Answer:
Option 4) The area of the flower bed is smaller than 4 square feet.
Step-by-step explanation:
Let’s solve for the area of the flower bed.
Consider that the flower bed is a rectangle.
The area of a recrangle is given by the formula:
A = length x width
The area of the flower bed is:
4 ft x 4/6 ft = 2 2/3 ft^2
2 2/3 ft ^2 < 4 ft^2
Therefore option 4 is the correct answer.
total number of chocolate boxes that can be produced: x+y (<,<=,>,>=) ___
restrictions based on demand of each: y(<,<=,>,>=) ___x
maximum amount of white chocolate production: y(<,<=,>,>=) ____
minimum amount of milk chocolate production: x(<,<=,>,>=) ____
minimum amount of white chocolate production: y(<,<=,>,>=) ____
vertices of feasible region : (0,0)(400,___)(____,___)(___,0)
optimization equation: profit = ____x+____y
your maximum profit is $____ .you should produce ____ boxes of milk chocolate and ____ boxes of white chocolate .
Answer:
Step-by-step explanation:
The idea here is to create lines according to the constraints we were given, graph the lines (which are actually inequalities), and then shade in the region that satisfies the inequality. Let's start at the beginning of the problem and we'll get our lines (inequalities) written.
The total number of boxes that can be produced according to the constraints is 800, so the inequality for that is
x + y ≤ 800 and solving for y:
y ≤ 800 - x
Another constraint on the white chocolate is that it has to be less than or equal to 200 boxes, so:
y ≤ 200
The max number of white chocolate boxes is half the number of milk chocolate, so:
y ≤ (1/2)x
The min number of milk chocolate boxes produced is:
x ≥ 0 and
The min number of white chocolate boxes produced is:
y ≥ 0 (This means that it is a possibility of making 0 milk chocolate boxes and all white chocolate boxes OR there is a possibility of making 0 white chocolate boxes and all milk chocolate boxes)
The production equation (which is used later) is:
2.25x + 2.50y (you make a profit of $2.25 on every milk chocolate box you sell and profit of $2.50 on every white chocolate box you sell).
The bold equations are the ones that need to be graphed (see graph below). Where those 3 lines intersect are the vertices of feasible region:
(0, 0), (400, 200), (600, 200), (800, 0).
Then take each x and y value from a coordinate and plug it into the profit equation (we don't need to use (0, 0)) starting with x = 400 and y = 200:
2.25(400) + 2.5(200) = $1400
Now using x = 600 and y = 200:
2.25(600) + 2.5(200) = $1850
Now using x = 800 and y = 0:
2.25(800) + 2.5(0) = $1800
So our max profit as seen by the evaluations is $1850, and that occurs when we sell 600 boxes of milk chocolate and 200 boxes of white chocolate.
What is the simplified form of the following expression?
Answer:
-( cube root of 2x)-6(cube root of x)
A nut company is determining how to package their new type of party mix. The marketing department is experimenting with different-sized cans for the party mix packaging. The designers use the equation r=Vhπ⎯⎯⎯⎯⎯⎯√r=Vhπ to determine the radius of the can for a certain height hh and volume VV. The company decides they want the can to have a volume of 1280πcm31280πcm3. Find the radius of the can if the height is 16cm16cm. Keep your answers in simplified radical form.
Answer:
The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]
Step-by-step explanation:
Radius of the can:
The radius of the can is given by:
[tex]r^2 = \frac{V}{h\pi}[/tex]
In which V is the volume and h is the height.
In this question:
[tex]V = 1280\pi, h = 16[/tex]
Thus
[tex]r^2 = \frac{V}{h\pi}[/tex]
[tex]r^2 = \frac{1280\pi}{16\pi}[/tex]
[tex]r^2 = 80[/tex]
[tex]r = \sqrt{80}[/tex]
[tex]r = \sqrt{5*16}[/tex]
[tex]r = \sqrt{5}\sqrt{16}[/tex]
[tex]r = 4\sqrt{5}[/tex]
The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]
Write an equation for a line containing (–2,8) that is perpendicular to the line containing the points (3,–4)and (–7,1).
Answer and I will give you brainiliest
Answer:
y = 2x + 12
Step-by-step explanation:
the formula for a line is typically
y = ax + b
a is the slope of the line (expressed as y/x ratio describing how many units y changes, when x changes a certain amount of units).
b is the offset of the line in y direction (for x=0).
we have the points (3, -4) and (-7, 1).
to get the slope of the line let's wander from left to right (x direction).
to go from -7 to 3 x changes by 10 units.
at the same time y changes from 1 to -4, so it decreases by 5 units.
so, the slope is -5/10 = -1/2
and the line equation looks like
y = -1/2 x + b
to get b we simply use a point like (3, -4)
-4 = -1/2 × 3 + b
-4 = -3/2 + b
-5/2 = b
so, the full line equation is
y = -1/2 x - 5/2
now, for a perpendicular line the slope exchanges x and y and flips the sign.
in our case this means +2/1 or simply 2.
so, the line equation for the perpendicular line looks like
y = 2x + b
and to get b we use the point we know (-2, 8)
8 = 2×-2 + b
8 = -4 +b
12 = b
so, the full equation for the line is
y = 2x + 12
Answer:
2x-y+12= 0 or y = 2x+12 is the answer
Step-by-step explanation:
slope of the line joining (3,-4) and (-7,1) is 1-(-4)/-7-3
= -5/10
= - 1/2
slope of the line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) = 2
Equation of the line line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) is y-8 = 2(x-(-2))
y-8 = 2(x+2)
y- 8 = 2x+4
y=2x+12 (slope- intercept form) or 2x-y+12= 0 (point slope form)
what is 32⋅(12)x+1=2x−14?
Answer:
[tex]x=-\frac{15}{382}[/tex]
Step-by-step explanation:
32 × 12x + 1 = 2x - 14
384x + 1 = 2x - 14
384x + 1 - 1 = 2x - 14 - 1
384x = 2x - 15
384x - 2x = 2x - 2x - 15
382x = - 15
382x ÷ 382 = - 15 ÷ 382
[tex]x=-\frac{15}{382}[/tex]
A die is rolled five times and a 5 or 6 is considered a success. Find the probability of
(i) at least 2 successes,
(ii) at least one but no more than 3 successes.
Answer:
(i) The probability of at least 2 successes is 0.2093.
(ii) The probability of at least one but no more than 3 successes is 0.9548.
Step-by-step explanation:
Now the total number of cases = {1, 2, 3, 4, 5, 6} = 6.
Favourable cases = {1, 6} = 2.
[tex]p = \frac{2} {3} = \frac{1} {3} \\\\q = 1- p\\\\q = \frac{2}{3} \\\\n=5[/tex]
i) at least 2 successes,
[tex]P(X\geq 2) = (^{n}C_{x} )\times p^{x} \times (1-p)^{n-x}\\\\P(X\geq 2) = 0.2093[/tex]
ii) at least one but no more than 3 successes,
[tex]P(X\leq 3) = (^{n}C_{x} )\times p^{x} \times (1-p)^{n-x}\\\\P(X\leq 3)= 0.9548[/tex]
Help please so lost!!!!!!!!!!!!
Answer:
hmmmmm please send the pic again
Camilla and Aisha are sisters and go to the same school. This morning, Camilla decided to bike to school, and Aisha decided to walk. They left home at the same time. Camilla’s speed was 6.5 miles per hour, and Aisha’s speed was 2 mph. When Camilla reached the school, Aisha was 1.5 miles behind. How far away from their house is the school?
Answer:
2 1/6
Step-by-step explanation:
6.5x=2x+1.6=1/3
1/3*6.5=2 1/6
Can someone help me thank youuu!!!
Answer:
D.
Step-by-step explanation:
cos is positive and sin is negative
=>
it must be in quadrant IV.
you remember, 1 = sin² + cos²
1 = sin² + (3/5)² = sin² + 9/25
25/25 = sin² + 9/25
16/25 = sin²
sin = 4/5 or -4/5
and as sin of this angle is < 0, our solution is -4/5
Clear parentheses by applying the distributive property.
-(-4s + 9t + 7)
Answer:
4s-9t-7
Step-by-step explanation:
multiply the negative one with all terms inside the bracket, since they are all unlike terms the answer remains the same
Flying with a tailwind, a flight crew flew 500 km in 4 hours. Flying against the tailwind, the crew flew 468 km in 4 hours. Find the speed of the plane in calm air and the speed of the wind, both in km per hour.
Answer:
spped of the plane in calm air=121 km/h
speed of the wind= 4km/h
Step-by-step explanation:
Let say V the speed of the plane in calm air
and v the speed of the wind
Flying with a tailwind, a flight crew flew 500 km in 4 hours ==> 500= (V+v)*4
Flying against the tailwind, the crew flew 468 km in 4 hours ==> 468 = (V-v)*4
We divide the 2 equations by 4 and then add the 2 results equations:
(500+468)/4=2V ==> V=121 (km/h)
We replace that value in the first equation:
V+v=500/4=125
v=125-121=4 (km/h)
easy! please help :( The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. On the bottom shelf are 3 fiction and 5 nonfiction books.
Choosing which 2 books describes a pair of dependent events?
Answer:
D: one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf
Step-by-step explanation:
A pair of 2 dependent events are simply those in which the choice of the second item depends on taking the first item such that the probability changes.
Because when the first item is taken without replacement, the sample size would have reduced and as such picking the exact same item will reduce the probability.
Now, what this means in relation to the question is that for 2 of the events to be independent, they must be on the same shelf and of same type of book such that the second book can't be selected until the first one has been selected.
The only option that fits this definition is option D where both books are on the same shelf and they are same type of books.
Answer:
one of the nonfiction books on the bottom shelf, and a second nonfiction book from the bottom shelf
Step-by-step explanation:
1/2-5(2/3x + 6)+4/5x?
Answer:
[tex]-29.5-\frac{38}{15}x[/tex]
Step-by-step explanation:
First, we must expand out the -5.
-5 times 2/3x is equal to -10/3x, and -5 times 6 is equal to -30. 1/2 minus 30 is equal to -29.5, and 4/5x minus 10/3x is equal to -38/15x.
How do i solve this quesiton 6(x − 2) > 15
Answer:
Step-by-step explanation:
[tex]\displaystyle\ \!\!6(x-2)>15 \\\\6x-12>15 \\\\6x>27\\\\ \boldsymbol{x>4,5 \ \ or \ \ x\in(4,5\ ; \infty)}[/tex]
Please help I really don’t understand anything at all !
Answer:
see explanation
Step-by-step explanation:
1
2(3x + 1) = 4(x + 2) ← distribute parenthesis on both sides
6x + 2 = 4x + 8 ( subtract 4x from both sides )
2x + 2 = 8 ( subtract 2 from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
------------------------------------------------------------
2
6x = 4(x - 3) ← distribute parenthesis
6x = 4x - 12 ( subtract 4x from both sides )
2x = - 12 ( divide both sides by 2 )
x = - 6
-----------------------------------------------------------
3
2(4x + 7) = 4x + 30 ← distribute parenthesis on left side
8x + 14 = 4x + 30 (subtract 4x from both sides )
4x + 14 = 30 ( subtract 14 from both sides )
4x = 16 ( divide both sides by 4 )
x = 4
---------------------------------------------------------------------
4
50 = - (y + 22) ← distribute parenthesis by - 1
50 = - y - 22 ( add 22 to both sides )
72 = - y ( multiply both sides by - 1 )
- 72 = y , that is
y = - 72
Suppose a rumor is going around a group of 210 people. Initially, only 34 members of the group have heard the rumor, but 3 days later 69 people have heard it. Using a logistic growth model, how many people are expected to have heard the rumor after 6 days total have passed since it was initially spread? (Round your answer to the nearest whole person.)
Answer:
116 people are expected to have heard the rumor after 6 days total have passed since it was initially spread.
Step-by-step explanation:
Logistic function:
The logistic function is given by:
[tex]P(t) = \frac{K}{1 + Ae^{-kt}}[/tex]
In which:
[tex]A = \frac{K - P(0)}{P(0)}[/tex]
Considering that K is the carrying capacity, k is the growth/decay rate and P(0) is the initial population.
Suppose a rumor is going around a group of 210 people.
This means that [tex]K = 210[/tex]
Initially, only 34 members of the group have heard the rumor:
This means that [tex]P(0) = 34[/tex] and:
[tex]A = \frac{210 - 34}{34} = 5.1765[/tex]
So
[tex]P(t) = \frac{210}{1 + 5.1765e^{-kt}}[/tex]
3 days later 69 people have heard it.
This means that [tex]P(3) = 69[/tex], and we use this to find k.
[tex]69 = \frac{210}{1 + 5.1765e^{-3k}}[/tex]
[tex]69 + 357.1785 e^{-3k} = 210[/tex]
[tex]357.1785 e^{-3k} = 141[/tex]
[tex]e^{-3k} = \frac{141}{357.1785}[/tex]
[tex]\ln{e^{-3k}} = \ln{\frac{141}{357.1785}}[/tex]
[tex]-3k = \ln{\frac{141}{357.1785}}[/tex]
[tex]k = -\frac{\ln{\frac{141}{357.1785}}}{3}[/tex]
[tex]k = 0.3098[/tex]
So
[tex]P(t) = \frac{210}{1 + 5.1765e^{-0.3098t}}[/tex]
How many people are expected to have heard the rumor after 6 days total have passed since it was initially spread?
This is P(6), so:
[tex]P(6) = \frac{210}{1 + 5.1765e^{-0.3098*6}} = 116[/tex]
116 people are expected to have heard the rumor after 6 days total have passed since it was initially spread.
Please Help me and don't report this
8 < x < 8.5 is your answer
other sides has to always be less than the hypotenuse
9514 1404 393
Answer:
0.5 < x < 16.5
Step-by-step explanation:
The sum of the two shortest sides of a triangle must always exceed the length of the longest side.
If x and 8.0 are the short sides, then ...
x + 8.0 > 8.5
x > 0.5
If 8.0 and 8.5 are the short sides, then ...
8.0 +8.5 > x
16.5 > x
So, for the given triangle to exist, we must have ...
0.5 < x < 16.5
_____
Additional comment
You will notice that the value 0.5 is the difference of the given sides, and 16.5 is their sum. This will always be the case for a problem like this. The third side length always lies between the difference and the sum of the other two sides.
Where A = -7 and b = 9 what is the value of the midpoint?
Answer:
Find the value of x if B is the midpoint of AC, AB = 2x + 9 and BC = 37
Step-by-step explanation:
Charles spent 1/4 of his allowance on a shirt, and 2/5 of the remainder on a book. A.What fraction of his allowance did he have left? B.If he spent $18 on the book, how much did he have at first?
Answer:
18.65
Step-by-step explanation:
1/4+2/5+18=18.65
18.65
hope it helps you good luck
Suppose we take a poll (random sample) of 3923 students classified as Juniors and find that 3196 of them believe that they will find a job immediately after graduation. What is the 99 % confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation.
Answer:
The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Suppose we take a poll (random sample) of 3923 students classified as Juniors and find that 3196 of them believe that they will find a job immediately after graduation.
This means that [tex]n = 3923, \pi = \frac{3196}{3923} = 0.8147[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 - 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.7987[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 + 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.8307[/tex]
The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).
the area for this shape.
Answer:
Step-by-step explanation:
A shopkeeper bought a second-hand car for Rs 1,50,000. He spent Rs 10,000
on its painting and repair and then sold it for Rs 2,00,000. Find his profit or loss.
Suppose 5 men and 7 women are on a crowded elevator. At the next floor, four people get off the elevator. Find the probability that three are women.
0.010
0.354
0.424
0.25
Total People=5+7+4=16
Women=7We know
[tex]\boxed{\sf P(W)=\dfrac{No.\:of\:women}{Total\:People}}[/tex]
[tex] \\ \sf \longmapsto \: p(w) = \frac{7}{16} [/tex]
88, 92, 76, 42, 88, 90, 100, 110, 115, 5, 88, 92, 95
Find the Mean, Median, Mode, Range and Outlier of the data set above?
Answer:
Mean = 83.15
Median = 90
Mode = 88
Range = 110
Outlier = 5
Step-by-step explanation:
Mean - (88+92+76+42+88+90+100+110+115+5+88+92+95)/2 = 83.15
Median - 5, 42, 76, 88, 88, 88, 90, 92, 92, 95, 100, 110, 115 = 90
Mode - 88, 92, 76, 42, 88, 90, 100, 110, 115, 5, 88, 92, 95 = 88
Range - 115 - 5 = 110.
Outlier - 88, 92, 76, 42, 88, 90, 100, 110, 115, 5, 88, 92, 95 = 5
hope it helps :)
please mark brainliest!!! (took a lot effort!)
Answer:
Step-by-step explanation:
Arrange the data from the lowest to the highest value ( after you rearrange them count to see if you still have the same amount of values -13 numbers)
5, 42, 76, 88, 88, 88, 90, 92, 92, 95, 100, 110, 115
Mean: sum up all the values /number of values
mean = (5+42+76+88+88+88+90+92+92+95+100+110+115)/13 ≅83.15
Median: is the number in the middle (or if you have an even amount of numbers you do the average of the 2 middle numbers)
median = 90
Mode: is the number that appears the most (a data set can have more than one mode if different numbers appear with the same frequency )
mode= 88
Range: is the difference between the biggest and smallest value
range = 115-5 = 110
Outlier: is a value that is significantly different than the rest of the values
outlier = 5
Select the correct answer
The equation of a line is y= 15x-2 What are its slope and y-intercept?
A.slope = 15 and y-intercept=-2
B.slope = 15 and y-intercept = 2
C.slope = 2 and y-intercept=15
D.siope =-2 and y-intercept=15
RES
Answer:
A
Step-by-step explanation:
Slope = term that multiply x
y intercept = the number without a variable
Can someone please help me with this; im a lil bit confused.... Q.solve for the values of x in the equation 2x² - 5x - 12 = 0 using the quadratic equation formula.
Answer:
The solutions for x are [tex]x = 4[/tex] and [tex]x = -1.5[/tex].
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
2x² - 5x - 12 = 0
This means that [tex]a = 2, b = -5, c = -12[/tex]
Solution:
[tex]\Delta = (-5)^2 - 4(2)(-12) = 121[/tex]
[tex]x_{1} = \frac{-(-5) + \sqrt{121}}{2*2} = 4[/tex]
[tex]x_{2} = \frac{-(-5) - \sqrt{121}}{2*2} = -1.5[/tex]
The solutions for x are [tex]x = 4[/tex] and [tex]x = -1.5[/tex].
Bailey wants to buy a house, paying approximately $1000 per month. The bank estimates a 4.5% annual interest rate for 15 years. Which formula approximates the total value of a house Bailey can afford?
A. P = 1000[1 - (1 + 0.045/12)^-180/0.045/12.
B. P = 1000(0.045/12)/1 - 1(1 + 0.045/12)^-180.
C. 1000 = d[1 -(1 + 0.045/12)/0.045/12]^-180.
D. 1000 = d(0.045/12)/1 -(1 + 0.045/12)^180.
Answer:
I=Principle × Rate × Time so 1000×4.5/100 × 15yrs
Josh sees a pair of trainers with a tags saying 75% off the recommended price of £80. Josh decided to buy the trainers. How many pounds will it cost him?
If it's possible to tell, decide if a and b are positive or negative: a-3>b-3 and b>4
PLEASE HELP NEED ASAPPPPPPP
Answer:
a and b are positive
Step-by-step explanation:
We are given that
[tex]a-3>b-3[/tex]
[tex]b>4[/tex]
We have to find that a and b are positive or negative.
We have
[tex]b>4[/tex]
It means b is positive and greater than 4.
[tex]a-3>b-3[/tex]
Adding 3 on both sides
[tex]a-3+3>b-3+3[/tex]
[tex]a>b>4[/tex]
[tex]\implies a>4[/tex]
Hence, a is positive and greater than 4.
Therefore, a and b are positive
URGENT 100 POINTS AND BRAINIEST
Question 9 (Essay Worth 10 points)
(04.01, 04.02 HC)
Ted practices two types of swimming styles for a total of 50 minutes every day. He practices the breaststroke for 20 minutes longer than he practices the butterfly stroke.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Ted practices the butterfly stroke every day (x) and the number of minutes he practices the breaststroke every day (y). (5 points)
Part B: How much time does Ted spend practicing the breaststroke every day? Show your work. (3 points)
Part C: Is it possible for Ted to have spent 45 minutes practicing the butterfly stroke if he practices for a total of exactly 50 minutes and practices the breaststroke for 20 minutes longer than he practices the butterfly stroke? Explain your reasoning. (2 points)
Answer:
Part A:
x + y = 50
y = x + 20
Part B:
Ted spends 35 minutes practicing the breaststroke every day.
Part C: It is not possible, as 45 + 65 isn't 50.
Step-by-step explanation:
