, after selecting a senior Physics major student there are 102 students remaining in the class.
Compute the probability of selecting a sophomore Physics major student as follows:
[tex]P(\text{Sophomore Physics Major})=\frac{n(\text{Sophomore Physics Major}) }{N}[/tex]
[tex]=\frac{20}{102}\\\\=0.1960784314\\\\\approx 0.1961[/tex]
Compute the probability that a senior Physics major and then a sophomore Physics major are chosen at random as follows:
[tex]P(\text{Senior}\cap \text{Sophomore})=P(\text{Senior})\times P(\text{Sophomore})[/tex]
[tex]=0.0485\times 0.1961\\\\=0.00951085\\\\\approx 0.0095[/tex]
Thus, the probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.
Suppose that a random sample of size 36 is to be selected from a population with mean 50 and standard deviation 7. What is the approximate probability that X will be within .5 of the population mean
Answer:
Step-by-step explanation:
Let us assume that x is normally distributed. The sample size is greater than 30. Since the the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = standard deviation
n = number of samples
From the information given,
µ = 50
σ = 7
n = 36
If x is within 0.5 of the population mean, it means that x is between (50 - 0.5) and (50 + 0.5)
the probability is expressed as
P(49.5 ≤ x ≤ 50.5)
For x = 49.5
z = (49.5 - 50)/(7/√36) = - 0.43
Looking at the normal distribution table, the probability corresponding to the z score is 0.334
For x = 49.5
z = (50.5 - 50)/(7/√36) = 0.43
Looking at the normal distribution table, the probability corresponding to the z score is 0.666
Therefore,
P(49.5 ≤ x ≤ 50.5) = 0.666 - 0.334 = 0.332
Multiply or divide as indicated x^10/x^4
Answer:
X^6
Step-by-step explanation:
Graph y < x2 + 4x. Click on the graph until the correct graph appears.
Answer: The correct answer is:
_________________________
The given "graph" in the bottom right, lowest corner
Step-by-step explanation:
_________________________
Note: When there is only one (1) equation give for a graph;
and/or: only one (1) "inequality given";
we look for the symbol.
If the symbol is "not" an "equals" symbol (i.e. not an: = symbol) ;
we check for the type of "inequality" symbol.
If there is a: "less than" (<) ; or a "greater than" (>) symbol; the graph of the "inequality" will have "dashed lines" (since there will be a "boundary").
If there is an "inequality" that is a: "less than or equal to" (≤) ;
or a: "greater than or equal to" (≥) ;
→ then there will be not be a dashed line when graphed;
but rather—a "solid line" ; since "less than or equal to" ;
or "greater than or equal to" —is similar to:
"up to AND including"; or: "lesser/fewer than AND including".).
_________________________
Note: We are given the "inequality" :
→ " y < x² + 4x " .
_________________________________
Note that we have a "less than" symbol (< ) ; so the graph will have a:
"solid line" [and not a "dotted line".].
_________________________________
Note that all of the graphs among our 4 answer choices have "dotted lines".
Not that all values (all x and y coordinated) within the "shaded portion" of the corresponding graph are considered part of the graph.
As such, given any point within the shaded part, the x and y coordinates must match the inequality (i.e. the given inequality must be true when one puts in the "x-coordinate" and "y-coordinate" into the "given inequality" :
→ " y < x² + 4x " .
_________________________
Likewise, we can take any point within the "white, unshaded" portion of any of the graph, and take the "x-coordinate" and "y-coordinate" of that point, and the inequality: → " y < x² + 4x " ; will not hold true when the "x-coordinate" and "y-coordinate" values of that point— are substituted into the "inequality".
_________________________
{Note: Answer is continued on images attached.}.
Wishing you the best!
A city has just added 100 new female recruits to its police force. The city will provide a pension to each new hire who remains with the force until retirement. In addition, if the new hire is married at the time of her retirement, a second pension will be provided for her husband. A consulting actuary makes the following assumptions: (i) Each new recruit has a 0.4 probability of remaining with the police force until retirement. (ii) Given that a new recruit reaches retirement with the police force, the probability that she is not married at the time of retirement is 0.25. (iii) The events of different new hires reaching retirement and the events of different new hires being married at retirement are all mutually independent events. Calculate the probability that the city will provide at most 90 pensions to the 100 new hires and their husbands. (A) 0.60 (B) 0.67 (C) 0.75 (D) 0.93 (E) 0.99
Answer:
E) 0.99
Step-by-step explanation:
100 recruits x 0.4 chance of retiring as police officer = 40 officers
probability of being married at time of retirement = (1 - 0.25) x 40 = 30 officers
each new recruit will result in either 0, 1 or 2 new pensions
0 pensions when the recruit leaves the police force (0.6 prob.)1 pension when the recruit stays until retirement but doesn't marry (0.1 prob.)2 pensions when the recruit stays until retirement and marries (0.3 prob.)mean = µ = E(Xi) = (0 x 0.6) + (1 x 0.1) + (2 x 0.3) = 0.7
σ² = (0² x 0.6) + (1² x 0.1) + (2² x 0.3) - µ² = 0 + 0.1 + 1.2 - 0.49 = 0.81
in order for the total number of pensions (X) that the city has to provide:
the normal distribution of the pension funds = 100 new recruits x 0.7 = 70 pension funds
the standard deviation = σ = √100 x √σ² = √100 x √0.81 = 10 x 0.9 = 9
P(X ≤ 90) = P [(X - 70)/9] ≤ [(90 - 70)/9] = P [(X - 70)/9] ≤ 2.22
z value for 2.22 = 0.9868 ≈ 0.99
Graph the line with slope -1/3 and y -intercept 6 .
Answer:
plot a point at 6 up from (0,0) and then go down one and over three places then plot another point- and so on - and so on
Step-by-step explanation:
To graph the line using the slope and intercept, first understand what the slope and intercept mean:
Slope is how steep or flat the line appears on the graph.
A very high or low slope (100 or -100) will be very steep on the graph.A slope very close to zero (0.0001 or -0.0001) will be very flat on the graph.A positive slope will travel northeast and southwest (for linear equations).A negative slope will travel northwest and southeast (for linear equations).The y-intercept is the point at which the line hits the y-axis. In this equation, the line hits the y-axis at positive 6, which means that the point is (0, 6).
You can use a method called "rise over run" to graph. The slope is negative one over three, so the line will "rise" negative one units after "running" three units.
So, for every one unit down, the line will travel three units to the right.
Graph this from the point (0, 6), your y-intercept, and plot the points according to the slope:
Score: 4 of 8 pts
TA
23.1.59
A ball is thrown upward and outward from a height of 5 feet. The height of the ball, f(x), in feet, can be mo
f(x) = -0.2x² +2.1x+5
where x is the ball's horizontal distance, in feet from where it was thrown. Use this model to solve parts (
a. What is the maximum height of the ball and how far from where it was thrown does this occur?
The maximum height is feet, which occurs feet from the point of release
(Round to the nearest tenth as needed.)
Answer:
10.5 ft high
5.3 ft horizontally
Step-by-step explanation:
The equation can be written in vertex form to answer these questions.
f(x) = -0.2(x² -10.5x) +5
f(x) = -0.2(x² -10.5x +5.25²) +5 +0.2(5.25²)
f(x) = -0.2(x -5.25)² +10.5125
The vertex of the travel path is (5.25, 10.5125).
The maximum height is 10.5 feet, which occurs 5.3 feet (horizontally) from the point of release.
A study seeks to answer the question, "Does Vitamin C level in the breast milk of new mothers reduce the risk of allergies in their breastfed infants?" The study concluded that high levels of vitamin C (measured in mg) were associated with a 30 percent lower risk of allergies in the infants. In this scenario, "levels of vitamin C (measured in milligrams)" is what type of variable?
Answer:
Quantitative variable
Step-by-step explanation:
The objective in this study is to find the of variable used to conduct the study. The type of variable used to conduct this study is Qualitative variable.
There are majorly two types of variable. These are:
Categorical VariableQuantitative variableCategorical variables are types of variables that are grouped based on some similar characteristics. The nominal scale and the ordinal scale falls under this group of variable.
The nominal scale is an act of giving name to a particular object or concept in order to identify or classify that particular thing.
On the other hand, The ordinal scale possess all the characteristics of nominal scale but here the variables can be ordered. It can be used to determine whether the item is greater or less. It express the indication of order and magnitude.
In Qualitative variables; variables are measured on a numeric scale. From the given question , This type of variable is used to measure the high levels of vitamin C (measured in mg) which were associated with a 30 percent lower risk of allergies in the infants.
The levels of vitamin C could range from 0 mg to certain mg therefore we can measure vitamin C in numerical values of measurement (Quantitative variable).
Q‒4. Suppose A is the set composed of all ordered pairs of positive integers. Let R be the relation defined on A where (a,b)R(c,d) means that a+d=b+c.
Prove that R is an equivalence relation.
Find [(2,4)].
Answer:
Step-by-step explanation:
REcall that given a set A, * is a equivalence relation over A if
- for a in A, then a*a.
- for a,b in A. If a*b, then b*a.
- for a,b,c in A. If a*b and b*c then a*c.
Consider A the set of all ordered pairs of positive integers.
- Let (a,b) in A. Then a+b = a+b. So, by definition (a,b)R(a,b).
- Let (a,b), (c,d) in A and suppose that (a,b)R(c,d) . Then, by definition a+d = b+c. Since the + is commutative over the integers, this implies that d+a = c+b. Then (c,d)R(a,b).
- Let (a,b),(c,d), (e,f) in A and suppose that (a,b)R(c,d) and (c,d)R(e,f). Then
a+d = b+c, c+f = d+e. We have that f = d+e-c. So a+f = a+d+e-c. From the first equation we find that a+d-c = b. Then a+f = b+e. So, by definition (a,b)R(e,f).
So R is an equivalence relation.
[(a,b)] is the equivalence class of (a,b). This is by definition, finding all the elements of A that are equivalente to (a,b).
Let us find all the possible elements of A that are equivalent to (2,4). Let (a,b)R(2,4) Then a+4 = b+2. This implies that a+2 = b. So all the elements of the form (a,a+2) are part of this class.
Find the percent of area under a normal curve between the mean and the given number of standard deviations from the mean. (Note that positive indicates above the mean, while negative indicates below the mean.)0.20
Answer:
15.86%
Step-by-step explanation:
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.
Percent of area between the mean and 0.20 standard deviations from the mean:
pvalue of Z = 0.2 subtracted by the pvalue of Z = -0.2
Z = 0.2 has a pvalue of 0.5793
Z = -0.2 has a pvalue of 0.4207
0.5793 - 0.4207 = 0.1586
So this percentage is 15.86%
You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.3. A random sample of 735 men over the age of 50 found that 203 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim
Answer:
[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]
Now we can claculate the p value with this formula:
[tex]p_v =P(z<-1.42)=0.0778[/tex]
If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.
Step-by-step explanation:
Information to given
n=735 represent the random sample taken
X=203 represent the number of people who have their prostate regularly examined
[tex]\hat p=\frac{203}{735}=0.276[/tex] estimated proportion of people who have their prostate regularly examined
[tex]p_o=0.3[/tex] is the value to verify
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true proportion is less than 0.3, the ystem of hypothesis are.:
Null hypothesis:[tex]p \geq 0.3[/tex]
Alternative hypothesis:[tex]p < 0.3[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]
Now we can claculate the p value with this formula:
[tex]p_v =P(z<-1.42)=0.0778[/tex]
If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.
A random sample of 1,000 StatCrunchU students contains 598 female and 402 males. We analyze responses to the question, "What is the total amount (in dollars) of your student loans to date?" Two sample T confidence interval: μ 1: Mean of Loans where Gender="Female" μ 2: Mean of Loans where Gender="Male" μ 1 − μ 2: Difference between two means (without pooled variances) 95% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit μ 1 − μ 2 516.74334 368.41116 907.34739 -206.29374 1239.7804 What can we conclude from the 95% confidence interval? Check all that apply. Group of answer choices
Based on the information given, these are the conclusions we can draw from the 95% confidence interval.
Here, we have,
From the provided 95% confidence interval, we can make the following conclusions:
The point estimate of the difference between the mean student loans for females and males is 516.74334 dollars.
The standard error of the difference between the means is 368.41116 dollars.
The degrees of freedom (DF) associated with the confidence interval is 907.34739.
The lower limit of the confidence interval is -206.29374 dollars.
The upper limit of the confidence interval is 1239.7804 dollars.
The confidence interval does not contain zero.
Since zero is not within the interval, we can conclude that the difference between the mean student loans for females and males is statistically significant at the 95% confidence level.
Based on the information given, these are the conclusions we can draw from the 95% confidence interval.
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The estimated difference in the mean student loans between females and males is 516.74334.
There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.
Based on the 95% confidence interval provided for the difference in means between the loans of female and male StatCrunchU students, we can draw the following conclusions:
The sample difference in means is 516.74334.
The standard error of the difference is 368.41116.
The degrees of freedom (DF) for the analysis is 907.34739.
The lower limit of the confidence interval is -206.29374.
The upper limit of the confidence interval is 1239.7804.
Therefore, we can conclude the following:
The estimated difference in the mean student loans between females and males is 516.74334.
There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.
Note: Since the confidence interval includes both positive and negative values, we cannot conclude with certainty whether there is a significant difference or not in the mean student loans between females and males. The confidence interval suggests that the difference could be positive, negative, or even zero.
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Please answer this correctly
Answer:
676
Step-by-step explanation:
lxw
14x35
4x24
6x15
676
Solve the equation and state a reason for each step.
23+11a-2c=12-2c
Simplifying
23 + 11a + -2c = 12 + -2c
Add '2c' to each side of the equation.
23 + 11a + -2c + 2c = 12 + -2c + 2c
Combine like terms: -2c + 2c = 0
23 + 11a + 0 = 12 + -2c + 2c
23 + 11a = 12 + -2c + 2c
Combine like terms: -2c + 2c = 0
23 + 11a = 12 + 0
23 + 11a = 12
Solving
23 + 11a = 12
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-23' to each side of the equation.
23 + -23 + 11a = 12 + -23
Combine like terms: 23 + -23 = 0
0 + 11a = 12 + -23
11a = 12 + -23
Combine like terms: 12 + -23 = -11
11a = -11
Divide each side by '11'.
a = -1
Simplifying
a = -1
1. O perímetro de um quadrado é 20 cm. Determine sua diagonal. 1 ponto a) 2 √5 cm b) 20√2 cm c) 5√2 cm d) 2√10 cm
Answer:
c) 5√2 cm
Step-by-step explanation:
A square with side length l has a perimeter given by the following equation:
P = 4l.
In this question:
P = 20
So the side length is:
4l = 20
l = 20/4
l = 5
Diagonal
The diagonal forms a right triangle with two sides, in which the diagonal is the hypothenuse. Applying the pytagoras theorem.
[tex]d^{2} = l^{2} + l^{2}[/tex]
[tex]d^{2} = 5^{2} + 5^{2}[/tex]
[tex]d^{2} = 50[/tex]
[tex]d = \pm \sqrt{50}[/tex]
Lenght is a positive meausre, so
[tex]d = \sqrt{50}[/tex]
[tex]d = \sqrt{2 \times 25}[/tex]
[tex]d = \sqrt{2} \times \sqrt{25}[/tex]
[tex]d = 5\sqrt{2}[/tex]
So the correct answer is:
c) 5√2 cm
∠BAD is bisected by . If m∠BAC = 2x - 5 and m∠CAD = 145, the value of x is:
Answer:
x = 75
Step-by-step explanation:
Assuming the angles are equal ( bisected means divided in half)
2x-5 = 145
Add 5 to each side
2x-5+5 = 145+5
2x = 150
Divide by 2
2x/150/2
x = 75
Answer:
x=75
Step-by-step explanation:
∠BAD is bisected by AC and measurement of BAC is equal to 2x - 5 and measurement of CAD is equal to 145. Since they are bisected, they are equal and the solution is shown below:
m ∠ BAC = m ∠ CAD
2x - 5 = 145 , transpose -5 to the opposite side such as:
2x = 145 + 5 , perform addition of 145 and 5
2x = 150
2x / 2 = 150 / 2 , divide both sides by 2
x = 75
The answer is 75 for the x value.
Ares is making 14 jars of honey peanut butter. He wants to use 45 milliliter (ML) of honey in each jar. How much honey (in ML) will ares use in all?
Answer:
630 milliliters.
Step-by-step explanation:
The statement tells us that the final product is 14 jars of honey peanut butter and that in each jar use 45 mliliters of honey. This means that to know the total honey to be used, the required quantity for each jar must be multiplied by the total number of jars, that is:
14 * 45 = 630
Which means that he would spend a total of 630 milliliters.
Step-by-step explanation:
Ares uses 630 ml of honey, because 14×45=630