Answer:
(a) 0.16759
(b) 0.9649
Step-by-step explanation:
Given that:
n = 10 , p = 0.3 and [tex]\hat p = 0.4[/tex]
[tex]P(|\hat p - p| > 0.2 ) = 1 - P ( |\hat p -p| \leq 0.2)[/tex]
= [tex]1 - P(-0.2 \leq \hat p-p \leq 0.2)[/tex]
= [tex]1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{\dfrac{pq}{n}}} \leq \dfrac{\hat p -p}{\sqrt{\dfrac{pq}{n}}} \leq \dfrac{0.2}{\sqrt{\dfrac{pq}{n}}} \end {pmatrix}[/tex]
[tex]=1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{\dfrac{(0.3)(1-0.3)}{10}}} \leq Z \leq \dfrac{0.2}{\sqrt{\dfrac{(0.3)(1-0.3)}{10}}} \end {pmatrix}[/tex]
[tex]=1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{\dfrac{(0.3)(0.7)}{10}}} \leq Z \leq \dfrac{0.2}{\sqrt{\dfrac{(0.3)(0.7)}{10}}} \end {pmatrix}[/tex]
[tex]=1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{0.021}} \leq Z \leq \dfrac{0.2}{\sqrt{0.021}} \end {pmatrix}[/tex]
[tex]=1 - P \begin {pmatrix} -1.380 \leq Z \leq 1.380 \end {pmatrix}[/tex]
= 1 - P( Z ≤ 1.380) - P(-1.380)
= 1 - ( 0.91620 - 0.08379 )
= 1 - 0.83241
= 0.16759
b) when n = 400; p =0.3 , q = 1 - p = 1 - 0.3 = 0.7
[tex]P( |\hat p - p | > 0.001) = 1- P ( |\hat p - p | < 0.001 )[/tex]
[tex]= 1- P ( -0.001 < \hat p - p < 0.001 )[/tex]
[tex]= 1- P ( \dfrac{-0.001}{\sqrt{\dfrac{pq}{n}}} < \dfrac{ \hat p - p}{\dfrac{pq}{n}} < \dfrac{0.001}{\sqrt{\dfrac{pq}{n}}} )[/tex]
[tex]= 1- P ( \dfrac{-0.001}{\sqrt{\dfrac{0.3\times 0.7}{400}}} < Z < \dfrac{0.001}{\sqrt{\dfrac{0.3 \times 0.7}{400}}} )[/tex]
[tex]= 1- P ( \dfrac{-0.001}{\sqrt{5.25 \times 10^{-4}}} < Z < \dfrac{0.001}{\sqrt{5.25 \times 10^{-4}}} )[/tex]
[tex]= 1- P ( -0.0436< Z < 0.0436)[/tex]
= 1 - P ( Z < 0.0436) - P ( -0.0436)
= 1 - (0.5176 - 0.4825)
= 1 - 0.0351
= 0.9649
Write an equation of the line passing through the points (3,7) and (-1,-13)
Answer:
Step-by-step explanation:
(-13 - 7)/(-1 + 3) = -20/2 = -10
y - 7 = -10(x - 3)
y - 7 = -10x + 30
y = - 10x + 37
A toy company uses the linear model y=-2x+380 to predict the decline in sales of a toy after it has been on the market more than one year. If x is the number of months after the first year and y is the number of toys sold in hundreds during that month how many toys will be sold 11 months after the first year
Answer:
358 toys sold 11 months after the first year.
Step-by-step explanation:
y = - 2x + 380
x is number of months after release in this case x = 11
y is number of toy sold in the hundreds.
y = - 2 ( 11 ) + 380
y = - 22 + 380
y = 358
Number of toys sold 11 months after the first year = 358
What is linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.
Given,
Linear equation
y = - 2x + 380
x is number of months after release
y is number of toy sold in the hundreds.
No. of months, x = 11
Putting value of x in above equation
y = - 2 ( 11 ) + 380
y = - 22 + 380
y = 358
Hence, 358 toys sold 11 months after the first year.
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What percent of 150 is 900
Answer:
600 %
Step-by-step explanation:
x · 150 ÷ 100 = 900
150x = 90000
x = 600
Help me find this asap
Answer:
DQ = [tex]\frac{5}{(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}-\sqrt{x+h})}[/tex]
Step-by-step explanation:
Given function is f(x) = [tex]\frac{5}{2-\sqrt{x}}[/tex]
f(x + h) = [tex]\frac{5}{2-\sqrt{x+h} }[/tex]
Therefore, indicated difference quotient will be,
DQ = [tex]\frac{f(x+h)-f(x)}{h}[/tex]
Now we substitute the values in the difference quotient,
DQ = [tex]\frac{\frac{5}{2-\sqrt{x+h} }-\frac{5}{2-\sqrt{x}}}{h}[/tex]
= [tex]\frac{5(2-\sqrt{x})-5(2-\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]
= [tex]\frac{10-5\sqrt{x}-10+5\sqrt{x+h}}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]
= [tex]\frac{-5\sqrt{x}+5\sqrt{x+h}}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]
= [tex]\frac{5(-\sqrt{x}+\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]
= [tex]\frac{5(-\sqrt{x}+\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]
= [tex]\frac{5[(x+h)-x]}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]
= [tex]\frac{5h}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]
= [tex]\frac{5}{(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]
100 POINTS I NEED HELP ASAP
If h(x) = |2x-4| , find (h-7)
Answer:
The answer is 18.
Step-by-step explanation:
You just need to plug in -7 to the equation 2x-4. You get -18, but absolute value is always positive, so its 18.
The answer is 18.
Sorry no explanation im soooo sorry
Using the slope formula, find the slope of the line through the given points.
(2,6) and (6,2)
Answer:
m=(y2-y1)/(x2-x1)
=(2-6)/(6-2)
=-4/4
=-1
Step-by-step explanation:
The temperature is _____ °C
Answer:
25 0r 26 F
Step-by-step explanation:
around .5 - 1 C
Angie and Kenny play online video games. Angie buys 1 software and of game play. Kenny 2 buys software and 6 months of game play. Each software package costs $50. If their total cost is $295, what is the cost of one month of game play?
Answer:$12
Step-by-step explanation:
Answer:
months of game play (m) =$11
Step-by-step explanation:
You want to share 1000 dollars between you and 5 friends,
Can you share the money evenly
What is the maximum amount that can be shared evenly
What is then the leftover as a fraction
Answer:
the answer is 200
Step-by-step explanation:it's because
you have to divide 1000 in to 5 and 1000 divided by 5 is 200
Which planet is an inner planet, and which one is an outer planet? Explain your answer.
The correct answers are Planet A 16 hours - Inner planet and planet B 1,408 hours - Outer planet.
What is a planet?Large, circular celestial objects that are neither stars nor their remnants are known as planets. The inner planets are the ones that are much closer to the sun, thus they have much smaller orbits around it and it takes them much less time to circle around it. Also, these planets are much smaller, which enables them to spin around their axis much quicker too, so one day passes much quicker.
The outer planets are the total opposite. They are much further from the sun, so for them to be able to make a single circle around the sun it takes much more time, and also because they are much bigger, it takes them much more time to spin around their own axis, thus making one day much longer than the days of the inner planets.
The complete question is given below as:-
Which planet is an inner planet, and which one is an outer planet? Explain your answer. Planet A 16 hours planet B 1,408 hours
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If Mikayla rides for 2 hours on a bicycle, what is her rate if she rides for 22 miles?
SOLVING EQUATIONS
1) Solve 3x - 5 = -26
SOLVING QUADRATIC EQUATIONS
Answer:
x = -7
Step-by-step explanation:
This isn't a quadratic.
Step 1: Write out equation
3x - 5 = -26
Step 2: Add 5 to both sides
3x = -21
Step 3: Divide both sides by 3
x = -7
Step-by-step explanation:
[tex]\sf \bf We \: have,[/tex]
[tex]\sf 3x - 5 = -26[/tex]
[tex]\sf : \implies \bf 3x - 5 \green{+5}= -26\green{+5}[/tex]
[tex]\sf : \implies \bf 3x =-21[/tex]
[tex]\sf : \implies \bf 3x× \green{\dfrac{1}{3}}=-21× \green{\dfrac{1}{3}}[/tex]
[tex]\sf : \implies \bf \underline{\boxed{\sf \bf x = -7}}[/tex]
Suppose R is the solid bounded by the plane z=5x, the surface z=x2, and the planes y=0 and y=3. Write an iterated integral in the form below to find the volume of the solid R.
I have attached the complete question.
Answer:
See 2nd attachment
Step-by-step explanation:
We are told that R is the solid bounded by the plane z = 5x, the surface z = x², and the planes y = 0 and y = 3.
Thus, the region in the xz plane would be defined as;
0 ≤ x ≤ 3 and x² ≤ z ≤ 5x
For the iterated integral for the volume of the solid R, see 2nd attachment.
An elm tree is 3 times as tall as an apple tree. The apple tree is 10 feet tall. How tall is the elm tree?
Answer:
LET ME GUESS hmmmm... OH WAIT 30
Step-by-step explanation:
Answer:
30 ft
Step-by-step explanation:
The elm tree is 3 times as tall as the apple tree.
The elm tree is 3 times as tall as 10 ft.
3 * 10 ft = 30 ft
Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)
Answer:
The standard equation of the sphere is [tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53[/tex]
Step-by-step explanation:
From the question, the end point are (3,-2,4) and (7,12,4)
Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.
The midpoint can be calculated thus
Midpoint = [tex](\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})[/tex]
Let the first endpoint be represented as [tex](x_{1}, y_{1}, z_{1})[/tex] and the second endpoint be [tex](x_{2}, y_{2}, z_{2})[/tex].
Hence,
Midpoint = [tex](\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})[/tex]
Midpoint = [tex](\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})[/tex]
Midpoint = [tex](\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\[/tex]
Midpoint = [tex](5, 5, 4)[/tex]
This is the center of the sphere.
Now, we will determine the distance (diameter) of the sphere
The distance is given by
[tex]d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }[/tex]
[tex]d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}[/tex]
[tex]d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}[/tex]
[tex]d = \sqrt{16 +196 + 0[/tex]
[tex]d =\sqrt{212}[/tex]
[tex]d = 2\sqrt{53}[/tex]
This is the diameter
To find the radius, r
From [tex]Radius = \frac{Diameter}{2}[/tex]
[tex]Radius = \frac{2\sqrt{53} }{2}[/tex]
∴ [tex]Radius = \sqrt{53}[/tex]
r = [tex]\sqrt{53}[/tex]
Now, we can write the standard equation of the sphere since we know the center and the radius
Center of the sphere is [tex](5, 5, 4)[/tex]
Radius of the sphere is [tex]\sqrt{53}[/tex]
The equation of a sphere of radius r and center [tex](h,k,l)[/tex] is given by
[tex](x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}[/tex]
Hence, the equation of the sphere of radius [tex]\sqrt{53}[/tex] and center [tex](5, 5, 4)[/tex] is
[tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}[/tex]
[tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53[/tex]
This is the standard equation of the sphere
what is the answer to 1.58x1.78=
The mean absolute deviation is best described as:
The value obtained when averaging the distances between each data point in the data set and the mean.
The value obtained when you add all the values in the data set and divide by the number of values.
The difference between the means of two similar data sets.
An approximation of the center of a data set.
Answer: It’s the second one
Step-by-step explanation:
Write 18% as a fraction
Hi there!
~
[tex]18[/tex]% [tex]= \frac{9}{50}[/tex]
Answer9/50:
Step-by-step explanation:
18/100
18÷2
100÷2
9/50
The sum of ten and the quotient of a number 2 and 6.
Answer:
10+(n/2)=6
Step-by-step explanation:
Let the number be n
Quotient of n and 2 is (n/2)
Sum of this and 10 is
10+(n/2)=6
(3 + 5i) + (11 -7i) Write answer in standard form a +bi
Answer:
14-2i
Step-by-step explanation:
[tex]\left(3+5i\right)+\left(11-7i\right)\\\\Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number\\\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\\\=\left(3+11\right)+\left(5-7\right)i\\3+11=14\\5-7=-2\\\\=14-2i[/tex]
1 point
#11: At MVP Fitness, the enrollment fee is $95 and it costs $40 per month.
At the Body Factory, the enrollment fee is only $25, but it costs $50 per
month. Write and solve an equation to find the number of months at which
the total cost charged by the two companies would be the same.
Your answer
Evaluate 10bc-b+c, when b = 3 and c= 2.
I need help ASAP!!!!!!!
Find the counterexample to show that the statement is incorrect. The difference of any two counting numbers will be a counting number Choose the correct answer below. A. 3-5= -2, which is not a counting number. B. 7-4 = 3, which is not a counting number. C. 10-2 = 8, which is counting number D. There is no counterexample. The statement is correct.
Answer:
A. 3-5= -2, which is not a counting number.
Step-by-step explanation:
Counting numbers are non negative numbers greater than 1 up to infinity. Counting numbers are also called natural numbers, and they do not include the negative numbers.
The statement states that "The difference of any two counting numbers will be a counting number"
From option A we can disprove that, since we can see that not all the difference between two counting numbers gives a counting number.
3 is a counting number
5 is a counting number
The difference between 3 and 5 gives -3, which is not a counting number.
This is a counterexample to the statement above.
Write down an expression for the nth term of the following sequence 7,16,25,34,43
Answer:
So in this sequence, we are adding by 9 in each term
So our pattern is: 7 , 7 +9 , 7 + 2(9) , 7 + 3(9) .....
hence, we can write it as: 7 + [tex]9^{n-1}[/tex] where n is the number of the term you want
How can you tell that 7. 630 and 7. 63 are equivalent decimals?
because if you add a zero onto something after the decimal point it doesn't increase or decrease the value of the number.
7.630 is literally just 7.63.
but if it was 76.3 and 760.3 it would be different.
The temperature in Fahrenheit, x, is converted into the temperature in Celsius with the formula [tex]c(x)=\frac{5}{9}(x-32)[/tex]. What transformations are used in transforming the parent graph y = x, to obtain the graph of [tex]c(x)=\frac{5}{9}(x-32)[/tex]
horizontal translation
vertical compression
reflection in the x-axis
vertical translation
reflection in the y-axis
The temperature in Fahrenheit, x, is converted into the temperature in Celsius with the formula . What transformations are used in transforming the parent graph y = x, to obtain the graph of blank. The answers would be:
horizontal translationvertical compressionTo obtain the graph of c(x) = (5/9){ x - 32 } we need as horizontal transformation. The correct option is A.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Given function of temperature is c(x) = (5/9){ x - 32}. The two graphs are plotted on the x-y plane. It is observed that y = x is transformed to the horizontal direction.
The graph of the two functions y = x and c(x) = (5/9){ x - 32 } is attached with the answer below.
Therefore, to obtain the graph of c(x) = (5/9){ x - 32 } we need as horizontal transformation. The correct option is A.
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The shaded set of numbers shown on the x-axis can be expressed in interval notation as _____
This is basically saying [tex]1 \le x < 4[/tex]
The square bracket says "include this endpoint" while the curved parenthesis means "exclude this endpoint". We can tell what is included/excluded based on how the endpoint is drawn.
Open circle = exclude endpoint
Closed/filled in circle = include endpoint
Your teacher has also drawn a square bracket at the left endpoint, and a curved parenthesis at the right endpoint. This style of drawing the endpoints helps set up [1, 4). Though sometimes you might see the use of open/closed circles instead for the endpoints. I'm referring to the number line portion.
We want to express the shaded set of numbers on the x-axis with interval notation.
The interval notation is:
[1, 4)
Let's start by analyzing the graph.
We have two ends, one at x = 1, with a colored dot, which means that that value belongs to the set.
We have the other end at x = 4, with a white dot, which means that the value does not belong to the set.
Then the interval notation is:
[1, 4)
Where [] are used for colored dots.
() are used for white dots.
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Business: Discount Pricing A store sells refurbished
iPhones that cost 12% less than the original price. If the new price of a refurbished iPhone is $572, what was the original price? How much is saved by purchasing the refurbished
The original price of the iPhone will be $650 thus the buyer saved $78 by buying the refurbished mobile.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
Let's say the original price of the mobile is x.
12% of x is 0.12x
The cost of refurbished mobile will be as x - 0.12x = 0.88x
0.88x = 572
x = $650
The amount saved = $650 - $572 = $78
Hence "The original price of the iPhone will be $650 thus the buyer saved $78 by buying the refurbished mobile".
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Find a vector equation for the line through the point P = (4, 2, 4) and parallel to the vector v = < -2, -5, -3 > . Assume r(0) = 4i + 2j + 4k and that v is the direction vector of the line. R(t) = Rewrite this in terms of the corresponding parametric equations for the line. x = ______y = ______z = ______
Answer:
The parametric equations are
x = - 2 t + 4 , y = - 5 t + 2 , z = - 3 t + 4
Step-by-step explanation:
Step(i):-
Given point P = ( 4,2,4)
Given vector is -2 i - 5 j - 3 k
The vector equation of a line through the point a⁻ and parallel to b⁻ is
r⁻ = a⁻ + t b⁻
Given r⁻ = 4 i + 2 j + 4 k
r⁻ = 4 i + 2 j + 4 k + t (-2 i - 5 j - 3 k)
Step(ii):-
The Cartesian form
[tex]\frac{x-a_{1} }{b_{1} } = \frac{y-a_{2} }{b_{2} } = \frac{z-a_{3} }{b_{3} } = t[/tex]
[tex]\frac{x-4 }{-2 } = \frac{y-2 }{-5 } = \frac{z-4 }{-3 } = t[/tex]
[tex]\frac{x-4 }{-2 } = t[/tex]
⇒ x - 4 = -2 t
⇒ x = - 2 t + 4
[tex]\frac{y-2 }{-5 } = t[/tex]
⇒ y - 2 = - 5 t
⇒ y = - 5 t + 2
[tex]\frac{z-4 }{-3 } = t[/tex]
z - 4 = -3 t
z = - 3 t + 4
Conclusion:-
The parametric equations are
x = - 2 t + 4 , y = - 5 t + 2 , z = - 3 t + 4
What is the image of (-5, -8) after a reflection over the y-axis?
Answer:
[tex](5,-8)[/tex]
Step-by-step explanation:
The rule for a reflection over the y-axis is
[tex](x,y) -> (-x,y)[/tex]
In this situation, we have to change the sign of x.
[tex](-5,-8) -> (5,-8)[/tex]