The population grows according to the recursive rule is-
Pn = 60 + n×80P100 = 8060Explain the term recursive rule?A recursive rule provides the first term and terms of the a sequence and uses a recursive equation to show how each term relates to the term(s) before it. Sequences in mathematics and geometry, for instance, can be represented recursively.For the stated question-
initial population p0 = 60recursive rule pn = p(n − 1) + 80Then,
P1 = P0 + 80
P1 = 60 + 80 = 140
P2 = P1 + 80
P2 = 140 + 80 = 220
Thus, an explicit formula for the population
Pn = P0 + n×80 = 60 + n×80
P100 = 60 + 100×80 = 8060
Thus, explicit formula for the population growth is
To know more about the recursive rule, here
https://brainly.com/question/7320653
#SPJ4
The complete question is-
Consider a population that grows according to the recursive rule pn = p
(n − 1) + 80 , with initial population p0 = 60
Find an explicit formula for the population. Your formula should involve n (use lowercase n)
Pn=
Use your explicit formula to find
P100 =
Hi I need some help! This is algebra work btw
The solution to the system of equation y = - 2x - 7 and 9x - 10y = 12 is,
x = - 2 and y = - 3.
What are the types of solutions for a system of linear equations?If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.
Substitution in mathematics is when we replace some specific numerical values with variables according to our wants or given in the problem.
Given, Are two linear equations y = - 2x - 7 and 9x - 10y = 12.
Therefore,
9x - 10y = 12.
9x - 10(- 2x - 7) = 12.
9x + 20x + 70 = 12.
29x = - 58.
x = - 2 and hence y = - 2(-2) - 7 ⇒ y = - 3.
learn more about substitution here :
https://brainly.com/question/18330729
#SPJ1
Victoria deposited $5000 into a savings account that earns an annual simple interest rate of 0.3%. To the nearest tenth of a year, how long will it take for the account to reach $5500?
The account, will reach $5500 in 33.33 years. if Victoria deposits $5000 into a savings account.
What exactly is simple interest?The direct crediting of cash flows associated to an investment or deposit is referred to as simple interest. Simple interest is a quick and straightforward way to calculate the interest amount on a loan. Simple interest is calculated by multiplying the daily interest rate by the principle by the number of days between payments.
The written formula is "Simple Interest = Principal x Interest Rate x Time." This is the most fundamental method of calculating interest.
Victoria deposited $5000 into a savings account with an annual basic interest rate of 0.3%.
Simple Interest Formula
A = P(1 + rt)
5500 = 5000(1 + 0.003t)
5500 = 5000 + 15t
15t = 500
The account will reach $5500 in 33.33 years.
To know more about simple interest, visit,
https://brainly.com/question/25845758
#SPJ1
Which pairs of figures are congruent? Which pairs are similar?
Answer:
Step-by-step explanation:
B becuase the way the angle is
a.write an equation to model the relationship
b.explain how you know if an equation or a graph represents a proportional relationship
Answer:
a) 12 · y = x
b) If the points show equivalent fractions and the line goes through (0,0)
Step-by-step explanation:
a1) divide any numbers from the x and y line (for example, 2 ÷ 24 would give us 12)
a2) This equation makes sense because any number from the x line (for example, 2) multiplied by 12 would give us the number from the y line (in this example, 24).
the area of a rectangle is 17.6 square centimeters. find the value of x when the length of the rectangle is x 2.3 and the width is x.
The width of the rectangle, x is 2.76 cm
Given,
The area of a rectangle = 17.6 square centimeters
Length of the rectangle = 2.3x
Width of the rectangle = x
We have to find the value of x.
Here,
Area of rectangle = length × width
Then,
17.6 = 2.3x × x
17.6 = 2.3x²
x² = 17.6/2.3
x² = 7.65
x = √7.65
x = 2.76
Now,
Width of the rectangle = 2.76 cm
Length of the rectangle = 2.76 × 2.3 = 6.35 cm
Therefore,
The value of x, that is the width of the rectangle is 2.76 cm
Learn more about area of rectangle here;
https://brainly.com/question/20693059
#SPJ4
To explain that the expression 20m−60n+20 can be written as 20(m−3n), John first factors 20m as 20 ⋅ m and 60n as 20 ⋅ 3n, and leaves 20 unchanged. Then, he factors 20 from each term of the expression 20m−60n+20 and puts the remaining factors together within a pair of brackets.
• Explain why John’s reasoning is incorrect.
• Factor 20m−60n+20
• Explain how you found the answer.
The expression 20 m−60 n+20 can be written as 20(m−3 n +1).
What is the equation?
The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Given expression,
20 m−60 n+20
can be factorized as
20(m−3 n +1).
A) John’s reasoning is incorrect because he has not included the constant term in the expression.
B) 20 m−60 n+20 can be factorized as 20(m−3n +1).
C) The expression can be factorized by taking common from each and every term of the expression.
Therefore,The expression 20 m−60 n+20 can be written as 20(m−3 n +1).
Learn more about the equation here:
brainly.com/question/10413253
#SPJ2
Math
Omar opened a savings account and deposited $800.00. The account earns 6% interest,
compounded annually. If he wants to use the money to buy a new bicycle in 2 years, how
much will he be able to spend on the bike?
A
Round your answer to the nearest cent.
$
Recommendations
Answer:
898.88
Step-by-step explanation:
if you multiply 800 by 1.06, then multiply that answer by 1.06, you get 898.88
about 22% of the population of a large country is allergic to pollen. if two people are randomly selected, what is the probability that both will be allergic to pollen? (round your answer to two decimal places) what is the probability that at least one person is allergic to pollen? (round your answer to two decimal place
The probability that both will experience allergies to pollen is 0.0484, and the probability that at least one will is 0.9516.
The following information is provided in the question:
A large country has a pollen allergy rate of about 22%.
As a result, the probability of people has a chance of having an allergy is 0.22.
P(allergic) = 0.22
P(Not allergic) = 1 - 0.22 = 0.78
If A and B are independent even, then,
P(A∩B) = P(A) × P(B)
Two people are randomly selected.
a) P( both will be allergic to pollen)
Since these are independent events,
P(both will be allergic to pollen)= P(allergic)*P(allergic)
= 0.22*0.22 = 0.0484
b) P(at least one person is allergic to pollen)
= 1 - P(both are not allergic to pollen)
= 1 - P(P(not allergic)*P(not allergic))
= 1 - (0.22*0.22)
= 0.9516
To learn more about probability, visit the link below:
brainly.com/question/15102803
#SPJ4
The number 100 went into a machine (input), and
after an increase of 60%, a number came out
(output).
What number was output of the machine?
Answer:
outpot=160
Step-by-step explanation:
outpot= 100+ 100×0.6=160
a sample of 60 information system managers had an average hourly income of $45.80 with a standard deviation of $7.00. what is the lower limit for the 95% confidence interval estimate for the average hourly wage of all information system managers? round your answer to two decimal places.
The lower limit for the 95%confidence interval for the given mean and standard deviation is equal to 39.03.
As given in the question,
Sample size 'n' = 60
Mean 'μ' = $40.80
Standard deviation 'σ' = $7.00
Using z-score table of normal distribution
z-value for 95%confidence interval = 1.96
Formula used
Confidence interval
= μ ± ( z-value × σ ) /√n
= 40.80 ± (1.96 × 7)/√60
= 40.80 ± (13.72 /7.75)
= 40.80 ±1.770
Lower limit of the confidence interval is equal to :
40.80 - 1.770 = 39.03
Upper limit of the confidence interval is equal to :
40.80 + 1.770 = 42.57
Therefore, the lower limit for the 95% confidence interval is equal to 39.03.
Learn more about lower limit here
brainly.com/question/13531591
#SPJ4
Slope of line that passes through (2,7) and (-4,19)
To calculate the slope of the line, we have that its points are A(x₁, y₁) and B(x₂,y₂), we apply the following formula:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{\Delta y}{\Delta x} \iff m=\frac{y_2-y_1}{x_2-x_1} } \end{gathered}$}}[/tex]
To solve, we have that the points are:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{A(x_1=\underbrace{2} \ \ , \ \ y_1=\overbrace{7} \ ) \ and \ B(x_2=\underbrace{-4} \ \ , \ \ y_2=\overbrace{19} } \end{gathered}$}}[/tex]
What we do to solve is that we substitute this data in the formula provided above.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\dfrac{y_2-y_1}{x_2-x_1} } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{19-7}{-4-2} } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{12}{-6}=-2 } \end{gathered}$}}[/tex]
The slope of the line that passes through (2,7) and (-4,19) is -2.a rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). what dimensions should be used so that the enclosed area will be a maximum?
The dimensions that need to be used so that the enclosed area of the two adjacent rectangular corrals will be maximum is 90 by 120 feet.
What do you mean by adjacent?
Adjacent refers to something that is close to or nearby. Your next-door neighbor is the person who lives in the home or apartment that is next to yours, even though you may consider the individuals who live up and down your street to be your neighbor.
Two things can be considered adjacent if they contact each other or share a wall or border. If two angles in geometry share a side and a vertex, they are said to be adjacent. In other words, neighbor angles do not overlap and are adjacent to each other immediately.
Solution Explained:
So according to the question, we get the equation
Perimeter is 4x + 3y = 720
⇒ x = 180 - [tex]\frac{3}{4}y[/tex]
Taking Area = 2xy
= 2(180 - [tex]\frac{3}{4} y[/tex])y
= 360y - [tex]\frac{3}{2} y^{2}[/tex]
Differentiating the function w.r.t y
A'(y) = 360-3y
Setting to 0
0 = 360 - 3y
⇒ y = 360 / 3 ⇒ 120
Now putting the value of y in
x = [tex]180- \frac{3}{4} X 120[/tex]
x = 180 - 90 = 90
So, the dimensions are 90 by 120 feet.
To learn more about adjacent, use the link given
https://brainly.com/question/25713164
#SPJ4
a student began his part ii titration with an air bubble in the buret tip. the bubble was released, unnoticed, at some point during the titration. briefly describe the error that the bubble would have caused in his titration results if: (a) the bubble had been released prior to the equivalence point of the titration. (b) the bubble had been released after the equivalence point.
Part a: The volume of such base would appear to be larger than it was if the bubble was already let go before the titration's equivalence point.
Part b: There would be no impact if the bubble had already been let go after the equivalent point.
Explain the term titration?A titration is a method for figuring out the concentration of an unidentified solution by using a solution with known concentration. Until the reaction is finished, the titrant (the known solution) is typically added from just a buret to a known volume of the analyte (this same unknown solution).For the stated condition-
An air bubble was present in the buret tip as the student started his part II titration. Unnoticed bubble release occurred at some point in the titration.
The inaccuracy in his titration findings that the bubble would've have made if:
Part a: If the bubble had burst before the titration's equivalence point, the base's volume would have appeared larger than it originally was, having the base seem stronger than it is, and changing calculations.
Part b: There would be no impact if the bubble had already been let go after the equivalent point.
To know more about the titration, here
https://brainly.com/question/15170788
#SPJ4
Determine if the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. Select true or false for each statement. This set is closed under scalar multiplications This set is a subspace This set is closed under vector addition The set contains the zero vector
If the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. The statement: This set is closed under scalar multiplications This set is a subspace .This set is closed under vector addition The set contains the zero vector is False.
Vector:A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity.
Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight. A quantity or phenomenon that exhibits magnitude only, with no specific direction, is called a Scalar . Examples of scalars include speed, mass, electrical resistance, and hard-drive storage capacity.
Scalar Multiplication:Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and is to be distinguished from inner product of two vectors (where the product is a scalar).
For quaternion scalars and matrices:
λ = 2 A = [tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
2A = 2[tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}2a&2b\\2c&2d\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}a.2&b.2\\c.2&d.2\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex] × 2 = A2
Subspace:In mathematics, and more specifically in linear algebra, a linear subspace, also known as a vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces.
Learn more about Scalar Multiplication:
https://brainly.com/question/8349166
#SPJ4
n this scenario, what is the test statistic? a business loan broker would like to test the claim that the average small business loan is different than 20 thousand dollars. sample size
The test statistic results for that scenario is -1.5.
How to calculate test statistic?Simplified the calculation by eliminating thousands of dollars.
[tex]\bar x[/tex] = sample mean = 18.5
s = sample standard deviation = 5
n = sample size = 25
[tex]\mu_{0}[/tex] = population mean for the null hypothesis = 20
Since the question provide us a test statistic formula. So,
[tex]t_{0}[/tex] = [tex]\frac{\bar x - \mu_0}{\frac{s}{\sqrt{n}}}[/tex]
= [tex]\frac{18.5 - 20}{\frac{5}{\sqrt{25}}}[/tex]
= [tex]\frac{-1.5}{\frac{5}{5}}[/tex]
= -1.5 / 1
= -1.5
Thus, the result for test statistic in that scenario is -1.5.
Your question is incomplete, but most probably your full question was (image attached)
Learn more about test statistic here:
brainly.com/question/29543821
#SPJ4
In Wednesday 36%of the customer who bought at a gas station ñ.made additional purchase.there was 225 customers who bought doughnuts
There were a total of 625 customers who bought at a gas station on Wednesday
How to determine the total number of customers?From the question, we have the following parameters that can be used in our computation:
Number of customers that purchase doughnuts = 225
Proportion of customers who made additional purchase = 36%
The above parameters mean that:
Proportion of customers who made additional purchase = 36% of The total number of customers
Using the above as a guide, we have the following equation
36% * The total number of customers = 225
Divide both sides by 36%
The total number of customers = 625
Hence, the total number of customers is 625
Read more about proportions at
https://brainly.com/question/16828793
#SPJ1
Help please 17. G(9)+h(-14)
Answer:
15
Step-by-step explanation:
Given functions:
[tex]g(x)=14-\dfrac{2}{3}x[/tex]
[tex]h(x)=-x-7[/tex]
g(9) means to substitute x = 9 into function g(x):
[tex]\begin{aligned}\implies g(9)&=14-\dfrac{2}{3}(9)\\&=14-\dfrac{18}{3}\\&=14-6=8\end{aligned}[/tex]
h(-14) means to substitute x = -14 into function h(x).
[tex]\begin{aligned}\implies h(-14)&=-(-14)-7\\&=14-7\\&=7\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\implies g(9)+h(-14)&=8+7\\&=15\end{aligned}[/tex]
As one calculation:
[tex]\begin{aligned}\implies g(9) + h(-14)&=\left(14-\dfrac{2}{3}(9)\right)+\left(-(-14)-7\right)\\&=\left(14-\dfrac{18}{3}\right)+\left(14-7\right)\\&=\left(14-6\right)+\left(14-7\right)\\&=8+7\\&=15\end{aligned}[/tex]
a. Lin is using the diagram to prove the statement, "If a parallelogram has one
right angle, it is a rectangle." Given that EFGH is a parallelogram and angle
HEF is a right angle, write a statement that will help prove angle FGH is also
a right angle.
b. Han then states that the 2 triangles created by diagonal BG must be congruent.
Help Han write a proof that triangle EHG is congruent to triangle GFE.
The congruence of the angles and triangles are proven as follows;
a. The composition angles of FGH are alternate interior angles to the composition angles of angle AHEF
b. The three sides of triangle ∆EHG are congruent to the three sides of triangle ∆GFE, therefore, triangles ∆EHG and ∆GFE are congruent by SSS congruency rule
What are congruent triangles?The lengths of the three sides of triangles that are congruent.
a. The shape of quadrilateral EFGH = A parallelogram
The measure of angle HEF = 90°
Angle HEF = 90°
Angle HEF = Angle HED + Angle DEF
Angle HED is congruent to angle FGD (Alternate interior angles theorem)
Angle HED = angle FGD
Angle DEF is congruent to angle DGH (Alternate interior angles theorem)
Angle DEF = angle DGH
Angle FGH = Angle FGD + Angle DGH
Angle FGH = Angle HED + Angle DEF (Substitution property)
Angle FGH = Angle HEF (Transitive property)
Angle FGH = Angle HEF = 90°
Therefore, the statement that will help prove angle FGH is also a right is that angle FGH is the sum of angles FGD and angle DGH which are alternate interior angles to angles HED and DEF which makes up angle HEF, which is a right angle.
b. The two-column method can be used to prove that triangle EHG and triangle GFE are congruent as follows;
Statement. Reason
EF is congruent to HG. Opposite sides of a parallelogram are congruent
EH is congruent FG Opposite sides of a parallelogram are congruent
EG is congruent to EG Reflexive property of congruency
∆EHG is cong. to ∆GFE SSS, Side-Side-Side, congruency rule
Learn more about the triangle congruency rules here:
https://brainly.com/question/15338506
#SPJ1
Four decimal numbers that have an even number in the tenths place, an odd number in the hundredths place, and a prime number in the thousandths place.
The decimal numbers that have an even number in the tenths place, an odd number in the hundredths place, and a prime number in the thousandths place include 0.237, 0.893, 0.475, and 0.652.
What is the definition of an even number?An even number is any number that can be divided exactly by two. Even numbers always have a last digit of 0, 2, 4, 6, or 8. Even numbers include 2, 4, 6, 8, 10, 12, 14, and 16.
Odd numbers are those that cannot be divided evenly by two. It cannot be evenly divided into two separate integers. When we divide an odd number by 2, we get a remainder. Odd numbers include 1, 3, 5, 7, and so on.
A prime number is a natural number greater than one that cannot be calculated as the product of two smaller natural numbers. A composite number is a natural number greater than one that is not prime. 5 is prime, for example, because the only ways to write it as a product, 1 5 or 5 1, involve 5 itself.
A prime number is a whole number greater than one with only the number one and itself as factors. A factor is a whole number that can be divided into other numbers evenly.
In this case, 0.237, 0.893, 0.475, and 0.652 have an even number in the tenths place which is the first place after the decimal point. Also, there's an odd number in the hundredths place, and a prime number in the thousandths place.
Learn more about prime numbers on:
https://brainly.com/question/881160
#SPJ1
Complete question
Write four decimal numbers that have an even number in the tenths place, an odd number in the hundredths place, and a prime number in the thousandths place
help guys can you help me
Answer:
Help guys can you help me
B) Find the measure of the indicated angle in each rhombus.
Answer:
4) ∠J = ∠L = 88°; ∠K = 92°
5) ∠P = ∠R = 34°; ∠S = 146°
6) ∠T = 54°; ∠U = ∠W = 126°
Step-by-step explanation:
You want the remaining angles in each rhombus where one angle is specified.
Angle relationsIn a rhombus, as in any parallelogram, opposite angles are congruent, and adjacent angles are supplementary.
ApplicationIn each of the rhombi, the adjacent angle is supplementary:
4) 180° -92° = 88°
5) 180° -146° = 34°
6) 180° -54° = 126°
Then the angle measures of interest are ...
4) ∠J = ∠L = 88°; ∠K = 92°
5) ∠P = ∠R = 34°; ∠S = 146°
6) ∠T = 54°; ∠U = ∠W = 126°
Is 3x 1/2 = 3 true or false?
Answer:
Step-by-step explanation:
true
use a binomial model to calculate the probability that, in a random sample of 100 people, at least 6% of those in the sample believe the thing about reptilian people controlling our world.
The probability that at least 6% of those in the sample believe the thing about reptilian people controlling our world is 0.0567
What is binomial probability distribution?
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
According to the given question:
n = 100 random sample
p = 0.6 probability of success
P(X = x) = n to x pˣ(1-p)ⁿ⁻ˣ
P(X = 30) = 100 to 30 (0.6)³⁰(0.4)⁷⁰
= 0.0567
Hence the probability that at least 6% of those in the sample believe the thing about reptilian people controlling our world is 0.0567
To know more about binomial probability distribution visit
https://brainly.com/question/15583307
#SPJ4
given r(x)=x^3-4x^2+4x-6, find the value of r(2). what does your answer tell you about x-2 as a factor of r(x)?
The Value of r(2) is -6 and x-2 is not a factor of r(x).
What is the value of a function on a Variable?
A real-valued function of a real variable is a function that takes as input a real number, commonly represented by the variable x, for producing another real number, the value of the function, commonly denoted f(x).
What is Factor?
A factor of polynomial P(x) is any polynomial that divides evenly into P(x).
How to find out the value of r(x)?
Given r(x)=x^3-4x^2+4x-6,
Put x = 2 ,
r(2)=2^3-4(2)^2+4(2)-6
r(2)=8-16+8-6
r(2)=-6
As we see that x=2 is not equal to zero,
implies x-2 does not divide r(x) evenly.
thus x-2 is not a factor of given r(x).
in how many ways can we arrange the face cards in a 52-card deck? (face cards are jack, king, queen) show your work.
By using the principle of counting, it can be calculated that
Total number of ways to arrange the four face cards in a 52-card deck = 11880
What is principle of counting?
Principle of counting states that if there are m ways to do one job and m ways to do another job after that job, there are m [tex]\times[/tex] n ways to do both the jobs together.
There are three face cards of hearts, three face cards of diamonds, three face card of clubs and three face cards of spade
Total number of face cards = 3 + 3 + 3 + 3 = 12
We can arrange the four face card in [tex]{12 \choose 4}[/tex] ways = 495 ways
The four cards should be arranged in a row.
Number of choices for the first card = 4
Number of choices for the second card = 3
Number of choices for the third card = 2
Number of choices for the fourth card = 1
Total number of ways to arrange the four cards in a row = 4 [tex]\times[/tex] 3 [tex]\times[/tex] 2 [tex]\times[/tex] 1 = 24
Total number of ways to arrange the four face cards in a 52-card deck =
495 [tex]\times[/tex] 24 = 11880
To learn more about principle of counting, refer to the link-
https://brainly.com/question/16858325
#SPJ4
answer quickly please!!!!!!!!
Answer:
56 in^2
Step-by-step explanation:
The formula for calculating area of a triangle is:
h × b ÷ 2 (h: height, b: base)The height is 7t and base is 4t:
4t × 7t ÷ 2 = 14tthe value of t = 4 so replace x with 4:
4*14 = 56 in^2theo started watching a movie at 19:30 The movie was 1 hour 56 minutes long,but part-way through he paused it for 12 minutes what was the time the movie finished
Answer: 21:38 on a 24 hour clock and 9:38 on a 12 hour clock
Step-by-step explanation:
So if Theo started the movie at 7:30 and the movie was 1 hour 56 minutes, and he paused half way for 12 minutes, we can conclude that the total time taken to watch the movie/break was 2 hours and 8 minutes.
Now we just add that time
7:30 + 2 hours and 8 minutes = 9:38
On a 24 hour clock the answer would be 21:38
you intend to estimate a population mean with a confidence interval. you believe the population to have a normal distribution. your sample size is 15. find the critical value that corresponds to a confidence level of 90%. (report answer accurate to three decimal places with appropriate rounding.)
The critical value that corresponds to a confidence level of 90 % [1.34503037 , ∞ ).
Given:
you intend to estimate a population mean with a confidence interval. you believe the population to have a normal distribution. your sample size is 15. find the critical value that corresponds to a confidence level of 90%.
sample size n = 15
confidence interval ci = 90
we know that,
Degrees of freedom df = n - 1
here n = 15
df = n - 1
= 15 - 1
= 14
Using the graphical t value calculator:
with df = 14 significance level = 1 - 0.90 = 0.10
so t = [1.34503037 , ∞ )
Learn more about the normal distribution here:
https://brainly.com/question/29509087
#SPJ4
how much time should be allowed for a 605 mile card ship if the car will be traveling at an average speed of 55 mph
The time that the car will travel when the average speed is 55mph is 11 hours.
How to calculate the time?Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.
From the information, the car has an average speed of 55 mph and it's travelling at 605 miles.
It should be noted that time will be calculated as the distance divided by the speed that given and this will be:
Time = Distance / Speed
Time = 605 / 55
Time = 11
The time is 11 hours.
This simply illustrates the time.
Learn more about time on:
brainly.com/question/26046491
#SPJ1
A restaurant decides to test their oven's thermostat to see if it is working properly, that is, if the actual temperature inside the oven is the same as the temperature to which the thermostat was set. Twenty times, the oven was set at 350 degrees and then the temperature was measured with a thermometer
The p-value when the test statistic is equal to 2.30 is 0.033.
What is the p-value?A statistical measurement known as a p-value is employed to check a hypothesis' validity against actual data.
A p-value calculates the likelihood of getting the outcomes that were observed, presuming that the null hypothesis is correct.
The statistical significance of the difference that was found increases with decreasing p-value.
The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.
So, the p-value will be:
The t-value for (n-1 = 20-1 = 19) degrees of freedom serves as the test statistic in this experiment.
Using the formula: T.DIST.2T(2.3,19)
The p-value will be 0.033.
Therefore, the p-value when the test statistic is equal to 2.30 is 0.033.
Know more about a p-value here:
https://brainly.com/question/4621112
#SPJ4
Complete question:
A restaurant decides to test their oven's thermostat to see if it is working properly, that is if the actual temperature inside the oven is the same as the temperature to which the thermostat was set. Twenty times, the oven was set to 350 degrees and then the temperature was measured with a thermometer.
H o: μ=350 and Ha: μ≠350
The test statistic is equal to 2.30. What is the p-value _____?