Answer:
An equation in standard form for the line is:
[tex]\frac{5}{2}x-y=-4[/tex]
Step-by-step explanation:
Given the points
(-2, -1) and (0, 4)The slope between two points
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:4\right)[/tex]
[tex]m=\frac{4-\left(-1\right)}{0-\left(-2\right)}[/tex]
[tex]m=\frac{5}{2}[/tex]
Writing the equation in point-slope form
As the point-slope form of the line equation is defined by
[tex]y-y_1=m\left(x-x_1\right)[/tex]
Putting the point (-2, -1) and the slope m=1 in the line equation
[tex]y-\left(-1\right)=\frac{5}{2}\left(x-\left(-2\right)\right)[/tex]
[tex]y+1=\frac{5}{2}\left(x+2\right)[/tex]
[tex]y=\frac{5}{2}x+4[/tex]
Writing the equation in the standard form form
As we know that the equation in the standard form is
[tex]Ax+By=C[/tex]
where x and y are variables and A, B and C are constants
so
[tex]y=\frac{5}{2}x+4[/tex]
[tex]\frac{5}{2}x-y=-4[/tex]
Therefore, an equation in standard form for the line is:
[tex]\frac{5}{2}x-y=-4[/tex]
What are steps I need to take to find a? Please include working out ❤️❤️
A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. An SRS of 28
stores this year shows mean sales of 64 units of a small appliance, with a standard deviation of 13.8 units. During the same point in time last year, an SRS of 28 stores had mean sales of 48.958 units, with standard deviation 15.4 units. An increase from 48.958 to 64 is a rise of about 24%.
1. Construct a 99% confidence interval estimate of the difference μ1−μ2
μ1−μ2, where μ1 is the mean of this year's sales and μ2 is the mean of last year's sales.
(b) The margin of error is
2. At a 0.01 significance level, is there sufficient evidence to show that sales this year are different from last year?
Answer:
Confidence interval = (4.61972, 25.46428)
Margin of Error = 3.9078675
Step-by-step explanation:
Given that :
This year:
Mean (μ1) = 64
Standard deviation (s1) = 13.8
Sample size (n1) = 28
Last year:
Mean (μ2) = 48.958
Standard deviation (s2) = 15.4
Sample size (n2) = 28
99% confidence interval estimate of the difference μ1−μ2
α = 1 - 99% = 0.01
(μ1−μ2) ± t0.01,27 * (√s1²/n1 + s2²/n2)
t0.01, 27 = 2.770683 (t value calculator)
√s1²/n1 + s2²/n2 = √13.8^2/28 + 15.4^2/28 = 3.9078675
(64 - 48.958) ± 2.667(3.9078675)
15.042 ± 10.42228
(15.042 - 10.42228), (15.042 + 10.42228)
(4.61972, 25.46428)
The margin of error :
√(s1²/n1) + (s2²/n2)
√(13.8^2/28) + (15.4^2/28)
√(6.8014285 + 8.47)
√15.2714285
= 3.9078675
A hot air balloon rising vertically is tracked by an observer located 4 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is pi/6, and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?
Answer:
0.533 miles/min
Step-by-step explanation:
Calculate how fast the balloon is rising at the moment : dy /dt
location from the lift-off point = 4 miles
angle between the observer's line-of-sight and the horizontal ( ∅ ) = [tex]\frac{\pi }{6}[/tex]
d∅ / dt = 0.1 rad/min
tan ∅ = y / 4
derivate
sec^2 ∅ . d∅ / dt = 1/4 . dy/dt
= sec^2 [tex]\frac{\pi }{6}[/tex] . 0.1 = 1/4 . dy/dt
= ( sec^2 0.5238 * 0.1 ) * 4 = dy/dt
dy/dt = 8 / 15 miles/min
helpp plssssss i need
Answer:
3m^4
Step-by-step explanation:
x^y
x is the base and y is the exponent
Please help me and explain this.
A music store has 1,440 CDs. Each CD rack holds 90 CDs. How many racks does the store need to use to hold all the CDs?
Answer:
16 cd racks
Step-by-step explanation:
1,440%90
Gina wants to make
hamburgers for 12 people.
Her recipe serves 8 people
and calls for 4.5 pounds of
ground beef. How much
ground beef should
Gia purchase?
h
Answer:
6.75 pounds
Step-by-step explanation:
This question is of direct variation. We will use x as our answer. 8 is 2/3 of 12, so 4.5 should be 2/3 of x. We can now make an equation.
[tex]4.5=\frac{2}{3} x\\4.5*\frac{3}{2} =\frac{2}{3} x*\frac{3}{2} \\6.75=x[/tex]
In order to solve the equation, we multiply both sides by the reciprocal of 2/3, which is 3/2.
* stands for multiplication
From solving our equation, we get 6.75. We can't forget the units, so the answer is 6.75 pounds.
I don't know how to solve this.Please help!
3^x=2
Find the product
(3x+4y)(x+y)
Answer:
Step-by-step explanation:
(3x+4y)(x+y)
Solution=3x^2+4xy+3xy+4y^2
=3x^2+7xy+4y^2
1. Delia purchased a new car for $23,350. This make and model straight line depreciates to zero after 13 years.
a. Identify the coordinates of the x- and y- intercepts for the depreciation equation.
b. Determine the slope of the depreciation.
c. Write the straight-line depreciation equation that models this situation.
Answer:
a. y-intercept = 23350 and x-intercept = 13
b. [tex]m = -\frac{23350}{13}[/tex]
c. [tex]y = -\frac{23350}{13}x + 23350[/tex]
Step-by-step explanation:
Given
[tex]Years = 13[/tex]
[tex]Total\ depreciation = \$23350[/tex]
Solving (a): The x and y intercepts
The y intercept is the initial depreciation value
i.e. when x = 0
This value is the value of the car when it was initially purchased.
Hence, the y-intercept = 23350
The x intercept is the year it takes to finish depreciating
i.e. when y = 0
From the question, we understand that it takes 13 years for the car to totally get depreciated.
Hence, the x-intercept = 13
Solving (b): The slope
The slope (m) is the rate of depreciation per year
This is calculated by dividing the total depreciation by the duration.
So:
[tex]m = \frac{23350}{13}[/tex]
Because it is depreciation, it means the slope represents a deduction.
So,
[tex]m = -\frac{23350}{13}[/tex]
Solving (c): The straight line equation
The general format of an equation is:
[tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
[tex]b = y\ intercept[/tex]
In (a), we have that:
[tex]y\ intercept = 23350[/tex]
In (b), we have that:
[tex]Slope\ (m) = -\frac{23350}{13}[/tex]
Substitute these values in [tex]y = mx + b[/tex]
[tex]y = -\frac{23350}{13}x + 23350[/tex]
Hence, the depreciation equation is: [tex]y = -\frac{23350}{13}x + 23350[/tex]
Find the product. Enter your final answer as a simplified fraction.
-1/8•7•2/5=
Answer:
-7/20
Step-by-step explanation:
Answer:
-1/140
Step-by-step explanation:
-1/8*7*2/5
-7/8*2/5
-7/20
Daniel has 1615 Skittles stored in boxes. If there are 85 boxes, how many Skittles must go in each box?
Answer:
19
Step-by-step explanation:
While it's really easy to just divide, I'm sure your teacher wants an equation so:
1615=85x here x= skittle boxes
1615/85=x In this line you can use divide to cancel out the multiplication, giving you
x=19
If the income of the consumer increases, the budget constraint line will shift:
a.
away from the origin, but its slope will remain the same
b.
away from the origin, and its slope will become steeper
c.
toward the origin, but its slope will remain the same
d.
toward the origin, and its slope will become steeper
Answer:
b
Step-by-step explanation:
this is for the 20 characters thing
Write the slope intercept form of the equation of the line through the given point plz
What would the set notation for the domain and range of the function, (-3, 6), (-2, -3), and (-1, 6)
Answer:
Domain: {-3, -2, -1}
Range: {-3, 6}
General Formulas and Concepts:
Domain is the set of x-values that can be inputted into function f(x). Range is the set of y-values that are outputted by function f(x).Step-by-step explanation:
Step 1: Define
(-3, 6)
(-2, -3)
(-1, 6)
Step 2: Identify x-values
x = -3, -2, -1
Step 3: Identify y-values
y = -3, 6, 6
You move down 6 units and left 9 units. You end at (-5, -3). Where did you start?
how many diagonals does a nanogon have
Answer:
nanogon have 27 diagnals
You move up 2 units and down 7 units. You end at (1, -2). Where did you start?
(5,-2)
that's all. up and down basically means that the point is moving along the x axis.
The cougars baseball team played 16 games last year and won 12 of them. They are scheduled to play 28 games. If they end up winning the same percentage,how many games will they win? Pls help ASAP!!
One pound of beef costs $4.25. One pound of turkey cost $2.85. How much more does 1.25 pounds of the beef cost than 1.25 pounds of turkey?
Answer: $1.75
Step-by-step explanation:
Increase 1.25 by 4.25
5.31
Presently increase 1.25 by 2.85
3.56
Take away 3.56 from 5.31
1.75
Answer:
Beef= 5.75
Turkey=4.35
Beef cost is $1.40 more than turkey.
Step-by-step explanation:
Cleo buys 2/4 pounds of turkey. Tyler buys 1/2 pounds of turkey. Who buys more turkey? Pls explain.
Answer:
No one because They bought the same amount. 2/4 is equvalent to 1/2, meaning they both are half a pound. :)
Step-by-step explanation:
If this helps pls mark me brainliest
Have a great day :)
Use a calculator, spreadsheet, or another tool to solve for the unknown sides of the given right triangle. The length of the hypotenuse is 12. a is the length of the side opposite the 10 degree angle and b is the length of the opposite angle B. Round your answers to four decimal places.
Answer:
27
Step-by-step explanation:
2 TIMES 3
The length of the side a and b is 2.0837 and 11.8176 respectively.
Length of side a and b to be determine, hypotenuse is 12 and a is the length of the side opposite the 10 degree angle and b is the length of the opposite angle B.
Trigonometry is branch of mathematics that helps in elevation and angle problems.
Let assume that one angle of triangle is right angle.
So in right angles triangle,
hypotenuse = 12
cos10 = length of b /12
length of b = 12 cos10
length of b = 11.8176
Now,
sin 10 =length of a/ 12
length of a = 12 sin10
length of a = 2.0837
Thus, the length of the side a and b is 2.0837 and 11.8176 respectively.
Learn more about trigonometry here:
https://brainly.com/question/26719838
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What is the nth term rule of the linear sequence below?
-9, -5, -1,3,7,...
Answer:
Step-by-step explanation:
Given sequence
-9, -5, -1,3,7,...
Is A.P(,airthmetic progression)
So
nth term of an A.P =a+(n-1)d
Where a=first term (-9)
D=difference=(-5)-(-9)=4
So nth term=-9+(n-1)4
=4n-13
Answer is 4n-13
Please please help me get the anwser I just want the anwser I got a 33.3 on my last attempt and this is my last please :( I will literally give you 87 points I need help ASAP please I set it to 87 points please take Time and anwser correctly or I will report please :( I only have 11/6/2020
Answer: A
Step-by-step explanation:
Answer:
Its b
Step-by-step explanation:
Helppppppp
I need to find the area for this
Answer:
126
Step-by-step explanation:
70+56
ILL GIVE BRAINLIEST FOR BEST AWNSER!!!
A football player kicks a ball with a force of 50 N
How does the impulse above change if he doubles the amount of time that his foot is in contact with the ball?
Answer: AP= 30 kgm/s c) Calculate the final velocity of the object, if it was initially at rest. A 0.5kg baseball experiences a 10N force for a duration of 0.1s.
Step-by-step explanation:
-4-5(2x -4) = 76
-6
9
-4
7
9514 1404 393
Answer:
x = -6
Step-by-step explanation:
-4 -10x +20 = 76 . . . . . eliminate parentheses
-10x = 60 . . . . . . . . . . . subtract 16
x = -6 . . . . . . . . . . . . . . divide by -10
Plz answer quick I need to get it bc it’s a quiz
Answer:
slope equals 2
Step-by-step explanation:
graph points and calculate rise over run
Tiffany took her friends out to dinner. If the dinner was $29.53 and she gave a 20% tip, how much money did she spend on dinner?
Answer: The answer is 35.43 because 29.53 times 20% is 5.90, so you add 5.90 to 29.53 to get 35.43.
What additional information could be used to prove that triangle XYZ is congruent to triangle Fe.g. using asa or aas check all that apply
Answer:
its the first one and the last one ..that's the answer.