Answers
the area of the triangle is approximately 71.82 square units.
HOW TO SOLVE THE PROBLEM?
Using the Pythagorean theorem, we can find the length of the base of the right triangle:
Base² = Hypotenuse²- Perpendicular²
Base²= 18²- 15²
Base² = 324 - 225
Base² = 99
Taking the square root of both sides, we get:
Base = √99
Simplifying the square root of 99, we get:
Base = √(9 x 11)
Base = 3√11
Therefore, the length of the base of the right triangle is 3√11.
to find the area of the triangle 3√11-8=1.94
then we can find three side of triangles
which are 15,18,15.12
To find the area of a triangle when the lengths of its three sides are known, we can use Heron's formula:
Area = √[s(s-a)(s-b)(s-c)]
where s is the semiperimeter of the triangle, and a, b, and c are the lengths of its sides.
The semiperimeter s is half the perimeter of the triangle:
s = (15 + 18 + 15.14) / 2 = 24.57
Using this value for s, and plugging in the lengths of the sides a = 15, b = 18, and c = 15.14, we get:
Area = √[24.57(24.57-15)(24.57-18)(24.57-15.14)]
= √[24.57(9.57)(6.57)(9.43)]
= √5153.5853
= 71.82 (approx)
Therefore, the area of the triangle is approximately 71.82 square units.
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Related Questions
You met Jonathan while waiting for your plane in the airport at Brownsville. He is working in the marketing research department for a company that manufactures and sells memory chips for microcomputers. He has established the following price- demand and revenue functions: P(x) = 75 - 3x R(x) = x P(x) Where P(x) is the wholesale price in dollars at which x million chips can be sold, and R(x) is in millions of dollars. Both functions have a domain 1 ≤ x ≤ 20.
Answers
a. The revenue functiοn R(x) = 75x - 3x² graph plοtted belοw.
b. Value οf x is 12.5 and maximum revenue prοduces $468.75
c. Whοlesale price/chip that prοduces the maximum revenue is $37.50
Define the term revenue?A cοmpany's οr business's revenue is the tοtal amοunt οf mοney it receives frοm sales οf its prοducts οr services οver a given time periοd.
a) Tο sketch a graph οf the revenue functiοn R(x), we first need tο calculate R(x) using the given fοrmula:
⇒ R(x) = x P(x)
⇒ R(x) = x(75 - 3x)
⇒ R(x) = 75x - 3x²
Nοw we can plοt this functiοn οn a rectangular cοοrdinate system. Belοw is an sketch οf the graph.
b) Taking the derivative οf R(x) and setting it equal tο 0:
⇒ R'(x) = 75 - 6x = 0
⇒ 6x = 75
⇒ x = 12.5
Sο, x = 12.5 is the value οf x that will prοduce the maximum revenue. Tο find the maximum revenue, we can substitute x = 12.5 intο the revenue functiοn R(x) = x (75 - 3x)
⇒ R(12.5) = 12.5 (75 - 3 (12.5)) = 468.75
⇒ R(12.5) = $ 468.75
Therefοre, the maximum revenue is $468.75
c) Tο find the whοlesale price per chip that prοduces the maximum revenue, we can substitute x = 12.5 intο the price functiοn, P(x) = 75 - 3x
⇒ P(12.5) = 75 - 3(12.5)
⇒ P(12.5) = $37.50 per chip
Therefοre, the whοlesale price per chip that prοduces the maximum revenue is $37.50.
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Complete question:
A deck of cards contains red cards numbered 1,2,3,4,5, blue cards numbered 1,2,3,4,5,6,7,8,9 and green cards numbered 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15. If a single card is picked at random, what is the probability that the card is green?
Give your answer as a fraction.
Answers
The probability of picking a green card at random is 15/29.
What is the probability?Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
The total number of cards in the deck is:
Red cards: 5
Blue cards: 9
Green cards: 15
So, the total number of cards in the deck is 5 + 9 + 15 = 29.
The probability of picking a green card at random is the ratio of the number of green cards to the total number of cards in the deck:
Probability of picking a green card = Number of green cards / Total number of cards
Probability of picking a green card = 15 / 29
Hence, the probability of picking a green card at random is 15/29.
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The table below shows the salary that Ellen earned at her job based on her years of experience.
Years of
Experience
Salary
4 $31,900
5 $32,625
6 $33,350
7 $34,075
8 $34,800
9 $35,525
10 $36,250
Which explicit formula can be used to determine the salary, f(n), that Ellen earned with n years of experience?
Answers
Find the difference between year 4 and year 5 salary.
[tex]32,625 - 31,900 = 725[/tex] (rate of change)
Multiply [tex]4 \times 725[/tex] then subtract that number from 31,900 to find out base salary
[tex]4\times 724 = 2,900[/tex]
[tex]31,900 - 2,900 = 29,000[/tex]
That's the constant.
So,
[tex]f(n) = 725n + 29,000[/tex]
find the equation of a line passing through the point (-1,5) and (1,-5)
Answers
The equation of the line passing through the points (-1, 5) and (1, -5) is y = -5x.
What is equation of line?The collection of points that make up a line in a coordinate system are represented algebraically by a line's equation. The many locations that make up a line on a coordinate axis are denoted by the letters (x, y), and the relationship between x and y results in an algebraic equation that is known as an equation of a line. We can determine whether a given point falls on a line using the equation of any line.
We can use the point-slope form of the equation of a line to solve this problem, which is:
y - y₁ = m(x - x₁)
where:
m = slope of the line
(x₁, y₁) = coordinates of one of the points on the line
First, let's find the slope (m) of the line using the two given points:
m = (y₂ - y₁) / (x₂ - x₁)
m = (-5 - 5) / (1 - (-1))
m = -10 / 2
m = -5
Now we can use one of the points, say (-1, 5), and the slope (-5) to write the equation of the line:
y - 5 = -5(x - (-1))
Simplifying and rearranging the equation:
y - 5 = -5x - 5
y = -5x + 0
Therefore, the equation of the line passing through the points (-1, 5) and (1, -5) is y = -5x.
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Assume that Keisha's marginal tax rate is 40% and her tax rate on dividends is 15%. If a city of Atlanta bond pays 7.48% interest, what dividend yield would a dividend-paying stock (with no growth potential) have to offer for Keisha to be indifferent between the two investments from a cash-flow perspective?
Answers
The dividend yield is 8.8%.
What is the marginal tax rate?
The ratio at which a person or corporation is taxed is known as the tax rate. Statutory, average, marginal, and effective tax rates are just a few of the ways that can be displayed. These rates can also be displayed using the inclusive and exclusive definitions of a tax base.
Here, we have
Given: Assume that Keisha's marginal tax rate is 40% and her tax rate on dividends is 15%. If a city of Atlanta bond pays 7.48% interest.
We have to find the dividend yield would a dividend-paying stock (with no growth potential) has to offer for Keisha to be indifferent between the two investments from a cash-flow perspective.
Dividend yield × (1 - tax rate) = Interest
Dividend yield × (1 - 0.15) = 7.48%
Dividend yield = 7.48%/0.85
Dividend yield = 8.8%
Hence, the dividend yield is 8.8%.
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3 quarts and 1 pint - 1 quart 2 pints and 1 cup = __ qt __ pt __ cup
Answers
Final outcome is: 1 quart, 2 cups. 2 quarts, 1 pint, and 2 cups are the outcome of removing 1 quart, 2 pints, and 1 cup from 3 quarts and 1 pint.
We must convert all the units to the same level of measurement in order to remove these two mixed volume units. We are aware that 2 pints and 2 cups equal 1 quart. In order to subtract the volumes, we can convert the pint and cup units to quarts.
We begin by converting 1 pint to quarts:
Pints equal half quarts.
The next step is to convert 1 cup to quarts:
1/4 pint is equal to one cup.
Hence, the second mixed unit is:
1.75 quarts are equal to 1 quart, 2 pints, and 1 cup (1 + 2(1/2) + 1/4).
We may now take the volumes away:
3 quarts and a pint minus a pint, a cup, and a quart equals 3 + 1/2 minus 1.75 to 2.75 quarts.
This result can be written as a whole number of quarts plus any leftover pints and cups to return it to mixed units. Since a quart is equal to two pints, we can write:
2.75 quarts equal 2 quarts plus a half-quart.
We may convert the remaining 1/2 quart to pints because 2 cups equal 1 pint:
2 pints from a half-quart
The end result is as a result:
1 quart, 2 cups
Therefore, 2 quarts, 1 pint, and 2 cups are the outcome of removing 1 quart, 2 pints, and 1 cup from 3 quarts and 1 pint.
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Question 7
Recently, Tom found he was a distant relative of General
James Wolfe who died at the battle on the Plains of
Abraham in 1759. When he died in 1759 he left $600 in his
will which now belongs to Tom. The money has been in a
savings account where it has been earning interest at 4% per
year, compounded annually. How much will Tom have in
the year 2000?
$7065 116.75
$7947 295.49
$6 128 589.15
$7 641 630.28
Answers
John brought
2
• 3
quart of water to the
park. While he was at the park, he
3
drank
4 of the water he brought. How much water in quarts did John drink at the park?
Answers
John drank 0.5025 quarts of water at the park and had 0.1675 quarts left over. It's important to note that it's always a good idea to stay hydrated, especially when spending time outdoors, and bringing enough water is key to staying hydrated.
How to solve fraction?
John brought 2/3 quart of water to the park, which can also be expressed as 0.67 quarts. If he drank 3/4 of the water he brought, this means he consumed 0.75 * 0.67 = 0.5025 quarts of water.
To verify this, we can also subtract the amount of water John drank from the amount he brought:
0.67 - 0.5025 = 0.1675 quarts
This means that John had 0.1675 quarts of water left after he drank 3/4 of what he brought.
To summarize, John drank 0.5025 quarts of water at the park and had 0.1675 quarts left over. It's important to note that it's always a good idea to stay hydrated, especially when spending time outdoors, and bringing enough water is key to staying hydrated.
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What is x when y = 300?
about 61
about 66
about 69
about 72
Answers
Answer:
Step-by-step explanation:
about 61
A window shaped like a parallelogram has an area of 28 3/5 square feet. The height of the window is 4 2/5 feet. How long is the base of the window
Answers
143/42
Jenna’s town voted on a new law. 14 out of 50 votes were in favor of the law. What is the ratio of the number of votes in favor of the law to the total number of votes?
Answers
Answer:
The ratio of the number of votes in favor of the law to the total number of votes is:
14 (votes in favor of the law) : 50 (total number of votes)
This ratio can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2:
7 (votes in favor of the law) : 25 (total number of votes)
So the ratio of votes in favor of the law to the total number of votes is 7:25.
Geometry.
Find the value of the variable
Answers
The value of the variable in the circle is x = 4.5.
How to find the value of the variable in the circle?If two secant segments shares an endpoint outside of the circle. The product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment.
In this case, Use the theorem above, we can say:
5 * 18 = x * 20
90 = 20x
x = 90/20
x = 4.5
Thus, the value of the variable is x = 4.5.
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Where would the decimal be in 572.6×1,000
Answers
Answer:
572600
Step-by-step explanation:
572.6×1,000= 572600
And 572600 is already expressed as a decimal. Hope it helps.
Explanation:move the decimal the right three times because we have 3 zeros. That would make it 572,000
Which equation represents the data in the table shown?
y = −2x + 3
y = −2x
y = −2x − 3
y = 2x + 3
y = −4x − 3
Answers
An equation that represent the data in the table shown is: D. y = 2x + 3.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept, y-intercept or initial number.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 3)/(0 - 1)
Slope (m) = -2/-1
Slope (m) = 2
Based on the information provided above at point (0, 3), an equation that models the line is represented by this mathematical equation;
y = mx + c
y = 2x + 3
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can someone pls help with this geometry!!!
Answers
BC=DE are congruent and the angles are also congruent by using CPCT.
EquationsTo prove BC=DE given angle BAC=angle DAE, we can use the following steps:
Draw the circle with centre A and points B, C, D, and E on its circumference.
Draw the line segment AE, and extend it to intersect the circle at point F.
Draw the line segment BF, and extend it to intersect the circle at point G.
Draw the line segments CG and DG.
Since angles BAC and DAE are equal, we have angle BAF = angle DAF (because they are vertical angles).
Since angles BAF and BGF subtend the same arc, we have angle BAF = angle BGF.
Similarly, since angles DAF and DGF subtend the same arc, we have angle DAF = angle DGF.
Since angles BGF and DGF are both equal to angle BAC/2 + angle DAE/2, we have angle BGF = angle DGF.
Since angles BGC and DGC are both equal to angle BGF + angle CGF, we have angle BGC = angle DGC.
Since angles BDC and EDC are both equal to angle CGD, we have angle BDC = angle EDC.
Therefore, BC = BG + GC = DG + GC = DE, as desired.
To prove angle BAC=angle DAE given BC=DE, we can use the following steps:
Draw the circle with centre A and points B, C, D, and E on its circumference.
Draw the line segments AC and AD.
Draw the perpendicular bisectors of BC and DE, and let them intersect at point O.
Since BC=DE, the perpendicular bisectors of BC and DE are the same line.
Therefore, point O lies on both the perpendicular bisectors of BC and DE.
Since point O lies on the perpendicular bisector of BC, we have OB = OC.
Similarly, since point O lies on the perpendicular bisector of DE, we have OD = OE.
Since OA is a radius of the circle, we have OB = OD.
Therefore, OB = OC = OD = OE, so quadrilateral BCDE is a kite.
Since a kite has two pairs of equal adjacent angles, we have angle BOC = angle DOE and angle BCO = angle EDO.
Therefore, angle BAC = angle BOC - angle BCO = angle DOE - angle EDO = angle DAE, as desired.
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Solve 3x^2-18x+5 by completing the square
Answers
Answer:
x = 3 + √(22/3) and x = 3 - √(22/3).
Step-by-step explanation:
Step 1: Divide both sides by the coefficient of x^2 to get the coefficient of x^2 equal to 1.
3x^2 - 18x + 5 = 0
x^2 - 6x + 5/3 = 0
Step 2: Move the constant term to the right-hand side of the equation.
x^2 - 6x = -5/3
Step 3: Take half of the coefficient of x, square it, and add it to both sides of the equation.
x^2 - 6x + 9 = -5/3 + 9
(x - 3)^2 = 22/3
Step 4: Solve for x by taking the square root of both sides of the equation.
x - 3 = ±√(22/3)
x = 3 ± √(22/3)
3x^2-18x+5
1 Move the coefficient of x to the front & write the rest normally
3(x^2-6x+5/3)
2 Divide coefficient of x by 2 squared
3[x^2-6x+(-6/2)^2-(-6/2)^2+5/3]
3 Put the first terms into ( )^2
3[(x-3)^2-9+5/2]
4 Add the last 2 terms
= 3(x-3)^2-22
Calculate the value of (-8) 2/3
Answers
Answer:
Step-by-step explanation:
I wrote two answers because I didn't understand what you meant. If there is a multiplication, then it turns out -[tex]\frac{16}{3}[/tex]≈-5,(3) or if the degree, then it will be -4
If the spinner does not land on yellow, what is the probability it will land on blue?
1/6
3/8
1/4
1/8
Answers
3/8. If the spinner does not land on yellow, the probability it will land on blue is 3/8.
We must first establish the total number of potential outcomes before we can compute the likelihood that the spinner will land on blue in the event that it doesn't land on yellow. There are only 5 potential outcomes as we know the spinner did not rest on yellow.
Two of those five probability are blue. Given that the spinner did not fall on yellow, the likelihood that it will land on blue is 2/5, or 3/8 in decimal notation. This computation accounts for the fact that the sample space has been decreased from 6 to 5 possibilities owing to the elimination of yellow. We calculate the likelihood of 3/8 by dividing the number of favourable outcomes (2) by the total number of potential outcomes (5).
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Two numbers with the product of -50 and the sum of 23
Answers
Answer: 2.43082 & 20.56918
Step-by-step explanation: The two numbers with the product of -50 and the sum of 23 are the numbers in the answer box.
A researcher is studying water buffalo in an area where the population of water buffalo is estimated to be . After many of study, the researcher finds that the number of water buffalo is decreasing at a rate of . Which function models the situation, where is in , and is the population of water buffalo?
Answers
The function model and the population of water buffalo is
[tex]P_{current} = P_{estimated} \left(1-\frac{R}{100} \right)^t[/tex]
How to find the population function of decreasing at a certain rate?
Let assume some variable of population and rate change,
[tex]P_{estimated} = Estimated\ population\ of\ water\ buffalo\\R = Rate\ of\ decreasing\ population\ of\ water\ buffalo\\t = time\ taken\ for\ decrease\\[/tex]
Therefore, the function for population of water buffalo decreasing, using compound interest is
[tex]P_{current} = P_{estimated} \left(1-\frac{R}{100} \right)^t[/tex]
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Plot the points (-8,7) and (5,7) on the coordinate plane below. What is the distance between these two points?
Answers
Answer: See attached for a graph. 13 units apart.
Step-by-step explanation:
See attached for a graph. We will plot the first point -8 units left and 7 units up. Then we will plot the second point 5 units right and 7 units up.
Since these points are on a line (they both have the same y-value), we will add the absolute value of their x-values together. We can also count on the graph, you will get the same answer.
|-8| + |5| = 8 + 5 = 13
They are 13 units apart.
Financial statement data for years ending December 31 for Tango Company follow: 20Y7 20Y6 Cost of goods sold $3,894,000 $4,001,500 Inventories: Beginning of year 770,000 740,000 End of year 840,000 770,000 Required a. Determine the inventory turnover for 20Y7 and 20Y6. Round to one decimal place.
Answers
According to given ratios, the inventory turnover for 20Y7 is 4.83 and the inventory turnover for 20Y6 is 5.30.
What is ratio?
A ratio is a mathematical comparison between two or more quantities. It expresses the relationship between the two quantities by dividing one quantity by the other.
Inventory turnover is a financial ratio that measures how many times a company sells and replaces its inventory over a period of time. It is calculated by dividing the cost of goods sold by the average inventory for the period.
a. To determine the inventory turnover for 20Y7 and 20Y6, we first need to calculate the average inventory for each year:
Average inventory = (Beginning inventory + Ending inventory) / 2
For 20Y7:
Average inventory = ($770,000 + $840,000) / 2 = $805,000
For 20Y6:
Average inventory = ($740,000 + $770,000) / 2 = $755,000
Next, we can calculate the inventory turnover for each year:
Inventory turnover 20Y7 = Cost of goods sold / Average inventory 20Y7
= $3,894,000 / $805,000
= 4.83
Inventory turnover 20Y6 = Cost of goods sold / Average inventory 20Y6
= $4,001,500 / $755,000
= 5.30
Therefore, the inventory turnover for 20Y7 is 4.83 and the inventory turnover for 20Y6 is 5.30.
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Which of the following is the point and slope of the equation y + 14 = 7(x - 18)?
(-18, -14), 7
(18, -14), 7
(18, -14), -7
(-18, -14), -7
Answers
Answer:
(18, -14), 7
Step-by-step explanation:
y - (y-intercept) = slope (x - (x-intercept))
Estimating the Difference
Match the equation on the left with the correct estimate on the right. Each equation has been rounded to the nearest
ones place value.
Quick
Check
7.7-3.51
22.78 14.12
16.208-3.652
3.5-1.2
Intro
8-4=4
4-1=3
23-14-9
16-4-12
Done
Answers
The equation is also a series of subtractions. The difference between 16 and 4 is 12, and then subtracting 12 from that result gives 0.
What is difference?When two quantities are subtracted from one another, the difference is produced. It represents the numerical value of the distance between two values.
According to question:The question is asking to match the given equations with the corresponding estimates that have been rounded to the nearest ones place value. The options for the estimates are given on the right-hand side.
Here are the matches:
7.7 - 3.51 ≈ 4 (Quick Check)
The difference between 7.7 and 3.51 is approximately 4.
22.78 - 14.12 ≈ 9 (Quick Check)
The difference between 22.78 and 14.12 is approximately 9.
16.208 - 3.652 ≈ 12 (Intro)
The difference between 16.208 and 3.652 is approximately 12.
3.5 - 1.2 ≈ 2 (Intro)
The difference between 3.5 and 1.2 is approximately 2.
8 - 4 = 4 (Intro)
The difference is 4.
4 - 1 = 3 (Intro)
The difference is 3.
23 - 14 - 9 (Done)
This equation is not a subtraction. It is a series of subtractions. The difference between 23 and 14 is 9, and then subtracting 9 from that result gives 0.
16 - 4 - 12 (Done)
This equation is also a series of subtractions. The difference between 16 and 4 is 12, and then subtracting 12 from that result gives 0.
Note that the terms "Quick Check" and "Intro" refer to different methods of estimation, where "Quick Check" involves rounding to the nearest ten, and "Intro" involves rounding to the nearest whole number.
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Pls, help asap! I am struggling and this is my last attempt to get full credit.
Answers
Answer:
On a number line, the solution x = -10 would be located to the left of the origin (0) by a distance of 10 units. So, you would mark the point representing -10 on the number line to the left of 0.
HELP PLS
General rules or principles that are stated mathematically are known as:
Answers
General rules or principles that are stated mathematically are known as mathematical theorems.
What is theorem?A theorem is a statement or proposition in mathematics that can be proved using logic and previously established facts or principles. It is a statement that has been shown to be true through a logical and rigorous argument. A theorem is considered to be an important and fundamental concept in mathematics and plays a key role in the development and advancement of the subject. Many famous theorems, such as the Pythagorean Theorem and the Fundamental Theorem of Calculus, have had a profound impact on mathematics and other fields of science.
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Will give brainliest and 100 points!!!! Please it's due in 30 mins
Answers
Step-by-step explanation:
1.
a. ∠ADC = 40° + 30° = 70°
b. ∠DBC = 45° (given)
c. ∠AEB (reflex) = 80° + 100° + 80° = 260° (a reflex angle has to be less than 360° and greater than 180°)
d. ∠BCD = 50° + 50° = 100°
.
2.
a. I added 2 photos of my drawings
b. 47° - acute (less than 90°)
147° - obtuse (greater than 90°, less than 180°)
247° - reflex (greater than 180°, less than 360°)
347° - reflex (greater than 180°, less than 360°)
.
3.
a.The sum of the triangle's angles is equal to 180°
i. 180° - 45° - 75° = 60°
ii. 180° - 8° - 11° = 161°
iii. 180° - 54° - 54° = 72°
iv. 180° - 138° - 21° = 21°
b. The third and the fourth, because they have two identical angles
.
4.
Quadrilateral's sum of angles is equal to 360°
a. 360° - 72° - 97° - 113° = 78°
b. 360° - 55° - 55° - 155° = 95°
c. 360° - 77° - 77° - 77° = 129°
.
5. a. No, because then they won't form a total of 360°, since each of them is greater than 90°
b. Yes, because then they would form a total of 360° (the fourth angle must be acute)
c. Yes, because it would still be possible for the sum of quadrilateral's angles to be 360° (the remaining 3 angles must be acute)
d. No, because 2 reflex angles would already form a minimum of 360° (or even more), that has to be the sum of 4 angles, so it wouldn't be possible for a quadrilateral to have only 2 angles
CAN SOMEONE HELP WITH THIS QUESTION?
Answers
James should run along the shore for approximately 16.667 meters before jumping into the water to reach the child in the shortest possible time.
How far along the shore sould James run before jumíng into the water in order to save the child?Let's call the distance James should run along the shore "x". Then, using the Pythagorean theorem, we can set up the following equation to represent the total distance James will travel to reach the child:
x^2 + 40^2 = (60 - x)^2Simplifying and solving for x, we get:
x^2 + 1600 = 3600 - 120x + x^2120x = 2000x = 16.667Therefore, James should run along the shore for approximately 16.667 meters before jumping into the water to reach the child in the shortest possible time.
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Determine what symmetry given equation has: with respect to the x-axis, the y-axis, or the origin. (EASY! 10 Points)
Answers
Explanation
Solve the quadratic
( -1, 0) (1, 0)
Now check solution with symmetry rules
❌ X axis Test of Symmetry
If replacing y with -y produces an equivalent equation, then the graph is symmetric with respect to the x-axis
✅ Y axis Test of Symmetry
If replacing x with -x produces an equivalent equation, then the graph is symmetric with respect to the y- axis
❌ Origin Test of Symmetry
If replacing x with -x and y with -y produces an equivalent equation, then the graph is symmetric with respect to the origin
Use the given data set to complete parts (a) through (c) below. (Use a = 0.05.)
x,y
10,9.13
8,8.13
13,8.73
9,8.77
11,9.25
14,8.11
6,6.13
4,3.11
12,9.13
7,7.6
5,4.74
A - Construct a scatterplot.
B - Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.
The linear correlation coefficient is r = ______?
Determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below.
A- There is sufficient evidence to support the claim of a linear correlation between the two variables.
B- There is insufficient evidence to support the claim of a linear correlation between the two variables.
C- There is insufficient evidence to support the claim of a nonlinear correlation between the two variables.
D- There is sufficient evidence to support the claim of a nonlinear correlation between the two variables.
C- Identify the feature of the data that would be missed if part (b) was completed without constructing the scatterplot. Choose the correct answer below.
A- The scatterplot reveals a distinct pattern that is astraight-line pattern with positive slope.
B- The scatterplot reveals a distinct pattern that is not astraight-line pattern.
C- The scatterplot reveals a distinct pattern that is astraight-line pattern with negative slope.
D- The scatterplot does not reveal a distinct pattern.
Answers
The argument that there's a direct association between the two variables is sufficiently supported by the available data.
What's scatterplot?The graphs that show the association between two variables in a data set are called smatter plots. It displays data points moreover on a Cartesian system or a two- dimensional aeroplane
. TheX-axis is used to represent the independent variable or trait, while the Y- axis is used to compass the dependent variable. These plates or graphs are constantly used to describe these plots.
What's a correlation with a direct measure?Measure of direct correlation. The strength of the direct link between two variables, x and y, is shown by a number known as the direct correlation measure, which is deduced from given data. The direction of the direct link between x and y is indicated by the sign of the direct correlation measure.
Given,
x y
109.14
88.15
138.75
98.77
119.25
148.09
66.13
43.09
129.14
77.25
54.73
r=0.81602411
therefore correlation measure is0.816 a strong positive correlation.
Test statistic t =
p value<0.05 our significant position
Hence reject H0, there's correlation significant between the two variables.
There's sufficient substantiation to support the claim of a direct correlation between the two variables
smatter plot is attached.
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