Answer:
The p-value of the test is 0.015 < 0.05, which means that there is sufficient evidence at the 0.05 level to support the company's claim.
Step-by-step explanation:
The company's promotional literature claimed that more than 47% do not fail in the first 1000 hours of their use.
At the null hypothesis, we test if the proportion is of 47% or less, that is:
[tex]H_0: p \leq 0.47[/tex]
At the alternative hypothesis, we test if the proportion is of more than 47%, that is:
[tex]H_1: p > 0.47[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.47 is tested at the null hypothesis:
This means that [tex]\mu = 0.47, \sigma = \sqrt{0.47*0.53}[/tex]
A sample of 1300 computer chips revealed that 50% of the chips do not fail in the first 1000 hours of their use.
This means that [tex]n = 1300, X = 0.5[/tex]
Value of the statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.5 - 0.47}{\frac{\sqrt{0.47*0.53}}{\sqrt{1300}}}[/tex]
[tex]z = 2.17[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion above 0.5, which is 1 subtracted by the p-value of z = 2.17.
Looking at the z-table, z = 2.17 has a p-value of 0.9850
1 - 0.985 = 0.015
The p-value of the test is 0.015 < 0.05, which means that there is sufficient evidence at the 0.05 level to support the company's claim.
50T Q12 A man wants to buy bags of gravel to cover his driveway. He decides to work out the area of his driveway. 1 bag of gravel covers 14m2 3m Sketch of driveway Not to scale 3m 8m 6m What is the area of his driveway? How many bags of gravel must he buy?
Answer:
hi amki nai patajjdkfkejd
1. Write the polynomial function that models the given situation.A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.
2. Write the polynomial function that models the given situation. A square has sides of 24 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.
3. Write the polynomial function that models the given situation. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.
Answer:
1. (12 - 2x)(11 - 2x)x
2. 4(11 - 2x)²(x + 1)
3. π(x³ + 15x² + 63x + 81)
Step-by-step explanation:
1. Write the polynomial function that models the given situation.
A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.
Since the length of the rectangle is 12 units and its width 11 units and squares of x by x units are cut from its corners, it implies that a length x is cut from each side. So, the length of the open box is L = 12 - 2x and its width is w = 11 - 2x.
Since the cut corners of the rectangle are folded, the side x which is cut represents the height of the open box, h. so, h = x
So, the volume of the open box V = LWh = (12 - 2x)(11 - 2x)x
2. Write the polynomial function that models the given situation. A square has sides of 24 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.
Since the square has sides of 24 units and squares of x + 1 by x + 1 units are cut from its corners, it implies that a length x + 1 is cut from each corner and the length 2(x + 1) is cut from each side. So, the length of side open box is L = 24 - 2(x + 1) = 24 - 2x - 2 = 24 - 2 - 2x = 22 - 2x = 2(11 - x)
Since the cut corners of the square are folded, the side x + 1 which is cut represents the height of the open box, h. so, h = x + 1
Since the area of the base of the pen box is a square, its area is L² = [2(11 - 2x)]²
So, the volume of the open box V = L²h = [2(11 - 2x)]²(x + 1) = 4(11 - 2x)²(x + 1)
3. Write the polynomial function that models the given situation. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.
The volume of a cylinder is V = πr²h where r = radius and h = height of cylinder.
Given that r = x + 6 and h is 3 units more than r, h = r + 3 = x + 6 + 3 = x + 9
So, V = πr²h
V = π(x + 3)²(x + 9)
V = π(x² + 6x + 9)(x + 9)
V = π(x³ + 6x² + 9x + 9x² + 54x + 81)
V = π(x³ + 15x² + 63x + 81)
True or false?
A function assigns each value of the independent variable to exactly one
value of the dependent variable.
A. True
B. False
SUB
Answer:
This statement would be true.
Step-by-step explanation:
At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .50. Find the probability that in a sample of 14 customers, at least 7 will order a nonalcoholic beverage
For each customer, there are only two possible outcomes. Either they will order an alcoholic beverage, or they will not. The probability of a customer ordering an alcoholic beverage is independent of any other customer, which means that the binomial probability distribution is used to solve this question..
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .50
This means that [tex]p = 0.5[/tex]
Sample of 14 customers
This means that [tex]n = 14[/tex]
Probability that at least 7 will order a nonalcoholic beverage
This is:
[tex]P(X \geq 7) = 1 - P(X < 7)[/tex]
In which
[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{14,0}.(0.5)^{0}.(0.5)^{14} = 0.0001[/tex]
[tex]P(X = 1) = C_{14,1}.(0.5)^{1}.(0.5)^{13} = 0.0009[/tex]
[tex]P(X = 2) = C_{14,2}.(0.5)^{2}.(0.5)^{12} = 0.0056[/tex]
[tex]P(X = 3) = C_{14,3}.(0.5)^{3}.(0.5)^{11} = 0.0222[/tex]
[tex]P(X = 4) = C_{14,4}.(0.5)^{4}.(0.5)^{10} = 0.0611[/tex]
[tex]P(X = 5) = C_{14,5}.(0.5)^{5}.(0.5)^{9} = 0.1222[/tex]
[tex]P(X = 6) = C_{14,6}.(0.5)^{6}.(0.5)^{8} = 0.1833[/tex]
So
[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0001 + 0.0009 + 0.0056 + 0.0222 + 0.0611 + 0.1222 + 0.1833 = 0.3954[/tex]
[tex]P(X \geq 7) = 1 - P(X < 7) = 1 - 0.3954 = 0.6046[/tex]
0.6046 = 60.46% probability that at least 7 will order a nonalcoholic beverage.
For more on the binomial distribution, you can check https://brainly.com/question/15557838
PLEASE HELPPPPPPPPPP
Answer:
167/346 or 0.483
Step-by-step explanation:
From the question given above, the following data were obtained:
Number of Tails (T) = 167
Number of Heads (H) = 179
Probability of tail, P(T) =?
Next, we shall determine total outcome. This can be obtained as follow:
Number of Tails (T) = 167
Number of Heads (H) = 179
Total outcome (S) =?
S = T + H
S = 167 + 179
Total outcome (S) = 346
Finally, we shall determine the probability of tails. This can be obtained as follow:
Number of Tails (T) = 167
Total outcome (S) = 346
Probability of tail, P(T) =?
P(T) = T / S
P(T) = 167 / 346
P(T) = 0.483
Thus, the probability of tails is 167/346 or 0.483
I purchased a new Apple iPad on Amazon for $249.00. The tax rate is 8.625%. What is the total purchase price of the iPad?
Answer:
270.47625
Step-by-step explanation:
249 is the original price
(249/100) · 8.625 = 21.47625 the tax total
249 + 21.47625 = 270.47625
find the measure of a
Answer:
Hello,
answer D 48°
Step-by-step explanation:
In the right triangle down, a+42°=90° ==> a=90°-42°=48°
44y + 321x = 0 biết x=30000
Answer:
y= -240750/11
Step-by-step explanation:
44y + 321. 30000 = 0
44y = - 963000
y= -240750/11
Find the solution of x – 13 = 25, and verify your solution using substitution.
options:
A)
x = 12, 12 + 13 = 25, 25 = 25
B)
x = 39, 39 – 13 = 25, 25 = 25
C)
x = 37, 37 – 13 = 25, 25 = 25
D)
x = 38, 38 – 13 = 25, 25 = 25
Answer:
x = 38
Step-by-step explanation:
x-13 = 25
Add 13 to each side
x-13+13 = 25+13
x = 38
Check
38-13 = 25
25=25
Factor 64a^3 -8b^3 Explain all steps.
Answer:
[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]
Step-by-step explanation:
factor out the 8
then you have the sum/difference of cubes..
look that up SOAP: same opposite, always a plus
[tex]64a^3 -8b^3\\8(8a^3 -b^3)[/tex]
[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]
please help me with geometry
Answer:
A. If the side lengths are the same, then a triangle is not scalene.
Step-by-step explanation:
A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
Simply stated, any polygon with three (3) lengths of sides is a triangle.
In Geometry, a triangle is considered to be the most important shape.
Generally, there are three (3) main types of triangle based on the length of their sides and these include;
I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.
II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.
III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 2.1yd : 1.4yd
9514 1404 393
Answer:
3/2
Step-by-step explanation:
Multiplying numerator and denominator by 10 will convert the ratio to a ratio of whole numbers. Then dividing by the common factor of 7 will reduce it to simplest form.
[tex]\dfrac{2.1\text{ yd}}{1.4\text{ yd}}=\dfrac{2.1\times10}{1.4\times10}=\dfrac{21}{14}=\dfrac{3\times7}{2\times7}=\boxed{\dfrac{3}{2}}[/tex]
2. In a 100m race, Luke was 2m ahead of Azam. Chandra was 3m behind Luke, Maggie was 7m ahead of Chandra. Luke was 5m behind Darren. Who was in the first place?
Answer:
luke won
Step-by-step explanation:
he is 2 meters ahead of azam witch is in 2dn place
Álgebra 2 need help
Answer:
first term = -1/5
I cant see part b (sorry its too blurry)
thirteenth term = -0.2
part d: -19a/95a -0.2a
Step-by-step explanation:
socratic
please Help with my area math question. I don't remember how to do it. multiply or add? and what is the answer to this?
Answer:
100 inches^3
Step-by-step explanation:
The volume of the back rectangle is
V = l*w*h
V = 8*5*1 = 40 inches ^3
The volume of the front rectangle is
V = 6*2*5 = 60 inches^3
Add the volumes
40+60 = 100 inches^3
What is the sum of the interior angles of a regular polygon with 5 sides?
A. 1260
B. 180
C. 360
D. 540
Answer:
540 is the ans
Step-by-step explanation:
this is the correct answer
180
Step-by-step explanation:
the measure of interior angles of polygon =180×(n-2)
Below is a geometric sequence. 3, 9, 27, 51, ... (b) what is the common raters if the geometric sequence?
In a geometric sequence, t4 = 8 and t7 = 216. Find the value of t2
Question 14 plz show ALL STEPS ASAP
Answer:
8/9
Step-by-step explanation:
Let the geometric series have the first term=a and common ratio=r. ATQ, ar^3=8 and ar^6=216. r^3=27. r=3. a=8/3^3=8/27. t2=ar=8/9
This graph represents which expression?
Answer:
x >7
Step-by-step explanation:
There is an open circle at 7, which means it cannot equal 7. The line goes to the right
x >7
solve the equation
0.09w+1.8
Step-by-step explanation:
0.09w + 1.8 = 0
0.09w = 0 - 1.8
0.09w = - 1.8
0.09w ÷ 0.09 = - 1.8/ 0.09
w = - 20
I need help ASAP please
Answer:
5:10
6 (-2,0)
7 (-5,6)
8 (5,3)
9 No, ab=8 CD=6
Step-by-step explanation:
write the greatest and smallest four digit number by using 7,8,0,9 digit
Use the substitution methed to solve the system of equations. Choose the correct ordered pair.
2y+5x=13
2y+3x=5
Solve both equations for 2y :
2y + 5x = 13 ==> 2y = 13 - 5x
2y + 3x = 5 ==> 2y = 5 - 3x
Solve for x :
13 - 5x = 5 - 3x
8 = 2x
x = 4
Solve for y :
2y = 13 - 5×4
2y = -7
y = -7/2
As an ordered pair, the solution is then the point (x, y) = (4, -7/2).
Fill in the blank by performing the indicated elementary row operation(s).
6
1
5
-6R2+R
1
-5
0
Answer 7 Points
Keybo
<
Prev
In this question, we are given a matrix, and we have to perform the given operation.
The matrix is:
[tex]\left[\begin{array}{ccc}6&-1&|5\\1&-5&|0\end{array}\right][/tex]
The following operation is given:
[tex]R_1 \rightarrow -6R_2 + R_1[/tex]
In which [tex]R_1[/tex] is the element at the first line and [tex]R_2[/tex] is the element at the second line.
Updating the first line:
[tex]R_{1,1} = -6*1 + 6 = 0[/tex]
[tex]R_{1,2} = -6*-5 - 1 = 30 - 1 = 29[/tex]
[tex]R_{1,3} = -6*0 + 5 = 5[/tex]
Thus, the filled matrix will be given by:
[tex]\left[\begin{array}{ccc}0&29&|5\\1&-5&|0\end{array}\right][/tex]
For another example where row operations are applied on a matrix, you can check https://brainly.com/question/18546657
PLEASE HELP
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
2y-3x=10
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
Hey there! I'm happy to help!
Here is our equation.
[tex]2y-3x=10[/tex]
Let's add 3x to both sides.
[tex]2y=3x+10[/tex]
Divide both sides by 2.
[tex]y=\frac{3}{2}x+5[/tex]
Here is slope intercept form.
[tex]y=mx+b\\m=slope\\b=y-intercept[/tex]
So, we can just find those two things in the equation, and here are our answers.
[tex]y=\frac{3}{2}x+5\\m=\frac{3}{2}\\b=5[/tex]
The graph is down below. If our y-intercept is 5, then one of our points is (0,5). You can then plug a random x-value into the formula to find another point and then draw the line going through the two points.
[tex]y=\frac{3}{2}(2)+5\\y=3+5\\y=8\\(2,8)[/tex]
Have a wonderful day and keep on learning! :D
Please help do in an hour
Answer:
-4
Step-by-step explanation:
a1 = -8
an = an-1 +2
a2 = a1+2 = -8+2 = -6
a3 = a2+2 = -6+2 = -4
(07.03. 07.04 MC)
Part A: The area of a square is (4x2 + 20x + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show
your work (5 points)
Part B: The area of a rectangle is (4x2 - 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work
(5 points)
Answer:
A) 4x^2+20x+25=(2x)^2+2*(2x)*5+5^2=(2x+5)^2
Area=(side)^2, side=sqrt(area)=sqrt((2x+5)^2)=2x+5
B) 4x^2-9y^2=(2x-3y)(2x+3y), these are the dimensions of the rectangle
A) The length of each side of the square is (2x + 5).
B) The dimensions of the rectangle are (2x - 3y) and (2x + 3y).
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Given that,
Part A: The area of a square is [tex](4x^2 + 20x + 25)[/tex] square units.
Part B: The area of a rectangle is [tex](4x^2 - 9y^2)[/tex] square units.
A) Now the length of each side of the square is calculated by factoring the area expression completely,
[tex](4x^2 + 20x + 25)[/tex]
[tex]4x^2 + (10 + 10)x + 25[/tex]
[tex]4x^2 + 10x + 10x + 25[/tex]
[tex]2x (x + 5) + 5(2x + 5)[/tex]
[tex](2x + 5) (2x+5)[/tex]
Hence the length of each side of the square is (2x + 5).
B) the dimensions of the rectangle are calculated by factoring the area expression completely,
[tex](4x^2 - 9y^2)[/tex]
[tex](2x)^2 - (3y)^2[/tex]
[tex](2x - 3y) (2x + 3y)[/tex]
Therefore, the dimensions of the rectangle are (2x - 3y) and (2x + 3y).
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Find the first five terms of the sequence..
Answer:
The Next fiver tems are - 2, -2,-8,-12,-16
Step-by-step explanation:
Answer:
2,-6,2,-6,2
Step-by-step explanation:
a1 = 2
an = -an-1 -4
Let n =2
a2 = -a1 -4 = -2-4 = -6
Let n=3
a3 = -a2 -4 = - (-6) -4 = +6 -4 = 2
Let n = 4
a4 = -a3 -4 = -2 -4 = -6
Let n=5
a5 = -a4 -4 = -(-6) -4 = +6-4 = 2
What is the volume of the following rectangular prism?
Answer:
44/3
Step-by-step explanation:
V=L*W*H
WH=22/3
V=2*(22/3)
Find a vector v that is perpendicular to the plane through the points
A=(5,−4,4), B=(−5,0,−3), and C=(−4,2,−5).
v =
The value of vector v that is perpendicular to the plane through the points is,
⇒ v = (6, - 27, - 24)
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Points are,
A = (5,−4,4), B = (−5,0,−3), and C = (−4,2,−5).
Hence, We get;
AB = [- 10, 4, - 7]
AC = [-9, 6, -9]
So, The value of vector v that is perpendicular to the plane through the points is,
⇒ v = AB x AC
⇒ v = (- 10, 4, - 7) x (- 9, 6, - 9)
⇒ v = (6, - 27, - 24)
Thus, The value of vector v that is perpendicular to the plane through the points is,
⇒ v = (6, - 27, - 24)
Learn more about the multiplication visit:
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