C={ check example in book}
In a standardized normal distribution the mean is ____ while the standard deviation is ____.
A. 0; 1
B. 1; 0
C. 0; 0
D. 1; 1
Answer:
A. 0; 1
Step-by-step explanation:
Required
Mean and standard deviation of a standardized normal distribution
A standardized normal distribution is represented as:
[tex](\mu,\sigma) = (0,1)[/tex]
This implies that:
[tex]\mu = 0[/tex] -- mean
[tex]\sigma = 1[/tex] --- standard deviation
Hence, (a) is true
how to solve this trig
Hi there!
To find the Trigonometric Equation, we have to isolate sin, cos, tan, etc. We are also given the interval [0,2π).
First Question
What we have to do is to isolate cos first.
[tex] \displaystyle \large{ cos \theta = - \frac{1}{2} }[/tex]
Then find the reference angle. As we know cos(π/3) equals 1/2. Therefore π/3 is our reference angle.
Since we know that cos is negative in Q2 and Q3. We will be using π + (ref. angle) for Q3. and π - (ref. angle) for Q2.
Find Q2
[tex] \displaystyle \large{ \pi - \frac{ \pi}{3} = \frac{3 \pi}{3} - \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{2 \pi}{3} }[/tex]
Find Q3
[tex] \displaystyle \large{ \pi + \frac{ \pi}{3} = \frac{3 \pi}{3} + \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{4 \pi}{3} }[/tex]
Both values are apart of the interval. Hence,
[tex] \displaystyle \large \boxed{ \theta = \frac{2 \pi}{3} , \frac{4 \pi}{3} }[/tex]
Second Question
Isolate sin(4 theta).
[tex] \displaystyle \large{sin 4 \theta = - \frac{1}{ \sqrt{2} } }[/tex]
Rationalize the denominator.
[tex] \displaystyle \large{sin4 \theta = - \frac{ \sqrt{2} }{2} }[/tex]
The problem here is 4 beside theta. What we are going to do is to expand the interval.
[tex] \displaystyle \large{0 \leqslant \theta < 2 \pi}[/tex]
Multiply whole by 4.
[tex] \displaystyle \large{0 \times 4 \leqslant \theta \times 4 < 2 \pi \times 4} \\ \displaystyle \large \boxed{0 \leqslant 4 \theta < 8 \pi}[/tex]
Then find the reference angle.
We know that sin(π/4) = √2/2. Hence π/4 is our reference angle.
sin is negative in Q3 and Q4. We use π + (ref. angle) for Q3 and 2π - (ref. angle for Q4.)
Find Q3
[tex] \displaystyle \large{ \pi + \frac{ \pi}{4} = \frac{ 4 \pi}{4} + \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{5 \pi}{4} }[/tex]
Find Q4
[tex] \displaystyle \large{2 \pi - \frac{ \pi}{4} = \frac{8 \pi}{4} - \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{7 \pi}{4} }[/tex]
Both values are in [0,2π). However, we exceed our interval to < 8π.
We will be using these following:-
[tex] \displaystyle \large{ \theta + 2 \pi k = \theta \: \: \: \: \: \sf{(k \: \: is \: \: integer)}}[/tex]
Hence:-
For Q3
[tex] \displaystyle \large{ \frac{5 \pi}{4} + 2 \pi = \frac{13 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 4\pi = \frac{21 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 6\pi = \frac{29 \pi}{4} }[/tex]
We cannot use any further k-values (or k cannot be 4 or higher) because it'd be +8π and not in the interval.
For Q4
[tex] \displaystyle \large{ \frac{ 7 \pi}{4} + 2 \pi = \frac{15 \pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 4 \pi = \frac{23\pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 6 \pi = \frac{31 \pi}{4} }[/tex]
Therefore:-
[tex] \displaystyle \large{4 \theta = \frac{5 \pi}{4} , \frac{7 \pi}{4} , \frac{13\pi}{4} , \frac{21\pi}{4} , \frac{29\pi}{4}, \frac{15 \pi}{4} , \frac{23\pi}{4} , \frac{31\pi}{4} }[/tex]
Then we divide all these values by 4.
[tex] \displaystyle \large \boxed{\theta = \frac{5 \pi}{16} , \frac{7 \pi}{16} , \frac{13\pi}{16} , \frac{21\pi}{16} , \frac{29\pi}{16}, \frac{15 \pi}{16} , \frac{23\pi}{16} , \frac{31\pi}{16} }[/tex]
Let me know if you have any questions!
Suppose that 17 inches of wire costs 68 cents,
At the same rate, how much (in cents) will 39 inches of wire cost?
cents
?
Cost of 17 inches of wire = 68 cents
Cost of 1 inch of wire
= 68 cents/17
= 4 cents
Cost of 39 inches of wire
= 4 cents × 39
= 156 cents
= $1.56
Answer:
17 inches of wire costs 68 cents,
Step-by-step explanation:
x=234
b=456
The function f(x) = −x2 + 18x − 72 models the daily profit, in dollars, a gym makes for selling memberships, where x is the number of memberships sold, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
(10 points)
Answer:
Step-by-step explanation:
The way to do this so as to streamline both the vertex and finding the zeros is to complete the square. That method will provide us with the vertex, and then we can continue on to factor from that form to find the zeros. Completing the square requires us to set the quadratic equal to 0 then move over the constant, giving us
[tex]-x^2+18x=72[/tex] The leading coefficient HAS to be a positive 1; ours is negative 1 so we factor out the negative to get:
[tex]-(x^2-18x)=72[/tex] Now we're ready to complete the square.
Take half the linear term, square it, and add it to both sides. Our linear term is 18 (from -18x; don't worry about the negative because squaring it makes it positive anyway). Half of 18 is 9, and 9 squared is 81.
BUT on the left we have that -1 sitting out front that refuses to be ignored. What we actually added on to the left side, inside the parenthesis, is -1(81) which is -81. -81 is what we add to the right since that turns out to be what we added to the left:
[tex]-(x^2-18x+81)=72-81[/tex] and we clean that up.
The reason we complete the square is because when we simplify the left side, we end up with a perfect square binomial found from taking the square root of x-squared, the first sign we come to, then the square root of 81:
[tex]-(x-9)^2=-9[/tex]. Move the constant back over to get
[tex]-(x-9)^2+9=y[/tex] telling us that the vertex is (9, 9). In the context of the problem that means that the gym sells on average 9 memberships a day and the profit it makes on average per day is $9.
To factor, we will go back one step to
[tex]-(x-9)^2=-9[/tex] and begin by dividing both sides by -1 to get
[tex](x-9)^2=9[/tex] and undo the squaring by taking the square root of both sides to get
x - 9 = ±3 so
x = 9 + 3 and
x = 9 - 3 so
x = 6 and 12
Those are the zeros. This means that if they sell either 6 or 12 memberships they have a 0 profit. That may sound strange, but in business it does often work like that...selling too many of something makes your company lose money (this is often due to the cost required by you to produce or manufacture the product).
Independent simple random samples are selected to test the difference between the means of two populations whose standard deviations are not known. We are unwilling to assume that the population variances are equal. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the:
1) t distribution with 59 degrees of freedom.
2) t distribution with 58 degrees of freedom.
3) t distribution with 61 degrees of freedom.
4) t distribution with 60 degrees of freedom.
Answer:
2) t distribution with 58 degrees of freedom.
Step-by-step explanation:
Population standard deviations not known:
This means that the t-distribution is used to solve this question.
The sample sizes are n1 = 25 and n2 = 35.
The number of degrees of freedom is the sum of the sample sizes subtracted by the number of samples, in this case 2. So
25 + 35 - 2 = 58 df.
Thus the correct answer is given by option 2.
Instructions: Determine if the two triangles in
the image are congruent. If they are, state how
you know by identifying the postulate.
th
The 2 triangles are congruent
a playing card is chosen at random from a standard deck of cards. what is the probability of choosing 5 of diamonds or one jack
Answer:
1/52
Step-by-step explanation:
Help I have a time limit
Answer:
I think its C:37
Step-by-step explanation:
And if im wrong sorry :/
Find y when x = 22, if y varies directly as x,
and y = 42 when x = 5.
Answer:
184.8
Step-by-step explanation:
y =kx
k=y/x
k=42/5=8.4
y=8.4*22
What is the three hundred and twenty six to the nearest ten
Hi there!
»»————- ★ ————-««
I believe your answer is:
330
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
We are rounding the number 326 to the nearest tens.
The '2' is in the tens place, and the '6' is to the right of the digit.
Since the '6' is greater than or equal to 5, then we would round up.
326 ≈ 330
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Ronald types 360 words in 9 minutes.
If he types at a constant rate, how many words does Ronald type in 1 minute?
Answer:
40 per minute.
Step-by-step explanation:
360/9=40
The ratio of the number of boys to that of girls in a school is 4:3. If the number of girls in the school is 162, find the number of boys in it. Then find the ratio of the number of girls to the total number of students in the school.
Answer:
total number of boys in skool is 216
And
ratio of girls to boys is a 3:4
Step-by-step explanation:
let total no. of boys be X
ACCORDING TO QUESTION
ratio of boys to girls = 4:3
total number of girls = 162
now
4/3=X/162
or, 4×162= 3x
or, 4×162/3= X
hence
X = 216
therefore total number of boys is 216
and
ratio of girls to boys is =162/216
=3/4
=3:4
Annie is opening a savings account which earns 5.2% interest compounded continuously how much will she need to deposit in the account so she has $2300 after seven years
Hi
let's call X the initial deposit.
the interest rate is 5.2 %
so each year X increase by 1.052.
so we have : X *1.052^7 =2300
X = 2300/1.052^7
X = 1612,94
please note that the deposit was rounded to the next cent. as the result would be 1612,937...
Answer:
1686.22
Step-by-step explanation:
1686.22
2300=P(1+(0.052x7))
2300=P1.364
P=2300/1.364
=1686.217...
=1686.22..
=1686 for the nearest dollar
I need help ASAP please!
Answer:
Option C
We need to make the negative exponent positive.
The rule is: [tex]A^{-B} =\frac{1}{A^{B} }[/tex]
Here, A=x, B= 12
[tex]so,[/tex] [tex]x^{-12}[/tex]
[tex]=\frac{1}{x^{12} }[/tex]
OAmalOHopeO
What is the slope of the points (-2,7) and (2,-5)?
4
-3
-12
3
Answer:
-3
Step-by-step explanation:
Slope is equal to (-5-7)/(2-(-2)=-12/4=-3
what is 2x2x2x3x3 please give me answer
Answer:
The answer is 72.
I am right .
If the prism has 3 layers, what would the volume of the
prism be in cubic centimeters?
OA) 4 cubic centimeters
OB) 8 cubic centimeters
OC) 12 cubic centimeters
OD) 16 cubic centimeters
Answer:
OD) 16 cubic centimeters
Can someone help please! I need this last question answered
Answer: [tex]\frac{x^2}{16}+\frac{y^2}{49} = 1\\\\[/tex]
This is the same as writing (x^2)/16 + (y^2)/49 = 1
===========================================================
Explanation:
The general equation for an ellipse is
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1\\\\[/tex]
where
(h,k) is the center'a' is half the total width (along the x axis)'b' is half the total height (along the y axis)Notice how 'a' pairs with the x term, so that's why 'a' describes the horizontal width along the x axis. The horizontal width is 8 ft, which cuts in half to 4 ft. So a = 4.
The vertical length is 14 ft, which cuts in half to 7 ft. So b = 7.
The center isn't mentioned (other than the fact that the actor is located here), but I'm assuming by default it's at the origin (0,0).
With that all in mind, we then get the following:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1\\\\\frac{(x-0)^2}{4^2}+\frac{(y-0)^2}{7^2} = 1\\\\\frac{x^2}{16}+\frac{y^2}{49} = 1\\\\[/tex]
The graph is below. I used GeoGebra to make the graph.
From the graph, we can see that the horizontal width spans from x = -4 to x = 4. This is a total distance of |-4-4| = 8 feet. Similarly, the vertical length spans from y = -7 to y = 7 which is a distance of 14 feet.
3,6,6,12,9,?,12 what comes next. Options
A.15
B.18
C.11
D.13
Answer:
a
Step-by-step explanation:
3x tables
vhhvffffhhgfgfccf
Answer:
a
Step-by-step explanation:
Has pattern 3x tables. Answer is 15 A.
N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to
N?
A) 1 1/2
B 1 1/3
C) 5/3
D) 3/2
Answer:
it should be letter c 5/3 I could be wrong but I hope this help
Functions, f and g are given by f(x)= 3+ cos x and g(x) = 2x, x is a real number. Determine the value of c for which f(g(x))= g(f(x)) where 0[tex]\leq[/tex] x<2[tex]\pi[/tex]
9514 1404 393
Answer:
x = π
Step-by-step explanation:
You want f(g(x)) = g(f(x)):
3 +cos(2x) = 2(3 +cos(x))
cos(2x) -2cos(x) = 3 . . . . . . . rearrange
2cos(x)²-1 -2cos(x) = 3 . . . . . use an identity for cos(2x)
2(c² -c -2) = 0 . . . . . . . . . . . . substitute c = cos(x)
(c -2)(c +1) = 0 . . . . . . . . . . . factor
c = 2 (not possible)
c = -1 = cos(x) . . . . . true for x = π
The value of x that makes f(g(x)) = g(f(x)) is x = π.
_____
Additional comment
The substitution c=cos(x) just makes the equation easier to write and the form of it easier to see. There is really no other reason for making any sort of substitution. In the end, the equation is quadratic in cos(x), so is solved by any of the usual methods of solving quadratics.
A married couple had a combined annual income of $81,000. The wife made $9000 more than her husband. What was each of their incomes?
Step-by-step explanation:
Let the husband's income be x
Wife's income be x + 9000
X + X + 9000 = 81000
2X + 9000 – 9000 = 81000 – 9000
2X= 72000
X = 36000
Husband, 36000,
Wife, 9000+36000, 45000
properties of exponents. the answer is 1/2^3 i need help with the work
(2^-1)^2/2×2^0
2^(-1×2)/2^1
2^-2/2^1
2^(-2-1)
2^(-3)
(1/2)^3
Properties used (m^n)^a = m^na
(m)^-n = (1/m)^n
m^0 = 1
m^n/m^a = m^(n-a)
Must click thanks and mark brainliest
∫dx/(x+√(x^{2} +x+1)
Answer:
es1433
Step-by-step explanation:
Multiplying and bmbFREE BRAINLIST AND POINTS!! Fast! RIGHT ANSWERS ONLY! Scam and wrong answers will be reported and dealed with.
1. 6x(-4)=
3. (-11) x 5=
4. (-12) x (-7)=
5. (-2) x (-10)
6. 4 x (-15)=
Answer:
Step-by-step explanation:
-24
-55
84
20
-60
Solve the formula for t
V = 4(3.14)ct + 6(3.14)c^2
9514 1404 393
Answer:
t = (V -6(3.14)c^2)/(4(3.14)c)
Step-by-step explanation:
Isolate the term containing t, then divide by the coefficient of t
[tex]V=4(3.14)ct+6(3.14)c^2\\\\V-6(3.14)c^2=t(4(3.14)c)\\\\\boxed{t=\dfrac{V-6(3.14)c^2}{4(3.14)c}}[/tex]
Find X please
15 POINTS WORTH
Answer and Step-by-step explanation:
To find x, we must find the interior angles first, then we can find the value of x.
To find the interior angle, we need to use the exterior angle. We subtract the exterior angle from 180 to get the interior angle.
180 - 157 = 23
180 - 78 = 102
Now we need to find the last interior angle.
180 - 23 - 102 = 55
Now to find x.
180 - 55 = 125
x = 125
#teamtrees #PAW (Plant And Water) #ALM (All Lives Matter)
I hope this helps!
Answer:
the value of x is 124
Step-by-step explanation:
Find the volume of a right circular cone that has a height of 18m and a base with a radius of 5.8m
What is the perimeter of the triangle?
units
Answer:
Does the answer help you?
g (3 points)Set up but do no solve the integral required to calculate the volume formed by rotating the region bounded by f(x) = 1/x,g(x) = 1/x^3, andx= 2, andx= 4 around they-axis. Also draw a picture of the region (non-revolved).
Answer:
Hello,
Step-by-step explanation:
[tex]\displaystyleV=2*\pi*\int\limits^4_2 {(\dfrac{1}{x}-\dfrac{1}{x^3} )*x } \, dx \\=2*\pi*\int\limits^4_2 {(1-\dfrac{1}{x^2} ) } \, dx \\=2*\pi* [x+\dfrac{1}{x}]^4_2\\\\\boxed{V=\dfrac{7\pi}{2}}\\[/tex]
