The Pearson correlation coefficient r for the given points is 0.529, rounded to three decimal places.
What is statistics ?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of quantitative methods to gather, describe, and draw inferences from data, which can be used to make decisions, predictions, or conclusions about a population or a phenomenon.
We can use the following formula to calculate the Pearson correlation coefficient [tex]$r$[/tex] :
[tex]r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} $$[/tex]
where:
[tex]$n$[/tex] = the number of data points
[tex]$x$[/tex] and [tex]$y$[/tex] are the variables (in this case, the [tex]$x$[/tex] values are the first coordinate of each point and the [tex]$y$[/tex] values are the second coordinate of each point)
[tex]$\sum xy$[/tex]= the sum of the products of [tex]$x$[/tex] and [tex]$y$[/tex]
[tex]$\sum x$[/tex] and [tex]$\sum y$[/tex] = the sums of [tex]$x$[/tex] and [tex]$y$[/tex], respectively
[tex]$\sum x^2$[/tex] and [tex]$\sum y^2$[/tex] = the sums of the squares of [tex]$x$[/tex] and [tex]$y$[/tex] , respectively
Using this formula, we can calculate the necessary values:
[tex]n = 7$\\\\$\sum x = 28$\\\\$\sum y = 45$\\\\$\sum x^2 = 140$\\\\$\sum y^2 = 358$\\\\$\sum xy = 204$[/tex]
Plugging these values into the formula, we get:
[tex]r = \frac{7(204) - (28)(45)}{\sqrt{[7(140) - (28)^2][7(358) - (45)^2]}} $$[/tex]
[tex]$$ r = 0.529 $$[/tex]
Therefore, the Pearson correlation coefficient r for the given points is 0.529, rounded to three decimal places.
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I need help with this IXL special right triangles
Answer:
Step-by-step explanation:
m = 30
10√3 · √3 = 10·3 = 30
y=2/5+2 how to get the x intercept
Answer:
Step-by-step explanation:
The equation you provided, y = 2/5 + 2, appears to be missing the variable x. Assuming you meant y = 2/5x + 2, here's how you can find the x-intercept:
To find the x-intercept, we need to find the value of x when y = 0. This is because the x-intercept is the point on the graph where the line crosses the x-axis, and at that point, the y-coordinate is always 0.
So, we can set y = 0 in the equation:
0 = 2/5x + 2
Subtracting 2 from both sides:
-2 = 2/5x
Multiplying both sides by 5/2:
-5/2 = x
Therefore, the x-intercept is at the point (-5/2, 0).
This table shows the amount of money that Bradford saved in his savings account after different amounts of time.
Number of Months 4 8 18
Amount Saved ($) 50 100 225
What is the constant of proportionality?
Responses
0.08
0.08
12.5
12.5
25
25
50
Answer:
Number of Months 4 8 18
Amount Saved ($) 50 100 225
What is the constant of proportionality?
The constant of proportionality is 25.
Step-by-step explanation:
Help me! I need help with my homewor!
Answer:
Area of shaded region= 1142.96mm²
Step-by-step explanation:
•First calculate the Area covered by the interior circle.
•To calculate the Area of the exterior circle first add the two radii to get the radius from the centre of the interior circle to the circumference of the exterior circle.
•Use the calculated radius to calculate the Area covered from the centre to the circumference of the exterior circle.
•Now subtract the Area of the interior circle from the area covered by the bigger circle to get the Area of the shaded region.
Answer:
1141.76
Step-by-step explanation:
To solve for the area of the entire circle, we must first solve for the radius. Adding 6 and 14 will get us the total radius of the circle.
6 + 14 = 20Therefore, the radius of the entire circle is 20.
The expression you can use to solve for the area of a circle is:
Area = π × radius²Inserting the radius into the expression:
Area = π × 20²Therefore, the area of the entire circle is 400π.
If there is a hole in the circle in the shape of a circle, we must subtract the area of that hole to find the area of the shaded region.
Inserting 6 into the expression to solve for area:
Area = π × 6²Therefore, the area of the hole is 36π.
Now, we need to subtract the area of the gap from the area of the entire circle.
400π - 36π = 364πBecause π is approximately equal to 3.14, we can calculate an approximate value for 364π by multiplying 364 by 3.14. This gives us:
364 × 3.14 = 1141.76.Therefore, the area of the shaded region is [tex]1141.76^{2}[/tex]
fill in the sentence below with the description that most specially applies to the quadrilateral below
The quadrilateral is most specifically a parallelogram because the opposite sides are parallel to each other
What is a parallelogram?
A parallelogram is a geometric shape with four sides, where opposite sides are parallel and congruent (having the same length), and opposite angles are also congruent (having the same measure).
In other words, a parallelogram is a quadrilateral (a polygon with four sides) where both pairs of opposite sides are parallel.
The opposite sides of a parallelogram are equal in length, and its diagonals bisect each other. The area of a parallelogram is equal to the product of its base (one of its sides) and its height (the perpendicular distance between the base and the opposite side).
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Critical Thinking Question (5 pts.)
(You may use the back of the page to write your answer if needed). Here is a case-study for you to solve. Use what you learned
about blood types and Rhesus factor to solve this situation.
Two friends, Mike and Jake were returning late at night from a club in the same car. Suddenly, Mike, who was driving, lost control of
the car and they crashed into a big tree. Mike ended up with only a few bruises and scratches, but Jake got hurt.
Jake had internal bleeding and was taken to a hospital, but he lost a lot of blood and needed a blood transfusion. Mike, feeling
responsible for his friend's condition, wanted to donate blood to his friend. Both Mike and Jake had blood type O. So, in the ER, Mike
gave 2 pints of blood to Jake.
Two weeks later, Jake became anemic. So, Mike, being a good friend, decided to give blood again. However, after the second
transfusion, Jake went into an anaphylactic shock (severe immune response) and almost died.
What, do you think, was the problem here? Your answer should have two parts:
1. Explain, what happened in Jake's body after the first blood transfusion - why did he become anemic so soon after the transfusion?
(hint: it's not from bleeding)
2. Explain, what happened after the second blood transfusion - why did Jake go into an anaphylactic shock?
1.Jake became anemic after the first blood transfusion because his body reacted to the foreign antigens.
2.He went into an anaphylactic shock after the second transfusion due to an even stronger allergic reaction.
1. After the first blood transfusion, Jake became anemic because he was given type O blood, which is not compatible with his own blood type. Incompatible blood transfusions occur when a person is given blood that carries a different antigen than the one they have. In this case, Jake was given type O blood, which carries both the A and B antigens, while Jake’s own blood carries the Rh antigen. Therefore, Jake’s body reacted to the foreign antigens and created antibodies to fight against them. This reaction caused Jake to become equation anemic, as his body was not able to absorb the oxygen from the transfused blood.
2. After the second blood transfusion, Jake went into an anaphylactic shock because he was given type O blood, which carries both the A and B antigens, while Jake’s own blood carries the Rh antigen. Since Jake’s body had already created antibodies to fight against the foreign antigens, when it was exposed to the same foreign antigens a second time, his body reacted with an even stronger immune response. This reaction caused Jake to go into an anaphylactic shock. In other words, the second transfusion caused an allergic reaction in Jake’s body, which was much more severe than the allergic reaction caused by the first transfusion.
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√15y^3
Simplify.
Remove all perfect squares from inside the square root.
the answer would be 3.872983 but rounding that off would be 3.9
answer: 3.9
MATHEMATICS
1. If each interior angle of a regular polygon is five times the exterior angle, how many sides has the polygon? x° зх°6x° 4xº 4x° 2x⁰ 2. Find the value of X in the polygon drawn above.
1. The number of sides of the polygon is 8
2. The value of x is 36
What is a polygon?A polygon can be defined as a flat or plane. The sum of a regular polygon is expressed as (n-2)180. The sum of exterior angle of a polygon is 360.
Therefore the sum of the interior is 5 times the exterior.
(n-2)180 = 5×360
180n - 360 = 1800
180n = 1800-360
180n = 1440
divide both sides by 180
n = 1440/180
n = 8
therefore the number of sides of the polygon is 8
2. The number of sides of the polygon is 6
Therefore the sum of angle in the polygon = 6-2)180 = 4× 180
= 720°
x+3x+6x+4x+4x+2x = 720
20x = 720
x = 720/20
x = 36
therefore the value of x is 36
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what is the anwser to finding the radius
The radius of the circle is r = 3.75
What is the radius of a circle?The radius of a circle is the distance from its center to its circumference.
To find the radius of the circle, we see that there is a right-angle triangle there. So, using Pythagoras' theorem, we have that
AC² = AB² + BC²
(6 + r)² = 9² + r²
Expanding the brackets, we have that
36 + 12r + r² = 81 + r²
Cancelling out r², we have that
36 + 12r = 81
Subtracting 36 from both sides, we have that
12r = 81 - 36
12r = 45
r = 45/12
r = 15/4
r = 3.75
So, the radius is r = 3.75
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Ingrum Corporation produces and sells two products. In the most recent month, Product R38T had sales of $33,000 and variable expenses of $8,840. Product X08S had sales of $54,000 and variable expenses of $32,050. The fixed expenses of the entire company were $36,130. The break-even point for the entire company is closest to:
Answer:
Therefore, the break-even point for the entire company is approximately 0.784 or 78.4%.
Step-by-step explanation:
To calculate the break-even point, we need to find the total contribution margin, which is the difference between the total sales revenue and total variable expenses.
For Product R38T, the contribution margin is $33,000 - $8,840 = $24,160.
For Product X08S, the contribution margin is $54,000 - $32,050 = $21,950.
The total contribution margin for both products is $24,160 + $21,950 = $46,110.
To calculate the break-even point, we divide the total fixed expenses by the total contribution margin:
Break-even point = Total fixed expenses / Total contribution margin
= $36,130 / $46,110
= 0.784
Therefore, the break-even point for the entire company is approximately 0.784 or 78.4%.
Solve the system of equations using substitution. y = 4x y = 8x + 8 (−3, −12) (−2, −8) (2, 8) (3, 12)
Answer:
(- 2, - 8 )
Step-by-step explanation:
y = 4x → (1)
y = 8x + 8 → (2)
substitute y = 8x + 8 into (1)
8x + 8 = 4x ( subtract 4x from both sides )
4x + 8 = 0 ( subtract 8 from both sides )
4x = - 8 ( divide both sides by 4 )
x = - 2
substitute x = - 2 into (1)
y = 4x = 4(- 2) = - 8
solution is (- 2, - 8 )
Answer:(-2,-8)
Step-by-step explanation:
if you use a graph and find where they intercept that will give you the answer use desmos graphing
How much money should be deposited today in an account that earns 3.5% compounded monthly so that it will
accumulate to $12,000 in 3 years?
Click the icon to view some finance formulas.
The amount of money that should be deposited is
(Round up to the nearest cent as needed.)
orre
The amοunt οf mοney that shοuld be depοsited tοday is apprοximately $9,786.04 (rοunded up tο the nearest cent).
What dοes the mathematical term "cοmpοund" mean?The interest that is calculated using bοth the principal and the interest that has accrued during the previοus periοd is called cοmpοund interest.
It differs frοm simple interest in that the principal is nοt taken intο accοunt when determining the interest fοr the subsequent periοd with simple interest. Cοmpοund interest is cοmmοnly abbreviated C.I. in mathematics.
The amοunt that has tο be depοsited tοday can be determined using the calculatiοn fοr the future value οf an annuity.
FV is equal tο P * [(1 + r/n)(nt) - 1] / (r/n)
where:
$12k in future value P = principle (the amοunt tο be depοsited tοday)
3.5% as the annual interest rate
12 times every year are added tο the number n. (cοmpοunded mοnthly)
If t Equals time in years, then 3
When we enter the values, we οbtain:
[tex]12,000 = P * [(1 + 0.035/12)^{(12*3)} - 1] / (0.035/12)[/tex]
Simplifying:
[tex]12,000 = P * (1.035^{36} - 1) / (0.00291667) (0.00291667)[/tex]
[tex]P = 12,000 * (0.00291667) / (1.035^{36 }- 1)[/tex]
P ≈ $9,786.04
The sum that shοuld be depοsited as a result is abοut $9,786.04 tοday (rοunded up tο the nearest cent).
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HELP HELP FAST FAST QUICK BRAINLIEST
Answer:
the answer is 2 pls mark me brainliest
Look at the picture below
The arc length is 2.2π
What is the centre angle?The central angle is an angle with twο arms and a vertex in the middle οf a circle. The twο arms οf the circle's twο radii intersect the circle's arc at twο different lοcatiοns. A circle can be divided intο sectοrs by using the central angle. A central angle might be fοund οn a pizza slice.
Given that the radius οf the circle is 18 inches.
The fοrmula circumference οf a circle is 2πr.
The circumference οf a circle is 2×π×18 =36 π inches.
The tοtal degree οfa circle is 360°.
The arc length with a central angle 360° is 36 π
Apply unitary methοd:
The arc length with a central angle 1° is 36 π/360°.
The arc length with a central angle 22° is (36 π×22°)/360° = 2.2π
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plot and label point Z
Answer: Sorry, I need more info.
Step-by-step explanation:
Can you please post the graph and the value of point Z? It's impossible to answer without this information. I'm sorry I couldn't help very well.
24. A bag of candy contained a total of 1,000 candies before it was opened. Four students each pulled out 20 candies at random and recorded the color of the candies in this table.
According to this data, which was the most likely distribution of the colors of candies in the bag before it was opened?
A. 250 red, 250 blue, 250 green, 125 yellow, and 125 orange
B. 300 red, 250 blue, 200 green, 100 yellow, and 150 orange
C. 200 red, 200 blue, 200 green, 200 yellow, and 200 orange
D. 200 red, 200 blue, 200 green, 100 yellow, and 100 orange
A. 250 red, 250 blue, 250 green, 125 yellοw, and 125 οrange is the mοst likely distributiοn οf the cοlοrs οf candies in the bag befοre it was οpened
What is equatiοn?A mathematical equatiοn links twο statements and utilises the equals sign (=) tο indicate equality. In algebra, an equatiοn is a mathematical assertiοn that prοves the equality οf twο mathematical expressiοns. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical fοrmula may be used tο determine hοw the twο sentences οn either side οf a letter relate tο οne anοther. The lοgο and the particular piece οf sοftware are usually identical. like, fοr instance, 2x - 4 = 2.
We must make use οf the data the students cοllected in οrder tο calculate the mοst likely distributiοn οf the candy cοlοurs in the bag befοre it was οpened. Nοw, let's determine the tοtal amοunt οf sweets the pupils pulled οut:
40 sweets divided by 4 pupils is 80 candies.
We may assume that there were twice as many red candies in the bag befοre it was οpened if the kids tοοk οut 40 οf them:
4 x 250 = 1,000
By emplοying this technique, we may determine hοw many candies οf each hue were included in the bag priοr tο its οpening.
Thus, A. 250 red, 250 blue, 250 green, 125 yellοw, and 125 οrange is the mοst likely distributiοn οf the cοlοrs οf candies in the bag befοre it was οpened
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Please help ASPA
Graph the functions on the same coordinate axis.
f(x)=-2x+1
g(x)=x²-2x-3
What are the solutions to the system of equations?
Select each correct answer.
(-2, -3)
(-2,5)
(2, -3)
(2,5)
(2, 3)
Answer: (2,-3) and (-2,5)
Step-by-step explanation:
Let us graph the two equations one by one.
If we compare this equation with the slope intercept form of a line which is given as we see that m = -1 and c =1
Hence the slope of the line is -2 and the y intercept is 1.
Hence one point through which it is passing is (0,1) .
Let us find another point by putting x = 1 and solving it for y Let us find another point by putting x = 2 and solving it for y Hence the another point will be (2,-3)Let us find another point by putting x = -2 and solving it for y Hence the another point will be (-2,5)Now we have two points (0,1) ,(1,-1) , (2,-3) and (-2,5) we joint them on line to obtain our line 2.
It represents the parabola opening upward with vertices (1,-4)Let us mark few coordinates so that we may graph the parabola.i) x=0 ; ; (0,-3)ii)x=-1 ; ; (-1,0)iii) x=2 ; ;(2,-3)iii) x=1 ; ;(1,-4)iii) x=-2 ; ;(-2,5)Now we plot them on coordinate axis and line them to form our parabolaWhen we plot them we see that we have two coordinates (2,-3) and (-2,5) are common , on which our graphs are intersecting. These coordinates are solution to the two graphs.
Plot the following points and join them together and describe what you get, (1₁-1), (2,1), (3, 3), (4.5) (5.7)
Answer:
A positive line
Step-by-step explanation:
Answer:
Step-by-step explanation:
you get a straight line with a slope = 2
the line slants up and to the right
it passes through the y axis at the point (0, -3)
a retailer sold bat at 25% profit
Answer:
25% Profit = CP of 5 bats = 5x W
Step-by-step explanation:
1. Determine if the polygons are similar. Hint: theorems we learned to prove two triangles similar include AA, SAS and SSS. Are the triangles similar (yes or no)? yes
Triangle with smaller triangle inside H R J S T K 10 6 4.8 8
Work or explanation:
Which theorem can you use to prove the two triangles similar? SAS
Yes triangles are similar.
SAS theorem is used to prove triangles are similar.
Define Side-Angle-Side Similarity Criteria, or SASThe SAS similarity theorem states that if any two sides of the first triangle are exactly proportional to any two sides of the second triangle and the angle created by these two individual triangles is identical, then the two triangles must be similar. When we only know the length of two sides and the angle produced between those two sides in each triangle, this rule is often implemented.
ΔRST and ΔHJK triangles are similar.
According to the SAS theory,
∠ S=∠J (angles are equal)
SR/HJ=ST/JK
6/10=4.8/8.6=.6( both sides are proportional)
Triangles ΔRST and ΔHJK are hence identical.
Two triangles can be compared using the Side-Angle Theorem.
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You deposit $6000 in an account earning 6% interest compounded quarterly. How much will you have in the account in 15 years? Round your answer to the nearest cent.
Step-by-step explanation:
The formula to calculate the future value of a present value deposit with compounding interest is:
FV = PV × (1 + r/n)^(n*t)
Where:
PV = Present Value (the initial deposit)
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
Using this formula, we can calculate the future value of the $6000 deposit after 15 years:
PV = $6000
r = 6% = 0.06
n = 4 (compounded quarterly, i.e. 4 times per year)
t = 15 years
FV = $6000 × (1 + 0.06/4)^(4*15)
FV = $6000 × 1.458^60
FV = $6000 × 6.2565
FV = $37,539.00
Therefore, the future value of the $6000 deposit after 15 years with quarterly compounding at 6% interest rate is $37,539.00.
What are the coordinates of the point that is of the way from G to F?
OA. (3,2)
OB. (5,-2)
O C. (1.5, 3)
OD. (4.5, -3)
4
6
2
-6 -4-2 0
ON
-2
-4
-6
Ty
F
2
4
6
G
X
The coordinates of the point that is halfway between G (2,4) and F (6,-6) is (4, -2).
What is coordinate?Coordinate is a pair of numbers that represents a position on a two-dimensional plane. Coordinates are usually written in the form (x, y), with the x-coordinate representing a position along the horizontal axis, and the y-coordinate representing a position along the vertical axis. Coordinates can also be used to represent positions on a three-dimensional plane in the form (x, y, z). These coordinates can be used to pinpoint a specific location or to describe the shape of a figure on a graph.
This can be calculated by taking the average of the x coordinates (2 + 6 = 8/2 = 4) and the average of the y coordinates (4 - 6 = -2/2 = -2).
Therefore, the point is (4, -2).
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If Haechan has 1 apple and Mark has 2 and Jungwoo has 7 how much apples are there combined?
Answer:
9 apples
Step-by-step explanation:
1 apple + 2 apples + 7 apples= 9 apples
Answer:
1+7+2= 10
Step-by-step explanation:
1 apple + 7 apples + 2 apples = 10 apples
Use the image to determine the line of reflection. Graph of polygon ABCDE with point E at negative 3 comma 1. A second polygon A prime B prime C prime D prime E prime with E prime at negative 3 comma negative 3. Reflection across the x-axis Reflection across the y-axis Reflection across y = −1 Reflection across x = −3
The line of reflection is y = -1, which is the equation of the horizontal line passing through the midpoint of the line segment joining E and E'.
A line section is what?Two different points on a line define the boundaries of a line segment in geometry. Or, a line segment is a section of the line that links two points, as another alternative. In contrast to a line, which has no endpoints and can go on forever, a line segment has two distinct endpoints that are set or identifiable.
According to the given information:From the given image, we can see that the original polygon ABCDE has point E at (-3, 1), and the reflected polygon A'B'C'D'E' has point E' at (-3, -3). This means that the reflection must have occurred across the horizontal line passing through the point (-3, -1), which is the midpoint of the line segment joining E and E'.
Therefore, the line of reflection is y = -1, which is the equation of the horizontal line passing through the midpoint of the line segment joining E and E'.
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ngozi is twice as old as Ada and Agnes 13 1/3 of ada if sum of their age is 30 how old is ngozi
The age of Ngozi if ngozi is twice as old as Ada and Agnes 13 1/3 of ada if sum of their age is 30 is 3.68 years.
How old is Ngozi?Let
Ada age = x
Agnes age = 13 1/3x
Ngozi age = 2x
30 = x + 13 1/3x + 2x
30 = 3x + 40/3x
30 = 49/3x
divide both sides by 49/3
x = 30 ÷ 49/3
multiply by the reciprocal of 49/3
x = 30 × 3/49
x = 1.84 years
Ngozi age = 2x
= 2(1.84)
= 3.68 years
Therefore, Ngozi is 3.68 years old
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How to solve this problem
Fill the missing number: 0, 3, 8, 15, …….
Answer:
The next number is 24
Step by step explanation:
Write all the numbers down and make sure they are separated from each other. Example, 0 3 8 15.Find the difference between the numbers.0 3 8 15
+3 +5 +7(the difference here is 2) so the next one will be +9. 15+9=24.
You are conducting a study testing whether depression symptoms are lower after participating in therapy compared to before. Given this information, complete the hypotheses in symbols:
Given this information, the complete hypotheses in symbols for the study is:
H0:μ_Post-μ_pre ≥ 0H0:μ_Post-μ_pre < 0What are the hypotheses symbol?In statistics, the null hypothesis is usually represented by the letter H with the subscript '0' (zero), as in H0. It's spelled H-null, H-zero, or H-nought. Simultaneously, the alternative hypothesis expresses the observations caused by the non-random cause. It is represented by the letters H1 or Ha.
The null and alternative hypotheses in symbols would be:
H0: μafter ≤ μbeforeHa: μafter < μbeforeNote: Where: H0 = null hypothesis, Ha = alternative hypothesis, μafter = population mean of depression symptoms after therapy and μbefore = population mean of depression symptoms before therapy
The null hypothesis states that the mean depression symptoms after therapy is less than or equal to the mean depression symptoms before therapy. The alternative hypothesis states that the mean depression symptoms after therapy is less than the mean depression symptoms before therapy.
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144 is 90% what is the other 10 percent
Answer:
the missing 10% of 144 is 16. The whole amount would be 144 + 16 = 160.
Step-by-step explanation:
To find the missing 10%, you can use the fact that 100% is equal to the whole amount, and set up a proportion:
90/100 = 144/x
Simplifying this proportion, you can cross-multiply:
90x = 100 * 144
Then, you can solve for x:
x = (100 * 144) / 90
x = 160
Therefore, the missing 10% of 144 is 16. The whole amount would be 144 + 16 = 160.
Find the length of QS
Answer:
112
Step-by-step explanation:
you have to find the length of QT and ST, then QS will be the hypotenuse (opposite of the right angle) of the triangle QTS.
use the formula:
c²=a²+b²
a²=c²-b²
1. to find QT:
QT²=53²-45²
QT²=2,809-2,025
QT²=784
QT=28
2.to find ST:
ST²=117²-45²
ST²=13,689-2,025
ST²=11,664
ST=108
3. find QS:
QS²=28²+108²
QS²=784+11,664
QS²=12,448
QS=111.570605
QS≈112