Given:
Vertices of a parallelogram ABCD are A(7,-4), B(-1,-4), C(-1,-12), D(7, -12).
To find:
Whether the parallelogram ABCD is a rhombus, rectangle or square.
Solution:
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, we get
[tex]AB=\sqrt{(-4-(-4))^2+(-1-7)^2}[/tex]
[tex]AB=\sqrt{(-4+4)^2+(-8)^2}[/tex]
[tex]AB=\sqrt{0+64}[/tex]
[tex]AB=8[/tex]
Similarly,
[tex]BC=\sqrt{(-1-(-1))^2+(12-(-4))^2}=8[/tex]
[tex]CD=\sqrt{(7-(-1))^2+(-12-(-12))^2}=8[/tex]
[tex]AD=\sqrt{(7-7)^2+(-12-(-4))^2}=8[/tex]
All sides of parallelogram are equal.
[tex]AC=\sqrt{(-1-7)^2+(-12-(-4))^2}=8\sqrt{2}[/tex]
[tex]BD=\sqrt{(7-(-1))^2+(-12-(-4))^2}=8\sqrt{2}[/tex]
Both diagonals are equal.
Since, all sides are equal and both diagonals are equal, therefore, the parallelogram ABCD is a square.
We know that, a square is special case of rectangles and rhombus.
So, parallelogram ABCD is a rhombus, rectangle or square. Therefore, the correct option is c.
3. The Round Rock Express has a pitcher with an impressive winning record. Opposing teams are attempting to analyze his pitches. The pitcher throws a strike 35of the time. If the pitcher throws a strike the next pitch is a fastbal 40% of the time. If the pitcher doesn't throw a strike the next pitch is a fastball 80% of the time.
Answer:
0.66
Step-by-step explanation:
Given:
Let P(Throwing strike) = 0.35
So,
P(S') = 1 - 0.35 = 0.65
P(A / B) = P(A and B) / P(B)
P(Throwing fastball and thrown strike) = P(F / S) = 40% = 0.4
P(Throwing fastball not thrown strike) = P(F / S') = 80%
P(Throwing fastball not thrown strike) =0.8
So,
P(F and S) = 0.8 x 0.65
P(F and S) = 0.52
P(F) = [P(F / S) x P(S)] + [P(F / S') x P(S')]
= (0.4 x 0.35) + (0.8 x 0.65)
= 0.14 + 0.52
= 0.66
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are the weights in pounds of 11 players randomly selected from the roster of a championship sports team. Are the results likely to be representative of all players in that sport's league? 278 279 185 299 245 281 291 234 278 227 281
Answer:
Mean = 261.63 poundsMedian = 278 poundsModes: 278 & 281Mid-range = 242Yes all the results will be able to represent all players in the sports leagueStep-by-step explanation:
First of all, we will sort the data.
185 227 234 245 278 278 279 281 281 291 299
Mean:
Mean is defined as the sum of values divided by the number of values.
n = 11
[tex]Mean = \frac{sum}{n}\\= \frac{185+227 +234+ 245+ 278+ 278+ 279+ 281+ 281+ 291+ 299}{11}\\=\frac{2878}{11}\\=261.63\ pounds[/tex]
Median:
As the number of values is odd,
The median will be:
[tex]Median = (\frac{n+1}{2})th\ value\\= \frac{11+1}{2}\\=\frac{12}{2}\\=6th\ value[/tex]
The 6th value is 278
Median = 278
Mode:
Mode is the most frequent value in a data set.
In the given dataset,
278 and 281 are modes as both are repeated twice
Mid-range:
Mid-range is the average of maximum and minimum value
So,
Min = 185
Max = 299
So,
[tex]Mid-range = \frac{Max+Min}{2}\\= \frac{185+299}{2}\\= \frac{484}{2}\\= 242[/tex]
Hence,
Mean = 261.63 poundsMedian = 278 poundsModes: 278 & 281Mid-range = 242Yes all the results will be able to represent all players in the sports leagueThe demand on a power plant changes over time. cause or effect
Answer:
effect
Step-by-step explanation:
1. A certain manufacturing process to build phone batteries results in the production of defective batteries at a rate of 5% (0.05). Suppose that 10 batteries are produced. a. Find the expected number of defective batteries. b. Find the variance and standard deviation in the number of defective batteries. c. Find the probability that at least 1 battery is defective.
Answer:
0.5 ; 0.475 ; 0.689 ; 0.4013
Step-by-step explanation:
Given that:
Rate of production of defective batteries p = 0.05
Number of batteries produced (n) = 10
The expected number of defective batteries = mean = n * p = 10 * 0.05 = 0.5 batteries
Variance of defective batteries :
Var(X) = n * p * q ; q = 1 - p
Hence,
Var(X) = 10 * 0.05 * 0.95 = 0.475
Standard deviation (X) = sqrt(variance) = sqrt(0.475) = 0.689
Probability that atleast 1 battery is defective :
Using the binomial probability function
P(x ≥ 1) = 1 - p(x = 0)
= 1 - q^n
= 1 - 0.95^10
= 1 - 0.59873693923837890625
= 0.40126306076162109375
= 0.4013
Find the exact values of the six trigonometric ratios of the angle in the triangle 160 and 164
Answer:
[tex]\sin \theta = \frac{40}{41}[/tex], [tex]\cos \theta = \frac{3}{82}[/tex], [tex]\tan \theta = \frac{80}{3}[/tex], [tex]\cot \theta = \frac{3}{80}[/tex], [tex]\sec \theta = \frac{82}{3}[/tex], [tex]\csc \theta = \frac{41}{40}[/tex]
Step-by-step explanation:
We notice that figure represents a right triangle, the hypotenuse has a length of 164 units and the leg opposite to [tex]\theta[/tex] has a length of 160 units. The sine of [tex]\theta[/tex] is:
[tex]\sin \theta = \frac{160}{164}[/tex]
[tex]\sin \theta = \frac{40}{41}[/tex]
The leg adjacent to [tex]\theta[/tex] is determine by the Pythagorean Theorem:
[tex]r = \sqrt{164^{2}-160^{2}}[/tex]
[tex]r = 6[/tex]
Then, the cosine of [tex]\theta[/tex] is:
[tex]\cos \theta = \frac{6}{164}[/tex]
[tex]\cos \theta = \frac{3}{82}[/tex]
Lastly, we determine the remaining trigonometric ratios by using these identities:
[tex]\tan \theta = \frac{\sin \theta}{\cos \theta}[/tex] (1)
[tex]\cot \theta = \frac{1}{\tan \theta}[/tex] (2)
[tex]\sec \theta = \frac{1}{\cos \theta}[/tex] (3)
[tex]\csc \theta = \frac{1}{\sin \theta}[/tex] (4)
If we know that [tex]\sin \theta = \frac{40}{41}[/tex] and [tex]\cos \theta = \frac{3}{82}[/tex], then the trigonometric ratios are, respectively:
[tex]\tan \theta = \frac{\frac{40}{41} }{\frac{3}{82} }[/tex]
[tex]\tan \theta = \frac{80}{3}[/tex]
[tex]\cot \theta = \frac{1}{\frac{80}{3} }[/tex]
[tex]\cot \theta = \frac{3}{80}[/tex]
[tex]\sec \theta = \frac{1}{\frac{3}{82} }[/tex]
[tex]\sec \theta = \frac{82}{3}[/tex]
[tex]\csc \theta = \frac{1}{\frac{40}{41} }[/tex]
[tex]\csc \theta = \frac{41}{40}[/tex]
find the area of each trapezoid 32 ft x 16 ft 18 ft
Answer:
A = 432 ft^2
Step-by-step explanation:
[tex]A=\frac{a+b}{2} *h[/tex]
A = (32+16)/2 * 18
A = 48/2 * 18
A = 24*18
A = 432 ft^2
Does this matrix have an inverse?why or why not ?
Answer:
C. No, because it's determinant is zero
Step-by-step explanation:
[tex]A= \begin{bmatrix} 16 & - 4\\\\ 8 & - 2\end{bmatrix} [/tex]
[tex] det(A) =\begin{vmatrix} 16 & - 4\\\\ 8 & - 2\end{vmatrix} [/tex]
[tex] det(A) = 16\times (-2)-(-4)\times 8[/tex]
[tex] det(A) = -32+32[/tex]
[tex] det(A) = 0[/tex]
This matrix have no inverse, because it's determinant is zero.
It is given a 2*2 matrix of order 2.
To find this matrix have an inverse or not.
What is determinant?
A quantity obtained by the addition of products of the elements of a square matrix according to a given rule.
The given matrix is
A= [tex]\left[\begin{array}{ccc}16&-4\\8&-2\\\end{array}\right][/tex]
det A=16*(-2)-(-4)*8=0
det A=0
So, this matrix have no inverse, because it's determinant is zero.
Learn more about determinant here:
https://brainly.com/question/20367047
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carly mowed 2 more lawns than Roco each week for 6 weeks. carly mowed a total of 18 lawns. how many did Rocco mow each week?
Answer:
Rocco mowed 1 lawn a week.
Step-by-step explanation:
If Carly mowed 18 lawns in six weeks that’s 3 lawns a week and 3-2=1.
Thus Rocco mowed 1 lawn a week.
1 15/16 divided by 7/8
Answer:
Your answer is 2 2/7
Please I need help really badly
Answer:
with what
Step-by-step explanation:
I can't really see the question
Work out the value of x+y multiplied by z if x=3/5 ....
Answer:
1.056
Step-by-step explanation:
Because 2 4/5+ 3/5= 3 1/5
3 1/5 as a decimal is, 3.2
3.2× .33= 1.056
Translate the word phrase into a math expression.
1 less than a number.
A: n + 1
B: n−1
C: 15 ÷ n
D: 1−n
please help meeeeeeeeee
Answer:
39 degrees
Step-by-step explanation:
27 + |-12| = 39 to change from -12 to 27 you have to add the distance they are away from each other on a number line by adding the absolute value of -12 to 27 to find their distance
What is the reciprocal of 1/5?
5/1
4
1/5
in the figure above AB= 4×+6 and BC=7×+15. if AC=120 , find the length of segment AB.?
Answer:2x+6
Step-by-step explanation:
Find the quotient for 3/2 divided by 3/5
Answer:
2.5
Step-by-step explanation:
Answer:
5/2
Step-by-step explanation:
To divide fractions, you flip the second fractions and change it to multiplication.
(3/2) / (3/5) =
(3/2) x (5/3)
To multiply them, you just multiply their numerators together to get the new numerator and multiply the denominators together to get the new denominator.
(3/2) x (5/3) =
(3 x 5) / (2 x 3) =
15/6
This can be reduced to:
5/2
5. [Statistical independence] Consider a month consisting of exactly 28 days, split into four weeks of seven days each, such that the first of the month is a Monday. One of the 28 days will be selected uniformly at random (so that each day has probability 1/28 of being selected). Event A is that the selected day is a Monday or Wednesday. Event B is that the selected day falls either in the first or third weeks of the month. Are A and B independent or not? Show your work.
Answer:
They are independent events
Step-by-step explanation:
For independent events;
Pr(A & B) = Pr(A) × Pr(B)
Given that:
A = day is Monday or Wednesday
Since we have four weeks and each week will have one Monday and Wednesday each,
Pr(A) = (8/28)
B = day falls in the first or third week
Since, first and the third week has a total of 14 days,
Pr(B) = 14/28
Therefore;
Pr(A) × Pr(B) = 8/28 * 14/28
Pr(A) × Pr(B) = 1/7
Now, A and B = day is either Monday or Wednesday, and it is in the first or third week
There are four such days, Thus Pr(A and B) = 4/28 = 1/7
Since, Pr(A and B) = Pr(A) * Pr(B),
A and B are independent events
What is the sum of the first 34 numbers in the series below?
147 + 130 + 113 + 96 + . . .
-4,828
-4791
-4539
-4131
Answer:
-4539
Step-by-step explanation:
147 + 130 + 113 + 96 +
arithmetic, with
a = 147 and d 130 - 147 = -17
Sn = (n/2)(2a + d(n - 1))
S34 = (34/2)(2*147 - 17(34 - 1))
= 17(294 - 561)
hope it helps!
Answer:
What’s pad let?
Step-by-step explanation:
A university organization shows that 108 of the university's 253 assistant professors were women, along with 97 of the 301 associate professors and 78 of the 350 full professors. (a) What is the probability that a randomly chosen university professor (of any rank) is a woman
Answer:
[tex]Probability = 0.3131[/tex]
Step-by-step explanation:
Required
Determine the probability of selecting a woman
The given data can be represented to show women distribution as:
-------------------------------------- Women ------------------- Total
Assistant Professors ----------- 108 ----------------------253
Associate Professors ---------97 -------------------------301
Full Professors -----------------78---------------------------350
First, we calculate the number of women
[tex]Women = 108 + 97 + 78[/tex]
[tex]Women = 283[/tex]
Next, we calculate the total number of professors
[tex]Professors = 253 + 301 + 350[/tex]
[tex]Professors = 904[/tex]
Probability of selecting women is then calculated as:
[tex]Probability = \frac{Women}{Professors}[/tex]
[tex]Probability = \frac{283}{904}[/tex]
[tex]Probability = 0.31305309734[/tex]
[tex]Probability = 0.3131[/tex] -- (approximated)
Convert 45°C to Fahrenheit.
Answer:
113 degrees Fahrenheit
Step-by-step explanation:
What is the answer bbs
Patricia added 1 1/4 of salsa to a pot of her homemade chili. With the salsa the pot held 2 1/2 quarts of chili how many cups of salsa are in on quart of chili
A 1/2
B 2
C 5/8
D 1 & 1/4
Problem: According www.textrequest, an American between 18-24 sends and receives about 128 text messages per day. Assume that the population standard deviation is 30 for this age group. To get an idea about the true population mean you take a survey of 100 adults in that age group and find that their average is 135. Create a 90% confidence interval for the population average for this age group.
Answer:
(130.08, 139.92)
Step-by-step explanation:
Given that:
Mean (m) = 135
Standard deviation (σ) = 30
Sample size (n) = 100
α = 90%
The confidence interval value is obtained using the relation:
Mean ± Zcritical * (standard deviation / sqrt(n))
Zcritical at 90% = 1.64
standard deviation / sqrt(n) = 30 / sqrt(100)
= 30 / 10 = 3
Hence,
135 ± 1.64 * (3)
Lower limit : 135 - (1.64 * 3) = 130.08
Upper limit : 135 + (1.64 * 3) = 139.92
Hence,
Confidence interval = (130.08, 139.92)
A function f is onto if and only if, each element in the codomain of f is the image of at _____ one element in the domain of f
Answer:
A function f is onto if and only if, each element in the codomain of f is the image of at least one element in the domain of f.
Step-by-step explanation:
A function f is onto if and only if, each element in the codomain of f is the image of at least one element in the domain of f.
Let us consider a function f which maps the elements of X to each element in the domain of f, such that
f(1) = D
f(2) = B
f(3) = C
f(4) = C
From here, we can determine the domain and range, so
Domain X of f = {1, 2, 3, 4}
Domain Y of f = {D, B, C}
Therefore, it is clear that every element in the codomain of f is the image of at least one element in the domain of f.
the question is below
Answer:
use sin to find the angle x
Answer:
We can use the triginotemtric ratio inverse cos to solve this problem.
Cos=adjacent side/hypotenuse
cos(h)=21/69
[tex]cos^-1(21/69)=x\\cos^-1(0.30434782608) \\x=72[/tex]
Step-by-step explanation:
What is the distance between (–2 and one-half, –3) and (1, –3)?
–3 and one-half units
–1 and one-half units
1 and one-half units
3 and one-half units
Answer:
3 and 1/2 units
Answer:
3 and 1/2 units
Step-by-step explanation:
hope this helps you lol
E
Find the value of 'x'.
(x+40) (x+20)
the answer to your problem is 60=x
Which angle(s) is/are congruent? There may be more than one answer
Answer:
if they all have the same angle they r congruent
Step-by-step explanation:
Studies indicate that 10.5% of the US population has diabetes. A producer of medical devices is developing a test for diabetes diagnosis: a positive test suggests that a person has diabetes, a negative test suggests that a person does not have diabetes. However, medical tests can give false results: in particular, the probability that this test gives a negative result for a person who actually has diabetes is 0.05, while the probability that the test is positive for a person who in fact does not have diabetes is 0.10.1. What is the probability that the test gives a positive result for a person who is known to have diabetes? 2. What is the probability that a person has diabetes, given that the test gives a positive result?
Answer:
The answer is "0.95 and 0.5271".
Step-by-step explanation:
[tex]p (d) = 0.905 \\\\p( false\ negative) = 0.05\\\\p(false \ positive ) = 0.10 \\\\[/tex]
In point a)
p ( positive diabetes )[tex]= 1 - 0.05 = 0.95[/tex]
In point b)
[tex]p(\frac{d}{+ve}) = \frac{0.105 \times 0.95}{0.105 \times 0.95 +0.895 \times 0.10 }[/tex]
[tex]=\frac{0.09975}{0.09975+0.0895}\\\\=\frac{0.09975}{0.18925}\\\\= 0.5271[/tex]
A bag contains 4 red marbles, 3 blue marbles and 7 green marbles. If three marbles
are drawn out of the bag, what is the probability, to the nearest 1oth of a percent, thai
all three marbles drawn will be green?
Answer:
20%
Step-by-step explanation:
4+3+7=14
14÷7=2
2×10=20
If I am wrong please tell me I haven't had to do this me method in 3 years