The equation 7x² - 5x + 7y² + z² = 3 in the cylindrical coordinate system is 7r² - 5r cos θ + z² = 3.
What is the cylindrical coordinate?In the cylindrical coordinate system, cylindrical dimensions are ordered triples that describe the location of a point.
The equation is given below.
7x² - 5x + 7y² + z² = 3
The conversion of the cartesian coordinate to the cylindrical coordinate system.
x = r cosθ
y = r sinθ
z = z
Then put these values in the equation. Then we have
[tex]\begin{aligned} 7(r \cos \theta)^2-5(r \cos \theta) + 7(r \sin \theta)^2 + z^2 &=3\\\\7r^2 \cos ^2\theta-5r \cos \theta + 7r^2 \sin ^2\theta + z^2 &=3\\\\7r^2 (\sin ^2\theta + \cos ^2\theta ) - 5r \cos \theta + z^2 &= 3\\\\7r^2 - 5r \cos \theta + z^2 &= 3 \end{aligned}[/tex]
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A given line has the equation 10x 2y=−2 . what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y=−5x 12 5x y=12 y−12=5(x−0) 5x y=−1
The equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12) is y = -5x + 1
Equation of a lineA line is the distance between two points
Given the equation of a line expressed as 10x + 2y = -2. Determine the slope
2y = -10x -2
y = -5x - 1
Slope of the line is -5
The equation of a line in point-slope form is y - y1 = m(x-x1)
Substitute the point and the slope of the parallel line
y - 12 = -5(x - 0)
y - 12 = -5x
y = -5x + 12
Hence the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12) is y = -5x + 12
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Answer:
its d
Step-by-step explanation:
i got it
An answer and explanation on how to solve this would be most appreciated.
Answer:
cos theta = 5/13
Step-by-step explanation:
sin theta = opp side / hypotenuse
opp side = 12 and hypotenuse = 13
Using the pythgorean theorem
opp ^2 + adj ^2 = hypotenuse ^2
12 ^2 + adj^2 = 13^2
144 + adj ^2 = 169
adj^2 = 169-144
adj^2 = 25
Taking the square root of each side
adj = 5
cos theta = adj / hypotenuse
cos theta = 5/13
Murray tossed a coin 120 times. The coin landed on heads 54 times. Find the theoretical and experimental probability that the next toss will land on heads.
William ran 2 2/3 laps around a track in of an hour. If William keeps the 4/15 same pace, how many laps could he run in 1 hour?
Answer: Trust me if ur using acellus, the answer is 10
Step-by-step explanation: trust me, thank me later
William can run 10 laps in one hour with 4/15 same pace.
We have,
William ran 2 2/3 laps around a track in of an hour.
William keeps the 4/15 same pace.
So, William runs
= 2 2/3 ÷ (4/15)
= (8/3)÷ (4/15)
= 8/3 x 15/4
= 2 x 5
= 10 laps.
Thus, William runs 10 laps.
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Order the following numbers from least to greatest.
Help please
Answer:
[tex]2\frac{1}{3}[/tex], [tex]\sqrt{7}[/tex], [tex]\sqrt[3]{27}[/tex]
Step-by-step explanation:
If you want to make ordering these three numbers to be easier, it's best to find their exact or approximate values. [tex]\sqrt[3]{27}[/tex] is equivalent to 3, and [tex]\sqrt{7}[/tex] is less than [tex]\sqrt{9}[/tex] - which is 3 - so you know that [tex]\sqrt[3]{27}[/tex] is going to be the greatest number out of the set. Since [tex]\sqrt{7}[/tex] is approximately equal to 2.65, and [tex]2\frac{1}{3}[/tex] is approximately equal to 2.33, you can conclude that the correct order from least to greatest is going to be [tex]2\frac{1}{3}[/tex], [tex]\sqrt{7}[/tex], [tex]\sqrt[3]{27}[/tex].
Richard Henry takes out $25,000 of ordinary whole life when he is forty-three years old.
a, annual premium
b. semiannual premium
The ordinary whole life will mature after 57 years. Then the annual premium (AP) and the semiannual premium will be $ 438.60 and $219.30.
What is an ordinary whole life?A whole life insurance policy in which the premiums are paid for the duration of the insured's life. The contract somehow doesn't mature until the designated insured achieves the age of 100 or dies, whatever comes first.
Richard Henry takes out $25,000 of his ordinary whole life when he is forty-three years old.
The ordinary whole life will mature after 57 years.
Then the annual premium (AP) will be
[tex]\rm AP = \dfrac{\$ 2 5000}{57}\\\\AP =\$ 438.60[/tex]
Then the semiannual premium (SAP) will be
[tex]\rm SAP = \dfrac{\$ 2 5000}{57 \times 2}\\\\SAP =\$ 219.30[/tex]
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Question 11 of 11 The 6 students in Mrs. Baker's class were asked how many minutes it takes them to get to school in the morning. Here is what they answered. 4, 9, 12, 14, 7, 7. Find the mean and median travel times for these students. If necessary, round your answers to the nearest tenth.
Answer:
Mean=8.8, Median=8
Step-by-step explanation:
How to find the mean:
First, add all the #'s up. 4+9+12+14+7+7=53
Then divide that by the number or numbers. In this case it is 6.
53/6=8.833... So rounded=8.8
Median:
List numbers lowest to highest
4, 7, 7, 9, 12, 14
Go to the middle number.
Since it is between 7 and 9, it is 7+9=16. 16/2=8
8 is the median
Erica travels 4 blocks right and 4 blocks up between 2 locations on the map. which two locations does she travel between? (4 points)
a coordinate plane with the origin point, where the horizontal and vertical lines meet labeled zero. the horizontal line labeled x has tick marks numbered from one to ten. the vertical line labeled y has tick marks numbered from one to ten. there are six locations plotted on the coordinate plane. the soccer field is at two, two. the ice cream parlor is at one, six. the park is at six, six. the school is at nine, two. the town hall is at four, nine. the ice rink is at nine, ten.
a
town hall and ice rink
b
park and town hall
c
ice cream parlor and town hall
d
soccer field and park
Answer:
the answer is ice cream parlor and town hall
Step-by-step explanation:
because if you for 3 times right and 3 times up from ice cream parlor it will land to town hall
3. Solve the system:
y = x2 - 4x + 6
y = x + 2
EXPLAIN the difference between theoretical and experimental probability. Use an example.
Step-by-step explanation:
Theoretical probability describes how likely an event is to occur. We know that a coin is equally likely to land heads or tails, so the theoretical probability of getting heads is 1/2. Experimental probability describes how frequently an event actually occurred in an experiment.
EXAMPLE-
Theoretical probability:
For instance, since a flipped coin has two sides and each side is equally likely to land up, the theoretical probability of landing heads (or tails) is exactly 1 out of 2.
Experimental probability:-
For example, the probability of getting a head if you flip a coin is ½, since only 2 things could happen (a head or a tail) and each one has an equal chance of occurring.
mark me as brainliest if possible. :)
Determine which quadrant the angle Ф lies and the reference angle.
Then, find the indicated ratio for Ф' (must be an exact value).
Finally, determine the value for the original expression using the quadrants.
csc[tex]\cfrac{4\pi }{3}[/tex]
Answer:
[tex]\csc \left(\dfrac{4\pi}{3}\right)=-\dfrac{2}{\sqrt{3}}[/tex]
Step-by-step explanation:
[tex]\phi=\dfrac{4 \pi}{3}[/tex]
Therefore, this angle lies in quadrant III since it is between π and 3π/2
It's reference angle is:
[tex]\dfrac{4 \pi}{3}-\pi=\dfrac{\pi}{3}[/tex]
and so lies in quadrant I
[tex]\csc (\phi)=\dfrac{1}{\sin(\phi)}[/tex]
For sine, quadrant I and II are positive and quadrant III and IV are negative.
Therefore, as [tex]\sin \dfrac{\pi}{3}=\dfrac{\sqrt{3}}{2}[/tex] then [tex]\sin \dfrac{4\pi}{3}=-\dfrac{\sqrt{3}}{2}[/tex]
Finally,
[tex]\csc \left(\dfrac{4\pi}{3}\right)=\dfrac{1}{\sin\left(\dfrac{4\pi}{3}\right)}[/tex]
[tex]\implies \csc \left(\dfrac{4\pi}{3}\right)=\dfrac{1}{-\dfrac{\sqrt{3}}{2}}[/tex]
[tex]\implies \csc \left(\dfrac{4\pi}{3}\right)=-\dfrac{2}{\sqrt{3}}[/tex]
[tex]\\ \rm\Rrightarrow csc\dfrac{4\pi}{3}[/tex]
[tex]\\ \rm\Rrightarrow csc\left(\pi +\dfrac{\pi}{3}\right)[/tex]
So it lies in Q3 and it's reference angle is π/3Reference angle like usual lies in Q1 .Now for value
[tex]\\ \rm\Rrightarrow csc\left(\pi+\dfrac{\pi}{3}\right)[/tex]
In Q1 All are positiveIn Q2 sine and cosec are positive .In. Q3 tan and cot are positive .In Q4 cos and sec are positive.As it lies in Q3 it's negative
[tex]\\ \rm\Rrightarrow csc\left(-\dfrac{\pi}{3}\right)[/tex]
[tex]\\ \rm\Rrightarrow -csc\dfrac{\pi}{3}[/tex]
[tex]\\ \rm\Rrightarrow -\dfrac{2}{\sqrt{3}}[/tex]
What’s the difference between numbers that are to the power of with parentheses and no parentheses. For example (-2/5)^3 and -2/5^3. Please explain this rule and thank you.
Answer:
See below
Step-by-step explanation:
The first one 'cubes' the denominator AND the numerator:
(-2/5)^3 = -2/5 * -2/5 * -2/5 = -8/125
The second one 'cubes' only the denominator:
-2/5^3 = -2 / (5 * 5 * 5) = - 2 / 125
. a) In a group of 500 students, 280 like bananas, 310 like apples, and 55 do not like both the fruits.
(i) Find the number of students who like both the fruits.
(ii) Find the number of students who like only one fruit.
(iii) Show the result in a Venn-diagram.
Answer:
(i) 145
(ii) 300
Step-by-step explanation:
Given:
total students ... 500
like bananas ... 280
like apples ... 310
dislike fruits ... 55
(i) Find the number of students who like both fruits.
To find the number of students who like both fruits we first add students who like bananas and apples and then subtract students who like at least one fruit.
Students who like at least one of the fruits:
like fruit = total - dislike fruits
like fruit = 500 - 55 = 445
Students who like both fruits:
like both = (like bananas + like apples) - like fruit
like both = (280 + 310) - 445
like both = 145
(ii) Find the number of students who like only one fruit.
To find this we have to find how many students like ONLY bananas and ONLY apples.
like one fruit = like only apples + like only bananas
To find students who like only apples and like only bananas we subtract students who like both (calculated in (i)).
like only apples = like apples - like both = 310 - 145 = 165
like only bananas = like bananas - like both = 280 - 145 = 135
Therefore,
like one fruit = like only apples + like only bananas
like one fruit = 165 + 135
like one fruit = 300
(iii) Show the result in a Venn-diagram.
See attached picture.
A bag contains 10 marbles: 6 are green, 2 are red, and 2 are blue. Melissa chooses a marble at random, and without putting it back, chooses another one at
random. What is the probability that both marbles she chooses are green? Write your answer as a fraction in simplest form.
Answer:
1/3
Step-by-step explanation:
the probability of the first is 6/10 or simplified 3/5
she then repeats its without putting the marble back 5/9 (as she has to remove a green marble)
to find the odds multiply 5/9 and 3/5 you get 15/45 reduced to 1/3, so the probability is 1/3
HEL ASAP
Solve for x.
2(3x + 4) = 7x – 2x + 1
Answer:
x= -7
Step-by-step explanation:
[tex]~~~~~~2(3x+4) = 7x-2x+1\\\\\implies 6x +8 = 5x+1\\\\\implies 6x -5x = 1-8\\\\\implies x = -7[/tex]
please fill in the venn diagram and answer the question below. thanks!!!
Step-by-step explanation:
you understand how a venn diagram works ?
you have to put elements or the amount of elements into the different segments. there are segments that belong to only one category, segments with elements that are shared between 2 neighboring categories, and in this case 1 segment in the middle that has all elements shared between all 3 categories.
so, we know, the total of all elements (fans) is 36.
now imagine we place every fan exactly into the segment, where his or her allegiance lies.
the easiest way to start is with the center. there are 5 fans there, so write 5 in there.
these 5 people are therefore also part of the total number of Wild fans, of the Viking fans and the Twins fans, and of all the shared segments, of course.
so, we have only 7-5 = 2 shared Wild and Vikings only fans (in the segment above the center segment). they are not fans of the Twins.
we have 9-5 = 4 shared Wild and Twins only fans (in the segment left below the center). they are not fans of the Vikings.
we have 11-5 = 6 shared Vikings and Twins only fans (in the segment right below the center). they are not Wild fans.
what is left for the pure, single team fans ?
the Wild have 12-5-2-4 = 1 pure fan.
the Vikings have 16-5-2-6 = 3 pure fans.
the Twins have 22-5-4-6 = 7 pure fans.
so, we have 1+3+7 = 11 pure fans, 2+4+6 = 12 double team fans, and 5 all 3 teams fans. but that is only 28 fans altogether.
so, something is not right with the data here.
I assume we have 28 total from now on.
for Viking AND Wild fans we have the 2 fans that only like these 2 teams plus the 5 that like all 3 teams (including the Vikings and the Wild) = 7 out of the total of 28 fans.
the probability to pick one of them is then
7/28 = 1/4 =0.25
if the total of 36 questioned fans is still there and explained maybe outside of the given venn diagram (e.g. were asked but are fans of a totally different team or of no team at all), then the probability would be
7/36 = 0.194444444...
ABCD is a rhombus. The coordinates of A are (5, 11) The equation of the diagonal DB is y = 3x + 5 The equation of the diagonal AC can be written in the form y = mx + Ċ where m and c are integers. Work out the value of m and the value of c.
Applying the definition of the diagonals of a rhombus, the value of m is -3, and the value of c is 26.
What are the Diagonals of a Rhombus?The diagonals of a rhombus are perpendicular to each other and therefore have slopes that are negative reciprocals.
Equation of diagonal DB is, y = 1/3x + 5.
Slope (m) of DB is 1/3.
Therefore, the slope (m) of diagonal AC would be, -3.
To find the equation of diagonal AC, substitute m = -3 and (5, 11) = (a, b) into y - b = m(x - a)
y - 11 = -3(x - 5)
y - 11 = -3x + 15
y = -3x + 15 + 11
y = -3x + 26
m = -3; c = 26
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5x−2(x+1)=1/4 find x pretty please
Answer:
Delaney solve for X by isolating it, or getting it by it self
Step-by-step explanation:
5x−2(x+1)=1/4 (distribute the 2)
5x-2x - 2 = 1/4 (subtract 2x from 5x)
3x -2 +2 = 1/4 +2 (add 2 to both sides)
3x = 2_1/4 (put 2 & 1/4 together)
3x = 9/4 (convert 2_1/4 to 9/4)
[tex]\frac{1}{3}[/tex]*3*x = [tex]\frac{1}{3}[/tex]*[tex]\frac{9}{4}[/tex] ( mutilply both sides by 1/3)
X = 3/4 (cross multiply )
There you go
X = [tex]\frac{3}{4}[/tex]
Answer:
[tex]\huge\boxed{\bf\:x = \frac{3}{4}}[/tex]
Step-by-step explanation:
[tex]5x - 2(x+1)=\frac{1}{4}[/tex]
Use the distributive property for 2(x + 1).
[tex]5x - 2x - 2= \frac{1}{4}[/tex]
Subtract 2x from 5x.
[tex]3x - 2= \frac{1}{4}[/tex]
Bring 2 to the right hand side of the equation .
[tex]3x = \frac{1}{4} + 2[/tex]
Add 1/4 & 2.
[tex]3x = \frac{1}{4} + \frac{8}{4} \: \: [LCM = 4]\\3x = \frac{9}{4}[/tex]
Now, bring 3 to the right hand side of the equation .
[tex]x = \frac{9}{4} \times \frac{1}{3}\\x = \frac{9}{12}\\\boxed{\bf\:x = \frac{3}{4}}[/tex]
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Classify each number according to its value.
4.2 × 10-6
2.1 × 10-3
3.1 × 10-2
3.2 × 10-5
3.5 × 10-4
5.8 × 10-3
5.2 × 10-4
Answer:See below and attached
Step-by-step explanation:
Given numbers
4.2×10^-6, 2.1×10^-3, 3.1×10^-2, 3.2×10^-5, 3.5×10^-4, 5.8×10^-3, 5.2×10^-4
Greater than 3.1×10^-3
3.1×10^-2, 5.8×10^-3
Between 3.1 × 10^-3 and 4.3 × 10^-5
2.1×10 ^-3, 3.5×10^-4, 5.2×10^-4
Less than 4.3 × 10^-5
4.2×10^-6, 3.2×10^-5
Step-by-step explanation
:
pring 2022
English
Maribel was working at the fruit stand and had to find how much change to give a customer. The customer bought 11
oranges at $0.65 each and paid with a $10 bill. Use c to represent the amount of change and choose the correct
equation
Answer:
c = 10 - 11(0.65)
Step-by-step explanation:
The equation is :
c = 10 - 11(0.65)Change will be :
c = 10 - 7.15c = $2.85Let's find
c=10-11(0.65)c=10-11(65/100)c=10-7.15c=$2.85You want to obtain a sample to estimate a population proportion. at this point in time, you have no reasonable estimate for the population proportion. you would like to be 95% confident that you esimate is within 1% of the true population proportion. how large of sample size is required?
The sample size is, 9604 if you want to obtain a sample to estimate a population proportion at this point in time, you have no reasonable estimate for the population proportion.
What is the margin of error(MOE)?It is defined as an error that gives an idea about the percentage of errors that exist in the real statistical data.
As we know, the sample size can be evaluated using the expression:
[tex]\rm ME = Z_c\sqrt{\dfrac{pq}{n}}[/tex]
or
[tex]\rm n = \dfrac{Z^2}{ME^2}(pq)[/tex]
Here ME = 1% = 0.01
p = 0.5, q = 0.5
Z at α 0.05 (because 95% confident)
= 1.960
[tex]\rm n = \dfrac{1.960^2}{0.01^2}(0.5\times0.5)[/tex]
n = 9604
Thus, the sample size is, 9604 if you want to obtain a sample to estimate a population proportion at this point in time, you have no reasonable estimate for the population proportion.
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Find the Mean given Normal Curve Values
Answer:
mean = 33
Step-by-step explanation:
29 = mean - 2sd => 2sd = mean - 29
37 = mean + 2sd
37 = mean + mean - 29
mean = 66/2 = 33
help please it’s almost due
Answer:
77.4 is the circumference of the circle
Step-by-step explanation:
8.8 squared (8.8 times 8.8) gives you 77.44, but rounded to the nearest tenth, it is 77.4
5/9 x 4
PLS SHOW YOUR WORK IT HELPS ME A LOT!! :) TY
Answer:
20 over 36
You cant put into mixed fraction
Answer: 2 2/9
Step-by-step explanation:
5/9 * 4 = 20/9 = 2 2/9
Find the surface area of the composite figure. 2 cm 7 cm 2 cm 12 cm 12 cm 7 cm 7 cm
Step-by-step explanation:
12x7 + 2x7 = 84 + 14 = 98
sa=98
For the image, its surface area is mathematically given as
x= 98cm^2
What is surface area?The surface area of a three-dimensional object is the amount of space that covers the exterior of the object.
In conclusion, calculating the individual surfaces we have
x=12x7 + 2x7 = 84 + 14
x= 98cm^2
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What is 18 divided by 14?
I want it to be solved by hand - not Calculator.
If Correct I'll give Brainiest.
Answer:
1.28571
Step-by-step explanation:
is the answer
A marble is randomly selected from a bag containing 3 red marbles, 3 blue marbles, and 3 green marbles. What is the probability that the selected marble is green?
Answer:
1/3 of a chance
Step-by-step explanation:
3 red, 3 blue, 3 green
that all adds to 9 marbles and there are 3 out of 9 marbles that are green.
the probability is 3/9 or 1/3
Can someone help with this??
Answer:
2x+1
Step-by-step explanation:
The fuction of g(x) is 2x
And the function of f(x) is x+1
So we plug in g(x) in f(x)
2x would be plugged in x in x+1 then we add the 1
(2x)+1
In the same area where there are 3 Mankey Pokemon, 4 Pidgey Pokemon, and 2 Rattata Pokemon. What would be the probability of running into a Mankey Pokemon and then a Pidgey Pokemon (each time you defeat one it is replaced on the map)?
The probability of you running into a Mankey Pokemon and then a Pidgey Pokemonis 4/27.
Answer:
there is a 3 in 9 percent chance you can find a manky
Step-by-step explanation:
i say pidgey is better pedgiot is cool and very usefull and pidgey can help you in the vridian foreast becasue of all the bug types
Please help with this math problem pretty simple I think
[tex]\huge{\color{red}{\fbox{\textsf{\textbf{Answer}}}}} [/tex]
-1
Step-by-step explanation:
[tex] \sf \sqrt{7 - 3z} = 3 + cz \\ \\ \sf z = 2 [/tex]
We will just substitute the value of z in the equation
[tex] \sf \implies \sqrt{7 - 3(2)} = 3 + c(2) \\ \\ \sf \implies \sqrt{7 - 6} = 3 + 2c \\ \\ \sf \implies \sqrt{1} = 3 + 2c \\ \\ \sf \implies 1 = 3 + 2c \\ \\ \sf \implies 1 - 3 = 2c \\ \\ \sf \implies - 2 = 2c \\ \\ \sf \implies \frac{ - 2}{2} = c \\ \\ \sf \implies \large \red{ \mathfrak{ - 1 = c}}[/tex]