9514 1404 393
Answer:
π/4, 7π/4
Step-by-step explanation:
Adding √2 and dividing by 2 makes the equation ...
cos(θ) = (√2)/2
The first-quadrant solution is ...
θ = arccos((√2)/2) = π/4
The angle in the 4th quadrant with the same reference angle will have the same cosine value.
θ = 2π -π/4 = 7π/4
The two solutions are θ = π/4, 7π/4.
A bag contains colored tiles.
• 3 tiles are red
• 6 tiles are green
• 3 tiles are blue
A tile will be randomly selected from the bag. What is the probability in decimal form that the tile selected will be green?
Answer:
0.5
Step-by-step explanation:
add up the amount of tiles
6+3+3=12
then subtract the green tiles from the total amount
12-6=6
then divide 12/6
=0.5
Answer:
0.5
Step-by-step explanation:
The average value of a function f(x, y, z) over a solid region E is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the volume of E. For instance, if ???? is a density function, then ????ave is the average density of E. Find the average value of the function f(x, y, z) = 3x2z + 3y2z over the region enclosed by the paraboloid z = 4 − x2 − y2 and the plane z = 0.
Answer:
The average function [tex]f_{avg}[/tex] value = 4
Step-by-step explanation:
Given that:
[tex]f(x,y,z) = 3x^2z+3y^2z[/tex]
The enclosed region [tex]z = 4 -x^2 -y^2[/tex] and the plane z = 0.
Over an area E, the average value of a function f(x,y,z) is:
[tex]f_{avg} = \dfrac{1}{V_{E}} \iiint_E f(x,y,z) dV ------ (1)[/tex]
where;
[tex]V_E[/tex] = volume of region E
To find the volume use cylindrical coordinates;
[tex]x=rcos \theta; \ \ \ y = rsin \theta; \ \ \ z = z[/tex]
Then;
E = 0 ≤ r ≤2, 0 ≤ θ ≤ 2π, 0 ≤ z ≤ 4 - r²
[tex]V_E = \int^{2 \pi}_{0} \int^{2}_{0} \int^{4-r^2}_{0} \ rdzdrd \theta[/tex]
[tex]V_E = \int^{2 \pi}_{0} \int^{2}_{0} r(4-r^2) \ drd \theta[/tex]
[tex]V_E = \int^{2 \pi}_{0} \int^{2}_{0} (4r-r^3) \ drd \theta[/tex]
[tex]V_E = \int^{2 \pi}_{0} \Big(2r^2- \dfrac{r^4}{4} \Big)^2_0 \ d \theta[/tex]
[tex]V_E = 4(2 \pi)\\\\ V_E = 8 \pi[/tex]
However, from equation (1):
[tex]f_{avg} = \dfrac{1}{V_E} \iiint_E f(x,y,z) \ dV \\ \\ = \dfrac{1}{8 \pi} \iiint_E (3x^2z + 3y^2 z) dV \\ \\ = \dfrac{1}{8 \pi } \int^{2 \pi}_{0} \int^{2 }_{0} \int^{4 - r^2}_{0} \ \ 3zr^2 \ rdzdrd\theta \\ \\ = \dfrac{3}{8 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} \Big(\dfrac{z^2}{2}\Big)^{4-r^2}_{0} \ r^3 drd\theta \\ \\ = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (4-r^2)^2 \ r^3 \ dr d\theta[/tex]
[tex]= \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (16-8r^2 + r^4)r^3 \ dr d\theta \\ \\ = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (16r^3 -8r^5 + r^7) \ dr d \theta \\ \\ = = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \Big (4r^4 - \dfrac{8}{6}r^6 + \dfrac{r^8}{8} \Big)^2_0 \ d \theta \\ \\ = \dfrac{3}{16 \pi } (2 \pi) \Big (64 - \dfrac{8}{6} \times 64 \times \dfrac{256}{8} \Big) \\ \\ = \dfrac{3}{16 \pi} (2 \pi) (\dfrac{32}{3}) \\ \\ = 4[/tex]
Jim has 28 mangoes he gave Tom 8 how many does Jim has
Answer: 20 mangoes.
Step-by-step explanation: This is a simple subtraction problem. If you take away 8 from 28, you'll have 20.
28 - 8 = 20
How many positive integer values of x are solutions to the inequality 10 < -x + 13?
9514 1404 393
Answer:
2
Step-by-step explanation:
The solution to the inequality is ...
10 < -x +13
x < 3 . . . . . . . add x-10 to both sides
The additional restriction that x is positive makes this ...
0 < x < 3
The only integer solutions to this are x = 1 and x = 2.
There are two (2) positive integer values of x that are solutions.
Answer:
2
Step-by-step explanation:
We first solve the inequality:
10 < -x + 13
-3 < -x
3 > x.
The only positive integers less than 3 are 1 and 2, for a total of 2 solutions.
NEED HELP ASAP FREE BRAINLIST
Answer:
the correct answer is 904.78 cubic. inches
Hey I need help .. again we’re doing log lines
Answer:
Step-by-step explanation:
One side of a rectangle is parallel to the x-axis. One vertex of the rectangle is located at (5,2) and another vertex at (1,4). What are the coordinates of the other two vertices?
Answer:
(1,2) and (5,4)
Step-by-step explanation:
Hello There!
I had made a graph to make it easier to understand.
The points given to us are represented by the green points
The points that would make a rectangle with lines that are parallel with the x axis would be (1,2) and (5,4) (represented by the red points)
As you can see the points added had created a rectangle with sides that are parallel with the x axis
This meets all of the requirements therefore the other two vertices would have the points (1,2) and (5,4)
A gym knows that each member, on average, spends 70 minutes at the gym per week, with a standard deviation of 20 minutes. Assume the amount of time each customer spends at the gym is normally distributed. Suppose the gym surveys a random sample of 49 members about the amount of time they spend at the gym each week. What are the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym
Answer:
the expected value and the standard deviation of the sample mean is 70 and 2.86 respectively
Step-by-step explanation:
The computation of the expected value and the standard deviation of the sample mean is shown below:
The mean is 70
And, the standard deviation is
= 20 ÷ √49
= 20 ÷ 7
= 2.86
Hence, the expected value and the standard deviation of the sample mean is 70 and 2.86 respectively
Susie says that it she has a quick way to determine the least common multiple of two numbers; you just multiply the numbers. Susie checked it with 3 and 5 and with 4 and 7 and method worked both times. Is Susie’s method a valid way to determine the least common multiple of two counting numbers? Explain.
Answer:
No, it is not a valid way
Step-by-step explanation:
Required
Is Susie's method valid?
Susie's method worked because 4 & 7 and 3 & 5 do not have a common factor.
In other words, Susie's method will not work when the two numbers have a common factor.
Take for instance, the LCM of 2 and 4.
Using Susie's method, the LCM will be 8 (i.e. 2 * 4) whereas the LCM is 4.
A car salesperson sells cars at prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years.
The median car price is
. The distribution exhibits
.
Answer:
B. $25000
C. Symmetry
Step-by-step explanation:
Hope this helps
PLZ HELP I WILL MAKE YOU BRAINLIEST NO FAKE LINKS
Answer:
1/30 of an hour
Step-by-step explanation:
You earn $18 for watching three cars how much do you earn to Washing 2 cars
Answer:
$12
Step-by-step explanation:
3 cars divide that by $18 and u get $6 per car. multiply that by two cars nd you get $12.
HELP ASAP!!!!!. A spinner has three sections colored green, purple, and pink. If the spinner is spun twice, how many branches would the tree diagram that represents this situation have? 6 5 9 12
Answer:
9
Step-by-step explanation:
you would do 3+3+3 because there are 3 colors
And i just got it right on my quiz.
There will be 9 branches in the tree diagram of the situation.
What is tree diagram?In probability theory, tree diagrams can be used to represent probability spaces. A tree diagram can represent a set of independent events or conditional probabilities. Each node in the graph represents an event and is associated with the probability of that event.
Given,
A spinner of three sections colored green, purple and pink.
Number of outcomes = 3
spinner is spun twice,
then number of outcomes = 3 × 3 = 9
Number of branches in tree = 9
Hence, 9 branches will be there in probability tree diagram.
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(i will mark brainly)
Use the table to write a proportion.
Answer:
One proportion is 15 songs / 2.5 hours = 18 songs / h hours.
ok I'll try to answer
first the given 15/2.5=18/h
so the second hour is missing so we have to multiply cross then the result will be
15h=45
divide 15 for 15 and we got h
again divide 45 for 15
[h=3]
a reflection across y=2
HELP DUE VERY SOON
Answer:
n' = (-5,2) k' = (-1,1) t' = (-5,0)
Step-by-step explanation:
Subtract y from 5....
Answer:
5y-y= 5? I don’t know I’m not totally sure.
Step-by-step explanation:
HELP!!! Quick and easy!
Answer:
2r + 6 = 16
r = 5
P=(L+B), then B=_____?
Answer:
P = L+B
B = P-LHope it helps
Quadrilateral WXYZ has a length of five, six, seven, and eight. A new quadrilateral is created, using a scale factor of 1.2. Which of the following are stylings of the new quadrilateral?
Choose all that apply:
10
8.4
9.6
6
7.2
5
PLEASE HELP I Got 5 minutes
Answer:
10
8.4
5
Step-by-step explanation:
convert 6% to an equivalent decimal
Answer:
0.06
Step-by-step explanation:
How is this happening i was only gone for 2 weeks
Answer:
step it up dont lack
Step-by-step explanation:
keep answering and helping others
Plsssssss help and no one send me a file just tell me the answer
Either F or J
I think it's J, but it might be F :|
Graph the line.
Y= 4/3 x
Answer:
hope this helps :)
Step-by-step explanation:
student were asked to choose their favorite food and 5/6 chose either pizza or tacos if 2/6 of the students chose pizza what fraction chose tacos
Answer:
3/6 or 1/2
Step-by-step explanation:
the amount that chose pizza = 2/6
5/6 = the amount that chose pizza + the amount that chose tacos
5/6 = 2/6 + the amount that chose tacos
the amount that chose tacos = 5/6 - 2/6
the amount that chose tacos = (5-2)/6
the amount that chose tacos=3/6=1/2
Answer:
3/6
Step-by-step explanation:
In the figure, two poles are 25 m and 35 m high. A cable 23 m long Joins the tops of the poles. Find the distance between the poles.
Answer: 20.71 m
Step-by-step explanation:
Given
the length of the poles are 25m and 35 m
The length of the cable is 23 m
Suppose the distance between them is x
From the figure, apply Pythagoras theorem
[tex]\Rightarrow 23^=x^2+10^2\\\Rightarrow 529-100=x^2\\\Rightarrow x^2=429\\\\\Rightarrow x=\sqrt{429}=20.71\ m[/tex]
Distance between Poles is 20.71 m
An equation of the perpendicular bisector of the line segment with end points (3,0) and (-3,0) is
A) x = -3/2
B) x = 0
C) x = 3/2
D) X = 3
E) X = 6
Help please with steps
Answer:
[tex]x = 0[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (3,0)[/tex]
[tex](x_2,y_2) = (-3,0)[/tex]
Required
The equation of the perpendicular bisector.
First, calculate the midpoint of the given endpoints
[tex](x,y) = 0.5(x_1 + x_2, y_1 + y_2)[/tex]
[tex](x,y) = 0.5(3-3, 0+ 0)[/tex]
[tex](x,y) = 0.5(0, 0)[/tex]
Open bracket
[tex](x,y) = (0.5*0, 0.5*0)[/tex]
[tex](x,y) = (0, 0)[/tex]
Next, determine the slope of the given endpoints.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{0 - 0}{-3- 3}[/tex]
[tex]m = \frac{0}{-6}[/tex]
[tex]m = 0[/tex]
Next, calculate the slope of the perpendicular bisector.
When two lines are perpendicular, the relationship between them is:
[tex]m_2 = -\frac{1}{m_1}[/tex]
In this case:
[tex]m = m_1 = 0[/tex]
So:
[tex]m_2 = -\frac{1}{0}[/tex]
[tex]m_2 = unde\ fined[/tex]
Since the slope is [tex]unde\ fined[/tex], the equation is:
[tex]x = a[/tex]
Where:
[tex](x,y) = (a,b)[/tex]
Recall that:
[tex](x,y) = (0, 0)[/tex]
So:
[tex]a = 0[/tex]
Hence, the equation is:
[tex]x = 0[/tex]
choose the equation that best describes the following graph.
please answer ASAP.
a) y=-3/2x+5
b) y=-2/3x+5
c) y=-3/2x+3 1/2
d) y=-2/3x+3 1/2
Answer:
d) y= -2/3x+3 1/2
Step-by-step explanation:
Points on the graph: ( -4, 6) and ( -7, 8)
Slope:
m=(y2-y1)/(x2-x1)
m=(8-6)/(-7+4)
m= 2/(-3)
m= -2/3
Slope-intercept:
y - y1 = m(x - x1)
y - 6 = -2/3(x + 4)
y - 6 = -2/3x - 8/3
y = -2/3x + 3 1/2
●10 Kate is reading a 500-page book. The graph below represents the relationship between the
number of hours Kate has spent reading and the number of pages she has read.
Kate’s
rate
0 1
50
2
100
3
150
200
4 5
250
6
300
350
400
450
x
y
Reading Rate
Number of Pa
ges Read
Time (in hours)
(5, 200)
On the grid in your Student Answer Booklet, copy the x-axis, the y-axis, and the line
representing Kate’s reading rate exactly as shown. Be sure to label the line “Kate’s rate.”
"200" (and any subsequent words) was ignored because we limit queries to 32 words
Kate is reading 40 pages per hour.
The whole book takes 12.5 hour to complete.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
From the data we have (5, 200) and (5,0)
then slope= (200-0) / 5
= 40
So, Kate is reading 40 pages per hour.
Now, to read the whole book i.e., 500 pages it takes
= 500/40
= 12.5 hours
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58% of a $148 selling price goes toward paying expenses. How many dollars of the selling price is profit?
Answer:
62.16
Step-by-step explanation:
Solve for the area of the triangle in each of the following problems.
Answer:
area of triangle = 1/2×base×height
area of triangle =1/2×15m×16m
area of triangle =120m²