Answer:
28
Step-by-step explanation:
If we set up our equation using the unknown number of hot dogs and corn dogs with their individual prices attached to them, we can set the sum of them equal to $201. We know that a hot dog costs $3, so we can represent hot dogs monetarily by attaching the cost of a single hot dog to the h. For example, if a hot dog costs $3, and we represent the expression as 3h, with h being the number of hot dogs sold, if we sell 4 hot dogs at $3 apiece, we make $12. If we sell 6 hot dogs we will make $18. The same goes for the corn dogs. We don't know how many corn dogs or hot dogs we sold, but we do know that the sales of both made $201. So our expression for that is
3h + 1.50c = 201
That's great, but we have too many unknowns, and that's a problem. So let's look back up to where we are told that the number of hot dogs is 3 less than 2 times the number of corn dogs. "3 less than" is -3 algebraically. "Twice the number" is 2times and the words "is" and "was" represent the = sign. So putting those words into an algebraic equation looks like this:
h = 2c - 3
That says "the number of hot dogs was twice the number of corn dogs less 3". Now that we have an expression for hot dogs we can sub it into our money equation in place of h:
3h + 1.5c = 201 becomes 3(2c - 3) + 1.5c = 201
Now we have an equation with only c's in it.
Distribute through the parenthesis to get
6c - 9 + 1.5c = 201
Simplify to 7.5c = 210
Now divide by 7.5 to get that c = 28.
Now that we know that, we go back with that number and sub it in for c in
h = 2c - 3 --> h = 2(28) - 3 gives us that the number of hot dogs sold was 53
The total number of corn dogs sold is 28 corn dogs and number of hotdogs is 53
let
h = number of hotdogs
c = number of corndogs.
cost of hotdog = $3
corn dog = $1.50
The equation:
3h + 1.50c = 201 (1)
h = 2c - 3 (2)
substitute (2) into (1)
3(2c - 3) + 1.50c = 201
6c - 9 + 1.50c = 201
7.50c - 9 = 201
7.50c = 201 + 9
7.50c = 210
c = 210/7.50
c = 28
Therefore,
h = 2c - 3
= 2(28) - 3
= 56 - 3
= 53
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If g(x)=f(x)-1, then g(x) translates the function f(x) 1 unit _[blank]_.
Answer:
down
Step-by-step explanation:
Subtracting 1 from the y-coordinate moves a point down 1 unit. You know this because you know that the y-coordinate tells you the number of units the point is above the x-axis.
Every point on the graph of f(x) has coordinates (x, f(x)). If you subtract 1 from the y-coordinate, you have (x, f(x) -1) = (x, g(x)). The graph of this is a graph of f(x) that is 1 unit down from its original position.
In the equation g(x)=f(x)-1, g(x) translates the original function, f(x), one unit downward. This is an instance of vertical translation in mathematics.
Explanation:In the equation g(x)=f(x)-1, the function g(x) is a translation of the function f(x). This process is specifically called a vertical translation. The -1 in the function g(x) = f(x) - 1 implies that the translation is downward. Therefore, g(x) translates the function f(x) 1 unit downward.
To further illustrate, let's consider the function f(x) = x^2 and its translation g(x) = x^2 - 1. If we graph both of these functions, you can observe that the graph of g(x) is exactly the same as the graph of f(x), but it is shifted one unit downward. This is the meaning of vertical translation in mathematics.
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simplify this expression
5*sqrt(x^22) where x<0
Answer:
[tex]\boxed{5x^{11}, x < 0}[/tex]
Step-by-step explanation:
[tex]5\sqrt{x^{22}}[/tex]
Remember that we evaluate the term under the radical first.
Even though x < 0, x²² > 0
So,
[tex] 5\sqrt{x^{22}} = 5x^{11}[/tex]
The simplified expression is
[tex]\boxed{5x^{11}, x < 0}[/tex]
Is the relationship shown by the data linear? If so, model the data with an equation. x y 1 5 5 10 9 15 13 20 The relationship is linear; y – 5 = (x – 1). The relationship is not linear. The relationship is linear; y – 5 = (x – 1).
Answer:
The relationship is linear; y – 5 = 5/4*(x – 1)
Step-by-step explanation:
We have been given the following data set;
x: 1, 5, 9, 13
y: 5, 10, 15, 20
The values of x increase by 4 while those of y increase by 5. This would imply that the average rate of change between any pair of points is a constant and thus the relationship exhibited by the data is linear.
The average rate of change is equivalent to the slope;
(change in y) / (change in x)
Using the first two pair of points we have;
(10-5) / ( 5-1) = 5/4
The point-slope form of equation of the line is thus;
y - 5 = 5/4 (x - 1)
Steve collects oysters for a living and sells them to restaurants. While catching oysters, Steve keeps track of the total weight of his bag of oysters. A graph of the total weight, in ounces, of Steve's bag of oysters, y, with respect to the amount of time that he spends looking for them in minutes, x, is shown below.
What is the average rate of change over the interval [2, 10]?
20 ounces of oysters per minute
8 ounces of oysters per minute
2 ounces of oysters per minute
10 ounces of oysters per minute
5 ounces of oysters per minute
Answer:8 ounces of oysters per minute
Step-by-step explanation:
Answer:
5 ounces of oysters per minute
Step-by-step explanation:
We are given a graph of the total weight, in ounces, of Steve's bag of oysters, y, with respect to the amount of time that he spends looking for them in minutes, x,
Now we are supposed to find the average rate of change over the interval [2, 10]
Formula of Average rate : [tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
Now At x = 2 , f(2)= y = 20
At x=10 , f(10)= y = 60
Substitute the values in the formula
Average rate : [tex]\frac{f(10)-f(2)}{10-2}[/tex]
Average rate : [tex]\frac{60-20}{10-2}[/tex]
Average rate : [tex]\frac{40}{8}[/tex]
Average rate : [tex]5[/tex]
Thus he average rate of change over the interval [2, 10] is 5 ounces of oysters per minute
What is the surface area of this solid?
A. 40.82
B. 37.68
C. 28.26
D. 31.4
Answer:
40.82 is the surface area of this solid.
For this case we have that the surface area of the figure is given by the surface area of a cone plus the surface area of a cylinder.
The surface area of a cylinder is given by:
[tex]SA = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]
Where:
h: It's the height
A: It's the radio.
Substituting the values:
[tex]SA = 2 \pi * 1 * 3 + 2 \pi * 1 ^ 2\\SA = 6 \pi + 2 \pi * 1\\SA = 8 \pi\\SA = 25.12 \ units ^ 2[/tex]
On the other hand, the surface area of a cone is given by:
[tex]SA = \pi * r * s + \pi * r ^ 2[/tex]
Where:
A: It's the radio
s: inclination
Substituting the values:
S[tex]A = \pi * 1 * 6 + \pi * 1 ^ 2\\SA = 6 \pi + \pi\\SA = 7 \pi[/tex]
[tex]SA = 21.98 \ units ^ 2[/tex]
Thus, the surface area of the figure is:
[tex]47.1 \ units ^ 2[/tex]
ANswer:
[tex]47.1 \ units ^ 2[/tex]
Geometry Worksheet 11.1-11.2 Angles and Arcs in a Circle Name______________________________________ What is the difference between a minor arc and a major arc?____________________________________________________ How many letters do we use to name a MINOR arc?_______________ How many letters to name a MAJOR arc? __________________ How many degrees are in a semi-circle? ____________ How many letters to name a SEMI CIRCLE ? __________________ NAME the arc shown in bold, then state if it is a MINOR arc, MAJOR arc, or a SEMICIRCLE. 1. 2. 3. Name of arc: ________ Type of arc: _________ Name of arc: ________ Type of arc: _________ Name of arc: ________ Type of arc: _________ Determine whether the given arc is a MINOR arc, MAJOR arc, or SEMICIRCLE. 4. ______________ 5. ______________ 6. ______________ 7. ______________ 8. ______________ 9. ______________ 10. ______________ 11. ______________ Name the following for the circle at the right. 12. Two DIFFERENT minor arcs. __________ and ___________ 13. Two DIFFERENT major arcs. __________ and ___________ 14. Two DIFFERENT semi-circles.__________ and ___________ 15. There are ____________ degrees in a circle. 16. There are ____________ degrees in a semi-circle. 17. The measure of the arc is ____________________________ to the measure of the central angle. Find the measure of each arc. 18. m = _______ 19. m = ________ 20. m = ________ m = __________ m = ______ m = ______ 21. m = _______ 22. m = ________ 23. m = ________
Answer:
In the figures attached, the complete question is shown.
What is the difference between a minor arc and a major arc?
the measure of a minor arc is less than 180°
the measure of a major arc is greater than 180°
How many letters do we use to name a MINOR arc? 2
How many letters do we use to name a MAJOR arc? 3
How many degrees are in a semi-circle? 180°
How many letters to name a SEMI CIRCLE? 3
1. Name of arc: AB Type of arc: minor
2. Name of arc: ADB Type of arc: major
3. Name of arc: PSQ Type of arc: semi-circle
4. AE: minor
5. AEB: semi-circle
6. FDE: semi-circle
7. DFB: major
8. FA: minor
9. BE: minor
10. BDA: semi-circle
11. FBD: major
12. PQ and ST
13. QPT and PUS
14. PUT and QPU
15. There are 360° degrees in a circle.
16. There are 180° degrees in a semi-circle.
17. The measure of the arc is equal to the measure of the central angle.
18. mPQ: 50°, mPXQ: 310°
19. mPQ: 90° , mPRQ: 270°
20. mPQ: 150° , mPXQ: 210°
21. mQS: 45°, mQRS: 315°
22. mGH: 30°, mGFH: 330°
23. mAB: 75°, mADB: 285°
A system of equations has 1 solution. If 4x – y = 5 is one of the equations, which could be the other equation? y = –4x + 5 y = 4x – 5 2y = 8x – 10 –2y = –8x – 10
Answer:
y = –4x + 5
Step-by-step explanation:
We can put the offered choices into standard form and compare.
y = –4x + 5 ⇒ 4x +y = 5 . . . . . intersecting line; one solution
y = 4x – 5 ⇒ 4x -y = 5 . . . . . . same line, infinite solutions
2y = 8x – 10 ⇒ 4x -y = 5 . . . . same line, infinite solutions
–2y = –8x – 10 ⇒ 4x -y = -5 . . . . parallel line, no solutions
Answer:
IS A: y = –4x + 5
Hope this helps!
QUESTION 7
Which of the following gives an example of a set that is closed under multiplication? Choose all that apply.
The product of an even number and an oven number
The product of an odd number and an odd number
The product of a negative number and a negative number
|
The product of a perfect cube and a perfect cube
Answer:
The product of an even number and an oven numberThe product of an odd number and an odd numberThe product of a perfect cube and a perfect cubeStep-by-step explanation:
The product of two even numbers will have at least two factors of 2, so will be even: even numbers are closed under multiplication.
The product of two odd numbers will be an even number plus 1, so will be odd: odd numbers are closed under multiplication.
The product of two cubes will be the cube of the product of their cube roots: cubes are closed under multiplication.
__
The product of two negative numbers will be positive, so the set of negative numbers is not closed under multiplication.
What is the approximate volume of the cone? use 3.14 for
Answer:
157 cm²
Step-by-step explanation:
volume = (1/3) * π * r² * h
volume = (1/3) * π * 5² * 6
volume = (1/3) * π * 25 * 6
volume = (1/3) * π * 150
volume = (1/3) * 471
volume = 157 cm²
Answer:
157 cubic centimeters
Step-by-step explanation:
Please help me with this :)
Answer:
x = 74°
Step-by-step explanation:
The angle whose vertex lies on the circle, that is angle x is one- half the measure of it's intercepted arc, that is
x = 0.5 × 148° = 74°
Find the zeros of the function. Write the smaller solution first, and the larger solution second. G(x)=4x^2-484
Answer:
-11, 11
Step-by-step explanation:
You have to find when the function crosses the x-axis. You could find this using algebra by solving for x in the equation but I prefer to simply graph it using something like desmos and see when it crosses the x-axis. Doing that I can see the answers would be -11 and 11
Answer:
x = -11,11
Step-by-step explanation:
G(x)=4x^2-484
To find the zero's, set the function equal to zero
0 = 4x^2 - 484
Add 484 to each side
484 = 4x^2 -484+484
484 = 4x^2
Divide each side by 4
484/4 = 4x^2/4
121 = x^2
Take the square root of each side
sqrt(121) = sqrt(x^2)
±11 =x
x = -11,11
Please use the information below to complete this assignment.
y = 4
(1) What is the slope of this line?
(2) What is the x-intercept?
(3) What is the y-intercept?
Answer:
y = 4
That's a straight line.
The slope is 0.
There is no x-intercept.
The y-intercept is 4.
I'm only a few Brainliests away from ranking up, so one would be much appreciated. Thank you, and good luck!
Answer:
the slope is 0
the x intercept is 0
the y intercept is 4
Assume that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year. Find when the sale of cars will be more then the sale of motorcycles.
Answer:
Final answer is approx 6.644 years.
Step-by-step explanation:
Given that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year.
So we can use growth formula:
[tex]A=P\left(1+r\right)^t[/tex]
Then we get equation for motorcycles and cars as:
[tex]A=5.75\left(1+0.16\right)^t[/tex]
[tex]A=3.5\left(1+0.25\right)^t[/tex]
Now we need to find about when the sale of cars will be more than the sale of motorcycles. So we get:
[tex]3.5\left(1+0.25\right)^t>5.75\left(1+0.16\right)^t[/tex]
[tex]3.5\left(1.25\right)^t>5.75\left(1.16\right)^t[/tex]
[tex]3.5\left(1.25\right)^t>5.75\left(1.16\right)^t[/tex]
[tex]\frac{\left(1.25\right)^t}{\left(1.16\right)^t}>\frac{5.75}{3.5}[/tex]
[tex]\left(\frac{1.25}{1.16}\right)^t>1.64285714286[/tex]
[tex]t\cdot\ln\left(\frac{1.25}{1.16}\right)>\ln\left(1.64285714286\right)[/tex]
[tex]t>\frac{\ln\left(1.64285714286\right)}{\ln\left(\frac{1.25}{1.16}\right)}[/tex]
[tex]t>6.6436473051[/tex]
Hence final answer is approx 6.644 years.
Final answer:
To determine when car sales will surpass motorcycle sales given their growth rates, we use exponential growth formulas for both, set them equal to find the crossover point, and solve for the time required.
Explanation:
To find when the sale of cars will be more than the sale of motorcycles given their respective annual growth rates, we'll use the concept of exponential growth.
The initial sale of motorcycles is 5.75 million with an annual growth rate of 16%, and the initial sale of cars is 3.5 million with an annual growth rate of 25%. We will set up an equation where the sales of cars equals the sales of motorcycles and solve for the number of years it takes for this to occur.
The formula for exponential growth is:
Final Amount = Initial Amount × (1 + Growth Rate) ^ Years
For motorcycles, the formula becomes:
M = 5.75 × (1 + 0.16)^t
For cars, the formula becomes:
C = 3.5 × (1 + 0.25)^t
We want to find when C > M, so we set the formulas equal to each other and solve for t:
5.75 × (1 + 0.16)^t = 3.5 × (1 + 0.25)^t
After finding a common base and applying logarithms, we can solve for t, the number of years until the sale of cars surpasses that of motorcycles.
4.) What is the exact value of sinθ when θ lies in Quadrant II and cosθ=−513
Fill in the blanks.
___/___
10.) Suppose that a laser light, positioned 100 ft from the base of a flag pole, illuminates a flag that is 85 ft above the ground.
What is the angle of inclination (angle of elevation) of the light beam?
Express your answer in degrees rounded to the nearest hundredth.
Enter your answer in the box.
11.)
Suppose that a man standing at the edge of a cliff near the North Rim of the Grand Canyon is looking downward towards a campground inside the canyon. The elevation of the North Rim is 5389 ft and the elevation of the campground is 2405 ft. The man's range finder indicates that his line of sight distance to the campground is 3044 ft.
What is the angle of depression of the man's line of sight to the campground?
Express your answer in degrees rounded to the nearest hundredth.
Enter your answer in the box.
12.) What is the exact value of arcsin(0.5)?
Determine the value in degrees.
13.) Determine the exact value in degrees:
What is the exact value of arcsin−2√2
Answer:
Part 4) [tex]sin(\theta)=\frac{12}{13}[/tex]
Part 10) The angle of elevation is [tex]40.36\°[/tex]
Part 11) The angle of depression is [tex]78.61\°[/tex]
Part 12) [tex]arcsin(0.5)=30\°[/tex] or [tex]arcsin(0.5)=150\°[/tex]
Part 13) [tex]-45\°[/tex] or [tex]225\°[/tex]
Step-by-step explanation:
Part 4) we have that
[tex]cos(\theta)=-\frac{5}{13}[/tex]
The angle theta lies in Quadrant II
so
The sine of angle theta is positive
Remember that
[tex]sin^{2}(\theta)+ cos^{2}(\theta)=1[/tex]
substitute the given value
[tex]sin^{2}(\theta)+(-\frac{5}{13})^{2}=1[/tex]
[tex]sin^{2}(\theta)+(\frac{25}{169})=1[/tex]
[tex]sin^{2}(\theta)=1-(\frac{25}{169})[/tex]
[tex]sin^{2}(\theta)=(\frac{144}{169})[/tex]
[tex]sin(\theta)=\frac{12}{13}[/tex]
Part 10)
Let
[tex]\theta[/tex] ----> angle of elevation
we know that
[tex]tan(\theta)=\frac{85}{100}[/tex] ----> opposite side angle theta divided by adjacent side angle theta
[tex]\theta=arctan(\frac{85}{100})=40.36\°[/tex]
Part 11)
Let
[tex]\theta[/tex] ----> angle of depression
we know that
[tex]sin(\theta)=\frac{5,389-2,405}{3,044}[/tex] ----> opposite side angle theta divided by hypotenuse
[tex]sin(\theta)=\frac{2,984}{3,044}[/tex]
[tex]\theta=arcsin(\frac{2,984}{3,044})=78.61\°[/tex]
Part 12) What is the exact value of arcsin(0.5)?
Remember that
[tex]sin(30\°)=0.5[/tex]
therefore
[tex]arcsin(0.5)[/tex] -----> has two solutions
[tex]arcsin(0.5)=30\°[/tex] ----> I Quadrant
or
[tex]arcsin(0.5)=180\°-30\°=150\°[/tex] ----> II Quadrant
Part 13) What is the exact value of [tex]arcsin(-\frac{\sqrt{2}}{2})[/tex]
The sine is negative
so
The angle lies in Quadrant III or Quadrant IV
Remember that
[tex]sin(45\°)=\frac{\sqrt{2}}{2}[/tex]
therefore
[tex]arcsin(-\frac{\sqrt{2}}{2})[/tex] ----> has two solutions
[tex]arcsin(-\frac{\sqrt{2}}{2})=-45\°[/tex] ----> IV Quadrant
or
[tex]arcsin(-\frac{\sqrt{2}}{2})=180\°+45\°=225\°[/tex] ----> III Quadrant
Your town’s Public Library is building a new wheelchair ramp to its entrance. By the law, the maximum angle of incline for the ramp is 4.76°. The ramp will have a vertical rise of 2 ft. What is the shortest horizontal distance that the ramp can span?
A.) 15.3ft
B.) 3.5 ft
C.) 24.0 ft
D.) 9.5 ft
Use trigonometry to find the ramp distance.
sin(4.76°) = 2/r
Let r = ramp distance in feet
r = 2/sin(4.76°)
r = 24.1015718106
Round off to the nearest foot.
Doing so we get r = 24 feet.
The ramp is 24.0 feet long.
Answer: Choice C
at certain time of day , a 30 meter high building cast a shadow that is 31 meters long . what is the angle of the elevation of the sun? round to the nearest degree.
A. 46 degree
B. 16 degree
C.44 degree
D.75 degree
Answer:
Option C. 44 degree
Step-by-step explanation:
Let
A-----> the angle of the elevation of the sun
we know that
The tangent of angle A is equal to divide the opposite side angle A by the adjacent side angle A
In this problem
The opposite side is 30 meters
The adjacent side is 31 meters
[tex]tan(A)=\frac{30}{31}[/tex]
[tex]A=arctan(\frac{30}{31})=44\°[/tex]
If f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g)(2)?
Answer:
3x^2+2x-1
Step-by-step explanation:
Start by plugging in the 2 equations into their assigned places then simplify.
Answer:14
Step-by-step explanation:( 3X2+1)-(1-X)
=3X2+1 -1+X
=3X2+X
ANY WHERE WE SEE X WE PLACE 2
=3(2)(2)+2
3*4+2
=12+2
14
Find the 12th term of the sequence given by the rule tn=4n-2
A. 44 B. 48 C. 50 D. 46
Answer:
D. 46
Step-by-step explanation:
Put 12 where n is, then do the arithmetic.
t12 = 4·12 -2 = 48-2 = 46
Given six memory partitions of 300 kb, 600 kb, 350 kb, 200 kb, 750 kb, and 125 kb (in order, how would the first-fit, best-fit, and worst-fit algorithms place processes of size 115 kb, 500 kb, 358 kb, 200 kb, and 375 kb (in order?
Answer:
Step-by-step explanation:
first fit:
115 -> 300
500-> 600
358 -> 750
200 -> 350
375 -> not able to allocate
Best fit:
115 -> 125
500 -> 600
358 -> 750
200 -> 200
375 -> not able to allocate
worst fit:
115 -> 750
500 -> 600
358 -> not able to allocate
200 -> 350
375 -> not able to allocate
Find the volume of a cylinder with a diameter of 19km and height of 5 km. Label your answer
Answer:
1,417.64 km³
Step-by-step explanation:
The formula for the volume of a cylinder in terms of its diameter is ...
V = (π/4)d²·h
Fill in the given numbers and do the arithmetic.
V = π/4×(19 km)²×(5 km) ≈ 1,417.64 km³
The volume of a cylinder is found using the formula V = πR²h. To find the radius, we divide the diameter by 2, giving us 9.5 km. The volume is therefore approximately 1413.716 km³.
Explanation:To find the volume of a cylinder, we use the formula: V = πR²h. In this case, we are given the diameter and height of the cylinder. The diameter is double the radius, so to find the radius, we divide the diameter (19km) by 2, which gives us 9.5km. Substitute the radius and height into the formula, we get: V = π * (9.5 km)² * 5 km.
Now, we can calculate it. π is approximately 3.14159, (9.5 km)² equals 90.25 km², and multiply it all together with the height (5 km), we get approximately 1413.716 km³.
This is the volume of the cylinder.
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if UVWX is a parallelogram, what is the value of y?
Answer:
B. 60
Step-by-step explanation:
The opposite sides of a parallelogram are parallel and congruent.
This implies that:
|UV|=|XW|
From the diagram; |UV|=15
and [tex]|XW|=\frac{1}{4}y[/tex]
We equate the two side lengths to get:
[tex]15=\frac{1}{4}y[/tex]
We multiply both sides by 4 to obtain:
[tex]4\times 15=4\times \frac{1}{4}y[/tex]
This implies that:
y=60
Answer:
B!
Step-by-step explanation:
The perimeter of the original rectangle on the left is 30 meters. The perimeter of the reduced rectangle on the right is 24 meters. What is x, the width of the original rectangle on the left? Round to the nearest hundredth if necessary.
Answer:
5 meters
Step-by-step explanation:
If the perimeter of the rectangle on the right is 24 m, and the length is 8, the width has to be 4, since 8+4+8+4=24. Since the scale factor is 24÷30=0.8 or 4/5, and the width of the rectangle on the right is 4, 4÷0.8=5, which is the width of the rectangle on the left.
Hope this helps! (P.S. I got it right on Edgenutiy, spelled wrong on purpose).
The width of the original rectangle is 5m.
What is perimeter?The perimeter of a shape can be described as the path or boundary that surrounds it .
Perimeter of Rectangle = 2 (L + B)
L = length of rectangle
B = breadth of rectangle
Perimeter of the reduced rectangle = 24m
Let the length of original rectangle be L1
Let the breadth of original rectangle be B1
Let L1 = 8m, B1 = 4m
P = 2( L1 + B1) = 2(8 + 4) = 24m
Scale factor = P(Original Rectangle) / P(reduced rectangle)
Scale factor = 30 / 24 = 1.25
So, width of original rectangle = Scale factor * reduced width
Width of original rectangle = 1.25 * 4 = 5m
Hence, the width of the original rectangle is 5m.
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Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.
x 6 8 20 28 36
y 2 4 13 20 30
a = –2.79 + 0.950x
b = –3.79 + 0.897x
c = –2.79 + 0.897x
d = –3.79 + 0.801x
Answer:
b. .897x - 3.790 (that's in slope-intercept form; same thing as putting the y-intercept first)
Step-by-step explanation:
On your calculator, hit the "stat" button. Hit #4 to "ClrList", then hit 2nd and the number 1 to clear the list in L1. Then do the same to clear the list in L2. Hit #4, then hit 2nd and the number 2 to clear the list in L2.
Hit "stat" then 1 (edit) and you'll be at your table to enter the values. Use the left arrow key if needed to make sure you're entering your first values under column L1, which is our x values. Enter one at a time, hitting "enter" after each, even the last one. Then arrow over to the right and enter the y values one at a time under L2. Hit enter after each, even the last one. When you're done, hit "stat" again and arrow over to "calc". If you have a TI 83, choose "4:LinReg" and hit "enter". If you have a TI 84+, you will have to arrow down to choose "calculate". When the word "calculate" is highlighted, hit enter and you'll have your equation!
Equation of the regression line for the data given will be represented by the equation given in option B.
By using the utility for the regression line of the given data, equation of the regression line will be,
y = 0.89745x - 3.79005
y = 0.897x - 3.79
Or y = -3.79 + 0.897x
Therefore, equation of the regression line given in option B will be the answer.
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Ms. Ling and Mr Marshal have the same ratio of boys to girls in their classes. Ms. Ling has 6 boys and 14 girls. Mr. Marshal has 21 girls in his class. How many boys are in Mr. Marshals class?
Answer:
There are 13 boys in Mr. Marshals class
Step-by-step explanation:
Hello there! Mr. Marshal has 9 boys.
To find the number of boys Mr. Marshal has, start by finding the ratio. If there are 6 boys and 14 girls, the boys to girls ratio is 6:14. Simplified, the ratio is 3:7. So, if there are 21 girls, you want to find how many boys there are. To find this, find what you need to multiply 7 by to get 21 by and multiply 3 by that number.
21/7 = 3.
So, now we multiply 3 by 3 to get the number of boys.
3 x 3 = 9.
This means there are 9 boys, with a ratio of 9:21. If we simplify this, we get 3:7, making this answer correct.
I hope this helps and have a great day!
Can someone find x (the height) for me please!!
Answer:
x = √5
Step-by-step explanation:
The Pythagorean theorem tells you the square of the diagonal is the sum of the squares of the two sides:
(√7)² = (√2)² + x²
7 = 2 + x² . . . . . . simplify
5 = x² . . . . . . . . . subtract 2
√5 = x . . . . . . . . . take the square root
Please please help me
Answer:
x = 8.3
Step-by-step explanation:
Given a tangent and 2 secants drawn to the circle from an external point then
The square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant.
Using the secant with measure 4 + x, then
4(4 +x) = 7²
16 + 4x = 49 ( subtract 16 from both sides )
4x = 33 ( divide both sides by 4 )
x = 33 ÷ 4 = 8.25 ≈ 8.3 ( nearest tenth )
1. What is the ratio of the perimeters of the larger figure to the smaller figure?
2. What is the ratio of the areas of the larger figure to the smaller figure?
HELP
Answer:
Part 1) The ratio of the perimeters of the larger figure to the smaller figure is equal to [tex]\frac{16}{13}[/tex]
Part 2) The ratio of the areas of the larger figure to the smaller figure is [tex]\frac{256}{169}[/tex]
Step-by-step explanation:
Part 1) What is the ratio of the perimeters of the larger figure to the smaller figure?
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
Let
z-----> the scale factor
In this problem
The scale factor is equal to
[tex]z=\frac{32}{26}[/tex]
Simplify
[tex]z=\frac{16}{13}[/tex]
Remember
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
so
The ratio of the perimeters of the larger figure to the smaller figure is equal to [tex]\frac{16}{13}[/tex]
Part 2) What is the ratio of the areas of the larger figure to the smaller figure?
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z-----> the scale factor
we have
[tex]z=\frac{16}{13}[/tex]
so
[tex]z^{2}=(\frac{16}{13})^{2}=\frac{256}{169}[/tex]
therefore
The ratio of the areas of the larger figure to the smaller figure is [tex]\frac{256}{169}[/tex]
Jackie bought 2/ packages of papers for $5.80 each and 4 notebooks for d dollars each she spent $32 for the packages of paper and the notebooks Write
and equation using D that represents the situation above
Jackie's total spending on 2 packages of paper and 4 notebooks is represented by the equation 2(5.80) + 4d = 32, where d stands for the cost per notebook.
The student is looking to create an equation to represent the cost of Jackie's purchases of paper packages and notebooks. The given information is that Jackie bought 2 packages of papers for $5.80 each and 4 notebooks for d dollars each, and in total, she spent $32. To formulate the equation, we can use the following expression:
Total Cost = Cost of Paper Packages + Cost of NotebooksWe know the cost of the paper packages is 2 multiplied by $5.80, and the cost of the notebooks is 4 multiplied by d dollars.
So the equation using D that represents the situation is:
2(5.80) + 4d = 32Where d represents the cost of each notebook, and solving for d would give us the price per notebook.
a cylindrical barrel has a height of 8 feet and a diameter of 6 feet. what is the volume of the barrel?
Answer: The volume is about 226 feet squared
Step-by-step explanation:
Please help me out please
What we have here is called INTERSECTING CHORDS IN A CIRCLE.
The equation is:
10 times x = 7 times 7
10x = 49
x = 49/10
x = 4.9
answer 4.9cm
10times x=7times7(multiple it)
10x=49
x=49/10
x=4.9