How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 60 tissues during a cold. Suppose a random sample of 10 comma 000 people yielded the following data on the number of tissues used during a cold: x overbar equals 53 comma s equals 23. We want to test the alternative hypothesis Upper H Subscript a: muless than60. State the correct rejection region for alpha equals 0.05 .
Answers
Answer:
Null hypothesis: \( \mu \geq 60\)
Alternative hypothesis: \( \mu <60\)
Since the sample size is large enough we can assume that the distribution for the statistic is normal so then in order to find the critical value for this test taking in count the significance level given of 0.05 we need to look in the normal standard distribution a value who accumulates 0.05 of the area in the left and would be:
\( z_{crit}= -1.64\)
Step-by-step explanation:
For this case we have the following data given:
\( \bar X = 53\) represent the sample mean
\( s = 23\) represent the sample deviation
\(n = 10000\) represent the sample size.
We want to test for this case if the true mean is less than 60 so then the system of hypothesis are:
Null hypothesis: \( \mu \geq 60\)
Alternative hypothesis: \( \mu <60\)
Since the sample size is large enough we can assume that the distribution for the statistic is normal so then in order to find the critical value for this test taking in count the significance level given of 0.05 we need to look in the normal standard distribution a value who accumulates 0.05 of the area in the left and would be:
\( z_{crit}= -1.64\)
Related Questions
#7 find the answer with the offering 20% discount
Answers
Given a discount of 20% and a manufacturer's coupon of $200, the price after the discount and coupon, (C ∘ D)(x), is 0.8x - 200.
What is a discount?A discount is an amount that reduces the price of a retail item.
Discounts are offered as rates and the discounted price is computed by multiplying the discount factor and the price.
Discount rate on offer = 20%
Discounting factor = 80% or 0.8 (100 - 20%)
Manufacturer's coupon off the price = $200
Let the price of the bureau = x
The price after the discount (discounted price) is given by D(x)
D(x) = 0.8x
The price after the coupon = C(x) = x - 200
The price after applying the discount and the coupon, (C ∘ D)(x) = 0.8x - 200
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Complete Question:Wilson's Warehouse sells a certain brand's bureau. They are offering a 20% discount in addition to accepting a manufacturer's coupon for $200 off. Let the price of the bureau be x. If the price after the discount is given by D(x) and the price after the coupon is C(x), find (C ∘ D)(x).
The graph of the function f(x)=2x+4 is shown.
Answers
The inverse of f(x) = 2x + 4 can be written as → f ⁻¹(x) = x/2 - 2. The graph of the inverse of the function f(x) is attached at last.
What are the steps to find inverse of function ?Inverse of a function can be calculated by following the steps mentioned below -
Step 1 - Replace 'y' with 'x' and vice - versa.
Step 2 - Rewrite the equation by solving for 'y'.
Step 3 - Replace 'y' with f⁻¹(x).
We have a function given by → y = f(x) = 2x + 4 along with its graph.
In order to find the inverse of the function f(x), follow the steps discussed above. According to the question, the function is
y = f(x) = 2x + 4
Replace 'y' with 'x', we get -
x = 2y + 4
Now, solve for y -
x - 4 = 2y
y = x/2 - 2
Replace 'y' with f⁻¹(x) -
f⁻¹(x) = x/2 - 2
Therefore, the inverse of f(x) = 2x + 4 can be written as → f ⁻¹(x) = x/2 - 2.
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Please i need the answer fast k12
Answers
(A) The range and IQR for boxplot 1 is 10 and 6 respectively.
(B) The range and IQR for boxplot 2 is 12 and 7 respectively.
What is the IQR?The interquartile range defines the difference between the third and the first quartile.
The formula for the interquartile range is given below.
Interquartile range = Upper Quartile – Lower Quartile = Q3 – Q1
What is the range?The range is the difference between the lowest and highest values.
The formula for the interquartile range is given below.
Range = Maximum – Minimum
(A) For boxplot 1, we need to find the range and IQR from the given data set.
So, let 34 be the maximum and 24 be the minimum.
\(\text{Range}=\sf 34-24\)
\(\text{Range}=\sf10\)
Therefore, the range is 10.
Now time to find the IQR.
So, let 33 be Q3 and 27 be Q1.
\(\text{IQR}=\sf 33-27\)
\(\text{IQR}=\sf 6\)
Therefore, the IQR is 6.
(B) Now for boxplot 2, we will do the same thing as from part A.
Let's find the range.
So, let 24 be the maximum and 12 be the minimum.
\(\text{Range}=\sf 24-12\)
\(\text{Range}=\sf12\)
Hence, the range is 12.
Now for the IQR.
So, let 22 be Q3 and 15 be Q1.
\(\text{IQR}=\sf 22-15\)
\(\text{IQR}=\sf 7\)
Hence, the IQR is 7.
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The correlation coefficient is used to determine: a. a specific value of the y-variable given a specific value of the x-variable c. a specific value of the x-variable given a specific value of the y-variable c. the strength of the relationship between the x and y variables d. none of these
Answers
Answer:
c. the strength of the relationship between the x and y variables
Step-by-step explanation:
The correlation coefficient refers to the relationship between the two variables
Moreover, it has two mainly correlations i.e
Perfect positive correlation: In this, the correlation coefficient is 1
And, the other is negative correlation: In this, the co
if the correlation coefficient is 1 we have a perfect positive correlation and if the correlation coefficient is -1 than it would be a negative correlation
It lies value between the -1 and 1
hence, the correct option is c.
The option that correctly describes what the correlation determines is:
C "the strength of the relationship between the x and y variables"
What is the correlation coefficient?
When we have a measure of two variables that can be modeled with a line, we say that there is a correlation between these two variables.
A positive correlation means that when one variable increases, the other also increases, while a negative correlation means that when one decreases, the other increases.
Now, the value itself of the correlation tells us how much our measure "adjusts" to a line. If the correlation is equal to 1 or -1, then the two variables are linear.
If the correlation is smaller than 1 or larger than -1, then the variables behave kinda linearly, but not exactly.
So what the correlation determines is the relationship between the x and y variables, from that we conclude that the correct option is C: "The strength of the relationship between the x and y variables"
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PLEASE HELP! Mr. Smith makes $20 an hour working full time. He gets about 25% of his income taken out for taxes. He came up with the following monthly budget.
Household:
Rent: $700
Cable: $85
Cell Phone: $175
Electric: $100
Food: $350
Total: 1,410
Automobile
Car: $200
Car Insurance: $100
Gas: $90
Maintenance: $15
Total: $405
How much money does he have left over monthly to put into savings?
Answers
Answer:
$585/month
Step-by-step explanation:
To determine how much money Mr. Smith has left over monthly to put into savings, we need to first calculate his monthly income and his monthly expenses, including taxes.
Mr. Smith's hourly rate is $20, and he works full time, which is typically 40 hours per week. Therefore, his weekly income is:
$20/hour x 40 hours/week = $800/week
To find his monthly income, we multiply his weekly income by the number of weeks in a month:
$800/week x 4 weeks/month = $3,200/month
To find his monthly expenses, we add up the amounts for his household and automobile expenses:
$1,410/month (household) + $405/month (automobile) = $1,815/month
Since Mr. Smith gets about 25% of his income taken out for taxes, we need to calculate the amount of taxes he pays each month:
$3,200/month x 0.25 = $800/month (taxes)
Now we can subtract his monthly expenses and taxes from his monthly income to find out how much money he has left over to put into savings:
$3,200/month - $1,815/month - $800/month = $585/month
Therefore, Mr. Smith has $585/month left over to put into savings after paying his expenses and taxes.
Im diying:(
dont be mean man
Each level of a smartphone app adds more gems for you to match. On
level one, there were 13 gems. On level twelve, there were 123 gems.
When you complete all twelve levels, how
many total gems will you have
matched? (2 points)
O 748
• 816
O 660
O 605
Answers
Which term is defined by the following statement?
used to demonstrate the validity of a conjecture based on the truth of a first case, the assumption of truth of a kth case, and the demonstration of truth for the (k + 1)th case
a.
sigma notation
c.
Euler’s formula
b.
mathematical induction
d.
n factorial
Answers
Answer:
Mathematical notation
Step-by-step explanation:
edge 2021
A statement 'used to demonstrate the validity of a conjecture based on the truth of a first case, the assumption of truth of a kth case, and the demonstration of truth for the (k + 1)th case' defines mathematical induction.
The correct answer is option (b) mathematical induction.
What is sigma notation?"The sigma notation (Σ) is generally used to denote a sum of multiple terms."
What is Euler's formula?In geometry, V − E + F = 2
where, V, E, and F are the numbers of vertices, edges, and faces of any simple polyhedron
What is n factorial?For a positive integer n, the n factorial is the product of all the positive numbers preceding or equivalent to n.n! = n × (n-1) × . . . × 1What is mathematical induction?It is used to prove that an identity is valid for all integers n ≥ 1 .Steps to show a propositional function F(n) is true for all integers n ≥ a, where a is a fixed integer.- F(a) is true.
- if F(k) is true for some integer k ≥ a, then F(k + 1) is also true.
For given example,
a statement 'used to demonstrate the validity of a conjecture based on the truth of a first case, the assumption of truth of a kth case, and the demonstration of truth for the (k + 1)th case' defines mathematical induction.
Therefore, the correct answer is option (b) mathematical induction.
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3√b in exponential form
Answers
When you want to change a square root to exponential form, simply change it to the power of 1/2. And if you want to get rid of a square root, square the whole thing.
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 16 min to 72 min
Answers
Answer:
2/9
Step-by-step explanation:
16/72 is the same thing as 2/9, just simplified. If you make 16 to 72 in a fraction you get 16/72. You divide them with their GCF which is 8. 16 divided by 8 is 2 and 72 divided by 8 is 9. Therefore the answer is 2/9.
In the diagram above, Z1 = 135º.
Find the measure of Z3.
Z3 = ?
Answers
Answer:
Angle 3= 135
Step-by-step explanation:
Angle 3=Angle 1 because they are corresponding angles meaning they are equal and on the same side of the traversal.
Hope this helped and the answer was right in the question
Answer:
∠3 = 135°Step-by-step explanation:
corresponding angles are congruent, equal to each other.
therefore, ∠1 ≅ ∠3 which is 135°
Evaluate the expression when x = 3.
6) 21-X
Answers
Answer: 18
Step-by-step explanation: You would substitute x for 3 in the expression. This would equal 21-3, or 18 when simplified
5,323 ÷ 34
I need answers asap
Answers
Answer: 156.55882352941176470588235294118
Or 156.56 rounded to the nearest hundredth!
Hope this helps!
Answer: 156.558823529
Step-by-step explanation: You divide for example, 5,323 cookies to 34 people
Please reply me as soon as possible with step by step answer for this
Answers
The length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).
What is the length of the curve?To use the arc length formula, we need to find the derivative of the curve y = 5 - 4x:
y' = -4
Then, we can use the arc length formula:
L = ∫[a,b] √(1 + (y')^2) dx
where a and b are the limits of integration. In this case, a = -2 and b = 2.
L = ∫[-2,2] √(1 + (-4)^2) dx
= ∫[-2,2] √(17) dx
= √(17) * [x]_(-2)^(2)
= 4√(17)
So the length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).
To check this answer, we can note that the curve is a line segment with endpoints (-2, 13) and (0.75, 1), and we can calculate its length using the distance formula:
L = √((0.75 - (-2))^2 + (1 - 13)^2)
L = √(18.25 + 144)
L = √(162.25)
L = 4√(17)
This matches our previous answer, so we can be confident that the length of the curve is 4√(17).
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Which of the following is an example of closure? (1 point)
The equation 5 - 5 = 0 is an example of the natural numbers being closed under subtraction
The equation 1.5 +1.6 = 3.1 is an example of the rational numbers being closed under addition
The equation 4 - 6 = -2 is an example of the whole numbers being closed under subtraction
The equation 1+0= 1 is an example of the natural numbers being closed under addition
Answers
Answer:
The equation 1+0=1
Step-by-step explanation:
Other options are not eligible because
1 option -Natural numbers cannot be closed under subtraction
2 option-The equation is not having proper rational numbers, they are decimals
3 option-Whole numbers cannot be closed under subtraction
Thank you!
A recipe calls for 2/3 cups of sugar. I have 5 1/2 cups of sugar. How many batches can I make, assuming I have a large quantity of all other ingredients?
Answers
Answer:
8.25 batches.
(Or, if rounding to the lowest amount of batches, 8 batches)
Step-by-step explanation:
We have in total 5 1/2 cups of sugar.
And the recipe calls for 2/3 cups of sugar.
So, to find out how many batches we can make, we can divide the amount of have by the amount needed. So:
\(5\frac{1}{2}\div\frac{2}{3}\)
Let's convert the first fraction to improper form. We have 5 1/2. So, in improper form, it will be (5(2)+1)/2 or 11/2.
Therefore:
\(=\frac{11}{2}\div\frac{2}{3}\)
To divide fractions, we keep, change, and flip. Therefore:
\(=\frac{11}{2}\times\frac{3}{2}\)
Multiply straight across:
\(=\frac{33}{4}=8.25\)
So, we can make 8.25 batches.
Or, we can make 8 full batches.
3. What is the proper ordering
(from greatest to least) of the
following numbers?
I.58/67
II.0.58%
III.58%
IV.5.8%
O I, III, II,
O III, IV, II, I
O I, III, IV, II
O IV, I, III, II
Answers
Answer:
C) I, III, IV, II
Step-by-step explanation:
Convert each number into a decimal:
\(\textsf{I.} \quad \dfrac{58}{67}=0.86567...\)
\(\textsf{II.} \quad 0.58\%=\dfrac{0.58}{100}=0.0058\)
\(\textsf{III.} \quad 58\%=\dfrac{58}{100}=0.58\)
\(\textsf{IV.} \quad 5.8\%=\dfrac{5.8}{100}=0.058\)
Comparing the tenths of all the numbers, 8 is the biggest tenth, so 58/67 is the largest number.
The next biggest tenth is 5, so 58% is the next largest number.
The two remaining numbers have zero tenths, so compare their hundredths. 5 is the largest hundredth, so 5.8% is the next largest number. Therefore, 0.58% is the smallest number.
Therefore, the given set of numbers in order from greatest to least is:
I, III, IV, IIAnswer:
c) I, III, IV, II
Step-by-step explanation:
Values of l, ll, lll & lV respectively,
→ 58/67, 0.58%, 58%, 5.8%
→ 0.87, 0.0058, 0.58, 0.058
Arranging them in descending order,
→ 0.87 > 0.58 > 0.058 > 0.0058
→ 0.87, 0.58, 0.058, 0.0058
→ l, lll, lV, ll
Hence, the option (c) is correct.
Stacy says there is not enough information to prove that ACXBCX. Explain why Stacy's statement is incorrect.
Answers
Stacy's statement is incorrect because Stacey did not consider the side common side to both triangles such that by Reflexive Property of Congruence.
Reflexive Property of Congruence:
An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry.Stacey did not consider the side common side to both triangles such that by Reflexive Property of Congruence. Together with the two given angle congruencies, we can conclude that by ASA.Stacey did not consider the side common side to both triangles such that by Reflexive Property of Congruence.
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What is the fraction of 17/7 as a repeating decimal
Answers
2.428571428571428571
what is the solution to the equation:
5(n - 1/10) = 1/2
a. n= 13/5
b. n= 3/25
c. n= 0
d. n= 1/5
Answers
\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)
\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)
\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)
\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)
\( \sf \longrightarrow \: \: 100n =20\\ \)
\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)
\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)
Answer:-
Answer:- D) n = ⅕ ✅To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:
Step 1: Distribute the 5 on the left side:
\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)
Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:
\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)
\(\sf 5n = 1 \\\)
Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):
\(\sf \frac{5n}{5} = \frac{1}{5} \\\)
\(\sf n = \frac{1}{5} \\\)
Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).
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A sea lion swims 23 miles in ; hour. Part A. What is the unit rate of the swimming speed of the sea lion? Part B. At this rate, how long will it take the sea lion to swim 75 miles? Enter the correct answers in the boxes. A. miles per hour B. hour(s)
Answers
A sea lion swims 23 miles in 1/5 hours.
We can calculate the unit rate of the swimming speed dividing the number of miles he swims in a certain period of time, by the hours of this period of time.
We can calculate this as:
\(v=\frac{23\text{ miles}}{\frac{1}{5}\text{hours}}=23\cdot\frac{5}{1}=115\text{ miles per hour}\)We could have also calculated that if, in 1/5 of an hour, he travels 23 miles, in one hour (equal to 5/5) he would swim 23*5=115 miles.
At this rate it will take him 15/23 hours (approximately 0.65 hours) to swim 75 miles:
\(t=\frac{x}{v}=\frac{75\text{ miles}}{115\text{ miles/hour}}=\frac{15}{23}\text{hours}\)1 Simplify the ratio of 464: 128
Answers
Answer:
29 : 8
.........................
Factor the expression using the GCF
14x - 98 =
Answers
Answer:
14(x-7)
Step-by-step explanation:
Use a calculator to graph f(x) = 2x ^ 3 - 6x ^ 2 - 4x + 1 Which are the approximate x-values of the local maximum and local minimum rounded to the nearest tenth?
A) max ≈ -15.6 , min ≈ 1.6
B) max ≈ 1.6 , min ≈ -15.6
C) max ≈ 2.3 , min ≈ -0.3
D) max ≈ -0.3 , min ≈ 2.3
Answers
The approximate x-values for the local maximum and the local minimum are given as follows:
D) max ≈ -0.3 , min ≈ 2.3.
What are the relative minimums and the relative maximums of a function?The relative minimums of a function are given by the points in which the function's behavior changes from decreasing to increasing.The relative maximums of a function, meanwhile, are given by the points in which the function's behavior changes from increasing to decreasing.Hence the critical points of the graphed function are given as follows:
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Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?
Answers
Answer:
There were 378 students who chose to study French their freshman year. This means that 72% of the total number of students chose to study French their freshman year. Therefore, the total number of students must be 378 / 0.72 = 527.5. This means that there were 148.5 students who chose not to take French their freshman year.
Step-by-step explanation:
The weight of an object on a particular scale is 145,2 lbs. The measured
weight may vary from the actual weight by at most 0.3 lbs. What is the range
of actual weights of the object?
Answers
Answer:
145.2 + .3 = 145.5
145.2 - .3 = 144.9
C. 144.9 <= x <= 145.5
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!
Answers
Answer:
BS = 8
Step-by-step explanation:
CU/TU = BU/SU
6/18 = BU/12
BU = 12(6/18) = 4
BS = SU - BU = 12 - 4 = 8
Ronald repairs computers. He charges $25 for a house call and $24 per hour. If Ronald charges $145 for one of his jobs, including the house call, which equation can be used to find h, the number of hours he worked?
Answers
Answer:
25+24h=145
Step-by-step explanation:
Answer pls urgent shhzhzhsensnsj
Answers
Answer:
1/6 + 1/2 = 1/6 + 3/6 = 4/6
SIMPLIFIED IS = 2/3
Step-by-step explanation:
HELP ME IM DESPERATE!!!!!!!!!!!What is the vector that results from transforming a⃗ by the transformation matrix?
Enter your answer by filling in the boxes.
Answers
Answer:
the vector is 24 OVER 67
Step-by-step explanation:
and never the less the vector is the number u Will have total of 67 and 24
4) Students in Ms. Udon
science class planted 13
conifers in different places
around the school yard. They
measured the heights (in inches)
of the conifers one month after
planting them. How many
conifers are greater than 6 1/4
inches tall but less than 8 1/2
inches tall?
Answers
Considering the dot plot, the tallest conifer is 3.25 inches taller than the shortest conifer.
This shows, with dots, the number of times that each of the measures appears in a data set.
For finding the dot plot, we have that:
The shortest conifer measures 6 and 1/4
= 6.25 inches.
The tallest conifer measures 9.5 inches.
The difference is:
9.5 - 6.25 = 3.25 inches.
Therefore the tallest conifer is 3.25 inches taller than the shortest conifer.
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