[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{21})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{42}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{42}-\stackrel{y1}{21}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}}\implies \cfrac{21}{2}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{21}=\stackrel{m}{\cfrac{21}{2}}(x-\stackrel{x_1}{2}) \\\\\\ y-21=\cfrac{21}{2}x-21\implies y=\cfrac{21}{2}x[/tex]
Measuring the height of a tree is usually more difficult than measuring the diameter of the tree. Therefore, many researchers use regression models to predict the height of a tree from its diameter measured at 4 feet 6 inches from the ground. The following computer output shows the results of a linear regression based on the heights, in feet, and the diameters, in inches, recorded from 31 felled trees.
Estimate Std Error t-value Pr(>|t|)
Intercept 62. 031 4. 383 14. 15 0. 0000
Diameter 1. 054 0. 322 0. 2028 3. 27
Required:
What is a 95 percent confidence interval for the slope of the population regression line?
Measuring the height of a tree is usually more difficult than measuring the diameter of the tree, confidence interval for the slope is mathematically given as
C=(0.396, 1.712)
What is a 95 percent confidence interval for the slope of the population regression line?Generally, the equation for the confidence interval is mathematically given as
[tex]C=\beta-tn-2, \alpha /2 (S.E)[/tex]
Where
[tex]\beta=1.054[/tex]
Therefore
C=(1.054-t29, 0.025*0.322)
C=(0.396, 1.712)
In conclusion, the 95 percent confidence interval is
C=(0.396, 1.712)
Read more about Confidence interval
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Keisha makes individual servings of nuts by dividing 4 1/2 cups of nuts into individualcup servingsHow many individual 3 8 . servings can Keisha make?Show work
Answer:
4 1/2 = 9/2
Dividing 9/2 by 3/8,
9/2 x 8/3 = 72/6 = 12
Therefore, Keisha made 12 individual servings.
Use the Fundamental Counting Principle to find the total number of possible outcomes.
Beverage
Size Small, Medium, Large
Flavor
Orange juice, Apple juice,
Lemonade, Milk
Answer:
There are 12 possible outcomes.
Step-by-step explanation:
For each of the three sizes of beverages, there are four flavors. So there are 3 * 4, or 12, possible outcomes.
Our sense of smell is responsible for ___ of our overall chocolate tasting experience. Group of answer choices 10% 30% 50% 70%
Answer:
70%
Step-by-step explanation:
Our sense of smell is responsible for 70% of our overall chocolate tasting experience.
Which picture shows the inverse, f −1, of the function shown?
Domain: 8, 10, 12. Range: 6, 9, 3. 8 goes to 6; 10 goes to 9; 12 goes to 3.
CLEAR CHECK
Inverse of f. Domain: 8, 10, 12. Range: negative 6, negative 9, negative 3. 8 goes to negative 6; 10 goes to negative 9; 12 goes to negative 3.
Inverse of f. Domain: 6, 9, 3. Range: one-eighth, one-tenth, one-twelfth. 6 goes to one-eighth, 9 goes to one-tenth; 3 goes to one-twelfth.
Inverse of f. Domain: 8, 10, 12. Range: one-sixth, one-ninth, one-third. 8 goes to one-sixth; 10 goes to one-ninth; 12 goes to one-third.
Inverse of f. Domain: 6, 9, 3. Range: 8, 10, 12. 6 goes to 8; 9 goes to 10; 3 goes to 12.
Answer:
(d) Inverse of f. Domain: 6, 9, 3. Range: 8, 10, 12. 6 goes to 8; 9 goes to 10; 3 goes to 12.
Step-by-step explanation:
Apparently function f is defined by the ordered pairs (8, 6), (10, 9), (12, 3).
The inverse function will be defined by the ordered pairs with the input and output reversed:
(6, 8), (10, 9), (3, 12)
This seems to be described by the last answer choice.
A shopkeeper bought 30 pens for 150 and sold 20 of them for 140. Find his profit or loss percentage
Answer:
Because the cost price of 30 pens = Rs. 150
So, the cost price of 1 pen = 150/30 =5
so, the cost price of 20 pens =
Rs. 5 x 20 = 100
Cp is Rs. 100
Sp is Rs. 140
So, profit = 140-100 = Rs. 40
Profit % = (Profit x 100)xCp
=(40 x 100)/100
= 4000/100
= 40% profit
Step-by-step explanation:
Which function’s graph is shown below?
.divide the problem.
Answer:
[tex]x - 2x - 15 \: divided \: by \: x - 3[/tex]
according to the above x²-2x-15 divided by the number below x-3 first I cancel out the x[tex]x - 2x - 15 \: divided \: by \: - 3[/tex]the we solve the next x-5 divided by x²-9 then as usual rule out the x[tex] - 5 \: divided \: by \: x - 9[/tex]now we only have x-2x-15 divided by-3 divided by-5÷x-9 now our next step is to again single the equations out [tex]x - 2x - 15 \: divided \: by \: - 3 \: lets \: rue \\s \: rule \: out \: - 3 \: and \: 15 \: giving \: us \: x - 2x - 5[/tex]now the next -5 divided by x-9 here there's nothing to rule out therefore the sign "÷" is changed to "×" cancel out the -5 and therefore we have [tex]x - 2x = x - 9 \: as \: final \: answer[/tex]Nikkita sold her old textbooks for $54 a piece. When she was done, she had $324, but she still had 8 textbooks left. How many textbooks did she start with?
Answer:
14 :D
Step-by-step explanation:
First we must divide!!
324/54 = 6
Now we add :)
6 + 8 = 14
Have an amazing day!!
Please rate and mark brainliest!!
What is 18.5% of 500?
9.25
92.5
925
0.925
Answer:
92.5
Step-by-step explanation:
[tex]\frac{18.5}{100} = \frac{x}{500}[/tex]
cross multiply:
18.5 · 500 = 9250
100 · x = 100x
isolate x by dividing 100 from both sides:
x = 92.5
hope this helps!
Find the missing side lengths. Leave your answers as radicals in simplest form.
Answer:
B x = 3, y= 3
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta[/tex] = 45°O = [tex]x[/tex]A = [tex]y[/tex]H = [tex]3\sqrt{2}[/tex][tex]\implies \sin(45^{\circ})=\dfrac{x}{3\sqrt{2}}[/tex]
[tex]\implies x=3\sqrt{2}\sin(45^{\circ})[/tex]
[tex]\implies x=3\sqrt{2} \cdot \dfrac{\sqrt{2}}{2}[/tex]
[tex]\implies x=\dfrac{3\sqrt{2} \sqrt{2}}{2}[/tex]
[tex]\implies x=\dfrac{3 \cdot 2}{2}=3[/tex]
[tex]\implies \cos(45^{\circ})=\dfrac{y}{3\sqrt{2}}[/tex]
[tex]\implies y=3\sqrt{2}\cos(45^{\circ})[/tex]
[tex]\implies y=3\sqrt{2} \cdot \dfrac{\sqrt{2}}{2}[/tex]
[tex]\implies y=\dfrac{3\sqrt{2} \sqrt{2}}{2}[/tex]
[tex]\implies y=\dfrac{3 \cdot 2}{2}=3[/tex]
solve the system of linear equations by graphing
x+y=18
y=x+12
Answer:
it equals =204 y=12
A $35 item is marked down 25%. What is the new price?
Answer:
$26.25
Step-by-step explanation:
35*.25 is 8.75
35-8.75=$26.25
A bus travels two different routes: the Green Route and the Blue Route.
•On Monday the bus traveled the Green Route 6 times and the Blue Route 5 times, traveling a total of 52 miles.
• On Tuesday the bus traveled the Green Route 12 times and the Blue Route 13 times, traveling a total of 119 miles.
What is the length of the Green Route in miles?
Answer:4.5
Step-by-step explanation: Check the file for my explanation
Calculate the sale price on a mobile phone with a marked price of $145, and a
discount of 53%
$68.15
P=Original price=145
D=Discount=53%
Sales=S
S=P-PD
S=145-(145×53%)
Please help me and you will get the brainiest answer.
Answer:
the right answer is c(5) . because the last digit of the second number is 2 . every number that its last digit is 2 squared , the last digit of the result will always be 4 . also , in every number that its last digit is five , the result will also always be 5 . so if the last digit of the first number is 5 this equasion is correct (because the last digit of the answer is 9 )(5+4)
hope that helped
Dennis drew the line of best fit on the scatter plot shown below:
What is the approximate equation of this line of best fit in slope-intercept form?
y = −15x + 2/3
y = -2/3 x + 15
y = −15x + 3/2
y = -3/2 x + 15
Answer:
4th option
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 12) and (x₂, y₂ ) = (6, 6) ← 2 points on the line
m = [tex]\frac{6-12}{6-2}[/tex] = [tex]\frac{-6}{4}[/tex] = - [tex]\frac{3}{2}[/tex]
the line crosses the y- axis at (0, 15 ) ⇒ c = 15
y = - [tex]\frac{3}{2}[/tex] x + 15 ← approximate equation of line of best fit
4x + 9y - 9 = 0
y intercept =
Please help me with this :)))))
If
Answer:
c) x = 20, angle COD = 70 °
Step-by-step explanation:
(x+50)° + 90° +20° = 180°
x + 160° = 180°
x = 180°- 160°
x = 20
Angle COD = (x+50)° = (20 +50)° = 70°
Hope this helps
6.4r−7−2.9r simplified is
Answer:
3.7r -7
Step-by-step explanation:
Basically you would subtract 6.4 and 2.9 because there is a negative sign and they have the same variable. Then you would put it (2.9r)first since it is in order and you can't combine 7 and 2.9r so you leave it like that.
Amy works and is paid by the hour. Her sister Jo helps her work. As shown in the table identify the independent and dependent ( first gets some!)
Answer:
The dependent variable is Amy's pay
The independent variable is Jo's pay
Step-by-step explanation:
Depending on how much Amy gets paid, Jo gets 20% of it.
I need help with 15.) 17.) and 19.) I have attached the answers I just need help with how to solve them
Answer:
Step-by-step explanation:
They are all solved kind of the same way. If the vertex of the angle is outside of the circle, subtract the intercepted arcs and divide by 2
for 15) one arc is marked but you can figure out the other arc because there are 360 degrees in a circle 360 - 102 = 258. So the two arcs are 102 degrees and 258 degrees.
some of the problems you can set up the equation and solve.
17) 63 = {(360-x) - x} /2 multiply by 2
126 = {(360-x) - x} combine like terms
126 = 360 - 2x subtract 360
-234 = -2x divide by -2
117 = x
? = 117 degrees
good luck
Ming was planning a trip to western smaoa be fore she was going she did some research and learned that the exchange rate is 6 tala for 2$ how many tala would she get if she exchanged 6$
Answer:
18 tala
Step-by-step explanation:
The exchange is proportional, so the number of tala Ming receives will be proportional to the number of dollars she exchanges.
x / ($6) = 6 tala / ($2)
__
Multiplying by $6, we have ...
x = (6 tala)($6/$2) = 18 tala
Ming would get 18 tala when exchanging $6.
The graph of a function is a transformation of the graph of its parent function in which the graph is
vertically stretched by a factor of 2;
shifted left 3 units; and
shifted up 2 units.
write an equation for the function.
Answer:
f(x) = 2(x+3)+2
Step-by-step explanation:
8. (3x-5) mZS = 0 MZR = Р T con A (117 Bux+5)* S
Answer:
95°, 110°
Step-by-step explanation:
Since we're dealing with a cyclic quadrilateral ,
m<T + m<R 180°
7y + 11y = 180°
18y = 180°
y = 10°
Also,
m<S + m<U = 180°
3x+5+3x-5= 180°
6x = 180°
x = 30°
m<S = 3x+5 = 3(30)+5
= 95°
m<R = 11y = 11(10)
= 110°
Given -
m∠R = (11y)°m∠S = (3x + 5)°m∠T = (7y)°m∠U = (3x - 5)°To find -
m∠Rm∠S(nullifying x and y)
Explanation -
As we know this is a cyclic quadrilateral and it's either pair of the opposite angles sum up to 180°.
Therefore,
m∠S + m∠U = 180° ---(1)
m∠R + m∠T = 180° ---(2)
Solution -
Substituting the values of the measure of angles in (1)
➜ m∠S + m∠U = 180°
➜ (3x + 5)° + (3x - 5)° = 180°
➜ 6x = 180°
➜ x = 180/6
➜ x = 30
Therefore, m∠S = (3x + 5)° = {3(30)+5}° = (90+5)°
m∠S = 95°
Substituting the values of the measure of angles in (2)
➜ m∠R + m∠T = 180°
➜ (11y)° + (7y)° = 180°
➜ 18y = 180°
➜ y = 180/18
➜ y = 10
Therefore, m∠R = (11y)° = (11×10)° = 110°
The rectangles below have the same perimeter.
AS BASICALLY IF I TELL U THE CORRECT ANSWER OF ORANGE RECTANGLE IS16ML2
Answer:
16 mi squared
Step-by-step explanation:
Gray perimeter :16 (5,5,3,3)
Orange perimeter :16 (4,4,4,4)
Area of Gray :15 (5x3)
Area of Orange :16(4x4)
11. Write down three different whole numbers so that: • the median of the three numbers is 13, the range of the three numbers is 5.
Step-by-step explanation:
Let the numbers be a, b, c in ascending order.
Mean is 7, i.e. (a+b+c)/3 = 7 or a+b+c=21
Median(middle number) is 5, i.e. b=5
Range is 8, i.e. c-a=8 or c=8+a
Solving the above three equations simultaneously, we have
a+5+8+a=21
a=4, hence c=12
Therefore the three numbers are 4, 5 and 12
At what rate per cent per annum will $400 yield an interest of $78 in 1 1/2 years?
Use language that's easy-to-understand. If there's a piece of vocabulary that you feel needs clarifying, define it! 23
Step-by-step explanation:
Please answer this I’m struggling rn :(
Answer:
The answer is on a picture⊙﹏⊙Step-by-step explanation:
Have a great day✧◝(⁰▿⁰)◜✧What is the length of side PQ in this figure?
Answer:
[tex]\sqrt{52[/tex]
Step-by-step explanation:
hope it helps! im not completely sure but its the best answer!