The null and alternative hypothesis are H0 : μ = 444; Ha : μ < 444.
In the given question we have to determine the decision rule for rejecting the null hypothesis.
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444 gram setting.
[tex]\mu_{0}[/tex] = 444
A 9 bag sample had a mean of 441 grams with a standard deviation of 25.
A level of significance of 0.025 will be used.
There have claim that the machine is underfilling the bags.
So , the null and alternative hypothesis are
H0 : μ = 444
Ha : μ < 444
To learn more about null and alternative hypothesis link is here
brainly.com/question/27335001
#SPJ4
Find the nth term of this quadratic sequence
4, 9, 16, 25, 36, ..
The nth term of this quadratic sequence 4,9,16,25,36 is [tex]n^{2} + 2n + 1[/tex]
Given that:
the given sequence is 4,9,16,25,36
nth term of quadratic sequence is [tex]an^{2}+bn+c[/tex]
Now lets find out the value of each variable a,b,c
a = second difference divide by 2
lets find out second difference
4,9,16,25,36
the first difference between the terms are
5,7,9,11
The second difference between the terms
2,2,2
the value of a = second difference / 2
[tex]a = \frac{2}{2} = 1\\[/tex]
a = 1
Now we find the value of b
3a + b = first term of first difference
3a + b = 5
3(1) + b = 5
3 + b = 5
b = 5 - 3
b = 2
Now find the value of c
a + b + c = first term
a + b + c = 4
1 + 2 + c = 4
3 + c = 4
c = 1
Now we replace all the values to find the nth term
[tex]an^{2}+bn+c\\ \\n^{2}+2n+1[/tex]
Hence the answer is the nth term of this quadratic sequence 4,9,16,25,36 is [tex]n^{2} + 2n + 1[/tex].
To learn more about sequence click here https://brainly.com/question/6561461
#SPJ9
-18t=-3(t+5) distributive property and using division first HELP PLEASE
Answer: T= 1
Step-by-step explanation:
Whenever you are asked to construct and interpret a confidence interval, what are the steps to the process you must complete?
A. plan, state, do, conclude
B. state, plan, do, conclude
C. plan, do, state, conclude
D. state, do, conclude, plan
ANSWER IS B
HELP MEEEEE PLEASEE TYYY
Answer:
4 metters por el significado
help please/////////////////////////////////////////////////////////
Answer:
tan 25° = b / 8 m
Step-by-step explanation:
You need to know what the ratios are.
sin X = opp/hyp
cos X = adj/opp
tan X = opp/adj
For angle B, the opposite leg is b, ad the adjacent leg is 8 m.
The hypotenuse is AB.
sin B = sin 25° = opp/hyp = b/AB
tan B = tan 25° = opp/adj = b / 8 m
Identify the slope and y-intercept for the following equation.
-2y-10+2x=0
Slope:
Y-intercept:
I need help please!!!
the slope of the given point is m=−3/4
Given (x – 7)^2 = 36, select the values of x.
x = 13, x = 1, x = –29, x = 42
Answer:
x = 13 x = 1
Step-by-step explanation:
(13-7) = 6
6^2 = 36
1-7 = -6
(-6)^2 = 36
algebra 2 please help fast!!
The zeroes of the polynomial are -2,1,3,-1
What are the zeroes of the polynomial?The locations where a polynomial becomes 0 overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero (-1). The largest power of the variable x is referred to as a polynomial's degree.
How do you find the zeroes of the polynomial?In general, the value of P(k) at x = k is denoted by P(k), and it can be found by substituting x by k in P if P(x) is a polynomial in x and k is any real number. The real number k is referred to as the zero of a polynomial P(x) if P(k) = 0.
Given:- The polynomial is f(x)=(x+2)(x-1)(x-3)(x+1)
The polynomial is divided into its factors
we equate each of the factors with the term 0
x+2=0
x=-2
x-1=0
x=1
x-3=0
x=3
x+1=0
x=-1
Hence the zeroes of the polynomial f(x)=-2,-2,1,3
To learn more about zeroes of the polynomial visit :
https://brainly.com/question/29415775
#SPJ1
how many numbers must be randomly selected from the set \{1,3,5,7,9,11,13,15\}{1,3,5,7,9,11,13,15} to guarantee that at least one pair of these numbers add up to 1616?
The number of pairs that must be randomly selected from the set {1,3,5,7,9,11,13,15} to guarantee that at least one pair of these numbers add up to 16 is 5.
In the given set {1,3,5,7,9,11,13,15}, there are four pairs that sum up to 16, which are (1,15), (3,13), (5,11), and (7,9). Let k numbers be picked from the set. Consider k = 5, then using the pigeonhole principle, for one of the pairs described above, both of the endpoints must have been picked. Hence, if 5 numbers are picked from the set, then there exists a pair with a sum of 16.
To learn more about the pigeonhole principle and probability theorem,
https://brainly.com/question/24491336
#SPJ4
Which of the following is true of prime numbers?
A.
A prime number may be an even number or an odd number.
B.
A prime number is always an even number.
C.
A prime number is always an odd number.
D.
A composite number may be an even number or an odd number.
Answer:
a is right (prime number is always a even number)
Answer:
A.
a prime number may be an even or an odd number
the life expectancy of a particular brand of tire is normally distributed with a mean of 30,000 and a standard deviation of 6,000 miles. what is the probability that a randomly selected tire will have a life of at least 38,100 miles? a. 0.9115 b. 0.4115 c. 0.5885 d. 0.0885
The probability that a randomly selected tire will have a life of at least 38,100 miles is 0.9115.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
Let, the life expectancy of a particular brand of tire is normally distributed with a mean of 30,000 and a standard deviation of 6,000 miles.
So, μ = 30000, σ = 6000, x = 38100.
Therefore,
z = (x - μ) / σ
= (38100 - 30000) / 6000
= 8100 / 6000
= 81 / 60
z = 1.35
Now,
P(X = 38100) = P(z = 1.35) = 0.9115
Hence, the probability that a randomly selected tire will have a life of at least 38,100 miles is 0.9115.
To know more about the probability, click on the link
https://brainly.com/question/24756209
#SPJ4
The relative frequency table describes the relationship between students who completed an exam review and their performance on the exam.
Passed exam Did not pass exam. Row Totals
Completed exam review 55% 10% 65%
Did not complete exam review 20%. 15% 35%
Column Totals 75% 25%. 100%
Part A: What is the percentage of students who passed the exam, given that they completed the exam review? Round to the nearest percentage. (2 points)
Part B: What is the percentage of students who passed the exam, given that they did not complete the exam review? Round to the nearest percentage. (2 points)
Part C: Is there an association between passing the exam and completing the exam review? Justify your answer. (2 points)
a) The percentage of students who passed the exam, given that they completed the exam review is of 73%.
b) The percentage of students who passed the exam, given that they did not complete the exam review, is of 27%.
c) There is a positive association between passing the exam and completing the exam review.
How to obtain the percentages?A percentage is obtained by the division of the desired amounts by the total amounts, multiplied by 100%.
For item a, these amounts are given as follows:
Desired: 55% that passed and completed the exam review.Total: 75% that passed.Hence the percentage is of:
p = 55/75 = 0.73 = 73%.
For item b, these amounts are given as follows:
Desired: 20% that passed and did not completed the exam review.Total: 75% that passed.Hence the percentage is of:
p = 20/75 = 0.27 = 27%.
There is a positive association between passing the exam and completing the exam review, as the percentage of students who passed completing the review, found in item a, is greater than the percentage of students who passed without completing the review, found in item b.
More can be learned about percentages at https://brainly.com/question/843074
#SPJ1
PLEASE ANSWER I WILL MARK BRAINLIEST!!!!!!
Deon throws a ball into the air. The height h of the ball in meters at time T seconds is modeled by the function h(t) =-5t^2+9t+2. will the ball reach a height of 5 m??
(Also what is the discriminant)
It is possible that the ball may reach a height of 5 meters in accordance with the quadratic formula.
May the ball reach a height of 5 meters?
The height of the ball as a function of time is represented by a quadratic equation, in which we must determine if the ball may reach a height of 5 meters. First, substitute the height in the quadratic equation:
- 5 · t² + 9 · t + 2 = 5
5 · t² - 9 · t + 3 = 0
Second, use the quadratic formula to determine the roots of the resulting quadratic equation:
t = - (- 9) / (2 · 5) ± [1 / (2 · 5)] · √[(- 9)² - 4 · 5 · 3]
t = 9 / 10 ± (1 / 10) · √(81 - 60)
t = 9 / 10 ± √21 / 10
t = (9 ± √21) / 10
Since all roots of the quadratic equations are real, then the ball can reach a height of 5 meters above the ground.
To learn more on quadratic formula: https://brainly.com/question/9300679
#SPJ1
An element with a mass of 200 grams decays by 15.7% per minute. To the nearest minute, how long will it be until there are 60 grams of the element remaining?
Answer:
3.82%
Step-by-step explanation:
The points R(4, t), S(3, 8) and T(1, 2) lie on a same straight line. Find the value of t.
well, we know that R, S and T are on the same straight line, hmmmm wait a second!! that means that the slope for RS must be the same as the slope for ST, heck, what's the slope for ST anyway?
[tex]S(\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad T(\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{3}}} \implies \cfrac{ -6 }{ -2 } \implies 3[/tex]
ahha!! that means that the slope for RS is really 3, hmmmm
[tex]R(\stackrel{x_1}{4}~,~\stackrel{y_1}{t})\qquad S(\stackrel{x_2}{3}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{t}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{4}}} ~~ = ~~\stackrel{\textit{\LARGE m}}{3} \\\\\\ \cfrac{8-t}{-1}=3\implies 8-t=-3\implies 11-t=0\implies 11=t[/tex]
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 2 to 3. If there were 4335 total votes, how many yes
votes were there?
Answer: The number of no votes is 1876 votes.
What is the ratio?
"The ratio is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another".
For the given situation,
Let x be the number of votes.
The ratio of yes votes : no votes = 3x:2x
Total = 5x
Total votes = 4690 votes
⇒
Divide by 5 on both sides,
⇒
Thus the number of no votes =
⇒
⇒
Hence we can conclude that the number of no votes is 1876 votes.
Learn more about ratios here
brainly.com/question/13016636
#SPJ2
Step-by-step explanation:
Giving 50 points :)))
Pls need help on #7!!!
Answer:
6
Step-by-step explanation:
Each coordinate is six times the corresponding coordinate in the preimage.
the food and drug administration (fda) is a u.s. government agency that regulates (you guessed it) food and drugs for consumer safety. one thing the fda regulates is the allowable insect parts in various foods. you may be surprised to know that much of the processed food we eat contains insect parts. an example is flour. when wheat is ground into flour, insects that were in the wheat are ground up as well. the mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. if the fda finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption. the null hypothesis is that the mean number of insect parts per 100 grams is 75. the alternative hypothesis is that the mean number of insect parts per 100 grams is greater than 75. is the following a type i error or a type ii error or neither?
Since in the question we reject the alternative hypothesis hence type II error occurs.
What is Type I error?
When the null hypothesis is true but rejected in hypothesis testing, type 1 errors often confused with false positives occur. A general assertion or default attitude that there is no connection between two measurable phenomena is known as the null hypothesis.
What is Type II error?
Type II errors take place when you fail to reject the null hypothesis even though it is untrue.
The average number of insect parts per 100 gm in this problem is 75. This number cannot be demonstrated by the test to be larger than 75. This indicates that the test is producing a "false negative" since it is not detecting these insect parts.
Hence, this is a Type II error.
To learn more about hypothesis testing:
https://brainly.com/question/4232174
#SPJ4
Find the length of x
The length of x is 4.1.
Given:
Base = 9 + 4.5 = 13.5
From figure:
= [tex]\sqrt{9^{2}+5^{2} }[/tex]
= [tex]\sqrt{81+25}[/tex]
= [tex]\sqrt{96}[/tex]
= 9.797
4.5 opposite is equal to 4.5.
5 opposite equal to 5 and remaining to x - 5.
According to pythagorean theorem:
= [tex]\sqrt{4.5^{2}+(x-5)^{2} }[/tex]
[tex]13.5^{2} +x^{2} =(\sqrt{96}+\sqrt{4.5^{2} +(x-5)^{2} })^{2}[/tex]
[tex]\sqrt{13.5^{2} +x^{2} }[/tex] - [tex]\sqrt{96} = \sqrt{20.25+x^{2} +25 -10x}[/tex]
squaring on both sides
182.25 + [tex]x^{2}[/tex] - 96 = [tex]x^{2}[/tex] - 10x + 45.25
10x = 45.25 + 96 - 182.25
10x = 41
x = 4.1.
Therefore the value of x is 4.1.
Learn more about the length here:
https://brainly.com/question/8552546
#SPJ1
the diameter of a circle is 24 feet. what is the approximate circumference of the circle? use 3.14 for pie
Circumference = pi x d
Circumference = 3.14 x 24 = 75.36
I hope this helps!
For his phone service, Chang pays a monthly fee of $27, and he pays an additional $0.07 per minute of use. The least he has been charged in a month is
$121.71.
What are the possible numbers of minutes he has used his phone in a month?
Use m for the number of minutes, and solve your inequality for m.
1353 numbers of minutes he has used his phone in a month.
What do you mean by algebraic expression?
In mathematics, an algebraic expression is an expression composed of integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by exponents that are rational numbers).
Algebraic equations are equations that contain only algebraic expressions.
Algebraic expression is the idea of using letters or alphabets to represent numbers without specifying the actual value. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here.
It is given that Chang pays a monthly fee of $27, and he pays an additional $0.07 per minute of use.
Let m be the additional minutes
Then charge for additional minutes is $0.07m
Now , it is also given that least he has been charged in a month is
$121.71.
⇒ 0.07m + 27 = 121.71
⇒ 0.07m = 121.71 - 27
⇒ 0.07m = 94.71
⇒ m = 94.71/0.07 = 1353
Therefore, 1353 numbers of minutes he has used his phone in a month.
To learn more about the algebraic expression from the given link.
https://brainly.com/question/28036476
#SPJ1
I need help please!!
Answer:
1/2
Step-by-step explanation:
(-6-(-4)/(3-7)
(-6+4)/-4
-2/-4
1/2
Suppose that F(x) = x² and G(x) = -1/4 (x+7)². Which statement best compares
the graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) stretched vertically, flipped
over the x-axis, and shifted 7 units to the right.
B. The graph of G(x) is the graph of F(x) stretched vertically, flipped
over the x-axis, and shifted 7 units to the left.
C. The graph of G(x) is the graph of F(x) compressed vertically,
flipped over the x-axis, and shifted 7 units to the right.
OD. The graph of G(x) is the graph of F(x) compressed vertically,
flipped over the x-axis, and shifted 7 units to the left.
The statement that best compares the graph of G(x) with the graph of F(x) is the graph of G(x) is the graph of F(x) compressed vertically, flipped over the x-axis, and shifted 7 units to the left.
According to the question,
We have the following information:
F(x) = x² and G(x) = -1/4 (x+7)²
Now, the graph of G(x) will be the graph of F(x) but there will be certain changes in the graph according to its function.
Now, in this function, 7 is added to x then it means that it will shift 7 units to left.
There is a negative sign before the function which says that is flipped over the x-axis.
Now, the factor 1/4 in the multiplication says that it has been compressed.
Hence, the correct option is D.
To know more about graph of G(x) here
https://brainly.com/question/2120300
#SPJ1
5. A parabola has a directrix of y = -3 and a vertex
at (2,1). Which ordered pair is the focus of the
parabola?
The ordered pair of the force of the parabola will be (2, -1).
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
A parabola has a directrix of y = - 3 and a vertex at (2,1).
Since the directrix is upward, utilize the condition of a parabola that opens up or down.
(x − h)² = 4p(y − k)
The separation from the concentration to the vertex and from the vertex to the directrix is |p|. Deduct the worth of the directrix from the y direction of the vertex to track down p.
p = − 1 + 1 / 2
p = − 1/2
Then the equation is given as,
(x − 2)² = 4(1/2)(y + 1)
(x − 2)² = 2(y + 1)
The ordered pair of the force of the parabola will be (2, -1).
More about the parabola link is given below.
https://brainly.com/question/8495504
#SPJ1
How do you approximate on a calculator?
Answer:
enter a function and from there you approximate hope it helps
the sides of a square are dilated by a scale factor of 1/2. the perimeter of the bigger square is 24 ft. what is the perimeter of the smaller square? A. 48 feet B. 12 feet C. 8 feet D. 4 feet
The perimeter of the smaller square would be = 12feet. That is option B.
What is perimeter?Perimeter can be defined as the summation of all the sides and edges of an object.
Scale factor is also defined as the ratio of difference between an original object and a newly formed object.
A square has four sides and it's perimeter = 24 ft
This means that the sides of the square= 24/4 = 6ft.
If the original (smaller square) dialted by a factor of 1/2 to have 6 ft as its sides, it means that it's original side of the small square is 3ft.
This is because to form the bigger square, 1/2 × 6 = 3ft.
Therefore, the perimeter of small square = 3+3+3+3 = 12ft.
Learn more about scale factor here:
https://brainly.com/question/28339205
#SPJ1
Please help
What is the area, in square feet, of the shape below? Express your answer as a fraction in simplest form.
2/3 ft
4/3 ft
Answer:
4/9
Step-by-step explanation:
Area of a triangle is 1/2*base*height
1/2*2/3*4/3 = 8/18 = 4/9
Tyrone can type 87 words in three minutes at this rate how long will it take him to type 1624 words
Rewrite the following equation in slope-intercept form.
y + 9 = – (x + 10)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
The slope-intercept form of the equation can be written as y = -x - 19
Slope - Intercept FormThe slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis). Equation of line is the equation that is satisfied by each point that lies on that line.
The equation given is y + 9 = -(x + 10)
Rewriting this equation in y = mx + c format;
y + 9 = -(x + 10)
y + 9 = -x - 10
y = -x - 10 - 9
y = -x - 19
The equation is y = -x - 19
Learn more on slope-intercept form here;
https://brainly.com/question/4074386
#SPJ1