Please help correct answer wins crowns
Answer:
Given equation: x + 2y = 7
Rearrange the given equation to make y the subject:
[tex]\sf x + 2y = 7[/tex]
[tex]\sf \implies 2y=7-x[/tex]
[tex]\sf \implies y = \dfrac12(7-x)[/tex]
Now input the given x-values into the equation to determine the y-values:
[tex]\sf x=-2\implies y = \dfrac12(7-(-2))=4.5[/tex]
[tex]\sf x=-1\implies y = \dfrac12(7-(-1))=4[/tex]
[tex]\sf x=0\implies y = \dfrac12(7-0)=3.5[/tex]
[tex]\sf x=1\implies y = \dfrac12(7-1)=3[/tex]
[tex]\sf x=2\implies y = \dfrac12(7-2)=2.5[/tex]
[tex]\sf x=3\implies y = \dfrac12(7-3)=2[/tex]
As ordered pairs: (-2, 4.5) (-1, 4) (0, 3.5) (1, 3) (2, 2.5) (3, 2)
Plot the endpoints on the graph (-2, 4.5) and (3,2), then connect with a line segment.
The mayor of a city believes a large park in the city is becoming more popular and wants to expand nature programs at the park. A random sample of 30 summer days are selected and the number of park visitors is determined for each of those days. From this sample, the mean number of visitors was X(xbar) = 98.3 with a standard deviation of Sx = 11.2. Calculate a 99% confidence interval for the true mean number of visitors on summer days. Assume the conditions for inference are met.
a. 95.192 to 101.410 visitors
b. 34.123 to 162.480 visitors
c. 92.664 to 103.940 visitors
d. None of these is correct.
Using the t-distribution, as we have the standard deviation for the sample, it is found that the 99% confidence interval for the true mean number of visitors on summer days is given by:
c. 92.664 to 103.940 visitors
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 30 - 1 = 29 df, is t = 2.756.
The other parameters are given as follows:
[tex]\overline{x} = 98.3, s = 11.2, n = 30[/tex].
Hence, the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 98.3 - 2.756\frac{11.2}{\sqrt{30}} = 92.664[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 98.3 + 2.756\frac{11.2}{\sqrt{30}} = 103.94[/tex]
Hence option c is correct.
More can be learned about the t-distribution at https://brainly.com/question/16162795
If A=615.44 ft sq, what is the radius
I think the radius would be 13.9 ft
help!!
For what value of x is the value of the square of the binomial 2x +3
is 9 greater than the value of the square of the binomial 2x -3?
Answer:
x = 3/8
Step-by-step explanation:
The difference of the two squares can be found several ways. One way uses the "difference of squares" special form.
a² -b² = (a -b)(a +b)
For the given squares, this is ...
(2x +3)² -(2x -3)² = ((2x +3)-(2x -3))((2x +3) +(2x -3)) = 6(4x) = 24x
We want to find x that makes this difference be 9:
24x = 9
x = 9/24 = 3/8
For the value x = 3/8, the difference between the squares of the binomials will be 9.
Solve for x.
8.7 + X = 7
1.1
---
x = [?]
X = 62.4
:)
to get X, i would subtract, 71.1 - 8.7, and the answer would be X, not %100 sure though sorry.
Recall that in a 30 – 60 – 90 triangle, if the shortest leg measures x units, then the longer leg measures xStartRoot 3 EndRoot units and the hypotenuse measures 2x units. (150StartRoot 3 EndRoot – 75π) ft2 (300 – 75π) ft2 (150StartRoot 3 EndRoot – 25π) ft2 (300 – 25π) ft2.
The area of the shaded region is [tex]\rm (150\sqrt{3} \ - 75\pi ) \ feet^2[/tex] option first is correct.
It is given that a circle is inscribed in a regular hexagon with sides of 10 feet.
It is required to find the shaded area (missing data is attached shown in the picture).
What is a circle?It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
We have a hexagon with a side length of 10 feet.
We know the area of the hexagon is given by:
[tex]\rm A = \frac{3\sqrt{3} }{2} a^2[/tex] where a is the side length.
[tex]\rm A = \frac{3\sqrt{3} }{2} 10^2[/tex] ⇒ [tex]150\sqrt{3}[/tex] [tex]\rm feet^2[/tex]
We have the shortest length = x feet and from the figure:
2x = 10
x = 5 feet
The radius of the circle r = longer leg
[tex]\rm r = x\sqrt{3} \Rightarrow 5\sqrt{3}[/tex] feet
The area of the circle a = [tex]\pi r^2[/tex] ⇒ [tex]\pi (5\sqrt{3} )^2 \Rightarrow 75\pi \ \rm feet^2[/tex]
The area of the shaded region = A - a
[tex]\rm =(150\sqrt{3} \ - 75\pi ) \ feet^2[/tex]
Thus, the area of the shaded region is [tex]\rm (150\sqrt{3} \ - 75\pi ) \ feet^2[/tex]
Learn more about circle here:
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Answer:
option A
Step-by-step explanation:
A construction company takes
1/6 hours to remove 1/2
metric tons of dirt from a construction site.
What is the unit rate in metric tons per hour?
Write your answer in simplest form.
Answer:
3 tons per hour
Step-by-step explanation:
Since 0.5=1/6
you can multiply 0.5 by 6:
0.5x6= 3
With an ending result of 3 tons per hour
What is the value of x? The figure is not drawn to scale. Show work
Answer:
x = 21.
Step-by-step explanation:
AS there are parallel lines:
4/12 = 7/x
4x = 84
x = 84/4 = 21.
i dont know how to do this question please help!
Answer: 1/6
Step-by-step explanation: I think you multiply 3 times 3 because the other circle circle has an option the first doesn't have have.
A computer valued at $6500 depreciates at a rate of 14
.3% per year. Determine the value of the computer
after 5 years.
Answer:
A depreciation of 14.3% leaves you with 85.7%, right? Each year's value is 85.7% of the tear before.
So, 6500(0.857)3 = $4091.25
The function I = $19n represents the amount of income from ticket
sales for a single theater performance. The letter n represents the
number of tickets sold. The theater's maximum capacity is 400
people. What is a reasonable domain for this function?
The function I = 19n is a linear function
The reasonable domain of the function is [0,21]
How to determine the domain?The function is given as:
I = 19n
The smallest value of n is 0 i.e. the smallest number of ticket sold is 0
The maximum capacity is 400.
So, we have:
19n = 400
Divide both sides by 19
n = 21.05
Remove the decimals
n = 21
Hence, the reasonable domain of the function is [0,21]
Read more about domain at:
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Please help me with this math problem!! Will give brainliest!! Please explain how you got your answer! :)
ASAPPPPPPPPPPPPP!!!!!!!!
Answer:
73
Step-by-step explanation:
supplementary anges are equal to 180 so e is 180-107
Answer: 73∘.
Step-by-step explanation: With supplementary angles, the two angles have to add up to 180∘. According to the question, the measure of <F is 107∘. What we need to do is make <E and <F add up to 180∘. To do this, we can subtract 107∘ from 180∘ to find <E:
180∘ - 107∘ = 73∘, which means that <F is 107∘ and <E is 73∘, which both make 180∘.
Therefore, <E is 73∘.
Have a great day! :)
Anthony is six years older than Juntao. In three years' time, the ratio of Juntao's age to Anthony's age will be 2 : 5. How old is Juntao now?
Identify the equation that describes the line in slope-intercept form.
slope = 3, point (−2, −4) is on the line.
choices:
y = 3x − 10
y = 3x − 4
y = 3x + 2
y = 3x − 2
Pls help im in a test
Please help find Find cosR!
Step-by-step explanation:
when we look at the triangle try to reposition it at least in your mind to make R to be the center of the circle. then RP (29) is the radius of the circle and the angle indication of the angle R in this circle.
then we see QP is the sine, and RQ is the cosine of the angle R. but don't forget : all are multiplied by the radius, because the pure sin and cos functions deliver the values for the standard circle with radius 1.
so,
QR = cos(R)×RP
21 = cos(R) × 29
cos(R) = 21/29
the fourth answer is correct.
Answer:
the answer is D I took the test
PRESLEY
You are curious about the amount of coffee that the giant fountain cup could actually hold.
The dimensions of the fountain cup are as follows:
• Height is 8 feet.
• Diameter of the top is 6 feet.
• Diameter of the base is 4 feet.
Use this formula with height, h, radius of the base, roase, and radius of the top, rtop, to determine the volume
of the cup:
(πh).
V= -((rbase)+ (rbase) (stop) + (top)).
3
There are 7.5 gallons of liquid per cubic foot.
Enter the volume, in gallons, of the fountain cup.
The volume of the fountain cup in gallons is 4775.2 gallons
Volume of a frustumSince the fountain cup is in the shape of a frustum, its volume is given by
V = πh/3(r² + rr' + r'²) where
h = height of cup = 8 feet, r = radius of base of cup = 4 feet and r' = radius of top of cup = 6 feet.So, substituting the values of the variables into th equation, we have
V = πh/3(r² + rr' + r'²)
V = π × 8 ft/3[(4 ft)² + 4 ft × 6 ft + (6 ft)²]
V = π × 8 ft/3[16 ft² + 24 ft² + 36 ft²]
V = π × 8 ft/3 × (76 ft²)
V = 608π ft³/3
V = 1910.088 ft³/3
V = 636.69 ft³
V ≅ 636.7 ft³
Volume of the fountain cup in gallonsSince there are 7.5 gallons per cubic foot,
The volume of the fountain cup in gallons is V = 636.7 ft³ × 7.5 gallons/ft³ = 4775.2 gallons
So, the volume of the fountain cup in gallons is 4775.2 gallons
Learn more about volume of a frustum here:
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F(x)=2x^3-3x^2+7
F(-1)=_____
F(1)=_____
F(2)=_____
Answer:
f(-1)=2(-1)³-3(-1)²+7 = 2
f(1)=2(1)³-3(1)²+7 = 6
f(2)=2(2)³-3(2)²+7 = 11
help me !!How many years will it take for the Honda to be worth more than the Range Rover? Justify your
response mathematically.
Answer:
6.03 years
Step-by-step explanation:
The value of the Range Rover decreases 25% per year, so its value "growth" factor is 1-25% = 0.75. The initial value is 60,000, so its exponential value function can be written ...
r(x) = 60000(0.75^x)
The Honda has a "growth" factor of 18000/20000 = 0.90 and an initial value of 20,000, so its exponential value function can be written ...
h(x) = 20000(0.90^x)
__
We want to find x such that h(x) > r(x).
20000(0.90^x) > 60000(0.75^x)
0.90^x > 3(0.75^x) . . . . . . . divide by 20000
(0.90/0.75)^x > 3 . . . . . . . . divide by 0.75^x
x > log(3)/log(1.2) . . . . . . . . take logs, divide by log(1.2)
x > 6.025685
It will take about 6.03 years for the Honda to be worth more.
i) A number consists of two digits. If the number formed by reversing its digits
is added to it, the sum is 143 and if the same number is subtracted from it the
remainder is 9. Find the number.
Call the two-digit number : ab
The new number formed : ba
We have : 10a + b + 10b + a = 143
11a + 11b = 143
a+b = 143 : 11 = 13
So, we have a few combinations for a and b : (4;9) , (5;8) , (6;7) , (7;6) , (8;5) , (9;4)
Out of all these, only 76 is the satisfied number, as the new number formed is 67, and 76 + 67 = 143 ; 76 - 67 = 9
PLS HELP ASAP PLSSS PLSSS FIRST CORRECT ANSWER GETS BRAINLIEST PLS ANSWER
Answer:
sqrt(37) = arpox 6.1
Step-by-step explanation:
sqrt(1^2+6^2) = sqrt(37)
I NEED SOME HELP ON THIS! Which expression represents the volume of the rectangular prism shown? A) 3 x 4 + 11 B) x 2 + 2 x + 11 C) x 4 + 11 x 3 + 24 x 2 D) x 3 + 3 x 2 + x + 8
Answer:
C
Step-by-step explanation:
Volume = bhd
Volume = (x + 3)(x + 8)(x²)
start with (x + 3) and (x + 8), factor:
x² + 8x + 3x + 24
x² + 11x + 24
now bring x² back:
(x² + 11x + 24)(x²)
x⁴ + 11x³ + 24x²
Write 16^1/4 as a power then evaluate
Answer:
2
Step-by-step explanation:
[tex]16^{\frac{1}{4} }[/tex] = [tex]\sqrt[4]{16}[/tex] = 2. To find the fourth root, find the number that repeats itself four times using multiplication. 2 x 2 x 2 x 2 = 16
What is the area of the smaller square? *
16
32
36
81
The area of smaller square is 81
help me pls pls bro pls
Brainliest if correct
Answer:
The answer is 21/40
Step-by-step explanation:
Hope that helps!
Write any two necessary condition for collinearity.
Collinear points: Three points A, B and C are said to be collinear if they lie on the same straight line.
There points A, B and C will be collinear if AB + BC = AC as is clear from the adjoining figure.
In general, three points A, B and C are collinear if the sum of the lengths of any two line segments among AB, BC and CA is equal to the length of the remaining line segment, that is, either AB + BC = AC or AC +CB = AB or BA + AC = BC.
In other words,
There points A, B and C are collinear if:
(i) AB + BC = AC i.e.,
Or, (ii) AB + AC = BC i.e. ,
Or, AC + BC = AB i.e.,
Sandy is designing a circular garden as shown in this image. Her plan is to fill the rectangular region with hyacinths. She will need 78 square feet of space per hyacinth bulb. The hyacinth bulbs are sold in packages of 8.
What is the minimum number of packages Sandy must purchase to complete her plan?
Select from the drop-down menu to correctly complete the statement.
Sandy must purchase a minimum of _________
packages of hyacinth bulbs to complete her plan.
options are, 5,6,7,8
With one package (less actually) she can fill the 48ft^2 of the rectangular area.
How many packages does Sandy need?
We know that Sandy needs 7.8 square feet of space per hyacinth bulb, and the hyacinth bulbs are sold in packages of 8.
The rectangular region has a surface area of:
A = 8ft*6ft = 48 ft^2
The number of hyacinth bulbs that she can put in that surface is:
N = (48 ft^2/7.8 ft^2) = 6.15
So with 6 hyacinth bulbs, she can almost complete the rectangular area, and on each package there come 8 of them, so with one package she should be fine.
If you want to learn more about areas, you can read:
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Answer:
The answer is 7 PACKAGES
Step-by-step explanation:
I took the test!
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
75, 90, 108, ...
Find the 7th term.
The 7th term of the sequence to the nearest thousandth is 223.949
What are geometric sequences?These are sequence that increases in an exponential form.
The formula for calculating the nth term of a geometric sequence is expressed as:
Tn = ar^n-1
Given the following parameters
a = 75
r = 1.2
n = 7
Substitute the given parameter into the formula
T7 = 75(1.2)^6
T7 = 223.949
Hence the 7th term of the sequence to the nearest thousandth is 223.949
Learn more on geometric sequence here: https://brainly.com/question/9300199
Please help and explain 15 points
Write an equation of a circle with the given center and radius center (3,4) and radius 6
A.) (x-3)^2 + (y-4)^2 = 36
B.) (x-3)^2 + (y-4)^2 = 6
C.) (x-3)^2 + (y-4)^2 =36
D.) (x+3)^2 + (y-4)^2 = 6
Answer:
a
Step-by-step explanation:
General equation of a circle : [tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h,k) is at center and r = radius
Here, we want to find the equation of a circle with a given center at (3,4) and a given radius of 6
This is very simple, all we have to do is assign variables and then plug in the values of the variables into the general equation of a circle
First lets assign variables.
(h,k) is center and the circle has a given center at (3,4)
so (h,k) = (3,4) thus, h = 3 and k = 4
r = radius and the circle has a given radius of 6 so r = 6
now we plug this into the general equation of a circle.
recall equation : (x-h)² + (y-k)² = r²
h = 3, k = 4 and r = 6
plug in values
(x-3)² + (y-4)² = 6²
simplify exponent
(x-3)² + (y-4)² = 36
and we are done!
The answer is A