The null hypothesis set up for the hypothesis test of the population parameter is given by H₀: p ≥ 0.1 .
We would set up the hypothesis test.
For the null hypothesis,
H₀: p ≥ 0.1
For the alternative hypothesis,
Hₐ: p < 0.1
This is a two-tailed test.
Taking into account the population proportion, p = 0.1 q = likelihood of failure = 1 - p
q = 1 - 0.1 = 0.9
b) In light of the sample,
P = x/n = sample proportion
Where x = the number of successes, n = the number of samples, and p = 13/100 = 0.13
The test statistic, the z score, would be calculated as z = (P - p)/pq/n z = (0.13 - 0.1)/(0.1 0.9)/100 = 1.
The determined test statistic is 1 for the right tail and - 1 for the left tail.
Since α = 0.05, the critical value is calculated using the normal distribution table.
α₂ = 0.51/2 = 0.025 on the left
The z score for an area to the left of 0.025 is - 1.96
α₂ = 1 - 0.025 = 0.975 for the right
1.96 is the z score for an area to the right of 0.975.
The test statistic must be less than - 1.96 or larger than 1.96 in order to reject the null hypothesis.
We cannot reject the null hypothesis since - 1 > - 1.96 and 1 1.96.
As a result of the hypothesis test results, Eagle Outfitter should take the promotion national.
To learn more about null hypothesis visit:
https://brainly.com/question/16261813
#SPJ4
Discuss with your own words some ways that you see religion having social control in your everyday life . Be able to cite examples?
Answer: Religion reinforces and promotes social inequality and social conflict. It helps convince the poor to accept their lot in life, and it leads to hostility and violence motivated by religious differences. This perspective focuses on the ways in which individuals interpret their religious experiences.
Step-by-step explanation:
Over 2 years, how much more does $2000 in a savings account with an APR of 5.2% compounded quarterly earn in interest than the same amount in a savings account with an APR of 4.8% compounded monthly?
A savings account with just an APR of 5.2% compounded quarterly on a balance of $2,000 will yield $16.61 more interest than a similar account with just an APR of 4.8% compounded monthly on the same balance.
Explain the term compounded monthly?Compound monthly refers to a loan's interest rate, which is charged in installments each month and added to the principle.Assume we had two different sorts of savings accounts, each with a deposit of $2,000 in it.
Account A's quarterly interest rate is 5.2%.Account B has a monthly interest rate of 4.8%.We must now determine the earnings for both accounts.
The following formula will be used to determine the earning:
Here,
v = total income,Interest rate = r (in decimal form).p is the first main value.T is the number of years overall.n is the number of compounding years.Put the values for Account A now.
5.2 % in decimal form = 5.2/100= 0.052
v = 2000 x ( 1 + (0.052/4) )^(4*2)
v = 2217.71
Total earning for account A = $ 2217.71.
For Account B:
4.8 % in decimal form = 4.8/100= 0.048
v = 2000*( 1 + (0.048/12) )^(12*2)
v = 2201.10
Total earning for account A = $ 2201.10
We will now deduct B's earnings from A's earnings to see how much more A earned than B.
2217.71 - 2201.10 = $16.61
Consequently, account A made $16.61 more so than account B.
To know more about the compounded monthly, here
https://brainly.com/question/28020457
#SPJ1
A 90-inch pipe is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.
Answer:
5x+x=90
Step-by-step explanation:
5 times the other = 5x
the other piece is x
Answer: the small pipe is 15 inches long
Step-by-step explanation: since the larger pipe is 5 times larger than the small pipe, the 90 inch pipe would have too be divided by 6 to make sure the 5 times of the large pipe and the 1 small pipe. so, you would do 90/6=15. so the small pipe is 15 inches long. the large pipe is 75 inches long.
gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. it forms a pile in the shape of a right circular cone whose base diameter and height are always equal. how fast is the height of the pile increasing when the pile is 16 feet high? recall that the volume of a right circular cone with height h and radius of the base r is given by v=(1/3)xpix(r^2)xh
The height of the pile increasing when the pile is 16 feet high is 5/32 ft/min.
We are given dV/dt=10 cubic ft/min and we want to find dh/dt. Therefore, first we need to write a formula relating v and h.
V=pi*r^2*h/3 since d=h at any moment, we know that r=h/2 at any moment and if we substitute h/2 for r, we get
V=pi(h/2)^2*h/3 and if we simplify this, we get
V=pi*(h^3)/12
Now we need to take the derivative of both sides with respect to t
dV/dt = pi * ( 3 * h^2 ) */12 * dh/dt
= pi * h^2 / 4 * dh/dt, substitute 40 for dV/dt and 16 for h and solve for dh/dt and we get
40 = pi * 16^2/4*dh/dt
dh/dt = 40 * 4 / ( 256 * pi )
= 40/(256*pi) ft/min,
= 10/64
= 5/32 ft/min
Learn more about the height here:
https://brainly.com/question/10726356
#SPJ4
Dae and Eric are working together on a paper. Dae typed 333 words in 9 minutes, and Eric typed 252 words in 6 minutes. How many more words per minute did Eric type?
Eric typed 15 words more than Dae per minute.
What is a Linear Equation?Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line. A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.
To find the amount of words typed in 1 minute for both;
Dae = 333/9
Dae = 27 words per minute
Eric = 252/6
Eric = 42 words per minute
Therefore 42 - 27 = 15 words per minute
Eric typed 15 more words per minute.
Read more about linear equations: https://brainly.com/question/2030026
#SPJ1
First try was incorrect
Evaluate the following expression when x=2 (round to the nearest tenth, if necessary)
{x}/{19}
The value of the following expression x/19 when x=2 is 0.11.
What is meant by an expression?An expression or mathematical expression is a finite arrangement of symbols that are well-formed in line with context-dependent criteria. To help define the logical grammar and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping. A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Mathematicians are proficient in addition, subtraction, multiplication, and division. An expression has the following components: an expression, a number or variable, and a mathematical operator.
Given expression is x/19
When x=2,
Then the value of the given expression is:
x/19=2/19
=0.105
≈0.11
Therefore, The value of the following expression x/19 when x=2 is 0.11.
To know more about expression, visit:
https://brainly.com/question/1859113
#SPJ1
a high school statistics class wants to estimate the average number of chocolate chips in a generic brand of chocolate chip cookies. they collect a random sample of cookies, count the chips in each cookie, and calculate a 95% confidence interval for the average number of chips per cookie (18.6 to 21.3). items 28, 29, 30 and 31 present four different interpretations of these results. indicate if each interpretation is valid or invalid. We are 95% certain that each cookie of this brand has approximately 18.6 to 21.3 chocolate chips. We expect 95% of the cookies to have between 18.6 and 21.3 chocolate chips. We would expect about 95% of all possible sample means from this population to be between 18.6 and 21.3 chocolate chips. We are 95% certain that the confidence interval of 18.6 to 21.3 includes the true average number of chocolate chips per cookie.
1. This is not wrong at all, but there is a problem. In this case, the target parameter is not mentioned. Average in this case is not the most valid conclusion.
2. Not FALSE as in option #1, but the same problem occurs if the statement does not express a conclusion about the parameter of interest (mean) in this case.
3. This is not the case at all, as the statement refers to possible samples and not confidence levels or parameters of interest. So it's not the best option in this case.
4. true average number of chocolate chips per cookie.
This is the best interpretation, because confidence levels are used to construct the intervals. The most complete answer in this case, as the result is related to the parameter of interest.
Confidence Interval:
A confidence interval is "a range of values that is likely to encompass the values of a population with some degree of confidence. Often expressed as a percentage. The error bar is the range of values above and below the sample statistic in the confidence interval
Normal Distribution:
"A probability distribution that is symmetric about the mean and indicates that data close to the mean are more common than data far from the mean."
X : represents sample mean
μ: population mean (variable of interest)
s : represents sample standard deviation
n : represents sample size
2) The mean confidence interval is given by the formula:
X ± [tex]t_{\alpha /2} \frac{s}{\sqrt{n} }[/tex] --------------------------- (1)
The 95% confidence interval obtained in this case is (18.6; 21.3)
Based on this, the statements can be analyzed individually as :
1: We are 95 years old We believe that each cookie from this brand contains approximately 18.6 to 21.3 chocolate chips.
This is not wrong at all, but there is a problem. In this case, the target parameter is not mentioned. Average in this case is not the most valid conclusion.
2: His 95% of cookies are expected to contain 18.6 to 21.3 chocolate his chips.
Not FALSE as in option #1, but the same problem occurs if the statement does not express a conclusion about the parameters of interest in this case.
3: About 95% of all possible sample means from this population are expected to be between 18.6 and 21.3 chocolate chips. This is not the case at all, as you are not referring to some parameter. So it's not the best option in this case.
4: 95% confident that the confidence interval of 18.6 to 21.3 contains the true average number of chocolate chips per cookie.
This is the best interpretation because of the confidence level used to construct the interval. The most complete answer in this case, as the result is related to the parameter of interest.
Learn more about Confidence Interval:
https://brainly.com/question/20309162
#SPJ4
Which points have a distance of 6 units between them?
Select all that apply.
A-(-12,2) and B-(-6,2)
B-(-6,2) and C-(-6-4)
C-(-6-4) and D-(6,2)
D-(6.2) and E=(6,4)
E-(64) and F=(-12.4) please help me with this
The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).
Distance between two points:The distance between two points P(x₁, y₁) and Q(x₂, y₂) is given by
Distance PQ = [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} - y_{1})^{2} }[/tex]Here we have
A (-12, 2) and B(-6, 2)
B (-6, 2) and C(-6, -4)
C (-6, -4) and D(6, 2)
D (6, 2) and E(6, 4)
E (6, 4) and F(-12, 4)
Here we will find the distance between given points to find the point which has 6 units between them.
As we know Distance = [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} - y_{1})^{2} }[/tex]
For Option A
A (-12, 2) and B(-6, 2)
Distance = √(-6 + 12)² + (2 - 2)²
= √[(6)² + (0)²] = √36 = 6
For Option B
For B (-6, 2) and C(-6, -4)
Distance = √(-6 - (-6))² + ( - 4 - 2)²
= √[(0)² + (-6)²] = √36 = 6
For Option C
For C (-6, -4) and D(6, 2)
Distance =√(6 - (-6))² + (2 - (-4))²
= √(12)² + (6)² = √180 = 6√5
For Option D
For D (6, 2) and E(6, 4)
Distance = √(4 - 2)² + ( 6 - 6)²
= √[(2)² + (0)²] = √4 = 2
For Option E
For E (6, 4) and F(-12, 4)
Distance = √(-12 - 6)² + (4 - 4)²
= √[(18)² + (0)²] = √18² = 18
Therefore,
The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).
Learn more about the Distance between two points at
https://brainly.com/question/16725736
#SPJ1
Ac is a radius diameter or chord? please help! I dont have that much time.
The line AC in the figure is the diameter of the circle also it is a chord.
What is a chord of a circle?The chord of a circle is a straight path that connects two locations on the circle's circumference. The chord is one of the line segments whose ends are on the perimeter of a circle that can be drawn.
As per the information obtained from the figure,
The line AC in the given diagram is the diameter of the circle, but it is also a chord of the circle because another definition of diameter is as a chord that runs across the center of the circle.
Note the point that every diameter can be said as a chord, but every chord cannot be the diameter of the circle.
To know more about Chord:
https://brainly.com/question/19008587
#SPJ1
identify the independent variable in the following hypothesis: interstate migration in the united states lowers state poverty levels.
The independent variable in the following hypothesis: interstate migration in the united states lowers state poverty levels is IV ( Interstate migration ) and DV ( State poverty level ) .
Given :
identify the independent variable in the following hypothesis: interstate migration in the united states lowers state poverty levels.
Independent variable :
An independent variable is exactly what it sounds like. It is a variable that stands alone and isn't changed by the other variables you are trying to measure.
Here in the given statement the independent variable is :
IV = Interstate migration
DV = State poverty level
Unit of Analysis = U.S. states
Learn more about the variable here:
https://brainly.com/question/29696241
#SPJ4
Awnser if this is a function or not yes or no please.
Answer: NO
Step-by-step explanation:
This is not a function, since there are multiple outputs for ONE input.
Answer:
no
Step-by-step explanation:
to be a function, the x's can only have one partner. Here, 7 has two partners (7 goes to 20 and also to 18) and the 11 has two partners also. This relation is not a function.
Forest Fires and Acres Burned Numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned for 7 recent years are shown. Number of fires x 69 58 47 84 62 57 72 Number of acres burned y 64 53 42 79 57 52 67 The correlation coefficient for the data is r=1 and α=0.05. Should regression analysis be done? The regression analysis should not be done. The regression analysis should be done. Find the equation of the regression line. y′=a+bx a= Find y' when x=50
The equation of the regression line is y = 4 + x and the regression analysis of the given data need not be done.
Straight line equation is y = a + bx.
The normal equations are
∑y = a·n + b ∑x ∑ xy = a ∑x + b∑x² Hence the regression analysis of the data :
The values are calculated using the following table
x y x² x⋅y
58 62 3364 3596
47 51 2209 2397
84 88 7056 7392
62 66 3844 4092
57 61 3249 3477
72 76 5184 5472
69 73 4761 5037
hence :
∑x = 449
∑y = 477
∑x² = 29667
∑x⋅y = 31463
Substituting these values in the normal equations
7a+449b=477
449a+29667b=31463
Solving these two equations using Elimination method,
7a+449b=477
and 449a+29667b=31463
7a+449b=477→(1)
449a+29667b=31463→(2)
equation(1)×449
⇒3143a+201601b=214173
equation(2)×7
⇒3143a+207669b=220241
Substracting
⇒-6068b = -6068
⇒6068b = 6068
⇒b = 1
Putting b = 1 in equation (1), we have
7a+449(1) = 477
⇒7a = 477 - 449
⇒7a = 28 or a = 4.
Now Estimate y for x=50
y = a + bx , we get
y = 4 + 1×50
y = 4 + 50
y = 54
At x equals 50 we get the value of y as 54 .
To learn more about regression line visit:
https://brainly.com/question/7656407
#SPJ4
Select the correct symbol.
9.48 ? 9.480
The 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5
What is meant by Inequality expressions?An algebraic inequality is a mathematical statement that uses the inequality sign to connect an expression to a value, a variable, or another expression.
Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols, >,,, and. has the connotation "7 is greater than" (or "is less than 7," when read left to right).
Given the incomplete expression
1 1/4 × 2 1/5 _ 5/6 × 2 1/5
We are to fill it with the necessary inequality sign
For the expression:
1 1/4 × 2 1/5 = 5/4 * 11/5
1 1/4 × 2 1/5 = 55/20
1 1/4 × 2 1/5 = 2 3/4
For the expression 5/6 × 2 1/5
5/6 × 2 1/5 = 5/6 * 11/5
5/6 × 2 1/5 = 55/30
5/6 × 2 1/5 = 1 25/30
Since 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5
The complete question is : Select the correct symbol to compare the expressions below.
1 1/4 × 2 1/5 _ 5/6 × 2 1/5
Symbols: <, >, =
To learn more about inequality expression refer to :
https://brainly.com/question/25275758
#SPJ1
help!!
find the measures of each angle
The measures of angles x, y and z are 40°, 50° and 130° and measures of the segments are AY = 16, IY = 9, FG = 30, AP = 24
What is centroid?Centroid is the point in a triangle where all the medians of the triangle intersects.
Given are two triangles, in first we have to find the missing angles and in the second one we need to find the asked segments,
1) We know that, in a right triangle, one angle is 90° and the sum of other two sides is 90°,
Therefore, 40°+y = 90°
y = 50°
x+y = 90°
x = 90°-50°
x = 40°
z = 180°-50° (linear pair)
z = 130°
2) we know that, the centroid divides the medians into 2:1
AY = 2YP
AY = 16
IY = TY/2
IY = 9
FG = GY+YF (segment addition postulate)
GY = YF/2
GY = 10
FG = 10+20 = 30
PA = AY+YP (segment addition postulate)
PA = 8+16
PA = 24
Hence. the measures are x, y and z are 40°, 50° and 130° and AY = 16, IY = 9, FG = 30, AP = 24
For more references on centroid, click;
https://brainly.com/question/10708357
#SPJ1
Simplify (x − 4)(4x2 + x − 6).
Answer: To simplify the expression (x - 4)(4x^2 + x - 6), you can use the distributive property, which states that you can multiply a number or expression by each term inside a set of parentheses.
Here is the process for simplifying the expression:
Multiply the first term, "x - 4", by the first term inside the second set of parentheses, "4x^2": (x - 4)(4x^2) = 4x^3 - 16x^2
Multiply the first term, "x - 4", by the second term inside the second set of parentheses, "x": (x - 4)(x) = x^2 - 4x
Multiply the first term, "x - 4", by the third term inside the second set of parentheses, "-6": (x - 4)(-6) = -6x + 24
Add the three products together: 4x^3 - 16x^2 + x^2 - 4x - 6x + 24 = 4x^3 - 16x^2 + x^2 - 10x + 24 = 4x^3 - 15x^2 - 10x + 24
The simplified expression is: 4x^3 - 15x^2 - 10x + 24
So, (x - 4)(4x^2 + x - 6) = 4x^3 - 15x^2 - 10x + 24.
60 POINTS!!! As a special promotion for its 12-ounce cans of cold coffee, a coffee drink company printed a message on the bottom of each can. Some of the bottoms read, "Better luck next time!" whereas others read, "You won!" The company advertised the promotion with the slogan "One in five wins a prize!" Suppose the company is telling the truth and that every 12-ounce can of coffee has a one-in-five chance of being a winner. Six friends each buy one 12-ounce can of coffee at a local convenience store. Let X equal the number of friends who win a prize.
Part A: Explain why X is a binomial random variable.
Part B: Find the mean and standard deviation of X. Interpret each value in context.
Part C: The store clerk is surprised when two of the friends win a prize. Is this group of friends just lucky, or is the company's one-in-five claim inaccurate? Compute P(X ≥ 2) and use the result to justify your answer.
A) Yes, X is a binomial random variable because all of the requirements for a binomial distribution have been established
B) The mean and standard deviation are respectively; 1.2 and 0.6
C) The probability given as P(X ≥ 2) is 0.34464
How to solve binomial probability distribution?The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.
The general formula of binomial probability distribution is;
P(X = x) = nCr * p^(x) * (1 - p)^(n - x)
where;
p = probability of "success"
n = number of trials, or the sample size
x = the number of "successes" in the probability we are trying to calculate.
A) We are told that 6 friends each buy one 12-ounce bottle of the soda at a local convenience store. Let X = the number who win a prize.
Probability of success; p = 1/5
Number of events; n = 6 which is the random variable being binomial random variable:
There are two types of accomplishments: successes and failures.
Candies are unrelated to one another.
There is a set number of buddies available.
In addition, the chance of success is fixed.
Because all of the requirements for a binomial distribution have been established, then it is a binomial probability distribution.
B) The formula for the mean here is;
μ = np
Plugging in the relevant values gives;
μ = 6(1/5) = 1.2
Formula for the standard deviation is;
σ = √(np(1 - p))
Thus;
σ = √(6 * 1/5)(1 - (1/5)))
σ = 0.6
C) The probability P(X ≥ 2) calculated with online binomial probability calculator gives;
P(X ≥ 2) = 0.34464
Read more about Binomial Probability Distribution at; https://brainly.com/question/9325204
#SPJ1
Andreas has $18. Bonnie has 1 2/3 times as much as Andreas. Cheryl has 1 3/5 times as much as Bonnie.
How much money do
they have altogether?
I'm not sure what the reasoning is
The reasons that complete the statements are:
Statement 2: GivenStatement 4: SAS congruence propertyHow to determine the reasons that complete the statementsFrom the question, we have the following parameters that can be used in our computation:
Triangles = RST, and TUR
From the question, we have the following given parameters
∠SRT ≅ ∠UTR
This means that
Statement 2: ∠SRT ≅ ∠UTR ------ Given
At this point, we have
RS ≅ TU --- Congruent side (S)
∠SRT ≅ ∠UTR ------ Congruent angle (A)
RT ≅ TR --- Congruent side (S)
When these congruent sides and angles are combined, we have
SAS congruence property
The SAS congruent theorem implies that the corresponding sides of the triangles in question are congruent and the angles between the corresponding sides are also congruent
Hence, the additional information on the congruency of the triangles are Given and SAS congruence property
Read more about congruent triangles at
brainly.com/question/1675117
#SPJ1
A random sample of 115 observations results in 46 successes. Use Table 1.
a. Construct a 90% confidence interval for the population proportion of successes. (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answers to 3 decimal places.)
Confidence interval to
b. Construct a 90% confidence interval for the population proportion of failures. (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answers to 3 decimal places.)
Confidence interval to
Option a) 90% confidence interval for the population proportion of successes = 0.402
Option b) 90% confidence interval for the population proportion of failures = 0.598
According to the question given,
Critical values of Standard deviations are to be used to construct the proportions for the confidence interval.
The formula of a confidence interval that we will be using for the solution will be,
p = [tex]z_{a} * \sqrt{\frac{p(1-p)}{n} }[/tex]
In the above expression,
p = observed population.
n = sample size
[tex]z_{a}[/tex] = critical value of confidence interval
Now the given observations in question = 115
That result in success = 46
The resultant sample proportion = [tex]\frac{46}{115}[/tex]
⇒ 0.40 and it is for both success and failure
Here we can see that the answer for both parts will be identical.
The critical value of z at 90% confidence = 1.64
a) Lower bound = [tex]0.4 - 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]
⇒ 0.402
b) Upper bound = [tex]0.4 + 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]
⇒ 0.598
Confidence interval = 0.402 to 0.598
Therefore,
Option a) 90% confidence interval for the population proportion of successes = 0.402
Option b) 90% confidence interval for the population proportion of failures = 0.598
To know more about Probability,
https://brainly.com/question/17097944
#SPJ4
When you are testing hypotheses by using proportions, what are the necessary requirements? OA. np 25 and nq 25 ?B.np < 5 and nq < 5 C. The population standard deviation is unknown. D. p
The following conditions must be met in order to test hypotheses using proportions: np ≥ 5 and nq ≥ 5
To test hypotheses using proportions, the following requirements are necessary:
np ≥ 5 and nq ≥ 5: It is necessary to have a sufficient number of samples in each group being compared.
The rule of thumb is to have at least 5 observations in each group, where n is the sample size and p is the proportion in that group.
This ensures that the sampling distribution of the proportion is approximately normal, which is necessary for hypothesis testing.
Hence, the correct answer would be an option (A).
To learn more about the hypothesis here:
https://brainly.com/question/18064632
#SPJ1
What is the 3rd term of (4 - 5g)??
0896000g²
O 21g²
O-1050000g5
O 537600g2
The 3rd term of (4 - 5g) is -1050000g5
What does the term "arithmetic sequence" mean?An arithmetic sequence is a set of integers that are ordered and have a common difference between each following word. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
It is simple to establish a series by starting with a number and repeatedly adding a fixed constant (d). An arithmetic sequence is this kind of sequence.
Given,
(4 - 5g) simplifying
-1
So that is -1050000g5
The 3rd term of (4 - 5g) is -1050000g5
To learn more about arithmetic sequence refer to :
https://brainly.com/question/28369191
#SPJ1
The sum of two forces, one having a magnitude of 9 N acting due east and other having a magnitude of 4 N acting due north is _ _ _ _ _.
The sum of two forces, one having a magnitude of 9 N acting due east and other having a magnitude of 4 N acting due north is 9.85 N.
One of the forces is of magnitude 9 N acting due east
The second force is of magnitude 4 N acting due north
Therefore, the sum of the two forces (say F1 and F2) will be the resultant of the two forces,
that is: sqrt ( (F1) ^ 2 + (F2) ^ 2)
= sqrt ( (9) ^ 2 + (4) ^ 2) = sqrt (97) = 9.8488 N ≈ 9.85 N
To know more about forces:
https://brainly.com/question/10934010
#SPJ4
C d Question 13 (1 point) Spheres A and B are similar. The volume of Sphere A x 27 = the volume of Sphere B How many times greater is the radius of sphere A? b The surface area and the base Od 16 3 4 27
I will give brainliest to anyone who answers.
The radius of the sphere B is 3 times greater than the radius of the sphere A or radius of the sphere A is 1/3 times greater than the radius of the sphere B.
What is Sphere?A sphere is a three dimensional shape formed by the set of all points which are at equidistance from a point called the center of the sphere.
Volume of a sphere = [tex]\frac{4}{3}[/tex] π r³
Let the volume and radius of sphere A is V₁ and r₁ respectively and the volume and radius of sphere B be V₂ and r₂ respectively.
We have,
V₁ × 27 = V₂
[tex]\frac{4}{3}[/tex] π r₁³ × 27 = [tex]\frac{4}{3}[/tex] π r₂³
Common terms [tex]\frac{4}{3}[/tex] π get cancelled.
⇒ 27r₁³ = r₂³
⇒ r₁³ / r₂³ = 1 / 27
Taking cube root on both sides,
⇒ r₁ / r₂ = 1 / 3
⇒ 3r₁ = r₂
⇒ r₁ = [tex]\frac{1}{3}[/tex] r₂
Hence the radius of the sphere A is 1/3 times greater than the radius of the sphere B.
To learn more about Sphere, click:
https://brainly.com/question/11374994
#SPJ1
Solve for y. y = 2 · 32 ÷ 3 Responses A 25325 3 B 1212 C 22 D 6
The value of y is 21.3333. And from the options, 21.3333 is closest to 22.
So, the correct option is C. 22.
What is an expression?A term is composed of one mathematical expression. A single variable (a letter), a single integer (positive or negative), or a number of variables that have been multiplied but never added or subtracted are all examples of single variables. There is a number in front of certain words that are variables. When a phrase is used, a coefficient is given.
We have the expression,
y = 2 · 32 ÷ 3
Simplifying,
y = 2 x 32 ÷ 3
To solve for y:
Using PEMDAS,
the abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations.
P is for "parentheses,"
E is for "exponents,"
M is for "multiplication,"
D is for division,
A is for addition,
and S is for subtraction.
y = 2 x 32 ÷ 3
Firstly, we multiply the number,
y = 64 ÷ 3
Now, the division,
y = 21.3333
Therefore, the value of y is 21.3333.
To learn more about the expression;
brainly.com/question/24242989
#SPJ1
please answer this is a final
[tex]a_n = 11n + 91[/tex] is the nth term arithmetic progression for the following term.
What is arithmetic progression?The difference between any two successive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.
For instance, the sequence 1, 2, 3, 4, 5, 6,... The standard progression in mathematics is a, (a + d), (a + 2d), and (a + 3d).
Given that,
the first five terms given in the table with position.
Denoted as: a₁ = 102, a₂ = 113, a₃ = 124, a₄ = 135, and a₅ = 146
Thus, the nth term for the arithmetic sequence is given as:
[tex]a_n = a_1 + (n-1)d[/tex]
here, d = (113-102) = 11
[tex]a_1 = 102[/tex]
d is the common difference
So, [tex]a_n = 102 + (n-1)11[/tex]
or, [tex]a_n = 102 +11n-11[/tex]
or, [tex]a_n = 11n + 91[/tex]
To know more about arithmetic progression refer to:
https://brainly.com/question/6561461
#SPJ1
Suppose that in an election voter preference is sharply divided along gender lines. 60% of women will vote for Candidate J, the rest will vote for Candidate K; 30% of men will vote for Candidate J, the rest for Candidate K. Which of the following represents the lowest percentage of voters that must be women on election day, in order that Candidate J wins the election?
* 65%
* 67%
* 69%
* 71%
* 73%
By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.
What exactly is a ratio ?A percentage is a component of a total amount, and the three-step rule is used to relate the measurements.
The percentage of voters who select Candidate J is:
60% of x are voters are female
30% of (1 - x), who vote are male
If the total of these percentages is larger than 50% = 0.5, Candidate J will be elected; therefore:
0.6x + 0.3(1 - x) > 0.5
0.6x + 0.3 - 0.3x > 0.5
0.3x > 0.2
x > 2/3
x > 0.667
x > 67%
By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.
To know more about Proportions
https://brainly.com/question/13419413
#SPJ1
A student completes ⅘ of a math project in ⅔ hour. If the student continues at the same rate, how long will it take the student to complete the project?
The number of hours it will take the student to complete the project is 5 / 6 hours.
How to find the time the project will be completed?A student completes ⅘ of a math project in ⅔ hour. If the student continues at the same rate, the time it will take the student to complete the project can be calculated as follows:
Therefore,
let
x = time it will take the student to complete the project
Hence
if 4 / 5 x = 2 / 3 hours
x = ? hours
cross multiply
Therefore,
number of hours to complete the whole math project = x × 2 / 3 ÷ 4 / 5 x
number of hours to complete the whole math project = 2 / 3 x × 5 / 4x
number of hours to complete the whole math project = 10x / 12x
number of hours to complete the whole math project = 10 / 12
number of hours to complete the whole math project = 5 / 6 hours
learn more on rate here: https://brainly.com/question/26053073
#SPJ1
52% of 70
what is the answer
Answer: 36.4
Step-by-step explanation:
Just convert the percentage to decimal and multiply.
70 x 0.52 = 36.4
For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). A portion of the regression results is as follows. Use Table 2 and Table 4.
ANOVA df SS MS F Significance F
Regression 2 188,246.8 94,123.4 9.04E-07
Residual 17 45,457.32 2,673.96 Total 19 233,704.1 Coefficients Standard Error t Stat p-value Lower 95% Upper 95%
Intercept −301.62 549.7135 −0.5487 0.5903 −1,461.52 858.28
Poverty 53.1597 14.2198 3.7384 0.0016 23.16 83.16
Income 4.9472 8.2566 0.5992 0.5569 −12.47 22.37
a. Specify the sample regression equation. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
11formula272.mml = + Poverty + Income
b-1. Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related.
H0: β1 ≥ 0; HA: β1 < 0
H0: β1 ≤ 0; HA: β1 > 0
H0: β1 = 0; HA: β1 ≠ 0
b-2. At the 5% significance level, what is the conclusion to the test?
Reject H0; the poverty rate and the crime rate are linearly related.
Reject H0; the poverty rate and the crime rate are not linearly related.
Do not reject H0; we can conclude the poverty rate and the crime rate are linearly related.
Do not reject H0; we cannot conclude the poverty rate and the crime rate are linearly related.
c-1. Construct a 95% confidence interval for the slope coefficient of income. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
Confidence interval to
c-2. Using the confidence interval, determine whether income influences the crime rate at the 5% significance level.
Income is significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero.
Income is not significant in explaining the crime rate, since its slope coefficient significantly differs from zero.
Income is significant in explaining the crime rate, since its slope coefficient significantly differs from zero.
Income is not significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero.
d-1. Choose the appropriate hypotheses to determine whether the poverty rate and income are jointly significant in explaining the crime rate.
H0: β1 = β2 = 0; HA: At least one β j < 0
H0: β1 = β2 = 0; HA: At least one β j > 0
H0: β1 = β2 = 0; HA: At least one β j ≠ 0
d-2. At the 5% significance level, are the poverty rate and income jointly significant in explaining the crime rate?
Yes, since the null hypothesis is rejected.
Yes, since the null hypothesis is not rejected.
No, since the null hypothesis is rejected.
No, since the null hypothesis is not rejected.
Answer: You must give more points for questions that are this long
sincerely,
A Friend
Step-by-step explanation:
Suppose that the daily number of miles driven per school bus driver in the United States is normally distributed with a mean of 300 mi and standard deviation equal to 26 mi. A local school bus budget committee believes the daily number of miles driven per bus driver in their community is different from 300 mi, but they are not sure if it is greater than or less than the national average.
To test their hypothesis, the committee chooses a random sample of 40 school bus drivers and records how many miles each of them drives per day during a typical week. On average, the bus drivers from the sample drive 309 mi per day. To test the hypothesis that the average number of miles driven by local bus drivers is different from the national average, the budget committee calculates the z-statistic to be 2.19 standard deviations above the population mean.
Use the standard normal z-distribution table to calculate the P-value that represents the probability of mistakenly rejecting the claim that the daily number of miles driven by local bus drivers is not statistically different from the national average. Give your answer as a decimal rounded to four places.
P-value:
The p-value for the z-distribution table is 0.4854.
What is z-distribution?
A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardise it. Z scores provide the number of standard deviations from the mean that each value falls within.
Given that the z statistic to be 2.19 standard deviation above the population mean.
2.19 can be written as 2.1 + 0.09
Z₂.₁₉ = Z₂.₁₊₀.₀₉ = 0.4854
Therefore p-value is 0.4854.
To learn more about p-value, click on below link:
https://brainly.com/question/14790912
#SPJ1
