Answer:
[tex]x^2+y^2=36100000[/tex]
Step-by-step explanation:
Here it is mentioned that the there are two concentric circles this means that they have the same center.
The center of the circles are the origin [tex](0,0)[/tex].
Radius of the outer circle is
[tex]r=\dfrac{3800}{2}=1900\ \text{m}[/tex]
Equation of a circle
[tex](x-a)^2+(y-a)^2=r^2[/tex]
where
[tex]a\ \text{and}\ b\ \text{are the}\ x\ \text{and}\ y\ \text{coordinates of the center}[/tex]
[tex]r=\text{Radius of the circle}[/tex]
Here the equation will be
[tex](x-0)^2+(y-0)^2=1900^2\\\Rightarrow x^2+y^2=3610000[/tex]
The equation of the outer circle is [tex]x^2+y^2=3610000[/tex]
2〖sen〗^2 x+3 senx+1=0
2cotxsecx+ 2secx+cotx+1=0
senx〖cos〗^2 x=senx
2〖cos〗^2 x+2senx-12=0
2〖csc〗^2 x+〖cot〗^2 x-3=0
2 sin²(x) + 3 sin(x) + 1 = 0
(2 sin(x) + 1) (sin(x) + 1) = 0
2 sin(x) + 1 = 0 OR sin(x) + 1 = 0
sin(x) = -1/2 OR sin(x) = -1
The first equation gives two solution sets,
x = sin⁻¹(-1/2) + 2nπ = -π/6 + 2nπ
x = π - sin⁻¹(-1/2) + 2nπ = 5π/6 + 2nπ
(where n is any integer), while the second equation gives
x = sin⁻¹(-1) + 2nπ = -π/2 + 2nπ
2 cot(x) sec(x) + 2 sec(x) + cot(x) + 1 = 0
2 sec(x) (cot(x) + 1) + cot(x) + 1 = 0
(2 sec(x) + 1) (cot(x) + 1) = 0
2 sec(x) + 1 = 0 OR cot(x) + 1 = 0
sec(x) = -1/2 OR cot(x) = -1
cos(x) = -2 OR tan(x) = -1
The first equation has no (real) solutions, since -1 ≤ cos(x) ≤ 1 for all (real) x. The second equation gives
x = tan⁻¹(-1) + nπ = -π/4 + nπ
sin(x) cos²(x) = sin(x)
sin(x) cos²(x) - sin(x) = 0
sin(x) (cos²(x) - 1) = 0
sin(x) (-sin²(x)) = 0
sin³(x) = 0
sin(x) = 0
x = sin⁻¹(0) + 2nπ = 2nπ
2 cos²(x) + 2 sin(x) - 12 = 0
2 (1 - sin²(x)) + 2 sin(x) - 12 = 0
-2 sin²(x) + 2 sin(x) - 10 = 0
sin²(x) - sin(x) + 5 = 0
Using the quadratic formula, we get
sin(x) = (1 ± √(1 - 20)) / 2 = (1 ± √(-19)) / 2
but the square root contains a negative number, which means there is no real solution.
2 csc²(x) + cot²(x) - 3 = 0
2 (cot²(x) + 1) + cot²(x) - 3 = 0
3 cot²(x) - 1 = 0
cot²(x) = 1/3
tan²(x) = 3
tan(x) = ± √3
x = tan⁻¹(√3) + nπ OR x = tan⁻¹(-√3) + nπ
x = π/3 + nπ OR x = -π/3 + nπ
The coordinates of point T are (0,6). The midpoint of ST is (4.-6). Find the coordinates
point S.
Answer:
The coordinates of endpoint S are [tex]S(x,y) = (8,-18)[/tex].
Step-by-step explanation:
Let [tex]T(x, y) = (0, 6)[/tex] and [tex]M(x,y) = (4,-6)[/tex], which is the midpoint of line segment ST. From Linear Algebra we get that midpoint is the following vector sum of endpoints S and T. That is:
[tex]M(x,y) = \frac{1}{2}\cdot S(x,y) + \frac{1}{2}\cdot T(x,y)[/tex] (Eq. 1)
Now clear S in the previous expression:
[tex]S(x,y) = 2\cdot M(x,y) - T(x,y)[/tex] (Eq. 1b)
Then, the coordinates of point S are:
[tex]S(x,y) = 2\cdot (4,-6) - (0,6)[/tex]
[tex]S(x,y) = (8, -18)[/tex]
The coordinates of endpoint S are [tex]S(x,y) = (8,-18)[/tex].
Of 1000 randomly selected cases of lung cancer, 838 resulted in death within 10 years. Construct a 95% two-sided confidence interval on the death rate from lung cancer. (a) Construct a 95% two-sided confidence interval on the death rate from lung cancer. Round your answers to 3 decimal places. (b) Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03
Answer:
0.8152 ≤ p ≤ 0.8608
579
Step-by-step explanation:
Given the following :
Samples size n = 1000
Deaths within 10 years, p = 838
α = 95%
Construction a two way confidence interval:
p ± Zα/2 * √p(1-p) / n
point estimate p = 838/n = 838/1000 = 0.838
Z0.05/2 = Z0.025 = 1.96
0.838 - 1.96√0.838(1-0.838) / 1000
0.838 - 1.96*0.0116514 = 0.8152
0.838 + 1.96√0.838(1-0.838) / 1000
0.838 + 1.96*0.0116514 = 0.8608
0.8152 ≤ p ≤ 0.8608
b) Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03
Error (E) = 0.03
To find the samome size, use the relation:
n = (Zα/2 / E)² * p(1-p)
n = (1.96/0.03)² * 0.838(1-0.838)
n = (1.96/0.03)² * 0.838 * 0.162
n = 4268.4444 * 0.838 * 0.162
n = 579.46
n = 579
can you write an equivalent fraction for 9/11 and 6/7 using the least common denominator ?
Answer:
The least common denominator is 77 so the fractions would become 63/77 and 66/77.
Question 3: Determine the missing base in the equation problem below. 75eight = 23 base
Answer:
29
Step-by-step explanation:
Given the expression [tex]75_8 = 23_x[/tex] where x is the unknown base:
[tex]75_8 = 23_x\\7\times8^1 +5\times8^0 = 2\times x^1+3 \times x^0\\56+5 = 2x+3\\61 = 2x+3\\2x = 61-3\\2x = 58\\x = 58/2\\x = 29[/tex]
Hence the missing base is 29
Graph the linear function f(x) = 3 – 6x .
Answer:
put one point at (0,3)
put another point at (1,-3)
draw a line between them
Step-by-step explanation:
could u vote me brainliest plz? thx :)
The standard formula for calculating the equation of a line is expressed as
y = mx + b
m is the slope of the line
b is the y-intercept of the line
Given the equation to graph expressed as g(x) = 3 - 6x
First, we need to get the x and y-intercept of the line expressed as:
For the x-intercept, y = 0
0 = 3 - 6x
6x = 3
x = 0.5
The x-intercept is at (0.5, 0)
For the y-intercept, x = 0
y = 3 - 6(0)
y = 3
The y-intercept is at (0, 3)
Plot the graph of a line passing through the coordinate points (0.5, 0) and (0, 3) as shown below;
Learn more here: https://brainly.com/question/17003809
Point B is on line segment AC. Given BC
7 and AC
11, determine the length
AB.
Answer:
4
Step-by-step explanation:
Since the entire length is 11, and one segment is 7, you'll subtract and end up with the answer 4.
The length of AB if Point B is on the line segment AC, BC = 7 and AC = 11, is 4.
What is a line segment?A line segment is a measurable route between two points. Line segments can make up any polygon's sides because they have a set length.
Given:
Point B is on the line segment AC, BC = 7 and AC = 11,
Write the expression for the above phrase as shown below,
The length of the AC = The length of AB + the length of BC
11 = 7 + The length of AB
The length of AB = 11 - 7
The length of AB = 4
Thus, The length of AB is 4.
To know more about line segments:
brainly.com/question/17006091
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What is the solution to the equation? √x - 3 + 1 = 6
A. 64
B. 46
C. 28
D. 22
The solution of the given equation √x - 3 + 1 = 6 will be x = 64 so option (A) will be correct.
What is the equation?An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
For example 8x + 7y = 15.
Given the equation,
√x - 3 + 1 = 6
√x + (-3 + 1) = 6
√x - 2 = 6
√x = 6 + 2 = 8
By squaring
x = 8² = 64.
Hence "The solution of the given equation √x - 3 + 1 = 6 will be x = 64".
For more about the equation,
brainly.com/question/10413253
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Answer:the correct answer is C.28
Step-by-step explanation:
Jamal buys 33 bolts that cost $0.38 each,hich equation represents the best estimate for the total cost of all of the bolts
Answer:
12.54
Step-by-step explanation:
Solve each equation.
Show all steps
4) -8(-6-5k)=-232
the answer is k=4.6. hope this helps
Given the equation y=1/3x+2 what is the rate of change?
Answer:
1/3
Step-by-step explanation:
thats the slope so im assuming :/
Please help!!!!!!!! What is the measure of angle 4?
Answer:
30°
Step-by-step explanation:
<4=<2=30
(vertical opposite angles are equal)
Answer:
30 degrees
Step-by-step explanation:
Since 4 is equal on the other side of 2, it would be congruent, which is the same as 2. So, 30 degrees.
convert 2 3/7 to an improper fraction
Answer:The mixed number 2 3/7 can be converted to the improper fraction 17/7. The easiest way to do this is to multiply the denominator of the fraction (7 in...
Step-by-step explanation:
Use the number line below, where RS=9y+2, ST=2y+6, and RT= 52
Answer:
Step-by-step explanation:
Given
RS=9y+2, ST=2y+6, and RT= 52
The addition postulate is true for the number line.
RS+ST = RT
Substitute
9y+2+(2y+6) = 52
9y+2y+8 = 52
11y = 52-8
11y = 44
y = 44/11
y = 4
Find RS
RS = 9y+2
RS = 9(4)+2
RS = 36+2
RS = 38
Find ST:
ST = 2y+6
ST = 2(4)+6
ST = 8+6
ST = 14
Hence y = 4, RS = 38 and ST = 14
Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 2525 dollars and a standard deviation of 88 dollars. (Round all decimals to at least 3 places.) (a) What proportion of the bank's Visa cardholders pay more than 2828 dollars in interest
Complete Question
Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 25 dollars and a standard deviation of 8 dollars. (Round all decimals to at least 3 places.) (a) What proportion of the bank's Visa cardholders pay more than 28 dollars in interest
Answer:
0.354
Step-by-step explanation:
We solve for z score in this question.
The formula is given as:
z = (x-μ)/σ, where
x is the raw score = $28
μ is the population mean = $25
σ is the population standard deviation = $8
z= 28 - 25/8
z = 0.375
P-value from Z-Table:
P(x<28) = 0.64617
P(x>28) = 1 - P(x<28)
= 1 - 0.64617
= 0.35383
Approximately to 3 decimal places = 0.354
The proportion of the bank's Visa cardholders pay more than 28 dollars in interest is 0.354.
Quadrilateral EFGH is a scaled copy of quadrilateral ABCD. Select the true statement.
Answer:
segment EF is twice as long as segment AB
Step-by-step explanation:
Quadrilateral EFGH and quadrilateral ABCD are similar polygons. We can say that two polygons are similar if their corresponding angles are equal to each other and their corresponding sides are proportional to each other.
From the image attached, we can see that side CD and side GH are corresponding sides. The ratio of their sides are to be proportional.
GH / CD = 12 / 6 = 2
Therefore Quadrilateral EFGH is twice the size of Quadrilateral ABCD. Since side EF and side AB are proportional, therefore segment EF is twice as long as segment AB
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Answer:
Ooooook?
Step-by-step explanation:
Fine
1. which group weighed the most per item on the scale? how much did it weigh?
which group weighed the least per item on the scale? how much did it weigh?
And also complete the table.
Please help it is due right now ASAP
Answer:
cars weighed the most per item and desks the least
List and describe the characteristics of a wave
Answer:
Crest = Highest point of the wave.
Trough = Lowest point of the wave.
Wavelength = Distance from one crest/trough to the next (m)
Wave Height = Height from trough to crest (m)
Wave steepness = ratio of wave height to wavelength.
Amplitude = distance from the centre of wave to the bottom of the trough (m)
Step-by-step explanation:
Which sentence can represent the inequality
Nine less than five times a number is equal to -30.
Answer: 5x-30-9
-159
Step-by-step explanation:
-159 is the answer
The Complex Conjugate of 2 + 5i is equal to: _______+_________i
Answer:
2 - 5i
Step-by-step explanation:
For any complex number like say "z" written in rectangular form as;
z = a + ib, then from definitions the complex conjugate is given by the relation:
z* = a − ib
Now, from our question, we want to find the complex conjugate of 2 + 5i.
From the relationship above, it's clear that the complex conjugate here is;
2 - 5i
The average of the first 3 weights was 14 pounds. The average of the next 7 was 4 pounds. What was the overall average of the weights?
Answer:
[tex]Average = 10[/tex]
Step-by-step explanation:
Given
[tex]First\ Three = 14[/tex] --- Average
[tex]Next\ Seven= 4[/tex] --- Average
Required
Determine the overall average
Represent the sum of the first three with x.
So:
[tex]\frac{x}{3} = 14[/tex]
Solve for x
[tex]x = 14 * 3[/tex]
[tex]x = 42[/tex]
Represent the sum of the next seven with y.
So:
[tex]\frac{y}{7} = 4[/tex]
Solve for y
[tex]y = 4 * 7[/tex]
[tex]y = 28[/tex]
The overall average is calculated as thus:
[tex]Average = \frac{x + y}{7}[/tex]
[tex]Average = \frac{42 + 28}{7}[/tex]
[tex]Average = \frac{70}{7}[/tex]
[tex]Average = 10[/tex]
Which sentence is true is 0.45<0.5
True.
When you break it down, it's 0.45 compared to 0.50, so 0.5 is greater than 0.45 by 0.05. Also, 0.5 is closer to 0.
Is 1.994 greater or lesser than 1.493
Answer:
greater than
Step-by-step explanation:
1.994 is closer to 2 than 1.493 so it is greater!
Select all the possible (x,y) coordinates for the following linear equation y=3x+2
Answer:
x = 2/3
Step-by-step explanation:
To find x-intercept/zero, subtract y = 0
0 = 3x + 2
Move variable to the left-hand side and change its sign
-3 = 2
Divide both ides of the equation by - 3
x = - 2/3
Solution
x = - 2/3
Alternate form
x = - 0.6
Maria needs 3/4 of a cup of sugar for one serving of her recipe. How many cups of sugar will she need for 5 servings?
Answer:
3.75 cups of sugar. I think
Answer:
3 3/4
Step-by-step explanation:
3/5 times 5
1.multiiply the numerator by 5
The numerator is the top number which is 3 in this case
So 3x5 is 15
You keep the denominator 4
so 15/4 that is an improper fraction now divide 15 by 4
or count by fours
4,8,12,16
16 is more than 15 so the new numerator is 12 and how many times did we count to fours? 3 times
so 3 is a whole now subtract the 12 you already took with 15. 3 is the extra so 3 wholes and 3 extras which is 3 3/4
*remember you keep the denominator the same
Suppose x = 5 is a solution to the equation 4x − 3(x + a) = 2. Find the value of a that makes the equation true.
a. -25
b. 2
c. 3
d. 1
Answer:
[tex]a = 1[/tex]
Step-by-step explanation:
Given
[tex]4x - 3(x + a) = 2[/tex]
[tex]x = 5[/tex]
Required
Determine the value of a
[tex]4x - 3(x + a) = 2[/tex]
Substitute 5 for x
[tex]4(5) - 3(5 + a) = 2[/tex]
Open all brackets
[tex]20 - 15 - 3a = 2[/tex]
[tex]5 - 3a = 2[/tex]
Collect Like Terms
[tex]-3a = 2 - 5[/tex]
[tex]-3a = -3[/tex]
Solve for a
[tex]a = -3/-3[/tex]
[tex]a = 1[/tex]
Find the slope of the line
Answer:
0
Step-by-step explanation:
Customers at the Palace Pro Shop receive a 10% discount if they are members. All customers must pay 7% in sales tax. The function f(x)=0.9x is used to determine the price of an item after the 10% member discount, where x is the regular price of the item. The function g(x)=1.07x is used to determine the total amount customers pay for a purchase after all discounts are applied. Which function can be used to determine T(x), the total amount a member pays for an item with a regular price of x dollars?
T(x)=0.963x
T(x)=0.17x
T(x)=1.19x
T(x)=1.97x
Answer:
0.963
Step-by-step explanation:
It’s correct