Option D is correct, (3, 1/2) point is a solution to the inequality y <1/3x+1/2.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given expression is y < 1/3x+1/2
y less than one divided by three times of x plus one divided by two.
Now let us check by plugging each ordered pair.
Now plug in (-2, 1)
1<1/3(-2)+1/2
1<-2/3+1/2
1<-4+3/6
Is false.
Now plug in (-1, 1)
1<-1/3+1/2
Is false.
Now plug in (0, 1/2)
1/2 < 1/2
is false.
Now plug in (3, 1/2)
1/2 < 3(1/3) + 1/2
1/2 < 1 + 1/2 is true.
Hence, (3, 1/2) point is a solution to the inequality y < 1/3x+1/2.
To learn more on Inequalities click:
https://brainly.com/question/28823603
#SPJ7
The volume of a spherical balloon is increasing at a constant rate of 3 in3/s. At what rate is the radius of the balloon increasing at the instant its radius is 2 inches?
Answer:
0.0597in/s
Step-by-step explanation:
The volume of the spherical balloon V= 4/3πr³
r is the radius of the balloon
The rate at which the volume is changing dV/dt is expressed as;\
dV/dt = dV/dr*dr/dt
dV/dr = 3(4/3πr²)
dV/dr = 4πr²
dV/dr = 4π(2)²
dV/dr = 16π
dV/dt = 3 in³/s
Substitute inti the formula
3 = 16πdr/dt
dr/dt = 3/16π
dr/dt = 3/50.24
dr/dt = 0.0597in/s
Hence the balloon is increasing at the rate of 0.0597in/s
Find an equation of the circle that satisfies the given conditions. (Use the variables x and y.)
Center at the origin;
passes through (4, 6)
Answer:
[tex]x^2 + y^2 = 52[/tex]
Step-by-step explanation:
Distance between two points:
Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Equation of a circle:
The equation of a circle with center [tex](x_0,y_0)[/tex] and radius r has the following format:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
Center at the origin;
This means that [tex]x_0 = 0, y_0 = 0[/tex]
So
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
[tex](x - 0)^2 + (y - 0)^2 = r^2[/tex]
[tex]x^2 + y^2 = r^2[/tex]
Passes through (4, 6)
The radius is the distance from this point to the center. So
[tex]r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]r = \sqrt{(4-0)^2+(6-0)^2}[/tex]
[tex]r = \sqrt{16+36}[/tex]
[tex]r = \sqrt{52}[/tex]
So
[tex]r^2 = 52[/tex]
Then
[tex]x^2 + y^2 = r^2[/tex]
[tex]x^2 + y^2 = 52[/tex]
Question 2
Find the volume.
Answer:
Volume of cone = 686π/3 or 718.67 in³
Step-by-step explanation:
Given the following data;
Radius, r = 7 in
Height, h = 14 inches
From the diagram, we can see that the object is a cone
To find the volume of a cone;
Mathematically, the volume of a cone is given by the formula;
[tex] V = \frac{1}{3} \pi r^{2}h[/tex]
Where;
V is the volume of the cone.
r is the radius of the base of the cone.
h is the height of the cone.
Substituting into the equation, we have;
[tex] Volume = \frac{1}{3} * \frac {22}{7} *7^{2}*14 [/tex]
[tex] Volume = \frac{1}{3} * 22 * 7 * 14 [/tex]
[tex] Volume = \frac{1}{3} * 2156 [/tex]
[tex] Volume = 718.67 [/tex]
Volume of cone = 718.67 in³ or 686π/3 in³
Help troll or report Help plsssss
Answer:
11. (a) 3/4+1/2=5/4
(b) 4/5= 8/10 , 16/20
12. 8 children don't like choc ice cream
Step-by-step explanation:
11. 3/4 +2/4=5/4(change 1/2 by making it the same as the one next to it)
12. 3/5 of 20 = 12
20-12=8
What’s the ara of each figure?
Answer:
433 in.²
Step-by-step explanation:
Divide the figure into 2 rectangles
Area of the figure = area of the bigger rectangle + area of smaller rectangle
✔️Area of bigger rectangle = L*W
L = 29 in.
W = 13 in.
Area of the bigger rectangle = 29*13
= 377 in.²
✔️Area of the smaller rectangle = L*W
L = 7 in.
W = 8 in.
Area of the bigger rectangle = 7*8
= 56 in.²
✅Area of the figure = 377 + 56 = 433 in.²
Answer to the question
Answer:
x = 4
Step-by-step explanation:
180 = 102 + 24x - 18
102 - 18 = 84subtract 84 from both sides96 = 24xdivide both sides by 44 = xPLEASSSSSSSSSSSEEEEEEEE HELPPP IM BEGGING SOMEONE PLEASEEEEEEEE PLEASEEEEEEEEEEE HELPPPP
Answer:
20 degree
Step-by-step explanation:
x + x + 70 = 110 degree (sum of two opposite interior angle equal to the exterior angle formed)
2x = 110 - 70
x = 40/2
x = 20 degree
Can y’all help me please?
Answer:
(A) [tex]5\frac{1}{4}*4\frac{1}{5}[/tex]
Step-by-step explanation:
The area of a parallelogram is the same as the area of a rectangle which is A=bh where b is the base and h is the height. Therefore, Erica can use the expression [tex]5\frac{1}{4}*4\frac{1}{5}[/tex] to find the area of the parallelogram.
In 42 - 15 = 27, the number 42 is called the
the number 15 is called the
and the number 27 is called
Answer:
The Answer to the Ultimate Question of Life, the Universe, and Everything is 42
Step-by-step explanation:
In this equation, the number 42 is called a minuend.
15 is a subtrahend because it is being subtracted from another number.
The number 27 would be called the difference.
an arrow is shot vertically upward from a platform 33ft high at a rate of 174 ft/sec. when will the arrow hit the ground?
Answer:
h(t) = -16t2 + 186t + 43
at the ground h = 0
hence; -16t2 + 186t + 43 = 0
solving this quadratic equation using the quadratic formula ; a = -16, b = 186, c = 43 ; x = (-b +-(b2 - 4ac)1/2)/2a
gives t = 11.8 seconds to the nearest tenth (note that the negative root has no practical significance)
Step-by-step explanation:
What is the value of this number in decimal form?
Three hundred sixty-seven thousandths.
Step-by-step explanation:
the other answer is correct.
just for a little bit of explanation :
the first position after the decimal point is for tenths. the second position for hundredths. the third for thousandths. then ten-thousandths, hundred-thousandths, millionths, ...
so, you would need 1000 thousandths to have a 1 at the first position before the decimal point. everything less than that has to be a number after the decimal point. and thousandths have to end (writing from left to right) with the thousandths-position. hundredths with the hundredths-position and so on.
95-3/4 step by step pls answer
Answer:
[tex]95 - \frac{3}{4} [/tex]
[tex] = \frac{95}{1} - \frac{3}{4} [/tex]
[tex] = \frac{380}{4} - \frac{3}{4} [/tex]
[tex] = \frac{380 - 3}{4} [/tex]
[tex] = \frac{377}{4} [/tex]
[tex] = 376\frac{1}{4} [/tex]
I need help with this problem-
Answer:
wat
Step-by-step explanation:
9.
slove this question
Answer:
[tex]\sqrt{x^2 + y^2}[/tex]
Step-by-step explanation:
to find diatance between AB
A(0 , 0) = (x1 , y1)
B(x , y) = (x2 , y2)
distance formula = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
=[tex]\sqrt{(x - 0)^2 + (y - 0)^2}[/tex]
=[tex]\sqrt{x^2 + y^2}[/tex]
Pls help luv y’a thx
4x – 26 = 18 pls answer fast
Answer:
X = 11
Step-by-step explanation:
4x - 26 = 18
Add 26 on both sides to get 4x alone.
4x - 26 + 26 = 18 + 26
4x = 44
44 divided by 4 is 11.
Therefore X is 11.
Answer: x=11
Step-by-step explanation:
Add 26 to both sides
4x-26+26=18+26
4x=44
Divide by 4 and get 11
x=11
Let’s Say I Left The House At 11:32 And Then I Came Back At 1:42, How Many Hours Have I Been Gone.
Example: 1hours and 20min
Just an example not the answer ^
i think the correct answer is 2 hours and 10 mins
you sight a rock climber on a cliff at a 32° angle of elevation. your eye level is 5.5 feet above the ground and you are 1000 feet from the base of the cliff. what is the approximate height of the rock climber from the ground?
Answer:
630 feets
Step-by-step explanation:
From the triangle attached :
Using trigonometry, the height h, which is the height of climber to your eye level :
Tan θ = opposite / Adjacent
Tan 32 = h / 1000
h = tan 32 * 1000
h = 0.6248693 * 1000
h = 624.86935
Height from the ground :
624.86935 + 5.5
= 630.369 feets
= 630 feet
help please anyone ??
If you are just given the two points it is the same formula. Find the midpoint between the points (4,-5) and (-4,5)
mid point =((4+(-4))/2,(-5+5)/2)
=(0,0)
The midpoint between the points (4, -5) and (-4, 5) is (0, 0).
To find the midpoint between two points ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex]), you can use the midpoint formula:
Midpoint = [tex]((x_1+ x_2)/2, (y_1+ y_2)/2)[/tex]
In this case, the two points are (4, -5) and (-4, 5).
So, the midpoint using the formula:
[tex]x_1[/tex] = 4
[tex]y_1[/tex] = -5
[tex]x_2[/tex]= -4
[tex]y_2[/tex] = 5
Midpoint
= ((4 + (-4)) / 2, (-5 + 5) / 2)
= (0 / 2, 0 / 2)
= (0, 0)
Therefore, the midpoint between the points (4, -5) and (-4, 5) is (0, 0).
Learn more about midpoint here:
https://brainly.com/question/24089949
#SPJ2
A Driver’s Ed program is curious if the time of year has an impact on number of car accidents in the U.S. They assumethat weather may have a significant impact on the ability of drivers to control their vehicles. They take a randomsample of 150 car accidents and record the season each occurred in. They found that 27 occurred in the Spring, 39 inthe Summer, 31 in the Fall, and 53 in the Winter.
Required:
Can it be concluded at the 0.05 level of significance that caraccidents are not equally distributed throughout the year?
Answer:
p-value = 0.0145
Hence, Since p-value ( 0.0145 ) is less than significance level ( 0.05 )
we reject null hypothesis.
Therefore, there is sufficient evidence to conclude that Car accidents are NOT equally distributed throughout the year
Step-by-step explanation:
Given the data in the question;
Hypothesis;
Null hypothesis : H₀ : Car accidents are equally distributed throughout the year
Alternative hypothesis : Hₐ : Car accidents are NOT equally distributed throughout the year
significance level ∝ = 0.05
x ;
Spring = 27
Summer = 39
Fall = 31
Winter = 53
Test Statistics;
Chi Square = ∑[ (O – E)²/E ]
O E (O – E)²/E
Spring 27 37.4 2.94
Summer 39 37.4 0.06
Fall 31 37.4 1.1267
Winter 53 37.4 6.4067
Total 150 150 10.5334
so; z = ∑[ (O – E)²/E ] = 10.5334
{from table}
p-value = 0.0145
Hence, Since p-value ( 0.0145 ) is less than significance level ( 0.05 )
we reject null hypothesis.
Therefore, there is sufficient evidence to conclude that Car accidents are NOT equally distributed throughout the year
In this exercise we have to use probability knowledge to calculate the distribution during the year, so we find that:
There is sufficient evidence to conclude that car accidents are not equally distributed throughout the year.
Given the data in the question;
[tex]Null \ hypothesis: H_0[/tex][tex]Alternative \ hypothesis : H_a[/tex] [tex]Significance\ level = 0.05[/tex]Now the values given in the statement can be exemplified below as:
[tex]Spring = 27[/tex][tex]Summer = 39[/tex][tex]Fall = 31[/tex][tex]Winter = 53[/tex]In this way, we can assemble a table of values with the statistical data previously informed and using the formula given below:
[tex]Z=\sum[\frac{(O-E)^2}{E}][/tex]
[tex]Z = 10.5334[/tex]
So:
[tex]\ \ \ \ \ \ \ \ \ \ \ O \ \ \ \ \ E \ \ \ \ (O - E)^2/E\\Spring \ \ 27 \ \ 37.4 \ \ \ \ 2.94\\Summer \ 39 \ 37.4 \ \ \ \ 0.06\\Fall \ \ \ \ \ \ 31 \ 37.4 \ \ \ \ 1.1267\\Winter \ \ \ 53 \ 37.4 \ \ \ 6.4067\\Total \ 150 150 \ 10.5334[/tex]
Hence, Since pvalue ( 0.0145 ) is less than significance level ( 0.05 ), so we reject null hypothesis.
See more about probability at brainly.com/question/795909
Bill makes $240 per hour for a standard 40 hour work week. He earns time- and - a - half for every overtime hour he works. Bill earned a total of$11,400 in one week,how many overtime hours did her work?
Answer:
5 overtime hours
Step-by-step explanation:
Given that :
Pay per hour = 240
Overtime pay = 1 1/2 * pay per hour = 1 1/2 * 240 = 360 per hour
Amount earned for the week = 11400
Let overtime hours = x
Total hours worked = 40 + x
Earning for the week based on hours worked :
240(40) + 360x = 11400
9600 + 360x = 11400
360x = 1800
x = 1800 / 360
x = 5 hours
You purchase a painting for 9,000 that has an appreciation rate of 12%. What is the growth
factor?
Answer:
Step-by-step explanation:
Answer:
$1080
Step-by-step explanation:
I think I am not sure
Surface Area of a Triangular Pyramid, please help!
Answer:
surface area of the triangular pyramid
=(1/2×9×7.8)+(3×1/2×9×12.3)
=35.1+166.05
=201.15 inch²
School is out ladies and Gentlemen hope y’all have a great summer!
Hey there!
I hope you have a great one too :)
Canterbury Cycles sells Harleys and pays each salesperson a commission of $800 for each cycle sold. During the month of December, a salesperson sold 3 cycles. The company pays commissions on the 5th day of the month following the sale. Which of the following statements is true?a. The salesperson will recognize commission revenue earned in the amount of 2400 in Decemberb. The company will recognize commission expense in the amount of $2,400 in December.c. The salesperson will recognize commission expense in the amount of $2,400 in January.d. The salesperson will recognize revenue in the same month that the cycle dealer recognizes expense.
Answer: The company will recognize commission expense in the amount of $2,400 in December
Step-by-step explanation:
Based on the information given in the question, the company will recognize commission expense in the amount of $2,400 in December.
A commission is regarded as a fee which is paid to a salesperson by a company in exchange for completing a sale.
It should be noted that in the accrual basis of accounting, commission should be recorded in the same period as when the sale generated was generated.
Answer:
b. The company will recognize commission expense in the amount of $2,400 in December.
Step-by-step explanation:
Based on the information given the statements that is true will be: THE COMPANY WILL RECOGNIZE COMMISSION EXPENSE IN THE AMOUNT OF $2,400 IN DECEMBER reason been that each salesperson were paid a commission in the amount of $800 for each cycle sold, which is 3 cycles during the month of December.
Calculation to determine the Commission Expense
Commission Expense=$800*3 cycles
Commission Expense=$2,400
Therefore The company will recognize commission expense in the amount of $2,400 in December.
If M is the midpoint of AB, find the coordinates of A if M(-3, 5) and B(6, -11)
midpoint= (x, y)
where x=(x1 + x2)/2
y=(y1 + y2)/2
x1=-3, x2=6, y1=5, y2=-11
so x=(-3 + 6)/2= 3/2
y=(5 + -11)/2= (5-11)/2= -6/2= -3
so mid point =(3/2, -3)
hope this helps
the volume of a cone with a radius of 6 and slant height of 10
Answer:
21.161
Step-by-step explanation:
use Pythagoras theorem ti find your slant height
then you use your formula which
[tex]1 \3\pi {r }^{2} h[/tex]
Austin was budgeted $ 825 to spend on chairs for his upcoming event. If each chair costs $ 15 , how many chairs can he purchase?
Answer:
55 chairs
Step-by-step explanation:
825/15=55
Plz help I’ll award brainliest!!!
That is the same as writing [tex]10\sqrt{30}[/tex]
======================================================
Explanation:
The diagram shows that
AC = 60AD = 50That must mean DC = AC-AD = 60-50 = 10
We'll use this to help find BD as shown below
AD/BD = BD/DC
AD*DC = BD*BD .... cross multiply
(BD)^2 = AD*DC
BD = sqrt(AD*DC) ..... geometric mean formula
BD = sqrt(50*10)
BD = sqrt(500)
----------------------
Now apply the pythagorean theorem to find AB. Focus on triangle ABD.
(AD)^2 + (BD)^2 = (AB)^2
(AB)^2 = (AD)^2 + (BD)^2
(AB)^2 = (50)^2 + (sqrt(500))^2
(AB)^2 = 2500 + 500
(AB)^2 = 3000
AB = sqrt(3000)
AB = sqrt(100*30)
AB = sqrt(100)*sqrt(30)
AB = 10*sqrt(30)
