Answer:
a) 952
b) 136
Step-by-step explanation:
Ratio of b:g = 3:4, based on this we have:
Number of boys = 3xNumber of girls = 4xTotal number of pupils = 3x+4x = 7xNumber of spectacle wearers:
1/3*3x + 3/8*4x = x + 3/2x = 2.5xNumber of those not wearing spectacles:
7x - 2.5x= 4.5xAnd this number equals to 612, then we can find the value of x:
4.5 x = 612x= 612/4.5x= 136a) Total number of pupils:
7x = 7*136 = 952b) The difference in the number of boys and girls:
4x-3x= x = 136Answer:
total number of students: 952
number of girls more than boys :136 more girls
Step-by-step explanation:
1/3 of boys +3/8 girls= spectacles
612 people do not wear spectacles
3:4= boys: girls
total number of students
3+4=7
boys + girls = total ratio
7= total ratio
1/3×3=1 3/8×4=3/2
1+3/2=5/2
7-5/2=9/2 9/2=612 students
If 9/2=612 Then 7=?
7= 7÷ 9/2×612
=952 people
Girls more than boys
if 7= 952
3= 3/7 × 952=408 boys
if 7 = 952
4= 4/7 ×952=544girls
Girls - boys
544- 408 = 136 girls
a) Show that the equation 2 x + 3 cos x + e^x = 0 has a root on the
interval (-1,0)
b) Use the Bisection method to find the solution of 2 x + 3 cos x +
e^x = 0. accurate with in 10-3. On (-1,0). (Use four digits-Rounding)
a) The equation has a root in the interval (-1,0)
b) The solution of [tex]2x+3cos(x)+e^{x}=0[/tex] by using the Bisection Method is x=0.9977 accurate within [tex]10^{-3}[/tex]
a) The intermediate zero theorem (Bolzano's Theorem) tells us that whenever you have a continuous function in a given interval and the extremes of the functions on this interval have oposite signs, then there must be a zero in between those extreme values.
A formal definition of this theorem is written like this:"If a function f on the closed interval [a,b] is a continuous function and it holds that f(a)>0 and f(b)<0 or f(a)<0 and f(b)>0, then there is at least one x-value such that f(x)=0"
So basically we need to evaluate the given equation for both extremes of the interval x=-1 and x=0, if they return results opposite in sign, then there must be a zero in that interval, so let's evaluate the function for x=-1:
[tex]2x+3cos(x)+e^{x}[/tex]
[tex]2(-1)+3cos(-1)+e^{-1}=-0.0112[/tex]
Let's now test for x=0
[tex]2x+3cos(x)+e^{x}[/tex]
[tex]2(0)+3cos(0)+e^{0}=4[/tex]
So notice we ended up with two values -0.0112 and 4. One is positive and the other is negative, therefore there must be a zero in that interval.
b) The zero is located at x=-0.9977
The idea of the bisection method is to find values for x in the middle of two x-values that return opposite sign answers when evaluated on the given function. So we can start with the extremes of the given interval:
x=-1 and x=0
so we find the value in the middle by using the following formula:
[tex]mid-value=\frac{x_{1}+x_{2}}{2}[/tex]
so we get:
[tex]mid-value=\frac{-1+0}{2}[/tex]
mid-value=-0.5
Next, we evaluate the given function for that value:
[tex]2(-0.5)+3cos(-0.5)+e^{-0.5}=2.2393[/tex]
Since we got a positive answer, we now find the midpoint between -0.5 and -1 (which was the last x-value that returned a negative answer) so we get:
[tex]mid-value=\frac{-1-0.5}{2}[/tex]
mid-value=-0.75
Next, we evaluate the given function for that value:
[tex]2(-0.75)+3cos(-0.75)+e^{-0.75}=1.1674[/tex]
and we repeat the process until que get to the desired accuracy. I uploaded a table that has the corresponding iterations and its answers. There were 14 iterations done until we got to the final answer x=-0.9977.
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Consider the polynomial 2x5 + 4x3 - 3x8
Part A The polynomial in standard form is:
Part B: The degree of the polynomial is:
Part C: The number of terms in the polynomial is:
Part D: The leading term of the polynomials:
Part E: The leading coefficient of the polynomial is:
Answer:
Step-by-step explanation:
Considering the polynomial 2x⁵ + 4x³ - 3x⁸. The polynomial is not yet in standard form. For a polynomial to be in standard form, the power of the variables must decrease as we progress to the right of the expression.
A) The polynomial in standard form is therefore - 3x⁸ + 2x⁵ + 4x³. We can see that the power are reducing as we move through each terms i.e from 8 to 5 then to 3.
B) The degree of a polynomial is the maximum degree among all the terms of the polynomial. The term that has the maximum degree is -3x⁸. Hence, the degree of the polynomial is 8
C) There are only 3 terms in the polynomial given. The terms are separated by mathematical signs. The terms if the polynomial are 2x⁵, 4x³ and - 3x⁸.
D) The leading term of the polynomial is the term that comes first after rewriting the polynomial in standard format. Given the standard from of the polynomial given as -3x⁸ + 2x⁵ + 4x³, the leading term will be - 3x⁸
E) Given the leading term to be - 3x⁸, the leading coefficient of the polynomial will be the coefficient of the leading term. The coefficient of -3x⁸ is -3
Can someone please help me with 1-10 please and thank you
Answer:
yes me me me me me ,,,,,,,,,,,,,,,,,,,, ....
the age of furaha is 1/2 of the age of her aunt if the sum of their ages is 54 years. find the age of her aunt
Answer:
I think it is twenty seven
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE explain thoroughly. Chapter 16
1. What is De Movire's Theorem and what plane is it related to?
2. What information do you need to be able to graph a parametric equation?
3. What is the relationship between rectangle coordinates and polar coordinates?
9514 1404 393
Answer:
complex plane; (cos(θ)+i·sin(θ))^n = cos(nθ) +i·sin(nθ)relationship between parameter and coordinatesbasically: (x, y) = (r·cos(θ), r·sin(θ)); can be solved for r, θStep-by-step explanation:
1. de Moivre's theorem (or identity) states that ...
[tex](\cos(\theta)+i\sin(\theta))^n=\cos(n\theta)+i\sin(n\theta)[/tex]
It is a statement about powers of complex numbers, so is related to the complex plane.
__
2. To graph a parametric equation, you need to know the relationship between the parameter and the coordinates you want to graph.
__
3. Here are the relationships:
(x, y) = (r·cos(θ), r·sin(θ))
(r, θ) = (√(x² +y²), arctan(y/x)) . . . with attention to quadrant
Find the equation of the para bola that has zeros of x = -2 and x = 3 and a y-intercept of (0,-30)
Answer:
y = 5x^2-5x-30
Step-by-step explanation:
A parabola with x-intercepts at (-2,0) and (3,0) has the equation
y = a(x+2)(x-3)
where a is to be determined.
We know that it passes through the point (0,-30), so
-30 = a(0+2)(0-3) = -6a
Therefore solve for a to get
a = 5
y = 5(x+2)(x-3)
y = 5(x^2-x+6)
y = 5x^2-5x-30
8. (01.02)
Given that f(x) = x2 + 2x + 3 and g(x)
X+4.
3
solve for f(g(x)) when x = 2.
2
5
11
33
Answer:
51.
Step-by-step explanation:
f(x) = x^2 + 2x + 3 and g(x) = x + 4.
f(g(x)) = (x + 4)^2 + 2(x + 4) + 3
= x^2 + 4x + 4x + 16 + 2x + 8 + 3
= x^2 + 8x + 16 + 2x + 11
= x^2 + 10x + 27.
x = 2.
f(g(2)) = 2^2 + 10 * 2 + 27
= 4 + 20 + 27
= 31 + 20
= 51.
Hope this helps!
What is the domain of the set of ordered pairs?
(8, -13); ( 0,-5); (4, -9); (-3,2)
The domain is the input values, which are the x values.
The x values in the given pairs are: 8, 0,4,-3
The domain set is (-3, 0, 4, 8)
The required domain of the set of ordered pairs is [8, 0, 4, -3]
Given that,
Set of ordered pair; (8, -13); ( 0,-5); (4, -9); (-3,2).
We have to determine,
The domain of the set of ordered pair.
According to the question,
The domain refers to the set of possible input values.
The domain of a graph consists of all the input values shown on the x-axis.
A relation is a set of ordered pairs.
The domain is the set of all the first components of the ordered pairs.
Then,
Set of ordered pair; (8, -13); ( 0,-5); (4, -9); (-3,2).
Here, Set of all the input values on the x-axis.
Therefore,
The set of values of x is { 8,0,4,-3 }
Hence, The required domain of the set of ordered pairs is [8, 0, 4, -3]
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Equation for parabola that has points (-4,2) (0,2) (-2,3)
Step-by-step explanation:
What is the equation of the parabola that has a vertex at
(
−
4
,
2
)
and passes through point
(
−
7
,
−
34
)
?
To solve this you need to use the vertex form of the equation of a parabola which is
y
=
a
(
x
−
h
)
2
+
k
, where
(
h
,
k
)
are the coordinates of the vertex.
Explanation:
The first step is to define your variables
h
=
−
4
k
=
2
And we know one set of points on the graph, so
x
=
−
7
y
=
−
34
Next solve the formula for
a
y
=
a
(
x
−
h
)
2
+
k
−
34
=
a
(
−
7
+
4
)
2
+
2
−
34
=
a
(
−
3
)
2
+
2
−
34
=
9
a
+
2
−
36
=
9
a
−
4
=
a
To create a general formula for the parabola you would put in the values for
a
,
h
, and
k
and then simplify.
y
=
a
(
x
−
h
)
2
+
k
y
=
−
4
(
x
+
4
)
2
+
2
y
=
−
4
(
x
2
+
8
x
+
16
)
+
2
y
=
−
4
x
2
−
32
x
−
64
+
2
So the equation of a parabola that has a vertex at
(
−
4
,
2
)
and passes through point
(
−
7
,
−
34
)
is:
y
=
−
4
x
2
−
32
x
−
62
How to write this sum 24,6 in expanded notation
Answer:
2.46×10
Step-by-step explanation:
24.6
2.46 ×10
.....................
Suppose X1, X2, . . . , Xn is a random sample from an exponential distribution with parameter ????. Assume that Xi’s are independence and the individual pdf is given by: ????(x, ????) = ????????. Find the Maximum likelihood estimator of this function
Step-by-step explanation:
whaatttttttttttttttt
g If the events A and B are independent with P( A) = 0.35 and P( B) = 0.45, then the probability that both events will occur simultaneously is:
Answer:
0.1575.
Step-by-step explanation:
Here, as they are independent, we multiply the probabilities:
P( A and B) = 0.35*0.45
= 0.1575.
The probability that both events will occur simultaneously is 0.1575.
Given that, the events A and B are independent with P( A) = 0.35 and P( B) = 0.45.
What is independent probability?Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).
Since, the events A and B are independent
We have P(A and B)
= P(A) × P(B)
= 0.35 × 0.45
= 0.1575
Hence, the probability that both events will occur simultaneously is 0.1575.
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If the legs of an isosceles right triangle have a length of 15 StartRoot 2 EndRoot ft, what is the length of the hypotenuse?
Answer:
30 ft
Step-by-step explanation:
a² + b² = c²
(15sqrt(2))² + (15sqrt(2))² = c²
225 * 2 + 225 * 2 = c²
c² = 900
c = sqrt(900)
c = 30
Answer: 30 ft
Answer:
30 ft
Step-by-step explanation:
a² + b² = c²
(15sqrt(2))² + (15sqrt(2))² = c²
225 * 2 + 225 * 2 = c²
c² = 900
c = sqrt(900)
c = 30
Answer: 30 ft
How do you find volume for prisms?
Answer:
V =140 units^3
Step-by-step explanation:
The volume of the prism is V = Bh
Where B is the area of the base and h is the height
B is the area of the triangle
B = 1/2 (5 * 7) = 35/2
V = 35/2 * 8
V =140 units^3
this person made an error. what is it, and what is the right answer?
Answer:
Base area (B) should not be added.
Step-by-step explanation:
Base area should not be added as cone is not solid. Only Lateral surface area is sufficient in order to find the required paper.
8 less than one-fourteenth of some number, w
Answer:
The answer is 1/14w-8
In 2014, the population of Ohio was 11.59 million people. One-hundred years earlier the population was 5.109 million people. Using scientific notation, how much did the population grow over the hundred-year span?
The answer is the population grew over the hundred-year span by [tex]6.481*(10)^6[/tex]
Given that in 2014, the population of people in Ohio = [tex]11.59[/tex] million
Also given that One-hundred years earlier of the year 1914, the population = [tex]5.109[/tex] million people
One-hundred years earlier in the year 2014 = 2014 [tex]- 100[/tex] years
One-hundred years earlier in the year 2014 = Year 1914
The scientific notation of the year 2014 population is [tex]11.59*(10)^6[/tex]
The scientific notation of the year 1914 population is [tex]5.109*(10)^6[/tex]
How much did the population grow over the hundred-year span?
Growth of the population from 1914-2014 = [tex]11.59*(10)^6 - 5.109*(10)^6[/tex]
Growth of the population from 1914-2014 = [tex]6.481*(10)^6[/tex]
Conclusion: The population grew over the hundred-year span by [tex]6.481*(10)^6[/tex]
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the ration of men to women in a certain factory is 3 to 4. there are 204 men. how many workers are there?
Answer:
476 workers
Step-by-step explanation:
Men: women : total
3 4 3+4 = 7
We want 204 men
204/3 =68
Multiply each by 68
Men: women : total
3*68 4*68 7*68
204 272 476
Answer:
There are 476 workers
Step-by-step explanation:
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
Match the provided functions to a graphed function with the same zero(s).
Answer:
1st:
[tex] {x}^{3} - 3 { x}^{2} - 3[/tex]
2nd:
[tex] {x}^{2} - 5x + 4[/tex]
3rd:
[tex] - 4x - 8[/tex]
Step-by-step explanation:
Graph all of them and see which ones cross the x- axis at the same points.
Let $x=5$, $y=\frac{3}{4}$, and $z=-\frac{1}{7}$. What is $$\frac{xz}{y}?$$
Answer:
-20/21Step-by-step explanation:
Given x = 5, y = 3/4 and z = -1/7, 2=we are to calculate [tex]\frac{xz}{y}[/tex]. Substituting the value of x, y and z into the expression will give;
[tex]= \frac{xz}{y}\\\\ \frac{5(-1/7)}{3/4} \\= \frac{-5/7}{3/4}\\\\= \frac{-5}{7} * \frac{4}{3}\\ \\ = \dfrac{-20}{21}\\[/tex]
Hence the value of the expression is -20/21
quanto e 45x12 (500-450-550)
Answer:
see below
Step-by-step explanation:
the simple answer is -270000
If the sample size is increased and the standard deviation and confidence level stay the same, then the margin of error will also be increased.
a. True
b. False
False!
The answer is: False.
Whomever stated the answer is "true" is wrong.
Jim took a loan of R30 000.00 for 18 months at a simple interest rate of 12.5% per year. Determine the amount that Jim
will pay in 18 months.
Answer:
R35625
Step-by-step explanation:
(R30,000×.125×18/12)+R30000
=R35625
find the h.c.f of 186,310,434
186|2
93|3
31|31
1
310|2
155|5
31|31
1
434|2
217|7
31|31
1
[tex]186=2\cdot3\cdot31\\310=2\cdot5\cdot31\\434=2\cdot7\cdot31\\\\\text{hcf}(186,310,434)=2\cdot31=62[/tex]
Convert 16,000 feet per second into kilometers per hour. step by step
The length of a rectangle is five times its width.
2
If the area of the rectangle is 180 in find its perimeter.
Answer:
72
Step-by-step explanation:
l = 5w
A = l*w
180 = 5w *w
180 = 5w^2
Divide each side by 5
180/5 = 5w^2 /5
36 = w^2
Taking the square root of each side
sqrt(36) = sqrt(w)^2
6 =w
l = 5w = 5*6 = 30
The perimeter is
P = 2(l+w)
P = 2(6+30) = 2(36) = 72
Please help! Thank you!
In the figure below, O is the center of the circle. Name a tangent of the circle.
A. AO
B. FG
C. AB
D. HK
Answer:
Its A
Step-by-step explanation:
The tangent of the given circle is FG hence the correct option will be an option (B).
What is a tangent of a circle?The tangent of a circle is a line that intersects the circle at the periphery of the circle.
If you draw a line that goes through the center to the tangent touching point then it will give you a 90-degree angle.
Given the circle it's clear that the tangent is only FG hence it will be the correct option
A circle can have an infinite number of tangents.
In other words, a straight line that only touches a circle twice is said to be tangent to it. The term point of intersection refers to this location
At the tangent line, the tangent to a circle is orthogonal to the radius.
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9. Find the volume of x and y if, (3x,10)=(9,5y).
Answer:
x=3 and y=2
Step-by-step explanation:
Comparing the oder pair, we have 3x=9 and 10=5y. x=3 and y=2
How would the margin of error change if the sample size increased from 200 to 400 students? Assume that the proportion of students who say yes does not change significantly.
Answer:
(MOE) the Margin of Error will decrease by the square root of 2
Step-by-step explanation:
The Margin of Error (MOE) is an inverse function of sample size n ( more precisely of the square root of sample size ). That relation means changes in sample size ( keeping constant other variables of the distribution) will imply opposite changes in the Margin of Error. If we double the sample size increasing it from 200 up to 400, the Margin of Error will decrease by the square root of 2