The correct answer is CI = (71.415%, 78.915%)
The correct option is (A)
What is Confidence level?A confidence interval is the mean of your estimate plus and minus the variation in that estimate.
Given:
x = 376
Sample = 500 students
CI= [(376/500-1.96 √((376/500)*(124/500)/500) , (376/500-1.96
√((376/500)*(124/500)/500)]
CI = (71.415%, 78.915%)
Hence, CI = (71.415%, 78.915%)
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If f(x) = 3x-2 and g(x) = x+²,
find f(g(x)).
f(g(x)) = [?]
Simplify your answer as much as possible.
Answer:
x
Step-by-step explanation:
[tex]f(g(x)) = 3(\frac{x+2}{3} )-2\\= x + 2 - 2\\= x[/tex]
Line l passes through point (−2,37) and line p is the graph of y+3=−5(x+4) .
If l is parallel to p what is the equation of l ?
The slope of line p is -5, so substitute into point-slope form, we get
[tex]\boxed{y-37=-5(x+2)}[/tex]
The rectangular prism has a vertex at (5, 6, 2). Which
ordered triples represent other vertices of the prism?
Check all that apply.
(0, 0, 2)
(0, 5,6)
(2,0, 5)
(5, 0, 2)
(5, 6, 0)
(6,2,0)
Answer:
A, D, E
Explanation:
It's right on edge lol
Use the calculator to graph the function y = 2x2 25x + 3. What are the coordinates of the turning point of the graph to the nearest hundredth?
Vertex = (
,
)
The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]In this problem, the function is given by:
y = 2x² + 25x + 3.
Hence the coefficients are a = 2, b = 25, c = 3, then the coordinates of the vertex are given as follows:
[tex]x_v = -\frac{25}{2(2)} = -6.25[/tex][tex]y_v = -\frac{25^2 - 4(2)(3)}{4(2)} = -75.13[/tex]The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).
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Answer:
6.25, -75.13
Step-by-step explanation:
it just is
Two trains going in opposite directions leave at the same time. Train B travels 5 mph faster than train A. In 3 hours the trains are 315 miles apart. Find the speed of each train
Answer:
Step-by-step explanation:
MAT 171
1. The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=-4
Find a possible formula for P(x)
2. The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at x=0 and x=-4. It goes through the point (5, 36).
Find a formula for P(x).
3. The polynomial of degree 3. P(x), has a root of multiplicity 2 at x=3 and a root of multiplicity 1 at x=-2. The y-intercept is y=-1.8.
Find a formula for P(x).
Using the Factor Theorem, the polynomials are given as follows:
1. [tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]
2. [tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
3. P(x) = -0.1(x³ - 4x² - 3x + 18)
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Item a:
The parameters are:
[tex]a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4[/tex]
Hence the equation is:
P(x) = (x - 1)²x²(x + 4)
P(x) = (x² - 2x + 1)(x + 4)x²
P(x) = (x³ + 2x² - 7x + 1)x²
[tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]
Item b:
The roots are:
[tex]x_1 = x_2 = 4, x_3 = 0, x_4 = -4[/tex]
Hence:
P(x) = a(x - 4)²x(x + 4)
P(x) = a(x² - 16)x(x - 4)
P(x) = a(x³ - 16x)(x - 4)
[tex]P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
It passes through the point x = 5, P(x) = 36, hence:
45a = 36.
a = 4/5
a = 0.8
Hence:
[tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
Item 3:
The roots are:
[tex]x_1 = x_2 = 3, x_3 = -2[/tex]
Hence:
P(x) = a(x - 3)²(x + 2)
P(x) = a(x² - 6x + 9)(x + 2)
P(x) = a(x³ - 4x² - 3x + 18)
For the y-intercept, x = 0, y = -1.8, hence:
18a = -1.8 -> a = -0.1
Thus the function is:
P(x) = -0.1(x³ - 4x² - 3x + 18)
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If : f(x)=x^2, g(x)=x-1. Find (f×g)(x).
Answer:
[tex] \boxed{ f\cdot{g}(x) = x {}^{3} - x {}^{2}}[/tex]Step by step explanation:
Given that,
[tex]f(x) = {x}^{2} [/tex]
[tex]g(x) = x - 1[/tex]
Solution:
Solving for (f•g)(x):
[tex] = f(x) \cdot g(x)[/tex]
Now substitute the given values.
[tex] = x {}^{2} \cdot(x - 1)[/tex]
[tex] = x {}^{2} (x - 1)[/tex]
Apply distributive property:
[tex] = (x ^{2} \cdot x) - x {}^{2} \cdot 1[/tex]
[tex] \boxed{ f\cdot{g}(x) = x {}^{3} - x {}^{2}}[/tex]Hence,f•g(x) will be [tex] x {}^{3} - x {}^{2}[/tex].
Which statement is true about the end behavior of the graphed function?
Step-by-step explanation:
both ends are going to the same direction so the degree is even. the right side is going up so the leading coefficient is positive.
1) Which relation is a function?
es
A) x = y² - 3
B) x = y - 4x²
C) y² = 4x - 6
D) x² = y²-10
Answer:
B
Step-by-step explanation:
x = y-4x^2 can be rearranged to get y = 4x^2 + x, which is a function
4 Pencils and 2 rulers cost $8. 2 pencils and 4 rulers cost $10. Find the cost of 3 rulers and 3 pencils
Answer:
$9
Step-by-step explanation:
Let, the price of pencils is x, and the price of rulers is y.
4x+2y=8.....(i)
2x+4y=10......(ii)
From eq(i),
2(2x+y)=8
2x+y=4
y=4-2x eq(iii) .....put in eq(ii)
2x+4(4-2x)=10
2x+16-8x=10
-6x=10-16
x=-6/-6
x=1 put in eq (iii)
y=4-2(1)
y=2
Now, the price of 3 rulers and 3 pencils = 3x+3y=3(1)+3(2)
=9
Please give me brainlist.
The table below shows the amount of money spent on skin diving and scuba equipment in some recent years.
Skin Diving and Scuba Equipment
Year
Sales ($millions)
1993
315
1994
322
1995
328
1996
340
1998
345
1999
363
Let x represent the year and y represent the amount of sales, in millions of dollars, in the regression equation.
y = 7.36 x minus 14,354.33,
Use the regression equation to predict the sales of skin diving and scuba equipment in the year 2008.
a.
44,000,000
b.
440,000,000
c.
42,455,000
d.
424,550,000
Please select the best answer from the choices provided
A
B
C
D
Mark this and return
The sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000
How to predict the sales in 2008?The regression equation is given as;
y = 7.36x - 14,354.33
In 2008, the value of x is
x = 2008
So, we have:
y = 7.36 * 2008 - 14,354.33
Evaluate
y = 424.55
Hence, the sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000
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The sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000.
We have given that,
The table below shows the amount of money spent on skin diving and scuba equipment in some recent years.
How to predict the sales in 2008?The regression equation is given as
y = 7.36x - 14,354.33
In 2008, the value of x is
x = 2008
So, we have y = 7.36 * 2008 - 14,354.33
Evaluate y = 424.55
Hence, the sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000
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10 problems for 50 points
Answer:
1. F
2. F
3. T
4. F
5. F
6. T
7. T
8. F
9. F
10. T
Step-by-step explanation:
1. For the rays to be opposite, they need to have the same starting point and go in different directions. Rays AP and BP use Point A and Point B, respectively, for their starting points.
2. They do not lie on the same line.
3. Points A, B, C, D all lie in the same plane therefore making them coplanar.
4. Points X, Y do not lie in the same plane as A, B.
5. Point X does not lie in the same plane as C, D, B
6. A, P, B are all points on the same line therefore any two of them could be used to represent the same line.
7. PX and PY start at the same point and go in the opposite directions, defining them as opposite rays.
8. Plane AXY cannot be defined as point X and Y are not in a plane.
9. Lines AB and CD cannot both be in a different plane.
10. Both rays sum up to equal Line XY.
Solve the system of equations by graphing.
y = x − 6
3x − 3y = 18
X = 6
Y = (-6)
What is the domain of the function y=√√x+6-7?
x>|-7
x>|-6
x>|6
x>|7
The domain of the function [tex]y=\sqrt{(x+6)}-7[/tex] is given by (B) that is [tex]x \geq-6[/tex]
Domain of a function refers to the values or range of input values of a function for which the function exists in real.
In this problem the given function is
[tex]y=\sqrt{(x+6)}-7[/tex]
Now the above function exists if the expression under square root is greater or equal to 0, since negative number cannot be square rooted in real, that gives imaginary number.
So, for existence of function it is must to
[tex]x+6\geq0[/tex]
[tex]x\geq-6[/tex]
Hence the domain of the given function is given by [tex]x\geq-6[/tex]
Hence the correct option is (B).
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Identify the category to which the following statement belongs: Brandon has two weeks to decide on the topic of his research paper.
O Not important - Not Urgent
O Not Important - Urgent
O Important - Not Urgent
O Important-Urgent
Answer:
Important- not urgent
Step-by-step explanation:
The research paper is important but since Brandon has two weeks to decide it is not urgent.
Solve the following systems using the elimination method. -3x+4y=-8 and 3x+ y=-17
Answer:
(-4, -5)
Step-by-step explanation:
-3x + 4y = -8
+
3x + y = -17
= 5y = -25 = y = -5
-3x + 4(-5) = -8
-3x - 20 = -8
-3x = 12
x = -4
Which pair of statements describes the end behavior of the graph of the function f(x) = x3 + 2x2 − 5x − 6?
A function assigns the values. The correct option is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete question is:
Which pair of statements describe the end behavior of the graph of the function f(x) = x³ + 2x² − 5x − 6?
A.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity.
B.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches negative infinity.
C.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches negative infinity.
D.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches infinity.
If we draw the graph of the given function f(x) = x³ + 2x² − 5x − 6, then it can be observed that as x approaches -∞, f(x) approaches -∞. As x approaches ∞, f(x) approaches infinity.
Hence, the correct option is D.
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Given that G=ab find the percentage increase in G when both a and b
increase by 10%
The percentage change in G is 21 %
What is Percentage change ?Percentage change is defined as the increase or decrease in the value as compared to the original value multiplied by 100.
It is given that
G = ab
when a is increased by 10% the new a will be = 1.1 a
When b is increased by 10% the new b will be 1.1 b
So,
G' = 1.1a *1.1 b
G' = 1.21 ab
G' = 1.21
(G' - G)*100/G = (1.21-1)*100/1
The percentage change is 21 %
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Identifying Proportional Relationships
Which graph represents a proportional relationship?
Answer:
I can't answer this if you don't have the answer choices
I'm sorry
Need the answer for number 3 please!!!!
Answer:
Perimeter = 2(l + b)
= 2(x + 5x³ + 4 - x²)
= 2x + 10x³ + 8 - 2x²
= 10x³ - 2x² + 2x + 8
Hence, ur answer is the first option.
Answer:
A.
Step-by-step explanation:
L = x
W = 5x³ + 4 - x²
P = 2L + 2W
P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²
P(x) 10x³ - 2x² + 2x + 8
L = x
W = 5x³ + 4 - x²
P= 2L + 2W
P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²
= P(x) 10x³ - 2x² + 2x + 8
Need help with this geometry question
Answer: 59
Step-by-step explanation:
The measure of an arc is equal to the measure of the central angle intercepted by it.
The fox population in a certain region has a continuous growth rate of 7 percent per year. It is estimated that the population in the year 2000 was 15000.
(a) Find a function that models the population
t
years after 2000 (
t
=
0
for 2000).
Your answer is
P
(
t
)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer)
There are 25773 foxes in the region in the year 2008
How to determine the function?The given parameters are:
Initial value, a = 15000Rate, r = 7% or 0.07Let the number of years after 2000 be x.
So, the function is
f(x) = a * (1 + r)^x
This gives
f(x) = 15000 * (1 + 0.07)^x
In 2008, we have:
x = 8
So, the equation becomes
f(8) = 15000 * (1 + 0.07)^8
Evaluate
f(8) = 25773
Hence, there are 25773 foxes in the region in the year 2008
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P(-4, 6), Q(2, 5), R(3, -1), S(-3, 0)
Use slope to determine whether the following is a parallelogram. Explain why or why not.
Find the slope of PQ
Find the slope of QR
Find the slope of RS
Find the slope of SP
Use this information to determine if the quadrilateral a parallelogram.
From the slopes it is confirmed that PQ || RS OR|| SP and therefore it is a parallelogram .
What is a Parallelogram ?A parallelogram is a quadrilateral in which the opposite sides are parallel.
The coordinates of a quadrilateral is given
To prove that it is a parallelogram
PQ || RS
OR|| SP
The slope of a straight line is given by
[tex]\rm m = \dfrac{y_2 -y_1}{x_2- x_1}[/tex]
For PQ
m = (-1/6) = -1/6
For QR
m = -6/1 = -6
For RS
m = 1/(-6) = -1/6
For SP
m = -6
From the slopes it is confirmed that
PQ || RS
OR|| SP
and therefore it is a parallelogram
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Flying against the wind, an airplane travels 2520 kilometers in 4 hours. Flying with the wind, the same plane travels 9450 kilometers in 9 hours. What is the rate of the plane in still air and what is the rate of the wind?
Using the relation between velocity, distance and time, it is found that:
The rate of the plane is of 840 km/h.The rate of the wind is of 210 km/h.What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
[tex]v = \frac{d}[t}[/tex]
Flying against the wind, an airplane travels 2520 kilometers in 4 hours, that is:
[tex]v - v_w = \frac{2520}{4}[/tex]
[tex]v - v_w = 630[/tex]
[tex]v = 630 + v_w[/tex]
Flying with the wind, the same plane travels 9450 kilometers in 9 hours, hence:
[tex]v + v_w = \frac{9450}{9}[/tex]
[tex]v + v_w = 1050[/tex]
[tex]v = 1050 - v_w[/tex]
Hence, solving for the wind's speed:
[tex]630 + v_w = 1050 - v_w[/tex]
[tex]2v_w = 420[/tex]
[tex]v_w = \frac{420}{2}[/tex]
[tex]v_w = 210[/tex]
For the plane, we have that:
v = 1050 - 210 = 840.
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A manufacturer of pacemakers wants the standard deviation of the lifetimes of the batteries to be less than 1.8 months. A sample of 20 batteries had a standard deviation of 1.6 months. Assume the variable is normally distributed. Find the 95% confidence interval of the standard deviation of the batteries. Based on this answer, do you feel that 1.8 months is a reasonable estimate?
Answer:
Look down my answer↓:
Step-by-step explanation:
What is true of an equilateral triangle? Two of its side lengths are equal. All its side lengths are equal. None of its side lengths are equal. None of its interior angles are equal. What is true of an equilateral triangle ? Two of its side lengths are equal . All its side lengths are equal . None of its side lengths are equal . None of its interior angles are equal .
Answer:
All its side lengths are equal
(and all the agle of 60°)
Step-by-step explanation:
What is true of an equilateral triangle? Two of its side lengths are equal. All its side lengths are equal. None of its side lengths are equal. None of its interior angles are equal. What is true of an equilateral triangle ? Two of its side lengths are equal . All its side lengths are equal . None of its side lengths are equal . None of its interior angles are equal .
Which statement about –2h2 – 15h – 7 is true?
One of the factors is (h + 2).
One of the factors is (3h – 2).
One of the factors is (2h + 1).
One of the factors is (h – 7).
Answer:One of the factors of the given expression is (2h + 1).
Step-by-step explanation:
ed
Answer:
C on edge 23
Step-by-step explanation:
because i said so
(h+k)(1) is
(k-h)(4) is
(k/h)(3) is
(h•k)(0) is
(k •h)(0) is
(h•k)(3) is
h(k(-2))
Answer:
Step-by-step explanation:
(h+k)(1)=h(1)+k(1)=2+(-1)=2-1=1
(k-h)(4)=k(4)-h(4)=0-(-1)=1
(k/h)(3)[tex]=\frac{k(3)}{h(3)} =\frac{-1}{0} =- \infty[/tex]
(h.k)(0)=h(0).k(0)=3(-2)=-6
(k.h)(0)=k(0).h(0)=-2(3)=-6
(h.k)(3)=h(3).k(3)=0(-1)=0
h(k(-2))=h(-3)=0
Separable differential equation
y’ln^2y+ysqrtx=0 y(0)=e
By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].
How to solve separable differential equation
In this question we must separate each variable on each side of the equivalence, integrate each side of the expression and find an explicit expression (y = f(x)) if possible.
[tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex]
[tex](\ln y)^{2}\,dy = -y \cdot \sqrt{x}\, dx[/tex]
[tex]-\frac{(\ln y)^{2}}{y}\, dy = \sqrt{x} \,dx[/tex]
[tex]-\int {\frac{(\ln y)^{2}}{y} } \, dy = \int {\sqrt{x}} \, dx[/tex]
If u = ㏑ y and du = dy/y, then:
[tex]-\int {u^{2}\,du } = \int {x^{\frac{1}{2} }} \, dx[/tex]
[tex]-\frac{1}{3}\cdot u^{3} = \frac{2\cdot x^{\frac{3}{2} }}{3} + C[/tex]
[tex]u^{3} = -2\cdot x^{\frac{3}{2} } + C[/tex]
[tex](\ln y)^{3} = - 2\cdot x^{\frac{3}{2} } + C[/tex]
[tex]C = (\ln e)^{3}[/tex]
[tex]C = 1[/tex]
And finally we get the explicit expression:
[tex]\ln y = \sqrt [3]{-2\cdot x^{\frac{3}{2} }+ 1}[/tex]
[tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex]
By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].
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Analyze the conditional statement below and complete the instructions that follow.
If an angle measures 90°, then it is a right angle.
Identify ~q.
O An angle does not have measure 90°.
OIt is not a right angle.
An angle measures 90°.
OIt is a right angle.
Answer: It is not a right angle.
