For -180°<θ<0 , which of the primary trigonometric functions may have positive values?
Answer:
cos theta = adj / hyp is positive (+/+)
Step-by-step explanation:
In this open interval, the hypotenuse (radius) is always positive, whereas the adjacent side is positive and the opposite side negative.
in this interval:
sin theta = opp / hyp is neg (-/+)
cos theta = adj / hyp is positive (+/+)
tan theta = opp / adj = (-/+) : negative
Chang has 2 shirts: a white one and a black one. He also has 2 pairs of pants, one blue and one tan. What is the probability, if Chang gets dressed in the dark, that
he winds up wearing the white shirt and tan pants? Show your work.
Answer:
1/4
Step-by-step explanation:
White = w
Black = B
Blue = b1
Tan = t
Wb1
Wt
Bbi
Bt
The answer will be 1/4, because there are 4 ways it can work and only 1 way it can be white shirt and tan pants.
Answer:
1/4
Step-by-step explanation:
it would be 1/4 because there are 4 different clothing pieces in total and there is only one way it would work the way the problem says.
which of the following values could NOT be a probability
Answer:
3/2, -1.1
Step-by-step explanation:
the probability cannot be greater than 1. probability is between 0 and 1
A boxcar contains six complex electronic systems. Two of the six are to be randomly selected for thorough testing and then classified as defective or not defective.
a. If two of the six systems are actually defective, find the probability that at least one of the two systems tested will be defective. Find the probability that both are defective.
b. If four of the six systems are actually defective, find the probabilities indicated in part (a).
Answer:
Step-by-step explanation:
Number of electronic systems = 6
(a) Number of defected systems = 2
Probability of getting at least one system is defective
1 defective and 1 non defective + 2 defective
= (2 C 1 ) x (4 C 1) + (2 C 2) / (6 C 2)
= 3 / 5
(b) four defective
Probability of getting at least one system is defective
2 defective and 2 non defective + 3 defective and 1 non defective + 4 defective
= (4 C 2 ) x (2 C 2) + (4 C 3 )(2 C 1) + (4 C 4) / (6 C 4)
= 1
Answer:
(a)P(At least one defective)[tex]=0.6[/tex]
P(Both are defective)[tex]=0.067[/tex]
(b)P(At least one defective)[tex]=14/15[/tex]
P(Both are defective)[tex]=0.4[/tex]
Step-by-step explanation:
We are given that
Total number of complex electronic system, n=6
(a)Defective items=2
Non-defective items=6-2=4
We have to find the probability that at least one of the two systems tested will be defective.
P(At least one defective)=[tex]\frac{2C_1\times 4C_1}{6C_2}+\frac{2C_2\times 4C_0}{6C_2}[/tex]
Using the formula
[tex]P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}[/tex]
P(At least one defective)[tex]=\frac{\frac{2!}{1!1!}\times \frac{4!}{1!3!} }{\frac{6!}{2!4!}}+\frac{\frac{2!}{0!2!}\times \frac{4!}{4!}}{\frac{6!}{2!4!}}[/tex]
Using the formula
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]
P(At least one defective)[tex]=\frac{2\times \frac{4\times 3!}{3!}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}+\frac{1}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}[/tex]
P(At least one defective)[tex]=\frac{2\times 4}{3\times 5}+\frac{1}{3\times 5}[/tex]
P(At least one defective)[tex]=\frac{8}{15}+\frac{1}{15}=\frac{9}{15}[/tex]
P(At least one defective)[tex]=\frac{3}{5}=0.6[/tex]
Now, the probability that both are defective
P(Both are defective)=[tex]\frac{2C_2\times 4C_0}{6C_2}[/tex]
P(Both are defective)=[tex]\frac{\frac{2!}{0!2!}\times \frac{4!}{4!}}{\frac{6!}{2!4!}}[/tex]
P(Both are defective)[tex]=\frac{1}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}[/tex]
P(Both are defective)[tex]=\frac{1}{3\times 5}[/tex]
P(Both are defective)[tex]=0.067[/tex]
(b)
Defective items=4
Non- defective item=6-4=2
P(At least one defective)=[tex]\frac{4C_1\times 2C_1}{6C_2}+\frac{4C_2\times 2C_0}{6C_2}[/tex]
P(At least one defective)[tex]=\frac{\frac{4!}{1!3!}\times \frac{2!}{1!1!} }{\frac{6!}{2!4!}}+\frac{\frac{4!}{2!2!}\times \frac{2!}{2!}}{\frac{6!}{2!4!}}[/tex]
P(At least one defective)[tex]=\frac{2\times \frac{4\times 3!}{3!}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}+\frac{\frac{4\times 3\times 2!}{2!\times 2\times 1}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}[/tex]
P(At least one defective)[tex]=\frac{2\times 4}{3\times 5}+\frac{2\times 3}{3\times 5}[/tex]
P(At least one defective)[tex]=\frac{8}{15}+\frac{6}{15}=\frac{8+6}{15}[/tex]
P(At least one defective)[tex]=\frac{14}{15}[/tex]
P(Both are defective)[tex]=\frac{4C_2\times 2C_0}{6C_2}[/tex]
P(Both are defective)[tex]=\frac{\frac{4\times 3\times 2!}{2\times 1\times 2!}\times \frac{2!}{2!}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}[/tex]
P(Both are defective)[tex]=\frac{\frac{4\times 3\times 2\times 1}{2\times 1\times 2\times 1}}{3\times 5}[/tex]
P(Both are defective)[tex]=\frac{6}{15}=0.4[/tex]
P(Both are defective)[tex]=0.4[/tex]
Perimeter (numerical) cm
Answer:
101 cm
Step-by-step explanation:
Add all the side lengths up to get 101 cm.
Create truth table to determine whether or not the following statements are logically equivalent
The statement is totally false.
[tex]\neg P\lor\neg Q \equiv \neg(P \land Q) \not\equiv P\land Q[/tex]
because (P and ¬P) is a contradiction.
if p, q, and r are all integers greather than 1 and p*q =27 and q*r =51, then which of the following gives the correct ordering of numbers?
Answer:
Step-by-step explanation:
pq = 27 = 3³
qr = 51 = 3×17
q = 3
p = 9
r = 17
By selling a radio for $8400 a dealer gained 12% .how much money did she gain
Answer:
Amount gained = $900
Step-by-step explanation:
Let the cost price be = x
Given selling price = 8400
And profit% = 12%
Profit = selling price - cost price
= 8400 - x
[tex]Profit \ \% = \frac{profit}{cost \ price} \times 100\\\\12\% = \frac{8400 - x}{x} \times 100\\\\\ 12 \times \frac{1}{100} = \frac{8400 - x}{x}\\\\\frac{12 \ x}{100} = 8400 - x \\\\\frac{12x}{100} + x = 8400\\\\12x + 100x = 8400 \times 100\\\\112x = 8400 \times 100\\\\x = \frac{8400 \times 100}{112} = 7500[/tex]
Therefore , cost price of the radio $7500
The amount she gained = 8400 - 7500 = $ 900
A consumer electronics company is comparing the brightness of two different types of picture tubes for use in its television sets. Tube type A has mean brightness of 100 and standard deviation of 16, and tube type B has unknown mean brightness, but the standard deviation is assumed to be identical to that for type A. A random sample of tubes of each type is selected, and is computed. If equals or exceeds , the manufacturer would like to adopt type B for use. The observed difference is . a. What is the probability that exceeds by 3.0 or more if and are equal
Answer:
The answer is "0.7794".
Step-by-step explanation:
Please find the complete question in the attached file.
Given:
[tex]\to n_{1}=n_{2}=25\\\\[/tex]
Hypotheses:
[tex]\to H_{0}:\mu_{B}-\mu_{A}\geq 0\\\\\to H_{a}:\mu_{B}-\mu_{A}< 0\\\\[/tex]
Testing statistics:
[tex]\to z=\frac{(\bar{x}_{B}-\bar{x}_{A})-(\mu_{B}-\mu_{A})}{\sqrt{\frac{\sigma^{2}_{B}}{n_{1}}+\frac{\sigma^{2}_{A}}{n_{2}}}}=\frac{3.5-(0)}{\sqrt{\frac{16^{2}}{25}+\frac{16^{2}}{25}}}=0.77[/tex]
The test is done just so the p-value of a test is
[tex]\to p-value = P(z < 0.77) = 0.7794[/tex]
Because the p-value of the management is large, type B can take it.
p and q are two numbers.whrite down an expression of. a.) the sum of p and q. b) the product of p and q
Answer:
A. p+q
B. (p)(q)
Step-by-step explanation:
A. The sum of the variables will be p+q, since we are just adding the two variables together.
B. The product of the variables will be (p)(q), or just pq, since you are simply multiplying the two variables.
Hope this Helps!!
khai niem hinh cat don gian ?
Answer:
khai niem hinh cat don gian?
I NEED HELP!! PLEASE
Answer:
Step-by-step explanation:
D is the answer. You shift the function to the left 5 units, hence the term |x+5|, and move it down 1, hence the term -1.
An isosceles trapezoid has a consecutive-sides of length: 10,6,10 and 14. Find the measure of each angle if the trapezoid.
Answer:
Angle A = Angle D = 69° 30'
Angle B = Angle C = 110° 30'
Step-by-step explanation:
B ___ C
/ \
/ \
A ________ D
AB and CD are 10
BC is 6
AD is 14
If we divide the trapezoid, we can imagine a line.
B_ F_C
/ | \
/ | \
A ___E____ D
AE = ED = 7 (14/2)
BF = FC = 3
So now, we draw another line from B or C to AE or ED
B_ F_ C
/ | | \
/ | | \
A ___E_ G_ D
EG = GD = 3.5 (7/2)
There is a right triangle now, GCD
GD is 3.5 and CD is 10. To determine angle D, we can apply trigonometric function:
CD is H, and GD is A
cos D = A/H
cos D = 3.5/10 → 0.35
angle D = 69° 30'
By theory, we know that angle D and angle A, are the same so:
Angle D = Angle A = 69° 30'
Angle B = Angle C
We also make a cuadrilateral, which is EFCD.
Angle D is 69° 30', Angle E is 90°, Angle F is also 90°
Sum of angles in cuadrilateral is 360°
360° - 69° 30' - 90° - 90° = Angle C = Angle B
Angle C = Angle B = 110° 30'
Let's confirm the angles in the trapezoid:
69° 30' + 110° 30' + 69° 30' + 110° 30' = 360°
A + B + C + D
Find x please step by step explanation need it
Answer:
19.27
Step-by-step explanation:
To find :-
The value of x .Answer :-
As we know that ,
→ cos ∅ = b/h
→ cos 33° = 16/x
→ 0.83 = 16/x
→ x = 16/0.83
→ x = 19.27
what is the discrimination of the polynomial below ?
9x2-18x+9
the adjacent sides of a parallelogram are (x + 3) and (x + 2). Find the perimeter of the parallelogram
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Answer:
4x+10
Step-by-step explanation:
For parallelogram adjacent sides a and b, the perimeter is ...
P = 2(a +b)
For the given sides, the perimeter is ...
P = 2((x +3) +(x +2)) = 2(2x +5)
P = 4x +10 . . . perimeter of the parallelogram
Which statement best compares the two functions?
A) Neither function A nor function B has an x-intercept.
B) Neither function A nor function B has a y-intercept.
C) The domain and range of both functions contain only
positive numbers.
D) The domain and range of both functions contain only
positive numbers and zero
Answer:
A) Neither function A nor function B has an x-intercept.
Step-by-step explanation:
Thorazine is available in a strength of 25 mg/mL. Express this strength as a percent.
Answer:
2.5%
Step-by-step explanation:
Thorazine is available in the strength of 25mg/mL.
To find out the percentage strength,
W/V = g/mL (weight in grams of solute/milliliters of solute.)
1mL of Thorazine contains 25mg.
Dissolve Thorazine with the 100mL solution.
Therefore, 25 x 100 = 2500mg
Which is equals to 2.5g
100mL solution contains 2.5g of Thorazine.
Percentage Strength (W/V) = 2.5 / 100 x 100 = 2.5%.
The percentage strength of Thorazine 25mg/mL has 2.5%
fifteen more than 3 times a number is 33. What is the equation and solve
Answer:
x = 6
Step-by-step explanation:
15 more represents “+15”
3 times a number represents “3*x” which is written as “3x”
So fifteen more than 3 times a number is 33 would be written as;
3x + 15 = 33
Now solve for x using algebra;
3x = 33 - 15
3x = 18
x = 18 / 3
x = 6
Hope this helps!
hope anyone help me please
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Answer:
a) Lahulspiti: -8; Srinigar: -2; Shimla: 5; Ooty: 14; Bengahuru: 22
b) 30
c) 6
d) yes; no
Step-by-step explanation:
a) The values are read from the graph.
__
b) 22 -(-8) = 22 +8 = 30 . . . . difference between highest and lowest
__
c) -2 -(-8) = -2 +8 = 6 . . . positive difference
(Technically, the difference between L and S is L - S = (-8) -(-2) = -6.)
__
d) -2 + 5 < 5 . . . . true
-2 + 5 < -2 . . . . false
1 and 2 are supplementary.If m1 = (3x-17) and m2= (5x+21) find the value of x
Answer:
22
Step-by-step explanation:
m1 + m2 = 180
3x - 17 + 5x + 21 = 180
3x + 5x + 21 - 17 = 180
8x + 4 = 180
8x = 180 - 4
8x = 176
x = 176 / 8
x = 22
Cyril has six more than twice as many mangoes as Kubie and half as many mangoes as Maxine. If Kubie has six mangoes, then, in terms of x, how many mangoes do Cyril, Kubie, and Maxine have combined?
Answer:
(7x + 18) or 60 Mangoes
Step-by-step explanation:
Let the no. of mangoes Kubie possesses be x
So,
Cyril has mangoes = 2x + 6 ...(i)
So,
Maxine has = 2 * (2x + 6)
= 4x + 12
Given that,
Kubie has mangoes = 6
∵ The combined mangoes they have in terms of x,
= Cyril + Kubie + Maxine
= (2x + 6) + x + (4x + 12)
= 7x + 18
A.T.Q.
Cyril has = 2x + 6
∵ Cyril has mangoes = 2 * (6) + 6
= 18 mangoes
∵ Maxine has = 2 * Cyril's mangoes
= 2 * 18
= 36
Thus,
Total mangoes = Cyril + Kubie + Maxine
= 18 + 6 + 36
= 60 Mangoes
Suppose the method of tree ring dating gave the following dates A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.
1241 1210 1267 1314 1211 1299 1246 1280 1291
a. Determine if the data meets the initial conditions to construct a confidence interval.
b. Find the sample mean year x and sample standard deviation σ.
c. What is the maximal margin of error when finding a 90 % confidence interval for the mean of all tree-ring dates from this archaeological site?
Answer:
(1238.845 ;1285.376)
Step-by-step explanation:
Conditions for constructing a confidence interval :
Data must be random
Distribution should be normal and independent ;
Based on the conditions above ; data meets initial conditions ;
C. I = sample mean ± margin of error
Given the data :
1241 1210 1267 1314 1211 1299 1246 1280 1291
Mean, xbar = Σx / n = 11359 / 9 = 1262.11
The standard deviation, s = [√Σ(x - xbar)²/n - 1]
Using a calculator ; s = 37.525
The confidence interval :
C.I = xbar ± [Tcritical * s/√n]
Tcritical(0.10 ; df = n - 1 = 9 - 1 = 8)
Tcritical at 90% = 1.860
C. I = 1262.11 ± [1.860 * 37.525/√9]
C.I = 1262.11 ± 23.266
(1238.845 ;1285.376)
± 23.266
The margin of error :
[Tcritical * s/√n]
[1.860 * 37.525/√9]
C.I = ± 23.266
find and sketch the domain of the function. f(x,y)=√(4-x^2-y^2) +√(1-x^2)
Answer:
Hello
Step-by-step explanation:
The domain is limited with 2 lines parallel: -1 ≤ x ≤ 1
and the disk ? (inside of a circle) of center (0,0) and radius 2
[tex]dom\ f(x,y)=\{(x,y) \in \mathbb{R} ^2 | \ -1\leq x \leq -1\ and \ ( -\sqrt{4-x^2} \leq \ y \leq \sqrt{4-x^2}\ ) \ \}\\[/tex]
if 3x=y+z, y=6-7, and z+x=8, what is the value of y/z?
Answer:
-4/25
Step-by-step explanation:
3x=y+z
y=6-7=-1
z+x=8
y/z=?
solution
3x=-1 + z
x= -1 + z\3 ...eq(*)
then, z= 8- x
z= 8 - (-1 +z)\3
z= 8 +(1- z )\3
z= 8+1\3 -z \3
= 24+1\3 - z\3
z=25\3-z\3
z+z\3=25\3
4z\3=25\3
4z=25
z=25/4
then,
25/4 +x = 8
x=8- 25/4
x= 32 - 25/4
x=7/4
so that,
y/z=-1 /25/4
=-4/25
PLEASE HELP WILL MARK BRAINLIEST
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Answer:
x = 10/3 = 3 1/3 ≈ 3.33
Step-by-step explanation:
Triangles ABC and ADE are similar, so corresponding sides are proportional.
DE/DA = BC/BA
x/(4+6) = 2/6
x = 10(2/6) = 10/3 = 3 1/3
Find the probability that the spinner will land on gray and then purple
Answer:
true the question is true and wait for others my could be wrong also
y
27
х
10
11
12
In order for the data in the table to represent a linear
, function with a rate of change of -8, what must be the
value of a?
a
11
O a = 2
O a = 3
O a = 19
a = 35
The value of a that would make the data in the table represent a linear function with a rate of change of -8 is a = 19.
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The rate of change of a linear function is also known as the slope of the function.
To determine the slope of the function represented by the given table, we need to calculate the change in Y for a unit change in X.
Using the values given in the table, we can calculate the slope as follows:
Slope = (Change in Y) / (Change in X)
So,
(a - 27) / (11 - 10) = (11 - 27) / (12 - 10) = -8
Setting this equation equal to -8, we get:
= (a - 27) / 1
= -8
Simplifying the equation, we get:
a - 27 = -8
a = 19
Therefore,
The value of a that would make the data in the table represent a linear function with a rate of change of -8 is a = 19.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ7
Determine the domain and range of the graph
Answer:
5 ≤ x ≤ 10 5 ≤ y ≥ -1
Step-by-step explanation:
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = -x+3
Step-by-step explanation:
Slope intercept form => y = mx+b
To find 'm', the slope, pick 2 coordinates.
(0,3)
(2,1)
Use this equation to find the slope using these 2 coordinates: (y1 - y2)/(x1 - x2)
(3 - 1)/(0 - 2) = -1
m = slope = -1
'b' is the y-intersept, or the point when a line passes through the y-axis. That's (0,3).
b = y-intercept = 3
So the equation will be y = -1x + 3, or y = -x + 3
