Answer:
B. r = 4cosθStep-by-step explanation:
Given the expression in rectangular coordinate as x²+y²−4x=0, in order to write the given expression in polar coordinates, we need to write the value of x and y as a function of (r, θ).
x = rcosθ and y = rsinθ.
Substituting the value of x and y in their polar form into the given expression we have;
x²+y²−4x=0
( rcosθ)²+( rsinθ)²-4( rcosθ) = 0
Expand the expressions in parenthesis
r²cos²θ+r²sin²θ-4rcosθ = 0
r²(cos²θ+sin²θ)-4rcosθ = 0
From trigonometry identity, cos²θ+sin²θ =1
The resulting equation becomes;
r²(1)-4rcosθ = 0
r²-4rcosθ = 0
Add 4rcosθ to both sides of the equation
r²-4rcosθ+4rcosθ = 0+4rcosθ
r² = 4rcosθ
Dividing both sides by r
r²/r = 4rcosθ/r
r = 4cosθ
Hence the correct equation in polar coordinates is r = 4cosθ
A house m by m is surrounded by a walkway m wide. 27 9 1.8 a) Find the area of the region covered by the house and the walkway. b) Find the area of the walkway.
Answer:
A. 385.56 square meters.
B. 142.56 square meters.
Step-by-step explanation:
A house 27m by 9m is surrounded by a walkway 1.8m wide.
a) Find the area of the region covered by the house and the walkway.
b) Find the area of the walkway.
Let
Length of the house=l=27m
Width of the house=w=9m
Wideness of the walkway=x=1.8m
Area of the region covered by the house and the walkway
=( L + 2*x) * (w + 2*x)
= (27+2*1.8)*(9+2*1.8)
=(27+3.6)*(9+3.6)
=(30.6)*(12.6)
=385.56 square meters.
b) Area of the walkway
= (L + 2*x)*(w + 2*x) - l*w
= (27+2*1.8)*(9+2*1.8) - 27*9
=(27+3.6)*(9+3.6) - 243
=(30.6)*(12.6) - 243
=385.56 - 243
=142.56 square meters.
5/3 x 6/7 real quick plz
Answer:
10/7 or 1 3/7. I hope this helps,
Step-by-step explanation:
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Theresa bought 2 pineapples for $6. She wants to find the constant of proportionality in terms of dollars per pineapple. She modeled this proportional relationship on a number line diagram, as shown.
Part B
How much would 4 pineapples cost?
The yellow bar is the total cost of 2 pineapples. The black line in the middle of the yellow splits it equally in half and is located at the 3.
The constant bod proportionality would be 3, which means each pineapple cost $3
Answer:
first of all, brainly better not delete my answer again. (the answer is 3)
Step-by-step explanation:
you have to multiply to find the number of pineapples. but unlike me i did skip count and write down my number's and I tried to find "what number skips until it ends to 6?'' i found 3 as my answer! 3,6,9,12,15,18,21 etc..
According to the Census Bureau, 3.34 people reside in the typical American household. A sample of 26 households in Arizona retirement communities showed the mean number of residents per household was 2.70 residents. The standard deviation of this sample was 1.17 residents. At the .10 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.34 persons?
(a) State the null hypothesis and the alternate hypothesis. (Round your answer to 2 decimal places.)
H0: ? ?
H1: ? <
(b)
State the decision rule for .10 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Reject H0 if t <
(c)
Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Value of the test statistic
(d)
Is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.34 persons?
H0. Mean number of residents less than 3.34 persons.
Answer:
Step-by-step explanation:
Given that:
Mean = 3.34
sample size = 26
sample mean = 2.7
standard deviation = 1.17
level of significance = 0.10
The null hypothesis and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o: \mu \geq 3.34} \\ \\ \mathtt{H_1: \mu < 3.34}[/tex]
degree of freedom = n - 1
degree of freedom = 26 -1
degree of freedom = 25
level of significance = 0.10
Since the alternative hypothesis contains <, then the test is left tailed
[tex]\mathtt{t_{\alpha, df} = t_{0.10, 25}}[/tex]
[tex]\mathtt{t_{0.10, 25}}[/tex] = - 1.316
The rejection region therefore consist of all values smaller than - 1.316, therefore ; reject [tex]H_o[/tex] if t < -1.316
The test statistics can be computed as follows:
[tex]t = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \dfrac{2.7 - 3.34}{\dfrac{1.17}{\sqrt{26}}}[/tex]
[tex]t = \dfrac{-0.64}{\dfrac{1.17}{5.099}}[/tex]
t = - 2.789
Decision Rule: To reject the null hypothesis if the t test lies in the rejection region or less than the rejection region.
Conclusion: We reject the null hypothesis since t = (- 2.789) < -1.316. Then we conclude that the mean number of residents in the retirement community household is less than 3.34 persons.
How many solutions does the system have? x+2y=2 2x+4y=−8
Answer:
Step-by-step explanation:
x + 2y = 2
2x + 4y = -8
-2x - 4y = -4
2x + 4y = -8
0 not equal to -12
no solution
What do we use mathematical induction for?
proving statements!
it's the very definition of it
HELP ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Option (B)
Step-by-step explanation:
The given expression is,
[tex]\sqrt{22x^6}\div\sqrt{11x^4}[/tex]
We can rewrite this expression as,
[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }[/tex]
Solving it further,
[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }=\frac{\sqrt{22(x^3)^2} }{\sqrt{11(x^2)^2} }[/tex] [Since [tex]x^3\times x^3=x^6[/tex] and [tex]x^{2}\times x^{2}=x^4[/tex]]
[tex]=\sqrt{\frac{22(x^3)^2}{11(x^2)^2} }[/tex] [Since [tex]\frac{\sqrt{a} }{\sqrt{b} }=\sqrt{\frac{a}{b} }[/tex]]
[tex]=\frac{x^3}{x^2}\sqrt{\frac{22}{11} }[/tex]
[tex]=x\sqrt{2}[/tex]
Therefore, quotient will be x√2.
Option (B) will be the correct option.
Time spent using e-mail per session is normally distributed with a mean = to 8 minutes and standard deviation = 2minutes. If a random samples of 36 sessions were selected, the computed sample standard deviation would be
a. 0.25
b. 0.3333
c. 0.42
d. 0.48
Answer:
The correct option is (b) 0.3333.
Step-by-step explanation:
The standard deviation of the sampling distribution of sample mean [tex](\bar x)[/tex] is known as the standard error [tex](\sigma_{\bar x})[/tex].
The standard error is given as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=8\\\\\sigma=2\\\\n=36[/tex]
Compute the standard deviation of the sample mean as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=\frac{2}{\sqrt{36}}\\\\=\frac{2}{6}\\\\=\frac{1}{3}\\\\=0.3333[/tex]
Thus, the standard deviation of the sample mean is 0.3333.
For the given data value, find the standard score and the percentile. A data value 0.6 standard deviations above the mean.
Answer:
The z-score is [tex]z = 0.6[/tex]
The percentile is [tex]p(Z < 0.6) = 72.57\%[/tex]
Step-by-step explanation:
From the question we are told that
The data value is 0.6 standard deviations above the mean i.e [tex]x = \mu + 0.6 \sigma[/tex]
Where [tex]\mu[/tex] is the population mean and [tex]\sigma[/tex] is the standard deviation
Generally the z-score is mathematically represented as
[tex]z = \frac{x - \mu }{\sigma }[/tex]
=> [tex]z = \frac{(\mu + 0.6\sigma ) - \mu }{\sigma }[/tex]
=> [tex]z = 0.6[/tex]
The percentile is obtained from the z-table and the value is
[tex]p(Z < 0.6) = 0.7257[/tex]
=> [tex]p(Z < 0.6) = 72.57\%[/tex]
Write the perimeter of the triangle as a
simplified expression.
3y + 5
бу
Y-4
Answer:
10y+1
Step-by-step explanation:
The perimeter is the three sides added together
3y+5+6y+y-4=
10y+1
Answer:
[tex]\huge\boxed{P_\triangle=10y+1}[/tex]
Step-by-step explanation:
The formula of a perimeter of a triangle:
[tex]P_\triangle=a+b+c[/tex]
We have:
[tex]a=3y+5,\ b=6y,\ c=y-4[/tex]
Substitute:
[tex]P_\triangle=(3y+5)+(6y)+(y-4)=3y+5+6y+y-4[/tex]
Combine like terms:
[tex]P_\triangle=(3y+6y+y)+(5-4)=10y+1[/tex]
A. f(x) = -x^2 - x - 4
B. f(x) = -x^2 + 4
C. f(x) = x^2 + 3x + 4
D. f(x) = x^2 + 4
Answer:
B: -x^2 + 4
Step-by-step explanation:
If the equation was [tex]f(x)=x^2[/tex], then the vertex would be at 0, and the "U" would be facing straight up. Here, the "U" is upside down, so that means the "x^2" would have to be a negative number ([tex]-x^2[/tex]) to get the upside-down "U". Then, we could see that the vertex is at positive 4, so that means that the parabola moved up 4 units, so the equation should end in +4.
Our answer is:
B: -x^2 + 4
=
Graphing an integer function and finding its range for a given...
The function h is defined as follows for the domain given.
h(x) = 2 -2x, domain = {-3, -2, 1, 5}
Write the range of h using set notation. Then graph h.
Answer:
Step-by-step explanation:
● h(x) = 2-2x
The domain is {-3,-2,1,5}
● h(-3) = 2-2×(-3) = 2+6 = 8
● h(-2) = 2 -2×(-2) = 2+4 = 6
● h(1) = 2-2×1 = 2-2 = 0
● h(5) = 2-2×5 = 2-10 = -8
The range is {-8,0,6,8}
state if the triangles in each pair are similar. If so State how you know they are similar and complete the similarity statement
Answer:
fourth option
Step-by-step explanation:
∠ FTC = ∠ MTL ( vertical angles )
Since FC and ML are parallel, then
∠ FCT = ∠ TML (corresponding angles )
Thus
Δ TCF ~ Δ TML by the AA postulate
Answer:
[tex]\large \boxed{\mathrm{similar, \ AA \ similarity}, \ \Delta TML}[/tex]
Step-by-step explanation:
The two triangles are similar.
We can prove by angle-angle similarity, in [tex]\mathrm{AA}[/tex] similarity, there are two pairs of congruent corresponding angles in two triangles, this proves the two triangles are similar.
[tex]\angle U[/tex] and [tex]\angle M[/tex] are a pair of congruent corresponding angles.
[tex]\angle V[/tex] and [tex]\angle L[/tex] are a pair of congruent corresponding angles.
Therefore,
[tex]\Delta TUV \sim \Delta TML[/tex]
a wolf population of 850 wolves is increasing by 7% each year. Find the wolf population after 7 years
Answer:
1,267 wolvesStep-by-step explanation:
Initial population of wolf = 850 wolves
If the wolves increases by 7% each year, yearly increment will be 7% of 850
= 7/100 * 850
= 7*8.5
= 59.5 wolves.
This shows that the wolves increases by 59.5 each year.
After 7 years, increment will be equivalent to 59.5 * 7 = 416.5
The wolf population after 7 years = Initial population + Increment after 7 years
= 850 + 416.5
= 1266.5
≈ 1267 wolves
Hence the population of the wolves after 7 years is approximately 1,267 wolves
Identify the slope and y-intercept of the function y = –2x+1.
Answer:
Below
Step-by-step explanation:
The function is y= -2x +1
● the slope is -2
● the y-intercept is 1
Mario invested $5100 at 13%
to be compounded daily. What will be the value of Mario's investment in 2 years? Round your answer to the nearest cent, if necessary. Note: 365 days in a year and 30 days in a month.
Answer:
Amount = $6614 and 19 cent
Step-by-step explanation:
Formula for compound interest is
A= p(1+r/n)^(nt)
Compounded daily
So n= 365*2= 730
T= 2
r= 0.13
P= 5100
A= p(1+r/n)^(nt)
A= 5100(1+0.13/730)^(730*2)
A= 5100(1+1.78082*10^-4)^(1460)
A= 5100(1.000178082)^1460
A= 5100(1.2969)
A= 6614.19
Amount = $6614 and 19 cent
The scale on a scale drawing is 1 : 30. What should you do with each measurement on the drawing to get the actual dimensions? Provide an example of a drawing that uses this scale. Include both the original and new dimensions.
Answer:
see below
Step-by-step explanation:
For the first question, you should multiply the scale dimension by 30 to get the actual dimension. This is because the scale is 1:30 where the scale dimension is the 1 and the actual dimension is 30, so therefore, the scale dimension is 1/30th of the actual dimension, so to get the actual dimension, we can multiply the scale dimension by 30. I'm not totally sure how to attach pictures from my phone on my computer (sorry) but an example of a drawing could be two rectangles, the first (this is the scale drawing) having dimensions of 1 by 2 units and the second (this is the actual drawing) having dimensions of 30 by 60 units. I hope this helps!
What is the domain of the set of ordered pairs?
(8, -13); ( 0,-5); (4, -9); (-3,2)
The domain is the input values, which are the x values.
The x values in the given pairs are: 8, 0,4,-3
The domain set is (-3, 0, 4, 8)
The required domain of the set of ordered pairs is [8, 0, 4, -3]
Given that,
Set of ordered pair; (8, -13); ( 0,-5); (4, -9); (-3,2).
We have to determine,
The domain of the set of ordered pair.
According to the question,
The domain refers to the set of possible input values.
The domain of a graph consists of all the input values shown on the x-axis.
A relation is a set of ordered pairs.
The domain is the set of all the first components of the ordered pairs.
Then,
Set of ordered pair; (8, -13); ( 0,-5); (4, -9); (-3,2).
Here, Set of all the input values on the x-axis.
Therefore,
The set of values of x is { 8,0,4,-3 }
Hence, The required domain of the set of ordered pairs is [8, 0, 4, -3]
To know more about Domain click the link given below.
https://brainly.com/question/19704059
Graph the function f(x) = 18(0.8)
[tex]f(x)=18(0.8)=14.4[/tex]
is a constant function, so it will be a straight line parallel to x axis and passing through y axis at $14.4$
Michael records the height of 1000 people. This data is a normal distribution and the sample mean was 0.75. Identify the margin of error for this data set.
Answer:
0.0284Step-by-step explanation:
The formula for calculating the Margin of error of a dataset is expressed as;
Margin of error = [tex]Z*\sqrt{\frac{p(1-p)}{n} } \\\\[/tex] where;
Z is the z-score of 95% confidence interval = 1.96
p is the sample proportion/mean = 0.75
n is the sample size = total number of people = 1000
Note that when the confidence interval is not given, it is always safe to use 95% confidence.
Substituting this values into the formula we have;
[tex]ME = 1.96*\sqrt{\frac{0.7(1-0.7)}{1000} } \\\\ME = 1.96*\sqrt{\frac{0.7(0.3)}{1000} } \\\\ME = 1.96*\sqrt{0.00021} } \\\\ME = 1.96*0.01449\\\\ME = 0.0284[/tex]
Hence the margin error for the dataset is 0.0284
please help me out! <3
Answer:
[tex]-1 \frac{3}{4}[/tex]
Step-by-step explanation:
Using this number line, we can plot our original number - [tex]\frac{3}{4}[/tex] (see picture attached)
Adding a negative is the same thing as subtracting - so we are subtracting [tex]2\frac{1}{2}[/tex] from [tex]\frac{3}{4}[/tex].
To subtract this, we can break up [tex]2\frac{1}{2}[/tex] into 3 parts: 1, 1, and [tex]\frac{1}{2}[/tex]. We can subtract each of these from the current number and see where we land up. (again see picture)
We land up at [tex]-1 \frac{3}{4}[/tex].
Hope this helped!
PLZ HLEP QUICK!!! Which of the following is an arithmetic sequence? -2, 4, -6, 8, ... -8, -6, -4, -2, ... 2, 4, 8, 16, ...
Answer:
-8, -6, -4, -2, ...
Step-by-step explanation:
-8, -6, -4, -2, ... is an arithmetic sequence: each new term is obtained by adding 2 to the previous term.
Answer:
-8, -6, -4, -2
Step-by-step explanation:
"An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence."
Complete the table for the given rule. Rule: y = x + 3. X ? Y 4. X ? Y 8. X ? Y 5
Answer:
X 1 for Y 4
X 5 for Y 8
X 2 for Y 5
Step-by-step explanation:
We can substitute the values of Y in the formula and then subtract three from both sides.
help help help help help help
Answer:
75 yards long and 90 yards wide.
Step-by-step explanation:
Let's first find the perimeter of the main rectangle:
100x2 + 65x2 =
330
_________________________________________
Next we need to find two numbers that match:
75 and 90
75x2 + 90x2 =
330
_________________________________________
75x90 is 6750 (More Area)
100x60 is 6500 (Less Area)
29. Identify the end behavior of the function f(x) = 3x^4 + x^3 − 7x^2 + 12.
options:
A. As x → –∞, y → +∞, and as x → +∞, y → –∞
B. As x → –∞, y → –∞, and as x → +∞, y → –∞
C. As x → –∞, y → +∞, and as x → +∞, y → +∞
D. As x → –∞, y → –∞, and as x → +∞, y → +∞
Answer:
C. As x → –∞, y → +∞, and as x → +∞, y → +∞
Step-by-step explanation:
The leading coefficient of this even-degree function is positive, so y goes to +∞ when the magnitude of x gets large.
_____
When the function is even degree, its value for large magnitude x heads toward the infinity with the same sign as the leading coefficient.
When the function is odd degree, its value for large magnitude x will head toward the infinity with the sign that matches the product of the sign of x and the sign of the leading coefficient.
A 160-lb man carries a 5-lb can of paint up a helical staircase that encircles a silo with radius 20 ft. If the silo is 90 ft high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top
Weight of man and paint = 160 + 5 = 165 total pounds.
Gravitational force is independent of the path taken so we can ignore the radius of the silo.
Work done = total weight x height
The problem says he climbs to the top so overall height is 90 feet
Work = 165 lbs x 90 ft = 14,850 ft-lbs
Diane has a rectangular poster that is 20 centimeters long and 15 centimeters wide. What is the area of the poster in square meters? Do not round your answer. Be sure to include the correct unit in your answer.
Answer:
0.03 square meters
Step-by-step explanation:
1. convert 20 cm, 15 cm into m by dividing the number by 100 then you got 0.2 m and 0.15 m respectively
2. calculate the area by multiply 2 numbers together
0.2 × 0.15 = 0.03 square meter
Please help with this
The shape has 11 sides.
Using the angle formula for polygons:
The sum of all the interior angles is:
11-2 x 180 = 9 x 180 = 1,620 degrees.
For one angle divide the total by number of sides:
1620 / 11 = 147.27 which rounds to 147.2
The answer is D.
two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 109 feet, and ball 2 is dropped from a height of 260 feet. Use the function f(t) -16t^2+h to determine the current height, f(t), of a ball from a height h, over given time t.
When does ball 1 reach the ground? Round to the nearest hundredth
Answer: 5.22 seconds
Step-by-step explanation:
t represents time and y represents the height.
Since we want to know when the ball hits the ground, find t when y = 0
Ball 1 starts at a height of 109 --> h = 109
0 = -16t² + 109
16t² = 109
[tex]t^2=\dfrac{109}{16}\\[/tex]
[tex]t=\sqrt{\dfrac{109}{16}}[/tex]
[tex]t=\dfrac{\sqrt{109}}{2}[/tex]
t = 5.22
=> H = 109
=> 0 = -16t² + 109
=> 16t² = 109
=> t² = 109/16
=> t = 109/2
=> t = 5.22 sec
Therefore, 5.22 second is the answer.
