The number 3 in the equation h(t) = -16t² + 6t+ 3 represents the initial height from which the ball is thrown.
The equation h(t) = -16t² + 6t+ 3 models the height of the ball thrown in the air, with h(t) measured in feet and time, t, measured in seconds. The number 3 in this equation refers to the height from which the ball is thrown. This is represented by the constant term 3, which is added to the equation after the sum of the variables. The formula h(t) = -16t² + 6t+ 3 can be broken down into three parts. The first part is the constant term, 3, which denotes the initial height of the ball. The second part is the linear term, 6t, which represents the acceleration of the ball due to gravity. Lastly, the quadratic term, -16t², is used to describe the rate at which the ball’s acceleration slows down due to air resistance. Therefore the number 3 in the equation h(t) = -16t² + 6t+ 3 represents the initial height from which the ball is thrown.
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10. In the diagram below, ABC~ DEC
If AC = 12, DC = 7, DE = 5, and the perimeter of AABC is 30, what is the perimeter of ADEC?
A. 12.5
B. 14.0
C. 14.8
D. 17.5
Answer: B 14.0
Step-by-step explanation:
Find the values of for which the series converges. Find the sum of the series for those values of x. sum ∞ (2^n)/(x^n)
DIVIDE 3000 RUPEES AMONG TEENA AND BEENA SO THE THEY GET 40% AND 60% RESPECTIVELY
Answer:
To divide 3000 rupees between Teena and Beena so that they get 40% and 60% respectively, we need to follow these steps:
Step 1: Find the total percentage that Teena and Beena will receive together:
40% + 60% = 100%
This means that Teena and Beena will receive 100% of the total amount, which is 3000 rupees.
Step 2: Calculate the amount that Beena will receive:
60% of 3000 rupees = 0.6 x 3000 = 1800 rupees
Step 3: Calculate the amount that Teena will receive:
40% of 3000 rupees = 0.4 x 3000 = 1200 rupees
Therefore, Beena will receive 1800 rupees, while Teena will receive 1200 rupees
Statistics Card Question!
You are dealt a hand of 8 cards from a standard deck of 52 cards. Find the probability of being dealt five clubs and three cards with one card of each other remaining suit.
Therefore , the solution of the given problem of probability comes out to be 0.00439, or about 0.44%.
Probability : What is it?The main goal of the mathematical field known as model parameters is to determine the probability that a statement is accurate or that a particular event will occur. It is possible to symbolise chance by using any ranging between range 0 and 1, where 1 typically denotes certainty and 0 typically denotes possibility. A probability diagram illustrates the likelihood that a particular occurrence will take place.
Here,
To calculate the likelihood of receiving a hand of five clubs, three cards, and one card from each remaining deck,
Five clubs can be obtained in the following ways:
=> C(13,5) = 1,287
where C(n,r) indicates how many different ways r things were combined from a total of n options.
After selecting the five clubs, we must select three cards, one from each of the remaining three decks.
=> C(13,2) * C(3,2) = 702
As a result, there are three cards from each of the other two decks and five clubs, giving rise to the following combinations:
=> C(13,5) * [C(39,3) - C(13,2) * C(3,2)] = 328,664
Finally, there are C(52,8) = 74,837,381 potential hands with 8 cards.
The likelihood of receiving five clubs and three cards, along with one card from each of the other three decks, is as follows:
=> P = 328,664 / 74,837,381
=> P ≈ 0.00439, or about 0.44%.
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Which net matches the figure?
___________________________________
(Reporting any spams/wrong answers)
(giving brainliest to the correct answer)
____________________________________
Answer:
Figure D.
Step-by-step explanation:
The given Figure is a cube , which is a three-dimensional shape that has six square faces, twelve edges, and eight vertices. All of its faces are congruent and perpendicular to each other.
Figure D will turn into Square box when it is folded. Rest all are either Cuboid or Irregular Shaped objects when folded.
37 students shared 5 pizzas equally? What fraction of the pizza did each student receive?
Answer:
Each student received 40/37 of a pizza slice.
Step-by-step explanation:
To find the fraction of the pizza each student received, we can start by finding the total number of pizza slices. Since each pizza was shared equally among 37 students, we can multiply the number of pizzas (5) by the number of slices in each pizza to get the total number of slices:
Total number of slices = 5 pizzas x 8 slices per pizza = 40 slices
Next, we can divide the total number of slices by the number of students to get the number of slices each student received:
Number of slices per student = 40 slices ÷ 37 students
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1:
Number of slices per student = 40/37 slices
Therefore, each student received 40/37 of a pizza slice.
Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]
To find the fraction of the pizza each student received, we need to divide the total number of pizzas by the total number of students:
5 pizzas ÷ 37 students = 5/37 pizzas per student
Therefore, each student received 5/37 of a pizza.
1. Some students like their squash strong and use the ratio of 1:2 of squash to water How many litres of water are needed to mix with 1 litre of squash?
Answer:
If the ratio of squash to water is 1:2, it means that for every 1 unit of squash, we need 2 units of water.
So, to mix 1 liter of squash, we need 2 liters of water.
Therefore, the number of liters of water needed to mix with 1 liter of squash is 2 liters.
Step-by-step explanation:
Dylan has a pitcher with 1.65 L of orange juice. He pours out 0.2 L
of the juice. Then he adds some sparkling water to the pitcher to
make orangeade. He ends up with 1.9 L of orangeade. Solve the
equation 1.65 -0.2 + x = 1.9 to find the amount of sparkling
water, x, Dylan adds to the pitcher. Show your work.
Answer:
Step-by-step explanation:
fork knife
Without using a calculator, compute the sine and cosine of
by using the reference angle. What is the reference angle?
degrees.
The reference angle is given as 45 degrees
the angle is in the 4th quadrant
sin 315 = - sqrt(2) / 2
cos 315 = sqrt(2) / 2
How to solve for the reference angleWe have θ = 315
θ is seen to lie between 270 degrees and 360 degrees in the 4th quadrant
In the fourth quadrant the reference angle has been solved by:
360 - θ
360 - 315
= 45 degrees
The reference angle is 45 degrees
sin 315 = sin( 360 - 45)
= [tex]-\frac{\sqrt{2} }{2}[/tex]
= - sqrt(2) / 2
cos 315 = cos (360 - 45)
= [tex]\frac{\sqrt{2} }{2}[/tex]
= sqrt(2) / 2
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The gas mileages (in miles per gallon) for cars are shown in the frequency distribution. Approximate the mean of the frequency distribution.
Gas Mileage
(in miles per gallon)
Frequency
Question content area bottom
Part 1
The approximate mean of the frequency distribution is
enter your response here.
The approximate mean of the frequency distribution is of 35.2 miles gallon.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
As we are given a frequency distribution, we take the midpoint of each interval, and thus the sum of the observations is given as follows:
10 x 30 + 12 x 35 + 3 x 40 + 4 x 45 = 1020.
There are 29 observations, hence the mean of these observations is given as follows:
1020/29 = 35.2 miles gallon.
Missing InformationThe frequency distribution is given as follows:
28-32 10
33-37 12
38-42 3
43-47 4
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QUESTION 5 1 POINT
If cost is represented by C(x) = 3.7x + 9,000 and revenues are represented by R(x) = 4.6x, which equation could be
used to find the break-even point?
Answer:
The function that represents the company's profits is [tex]P(x)=0.9x-9,000[/tex]
Step-by-step explanation:
We are given
The costs of a company are represented by the function
[tex]C(x)=3.7x+9,000[/tex]
Its revenues are represented by the function
[tex]R(x) = 4.6x[/tex]
we know that
[tex]\text{Profit = Revenue - Cost}[/tex]
[tex]P(x)=R(x)-C(x)[/tex]
now, we can plug
[tex]P(x)=4.6x-(3.7x+9,000)[/tex]
now, we can simplify it
[tex]P(x)=0.9x-9,000[/tex]
So,
the function that represents the company's profits is [tex]P(x)=0.9x-9,000[/tex]
The equation used to find the break-even point is 0.9x - 9000.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have,
The costs of a company are represented by the function
C(x) = 3.7x + 9,000
and, revenues function
R(x) = 4.6x
For Break even point
Profit = Revenue - cost
P = 3.7x + 9000 - 4.6x
P = 0.9x - 9000
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Write an equation(any form) for the quadratic graphed below:
Answer:
[tex]y = -2(x + 3)^{2} + 3[/tex]
Step-by-step explanation:
The equation for a quadratic graph can be expressed in the Vertex form:
[tex]y = a(x-h)^{2} + k[/tex]
Where:
[tex](h, k)[/tex] = Vertex of the parabola
= Extreme point of the parabola
Step I:
By reading from the graph:
[tex](h, k)[/tex] = [tex](-3, 3)[/tex]
Substitute the values of h and k in the above equation:
[tex]y = a[x- (-3)]^{2} + (3)[/tex]
[tex]y = a(x + 3)^{2} + 3[/tex]
Step II:
Determine a:
Based on the shape of the graph (which is an upside down U), the value of a will be negative:
Count one unit to the right from the vertex and see how far do you go down to touch the graph:
From the graph:
It seems you need to move 2 units down
∴a = [tex]-2[/tex]
Step III:
Substitute this value of a in the above equation:
[tex]y = -2(x + 3)^{2} + 3[/tex]
Find the x and y intercept
Find the vertical and horizontal asymptotes
s(x)=6/ x^2 - 5x - 6
Answer:
To find the x and y intercepts, we set x and y to zero respectively:
x-intercept: setting y = 0 gives us 6/(x^2 - 5x - 6) = 0, which has no real solutions.
y-intercept: setting x = 0 gives us s(0) = 6/(-6) = -1.
To find the vertical asymptotes, we set the denominator equal to zero and solve for x:
x^2 - 5x - 6 = 0
(x - 6)(x + 1) = 0
This gives us two vertical asymptotes at x = 6 and x = -1.
To find the horizontal asymptote, we need to look at the behavior of the function as x approaches infinity and negative infinity. As x becomes very large in magnitude, the terms involving x^2 become much larger than the terms involving x or the constant term, and so we can ignore those terms. This gives us:
s(x) ≈ 6/x^2 as x → ±∞
Therefore, the horizontal asymptote is y = 0.
In summary:
x-intercept: none
y-intercept: (0, -1)
vertical asymptotes: x = 6 and x = -1
horizontal asymptote: y = 0
If you have anymore questions, feel free to comment and I will answer them 8-5 I am on.
Step-by-step explanation:
The temperature at a point
(x, y, z)
is given by
T(x, y, z) = 200e−x2 − 5y2 − 9z2
where T is measured in °C and
x, y, z
in meters.
The answer οf the given questiοn based οn the temperature is at the pοint (1, 2, 3) is apprοximately -62.3 °C.
What is Three-dimensiοnal Gaussian?A three-dimensiοnal Gaussian οr nοrmal distributiοn is type οf prοbability distributiοn that describes three-dimensiοnal data set. It is characterized by its mean, which determines center οf distributiοn, and its standard deviatiοn, which determines spread οr width οf distributiοn.
The temperature at a pοint:
(x, y, z)
is given by
T(x, y, z)
= 200e − x² − 5y² − 9z²
where T is measured in °C and
x, y, z
in meters.
The expressiοn 200e−x² − 5y² − 9z² represents a three-dimensiοnal Gaussian οr nοrmal distributiοn, with the highest temperature lοcated at the οrigin (0, 0, 0) and the temperature decreasing as we mοve away frοm the οrigin in any directiοn.
Tο find the temperature at a specific pοint (x, y, z), we substitute these values intο the expressiοn T(x, y, z) = 200e−x² − 5y² − 9z² and simplify. Fοr example, the temperature at the pοint (1, 2, 3) is:
T(1, 2, 3) = 200e−12 − 5(2)² − 9(3)²
T(1, 2, 3) = 200e−1 − 20 − 243
T(1, 2, 3) ≈ -62.3 °C
Therefοre, the temperature at the pοint (1, 2, 3) is apprοximately -62.3 °C.
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How do I solve the satellite question?
What is the perimeter of ABCD?
Need help on these questions!
1. Find the balance in the same account: $3,000 principal, earning 3% compounding annually, after 4 years.
2. Find the balance in the same account: $2,000 principal, earning 7% compounding semi-annually, after 25 years.
3. A tractor costs $14,340 and depreciates in value by 15% per year. How much will the tractor be worth after 3 years?
The balance in the account after 4 years is $3,376.50.
The balance in the account after 25 years is $16,050.07.
The tractor will be worth $9,449.11 after 3 years.
What does your bank account balance read right now?All posted credit and debit transactions are included in your account balance. It's the balance in your account before any pending charges are subtracted. The amount that can be used for withdrawals or purchases is your accessible balance.
1. We can use the formula A = P(1 + r/n) to determine the account balance after 4 years with a $3,000 principal receiving 3% compounding annually (nt)
where A represents the balance, P represents the principal, r represents the yearly interest rate, n represents the number of times interest is compounded annually, and t represents the passage of time in years.
By typing in the indicated values, we get:
A = 3000(1 + 0.03/1)^(1*4)
A = 3000(1.03)^4
A = 3000(1.1255)
A = $3,376.50
Thus, $3,376.50 remains in the account after 4 years.
2. We can once more apply the formula: A = P(1 + r/n) to determine the account balance after 25 years with a $2,000 principal, receiving 7% compounding semi-annually (nt)
Then then, it's a case of the same thing happening again.
By typing in the indicated values, we get:
A = 2000(1 + 0.07/2)^(2*25)
A = 2000(1.035)^50
A = $16,050.07
Thus, the account has a balance of $16,050.07 after 25 years.
3. Considering that the tractor loses 15% of its value per year, we can apply the formula A = P(1 - r)t to determine how much it will be worth after three years.
where A represents the final value, P the starting point, r the depreciation rate, and t the passage of time in years.
By typing in the indicated values, we get:
A = 14340(1 - 0.15)^3
A = 14340(0.85)^3
A = $9,449.11
The tractor will therefore be valued $9,449.11 after three years.
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If you multiply a certain number by 5, and then subtract 3, the answer is 17. Find the number.
Answer:
The number is 4
Step-by-step explanation:
Let us make the unknown number xMake the question an equation{5x-3=17}Solve the equation(5x-3=17)Collect like terms (5x= 17+3)5x=20
Divide both sides by the coefficient of x5x/5=20/5
x=4
Step-by-step explanation:
so let the unknown be x
x+5-3=17
x+2=17
so then you carry +2 over to the left hand side which collecting of like terms
so we have
x=17-2
x=15
so therefore the unknown value x is 15
to check
we substitute 15 for x in the equation
let's go
so we have
15+5-3=17
now using this solve it .
I believe u can do it
or I just do it
so we hv the unknown to be x
x*5-3=17
5x-3=17
5x=17+3
5x=20
x=20/5
x=4
Following the procedures in graphing the sine function, graph the following functions.
1. y = tan x 2. y = csc x
Therefore , the solution of the given problem of function comes out to be y-intercepts of the function will be at y = 1 and y = -1.
Describe function.Numerous subjects, including mathematics, numbers, and their subsets, as well as building, construction, and both real and fictitious geographic locations, are covered in the mathematics programme. The relationships between various elements that all cooperate to create the same outcome are covered in a work. A utility is composed of several unique parts that, when combined, give particular outcomes for each input.
Here,
=> 1. Chart for y = tan x
The period of the function, which is, can be found in order to draw y = tan x.
The vertical asymptotes can then be found at x = /2 + n, where n is any number.
At x = n, where n is any positive number, the function will have x-intercepts.
The horizontal asymptotes at y = 1 and y = -1 are also accessible.
=> 2 .Chart for y = csc x
To draw y = csc x, we must first determine the function's period, which is 2.
The vertical asymptotes at x = n, where n is any number, can then be discovered.
The y-intercepts of the function will be at y = 1 and y = -1.
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30 POINTSSSSSS!!
A football coach orders one hoodie or one long sleeve performance shirt for each of his 45 players. Each hoodie costs $60 and each long sleeve performance shirt costs $45. The entire order totaled $2,400.
Use the substitution method or elimination method to determine the number of hoodies and performance shifts ordered. SHOW ALL STEPS IN SOLVING PROCESS.
According to the question the 25 hoodies and 20 performance shirts were ordered.
What is performance?Performance is the result of an individual or organization's efforts in terms of achieving a desired outcome or goal. It is usually measured in terms of objectives, tasks and outcomes, and is a way of assessing the effectiveness of an individual or organization.
Substitution Method:
Let x = the number of hoodies ordered
Let y = the number of performance shirts ordered
Then, x + y = 45 (The total number of items ordered)
60x + 45y = 2400 (The total cost of the order)
Solve for x by substituting y = 45 - x into the second equation:
60x + 45(45 - x) = 2400
60x + 2025 - 45x = 2400
15x = 375
x = 25 (25 hoodies were ordered)
Substitute x = 25 into the first equation:
25 + y = 45
y = 20 (20 performance shirts were ordered)
Therefore, 25 hoodies and 20 performance shirts were ordered.
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NEED HELP 35 POINTS!
Find x.
5 in.
8 in.
x
15 in.
Answer:
The answer is 24 in
Step-by-step explanation:
This solution is for "SIMILAR TRIANGLES";
Let us letter the shape starting from left to right A-B-C-D-E
Angle A is similar to Angle E, so is Angle B similar to Angle D, that is, "Alternate interior angles" while Angle ACB is similar to Angle DCE, that is, "Vertical Angles";
Line AB = 5 in is parallel to line DE = 15 in
So, K = DE / AB = 15 / 5 = 3
Line CD = K * CB = 3 * 8 = 24 in
Thabo travelled 95 kilometres in 2 hours. If he keeps going at the same rate, how long will it take him to go the remaining 165 kilometres of her trip?
Answer: Velocity, v= distance/time
Given: distance=95km & time= 2 hours
Velocity= 95/2 = 47.5km/hour
Step-by-step explanation:
Now, Distance= 165 km and we got velocity= 47.5km/hour
= 47.5 =165/time
Time taken = 165/47.5= 3hours and 50 minutes.
Therefore, Time taken to remaining 165 km of her trip is 3hours and 50 minutes.
Determine whether y^2=−2x−2 is a function
Answer:
It is not a function.
Geometry proof that opposite sides of a parallelogram are congruent.
The following is provided: parallelogram ABCD
The following is what we must demonstrate: segments AB, CD, and BC, and segment AD.
According to the definition of a parallelogram, section BC is parallel to segment AD since ABCD is a parallelogram.
The definition of a parallelogram is that segment AB is parallel to segment DC.
Segments BC and AD are transverse to line AC. As illustrated below, this transversal generates the alternate interior angles 1 and 4, which are equivalent.
In the same way, segment AB and segment DC are transversals for line AC. Alternate interior angles 2 and 3 are produced by this transversal, and they are equivalent.
Segment AC is also divided into segments by its reflexive property.
∠1 ≅ ∠ 4
∠2 ≅ ∠ 3
AC segment AC segment
Triangle ABC triangle ADC, by ASA
In light of the fact that similar parts of congruent triangles are also congruent, segment AB segment CD and segment BC AD.
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a cola company sells the drinks in cans and bottles of three sizes. Study the pictograph below and answer the questions that follow
If these are your questions:
Dally cola sales in Bholapur 300 ml Shop A 500 ml Shop B Ilitre (a) In which type of packing does the cola sell the most? (b) Which shop sells more cola? (c) What is the total amount of cola sold in Bholapur per day?
So here are the answers:
In packing 300 ml, it would be sold at a larger volume.
given: there are two shops - shop A, and shop B selling 300 ml and 500 ml bottles.
to find:
(a) In which type of packing does the cola sell the most?
(b) Which shop sells more cola?
(c) What is the total amount of cola sold in Bholapur per day?
solution: As shop A sells the same product at a low cost because of low quantity, whereas shop B sells the product in 500 ml bottles. So, most chances are people end up buying the cheaper product which is the 300 ml product.
Similar, logic as the number of sales of 300 ml bottles would be much larger than that of 500 ml bottle backing. So, Shop A (300 ml bottle packing) sells more of the goods.
(c ) for option c inappropriate information is there, so can not be calculated. But, according to our findings, Shop A sells more goods.
In packing 300 ml, it would be sold at a larger volume.
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Louise measured the perimeter of her rectangular scrapbook to be 138 cm. If the scrapbook is 39 cm wide, how long is the scrapbook?
Does A (1,2) and A prime (5,12) represent a dilation? Why or why not?
Hence, in response to the provided question, we can say that As a result, equation A(1,2) and A'(5,12) are not dilations.
What is equation?An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.
To evaluate if the points A(1,2) and A'(5,12) reflect a dilation, we must first determine the dilation's scale factor.
Let's use the given points to compute the scale factor:
(length of A' A) / scale factor (length of A)
A's length A [tex]=\ sqrt[(5-1)2 + (12-2)2] = \sqrt[16^2 + 10^2] =\ sqrt(296) (296)[/tex]
A's length is one.
[tex](\sqrt(296)) / 1\\\sqrt(x) = scale factor (296)[/tex]
As a result, the scaling factor is not an integer. That is, the transformation from point A to point A' is not a dilation with a whole number scale factor.
As a result, A(1,2) and A'(5,12) are not dilations.
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if a,b and c are such that a:b:c =1:3:4 and c =28 then, the sum of a+b+c is
Answer:
the sum of a+b+c is 56.
Step-by-step explanation:
If a:b:c = 1:3:4 and c = 28, we can find the values of a and b using the ratios.
Since a:b:c = 1:3:4, we can write:
a = x, b = 3x, c = 4x
where x is some constant of proportionality.
We are given that c = 28, so we can substitute this value to get:
4x = 28
Solving for x, we get:
x = 7
Therefore, a = x = 7 and b = 3x = 21.
The sum of a, b, and c is:
a + b + c = 7 + 21 + 28 = 56
So the sum of a+b+c is 56.
What is the surface area of the square pyramid?
______________________________________
(reporting wrong/spam answers)
(giving brainliest to the correct answer)
______________________________________
Answer:
105 in
Step-by-step explanation:
The area of the square pyramid = 4x( the area of the triangle) + the area of the squareArea of the triangle: the rule of multiplying the height divided by two4×(8×5) =80
2
5×5=25
25+80=105
how do i go about finding x° and ycm, please?
I've tried Sine Rule & Cosine Rule... I thought i had done it correctly until i worked out the angles added up to much higher than 180° so it cannot be correct... can anyone help?
From the solution;
x = 62.62°
y = 8.9 cm
What is the sine rule?The sine rule (also known as the law of sines) is a mathematical formula that relates the sides and angles of a triangle. Specifically, it relates the ratios of the lengths of the sides of a triangle to the sine of the opposite angles.
By the use of the sine rule;
a/Sin A = c/Sin C
Sin C = cSin A/a
C = Sin-1(cSin A/a)
C = Sin-1(7.8 * sin 66.4/9.2)
C = 50.98°
B = 180 - (50.98° + 66.4)
B = 62.62°
Then;
a/Sin A = b/Sin B
9.2/Sin66.4 = b/Sin 62.62
b = 9.2 * Sin 62.62/Sin66.4
b = 9.2 * 0.89/0.92
b = 8.9 cm
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Construct a 95% confidence interval for the data (mean of the differences). Report your answers to three decimal places.
( ), ( )
for trader joes safeway
n = 57 n=57
x= 2.9442 x= 3.4123
s= 1.7458 s= 2.0382
We can be 95% confident that the true population mean difference between the two samples falls within the range of 0.374 to 0.562
Computing 95% Confidence Interval for Mean DifferencesTo construct a 95% confidence interval for the data, we need to calculate
the mean difference between two sample means (x₁ - x₂)the standard deviation of the differences (sD)the margin of error (ME)the upper and lower bounds of the confidence interval (CI).The formula for the mean difference is:
x₁ - x₂ = 3.4123 - 2.9442 = 0.4681
The formula for the standard deviation of the differences is:
sD = √[(s₁²/n₁) + (s₂²/n₂)]
SD = √[(1.7458²/57) + (2.0382²/57)]
SD = 0.3555
The margin of error is calculated using the following formula:
ME = t * (sD / √(n))
where t is the critical value for a 95% confidence interval with 56 degrees of freedom
So, we have
ME = 2.003 * (0.3555 / √(57))
ME = 0.0943
Finally, we can calculate the upper and lower bounds of the confidence interval:
CI = (x₁ - x₂) ± ME
CI = 0.4681 ± 0.0943
CI = (0.4681 - 0.0943, 0.4681 + 0.0943)
CI = (0.3738, 0.5624)
Approximate
CI = (0.374, 0.562)
Thus, the 95% confidence interval for the mean differences is (0.374, 0.562), rounded to three decimal places.
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