The evidence suggests that the average distance hiked by each visitor has decreased to less than 25 kilometers, so the null hypothesis is rejected.
The p-value is the probability of getting a test statistic result at least as extreme as the one observed, given that the null hypothesis is true. If the p-value is less than the chosen level of significance (which is 0.05 in this case), then the null hypothesis is rejected. In this case, since the p-value is less than 0.05, the null hypothesis is rejected. This means that there is enough evidence to conclude that the mean distance hiked by each visitor is now less than 25 kilometers.
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5. Harry’s Carryout Stores has eight locations. The firm wishes to expand by
two more stores and needs a bank loan to do this. Mr. Wilson, the banker,
will finance construction if the firm can present an acceptable three-month
financial plan for January through March. The following are actual and
forecasted sales figures:
Actual Forecast Additional Information
November $260,000 January $400,000 April forecast $400,000
December 340,000 February 440,000 March 410,000
Of the firm’s sales, 60 percent are for cash and the remaining 40 percent
are on credit. Of credit sales, 20 percent are paid in the month after sale
and 80 percent are paid in the second month after the sale. Materials cost
20 percent of sales and are purchased and received each month in an
amount sufficient to cover the following month’s expected sales. Materials
are paid for in the month after they are received. Labor expense is 50
percent of sales and is paid for in the month of sales. Selling and
administrative expense is 15 percent of sales and is also paid in the month
of sales. Overhead expense is $31,000 in cash per month.
Depreciation expense is $10,600 per month. Taxes of $8,600 will be paid in
January, and dividends of $5,000 will be paid in March. Cash at the
beginning of January is $92,000, and the minimum desired cash balance is
$87,000.
For January, February, and March, prepare a schedule of monthly cash
receipts and monthly cash payments.
In January the Net cash flow: ($35,200) , In February Net cash flow: $6,400 and In march Net cash flow: $21,900.
What is Cash receipt?A cash receipt is an official document that is issued to a customer or client when they make a payment in cash. It serves as proof of the payment, and is an important record for both the buyer and the seller. A cash receipt typically contains the date and time of the transaction, the amount of cash received, and a description of the goods or services that were purchased. It is usually signed by both the seller and the buyer.
January
Cash receipts:
Cash sales: $400,000 x 60% = $240,000
Credit sales from November: $260,000 x 20% = $52,000
Credit sales from December: $340,000 x 20% = $68,000
Total cash receipts: $360,000
Cash payments:
Materials: $400,000 x 20% = $80,000
Labor: $400,000 x 50% = $200,000
Selling and administrative: $400,000 x 15% = $60,000
Overhead: $31,000
Depreciation: $10,600
Taxes: $8,600
Dividends: $5,000
Total cash payments: $395,200
Net cash flow: ($35,200)
February
Cash receipts:
Cash sales: $440,000 x 60% = $264,000
Credit sales from December: $340,000 x 20% = $68,000
Credit sales from January: $400,000 x 20% = $80,000
Total cash receipts: $412,000
Cash payments:
Materials: $440,000 x 20% = $88,000
Labor: $440,000 x 50% = $220,000
Selling and administrative: $440,000 x 15% = $66,000
Overhead: $31,000
Depreciation: $10,600
Total cash payments: $405,600
Net cash flow: $6,400
March
Cash receipts:
Cash sales: $410,000 x 60% = $246,000
Credit sales from January: $400,000 x 20% = $80,000
Credit sales from February: $440,000 x 20% = $88,000
Total cash receipts: $414,000
Cash payments:
Materials: $400,000 x 20% = $80,000
Labor: $410,000 x 50% = $205,000
Selling and administrative: $410,000 x 15% = $61,500
Overhead: $31,000
Depreciation: $10,600
Dividends: $5,000
Total cash payments: $392,100
Net cash flow: $21,900
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Which function has a constant additive rate of change of –1/4? A coordinate plane with a straight line with a negative slope. The line passes through (negative 2, 2) and (2, 1). A coordinate plane with a curved line passing through (negative 1, 2), (0, negative 1), the minimum (2, negative 2), and (4, negative 1). A two column table with five rows. The first column, x, has the entries, 20, 21, 22, 23. The second column, y, has the entries negative 1, negative 1.5, negative 2, negative 2.5. A two column table with five rows. The first column, x, has the entries, negative 12, negative 11, negative 10, negative 9. The second column, y, has the entries, 7, 11, 14, 17. Using Different Representations Which function has a constant additive rate of change of-1/4? y 20 -12 7 21 -1,5 -11 11 14 =2 241-2 22 ~2 -10 23 -2.5 -9 17'
In the picture the correct option is A when the function shown in graph (A) has a constant additive rate of change is -1/4.
Given that,
We have to find which function has an additive change rate that is -1/4 constant throughout time. a line in the coordinate plane with a downward slope. (negative 2, 2) and the line (2, 1).
We know that,
The line goes through the points:
(-2, 2) and (2, 1)
y - 1 = (1-2)/(2+2)[x -2]
y - 1 = (-1/4)[x -2]
y = -x/4 + 1/2 + 1
y = -x/4 + 3/2
The change at a constant additive rate is -1/4.
Therefore, In the picture the correct option is A when the function shown in graph (A) has a constant additive rate of change is -1/4.
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I forgot how to get this. Please help
The congruence statement for the triangle is that they gave same sides and angles.
What exactly are Congruent Triangles?When the three sides and three angles of two triangles are equal in any orientation, they are said to be congruent.
According to the Side Side Side (SSS) Theorem, if all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are congruent.
It should be noted that from the triangle given, the sides and angles are the same. This was illustrated. This illustrates the congruence and the triangle was reflected.
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Find the area in feet.
which of the following pairs of variables is likely to have a negative correlation? check all that apply.
The two variables to have a negative correlation are x and y.
Negative correlation is the relationship where x grows as y decreases.
Given,
Here, negative correlation is used to describe the relationship between two variables that results in independent variables moving in one direction while dependent variables move in another.
Positive correlation
Positive correlation is when the value of the variable x rises as the value of the variable y rises.
Negative Correlation
Negative correlation is the relationship where x grows as y decreases.
No correlation
No correlation exists between the two variables.
That example, the term "no-correlation" refers to the absence of a connection between two variables.
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The question is improper. Proper question is given below;
What two variables are likely to have a negative correlation
suppose that a community contains 15,000 people. at time time, t, the number n (t) of people who have a gene that causes a triangle on their forehead is 5,000 and is increasing at a rate of 500 per day.
The community will contain 15,000 people with the gene that causes a triangle on their forehead after 20 days.
The rate of change of n (t) with respect to time is 500 people per day. This means that the equation for n (t) is given by:
n (t) = 5,000 + 500t
where t is the number of days since time t. At time t, n (t) = 5,000, and as time passes, the number of people with the gene that causes a triangle on their forehead increases. After 20 days, n (t) = 5,000 +500*20 = 15,000, meaning that after 20 days, the community will contain 15,000 people with the gene that causes a triangle on their forehead.
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- 14 + x = 42, x = is 56 a solution
[tex]\fbox{x=56}[/tex]
Simplify:
[tex]x-14=42[/tex]
Add 14 to both sides:
[tex]x-14+14=42+14[/tex]
[tex]x=56[/tex]
Consider the data set. 2, 3, 5, 6, 7. use the defining formula to compute the sample standard deviation s. (round your answer to two decimal places.)
The sample standard deviations of the data set 2, 3, 5, 6, 7 rounded up to 2 decimal spaces is 2.07.
The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. Think about the following data: 2, 1, 3, 2, 4.
The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation. The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.
Number of data points (n)=5
Mean (x)= (2+3+5+6+7)/5= 4.6
Here x = 2, 3, 5, 6, 7
(x-x) = -2.6, -1.6, 0.4, 1.4, 2.4
[tex](x-X)^{2}[/tex] = 6.76, 2.56, 0.16, 1.96, 5.76
∑[tex](x-X)^{2}[/tex] = 17.2
Sample standard deviation :
[tex]\sqrt{\frac{(x-X)^{2}}{n-1} } \\\\\sqrt{\frac{17.2}{4} } \\\\[/tex]
= 2.07
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A prestigious university wants to estimate the average starting salary of its graduates. The alumni outreach department sends an email to the most recent address they have on file for every graduate. The email asks the graduates to participate in a survey about their employment history and starting salary.
What are some possible concerns?
Some graduates won't check their emails and therefore won't respond (non-response bias)
Graduates might claim they make more $ than they actually do (response bias)
The correct option is option C i.e., current students are not included in the sample for the survey.
Current students are not required to participate in this survey because its main objective is to learn about respondents' career histories and starting salaries .
Survey could mean:
Research into humans and statistics.
A statistical survey is a technique for gathering numerical data on constituents of a population.
Type of survey
Spatial measurement : measuring places and distances on Earth using the technique and science of surveyingPhotogrammetry, a method of collecting information using aerial photographs and satellite imageryCadastral surveyors provide paperwork, diagrams, plats, and maps to prove who owns the land.
Most of Western Canada is divided into one-square-mile pieces using the Dominion Land Survey technique for agricultural and other uses. Identifying and surveying land parcels in the United States using the Public Land Survey System.
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Ping is sewing a square tablecloth. The table she wants to cover is 5.5 feet on each side and she wants it to hang over on each side 9 inches. How many square feet of fabric will Ping need?
I've answered this question in two ways and I think I get to the right answer the second time but it's driving me crazy why it doesn't work the first way.
First way:
The cloth is now a rectangle length 66 in (5.5 feet x 12) by 75 in (5.5 feet x 12, plus 9).
a=l*w=66x75=4950 inches÷12 =412.5 sq ft.
Checking my answer for reasonableness, I thought, but if I just multiply 5.5 feet x 5.5 feet , sans adjustments, I get 30.25.
Second way: 9 inches/12 = .75 ft 5.5+.75 = 6.25 ft, and 5.5 x 6.25 ft = 34.375 SQ ft, makes much more sense. But WHY?
Answer:
The first way is rectangular. You also converted it wrong for the first one. the inches aren's squared. you're converting regular inches into regular feet, instead it should be square inches into square feet.
And Ping is sewing a square tablecloth, not a rectangular one. you have to add the 9 inches on both sides, not just one. You can convert it either way you want, but you have to add the 9 inches to both.
Ten families were randomly selected and their daily water usage (in gallons) before and after viewing a conservation video was recorded. The sample mean difference was found to be 4.8 and the corresponding standard deviation 5.25, where differences were found (Before - After). Assume the data is normally distributed. Find a 90% confidence interval for this data. State the lower bound [x] and the upper bound [y].
lower bound = 1.76
Upper bounds = 7.84
The 90% confidence interval for the given data is 4.8 ± 2.73.
What is Confidence interval?A confidence interval is a type of interval computation used in statistics that determines the true value of an unknown parameter based on the observed data. The interval estimates the deterministic parameter with a level of confidence that is quantified by the confidence level.
Given, sample mean (x) = 4.8
z at 90% confidence level = 1.645
sample standard deviation (s) = 5.25
sample size (n) = 10
We know that, Confidence interval = x ± (z × s) ÷ √n
= 4.8 ± (1.645×5.25)/√10
= 4.8 ± 8.63625/3.1622
= 4.8 ± 2.73
∴ Lower bound = 4.8 - 2.73 = 2.07
and, Upper bound = 4.8 + 2.73 = 7.53
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find the maclaurin expansion for the following functions and indicate for which values of x it actually represents the function
The maclaurin expansion for function eˣ is 1 + x + x²/2 + x³/6 + x⁴/24 + .....
A function's expansion series, which provides the function's derivatives' sum, is known as a Maclaurin series.
Series [f, x, 0, n] can be used to find a function's Maclaurin series up to order n.
When x = 0, it is a specific example of the Taylor series. The series of Maclaurin is provided by
[tex]f(x) = f(x_0) + f(x_0)(x - x_0) + \frac{f"(x_0)}{2!}(x - x_0)^2 + . . .[/tex]
The formula for maclurin series is :
[tex]f(x) = \sum^{\infty}_{n=0} \frac{f^n (x_0)}{n!} (x-x_0)[/tex]
Where,
f(xo), f’(xo), f’‘(xo)……. are the successive differentials when xo = 0.
Maclaurin expansion for the function eˣ
Firstly , We will derivate the function
f(x) = eˣ
=> f'(x) = e⁰ = 1
=> f''(x) = e⁰ = 1
=> f'''(x) = e⁰ = 1
and so on
Upon evaluation of all derivatives at x = 0, we obtain the value 1.
Moreover, f(0)=1, so we can deduce that the expansion of the Maclaurin Series as
=> eˣ = 1 + x + x²/2 + x³/6 + x⁴/24 + .....
The given question is incomplete , I answered the question in general according to the knowledge
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Which of these quantities is a vector?
A. Time
B. Momentum
C. Distance
D. Speed
On solving the provided question, by the given information we can say that Momentum is a vector quantity.
What is vector quantity?A physical quantity that only has magnitude is known as a scalar quantity. such as distance, speed, mass, density, etc. However, vector quantities—which include displacement, velocity, acceleration, force, and mass—are physical quantities that have both magnitude and direction.
Momentum is a vector quantity.
It is directed and has a magnitude. According to Isaac Newton's second law of motion, the force pushing a particle has an equal and opposite effect on the time rate at which its momentum changes. Consider Newton's laws of motion.
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A construction worker earns and average biweekly net pay of $1,764. Which compound inequality correctly shows the amount of money, t, the worker can spend if the monthly budget for food is between 10% and 20% ?
The compound inequality of amount of money is 176.4 < f < 352.8
What is compound inequality?
A compound difference (or combined difference ) is 2 or a lot of inequalities joined along with or or and.
Main Body:
Given,
A construction worker earns an average bi-weekly net pay of $1,764.00.
and, the worker can spend if the monthly budget for food is between 10% and 20%.
To find the which compound inequality correctly shows the amount of money?
Now, According to the question:
Total earning is $1,764.00
Amount can be spent on food is :
0.1× 1764.00 < f < 0.2 ×1764.00
176.4 < f < 352.8
Hence, The compound inequality of amount of money is 176.4 < f < 352.8
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pls help !
Solve the system using inverse
matrices.
(9x - 2y = 12
3x + 4y = 18
([? ],[ ])
The solved inverse matrices.
(9x - 2y = 12
3x + 4y = 18
([2],[3 ])
How to solve the system using inverse matrices?To solve a system of linear equations using inverse matrices, we can express the system in matrix form as follows:
[9 -2] [x] = [12]
[3 4] [y] [18]
Then we can find the inverse of the coefficient matrix, which is the matrix containing the coefficients of the variables in the system:
[9 -2]^⁻¹ = 1/((9)(4) - (-2)(3)) * [ 4 2]
[3 4] [ -3 9]
= 1/14 * [ 4 2] = [2/7 1/7]
[ -3 9] [-3/7 2/7]
We can then multiply both sides of the equation by the inverse matrix to obtain the solution:
[2/7 1/7] [9 -2] [x] = [2/7 1/7] [12]
[-3/7 2/7] [3 4] [y] [-3/7 2/7] [18]
[x] = [2/7 1/7]^-1 [2/7 1/7] [9 -2] [x]
[y] [-3/7 2/7] [-3/7 2/7] [3 4] [y]
[x] = [1 0] [9 -2] [x]
[y] [0 1] [3 4] [y]
This simplifies to the following system of equations:
9x - 2y = 12
3x + 4y = 18
Therefore in solving this system, we find that x = 2 and y = 3. So, the solution to the original system is (x, y) = (2, 3).
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Find the solution set 4x^2+9x-9=0
The solution sets for the given quadratic equation 4x²-9x-9=0 are -3/4, 3
What is a quadratic equation?Any equation in algebra that can be rearranged in standard form as follows is known as a quadratic equation (from Latin quadratus, which means "square").
[tex]{\displaystyle ax^{2}+bx+c=0\,,}[/tex]
While a, b, and c are known values, x is an unknown value, and vice versa. The assumption is that a > 0; equations with a = 0 are thought to be degenerate because they become linear or even simpler. The terms "quadratic coefficient," "linear coefficient," and "constant or free term" can be used to distinguish the three values that make up the equation's coefficients, respectively.
Given,
4x²-9x-9=0
4x²-12x+3x-9=0
4x(x-3)+3(x-3)=0
(4x+3)(x-3)=0
4x+3=0, x-3=0
4x-3=0
4x=3
x= -3/4
x-3=0
x=3
Therefore, the solution sets for 4x²-9x-9=0 are -3/4, 3
Hence, the solution sets for the given quadratic equation 4x²-9x-9=0 are -3/4, 3
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Please help me find the answer to this question
-------------------------------------------------------------------------------------------------------------
Answer: The top right table
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{y = 30 - 3x}[/tex]
Find: [tex]\textsf{Match the table of values with the equation}[/tex]
Solution: First we must understand what form our equation is in and what each of the numbers represent. This form is known as the slope intercept form which is formatted as y = mx + b. Our equation is slightly re-ordered but we can change that by converting it to y = -3x + 30 where m is equal to -3 and b is equal to 30. Let us know talk about what m and b are. M is the slope of the equation or also known as the rise/run or the change in y over the change in x. B is the y-intercept which is basically the value of y when x is equal to 0. In this case, our b is equal to 30.
Looking at the tables we can see what the value of y when x is equal to 0 for each table. The only table that matches up stating that y is equal to 30 when x is 0 is the top right table.
You do not have to go any further but if you want to confirm that the slope is as expected we can do the following: [tex]\frac{y_2\ -\ y_1}{x_2\ -\ x_1}[/tex].
Plug in the values and simplify
[tex]\frac{48\ -\ 30}{-6\ -\ 0}[/tex][tex]\frac{18}{-6}[/tex][tex]-3[/tex]Therefore, we can confirm that the slope matches up with the given equation as well. So, the final answer would be that the top right table would correspond to the equation y = 30 - 3x.
Find an equation of the tangent plane to the given parametric surface at the specified point. I and the tangent plane. r(u,v)=u cos v hat xi +u sin y dot y +vk ; u = 5 v = pi / 3
The equation of tangent plane to the given parametric surface [tex]r(u,v) = u.cos(v)i + u.sin(v)j + vk[/tex] is [tex]\frac{\sqrt3}{2}x - \frac{5}{2}y + 5z = \frac{5\pi}{3}[/tex] .
The given parametric surface is
[tex]r(u,v) = u.cos(v)i + u.sin(v)j + vk[/tex]
The tangent vectors are
⇒ [tex]r_u = \frac{dx}{du} i+ \frac{dy}{du}j + \frac{dz}{du}k[/tex]
⇒ [tex]r_u =[/tex] [tex]r(u,v) = cos(v)i + sin(v)j + 0k[/tex]
⇒ [tex]r_v = \frac{dx}{dv} i+ \frac{dy}{dv} j+ \frac{dz}{dv} k[/tex]
⇒ [tex]r_v =[/tex] [tex]r(u,v) = -u.sin(v)i + u.cos(v)j + 1k[/tex]
The normal vector to the tangent plane is
[tex]r_u r_v = \left[\begin{array}{ccc}i&j&k\\cos(v)&sin(v)&0\\-usin(v)&ucos(v)&1\end{array}\right][/tex]
⇒ [tex]r_u r_v =[/tex] [tex]sin(v)i - cos(v)j + u.k[/tex]
When u = 5, v = [tex]\frac{\pi }{3}[/tex], the normal vector becomes
⇒ [tex]sin(\frac{\pi}{3})i - cos( \frac{\pi}{3})j + k[/tex]
⇒ [tex]\frac{\sqrt{3} }{2}i - \frac{1}{2} j + k[/tex]
The point on the surface corresponding to the u = 5 & v= [tex]\frac{\pi}{3}[/tex] is
[tex]r(5, \frac{\pi}{3}) = (5)cos(\frac{\pi}{3})i + (5)sin(\frac{\pi}{3})j + (\frac{\pi}{3})k\\r(5, \frac{\pi}{3}) = \frac{5}{2}i + \frac{5\sqrt3}{2}j + \frac{\pi}{3}k[/tex]
If a is the position vector of a point on the plane & n is a vector normal to the plane, then the equation of the plane is
⇒ (r - a).n = 0
⇒ [tex](x - \frac{5}{2}) . ( \frac{5\sqrt3}{2}) + (y - \frac{5\sqrt3}{2}).(- \frac{5}{2}) + (z - \frac{\pi}{3}).(5) = 0[/tex]
⇒ [tex]\frac{\sqrt3}{2}x - \frac{5}{2}y + 5z = \frac{5\pi}{3}[/tex]
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Find the unknown angle:
Answer:
x = 36°, y = 72°, z = 108°, w = 72°----------------------------------------------
Given is the parallelogram.
Properties:
Adjacent angles are supplementary;Opposite angles are congruent.Solve the following:
2x + 3x = 1805x = 180x = 180/5x = 36y = 2x = 2*36 = 72z = 3x = 3*36 = 108w = 180 - z = 180 - 108 = 72Answer:
w = 72°
x = 36°
2x = 72°
3x = 108°
y = 72°
z = 108°
Step-by-step explanation:
The arrows on the sides of figure ABCD indicate that opposite sides are parallel. Therefore, ABCD is a parallelogram.
In a parallelogram:
Opposite angles are equal.Interior angles sum to 360°.Adjacent angles are supplementary (sum to 180°).As adjacent angles sum to 180°:
⇒ m∠A + m∠B = 180°
⇒ 3x + 2x = 180°
⇒ 5x = 180°
⇒ x = 36°
Therefore:
⇒ m∠A = 3(36) = 108°
⇒ m∠B = 2(36) = 72°
As opposite angles are equal:
⇒ y = m∠D = m∠B = 72°
⇒ z = m∠BCD = m∠A = 108°
Angles on a straight line sum to 180°:
⇒ z + w = 180°
⇒ 108° + w = 180°
⇒ w = 72°
which of the following will always pass through a vertex of a triangle
A line segment is a straight line connecting two points. In the case of a triangle, a line segment will always pass through a vertex, which is one of the three points that make up the triangle. A vertex is defined as the point at which two or more lines meet.
Which of the following will always pass through a vertex of a triangle?Option B. A line segment.The other two points of a triangle are known as the base and apex. The base is the line that connects two vertices and forms the base of the triangle. The apex is the point of the triangle that is opposite the base and is the highest point of the triangle. All three of these points are connected by line segments, and together they form a triangle. Each line segment will always pass through one of the vertices of the triangle, thus forming the sides of the triangle.
Since the question is not complete, here is the full task:Which of the following will always pass through a vertex of a triangle?
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find the area of a circle with a radius of 13 inches use 3.14 for pi do not round your answer
The area is:
530.66 in^2Explanation:
To find the circle's area, use the formula [tex]\sf{A=\pi r^2}[/tex].
where:
A = area;
π = 3.14 (pi);
r = radius
Diagram:
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 13\ in}\end{picture}[/tex]
Plug in the data:
[tex]\sf{A=3.14\times13^2}[/tex][tex]\sf{A=3.14\times169}[/tex][tex]\sf{A=530.66\:in^2}[/tex]
lian wants to advertise how many chocolate chips are in each big chip cookie at her bakery. she randomly selects a sample of 46 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 7.4 and a standard deviation of 2.7. what is the 95% confidence interval for the number of chocolate chips per cookie for big chip cookies? assume the data is from a normally distributed population. round answers to 3 decimal places where possible.
The big chip cookie's 95% confidence interval for the amount of chocolate chips per cookie is [8.325,6.474].
Given that,
The quantity of chocolate chips in each big chip cookie at Lian's bakery is something she wants to promote. She chooses a sample of 46 cookies at random and discovers that the average amount of chocolate chips per cookie has a standard deviation of 2.7 and a mean of 7.4.
We have to find what is the big chip cookie's 95% confidence interval for the amount of chocolate chips per cookie.
We know that,
The formula is
=x±Z(S/√n)
=7.4±2.326(2.7/√46)
=8.325 and 6.474
Therefore, the big chip cookie's 95% confidence interval for the amount of chocolate chips per cookie is [8.325,6.474].
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Find the dimensions of the rectangle of maximum area, with sides parallel to the coordinate axes, that can be inscribed in the ellipse given by x^2/144+y^2/16=1
The dimensions of the rectangle of maximum area are the length of 12√3 units and width of 4 units
How to find the dimensions of the rectangle of maximum area?
Given that the ellipse has the equation: x²/144 + y²/16 = 1
Make x the subject:
x²/144 + y²/16 = 1
(x²+9y²)/144 = 1
x² + 9y² =144
x² = 144-9y²
x = √(144-9y²)
The rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Thus, the rectangle has a length and width of 2x and 2y respectively
The area of a rectangle inscribed inside an ellipse is given by:
Area (A) = 4xy
A = 4(√(144-9y²))y
A = 4y√(144-9y²)
A = 4√(144y²-9y⁴)
The maximum area of the rectangle is at dA/dy = 0
dA/dy = 4[144-18³y/ (√(144y²-9y⁴))]
4[144-18y³/ (√(144y²-9y⁴))] = 0
144-18y³= 0
18y³ = 144
y³ = 144/18
y³ = 8
y = ∛8
y = 2
x = √(144-9y²)
x = √(144 - 9(2)²)
x = √108
x = 6√3
Thus, the dimensions are the length = 2x = 2×(6√3) = 12√3 units, the width = 2y = 2×2 = 4 units
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(i) The Government has imported large quantities of sugar as per trade agreement with other countries.(ii) The prices of sugar in the domestic market have fallen sharply in the recent months.A. Statement I is the cause and statement II is its effectB. Statement II is the cause and statement I is its effectC. Both the statements I and II are independent causesD. Both the statements I and II are effects of independent causesE. Both the statements I and II are effects of some common cause
The correct option is: A
Statement I is the cause and statement II is the effects.
Since the Government has imported large quantities of sugar as per trade agreement with other countries, the prices of sugar in the domestic market have fallen sharply in the recent months.
The reason behind this statement is:
An increase in supply always leads to a decrease in price.
Supply : Supply is a fundamental economic concept that describes the total amount of a particular good or service available to consumers. Supply can refer to the quantity available at a particular price or the quantity available across the price range displayed on the chart. It is closely related to the demand for goods or services at a particular price. All else being equal, when prices rise, producer supply increases as all firms try to maximize their profits.
Increase in Supply:
If the demand does not change, there is an inverse relationship between the supply and price of goods and services. When the supply of goods and services increases at the same demand, prices tend to fall resulting in lower equilibrium prices and higher equilibrium quantities of goods and services. When the supply of goods and services decreases for the same demand, prices tend to rise towards higher equilibrium prices and smaller quantities of goods and services.
Since the supply of sugar increases as government has over imported, the price of sugar decreases in domestic market.
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If the sample size is held constant, which of the following will produce the widest 90% confidence interval for the population mean difference for a repeated-measures study?Answer1. MD = 3 with s2 = 20 for the difference scores2. MD = 5 with s2 = 5 for the difference scores3. MD = 5 with s2 = 10 for the difference scores4. MD = 3 with s2 = 10 for the difference scores
The correct option is (d) i.e; MD = 3 with s2 = 20 for the difference scores because it generates a repeated-measures study's population mean difference with the widest 90% confidence interval.
Given that,
Which of the following will result in the widest 90% confidence interval for the population mean difference for a repeated-measures research, provided the sample size is kept constant?
MD = 3 with s2 = 20 for the difference scores.
Therefore, the correct choice is MD = 3 with s2 = 20 for the difference scores because it produces the widest 90% confidence interval for the population mean difference for a repeated-measures study.
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What is a rotational shape?; What shapes have rotational symmetry lines?; What is a shape with 3 rotational symmetry?; Is a wheel an example of rotational symmetry?
A wheel is an example of rotational symmetry . Many shapes such as squares, circles, and regular hexagons have rotational symmetry. As wheel is a rotational shape thing that's why it is consider as an example of rotational symmetry.
If the image is rotated 120 degrees of hers, then another 120 degrees of his, and finally 120 degrees of his third his, it will look the same in all three positions. This property is called rotational symmetry. Rotational symmetry is found, for example, in circles, squares, rectangles, and all regular polygons. Take an object and rotate it up to 180 degrees around its center. An object has rotational symmetry if it looked the same at any time before the revolution.
Center:
The center, fulcrum, or center of balance refers to a specific point at which an object can spin, spin, or rotate. When we find this position, we have found the center of the object. By rotating around this center, we can determine the rotational symmetry of the rectangles.
Rotational Symmetry and Order:
Rotational symmetry is a measure of how often an object appears to rotate 360 degrees in the same way. If it matches the original shape only twice, it has degree 2. If it matches 3 times, then the order is 3, and so on. Common rotation orders and object rotation amounts are: Order 2 is 180 degrees, order 3 is 120 degrees, and order 4 is 90 degrees. Order No. 5 has a temperature of 72 degrees, Order No. 6 has a temperature of 60 degrees.
Regular polygons:
Many everyday objects exhibit rotational symmetry. In mathematics, all regular polygons have rotational symmetry. For example, consider an equilateral triangle. An equilateral triangle corresponds three times as it rotates around its center. As a result, it exhibits cubic rotational symmetry.
Angle of Rotation:
Knowing the number of points required to rotate an object about its center is important for determining the degree of rotational symmetry, but where and when to adjust it to its original position. I know I should rotate it. In general, if you use an item frequently, physically rotating it will indicate the degree of rotation. Imagine a rectangular mobile phone. As a result, the rectangular shape of the phone has been rotated 180 degrees twice.
degree of rotation = 360°/degree of rotation
You can also calculate the degree by dividing the degree of rotation by: degree = 360°/degree of rotation
A starfish rotates 72 degrees and has an order of 5. The rotational symmetry of the chemical structure of the benzene molecule is of interest. This molecule has rotational symmetry of order 6 with a rotation of 60 degrees.
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If six granola bars contain 900 calories, write the equation to determine the calories for a single bar?
Answer:
[tex]6g=900[/tex]
Step-by-step explanation:
The number of calories in one bar multiplied by six is the number of calories in six bars. This is given to be equal to 900.
If P is the incenter of A JKL, find each measure. K 10 M P 7 17 32" 22' L
Although part of your question is missing, you might be referring to this full question: If P is the incenter of ΔJKL, find each measure (triangle as attached).
Based on the property of incenter, the measurements of the sides and the angles will be:
JK = 21.2 units
KL = 26.63 units
JL = 28.33 units
m∠K = 36°
By using the property of incenter:
PM = PN = PO = 7 units
∠MJP = ∠OJP = 32°
∠NLP = ∠OLP = 22°
By using the triangle sum theorem,
m∠JKL + m∠KLJ + m∠LJK = 180°
2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°
2(m∠NKP) + 2(22°) + 2(32°) = 180°
2(m∠NKP) = 180° - 108°
m∠NKP = 36°
Then, from ΔJMP,
tan(32°) = MP/MJ
tan(32°) = 7/MJ
MJ = 7/tan(32)°
MJ = 11.20
And from ΔPOL,
tan(22°) = OP/OL
tan(22°) = 7/OL
OL = 17.33
And from ΔKNP,
tan(36°) = NP/KN
tan(36°) = 7/KN
KN = 9.63
Hence, JK = MJ + MK = 21.2 units
KL = LN + KN = 26.63 units
JL = JO + OL = 28.33 units
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Describe the location of the point that has the following coordinates: negative abscissa, zero ordinatea. between Quadrant III and Quadrant IVb. between Quadrant II and Quadrant IVc. between Quadrant I and Quadrant IVd. between Quadrant II and Quadrant III
The correct location of the point is (d) between Quadrant II and Quadrant III.
We must choose the response that accurately describes the position of the point whose coordinates have a negative abscissa and a zero ordinate.
Any point with a negative abscissa and a zero ordinate on the XY plane in two dimensions can be represented as
Where a > 0, (x, y) = (-a, 0).
Let's plot (-1, 0), (-2, 0), (-3, 0), etc. on the coordinate plane as an example. The corresponding figure illustrates this.
The figure shows that every point of the type (-a, 0) is located on the X-axis' negative side.
The location of the negative X-axis between Quadrants II and III is known. As a result, the supplied point is situated between Quadrants II and III.
the appropriate answer is (d).
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A television station claims that the amount of advertising per hour of broadcast time has an average of 15 minutes and a standard deviation equal to 1.2 minutes. You watch the station for 1â hour, at a randomly selectedâ time, and carefully observe that the amount of advertising time is equal to 17 minutes. Calculate theâ z-score for this amount of advertising time. A. zequalsnegative 1.05 B. zequals1.05 C. zequals1.67 D. zequalsnegative 1.67
The z-score for the time spent on advertisement as calculated is 1.666 .
According to a television station, there is 15 minutes on average of advertising every hour of broadcast time, with a standard deviation of 1.2 minutes.
i.e.
mean = 15
SD =1.2
Per hour's worth of advertising is represented by the random variable x.
z = x - mean / SD
Since x=17 , we have
z = ( 17 - 15 ) / 1.2
= 2 / 1.2
= 1.666
Consequently, this amount of advertising time has a z-score of -1.666.
A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.
A standard normal table is a mathematical table for the values of, displaying the values of the cumulative distribution function of the normal distribution. It is also known as the unit normal table or the z-score table. The Z-score, commonly referred to as the standard score, expresses how far away from the mean an object is.
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