Answer
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to conclude that the machine is underfilling the bags
Step-by-step-explanation:
From the question we are told that
The population mean is [tex]\mu = 420.0 \ g[/tex]
The sample size is n = 33 bags
The sample mean is [tex]\= x = 417.0 \ g[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The variance is [tex]\sigma^2 = 576.0[/tex]
The null hypothesis is [tex]H_o : \mu = 420[/tex]
The alternative hypothesis is [tex]H_a : \mu < 420[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\sigma^2}[/tex]
=> [tex]\sigma = \sqrt{576 }[/tex]
=> [tex]\sigma = 24[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{ \= x - \sigma }{ \frac{\sigma}{\sqrt{n} } }[/tex]
=> [tex]z = \frac{417 - 420 }{ \frac{24}{ \sqrt{ 33} } }[/tex]
=> [tex]z = -0.71807[/tex]
From the z table the area under the normal curve to the left corresponding to -0.71807 is
[tex]p-value = P(Z < -0.71807 ) = 0.23636[/tex]
Generally looking at the values we see that
[tex]p-value > \alpha[/tex] , hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to conclude that the machine is underfilling the bags
Find the midpoint of the segment with the following endpoints.
(2, -4) and (6. – 10)
Answer:
midpoint (4,-7)
Step-by-step explanation:
please see work attached where you utilize the midpoint formula.
please give thanks :)
Answer:
[tex](4,-7)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Step-by-step explanation:
Step 1: Define
Endpoint (2, -4)
Endpoint (6, -10)
Step 2: Find Midpoint
Simply plug in your coordinates into the midpoint formula to find midpoint
Substitute [MF]: [tex](\frac{2+6}{2},\frac{-4-10}{2})[/tex]Add/Subtract: [tex](\frac{8}{2},\frac{-14}{2})[/tex]Divide: [tex](4,-7)[/tex]Which of these is an example of driving at an average rate of 20 miles per hour?
driving 10 miles in 2 hours
O driving 25 miles in 5 hours
O driving 15 miles in 5 hours
driving 40 miles in 2 hours
Answer:
driving 40 miles in 2 hours
A boy had 72 coins and lost 25% of them How muy coins
did he have left?
Answer:
54 coins left
Step-by-step explanation:
72 x .25 = 18
72 - 18 = 54
Answer:
100% - 25% = 75%
72 x 0.75 = 54
He had 54 coins left
Step-by-step explanation:
Ok, to solve this question, first divide 72 by 100--- 72/100=.72
next, multiply .72*25 and u get--- 18
next subtract 72 and 18--- 72-18=54
the answer is the boy has 54 coins left
hope this helps!
Which is the graph of arctan(x)?
Answer:
The Inverse Tangent Function (arctan)
Graph of y = tan x.
The graph of arctan(x) is second graph.
We have inverse function [tex]y=tan^{-1} x[/tex]
Creating the table
x 0 π/4 π/2 -π/2 -π/3 π/3
y 0 1 ∞ -∞ -√3 √3
From the given graphs we see that the second graph satisfies the values.
So, the correct graph for arctan(x) is second graph.
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Helpppppppppppppppppppppppppppppp
Answer:
Step-by-step explanation:
c and e is not polynomials
Define a variable, write an inequality, and solve: A number decreased by 7 is at least 15.
Answer:
x is greater than it equal to 22
Step-by-step explanation:
Have a nice day! xoxo Arael :)
. Mr. Ahmet, who won a prize of 1 million USD by participating in a quiz show, will
provide a significant return if he uses it in repo, time deposit and bonds. However, careful decisions need to be
made as to which area to invest. If the money is deposited in the bank, the bank pays interest once a month and
pays 16% interest. Mr. Ahmet wants to buy 2 houses, one worth 900000 USD and the other 500000 USD, in the
future, by investing this money in the bank. Accordingly, after how long is it possible for Ahmet Bey to buy these
two houses with the money and income he earned? If you were Mr. Ahmet, how would you advise him to use
this money?
Answer:
See below
Step-by-step explanation:
Mr. Ahmet needs:
(900000 + 500000) - 1000000 = 400000more to have enough money to buy those two houses.
Monthly, he gets interest paid:
1000000*0.16/12 = 13333.33Time to have required amount is:
400000/13333.33 = 30 months = 2.5 yearsWithout taking the deposit he would need time:
1400000/13333.33 = 105 months = 8 years and 9 months to buy two housesHe could wait and use the interest to buy houses provided they will still be available and price remains same.
What’s 3/6 as a mixed number
Answer:
It can't be made into a mixed number
Step-by-step explanation:
The length of a rectangle is (x+3)cm. If the width of the rectangle is two thirds its length and the perimeter is 27cm,find its area
Answer:
[tex]A = 43.74[/tex]
Step-by-step explanation:
Represent Length with L, Width with W and Perimeter with P
[tex]P = 27[/tex]
[tex]L=x+3[/tex]
[tex]W = \frac{2}{3}(x + 3)[/tex]
Required
Determine the Area
From the perimeter, we need to solve for x;
[tex]P = 2(L + W)[/tex]
Substitute values for P, L and W
[tex]27 = 2(x + 3 + \frac{2}{3}(x+3))[/tex]
[tex]27 = 2(x + 3 + \frac{2}{3}x+2)[/tex]
Collect Like Terms
[tex]27 = 2(3 + 2 + x + \frac{2}{3}x)[/tex]
[tex]27 = 2(5 + \frac{3x + 2x}{3})[/tex]
[tex]27 = 2(5 + \frac{5x}{3})[/tex]
Open bracket
[tex]27 = 10 + \frac{10x}{3}[/tex]
Collect Like Terms
[tex]27 - 10 = \frac{10x}{3}[/tex]
[tex]17= \frac{10x}{3}[/tex]
Solve for x
[tex]x = \frac{3*17}{10}[/tex]
[tex]x = \frac{51}{10}[/tex]
[tex]x = 5.1[/tex]
The Area is then calculated using:
[tex]A = L * W[/tex]
[tex]A = (x + 3)*\frac{2}{3}(x+3)[/tex]
[tex]A = \frac{2}{3}(x+3)^2[/tex]
Substitute 5.1 for x
[tex]A = \frac{2}{3}(5.1+3)^2[/tex]
[tex]A = \frac{2}{3}(8.1)^2[/tex]
[tex]A = \frac{2}{3}*65.61[/tex]
[tex]A = \frac{2*65.61}{3}[/tex]
[tex]A = \frac{131.22}{3}[/tex]
[tex]A = 43.74[/tex]
Hence, the area is [tex]43.71cm^2[/tex]
Helppppppppppppppppppppp!!!!!!!!
Because of some theory with angles on same sides of a line between parallel lines, take 180 and subtract the ones you have. 180-107=73 degrees= m angle B
180-46=134 degrees - m angle A
True or False?
The sample space is a collection of outcomes from an event?
When building a chair, a carpenter uses 2 pounds of wood and 4 ounces of glue. If the Carpenter has 8 pounds of wood and 6 ounces of glue, how many chairs will he be able to build
Answer:
He can build ...
... min(floor((available wood)/(wood per chair)), floor((available glue)/(glue per chair)))
... = min(floor(6/4), floor(12/6))
... = min(1, 2) = 1
The carpenter can build ...
... e. one chair
Step-by-step explanation:
Please help answer the first 2 boxes for brainslt
> for brainslt
y=mx+b
From a Graph:
m=3/2 b=3
Equation: y=3/2x+3
Non-Proportional
Negative Slope
2nd From a Graph:
m=5/2 b=4
Equation: y=5/2x+4
Non-Proportional
Negative Slope
Does anyone know the answer?
Write a linear function for each line that relates to y to x
Answer:
Please check the complete explanation below.
Step-by-step explanation:
We know that the slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
ANALYZING TABLE 1
Part A)
Given table 1
x 0 1 2 3
y 1 3 5 7
From table 1, the y-intercept can be determined by setting x=0 and checking the corresponding y-value.
so at x = 0, y = 1
Thus, the y-intercept is (0, 1).
From the graph, it is clear that the line W has a y-intercept (0, 1).
Therefore, table 1 represents the line W.
Part B)
Taking two points (0, 1) and (1, 3) to find the slope using the formula
m = (y₂-y₁) / (x₂-x₁)
m = 3-1 / 1-0 = 2/1 = 2
now substituting m = 2, and b = 1 in the slope-intercept form
y = mx+b
y = 2x+1
Thus, table 1 represents the line W with the equation line y = 2x+1
ANALYZING TABLE 2
Part A)
Given table 2
x 0 1 2 3
y 0 3 6 9
From table 2, the y-intercept can be determined by setting x=0 and checking the corresponding y-value.
so at x = 0, y = 0
Thus, the y-intercept (0, 0).
From the graph, it is clear that line F has a y-intercept (0, 0).
Therefore, table 2 represents the line F.
Part B)
Taking two points (0, 0) and (1, 3) to find the slope using the formula
m = (y₂-y₁) / (x₂-x₁)
m = 3-0 / 1-0 = 3/1 = 3
now substituting m = 3, and b = 0 in the slope-intercept form
y = mx+b
y = 3x+0
y = 3x
Thus, table 2 represents the line F with the equation y = 3x
ANALYZING TABLE 3
Part A)
Given table 1
x 0 1 2 3
y 2 3 4 5
From table 3, the y-intercept can be determined by setting x=0 and checking the corresponding y-value.
so at x = 0, y = 0
Thus, the y-intercept (0, 2).
From the graph, it is clear that line N has a y-intercept (0, 2).
Therefore, table 3 represents line N.
Part B)
Taking two points (0, 2) and (1, 3) to find the slope using the formula
m = (y₂-y₁) / (x₂-x₁)
m = 3-2 / 1-0 = 1/1 = 1
now substituting m = 1, and b = 2 in the slope-intercept form
y = mx+b
y = (1)x+2
y = x+2
Thus, table 2 represents the line N with the equation y = x+2
The mean of the numbers 15,21,17,26,18 and 29 is 21. Calculate the standard deviation.
Answer:
4.62910049578
Step-by-step explanation:
variation is standard deviation squared
variance = 21.428571428571
square root variance for answer.
Please asnerw this pic attached below
Answer:
x = 30
Step-by-step explanation:
Look at triangle LMN.
m<NLM + m<M + m<MNL = 180
90 + m<M + 45 = 180
m<M = 45
Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
<ONM is an exterior angle of triangle KMN.
The remote interior angles are <K and <M.
m<K + m<M = m<ONM
2x + 45 = 105
2x = 60
x = 30
Answer: x = 30
Complete the proof of the identity by choosing the Rule that justifies each step.
(1- cos x) so
secx sin tan
To see a detailed description of a Rule, select the More Information Button to the right of the Rule,
( 1 - cos²x ) secx
=> sin²x . secx
Here the rule ( rule 1 ) is the first trigonometric identity [ sin²A + cos²A = 1 ] by simplifying we have , [ 1 - cos²A = sin² ] . So here we substituted 1 - cos²x = sin²x .
=> sin²x [ 1/cosx ]
Here the rule ( rule 2 ) is secx = 1/cosx . So here we substituted secx = 1/cosx .
=> sinx [ sinx/cosx ]
Here the rule ( rule 3 ) is sin²x can be written as sinx . sinx , so we get sinx . sinx [ 1/cosx ] next by simplifying , sinx [ sinx/cosx ].
=> sinx tanx
Here the rule ( rule 4 ) is , in the above we got sinx/cosx and here we know that , sinx/cosx = tanx . So we have tan x .
The proof of the identity that justifies that ( 1 - cos²x ) secx equals sinx(tanx) has been described below with statements and rules.
Statement 1; ( 1 - cos²x ) secx
This is given
Statement 2; sin²x · secx
Rule 1; From trigonometric identities, we know that;
sin²x + cos²x = 1,
Thus; cos²x = 1 - sin²x
Thus; ( 1 - cos²x ) secx = sin²x · secx
Statement 3; sin²x (1/cosx)
Rule 2; The rule here according to trigionometric identities is that; secx = 1/cosx. Thus; secx = 1/cosx .
Statement 4; sinx (sinx/cosx )
Rule 3; The rule here is that sin²x can be expressed as (sinx * sinx)
Thus, we have; sinx . sinx (1/cosx) = sinx (sinx/cosx ).
Statement 5; sinx(tanx)
Rule 4; The rule here is that; sinx/cosx = tanx.
Thus; sinx (sinx/cosx ) gives us sinx(tanx)
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Please help me for the following questions please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!...…..
Answer:
All are corrects.
Step By Step Explanation:
It's all the same thing.
HELP Will mark Brainliest!! Ignore if you don't know, Geometry problem: Point D is the incenter of triangleABC, if DE=x^2 and DF= 20-8x, find each of the following
Answer:
X=2
DG=4
Step-by-step explanation:
Answer:
X=2
DE=4
THE ANSWER IS UPPP
Find the volume of the region between the cylinder z=3y^2 and the xy-plane that is bounded by the planes x=0,x=1 ,y=-1 and . z = y2 x = 0 x = 1 y = − 1 y =1
Answer:
The volume of the region V = 2
Step-by-step explanation:
Given that:
[tex]z_1 = 3y^2[/tex] ;
where initially;
[tex]z_o = 0; \ x_o = 0; \ x_1 = 1; \ y_o= -1; \ y_1 = 1[/tex]
The volume of the region is given by a triple which is expressed as:
[tex]V = \int_x \int_y \int_z \ dz \ dy \ dx[/tex]
[tex]V = \int \limits ^{x_1 = 1}_{x_o=0} \int \limits ^{y_1 = 1}_{y_o=-1} \int \limits ^{z_1 = 3y^2}_{z_o=0} \ dz \ dy \ dx[/tex]
[tex]V = \int \limits ^{1}_{0} \int \limits ^{ 1}_{-1} \int \limits ^{3y^2}_{0} \ dz \ dy \ dx[/tex]
[tex]V = \int \limits ^{1}_{0} \int \limits ^{ 1}_{-1} \Bigg [z \Bigg]^{3y^2}_{0} \ dy \ dx[/tex]
[tex]V = \int \limits ^{1}_{0} \int \limits ^{ 1}_{-1} \Bigg [3y^2 \Bigg] \ dy \ dx[/tex]
[tex]V = \int \limits ^{1}_{0} \Bigg [\dfrac{3y^3}{3} \Bigg]^1_{-1} \ dx[/tex]
[tex]V = \int \limits ^{1}_{0} \Bigg [\dfrac{3(1)^3}{3}- \dfrac{3(-1)^3}{3} \Bigg] \ dx[/tex]
[tex]V = \int \limits ^{1}_{0} \Bigg [1-(-1)\Bigg] \ dx[/tex]
[tex]V =2 \Bigg [x \Bigg] ^1_0[/tex]
V = 2
Thus, the volume of the region is 2
Find the exponential function of the 2 points (3, 7) and (5, 63). Use
the formula f(x) = a(b)”.
Answer:
We obtained the two exponential functions:
[tex]y\:=\:\frac{7}{27}\left(3\right)^x[/tex][tex]y\:=-\:\frac{7}{27}\left(-3\right)^x[/tex]Step-by-step explanation:
As we know that the exponential function is of the form
f(x) = abˣ
Given the points
(3, 7)(5, 63)We know these points belong to the exponential function.
so substituting the values (3, 7) and (5, 63) in the function
putting (3, 7)
y = abˣ
7 = ab³
also putting (5, 63)
y = abˣ
63 = ab⁵
Considering the 2nd equation
63 = ab⁵
as
[tex]a^b\times \:a^c=a^{b+c}[/tex]
so
63 = ab³×b²
substituting 7 = ab³ in 63 = ab³×b²
63 = 7 × b²
b² = 63/7
b² = 9
b = ± 3
If b = 3
plug in b = 3 in the equation 7 = ab³ to find the value 'a'
7 = ab³
7 = a(3)³
7 = a × 27
a = 7/27
so, a = 7/27 and b = 3 would give us the function
y = abˣ
[tex]y\:=\:\frac{7}{27}\left(3\right)^x[/tex]
if b = -3
plug in b = -3 in the equation 7 = ab³ to find the value 'a'
[tex]\:7\:=\:a\left(-3\right)^3[/tex]
[tex]a\left(-27\right)=7[/tex]
[tex]a=-\frac{7}{27}[/tex]
so, a = -7/27 and b = -3 would give us the function
y = abˣ
[tex]y\:=-\:\frac{7}{27}\left(-3\right)^x[/tex]
Thus, we obtained the two exponential functions:
[tex]y\:=\:\frac{7}{27}\left(3\right)^x[/tex][tex]y\:=-\:\frac{7}{27}\left(-3\right)^x[/tex]Olivia drinks 64 ounces of water every day. At breakfast, she drinks 16 ounces. What percentage of water does she drink at breakfast?
Answer:
25%
Step-by-step explanation:
16/64 = .25 x 100 = 25%
According to an accepted chemistry reference, the
heat of vaporization of water is 540 calories per
gram. A student determined in the laboratory that
the heat of vaporization of water was 620 calories
per gram. The student's results had a percent error
of
Answer:
14.8%
Step-by-step explanation:
Step 1: Given data
True value for the heat of vaporization of water (ΔH°vap(T)): 540 cal/g
Experimental value for the heat of vaporization of water (ΔH°vap(E)): 620 cal/g
Step 2: Calculate the experimental percent error
To determine the experimental percent error we will use the following expression.
%E = |ΔH°vap(T) - ΔH°vap(E)|/ΔH°vap(T) × 100%
%E = |540 cal/g - 620 cal/g|/540 cal/g × 100%
%E = 14.8%
the perimeter of a rectangle is 72 ft. the ratio of the length to width is 5:4. what are the dimensions of the rectangle?
Answer: 20 by 16
Step-by-step explanation:
5:4 OR 5x:4x
Perimeter = 2(l x w)
P = 2(5x x 4x)
P = 10x + 8x = 18 x
18x=72
x=4
5 x 4 = 20
4 x 4 = 16
What is the equivalent expression for 6x + 18
kingston made a pot of 29 1/2c of gumbo soup. His family ate some of the gumbo for lunch. this changed the amount of the pot by -7 3/4c. then he gave some gumbo to his neighbors. This changed the amount in the pot by -6 1/2c. How many cups of gumbo are left in the pot?
please answer quickly!!!!!!!
Answer:
29 1/2-7 3/4 is 21.75
Then 21.75-1/2 is 21.25
Step-by-step explanation:
There is [tex]15\frac{1}{4}[/tex]c of gumbo soup left after Kingston's family ate and he shared some with his neighbor.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Kingston made a pot of [tex]29\frac{1}{2}[/tex] of gumbo soup.
His family ate some of the gumbo for lunch. this changed the amount of the pot by [tex]-7\frac{3}{4}[/tex].
So, Reaming gumbo soup is ([tex]29\frac{1}{2} - 7\frac{3}{4}[/tex]).
= (59/2 - 31/4).
= (118 - 31)/4.
= 87/4c of gumbo soup.
Then he gave some gumbo to his neighbors. This changed the amount in the pot by -6 1/2c.
= (87/4 - 13/2)c.
= (87 - 26)/4c.
= 61/4.
= [tex]15\frac{1}{4}[/tex]c of gumbo soup.
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the 7s in 7,700 what is the value of the given digits
Answer:
the first 7 has a value of 7,000 while the second 7 has a value of 700
The students at Southern Junior high School are divided into four home rooms. Benjamin just moved into the school district and will be randomly assigned to one home room
Answer:
A 4 side dice.
Step-by-step explanation:
Benjamin has 4 possible homerooms with the same probability. This means that every homeroom has a 1/4 = 0.25 (or 25%) probability of getting chosen.
You could emulate this situation with a 4 sided dice (are like little pyramids) where each side of the dice would represent the selection of one of the homerooms.
Find the dot product of vectors u and v, where |u| = 12, |v| = 7, and the angle between is θ = 55°.
- u · v = 68.81
- u · v = 48.18
- u · v = 10.90
- u · v = 2.87
Answer:
u · v = 48.18
B on edge 2020
Step-by-step explanation:
Answer:
B on edge
Step-by-step explanation:
