Answer:
16
Step-by-step explanation:
x+y=30 solve for x x=30-y
substitute x with 30-y and solve
11.25x+22.4y=515.9
11.25(30-y)+22.4y=515.9
337.5+11.15y=515.9
11.15y=178.4
y=16
since we're solving for just large candles it's 16
if need small cangle number 30-16=14
Question 3 of 10
Find tan 0
[tex]\tan \theta = \dfrac{\text{Opposite side}}{\text{Adjacent side}} = \dfrac{16}{12}[/tex]
A random variables X and Y are distributed according to the joint PDF. The value of constant a = _______.f(x,y)=ax if 1<=1x<=y<=2 and 0 otherwise
======================================================
Explanation:
PDF = probability density function
The given joint PDF is
[tex]f(x,y) = \begin{cases}ax \ \ \ \text{ if } 1 \le x \le y \le 2\\0 \ \ \ \ \ \text{ otherwise}\end{cases}[/tex]
Let's focus on the [tex]1 \le x \le y \le 2[/tex]. Specifically the x term for now. Erasing out the y term, we have the inequality [tex]1 \le x \le 2[/tex] which says x is between 1 and 2, inclusive. We have almost the same story for y, but there's another condition attached to it: y must also be equal to or larger than x.
So let's say x = 1.5. This would mean [tex]1.5 \le y \le 2[/tex]. As another example, x = 1.7 leads to [tex]1.7 \le y \le 2[/tex]. In general, we would say [tex]x \le y \le 2[/tex] where x is between 1 and 2.
As x gets bigger, the range of possible y values gets smaller. If x = 2, then y has no choice but to be 2 as well.
-----------------
Based on that, we'll have a double integral that looks like this:
[tex]\displaystyle V = \int_{1}^{2}\int_{x}^{2}f(x,y)dydx\\\\[/tex]
The outer integral handles the x terms that range from 1 to 2, describing [tex]1 \le x \le 2[/tex]. Note the dx on the outside. The order of the dy and dx matters.
On the inside, we have the integral for dy ranging from x to 2 to describe the interval [tex]x \le y \le 2[/tex]
To have f(x,y) be a PDF, the volume under the f(x,y) surface must be 1, where the volume is based on the bounds set up. So we must have V = 1. We'll use this later.
-----------------
Let's simplify the double integral.
We'll start by computing the inner integral with respect to y.
[tex]\displaystyle V = \int_{1}^{2}\int_{x}^{2}f(x,y)dydx\\\\\displaystyle V = \int_{1}^{2}\int_{x}^{2}\left(ax\right)dydx\\\\\displaystyle V = \int_{1}^{2}\left(axy\Bigg|_{x}^{2}\right)dx\\\\\displaystyle V = \int_{1}^{2}\left(ax(2) - ax(x)\right)dx\\\\\displaystyle V = \int_{1}^{2}\left(2ax - ax^2\right)dx\\\\[/tex]
Then we'll finish it off by integrating with respect to x.
[tex]\displaystyle V = \int_{1}^{2}\left(2ax - ax^2\right)dx\\\\\displaystyle V = \left(ax^2 - \frac{1}{3}ax^3\right)\Bigg|_{1}^{2}\\\\\displaystyle V = \left(a(2)^2 - \frac{1}{3}a(2)^3\right) - \left(a(1)^2 - \frac{1}{3}a(1)^3\right)\\\\\displaystyle V = \left(4a - \frac{8}{3}a\right)-\left(a - \frac{1}{3}a\right)\\\\[/tex]
[tex]\displaystyle V = 4a - \frac{8}{3}a-a + \frac{1}{3}a\\\\\displaystyle V = 3a - \frac{8}{3}a + \frac{1}{3}a\\\\\displaystyle V = \frac{9}{3}a - \frac{8}{3}a + \frac{1}{3}a\\\\\displaystyle V = \frac{9-8+1}{3}a\\\\\displaystyle V = \frac{2}{3}a\\\\[/tex]
Side note: We don't have to worry about the "plus C" integration constant when working with definite integrals.
Recall that V = 1. So,
[tex]\displaystyle V = \frac{2}{3}a\\\\\displaystyle \frac{2}{3}a = 1\\\\\displaystyle a = \frac{3}{2} = 1.5\\\\[/tex]
a = 3/2 is the final answer.
What is the product?
(38b* )-822
Answer:
[tex]\boxed{\sf D)\:-24a^3b^7}[/tex]
Step-by-step explanation:
[tex]\sf (3a^2b^4)(-8ab^3)[/tex]
We'll use rule of exponents to simplify expression.
[tex]\sf 3^1a^2b^4(-8)^1a^1b^3[/tex]
Now, use the commutative property of multiplication.
[tex]\sf 3^1(-8)^1a^2a^2b^4b^4[/tex]
In order to multiply power of the same base, we add their exponents.
[tex]\sf 3^2(-8)^1a^{2+1}b^{4+3}[/tex]
→ Add exponents:
[tex]\sf 3^1(-8)^1a^3b^7[/tex]
→ Multiply 3* -8
[tex]\sf -24a^3b^7[/tex]
__________________________________________
[tex]5/4+3/4+1/4=[/tex]
Ordering decimals
Order these numbers from least to greatest.
1.509, 1.4062, 1.6, 1.56
Answer:
1.4062, 1.509, 1.56, 1.6
Step-by-step explanation:
1509/1000, 14062/10000, 16/10, 156/100
15090, 14062, 16000, 15600
1.4062, 1.509, 1.56, 1.6
Help help math math math
Answer:
113
Step-by-step explanation:
The supplement of angle 3 is congruent to 67, because they are corresponding angles. After you subtract the supplement from 180, you should get angle 3
180-67=113
Answer:
∠3 measures 113°
Step-by-step explanation:
These are consecutive interior angles. It's difficult to explain in words because none of the lines are marked in any way, but I marked the angles in the attached image. Because both downward facing lines are parallel, both sets of corresponding red and blue angles are congruent.
∠3 corresponds to the angle supplementary to the 67° angle. Supplementary angles add up to 180°, so ∠3 and 67° also have to add up to 180°. Hopefully my image makes that a little more clear.
[tex]x+67=180\\x=113[/tex]
∠3 measures 113°
what are the measurements of 1 and 2?
Answer:
8 tablespoons1/2 cup4 ounces10 tablespoons plus 2 teaspoons2/3 cup5.2 ounces12 tablespoons3/4 cup6 ounces16 tablespoons1 cup8 ounces
Line’s family has completed 70% of a trip. They have traveled 35 miles. How far is the trip?
Answer:
hi the answer to your question should be 50 miles
Step-by-step explanation:
hope this helps have a great day!
Write as a product 4x^4+8x^3-2x^2
Answer:
764x
Step-by-step explanation:
4^4=256
8^3=512
2^2=4
256-4+512=764
764x
Answer:
2x^2(2x^2+4x-1)
Step-by-step explanation:
The GCF is 2x^2 so pull apart each number and you will get your answer.
please i need help with this
Answer:
1.) Smith
2.) Johnson
Answer:
Step-by-step explanation:
Marco wants to buy a new smartphone that costs $495, with some additional accessories. He has already saved $75. Write and solve an inequality to find the least amount of money, m, that Marco still needs to save before he can buy the smartphone and accessories. Enter your answer in the box.
Answer:
495-75=m m=420
Step-by-step explanation:
He needs to save 495 dollars, and hes already saved 75
and needs to find out how much more he needs to save to have 495 dollars
To do this, take 495 and subtract 75. This is how we get the inequality
495-75=m
From here it is simple, just subtract 75 from 495 to get 420
Help please!!!!!!!!!!!!!!!!!
Answer:
You are correct it is indeed mortgage!
Step-by-step explanation:
This is because a fixed expense is something that cannot be changed easily. Like a mortgage, car payments, rent payments, or insurance.
Hope this helps, I tried to just briefly explain! :)
Pls help I’ll failing ASAP this is due in 10 minutes I need help with 5 and 8
Answer:
5) 3/5
8) 2/-4 or -2/4
Step-by-step explanation:
5, based on your work, is 3/5 because we use rise (3) and run (5)
And 8, based on your work, is 2/-4 or -2/4 because you go up 2, and go to the left 4.
Plz help well mark brainliest if you are correct!!…
Answer:
A. y<-3
Step-by-step explanation:
Given that the points (-32, - 10) and (-74, 11) lie on a line, what is the
equation of the line?
The equation of the line is:
[tex]y=\frac{-1}{2}x-26[/tex]
The point-slope equation of a line is given as:
[tex]y-y_1=m(x-x_1)[/tex]
where m represents the slope, and is calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For the line passing through the points (-32, - 10) and (-74, 11)
[tex]x_1=-32, y_1=-10, x_2=-74, y_2=11[/tex]
Substitute these points into the slope formula to get the slope of the line
[tex]m=\frac{11-(-10)}{-74-(-32)} \\\\m=\frac{11+10}{-74+32} \\\\m=\frac{21}{-42} \\\\m=\frac{-1}{2}[/tex]
Substitute [tex]m=\frac{-1}{2}, x_1=-32, y_1=-10[/tex] into the line equation
[tex]y-(-10)=\frac{-1}{2}(x-(-32))\\\\y+10=\frac{-1}{2}x-16\\\\y= \frac{-1}{2}x-16-10\\\\y=\frac{-1}{2}x-26[/tex]
The equation of the line is:
[tex]y=\frac{-1}{2}x-26[/tex]
Learn more on equation of a line here: https://brainly.com/question/13763238
4.
(03.02)
Match each statement (term) with its value in relation to 0 (definition). (10 points)
1.
Oliver owes his sister $27.
2.
A building is 38 feet tall.
3.
Erica jumped 2.7 feet above ground.
4.
The scuba diver was 38 feet below sea level.
5.
The basement is 8.3 feet below ground.
a.
38
b.
-38
c.
-8.3
d.
-27
e.
2.7
Answer:
Below
Step-by-step explanation:
1.-d
2.-a
3.-e
4.-b
5.-c
Answer:
-8.3ithink so
Step-by-step explanation:
Which of the following numbers can be expressed as a decimal that terminates? 3/2,2/3,3/4,5/7
Answer:
Step-by-step explanation:
An example of one fraction that does NOT terminate is 2/3.
2/3 = 0.666666666666666 .... That's the easy way to tackle the problem. Pick out the ones that don't terminate.
5/7 is the other one. It does not terminate either. It has 6 digits in a block that keeps on repeating itself forever.
5/7 = .571428 571428 which goes on forever.
So the two that do terminate are
3/2 which = 1.5
3/4 which = 0.75
please help. one algebra question for 20 points
Answer:
f(-18) = -5
Step-by-step explanation:
Substitute−18forxiny=
1/3 x+1:
y= 1/3x+1
y= 1/3(−18)+1
y=−5(Simplify both sides of the equation)
Which function has zeros at x = 10 and x = 2?
f(x) = x2 – 12x + 20
f(x) = x2 – 20x + 12
f(x) = 5x2 + 40x + 60
f(x) = 5x2 + 60x + 100
Answer:
f(x) = x2 – 12x + 20
Step-by-step explanation:
if it has those zeros, then it is (x-10)(x-2)
if you multiply that out, you get x^2 - 12x +20
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Use the domain {-3, -2, -1, 0, 1} and plot the points on the graph that would best satisfy the equation. The bold grid marks represent one unit, the horizontal red line represents the x-axis, and the vertical red line represents the y-axis.
y = 2-x
the side length of NS is 7.81 units.
Sarah buys a new car for $26,500 and pays 3% down payment the terms of her loan 4.5% apr over 4 years. How much is her monthly payment?
A. $586.16
B.558.99
C.562.61
D.549.74
Answer:
i guess it's will be C
Step-by-step explanation:
find all complex solutions of 5x^2+5x+4=0
Answer:
-1/2 + i/10 sqrt(55) , -1/2 - i/10 sqrt(55)
Step-by-step explanation:
5x^2+5x+4=0
a=5 b= 5 c=4
Using the quadratic formula
-b ± sqrt( b^2 -4ac)
---------------------------------
2a
-5 ± sqrt( 5^2 - 4(5)(4))
----------------------------------
2(5)
-5±sqrt( 25 - 80)
----------------------------
10
-5± sqrt(-55)
--------------------------
10
-5/10 ± 1/10 i sqrt(55)
-1/2 + i/10 sqrt(55) and -1/2 - i/10 sqrt(55)
Answer:
x= -5 ± i√55 / 10
Step-by-step explanation:
hope i helped
4) Change the recurring decimal 0.18 to a fraction. (2marks)
You must show all your working.
Answer:
18/100 or 9/50
Step-by-step explanation:
First, put 0.18 over 100 because there are 2 digits in the decimal, so you convert it to 18/100. Then, simplify it, and because the GCF is 2, divide the numerator and denominator. The final fraction ins 9/50.
Over the summer, Paulo opens a dog-washing business and begins with $32. The table shows how much he earns and spends each week. He works for 8 weeks washing dogs. When he starts back at school, he budgets $60 to spend each week. How many weeks pass before he needs to wash more dogs?
do my teeth look straight?
answer asap
Answer:
yeah your teeth is good and strong too
A group of 90 students plan to go camping over the weekend. At the last minute, some of the students decide not to go. The students who do go separated into four camps, where [tex]\frac{1}{7}[/tex] of the students stay at Hill Camp; [tex]\frac{1}{3}[/tex] of the students stay at Forest Camp; [tex]\frac{1}{4}[/tex] of the students stay at Field Camp; and the remaining students stay at Lake Camp. How many students were at Lake Camp?
Using fractions, it is found that of the students that went camping, [tex]\mathbf{\frac{23}{84}}[/tex] were at Lake Camp.
The students who went camping are divided according to the following fractions:
[tex]\frac{1}{7}[/tex] stayed at Hill Camp.[tex]\frac{1}{3}[/tex] stayed at Forest Camp.[tex]\frac{1}{4}[/tex] stayed at Field Camp.The remaining x stayed at Lake Camp.The sum of all these fractions is 100% = 1, hence:
[tex]\frac{1}{7} + \frac{1}{3} + \frac{1}{4} + x = 1[/tex]
[tex]\frac{12 + 28 + 21 + 84x}{84} = 1[/tex]
[tex]84x + 61 = 84[/tex]
[tex]84x = 23[/tex]
[tex]x = \frac{23}{84}[/tex]
Of the students that went camping, [tex]\mathbf{\frac{23}{84}}[/tex] were at Lake Camp.
A similar problem is given at https://brainly.com/question/24372153
Pls help I’ll brainlest ASAP
Answer:
slope = change over y/change over x
point 1: (-3,-4)
point 2: (2,3)
(-4-3)/(-3-2)=(-7)/(-5)=7/5
y=mx+b -> m=slope, b=y-intercept
y=(7/5)x+b
plug in one of the points
3=(7/5)*2+b
3=14/5+b
b=1/5
slope = 7/5, y-intercept = (0,1/5)
a carpet cleaning service charges a one-time service fee of $100 with an additional $15 per hour for their business. write a linear equation that represents the total cost (y) for the hours work (x)
Answer:
The answer is y= 100 +15x
Step-by-step explanation:
You start with a service fee of $100
$15 per hour
x because the amount of hours can vary
y which is the total cost
y= 100+ 15x
A self-storage center has many storage rooms that are 6 ft wide, 10 feet deep, and 12 ft high. What is the volume of the room?
The volume of the storage room is the amount of space in the storage room, and it is 720 cubic feet
The dimensions are given as:
[tex]Width = 6ft[/tex]
[tex]Depth = 10ft[/tex]
[tex]Height = 12ft[/tex]
The volume of the storage room is the product of the dimensions.
So, we have:
[tex]Volume= Width \times Depth \times Height[/tex]
Substitute values for Width, Depth and Height
[tex]Volume= 6ft \times 10ft \times 12ft[/tex]
Multiply the dimensions
[tex]Volume= 720ft^3[/tex]
Hence, the volume of the storage room is 720 cubic feet
Read more about volumes at:
https://brainly.in/question/2593668
The persons income increased from 27,000 to 40,000 over the last year. What is the percent change
Answer:
32.5
Step-by-step explanation: