Digital watches of a certain brand are advertised to have an average lifetime of 800 days. A customer is willing to purchase a watch unless it can be demonstrated that the average lifetime is shorter than what is advertised. A random sample of 50 watches is obtained from the manufacturer and the lifetime of each watch is recorded. In particular, one obtains the sample mean
X
ˉ
=738.44
days and sample variance
S 2
=1459.24
days squared from this sample of digital watches. 1. Explain why the test statistic
ζ= S/ 50
X
ˉ
−μ
has a normal distribution despite the experimenter being unaware of the distribution of the population of digital watches. 2. Devise an appropriate hypothesis test to determine whether the given customer is willing to purchase a digital watch. 3. Conduct the hypothesis test of 2 . at a significance level of
α=0.05
Answers
(1) The sample size (n)>30 and population standard deviation (σ) is unknown then we use one sample t-test we get.
(2) There is sufficient evidence to conclude that, the customer is willing to purchase a watch unless it can be demonstrated that the average lifetime is shorter than what is advertised.
Test the hypothesis that the client is prepared to buy a watch unless it can be shown that the average lifespan is shorter than what is claimed using a significance level of α=0.05.
Given that,
Sample size (n)=50
Sample mean (x−)=738.44
Sample standard deviation (S)=38.2 where (S)2=1,459.24
The null and alternative hypothesis are,
H(0): μ≥800
vs
H(1): μ<800
(1) In the given question we have to explain why the test statistic has a normal distribution despite the experimenter being unaware of the distribution of the population of digital watches.
The sample size (n)>30 and population standard deviation (σ) is unknown then we use one sample t-test we get.
(2) In the given question we have to devise an appropriate hypothesis test to determine whether the given customer is willing to purchase a digital watch.
Then test statistic becomes,
t = x−μ/(s/√n)
t = 738.44−800/(38.2/√50)
t = −61.56/5.40229
t = −11.40
Here the test is one tailed (left tailed) at α=0.05
Then degrees of freedom=(n-1)=(50−1)=49
Thus P-value becomes,
P-value = <0.00001
The P-value is less than or equal to α=0.05
Then we reject the null hypothesis H(0).
We use excel command to find the P-value we get,
=T.DIST( x, deg _freedom, TRUE)
=T.DIST(-11.40 , 49,TRUE)
=<0.00001
There is sufficient evidence to conclude that, the customer is willing to purchase a watch unless it can be demonstrated that the average lifetime is shorter than what is advertised.
To learn more about Hypothesis Test link is here
brainly.com/question/17099835
#SPJ4
The right question is given below:
Related Questions
PLEASE HELP ME ITS TIMED!!!
Answers
Answer: The coefficient of the term with t^3 and q^14 in the expansion of (3t - q)^17 is 816 / 3.
Step-by-step explanation: The coefficient of the term with a certain power of t and a certain power of q in the expansion of a binomial raised to a power can be found using the binomial formula. The formula is given by:
Copy code
(a + b)^n = sum_{k=0}^n choose(n, k) * a^(n-k) * b^k
In this case, we have a = 3t, b = -q, and n = 17. We want to find the coefficient of the term with t^3 and q^14, which means we need to find the coefficient of the term with a^(n-k) = t^3 and b^k = q^14. Plugging these values into the formula, we get:
Copy code
(3t - q)^17 = sum_{k=0}^17 choose(17, k) * 3^(17-k) * (-1)^k * t^(17-k) * q^k
To find the coefficient of the term with t^3 and q^14, we need to find the value of choose(17, k) for k = 3. The binomial coefficient choose(n, k) is equal to the number of ways to choose k items from a set of n items. It can be calculated using the formula:
Copy code
choose(n, k) = n! / (k! * (n-k)!)
where n! is the factorial of n, which is the product of all positive integers less than or equal to n. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.
In our case, we have n = 17 and k = 3, so the coefficient we are looking for is:
Copy code
choose(17, 3) = 17! / (3! * (17-3)!) = 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / (3 * 2 * 1 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) = 17 * 16 / 3 = 816 / 3
Therefore, the coefficient of the term with t^3 and q^14 in the expansion of (3t - q)^17 is 816 / 3.
In a class activity, all the 15 students wear hats. 7 students wear red hats, 6 students wear green hats and 2 students wear white hats. (I) two of the 15 students are picked at random. Show that the probability that these two students wear hats of the the same colour is 37/105. (I) three of the 15 students are picked at random. Find the probability that at least 2 of these students wear red hats.
Answers
The probabilities, using the hypergeometric distribution, are given as follows:
i) Two wear the same color: 37/105: 0.35238 = 37/105.
ii) At least 2 wear red: 0.4461.
What is the hypergeometric distribution formula?The mass probability formula is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are presented as follows:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.The probability of two red is given as follows:
[tex]P(X = 2) = h(2,15,2,7) = \frac{C_{7,2}C_{8,0}}{C_{15,2}} = 0.2[/tex]
The probability of two green is given as follows:
[tex]P(X = 2) = h(2,15,2,6) = \frac{C_{6,2}C_{9,0}}{C_{15,2}} = 0.14286[/tex]
The probability of two white is given as follows:
[tex]P(X = 2) = h(2,15,2,2) = \frac{C_{2,2}C_{13,0}}{C_{15,2}} = 0.00952[/tex]
Then the probability of two wearing the same color is given as follows:
0.2 + 0.14286 + 0.00952 = 0.35238 = 37/105.
The probability that out of 3 people, at least 2 wear red, is given as follows:
[tex]P(X = 2) = h(2,15,3,7) = \frac{C_{7,2}C_{8,1}}{C_{15,3}} = 0.3692[/tex]
[tex]P(X = 3) = h(3,15,3,7) = \frac{C_{7,3}C_{8,0}}{C_{15,3}} = 0.0769[/tex]
Hence:
0.3692 + 0.0769 = 0.4461.
More can be learned about the hypergeometric distribution at https://brainly.com/question/14741653
#SPJ1
The retail cost of a computer is 37% more than its wholesale cost?which statement is true?1. THe retail cost of the computer is 132% more than the wholesale price.2. THe wholesale cost of the computer is 68% if the retail price.3. THe retail cost of the computer is 132% of the wholesale price.4. the retail cost of the computer is 37% of the wholesale price.
Answers
when retail cost of the computer is 37% of the wholesale price then Retail price is 1.37times wholesale price
Retailers who acquire products in bulk are subject to wholesale pricing.
Selling products at a greater price than what it costs to produce them allows businesses to turn a profit.
Retail pricing is what merchants decide to charge customers as their ultimate selling price.
Consumers are the primary focus of retail pricing.
According to the question,
The retail cost of a computer is 37% more than its wholesale cost
Let Retail cost be "x" and wholesale cost be "y"
So , x = y + 0.37y
=> x = 1.37y
Therefore , The retail price is 1.37times the wholesale price
To know more about Retail price here
https://brainly.com/question/12929999
#SPJ4
Find the least common denominator of these fractions.
3/8 5/18
Answers
Option C } 72
Mark Brainly
Answer: 72
Step-by-step explanation
Let's just look at the denominators for this problem.
8 and 18
8 can go into 24, 3 times but 18 does not multiply into 24
18 can go into 36, 2 times but 8 does not multiply into 36
Therefore 72 is the least common denominator.
8 times 9 = 72
18 times 4 = 72
72 is the least common denominator.
Point B is located at
(-3,0)
(3,0)
(0,3)
(0,-3)
Answers
Answer:
(3,0)
have a nice day.(I needed 20 charecters so yeah i needed to say this)
Answer:
(3,0)
Step-by-step explanation:
The first number in the ordered pair tells us how far we are from the orgina (0,0) (the middle of the graph). We are 3 units to the right. The second number in the ordered pair tells us how far up or down from (0,0) we are. You do not go up for down so that number should be zero.
Bobby and Rick are in a 16-lap race on a one-mile oval track. Bobby, averaging 86 mph, has completed six laps just as Rick is getting his car onto the track. What speed does Rick have to average to be even with Bobby at the end of
the sixteenth lap?
To be even with Bobby at the end of the sixteenth lap, Rick has to average a speed of __ mph.
(Type an integer or a decimal.)
Answers
Hence, the speed that Rick must be driving on to even with Bobby at the end of the 16th lap should be: Distance = Speed × Time16=1084× Speed Speed=16×8410=134.4 mph.
The time taken by Bobby to complete 10 laps will be:
[tex]$$\begin{aligned}\text { Distance } & =\text { Speed } \times \text { Time } \\10 & =84 \times \text { Time } \\\text { Time } & =\frac{10}{84} \text { hours }\end{aligned}$$[/tex]
Hence, the speed that Rick must be driving on to even with Bobby at the end of the 16 th lap should be:
[tex]$$\begin{aligned}\text { Distance } & =\text { Speed } \times \text { Time } \\16 & =\frac{10}{84} \times \text { Speed } \\\text { Speed } & =\frac{16 \times 84}{10}=134.4 \mathrm{mph} .\end{aligned}$$[/tex]
To more learn about speed visit:
https://brainly.com/question/28224010
#SPJ1
Is there anyone that can help me with a finance question?
Answers
Answer:
Yes, there are many people who can help you with a finance question. Some of the people who can help you include: financial advisors, accountants, financial planners, and financial analysts. Additionally, there are many online resources available such as personal finance forums, websites, and blogs.
Step-by-step explanation:
Solve the equation 2x + 3y = 5 for x.
Answers
Answer:
x = [tex]\frac{5-3y}{2}[/tex]
Step-by-step explanation:
2x + 3y = 5
isolate variable: 2x = 5-3y
divide by 2: x = [tex]\frac{5-3y}{2}[/tex]
Please Help me!!!!! Will give brainliest 4 an EXPLAINATION!
Answers
The angles after solving the equations will be equal to 50°, and both angles will be the same as the corresponding angles. Hence, option B is correct.
What is an angle?An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol.
Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.
As per the given information in the question,
The equations for the angles are:
7x + 1 = 6x + 8
7x - 6x = 8 - 1
x = 7
So, the angles will be,
7x + 1 = 7(7) + 1 = 50°
6x + 8 = 6(7) + 8 = 50°
To know more about an angle:
https://brainly.com/question/28451077
#SPJ1
3. What type of angle is angle A?
obtuse
acute
right
straight
Answers
The angle A is an obtuse angle of the regular polygon.
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The interior angle of a polygon is [(n-2)180°]/n.
Where n is the number of sides of the polygon.
The number of sides of the polygon is 8.
The measure of the interior of the polygon is [(8-2)180°]/8
= 135°
The obtuse angle is an angle that more than 90°.
Therefore angle is an obtuse angle.
To learn more about interior angle, click on below link:
https://brainly.com/question/10566696
#SPJ1
MULTIPLE CHOICE Question 2 Look at the drawing below. Which of the following statements, if true, would alone prove pllq? Select all that apply. There are at least two correct answers.
Answers
Answer:
no c is right answer
Step-by-step explanation:
angle b and e should be supplementary
Answer:
A, B and C
Step-by-step explanation:
Statement A
According to the Alternate Exterior Angles Theorem, when a transversal line intersects two parallel lines, the resulting alternate exterior angles are congruent.
Given ∠c ≅ ∠f, and as ∠c and ∠f are alternate exterior angles, then p ║ q.
Statement B
According to the Corresponding Angles Postulate, when a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
GIven ∠d ≅ ∠g, and as ∠d and ∠g are corresponding angles, then p ║ q.
Statement C
According to the Same-side Interior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary.
Given ∠b and ∠e are supplementary, and as ∠b and ∠e are the interior angles on the same side of the transversal [tex]\ell[/tex], then p ║ q.
Statement D
∠f and ∠g are a linear pair, therefore ∠f and ∠g are supplementary. However, this does not given enough information to prove p ║ q.
the height of one tampa city center is 537 feet. convert 537 feet to meters by finding an equivalent rate. round to the nearest tenth
Answers
The equivalent rate is 163.7 meters.
What is an equivalent rate?
Equivalent rates are different rates that have the same value. Similar to finding equivalent ratios, you may find an equivalent rate by multiplying or dividing the numerator and denominator by the same number.
Here, we have
Given: the height of one Tampa city center is 537 feet.
We have to convert 537 feet to meters by finding an equivalent rate.
1 feet = 0.3048 meter
So, 537 feet = 537 × 0.3048 = 163.7 meters.
Hence, the equivalent rate is 163.7 meters.
To learn more about the equivalent rate from the given link
https://brainly.com/question/24734894
#SPJ1
Answer:
Hence, on a number line,-12 lies to the left of Zero.
Step-by-step explanation:
On a number line, zero lies exactly at the middle of the number line.Left to the zero, negative number lies and right to the zero, positive number lies.
A racetrack charges $85 for each seat in the lower section, $60 for each seat in the upper sections, and $35 for field tickets. There are three times the amount of seats in the upper section as compared to the lower section. The revenue from selling all 22,800 seats is $948,000. How many seats are in the upper section of the racetrack?
Answers
Using a system of equations, the number of seats in the upper section of the racetrack is 3,600.
What is a system of equations?A system of equations, also called simultaneous equations, is two or more equations solved concurrently.
We can use any of the following methods to solve simultaneous equations:
GraphicalSubstitutionEliminationMatrix.In this situation, after forming the equations, we can use substitution and elimination methods to solve them.
Racetrack charge per lower seat = $85
Racetrack charge per upper seat = $60
Racetrack charge per field ticket = $35
Let lower seats = x
Let upper seats = 3x
Let field tickets = y
4x + y = 22,800 ... Equation 1
y = 22,800 - 4x ...Equation 3
85x + 60(3x) + 35y = 948,000
85x + 180x + 35y = 948,000 ... Equation 2
Substitute Equation 3 in Equation 2 to eliminate y:
85x + 180x + 35(22,800 - 4x) = 948,000
85x + 180x + 798,000 - 140x = 948,000
125x = 948,000 - 798,000
125x = 150,000
x = 1,200
Determining the number of seats:
Seats in the Lower section = 1,200
Seats in the Upper section = 3,600 (1,200 x 3)
Field tickets, y = 22,800 - 4x
y = 22,800 - 4(1,200)
= 18,000
Check:
85x + 180x + 35y = 948,000
85(1,200) + 180(1,200) + 35(18,000) = 948,000
102,000 + 216,000 + 630,000 = 948,000
948,000 = 948,000
Thus, based on simultaneous equations, there are 3,600 seats in the upper section of the racetrack.
Learn more about simultaneous equations at https://brainly.com/question/28768577
#SPJ1
93 is what percent of 124
Answers
Answer: 75%
Step-by-step explanation:
93 is 75 percent of 124.
Explained in the picture attached...
Hope that helps...
Height (in inches) Mean Minimum Q1 Median Q3 Std Dev 4.21 Maximum 79 68.2 67 , 71 , Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches. Height (in inches) Q3 Mean 68. 2 Std Dev .21 Minimum 62 4 Q1 63 Median 67 Maximum 79 Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches. (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches.
Answers
Standard deviation will be √3.3516 .
To calculate the standard deviation for the given data first we have to calculate the total number of students , mid value , fiXi , fiXi².
After that , we have to calculate the Xbar by using
Xbar = ∑fiXi / N
for which we need the value of fi , Xi and N
N = 100
fiXi = 6478
we have calculated the values from the given data ,
Therefore ,
Xbar = 6478 / 100
= 64.78
Var(X) = αx² - ∑fiXi² / N - (Xbar²)
= 419980 / 100 - (64.78)²
= 4199.80 -4196.4484
=3.3516
Thus,
standard deviation ax = √var(X)
= √3.3516
Therefore , the standard deviation will be √3.3516
To learn more about Standard deviation
https://brainly.com/question/23859940
#SPJ4
The gardening club at school is growing vegetables. The club has 300 square feet of planting
beds.Cucumber plants require 6 square feet of growing space, and tomato plants require 4
square feet of growing space. The students want to plant some of each type of plant and have at
least 60 plants.
Select the combination of equations or inequalities that could describe this situation. Let c represent the number of cucumber plants and t represent the number of tomato plants.
Answers
Answer:
The answer is :
E - 6c + 4t < 300
Amy and three friends are renting a house near the campas for $2400 per month. She plays 1/4 of the rent. What is her monthly rent?
Answers
Answer:
Amy has to pay $600 every month for rent.
Step-by-step explanation:
To take 1/4 of a number is to multiply 1/4 and said number.
So you can do 0.25*number
or number/4.
For this problem, the number is 2400 because Amy is going to pay 1/4 of 2400 for rent.
[tex]rent = 2400/4\\rent = 600[/tex]
⭐if this response helped you, please mark it the "brainliest"!⭐
Ravi sells real estate. Based on previous data, he knows that 5% of home tours result in a sale. Assume that the results of these tours are independent from each other. Which of the following choices are binomial random variables? Choose all answers that apply: A. Take a random sample of 30 tours and let L = the number of tours that result in a sale. B. Take a random sample of 3 tours and let K = the number of tours that result in a sale. C. Take a random sample of 3 tours and let M = the amount of sales (in dollars) generated by the tours.
Answers
The options that represent binomial random variable are;
A. Take a random sample of 30 tours and let L = the number of tours that result in a sale.
B. Take a random sample of 3 tours and let K = the number of tours that result in a sale.
How to Identify Binomial Random Variables?There are 4 primary conditions for a random variable to be classified as binomial random variable and they are;
1. The number of observations n is fixed.
2. Each observation is independent.
3. Each observation represents one of two outcomes ("success" or "failure").
4. The probability of "success" p is the same for each outcome.
No, in this case, since 5% of home tours result in a sale, it therefore tells us that number of home tours is the independent variable while the amount of sales generated is the dependent variable.
From the above, we can access the given options and say that the last option is not a binomial random variable because the variable M is dependent and so does not satisfy one of the four conditions.
However, options A and B satisfy the 4 conditions and we say they are binomial random variables.
Read more about Binomial Random Variables at; https://brainly.com/question/15246027
#SPJ1
whats the domain,range, and y-intercept and tell me if its exponential or linear.
k(x)=50(1.3)^x
Answers
0.3% is the percentage rate of increase in exponential function.
What exactly makes a function exponential?
A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.
The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.
We have,
y = 50( 1.3)ˣ
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is
y(x)= a(1-r)^x such that r is the growth percent.
1 + r = 1.3
r = 0.3 ⇒ 0.3%
Learn more about exponential function
brainly.com/question/14355665
#SPJ1
The parabola of y= has a vertex of (3, - 2) and a focus of (3, - 2 1/16) opens downward
Answers
The equation of the parabola is y = -1/4 x² + 3/2 x - 17/4. Where the vertex of the equation is at (3, -2) and the focus is at (3, -2 2/16) that opens downwards.
What is the equation of a parabola?The equation of the parabola with vertex at (h, k) is
y = a(x - h)² + k
The focus of the parabola is represented by (h, k + 1/4 a).
Calculation:It is given that, the vertex of the parabola is (h, k) = (3, -2)
And the focus of the parabola is (h, k + 1/4 a) = (3, -2 1/16)
From the focus point, we can calculate the value of 'a'.
(h, k + 1/4 a) = (3, -2 1/16)
⇒ k + 1/4 a = -2 1/16 = -33/16
⇒ -2 + 1/4 a = -33/16
⇒ 1/4 a = -33/16 + 2
⇒ 1/4 a = -1/16
⇒ a = -1/16 × 4
∴ a = -1/4
Since a is negative the parabola is downwards.
Now, the equation of the parabola is
y = a(x - h)² + k
On substituting the values, we get
y = -1/4(x - 3)² - 2
= -1/4(x² - 6x + 9) - 2
= -1/4 x² + 3/2 x -9/4 - 2
= -1/4 x² + 3/2 x - 17/4
Therefore, the equation of the parabola is y = -1/4 x² + 3/2 x - 17/4.
Learn more about the equation of a parabola here:
https://brainly.com/question/12464740
#SPJ1
A man is in a boat 2 miles from the nearest point on the coast. He is to go to point Q, located 3 miles down the coast and 1 mile inland (see figure). He can row at a rate of 1 mile per hour and walk at 3 miles per hour. Toward what point on the coast should he row in order to reach point Q in the least time? (Round your answer to two decimal places.) 0.84 mile(s) down the coast
Answers
Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.
As given in the question,
Nearest point on the coast is 2 miles far away
rate of the row = 1mile per hour
Walk at the rate of 3 miles per hour
Let 'x' hours be the least time to reach point Q.
Time = distance / speed
Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3
Time taken to reach the coast = (√ 4 + x² ) / 1
Total time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3
To find least time dt/dx = 0
t = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3
⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )
⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )
Squaring both the side we get,
x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )
⇒3x² -24x +36 =0
⇒ x² -8x + 12 = 0
⇒ x = 2 or 6 hours
Therefore , the least time taken to reach the point Q is equal to 2 hours.
Learn more about least time here
brainly.com/question/17429465
#SPJ4
Find the area of a rectangle with the sides of x+7 and 3x-4
Answers
The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.
Define area of rectangle.Any shape's area can be calculated by counting how many unit squares will fit inside of it. A square with a side of 1 unit is referred to as a unit square in this context. Therefore, the quantity of unit squares that make up a rectangle's perimeter is its area. Alternately, the area of the rectangle is the area contained within the boundary of this shape. The unit-length tiles in your home are a good illustration of a rectangle form. By counting the number of tiles, you can quickly determine how much space the floor takes up. This will also enable you to calculate the rectangle floor's area.
Given
Sides = x+7 and 3x-4
Area of rectangle
Length ×Breadth
(x + 7) (3x - 4)
Multiplying,
x(3x - 4) + 7(3x - 4)
3x² - 4x + 21x - 28
3x² + 17x - 28
The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.
To learn more about area of rectangle, visit:
https://brainly.com/question/20693059
#SPJ1
A punter kicks a football. Its height h, in yard, t seconds after the kick is given by the equation h(t)=-4.9t^2+18.24t+0.8. The height of an approaching blocker's hand is modeled by the equation h(t)=-1.43t+4.26, using the same time. Can the blocker knock down the punt (do they intersect)? If so, at what point will that happen (the point of intersection)?
Answers
Part 1
[tex]-4.9t^2 +18.24t+0.8=-1.43t+4.26\\\\-4.9t^2 +19.67t-3.46=0\\\\\Delta =(19.67)^2 -4(-4.9)(-3.46)=319.0929 > 0[/tex]
Therefore, the blocker can knock down the punt.
Part 2
Using the quadratic formula,
[tex]t=\frac{-19.67 \pm \sqrt{319.0929}}{2(-4.9)}\\\\t \approx 0.18437, 3.82992[/tex]
Considering the graphs, it is clear to take the smaller solution. Thus, the point of intersection is [tex](0.18437, h(0.18437))=\boxed{(0.18437, 3.99635)}[/tex].
s formula to find a quadratic approximation of at the origin. estimate the error in the approximation if and .
Answers
A quadratic equation of at the origin, estimate the error = 0.000859M
The approximation is valid because is very small.
Calculation of concentration:
Since
0.85 M 0 0
(0.85-x)M x x
Now the value of x should be
x = 0.0000229
So based on this, the above concentration should be determined.
In order to demonstrate that the same value of x may be achieved either way, you will now solve using the quadratic formula rather than iterations. What are the values of a, b, and c and x, where a, b, and c are the coefficients in the quadratic equation [tex]ax^{2} +bx+c=0[/tex] and x is [h3o+], when using the quadratic equation to determine [h3o+] in 0.00250 m hno2? Keep in mind that ka=4.5104.
a : 1
b : 4.5x[tex]10^{-4}[/tex]
c : 1.125x[tex]10^{-6}[/tex]
[[tex]H_{3} O^{+}[/tex]] = 0.000859M
As [tex]HNO_{2}[/tex] is a weak acid, its equilibrium in water is:
[tex]HNO_{2} (aq)+H_{2} O(I)[/tex] ⇄ [tex]H_{3} O^{+} (aq)+N_{2} O^{-} (aq)[/tex]
Equilibrium constant, ka, is defined as:
ka = 4.5x[tex]10^{-4}[/tex] = [[tex]H_{3} O^{+}[/tex]] [NO₂⁻] / [HNO₂] (Equation-1)
Equilibrium concentration of each specie are:
[HNO₂] = 0.00250M - x
[H₃O⁺] = x
[NO₂⁻] = x
Replacing in (1):
4.5x[tex]10^{-4}[/tex] = [tex]\frac{x*x}{0.00250M-x}[/tex]
1.125x10⁻⁶ - 4.5x10⁻⁴x = x²
0 = x² + 4.5x10⁻⁴x - 1.125x10⁻⁶
As the quadratic equation is ax² + bx + c = 0
Coefficients are:
a: 1
b: 4.5x10⁻⁴
c: 1.125x10⁻⁶
Now, solving quadratic equation:
x = -0.0013 → False answer, there is no negative concentrations.
x = 0.000859
As [H₃O⁺] = x; [H₃O⁺] = 0.000859M
Therefore,
A quadratic equation of at the origin, estimate the error = 0.000859M
To learn more about Quadratic equation visit :
brainly.com/question/17177510
#SPJ4
look at attached photo
Answers
The correct answer is A) y = 9000x + 65,000.
Find a linear equation that models the value of the house after x years?The correct answer is A) y = 9000x + 65,000.
This is an equation in slope-intercept form, where "y" is equal to the value of the house after x years, "9000x" is the slope (or rate of change) of the equation, and 65,000 is the y-intercept (or the initial value of the house). The equation can be derived from the given information.The initial value of the house is 65,000, so the y-intercept must be 65,000. To find the slope, we can use the formula "rise/run", or change in y/change in x.The house has increased in value by 54,000 ($119,000 - $65,000) over 6 years (change in x), so the slope must be 9000 (54,000/6).
The equation y = 9000x + 65,000
models the value of the house after x years, where y is the value of the house,
9000x is the slope of the equation,
and 65,000 is the y-intercept.
This equation can be used to calculate the value of the house after any given number of years.To learn more about linear equation in slope-intercept form refer to:
https://brainly.com/question/1884491
#SPJ1
expresa 1405 en base 7 a base 10
Answers
1405 in base 7 = 544 in base 10
What is base-7 number system ?
The heptimal system is another name for base-7 numbers. Base 7 numbers are represented by the digits 0, 1, 2, 3, 4, 5, and 6.
The digits of a Base 10 number, on the other hand, are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If there isn't a subscript at the supplied number, Base 10 is used to write that number. The decimal system is sometimes known as base-10 numbers. Currently, in daily life, we frequently use numbers in the base 10 range.
base 7 to base 10 conversion:
Multiply each digits by the powers of 7 as follows:
Base 7 digits: 1 4 0 5
Multiply by: 7^3 7² 7^1 7^0
( 1*7^3) + (4*7² ) + (0* 7^1 )+ ( 5 * 7^0)
= 343 + 196 + 0 + 5
= 544
To learn more about the base-7 number system from the given link
https://brainly.com/question/1674893
#SPJ1
Solve the following equation by first writing the equation in the form a x squared = c: t squared minus 49 = 0 a. t = 49 b. t = plus-or-minus 49 c. t = 7 d. t = plus-or-minus 7 Please select the best answer from the choices provided A B C D
Answers
By solving the equation we get ,t = ± 7 using concept of square roots.
How to find the square roots ?
Square root, in mathematics, a factor of a number that, when multiplied by itself, gives the original number. For example, both 3 and –3 are square roots of 9.
For example, 2 is the square root of 4, and this is expressed as √4 = 2.
We know that every squared number has two square roots one is positive and another is negative.
In given que,
given condition is t squared minus 49 = 0
Form of equation is ax^ 2 = c.
given condition can also be written as t^2 - 49 = 0
i.e. t^2 = 49
where a = 1
x = t
c = 49
So, the square root are 7 and -7.
So, equation become t = ± 7.
Learn more about square roots using link given below :
https://brainly.com/question/428672
#SPJ1
0. Mardo ordered 2 reclining chairs for $230 each and a coffee table for $350. The shipping cost is $100. Marco is going to pay off his bill in 5 equal payments. How much is each of Marco's payments?
Answers
The amount of each Marco's payments for the 2 reclining chairs, a coffee table including with shipping cost is found as $182.
Explain the division operation?Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people belong to each group after a fair distribution is the basic objective of division.The data for the given question-
Mardo placed an order for a coffee table and two recliners for a total of $230 each. The price of shipping is $100. Marco will settle his debt in five equal payments.Thus, the total cost becomes-
Total cost = 2 x reclining chairs + coffee table + shipping cost
Total cost = 2 x 230 + 350 + 100
Total cost = $910
For the amount of each payment when there are 5 equal payments.
Total cost = 910/5
Total cost = $182
Thus, the amount of each Marco's payments for the 2 reclining chairs, a coffee table including with shipping cost is found as $182.
To know more about the division operation, here
https://brainly.com/question/4721701
#SPJ1
An area code has three digits. How many different area codes are possible
Answers
Answer:
1000
Step-by-step explanation:
If any of the digits 0-9 can be used then there are 10^3 possible codes.
10^3 = 1000
Examine the drawing below, which could be a value for x?
Answers
The value of 'a' can be 20. The correct option is C, 20.
What is triangle inequality theorem?As per the triangle inequality theorem, the sum of any two sides of the triangle should be greater than the third side.
As per triangle inequality theorem, the sum of the two sides of the triangle should be greater than the third side of the triangle.
As per the triangle inequality theorem, if 'a' is the longest side of the triangle then,
21 + 6 > a
27 > a
If a is not the longest side of the triangle,
21 + a > 6
a > -21 + 6
a > -15
6 + a > 21
a > 21 - 6
a > 15
Therefore, the value of a should be greater than 15 and less than 27. Since the only option under this condition is 20.
Hence, The correct option is C, 20.
Learn more about the Triangle Inequality Theorem here:
https://brainly.com/question/1163433
#SPJ1
