The 97% confidence interval for the proportion of yellow M&Ms in that bag is [0.118, 0.285]. (option c).
Now, let's apply this formula to our scenario. We are given the counts of each color of M&Ms in the sample, so we can compute the sample proportion of yellow M&Ms as:
Sample proportion = number of yellow M&Ms / sample size
= 22 / (22 + 21 + 13 + 17 + 22 + 14)
= 0.229
Next, we need to find the critical value from the standard normal distribution for a 97% confidence level. This can be done using a z-table or a calculator, and we get:
z* = 2.17
Finally, we need to compute the standard error using the formula mentioned earlier. Since we are interested in the proportion of yellow M&Ms, we can set p = 0.20 (the claimed proportion by Mars Inc.) and q = 0.80 (1 - p), and n = 109 (the sample size). Thus,
Standard error = √[(p * q) / n]
= √[(0.20 * 0.80) / 109]
= 0.040
Plugging in the values in the formula for the confidence interval, we get:
Confidence interval = 0.229 ± 2.17 * 0.040
= [0.118, 0.285]
Hence the correct option is (c).
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Complete Question:
Mars Inc. claims that they produce M&Ms with the following distributions:
| Brown = 30% || Orange = 10% | Red = 20% |Green = 10% |Yellow = 20% | Blue = 10%
A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were:
Brown = 22 | Red = 21| Orange = 13 | Green = 17| Yellow = 22 | Blue = 14
Find the 97% confidence interval for the proportion of yellow M&Ms in that bag.
a) [0.018, 0.235]
b) [0.038, 0.285]
c) [0.118,0.285]
d) [0.168, 0.173]
e) [0.118,0.085]
f) None of the above
use the intermediate value theorem to prove that there is a positive number c such that c2 = 2.
So lets try to prove it,
So let's consider the function f(x) = x^2.
Since f(x) is a polynomial, then it is continuous on the interval (- infinity, + infinity).
Using the Intermediate Value Theorem,
it would be enough to show that at some point a f(x) is less than 2 and at some point b f(x) is greater than 2. For example, let a = 0 and b = 3.
Therefore, f(0) = 0, which is less than 2, and f(3) = 9, which is greater than 2. Applying IVT to f(x) = x^2 on the interval [0,3}.
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Which of the following functions are solutions of the differential equation y'' + y = sin(x)? (Select all that apply.) y = − 1 2 x cos(x)
The function that is the solution of the differential y" + y = sin(x) is: y(x) = -1/2(x cos x)
What is a function?A function is an expression, rule, or law in mathematics that describes a connection between one factor (the independent variable) and another variable (the dependent variable).
What is the proof of the above function?Take a look at the the following differential equation:
y" + y = sin (x)
The auxiiliary equation is
m² + 1 = 0
m² + 1-1 = -1
m² + 0 = -1
m² = -1
m = ±√-1
m = ±i
So, the complimentary function is yₐ (x) = c₁ cos x + c₂ sin x
Let the particular integral be:
yₙ (x) = A cos x + B sin x
yₙ '(x) = - A sin x + B cos x
yₙ ''(x) = - A cos x + B cos x
yₙ ''(x) = - (A cos x + B cos x)
After we have substituted yₙ (x); and yₙ''(x) in the given differential equation
y'' + y = sin (x)
= - (A cos x + B cos x) + (A cos x + B cos x) = sin(x)
0 = sin (x)
If we take the particular integral to be:
yₙ (x) = x(A cos x + B cos x)
yₙ '(x) = x(-A sin x + B cos x) + A cos x + B cos x
yₙ ''(x) = x(-A cos x - B sin x) - A sin x + B cos x + -A sin x + B cos x
Substitute yₙ (x), yₙ''(x) into the stated differential equation
y'' + y = sin (x)
x (-Acosx - Bsin x) - Asinx + Bcosx + (-Asinx + Bcosx) - x (Acosx + Bsin x) = sin (x)
-Axcosx - Bxsin x - Asinx + Bcosx -Asinx + Bcosx - Axcosx + Bxsin x = sin (x)
-2Asinx + 2Bcosx = sin(x)
Compare the coefficients of like terms on both sides of the equation
-2A = 1, B = 0
A = -1/2, B = 0
Substitute A = -1/2, B =0 into the assumed solution.
yₙ(x) = x((-1/2)cosx + (0) sinx)
= -1/2xcosx +0
= -(1/2)xcosx
Now, the general solution for the given differential equation is:
y(x) = yₓ(x) +yₙ (x)
y (x) - c₁cosx + c₂sin x -1/2x cosx
Hence, the solution is:
y(x) = -1/2xcosx
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Full Question:
Which of the following functions are solutions of the differential equation y'' + y = sin x? (Select all that apply.)
A) y = 1 2 x sin x
B) y = cos x
C) y = x sin x − 5x cos x
D) y = − 1 /2 x cos x
E) y = sin x
give the volume and surface area of the sphere shown
Answer:
V≈3053.63
A≈1017.88
Step-by-step explanation:
V=[tex]\frac{4}{3}[/tex]π [tex]r^{3}[/tex]=[tex]\frac{4}{3}[/tex]·π·[tex]9^{3}[/tex] ≈3053.62806
A=4π[tex]r^{2}[/tex]=4·π·[tex]9^{2}[/tex] ≈1017.87602
Use the graph that shows the solution to f(x)=g(x).
f(x)=1/x−2
g(x)=x−2
What is the solution to f(x)=g(x)?
Select each correct answer.
−1
1
2
3
The solution to the system of equations is given as follows:
x = 1 and x = 3.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the two equations are:
[tex]\frac{1}{x - 2} = x - 2[/tex]
Applying cross multiplication:
(x - 2)(x - 2) = 1
x² - 4x + 4 = 1
x² - 4x + 3 = 0
(x - 1)(x - 3) = 0
Hence the solutions are:
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PLEASE HELP IM STUCK
Answer:
y =- [tex]\frac{1}{4}[/tex]x - 1
Step-by-step explanation:
You are asked to give the equation of the line in slope intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
Y-intercept is the point where the graph intersects the y-axis at point (b, 0). The graph seems to cross the y-axis at (-1, 0), so the b value is -1.
Slope is rise over run. Looking at the graph, it goes down 1 unit every 4 units to the right, so the slope is -1/4.
Answer:
Below in bold.
Step-by-step explanation:
The slope is -1/4 and y-intercept is -1
y = -1/4x - 1
please provide the answer?
Using the given table:
a) the average rate of change is 32.5 jobs/year.
b) the average rate of change is 12.5 jobs/year.
How to find the average rate of change?
For a function f(x), the average rate of change on an interval [a, b] is:
[tex]\frac{f(b) - f(a)}{b - a}[/tex]
a) The average rate of change between 1997 and 1999 is:
[tex]A = \frac{695 - 630}{1999 - 1997} = 32.5[/tex]
So the average rate of change is 32.5 jobs/year.
b) Now the interval is 1999 to 2001.
The rate this time is:
[tex]A ' = \frac{720 - 695}{2001 - 1999} = 12.5[/tex]
So the average rate of change is 12.5 jobs/year.
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Step 2 - Fill in the missing number: A vertical line and horizontal line combine to make a L shape. There is one row of entries in the shape including 1, negative 3, negative 10, 24. On the outside to the left of the L shape is 2 and to the outside below 1 is a. a =
The synthetic division's representation of the dividend is 2x3 + 10x2 + x + 5.
Given that
An L shape is created when two lines intersect vertically and horizontally.
The shape has entries in two rows.
Entries in row 1 are 2, 10, 1, and 5.
Blank, -10, and 0 are the entries in row 2.
A simplified method of dividing a polynomial with another polynomial equation of degree one is known as synthetic division.
On the exterior, to the left of the form, is entry number 5.
The entry stands for the divisor's zero.
If the variable is x, then this entry to the variable is;
2x³+10x²+x+5
The dividend is thus represented by synthetic division as
2x³+10x²+x+5
The Question is incomplete And complete question is given below!!
What dividend is represented by the synthetic division below? A vertical line and horizontal line combine to make a L shape. There are two rows of entries within the shape. Row 1 has entries 2, 10, 1, 5. Row 2 has entries blank, negative 10, 0, negative 5. Entry negative 5 is on the outside to the left of the shape, and a third row of entries is outside and below the shape. Row 3 has entries 2, 0, 1, 0. Negative 10 x squared minus 5 2 x cubed 10 x squared x 5 2 x squared 1 2 x cubed x.
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Answer:
The answer on Edge is A= 1
Step-by-step explanation:
If is any positive two-digit integer, what is the greatest positive integer that must be a factor of
Answer:
23
Step-by-step explanation:
small brain
Bob and Carol are teenagers. Bob is two years older than Carol. If the digits of Carol's age are reversed, the new number would be three times as large as Bob's age. Find Bob's age.
Bob is 2 years older than Carol and the reverse of Carol's age is 3 times Bob's age, which makes Bob's to be 17 years.
How can Bob's age be calculated?Let 1B represent Bob's age and let 1C represent Carol's age, we can write the following equations;
1B = 1C + 2Reversing Carol's age gives;
C1 = 3 × 1BThe multiples of 3 that have the form X1 have 7 as the rightmost number.
Given that 1B is a teenager, we have;
When;
1B = 171C = 17 - 2 = 15The reverse of Carol's age is therefore;
C1 = 51 = 3 × 17Therefore, from the given description, Bob's age 1B = 17 years
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Ayudaaaaaaa es para hoy:
Necesito saber cuanto es 389 pesos mexicanos con un 12% de rebaja,ayuda plis
El precio resultante con descuento de 12 % es igual a 342.32 pesos.
¿Cómo hallar el precio resultante con descuento?
En este problema tenemos que determinar el precio resultante, el cual es igual al precio inicial menos el descuento. A continuación, se presenta la siguiente expresión:
x = 389 · (1 - 12/100)
x = 389 - 46.68
x = 342.32
El precio resultante con descuento de 12 % es igual a 342.32 pesos.
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PLEASE HELP WILL GIVE YOU ALOT OF POINTS
What are the roots of the polynomial equation? –3, –2, 3 –3, 2 18, 32 18, 32, 66
The root of the polynomial function x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12 is -3, -2 and 3
How to determine the roots of the equation?The graph that completes the question is added as an attachment
The polynomial function is given as:
x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12
From the attached graph, we have the following highlight:
The curves of both equations intersect at
x = -3, x = -2 and x = 3
This means that the root of the polynomial function is -3, -2 and 3
Hence, the root of the polynomial function x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12 is -3, -2 and 3
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Complete question
Carlos graphed the system of equations that can be used to solve x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12
What are the roots of the polynomial equation?
A) –3, –2, 3
B) –3, 2
C) 18, 32
D) 18, 32, 66
Sample response: there is a common ratio of 2/3 between the height of the ball at each bounce. so, the bounce heights form a geometric sequence: 27, 18, 12. two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet. what did you include in your response? check all that apply. there is a common ratio between bounce heights. multiply 12 by 2/3. the height on the fourth bounce is 8 feet.
Answer:
Step-by-step explanation:
A Geometric sequence can be used:
To Model this sequence you need to use this formula
A (subscript n) = Ar(n-1)
a = value of the first term
n = the # of the term you want to find (For example, if you want to find the term number 3, it is 12)
r = the common ratio, this is obtained by dividing the second term in the sequence by the first.
So the value of r is = 2/3 because 27 times 2/3 = 18 which is the second term
n = 4 since you want to find the 4th term in the sequence
Plug it in and the results are
4th term = 27(2/3)^(4-1) = 8
The answer is 8
On a balance scale, $3$ green balls balance $6$ blue balls, $2$ yellow balls balance $5$ blue balls, and $6$ blue balls balance $4$ white balls. How many blue balls are needed to balance $4$ green, $2$ yellow and $2$ white balls
The number of blue balls that are needed to balance four green, two yellow and two white balls is 16 blue balls.
Numbers of blue balls neededGreen(g)
Blue (b)
Yellow (y)
White (w)
First step is to formula an equation
3g=6b
g=2b
2y=5b
y=5/2b
4w=6b
w=3/2b
Second step is to substitute
4g+2y+2w
=4(2b)+2(5/2b)+2(3/2b)
=8b+5b+3b
=16b
Therefore 16 blue balls are needed.
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-499" is to the __________ of "-500" on a number line
Answer: right
Step-by-step explanation:
[tex]-499 > -500[/tex], and larger numbers are to the right of numbers smaller than them on the number line.
Circle Q is shown. Secant L N and tangent P N intersect at point N outside of the circle. Secant L N intersects the circle at point M. Arc M P is y, arc L P is x, and arc M L is z.
Which equation is correct regarding the measure of ∠MNP?
m∠MNP = One-half(x – y)
m∠MNP = One-half(x + y)
m∠MNP = One-half(z + y)
m∠MNP = One-half(z – y)
By applying the Theorem of Intersecting Secant to circle Q, an equation which is correct about the measure of ∠MNP is: A. m∠MNP = One-half(x – y).
What is the Theorem of Intersecting Secant?The Theorem of Intersecting Secant states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
For this exercise, the following points should be noted:
x represents the major arc.y represents the minor arc.By applying the Theorem of Intersecting Secant to circle Q shown in the image attached below, we can infer and logically deduce that angle MNP will be given by this formula:
m∠MNP = One-half(x – y).
m∠MNP = ½(x – y)
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The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second. If the surface area of the completely inflated balloon is 784π cm2, how long will it take for the balloon to fully inflate?
Considering the surface area of the spherical ballon, it will take 7 seconds for the the balloon to fully inflate.
What is the surface area of a sphere?The surface area of a sphere of radius r is given by:
[tex]S = 4\pi r^2[/tex]
In this problem, the surface area is of [tex]784\pi[/tex] cm², hence the radius in cm is found as follows:
[tex]784\pi = 4\pi r^2[/tex]
[tex]4r^2 = 784[/tex]
[tex]r^2 = \frac{784}{4}[/tex]
[tex]r^2 = 196[/tex]
[tex]r = \sqrt{196}[/tex]
r = 14 cm.
The radius start at 0 cm, inflating at a rate of 2 cm/s, hence it will take 7 seconds for the the balloon to fully inflate, as 14 cm/(2 cm/s) = 7 s.
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Bd=16 and ac is the perpendicular bisector of bd. 2x-14 37-x d 2y-2 3 y=[?] enter
The value of y from the given expression is 5
Perpendicular Bisector
Given:
BD = 16
BC = 2y - 2
CD = y + 3
Since AC is a perpendicular bisector of BD:
BC = CD
2y - 2 = y + 3
2y - y = 3 + 2
y = 5
Hence, the value of y from the given expression is 5
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ASSIGNMENT
Evaluate -
[tex]\sf \: \displaystyle\int_{ - 1}^{25}\sf {e}^{x - [x]} [/tex]
- Need help!
Answer:
26
Explanation:
[tex]\int\limits^{25}_{-1} {e^{x-[x]}} \, dx[/tex]
simplify
[tex]\int\limits^{25}_{-1} {e^{0} \, dx[/tex]
any variable to the power 0 is 1
[tex]\int\limits^{25}_{-1} 1 \, dx[/tex]
integrating 1 gives x
[tex]\left[ \:x \: \right]^{25}_{-1}[/tex]
apply limits
[tex]25 - (-1)[/tex]
add terms
[tex]26[/tex]
[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^{x-[x]}dx[/tex]
[x] is x if x is a real number[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^{x-x}dx[/tex]
[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^0dx[/tex]
e⁰=1[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}dx[/tex]
[tex]\\ \rm\hookrightarrow \left[x\right]_{-1}^{25}[/tex]
[tex]\\ \rm\hookrightarrow 25-(-1)[/tex]
[tex]\\ \rm\hookrightarrow 25+1[/tex]
[tex]\\ \rm\hookrightarrow 26[/tex]
which of the following would be a good name for the function that takes the length of a race and returns the time needed to complete it?
A. time(length)
B.length(time)
C.cost(time)
D. time(race)
The answer choice which best fits the function described in the task content is; Choice A; time(length).
Which would be a good name for the function?It follows from the task content that the function takes the length of a race and returns the time needed to complete it.
On this note, it follows that the time taken is a function of the length of the race.
Hence, the appropriate name of the function is; Choice A.
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Surface=
Area=
Help please thanks
Surface area of the rectangular solid = 416 in.².
Volume = 480 in.³.
What is the Surface Area and Volume of a Rectangular Solid?Surface area = 2(wl+hl+hw)
Volume = (length)(width)(height).
Given the following:
Length (l) = 12 in.
Width (w) = 10 in.
Height (h) = 4 in.
Surface area = 2(wl+hl+hw) = =2·(10·12+4·12+4·10) = 416 in.².
Volume = (12)(10)(4) = 480 in.³.
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Is (x-4) a factor of f(x)=x^3- 2x^2 + 5x +1. use either the remainder theorem or the factor theorem to explain your reasoning
If x - 4 is a factor then x = 4 is a root:
f(4) = 4^3 - 2 * 4^2 + 5 * 4 + 1
= 64 - 32 + 20 + 1
= 53
since f(4) is not zero then 4 is not a root of the f(x)
Also, x - 4 is not a factor
In algebra, the remainder theorem, or Bezout's small theorem, applies the principle of polynomial division. It states that the remainder of dividing the polynomial f (x) by the linear polynomial {\ display style x-r} is equal to {\ display style f (r). }
In algebra, a factor set is a set of factors and roots of. Polynomial. This is a special case of the remainder theorem. The factor theorem shows that the polynomial f (x) has a factor only if f = 0.
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Select the statement that describes the expression 5 + (3 x 6) − 4. 5 times the sum of 3 and 6, then subtract 4 Add 5 to the product of 3 and 6, then subtract 4 Add 5 to the product of 3 and 6, then add 4 Add 5 to the quotient of 3 and 6, then subtract 4
Answer: Add 5 to the product of 3 and 6, then subtract 4
Step-by-step explanation:
We will use the order of operations. Looking at 5 + (3 x 6) − 4, we would:
[1] Multiply 3 x 6
[2] Add 5 to that product
[3] Subtract 4 from that value
This means the answer to your question is:
Add 5 to the product of 3 and 6, then subtract 4
Answer: B
i DiD tHe TeSt
How do you know that ABC is similar to BDC? Explain your answer.
Answer: No
Step-by-step explanation:
There is only one pair of congruent angles that can be determined, but to prove triangles similar, there needs to be two pairs of congruent angles.
A sequence is defined by the recursive function f(n + 1) =1/3 f(n). if f(3) 9= , what is f(1)
Answer:
f(1) = 81
Step-by-step explanation:
f(n + 1) = 1/3 f(n)
⇔ f(n) = 3 × f(n + 1)
……………………………
if f(3) = 9 ⇒ f(2) = 3 × f(3) = 3 × 9 = 27
Then
f(1) = 3 × f(2) = 3 × 27 = 81
Can someone help me? Just complete these 2 proofs (geometry), ASAP!!!!
Question 4
1) [tex]\overline{AC} \cong \overline{AE}, \overline{AB} \cong \overline{AD}[/tex] (given)
2) [tex]\angle A \cong \angle A[/tex] (reflexive property)
3) [tex]\triangle ABC \cong \triangle ADC[/tex] (SAS)
Question 5
3) [tex]\angle ABC \cong \angle DCB[/tex] (all right angles are congruent)
4) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)
5) [tex]\triangle ABC \cong \triangle DCB[/tex] (AAS)
Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative three and negative four.
The equation of the graphed parabola is y=a[tex](x+3)^{2}[/tex]-4.
Given that parabola is plotted, concave up , with vertex located at coordinates (-3,-4).
We are required to find the equation of the graphed parabola.
The equation of a quadratic function of vertex (h,k) is given by:
y=a[tex](x-h)^{2}[/tex]+k
In the above equation a is the leading coefficient.
We have been given point (-3,-4).
We have to just put the value of h=-3 and k=-4 and the required equation will be as under:
y=a[tex](x+3)^{2}[/tex]-4
Hence the equation of the parabola which is plotted, concave up, with vertex located at coordinates (-3,-4) is y=a[tex](x+3)^{2}[/tex]-4.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
The focus of a parabola is (0, -1). The directrix is the line y=0. What is the equation of the parabola in vertex form?
Check the picture below, so the parabola looks more or less like so, with the vertex half-way from the focus point and the directrix.
Now, the distance from the directrix to the focus point is only 1 unit, so half that, or namely the "p" distance is 1/2 unit, and since the parabola is opening downwards, "p" is negative, so
[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=0\\ k=-\frac{1}{2}\\[1em] p=-\frac{1}{2} \end{cases}\implies 4\left( -\frac{1}{2} \right)\left( ~~y-\left( -\frac{1}{2} \right) ~~ \right)~~ = ~~(x-0)^2 \\\\\\ -2\left( y+\frac{1}{2} \right)=x^2\implies y+\cfrac{1}{2} =\cfrac{x^2}{-2}\implies y = -\cfrac{1}{2}x^2-\cfrac{1}{2}[/tex]
now, we could also write that as either
[tex]y = -\cfrac{1}{2}(x^2+1)\qquad or\qquad y = \cfrac{1}{2}(-x^2-1)[/tex]
The reference angle for is, which has a terminal point of (2).
What is the terminal point of ?
(-²)
(-4/2, 4/2)
○ B. (2,-²)
(-2/²2,-4/2)
OA
A.
O C.
○ D. (22)
Answer: C
Step-by-step explanation:
[tex]\frac{5\pi}{4}[/tex] is in the third quadrant, so both x and y are negative.
Therefore, the only possible answer is C.
What is the distance between the points (22,27) and (2,-10)
Answer:
42.1
Step-by-step explanation:
The formula to calculate distance is √[(x₂ - x₁)² + (y₂ - y₁)²]. Using (22,27) as our x1 and y1, and (2,-10) as our x2 and y2.
Therefore our formula is √[(2 - 22)² + (-10 - 27)²].
(2 - 22)² = 400
(-10 - 27)² = 1369
(Make sure for both of these you put the negative number in parenthesis and the exponent outside them, if you are using a calculator of some sort)
Then we add and square root
√[400 + 1369] = 42.0594816896
The distance between the points (22,27) and (2,-10) is 42.1 units
How to determine the distance between the points?The coordinates of the points are (22,27) and (2,-10)
The distance is calculated as:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]d = \sqrt{(22 -2)^2 + (27 +10)^2[/tex]
Evaluate
[tex]d = \sqrt{1769[/tex]
Take the square root
d = 42.1
Hence, the distance between the points (22,27) and (2,-10) is 42.1 units
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