Using the z-distribution, with a critical z-score of z = 1.645, the 90% confidence interval is (-16.4%, -9.66%).
What are the mean and the standard error for the distribution of the difference of proportions?For each sample, the mean and the standard error are given as follows:
[tex]p_y = \frac{461}{1214} = 0.3797, s_y = \sqrt{\frac{0.3797(0.6203)}{1214}} = 0.0139[/tex].[tex]p_o = \frac{560}{1098} = 0.51, s_o = \sqrt{\frac{0.51(0.49)}{1098}} = 0.0151[/tex].Hence, for the distribution of differences, they are given as follows:
[tex]p = p_y - p_0 = 0.3797 - 0.51 = -0.1303[/tex].[tex]s = \sqrt{s_y^2 + s_o^2} = \sqrt{0.0139^2 + 0.0151^2} = 0.0205[/tex]What is the confidence interval?
The interval is:
[tex]p \pm zs[/tex]
In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
Then the bounds of the interval are:
p - zs = -0.1303 - 1.645(0.0205) = -0.164.p + zs = -0.1303 + 1.645(0.0205) = -0.0966.As a percentage, the 90% confidence interval is (-16.4%, -9.66%).
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You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
The company's first task is to cast the lead female roles of Fantine, adult Cosette, and Éponine, and the lead male roles of Jean Valjean, Inspector Javert, and Marius. You have received headshots and resumes from 28 women and 22 men who are interested in auditioning for these parts.
A: If no one has been cast yet, how many different ways are there to cast Fantine from the 28 women?
B: If Fantine has already been cast, how many different ways are there to cast adult Cosette from the remaining women?
C: If Fantine and adult Cosette have already been cast, how many different ways are there to cast Éponine from the remaining women?
Select one answer choice for part A, one answer choice for part B, and one answer choice for part C.
B: 27P2
C: 26
C: 26!
A: 28P3
B: 27
C: 26P1
A: 28
B: 27!
A: 28!
Question 2:
A: Which of the following expressions will calculate the number of ways the three lead female roles could be cast?
B: Evaluate the permutation from part A.
Select one answer choice for part A, and one answer choice for part B.
B: ≈3.05×10^29
A: 28P3
B: 19656
A: 3P28
B: ≈5.08×10^28
A: 28P25
The permutation shows that when one has been cast yet, the different ways that are there to cast Fantine from the 28 women is 28.
How to calculate the value?The different ways that are there to cast Fantine from the 28 women will be:
= 28!/(28 - 1)!
= 28!/27!
= 28
When Fantine has already been cast, the number of ways that are there to cast adult Cosette from the remaining women will be:
= 27!(27 - 1)!
= 27!/26!
= 26
When Fantine and adult Cosette have already been cast, the different ways that are there to cast Éponine from the remaining women is:
= (28 - 2)!/(28 - 2 - 1)!
= 26!/25!
= 25
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Select the properties of a rectangle Select the properties of a rectangle
Answer:
[tex]\large \boxed{\checkmark}} \quad \textsf{has four right angles}[/tex]
[tex]\large \boxed{\checkmark}} \quad \textsf{opposite sides are congruent}[/tex]
[tex]\large \boxed{\checkmark}} \quad \textsf{diagonals bisect each other}[/tex]
[tex]\large \boxed{\checkmark}} \quad \textsf{opposite sides are parallel}[/tex]
[tex]\large \boxed{\checkmark}} \quad \textsf{opposite angles are congruent}[/tex]
[tex]\large \boxed{\checkmark}} \quad \textsf{diagonals are congruent to each other}[/tex]
Step-by-step explanation:
Properties of a rectangle:
Two-dimensional quadrilateral (4-sided figure)Opposite sides are equal in lengthOpposite sides are parallel to each otherFour equal interior angles (each angle is 90°)Diagonals bisect each other (divide into 2 equal parts)Length of diagonals are equalTherefore, the correct answer options are:
has four right anglesopposite sides are congruentdiagonals bisect each otheropposite sides are parallelopposite angles are congruentdiagonals are congruent to each otherAccording to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze.
The probability that exactly 8 individuals do not cover their mouth is
The probability that exactly 8 individuals do not cover their mouth is 0.0037.
How to calculate the probability?It should be noted that the probability will be solved by using the binomial distribution.
From the information, the probability that a randomly selected individual will not cover his or her mouth when sneezing is 0.267.
Therefore, the probability that thee person will not cover their mouth will be:
= 1 - 0.267
= 0.733
This will be:
= 12C8 × (0.267)^8 × (1 - 0.267)⁴
= 12C8 × (0.267)^8 × 0.733⁴
= 495 × 0.00002582 × 0.28867
= 0.0037
In conclusion, the probability is 0.0037.
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Use a half angle formula to find the exact value of the expression tan 22.5 degree
Answer:
Step-by-step explanation:
Theorems Involving Similarity
The theorem of similarity implies that the line segment divided the triangle into the proportional segment.
How to illustrate the theorem?It should be noted that the theorem of similarity states that the line segment splits two sides of a triangle into proportional segments.
This occurs when the side is parallel to the third side of the triangle.
These three theorems, known as Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side are foolproof methods for determining similarity in triangles.
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1. Name a pair of supplementary angles in this figure.
angles FEH and KED
angles FEK and FEH
angles FEK and FEJ
angles FEJ and JED
Answer:
FEJ and JED
Step-by-step explanation:
Supplementary means that the pair of angles add up to 180° or a straight angle. FEJ and JED are both 90° and so they add up to 180° But there are many pairs of angles that are NOT 90° that add up to 180° (but they just weren't in the answer choices)
The midpoint of the line segment from P₁ to P₂ is (-4,1). If P₁ = (-9,5), what is P2?
[tex] - 4 = \frac{ - 9 + x}{2} \\ - 8 = - 9 + x \\ x = 1[/tex]
[tex]1 = \frac{5 + y}{2} \\ 2 = 5 + y \\ y = - 3[/tex]
P² ( 1 , -3 )(1 point) A tank contains 50 kg of salt and 1000 L of
water. A solution of a concentration 0.025 kg of salt
per liter enters a tank at the rate 5 L/min. The solution
is mixed and drains from the tank at the same rate.
(a) What is the concentration of our solution in the
tank initially?
concentration = .05 (kg/L)
(b) Find the amount of salt in the tank after 1 hours.
O (kg)
amount =
(c) Find the concentration of salt in the solution in the
tank as time approaches infinity.
concentration = .025 (kg/L)
Your answers for (a) and (c) are correct.
(b) Salt flows into the tank at a rate of
[tex]\left(0.025 \dfrac{\rm kg}{\rm L}\right) \left(5 \dfrac{\rm L}{\rm min}\right) = 0.125 \dfrac{\rm kg}{\rm min} = \dfrac18 \dfrac{\rm kg}{\rm min}[/tex]
If [tex]A(t)[/tex] is the amount of salt (in kg) in the tank at time [tex]t[/tex] (in min), then the salt flows out of the tank at a rate of
[tex]\left(\dfrac{A(t)}{1000+(5-5)t} \dfrac{\rm kg}{\rm L}\right) \left(5 \dfrac{\rm L}{\rm min}\right) = \dfrac{A(t)}{200} \dfrac{\rm kg}{\rm min}[/tex]
The net rate of change in the amount of salt in the tank at any time is then governed by the linear differential equation
[tex]\dfrac{dA}{dt} = \dfrac18 - \dfrac{A(t)}{200}[/tex]
[tex]\dfrac{dA}{dt} + \dfrac{A(t)}{200} = \dfrac18[/tex]
I'll solve this with the integrating factor method. The I.F. is
[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{200}\right) = e^{t/200}[/tex]
Distributing [tex]\mu[/tex] on both sides of the ODE gives
[tex]e^{t/200} \dfrac{dA}{dt} + \dfrac1{200} e^{t/200} A(t) = \dfrac18 e^{t/200}[/tex]
[tex]\dfrac d{dt} \left(e^{t/200} A(t)\right) = \dfrac18 e^{t/200}[/tex]
Integrate both sides.
[tex]\displaystyle \int \frac d{dt} \left(e^{t/200} A(t)\right) \, dt = \frac18 \int e^{t/200} \, dt[/tex]
[tex]e^{t/200} A(t) = \dfrac{200}8 e^{t/200} + C[/tex]
[tex]A(t) = 25 + Ce^{-t/200}[/tex]
Given that [tex]A(0)=50\,\rm kg[/tex], we find
[tex]50 = 25 + Ce^0 \implies C = 25[/tex]
so that
[tex]A(t) = 25 + 25e^{-t/200}[/tex]
Then the amount of salt in the tank after 1 hr = 60 min is
[tex]A(60) = 25 + 25e^{-60/200} = \boxed{25 \left(1 + e^{-3/10}\right)}[/tex]
A rectangular garden is to be twice as long as it is wide. If 360 yards of fencing, including the gate, will enclose the garden, what will be the length of the garden, in yards?
Step-by-step explanation:
length = 2 × width
the perimeter of a rectangle is
2×length + 2×width
and it is 360 yards in our case
2×length + 2×width = 360
and then we use the first equation (2×width = length) in this second equation :
2×length + length = 360
3×length = 360
length = 360/3 = 120 yards
Rewrite 4/10 : 1/25 as a unit rate
Answer:
0.4 : 0.04
Step-by-step explanation:
4 ÷ 10 = 0.4
1 ÷ 25 = 0.04
Brian wants to buy the latest iPhone for $1000. He has
$100 and earns $15 for 1 hour (h) of tutoring.
Enter the minimum number of hours Brian must tutor to
be able to buy the iPhone.
0000
15h+1001000, h-60
15h 100 1000, h>=60
15h 1001000, h>60
15h 100 1000, h-60
Answer:
Step-by-step explanation:
Find all real zeros of the function y= -9x - 1
A. -9
B. - 1/9
C. 1/9
D. -9, -1
Answer: -1/9 which is choice B
Explanation:
The term "zeros" refers to the x intercepts.
Plug in y = 0 and solve for x.
y = -9x-1
0 = -9x - 1
9x = -1
x = -1/9
Which expression below can be obtained from 4sin4t by using a power reducing formula?
Select the correct answer below:
1+2cos(4t)
32−2cos(2t)+12cos(4t)
32+2cos(2t)+12cos(4t)
3−2cos(2t)+2cos(4t)
Step-by-step explanation:
4×sin(4t) = 4×sin(2t + 2t) =
= 4×(sin(2t)cos(2t) + cos(2t)sin(2t)) =
= 4×2×sin(2t)cos(2t) = 8×sin(2t)cos(2t)
but that did not lead anywhere near to any of the answer options.
so, i guess, you made typos in the description and in the answer options.
did you mean maybe
4×sin⁴(t) ?
sin⁴(t) = (3 - 4×cos(2t) + cos(4t))/8
4×sin⁴(t) = 4×(3 - 4×cos(2t) + cos(4t))/8 =
= (3 - 4×cos(2t) + cos(4t))/2 =
= 3/2 - 2×cos(2t) + 1/2 × cos(4t)
is that the real answer option 2 ?
then that is the correct answer.
Could someone help me out?
The equation of the line is y = -11x + 232
How to determine the equation?The given parameters are:
Slope (m)= -11
Point (x1, y1) = (31, -109)
The linear equation is then calculated as:
y = m(x - x1) + y1
This gives
y = -11(x - 31) - 109
Evaluate the product
y = -11x + 341 - 109
Evaluate the like terms
y = -11x + 232
Hence, the equation of the line is y = -11x + 232
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Given that
f
(
x
)
=
x
2
+
7
x
and
g
(
x
)
=
x
+
7
, calculate
(a)
(
f
∘
g
)
(
−
5
)
Answer:
18
Step-by-step explanation:
We want to find the composite function at a specific value (-5).
Thus, we can write and think of the function like this:
f[g(-5)]
So we substitue the -5 for every x in the g(x) function:
g(x) = -5 + 7 = 2
Then we substitute this 2 for every x in the f(x) function:
f(x) = 2^2+7(2) = 4 + 14 = 18
What is the Query Key Value paradigm in Transformer architectures and what does it mean?
Answer:
za
Step-by-step explanation:
x + 8 = -3 solution for x
(9^6 * 7^-9)^-4.
Thanks!
Answer:
[tex]\frac{7^{36}}{9^{24}}[/tex]
Step-by-step explanation:
Check the picture
I need help with this
Answer:
Minimum
Step-by-step explanation:
The equation is a quadratic function meaning the the shape is a parabola. The sign of x^2 is + so the graph open upward. Thus the vertex is the minimum point on the graph.
Please solve this for me, thank you!
The answer to this question is y = 847728300000/1366991599
Given 4y/1.025⁴ ₊ y ₋ 2y × 1.05² = 1500
1. covert decimal to fraction
= 4y/(1025/1000)⁴ ₊ y ₋ 2y × (105/100)² = 1500
2. Calculate the power
4y/2825761/2560000 ₊ y ₋ 2y × 441/400 = 1500
3. Divide the fraction by multiplying its reciprocal
4y × 2560000/2825761 ₊ y ₋ 2y × 441/400 = 1500
4. Multiply the monomials
10240000/2825761 y ₊ y ₋ 2y × 441/400 =1500
5. Combine like terms
10240000/2825761 y ₊ y ₋ 441/200 y = 1500
1366991599/565152200 y = 1500
6. Divide both sides of the equation by the coefficient of variable.
y = 1366991599/565152200 × 1500
y = 847728300000/1366991599
Hence we get the final value as y = 847728300000/1366991599
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Manny plans to save 1/14 of his salary each week. If his weekly salary is $378, find the amount he will save each week.
Answer:
27
Step-by-step explanation:
Find (f-g)(x) where f(x) = -x^2, g(x) = -(x+4)²
Answer:
8x + 16
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
g(x) = -(x+4)(x+4)
= -(x² + 4x + 4x + 16)
= -(x² + 8x + 16)
= -x² - 8x - 16
1) Subtract the two functions.
= (-x²) - (-x² - 8x - 16)
= -x² + x² + 8x + 16
= 8x + 16
A washer and a dryer cost $572 combined. The washer cost $78 less than the dryer. What is the cost of the dryer?
Answer:
$325
Step-by-step explanation:
Let the dryer price be x, then the washer price would be x-78
x+x-78 = 572
2x = 650
x = 325
You deposit Php1000 in a savings account that earns 6% interest per year Compound interest
Answer:
that is all I could do. hope you have gotten your answer.good day.
Which expression is a polynomial?
–13
Polynomials are algebraic expressions whose standard form is defined below:
[tex]p(x) = \sum \limit_{i=0}^{n} c_{i}\cdot x^{i}[/tex]
The expression p(x) = - 13 represents a zeroeth polynomial.
What is a polynomial?
Herein we must present what the form of polynomials are. Polynomials are algebraic expressions whose standard form is defined below:
[tex]p(x) = \sum \limit_{i=0}^{n} c_{i}\cdot x^{i}[/tex] (1)
Where:
[tex]c_{i}[/tex] - i-th coefficientn - Gradex - Independent variableAn example is the expression p(x) = - 13, real numbers can be define as zeroeth polynomials. In this regard, the example can be seen as:
p(x) = 0 · xⁿ + 0 · xⁿ⁻¹ + ... + 0 · x² + 0 · x - 13
RemarkThe statement is incomplete. We decided to re-define the statement to what polynomials are.
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Review the graph of a piecewise function.
On a coordinate plane, a curve goes through closed circle (negative 3, negative 1) and curves up and approaches x = negative 1 in quadrant 1. A line starts at closed circle (negative 1, negative 3) and goes to open circle (1, negative 1). It then goes to open circle (3, negative 1). A horizontal line starts at open circle (3, negative 3) and goes to (5, negative 3). A closed circle is at (3, negative 4).
For which value of x is the function continuous?
Using the continuity concept, it is found that the function is continuous at x = -3.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
These three values are equal for x = -3, hence the function is continuous at x = -3.
For the other options, the function is not continuous for the reasons given as follows:
x = -1: Different lateral limits.x = 1: f(1) is not defined.x = 3: Different lateral limits.More can be learned about continuity at brainly.com/question/24637240
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Line segment PQ is a directed line segment beginning at P(6,-5) and ending at QX-2,4).
Find point R on the line segment PQ that partitions it into the segments PR and RQ in the ratio 3:2.
O A. (8,3)
OB. (¹,-)
oc. (-1,3)
C.
O.D. (1,3)
The coordinates of R is (1.2, 0.4)
How to determine the partition?The points are given as:
P= (6, -5)
Q = (-2, 4)
The ratio is given as:
m : n = 3 : 2
The location of R is calculated as:
[tex]R = \frac{1}{m + n}* (mx_2 + nx_1, my_2 + ny_1)[/tex]
So, we have:
[tex]R = \frac{1}{3 + 2}* (3 * -2 + 2 * 6, 3 * 4 + 2 * -5)[/tex]
Evaluate the products
[tex]R = \frac{1}{5}* (6, 2)[/tex]
This gives
R = (1.2, 0.4)
Hence, the coordinates of R is (1.2, 0.4)
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Help me with this please :V
Answer:
refer to the above attachment
what is the functions domain ?
what is the functions range ?
find the values of the function f(-5)= and f(-1)=
Answer:
domain: -∞ < x < ∞range: -∞ < y ≤ -1f(-5) = -2f(-1) = -4Step-by-step explanation:
Function values and the extent of the graph can be determined by reading the graph.
DomainThe domain of the function is the set of values for which the function is defined. It is the horizontal extent of the graph. The graph shows the function is defined for all real numbers.
The domain is -∞ < x < ∞.
RangeThe range of the function is the set of output values the function may have. It is the vertical extent of the graph. The graph shows the function can have any value no greater than -1.
The range is -∞ < y ≤ -1.
Function valuesFunction values can be read from the graph by locating the x-value on the x-axis, and following the vertical line to its intersection with the function graph. The y-value of that point is the function value.
f(-5) = -2
f(-1) = -4
Or, we can write the function definition based on the graph, and use that definition to find the values at specific points. The graph is of the absolute value function reflected over x and translated <-4, -1>.
f(x) = -|x+4| -1
f(-5) = -|-5 +4| -1 = -1 -1 = -2
f(-1) = -|-1 +4| -1 = -3 -1 = -4
. A bus covers 44 kilometres in 3 2/3 -hours. How much distance it has covered in 1 hour ? please need fast
Answer:
12km
Step-by-step explanation:
Let unknown= x
40 km = 3 2/3 hrs
xkm = 1 hr
cross multiplying
x =44÷ 3 2/3
=12 km