The Probability that 2 or fewer will withdraw without completing the introductory statistics course is 0.4547 .
The Binomial Distribution formula is
P(X=x) = C(n,x)*pˣ*qⁿ⁻ˣ
where ,
n is the number of trials
x is the number of times success occurs
p is the probability of success
q is the probability of failure .
In the given question ;
it is given that
students that are registered for the course = 20
so , n=20
Let x denote the number of students that withdraw without completing the course .
given that 14 % students withdraw without completing the course ,
hence p = 14% = 0.14
So , q= 1-p = 1-0.14 = 0.86
the probability that 2 or fewer will withdraw from the course is denoted by P(X ≤ 2) and is calculated using
the formula , P(X≤2)=P(X=0)+P(X=1)+P(X=2) ...(i)
using Binomial Probability we get
P(X=x) = C(n,x)*pˣ*qⁿ⁻ˣ
P(X=0) = C(20,0)*(0.14)⁰*(0.86)²⁰⁻⁰
= C(20,0)*(0.14)⁰*(0.86)²⁰
= 1*1*(0.0489)
= 0.0489
So , P(X=0)=0.0489 ...(ii)
P(X=1) = C(20,1)*(0.14)¹*(0.86)¹⁹
= 20*0.14*0.0569
= 0.1593
So , P(X=1)=0.1593 ...(iii)
P(X=2) = C(20,2)*(0.14)²*(0.86)¹⁸
= 190*0.0196*0.0662
= 0.2465
So , P(X=2)=0.2465 ...(iv)
Substituting the values of (ii) , (iii) and (iv) in (i) , we get
P(X≤2)=P(X=0)+P(X=1)+P(X=2)
P(X ≤ 2) = 0.0489 + 0.1593 + 0.2465
= 0.4547
Therefore , the Probability that 2 or fewer will withdraw without completing the introductory statistics course is 0.4547 .
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Find the distance between each pair of points round to nearest tenth if needed
Answer: 3.6
20
8.25
Step-by-step explanation:
7 - 10 = 3
-6 - -8 = 2
[tex]\sqrt{3^{2} +2^{2} } =3.6[/tex]
Determine the range of f(x) = |x| + 3.
A {y|-∞
B {yl-3 ≤y<∞}
C {y|0 ≤y<∞o}
D {y|3≤y<∞0}
Answer:
B
Step-by-step explanation:
The range of |x| is [tex]{y|0 \leq y <\infty\}[/tex]. Adding 3 to this yields option B.
A person has a choice of receiving 3000 now or 4000 after she graduates from college in five years she decided to take the 3000 and the best add expected 10% annual rate of return. Did she make a wise decision?
Yes she made a wise decision as she will get an amount of 4500 after 5 years which is better than getting 4000 after 5 years.
Given that ,
Let us assume that the person takes the amount 3000 from the college, and invests it on a annual rate of 10% for a period of 5 years,
means,
Principal amount = 3000
Rate of Interest = 10%=0.1
Time = 5 years
What Is the Future Value Simple Interest ?The future value simple interest formula is the addition of the principal amount that we have in the beginning and the interest earned on that principal amount after the completion of the period. The Future Value Simple Interest Formula is given as,
F V = P + I or F V = P(1 + rt)
Here,
P is the principal amount,
I is the interest,
r is the rate, and
t is the time.
So, We know that
Simple Interest = Principal amount * Rate of Interest * Time
Simple Interest = 3000*0.1*5
Simple Interest = 1500
So, The person will have a Future value of
Principal amount + Simple Interest
= 3000+1500
=4500
Therefore, If the person invests after 5 years will get a amount of 4500 in return which is a wise decision than not investing and getting a amount of 4000 .
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Geometry, if |AC| = |CD|, find angle x.
From the given figure the value of angle x is 40 degrees
How to find angle x|AC| = | CD |
Δ ( ACD ) = Δ ( DCB )
< ( BAC ) = 70 degrees
Since |AC| = | CD | then the base angles are equal, hence
< ( ADC ) = < ( BAC ) 70 degrees. ( base angles of isosceles triangle )
< ( ADC ) + < ( BAC ) + < ( ACD ) = 180 degree ( sum of angles in a triangle)
note < ( BAC ) = < ( DAC )
< ( ACD ) = 180 - 70 - 70
< ( ACD ) = 180 - 140
< ( ACD ) = 40 degrees
If Δ ( ACD ) = Δ ( DCB ) then the angles should be equal
Δ ( ACD ) has angles:
< ( ADC ) = 70
< ( DAC ) = 70
< ( ACD ) = 40
Then Δ ( DCB ) should have angles 70, 70, and 40. The figure did not give enough information to put the angles where it should be.
Comparing with the options, only angle 40 degrees is in the option, hence the correct answer
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Half a number increased by 15 is equal to the sum of five and the product of three and the number what is the number 
The number is (x/2)+15=5+3x if Half of Number augmented by 15 equals the sum of 5 and the product of 3 and the number.
Explain what a number system is?A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.
Which four different number systems are there?Decimal Number System is one of the four popular forms of number systems and other 3 are -
System of binary numbers.
System of Octal Numbers.
System of Hexadecimal Numbers.
From the given question,
X is the number. first we have to halve it , then we add 15.
Next ,set it equal to the other side . the second side is 5+ ( because it is the sum)
3x( the product of 3 and x means multiply them)
Hence the number is (x/2)+15=5+3x
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It takes 107 pounds of seed to completely plant an 11 acre field
How many acres can be planted per pound of seed
Answer:
0.103 acres
Step-by-step explanation:
This question tests on the concept of Conversion.
Given from the question, we know that:
107 pounds of seed = 11 acre field
To find the acres of field we can plant per pound of seed, we simply divide both sides of the equation by 107.
(107 ÷ 107) pounds of seed = (11 ÷ 107) acres of fiels
1 pound of seed = 0.103 acres of field (Rounded off to 3 significant figures)
Find the distance between the points (9,-6) and (-3,-9).
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{9}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-3 - 9~~)^2 + (~~-9 - (-6)~~)^2} \implies d=\sqrt{(-3 -9)^2 + (-9 +6)^2} \\\\\\ d=\sqrt{( -12 )^2 + ( -3 )^2} \implies d=\sqrt{ 144 + 9 } \implies d=\sqrt{ 153 }\implies \boxed{d\approx 12.37}[/tex]
Hurry! *50 point's and brainly to the one who solve this!!* Please and thank you!
2 .) What is the special angle pair relationship between < 8 and < 4?
3.) What is the special pair relationship < 2 and < 3?
4, using the figure below, Maggie used the definition of vertical angles to help her solve for x. Since vertical angles are congruent, she set the two given expressions equal other. After solving for x, her teacher said she got the wrong value for x. Exaple where Maggie made her mistake when solving for x.
Answer:
Step-by-step explanation:
2) What type of angle is 4 and 8?
I What is the special angle pair relationship between < 8 and < 4?
Angle 4 and angle 8 are also alternate interior angles. Alternate exterior angles: Pairs of exterior angles on opposite sides of the transversal. Angle 2 and angle 7 are alternate exterior angles.
3)Twos are generally thoughtful, people-oriented, and caring, while Threes are resourceful, energetic, and determined.
4) Do not use a protractor. Use the properties of straight and vertical angles to help you.
To pay for a home improvement project that totals $16,000, Genesis is choosing between taking out a simple interest bank loan at 8% for 3 years or paying with a credit card that compounds monthly at an annual rate of 15% for 7 years. Which plan would give Genesis the lowest monthly payment?
well, let's first check with the Bank
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$16000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &3 \end{cases} \\\\\\ A=16000[1+(0.08)(3)] \implies A = 19840~\hfill \underset{monthly~payment}{\stackrel{19840~\div \stackrel{months}{36}}{\approx \text{\LARGE 551.11}}}[/tex]
now let's check with the Credit Card
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$16000\\ r=rate\to 15\%\to \frac{15}{100}\dotfill &0.15\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &12\\ t=years\dotfill &7 \end{cases}[/tex]
[tex]A=16000\left(1+\frac{0.15}{12}\right)^{12\cdot 7} \implies A \approx 45425.81~\hfill \underset{monthly~payment}{\stackrel{45425.81~\div \stackrel{months}{84}}{\approx\text{\LARGE 540.78}}}[/tex]
well, seems the Credit Card is the better deal monthly wise, though in the long run is a lot of dough.
A plan which would give Genesis the lowest monthly payment is the monthly payment on a bank loan would be $317.50.
What is simple interest?Mathematically, the simple interest earned can be calculated by using this formula:
A = P(1 + rt)
Where: A represents the future value.
P represents the principal or original value.
r represents the interest rate.
t represents the time.
Now Substituting the given parameters into the formula, we have,
A = 9000[1 + (0.09 × 3)]
A = 9000[1 + 0.27]
A = 9000 × 1.27
Future value, A = $11,430.
Next, we will calculate the monthly payment over a period of 36 months as follows:
Monthly payment = Future value/Time
Monthly payment = 11,430/36
Monthly payment = $317.50.
Similarly, we will calculate the compound interest earned on the credit card :
A = 9000[1 + (0.18/12)]⁽¹² ˣ ⁷⁾
A = 9000[1 + 0.015]⁸⁴
A = 9000 × 1.015⁸⁴
A = 9000 × 3.49258954
Future value, A = $31,433.31.
Next, we will calculate the monthly payment over a period of 84 months as follows;
Monthly payment = Future value/Time
Monthly payment = 31,433.31/84
Monthly payment = $372.21.
In this context, A plan which would give Genesis the lowest monthly payment is the monthly payment on a bank loan would be $317.50.
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hat is the complement of an
angle?
8)
What is the supplement of a 92° angle?
9)
What is the complement of a 56° angle?
For # 10-12, use the diagram to the right.
10) m/2=
88• degres
34⁰ degrees
Answer:
9. 178
Step-by-step explanation:
To find the complement subtract from 90
because complementary means sum of the angles is 90 degrees.
To find supplement, subtract from 180
because supplementary means sum of the angles is 180 degrees.
SHOW YOUR WORK FOR BRAINLIEST
Solve for x. Assume that lines which appear to be diameters are actual diameters.
The Answer is -6
Answer:
if x = -6, r = 180/pi and D = 360/pi
without knowing the actual D or r, one cannot truly solve for x.
Step-by-step explanation:
looking at the angle, [tex]125^o[/tex], it is part of two supplementary parts of the circle, let us call the angle between [tex]55^o\ \&\ 125^o[/tex] y. given that 125 is supplementary to y:
125+y=180
and so...
y=55
now, let us call the angle associated with the arc-length, x+76 z.
Knowing that y+55 and z are supplementary (given the length is a diameter), we can write the equation:
y + 55 + z = 180
substituting y=55 gives:
55 + 55 + z = 180
combining like terms gives:
110 + z = 180
further simplifying gives:
z = 70
x + 76 is the arc-length of the section of the circle, whose angle is now denoted by z = 70.
Arc-length = Circumference * percentage of circle
circumference is given as C = π * D OR C = 2r * π (because 2r = D)
percentage of circle is simply (number of degrees covered ÷ total degrees of a circle)
so, we have that the percentage = 70/360 [360 degrees in a circle, 70 degrees covered by the angle, z]
and the circumference is unknown without a radius or diameter length, so we will use the equation C = π * D
using the formula for arc-length:
Arc-length = π * D * 70/360
Arc-length also happens to equal x + 76, so:
x + 76 = π * D * 70/360
reduce:
x + 76 = π * D * 7/36
simplify by getting x alone:
x = π * D * 7/36 - 76
we can further simplify by creating one fraction:
[tex]x = \frac{7D\pi - 2736}{36}[/tex]
it can also be shown as:
[tex]x = \frac{7r\pi - 1368}{18}[/tex]
because, D = 2r and you could factor 2 from (7*2*r*pi - 2736) and then reduce by dividing top and bottom each by 2.
You can divide top and bottom by 2 because:
[tex]\frac{2}{36} = \frac{1}{18}[/tex]
which is because [tex]\frac{km}{ln}=\frac{k}{l} * \frac{m}{n}[/tex]
if we say km = 2 and ln = 36, then k = 2, m = 1 is the only options for k and m
and l and n can be any set of factors of 36, which include 2*18, 3*12, 6*6, 9*4.
if we choose l = 2 and n = 18, then k = l = 2 and:
[tex]\frac{k}l=\frac{2}2 = \frac{r}{r}[/tex]
which is to say that k = r = l = 2, which I only show to say generally that when k = l or you have r ÷ r, it is equal to 1.
1 * s = s
and if s = m ÷ n, then [tex]\frac{km}{ln} = \frac{m}{n}\ whenever\ k = l[/tex]
given that the answer to what is x, is -6, the arc length is therefore 70. we can plug in this 70 now to find r and therefore, D.
[tex]70 = \pi * D * \frac{70}{360}\\\\multiply\ by\ \frac{360}{70}\ on\ both\ sides\ to\ get:\\360=\pi * D\\divide\ by\ \pi\ on\ both\ sides\ to\ get:\\360/\pi = D\ OR\ 180/\pi=r[/tex]
Please help!!!!! I need an answer asap
Answer:
c
Step-by-step explanation:
I have finished all my math classes
This figure has two intersecting lines and a ray.
What is the value of x?
Enter your answer in the box.
x =
The figure contains a pair intersecting lines. One of the four angles formed by the intersecting lines is labeled 146 degrees. The angle opposite and not adjacent to this angle is broken into two smaller angles by a ray that extends from the point where the two lines intersect. One of these smaller angles is labeled 58 degrees, and the other smaller angle is labeled x degrees.
The 146°, and the x and 58° which are vertical angles formed by the two intersecting lines where the x and 58° are formed by the ray gives the measure of x as 88°
What are vertical angles?Vertical angles or vertically opposite angles are the angles formed by two intersecting lines and which are on either side to each other
The description parameters are;
The objects in the figure includes; Two intersecting lines and a ray
The measure of one of the angles formed by the intersecting lines = 146°
The vertically opposite angle to the 146° angle is broken into = x and 58°
Required; The value of x
Solution; The vertical angles theorem states that vertically opposite angles that are formed when two lines intersect, are congruent.
In geometry, two figures are congruent when they exactly coincide when they are superimposed, which means that the two figures have the same measurement.
Given that 146° is congruent to x + 58°, we have;
146° = x + 58° Definition of congruency and angle addition postulate
x = 146° - 58° = 88°
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Solve y = X + 8 for 4
Answer:
I don't understand the equation....pls rewrite it
Answer:
if x=4 y=12
if y=4 x=-4
Step-by-step explanation:
y=4+8 (add)
y=12
4=x+8 (subtract 8 from each side)
-4=x
help me out please i think it's correct but
Answer:
Step-by-step explanation:
your answer along with the work is down below please go and check it out also sorry I'm wrong have nice day:)
Recommendations Math Language arts Science Elghth grade) Y.2 Find the slope from two points ZAC Find the slope of the line that passes through (5,8) and (3, 3). Simplify your answer and write it as a proper fraction, improper fraction, or inte Submit Work it out
Jordon is calculating the slope of the trend in the scatter plot below. How can Jordon use the plot to check the reasonableness of his answer
Answer: His slope should be positive because the trend line is slanted up to the right.
Step-by-step explanation:
This answer is correct because the third line is slanted up to the right, so it makes it positive.
find thesum using a number line
7t5=
Answer:
12
Step-by-step explanation:
Did you mean 7+5?
If so, then 7 + 5 = 12
a function f(x) is defined by the set of coordinate pairs {(-3,8),(2,5),(7,-1),(11,3)} explain why it is impossible to give a value for f(-1)
It is impossible to give a value for f(-1) because -1 is not in the domain of the function f.
It is given in the question that function f(x) is defined by the set of coordinate pairs {(-3,8),(2,5),(7,-1),(11,3)}.
Here, the ordered pair (a,b) represents (x ,f(x))
Which means:-
f(-3) = 8 , f(2) = 5, f(7) = -1, f(11) = 3.
Here, the elements of domain are -3, 5, -1 and, 3 and the elements of range are 8, 5, -1 and, 3.
We cannot find the value of f(-1) because -1 is not present in the domain of the function.
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The ordered pair (a,b) satisfies the inequality y
The ordered pair that satisfies the inequality is (aₓ ,bₓ) .
In mathematics, an inequality is a link that compares two numbers or other mathematical expressions unfairly.
Size comparisons between two numbers on the number line are most usually made.Various types of inequalities can be represented using various notations.By definition, any monotonically growing function can be applied to both sides of an inequality without destroying their relationship (provided that both expressions are in the domain of that function). An inequality relation would be reversed if a monotonically dropping function were applied to both sides of the inequality. Examples of how to employ a monotonically declining function are the rules for the additive and multiplicative inverses for positive values.The notation a b c denotes "a b and b c," from which it also follows that a c, in accordance with the transitivity aspect discussed above. The aforementioned laws state that all three components can be changed by either adding or subtracting the same number, or by multiplying or dividing all three terms by a nonzero number, and reversing any inequalities if the number is negative. As a result, a + e + b + c is the same as a + b + e + c.Therefore we can conclude that (aₓ, bₓ) satisfies the inequality.
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I need help with this math problem
Answer:
AB = 4.5 cm
Step-by-step explanation:
the total area (A) of the 2 rectangles is calculated as
A = x(x - 4) + 3x(x - 2)
= x² - 4x + 3x² - 6x
= 4x² - 10x
Given A = 36 , then equating
4x² - 10x = 36 ( subtract 36 from both sides )
4x² - 10x - 36 = 0 ( divide through by 2 )
2x² - 5x - 18 = 0 ← as required
To factorise the equation
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 18 = - 36 and sum = - 5
the factors are + 4 and - 9
use these factors to split the x- term
2x² + 4x - 9x - 18 = 0 ( factor the first/second and third/fourth terms )
2x(x + 2) - 9(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(2x - 9) = 0
equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
2x - 9 = 0 ⇒ 2x = 9 ⇒ x = 4.5
but x > 0 , then x = 4.5
Then
AB = x = 4.5 cm
Answer:
AB = 4.5 cm
Step-by-step explanation:
[tex]\boxed{\textsf{Area of a rectange}=\sf width \times length}[/tex]
Area of the smaller rectangle:
[tex]\implies A=x(x-4)[/tex]
[tex]\implies A=x^2-4x[/tex]
Area of the larger rectangle:
[tex]\implies A=(2x+x)(x-2)[/tex]
[tex]\implies A=3x(x-2)[/tex]
[tex]\implies A=3x^2-6x[/tex]
The area of the compound shape is the sum of the areas of the two rectangles:
[tex]\implies A=(x^2-4x)+(3x^2-6x)[/tex]
[tex]\implies A=x^2+3x^2-4x-6x[/tex]
[tex]\implies A=4x^2-10x[/tex]
If the area of the compound shape equals 36 cm² then:
[tex]\implies 36=4x^2-10x[/tex]
[tex]\implies 36-36=4x^2-10x-36[/tex]
[tex]\implies 0=4x^2-10x-36[/tex]
[tex]\implies 4x^2-10x-36=0[/tex]
[tex]\implies \dfrac{4x^2}{2}-\dfrac{10x}{2}-\dfrac{36}{2}=\dfrac{0}{2}[/tex]
[tex]\implies 2x^2-5x-18=0[/tex]
The length of AB is x cm.
To find the value of x, factor the quadratic.
To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].
[tex]\implies ac=2 \cdot -18=-36[/tex]
[tex]\implies b=-5[/tex]
Therefore, the two numbers are: -9 and 4.
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies 2x^2-9x+4x-18=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(2x-9)+2(2x-9)=0[/tex]
Factor out the common term (2x - 9):
[tex]\implies (x+2)(2x-9)=0[/tex]
Apply the zero-product property:
[tex](x+2)=0 \implies x=-2[/tex]
[tex](2x-9)=0 \implies x=\dfrac{9}{2}=4.5[/tex]
As length is positive, x = 4.5 only.
Therefore, AB = 4.5 cm.
exponential functions with radical bases: simplify: 64 1/4
The simplified form of the exponential expression [tex]64^{\frac{1}{4} }[/tex] is [tex]2\sqrt{2}[/tex]
The given expression = [tex]64^{\frac{1}{4} }[/tex]
The exponential function is the function in the form of f(x)= [tex]a^{x}[/tex], where x is the variable and a is the constant. The constant term is the base of the exponential function.
The given expression = [tex]64^{\frac{1}{4} }[/tex]
Here we have to use the power rule of the exponents
[tex](a^{m})^{n}=a^{mn}[/tex]
To increase a number with an exponent to the power, we have to multiply the exponent times the power
We know
64 = [tex]2^{6}[/tex]
Then
[tex]64^{\frac{1}{4} }[/tex] = [tex](2^{6})^{\frac{1}{4} }[/tex]
Apply the power rule of the exponent
[tex](2^{6})^{\frac{1}{4} }[/tex] = [tex]2^{(6)(\frac{1}{4} )}[/tex]
= [tex]2^{\frac{3}{2} }[/tex]
= [tex]2\sqrt{2}[/tex]
Hence, the simplified form of the exponential expression [tex]64^{\frac{1}{4} }[/tex] is [tex]2\sqrt{2}[/tex]
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Solve the inequality 8(3g-2) ≤12(2g+1)
[tex]24g - 16 \leqslant 24g + 12 \\ 24g - 24g \leqslant 12 + 16 \\ 0 \leqslant 28[/tex]
THAT IS WHERE THE INEQUALITY LEADS US THERE IS NO CERTAIN VALUE FOR g .
HOPE THIS HELPS
Find a point-slope form for the line with slope = 1/5 and passing through the point
(- 2, -3).
The equation of the line in point-slope form is…
Answer:
y+3= 1/5 (x+2)
Step-by-step explanation:
The point slope form looks like this.
y - y1 = m (x - x1)
the m represent slope and (x1, y1) are the coordinates of the point that the line passes through.
Question 5
Point C is the midpoint of AB and point B is between points A and D. If AD = 15 and
BD = 7, what is CD?
CD
If C is the midpoint of AB then the length of CD is 11 units.
The midpoint of a line segment is referred to as the midpoint in geometry.
It functions as the centroid of the segment and the endpoints, and it is equally separated from both. It cuts the portion in half. As there is no distinguishing point to act as the point at infinity (any point in a geometric range may be protectively transferred into any other point in (the very same or some other) projective range), the midpoint is difficult to define in projective geometry. On the perception line in question, an affine structure can be defined by fixing a point at infinity and then using the aforementioned concept.Given C is the midpoint of AB.
AD = 15 and BD = 7
Now AB = 15 - 7 = 8
Again AC = BC
Therefore = BC = 8 / 2 = 4
Now CD = BC + BD = 4 + 7 = 11
Therefore the length of CD is 11 units.
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portia can read 23 pages i 10 minutes. at this rate how many can she read in 55 minutes
The rate at which Portia reads is 2.3 pages per minute, at this rate, she can read 126.5 pages in 55 minutes.
How many pages can she read in 55 minutes?We know that Portia can read 23 pages in 10 minutes, so the number of pages she reads per minute is given by the rate:
R = (23 pages)/(10 minutes) = 2.3 pages per minute.
Now, the number of pages she can read in 55 minutes is given by the product between the rate and 55 min, so we will get:
(2.3 pages/min)*55 min = 126.5 pages
We conclude that Portia can read 125.6 pages in 55 minutes.
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A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of finished products and computes the sample mean product weight. If test results over a long period of time show that of the values are over pounds and are under pounds, what are the mean and the standard deviation for the population of products produced with this process?.
The mean and the standard deviation for the population of products produced with this process are 2.0 and 0.3329
The population mean is given by
ц = [tex]\frac{L+U}{2}[/tex]
where L and U are the two given boundaries
Here, L = 1.9 and U = 2.1
⇒ ц = [tex]\frac{1.9+2.1}{2}[/tex]
⇒ ц = 2.0
Now, the z value when p =5%, from z table of probability will be
z = -1.645
Standard Deviation denoted by σ is a measure of how dispersed the data is in relation to the mean.
The Standard Deviation can be calculated by the z-score which is given as:
z = (x-ц) / (σ / [tex]\sqrt{n}[/tex])
where z is the Standard score, x is observed value, ц is mean of the sample, σ is standard deviation and n is sample size
-1.645 = (1.9 - 2.0) / (σ / [tex]\sqrt{30}[/tex])
-1.645 × (σ / [tex]\sqrt{30}[/tex]) = -0.1
1.645 × (σ / 5.477) = 0.1
σ = 0.3329
Therefore, the mean and the standard deviation for the population of products produced with this process are 2.0 and 0.3329
Complete Question: A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of 30 finished products and computes the sample mean product weights [tex]x^{-}[/tex]. If test results over a long period of time show that 5% of [tex]x^{-}[/tex] the values are over 2.1 pounds and are under 1.9 pounds, what are the mean and the standard deviation for the population of products produced with this process?
Know more about Normal Distribution: - https://brainly.com/question/23418254
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Can someone please explain this to me
Answer:
[tex]15u^{2}[/tex]
Step-by-step explanation:
let's say each square is = [tex]1u^{2}[/tex]
triangle A area: 2*5
[tex]\frac{2*5}{2}=5u^{2}[/tex]
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triangle B area: 2*2
[tex]\frac{2*2}{2}=2u^{2} \\Triangle A - B = 5 - 2= 3u^{2}[/tex]
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next figure
triangle C area 3*3
[tex]\frac{3/3}{2}=4.5u^{2}\\ -------------\\\\3u^{2}+4.5u^{2}=7.5u^{2}\\ -------------\\[/tex]
And since the other figure is a reflection *2
[tex]7.5u^{2}*2=15u^{2}[/tex]
Answer:
A = 15 units²
Step-by-step explanation:
the area (A) of the shaded triangle is calculated as
A = area of rectangle enclosing the triangle - area of white triangles on either side of shaded triangle and the one on top
area of rectangle = 10 × 5 = 50 units²
area of 2 congruent triangles = 2 × [tex]\frac{1}{2}[/tex] × 5 × 5 = 5 × 5 = 25 units²
area of top triangle = [tex]\frac{1}{2}[/tex] × 10 × 2 = 5× 2 = 10 units²
A = 50 - 25 - 10= 15 units²
(x^3-2x^2-13x) divided by (x+5)
PLS HELP AND EXPLAIN pls
Check the picture below.
[tex]\stackrel{\measuredangle N}{(5x-8)}~~ + ~~\stackrel{\measuredangle O}{(x-5)}~~ + ~~\stackrel{\measuredangle P}{(6x+1)}~~ = ~~180 \\\\\\ 12x-12=180\implies 12x=168\implies x=\cfrac{168}{12}\implies x=14 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle O}{(x-5)}\implies (14)-5\implies {\Large \begin{array}{llll} \stackrel{\measuredangle O}{9} \end{array}}[/tex]