Answer:
2x + y = -4
Step-by-step explanation:
standard form of equation of straight line is
ax+by = c
that is terms containing x and y should be on LHS and constant term should be on RHS
______________________________________________
Given equation
y + 1 = - 2x - 3
lets bring -2x on LHS ,
add 2x on lHS and RHS
y + 1 + 2x = - 2x - 3 + 2x
=> y + 1 + 2x = -3
on lHS, 1 is there which constant term lets bring it on RHS
subtract 1 from both sides
y + 1 + 2x - 1= -3 -1
y + 2x = -4
rearranging it
2x + y = -4 (Answer)
the petit chef co has 11.7 percent coupon bonds on the market with elven years left to maturtiy. The bonds make annuly payments and have a par value of 1000. If the bonds curtently sell for 1153.60 what is tje ytm
Answer:
9.40%
Step-by-step explanation:
Given:
Annual coupon rate = 11%
Time left to maturity = 11 years
Par value of bond = 1000
Present value of bond = 1153.60
Required: Find Yeild to Maturity (YTM)
To find the yield to maturity, use the formula below:
YTM = [Annual coupon+(Face value-Present value)/time to maturity]/(Face value+Present value)/2
where annual coupon = 1000 * 11% = 110
Thus,
[tex]YTM = \frac{\frac{110+(1000-1139.59}{9}}{\frac{(1000+1139.59)}{2}}[/tex]
YTM = 9.40%
Therefore the approximate YTM is 9.40%
I have attached the file
Answer:
sorry i am not able to understood
Step-by-step explanation:
If y>0, which of these values of x is NOT in the domain of this equation? y=x2+7x
Answer:
[tex]\boxed{\sf \ \ \ [-7,0] \ \ \ }[/tex]
Step-by-step explanation:
Hello
[tex]y=x^2+7x=x(x+7) >0\\<=> x>0 \ and \ x+7 >0 \ \ or \ \ x<0 \ and \ x+7<0\\<=> x>0 \ \ or \ \ x<-7\\[/tex]
So values of x which is not in this domain is
[tex]-7\leq x\leq 0[/tex]
which is [-7,0]
hope this helps
Determine the domain of the function. f as a function of x is equal to the square root of x plus three divided by x plus eight times x minus two.
All real numbers except -8, -3, and 2
x ≥ 0
All real numbers
x ≥ -3, x ≠ 2
Answer:
[tex]\huge \boxed{{x\geq -3, \ x \neq 2}}[/tex]
Step-by-step explanation:
The function is given,
[tex]\displaystyle f(x)=\frac{\sqrt{x+3 }}{(x+8)(x-2)}[/tex]
The domain of a function are all possible values of x.
There are restrictions for the value of x.
The denominator of the function cannot equal 0, if 0 is the divisor then the fraction would be undefined.
[tex]x+8\neq 0[/tex]
Subtract 8 from both parts.
[tex]x\neq -8[/tex]
[tex]x-2\neq 0[/tex]
Add 2 on both parts.
[tex]x\neq 2[/tex]
The square root of x + 3 cannot be a negative number, because the square root of a negative number is undefined. x + 3 has to equal to 0 or be greater than 0.
[tex]x+3\geq 0[/tex]
Subtract 3 from both parts.
[tex]x\geq -3[/tex]
The domain of the function is [tex]x\geq -3[/tex], [tex]x\neq 2[/tex].
The domain of the given function will be x ≥ -3 and x ≠ 2.
What is the domain of a function?The entire range of independent input variables that can exist is referred to as a function's domain or,
The set of all x-values that can be used to make the function "work" and produce actual y-values is referred to as the domain.
As per the data given in the question,
The given expression of function is,
f(x) = [tex]\sqrt{\frac{x+3}{(x-8)(x-2)} }[/tex]
The fraction would indeed be undefined if the base of the function were equal to zero, which is not allowed.
x + 8 ≠ 0
x ≠ -8
And, x - 2 ≠ 0
x ≠ 2
Since the square root of a negative number is undefined, x+3 cannot have a negative square root. x+3 must be bigger than zero or identical to zero.
So,
x + 3 ≥ 0
x ≥ -3
So, the domain of the function will be x ≥ -3 and x ≠ 2.
To know more about Domain:
https://brainly.com/question/28135761
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A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 95% confidence interval for the mean score, , of all students taking the test
Answer:
The 95% confidence interval for the mean score, , of all students taking the test is
[tex]28.37< L\ 30.63[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 59[/tex]
The mean score is [tex]\= x = 29.5[/tex]
The standard deviation [tex]\sigma = 5.2[/tex]
Generally the standard deviation of mean is mathematically represented as
[tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x} = \frac{5.2 }{\sqrt{59} }[/tex]
[tex]\sigma _{\= x} = 0.677[/tex]
The degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
substituting values
[tex]df = 59 -1[/tex]
[tex]df = 58[/tex]
Given that the confidence interval is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 -95[/tex]
[tex]\alpha =[/tex]5%
[tex]\alpha = 0.05[/tex]
Now the critical value at this significance level and degree of freedom is
[tex]t_{df , \alpha } = t_{58, 0.05 } = 1.672[/tex]
Obtained from the critical value table
So the the 95% confidence interval for the mean score, , of all students taking the test is mathematically represented as
[tex]\= x - t*(\sigma_{\= x}) < L\ \= x + t*(\sigma_{\= x})[/tex]
substituting value
[tex](29.5 - 1.672* 0.677) < L\ (29.5 + 1.672* 0.677)[/tex]
[tex]28.37< L\ 30.63[/tex]
need help thankssssss
Answer:
301.44
Step-by-step explanation:
V=π r² h
V=π (4)² (12)
V= 603.19
divide by 2 to find half full: ≈ 301
301.44
You change oil every 6000 miles and drive 2000 miles a month; how many times a year do you change oil?
Answer:
you would change it 4 times a year
Step-by-step explanation:
if there is 12 months in a year and 3 mounths equal 6000 then divide 12/3=4
Use an appropriate series to find Taylor series of the given function centered at the indicated value of a. Write your answer in summation notation.
sinx, a= 2π
Answer:
The Taylor series is [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
Step-by-step explanation:
From the question we are told that
The function is [tex]f(x) = sin (x)[/tex]
This is centered at
[tex]a = 2 \pi[/tex]
Now the next step is to represent the function sin (x) in it Maclaurin series form which is
[tex]sin (x) = \frac{x^3}{3! } + \frac{x^5}{5!} - \frac{x^7}{7 !} +***[/tex]
=> [tex]sin (x) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
Now since the function is centered at [tex]a = 2 \pi[/tex]
We have that
[tex]sin (x - 2 \pi ) = (x-2 \pi ) - \frac{(x - 2 \pi)^3 }{3 \ !} + \frac{(x - 2 \pi)^5 }{5 \ !} - \frac{(x - 2 \pi)^7 }{7 \ !} + ***[/tex]
This above equation is generated because the function is not centered at the origin but at [tex]a = 2 \pi[/tex]
[tex]sin (x-2 \pi ) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x - 2 \pi)^{2n+1}][/tex]
Now due to the fact that [tex]sin (x- 2 \pi) = sin (x)[/tex]
This because [tex]2 \pi[/tex] is a constant
Then it implies that the Taylor series of the function centered at [tex]a = 2 \pi[/tex] is
[tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
PLEASE HELPPP ITS TIMED Consider the following functions. f(x) = x2 – 4 g(x) = x – 2 What is (f(x))(g(x))? a.(f(x))(g(x)) = x + 2; x ≠ 2 b.(f(x))(g(x)) = x + 2; all real numbers c.(f(x))(g(x)) = x3 – 2x2 – 4x + 8; x ≠ 2 d(f(x))(g(x)) = x3 – 2x2 – 4x + 8; all real numbers
Answer:
d(f(x))(g(x)) = x3 – 2x2 – 4x + 8; all real numbersStep-by-step explanation:
(f(x))(g(x)) = (x²- 4)*(x-2) =x³ - 2x² - 4x + 8Choice d. is correct
a.(f(x))(g(x)) = x + 2; x ≠ 2 incorrectb.(f(x))(g(x)) = x + 2; all real numbers incorrectc.(f(x))(g(x)) = x3 – 2x2 – 4x + 8; x ≠ 2 incorrectd(f(x))(g(x)) = x3 – 2x2 – 4x + 8; all real numberscorrectAnswer:
D
Step-by-step explanation:
3 is what percentage of 12?
Answer:
25%
Step-by-step explanation:
First you have the fraction of 3/12 and need to turn it into a decimal. So to do that you divide 3 by 12 = 0.25. So your percent is 25%
A submarine is moving parallel to the surface of the ocean at a depth of 626 m. It begins a
constant ascent so that it will reach the surface after travelling a distance of 4420 m.
a) What angle of ascent, to the nearest tenth of a degree, did the submarine make? (3
marks)
b) How far did the submarine travel horizontally, to the nearest metre, during its ascent to
the surface? (3 marks)
Answer:
a) the angle of ascent is 8.2°
b) the horizontal distance traveled is 4375 m
Step-by-step explanation:
depth of ocean = 626 m
distance traveled in the ascent = 4420 m
This is an angle of elevation problem with
opposite side to the angle = 626 m
hypotenuse side = 4420 m
a) angle of ascent ∅ is gotten from
sin ∅ = opp/hyp = 626/4420
sin ∅ = 0.142
∅ = [tex]sin^{-1}[/tex] 0.142
∅ = 8.2° this is the angle of ascent of the submarine.
b) The horizontal distance traveled will be gotten from Pythagoras theorem
[tex]hyp^{2}[/tex] = [tex]opp^{2}[/tex] + [tex]adj^{2}[/tex]
The horizontal distance traveled will be the adjacent side of the right angle triangle formed by these distances
[tex]4420^{2}[/tex] = [tex]626^{2}[/tex] + [tex]adj^{2}[/tex]
adj = [tex]\sqrt{4420^{2}-626^{2} }[/tex]
adj = 4375 m this is the horizontal distance traveled.
Find the surface area of the triangular prism (above) using its net (below).
Answer:
96 square units
Step-by-step explanation:
The surface area of the prism can be calculated using its net.
The net consists of 3 rectangles and 2 triangles.
The surface area = area of the 3 rectangles + area of the 2 triangles
Area of 3 rectangles:
Area of 2 rectangles having the same dimension = 2(L*B) = 2(7*3) = 2(21) = 42 squared units
Area of the middle triangle = L*B = 7*6 = 42 square units.
Area of the 3 triangles = 42 + 42 = 84 square units.
Area of the 2 triangles:
Area = 2(½*b*h) = 2(½*6*2) = 6*2
Area of the 2 triangles = 12 square units
Surface area of the triangular prism = 84 + 12 = 96 square units.
Answer:
It's 96 unit2
Step-by-step explanation:
I just do it in khan and it's correct
The SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36 scores is selected. a) What is the probability that the sample mean will be larger than 1224
Answer:
the probability that the sample mean will be larger than 1224 is 0.0082
Step-by-step explanation:
Given that:
The SAT scores have an average of 1200
with a standard deviation of 60
also; a sample of 36 scores is selected
The objective is to determine the probability that the sample mean will be larger than 1224
Assuming X to be the random variable that represents the SAT score of each student.
This implies that ;
[tex]S \sim N ( 1200,60)[/tex]
the probability that the sample mean will be larger than 1224 will now be:
[tex]P(\overline X > 1224) = P(\dfrac{\overline X - \mu }{\dfrac{\sigma}{\sqrt{n}} }> \dfrac{}{}\dfrac{1224- \mu }{\dfrac{\sigma}{\sqrt{n}} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{1224- 1200 }{\dfrac{60}{\sqrt{36}} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{\dfrac{60}{6} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{10} })[/tex]
[tex]P(\overline X > 1224) = P(Z > 2.4 })[/tex]
[tex]P(\overline X > 1224) =1 - P(Z \leq 2.4 })[/tex]
From Excel Table ; Using the formula (=NORMDIST(2.4))
P(\overline X > 1224) = 1 - 0.9918
P(\overline X > 1224) = 0.0082
Hence; the probability that the sample mean will be larger than 1224 is 0.0082
6x-5<2x+11. plz helpppppp
Answer:
x < 4 or x = ( -∞, 4)
Step-by-step explanation:
6x - 5 < 2x + 116x - 2x < 11 + 54x < 16 x < 16/4x < 4or
x = ( -∞, 4)
[tex]\text{Solve the inequality for x:}\\\\6x-5<2x+11\\\\\text{Subtract 2x from both sides}\\\\4x-5<11\\\\\text{Add 5 to both sides}\\\\4x<16\\\\\text{Divide both sides by 4}\\\\\boxed{x<4}[/tex]
solve the rational equation 5/x = 4x+1/x^2
Answer:
x = 1
Step-by-step explanation:
Set up the rational expression with the same denominator over the entire equation.
Since the expression on each side of the equation has the same denominator, the numerators must be equal
5x =4x+1
Move all terms containing x to the left side of the equation.
Hope this can help you
A point P has coordinates (-5, 4). What are its new coordinates after reflecting
point Pover the y-axis?
A. (-5, -4)
B. (-5, 4)
C. (5, 4)
D. (5, -4)
Answer:
C(5, 4)
Step-by-step explanation:
The rule for a reflection over the y -axis is (x,y)→(−x,y) .
Answer:
(5, 4)
Step-by-step explanation:
when you reflect off the y-axis, you switch (x,y) to (-x,y)
So
(-5, 4) --> (5, 4)
Hope this helps,
Feel free to ask more questions if I need to explain more.
The average college lecture hall (auditorium) can seat 60 students with a standard deviation of 21. Assume that a total of 60 lecture halls are selected for a sample. What is the standard deviation for the sample mean?
Answer:
The standard deviation of the sample mean is [tex]\sigma _ {\= x } = 2.711[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\= x = 60[/tex]
The standard deviation is [tex]\sigma = 21[/tex]
The sample size is [tex]n = 60[/tex]
Generally the standard deviation of the sample mean is mathematically represented as
[tex]\sigma _ {\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _ {\= x } = \frac{ 21 }{\sqrt{60} }[/tex]
[tex]\sigma _ {\= x } = 2.711[/tex]
√9m^2n^2 + 2√m^2n^2 - 3mn
Answer:
I think it is
Step-by-step explanation:
Answer:
5n√2m^ - 3mn
Step-by-step explanation:
please show on graph (with x and y coordinates) state where the function x^4-36x^2 is non-negative, increasing, concave up
Answer:
[tex] y'' =12x^2 -72=0[/tex]
And solving we got:
[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]
We can find the sings of the second derivate on the following intervals:
[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up
[tex]x=-\sqrt{6}, y =-180[/tex] inflection point
[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down
[tex]x=\sqrt{6}, y=-180[/tex] inflection point
[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up
Step-by-step explanation:
For this case we have the following function:
[tex] y= x^4 -36x^2[/tex]
We can find the first derivate and we got:
[tex] y' = 4x^3 -72x[/tex]
In order to find the concavity we can find the second derivate and we got:
[tex] y'' = 12x^2 -72[/tex]
We can set up this derivate equal to 0 and we got:
[tex] y'' =12x^2 -72=0[/tex]
And solving we got:
[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]
We can find the sings of the second derivate on the following intervals:
[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up
[tex]x=-\sqrt{6}, y =-180[/tex] inflection point
[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down
[tex]x=\sqrt{6}, y=-180[/tex] inflection point
[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up
Can you draw the reflection Across the y-axis of the attached image.
Answer:
see graph
Step-by-step explanation:
A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.
A circular chicken house has an area of 40m². What length of chicken wire is required to fence the house without any wire left over?
What is the value of y iin this equation? 4(y-3) =48
Answer:
y = 15Step-by-step explanation:
Question:
4(y - 3) = 48
1. Distribute
4y - 12 = 48
2. Simplify Like terms
4y - 12 = 48
+ 12 + 12
4y = 60
3. Solve
4y = 60
/4 /4
y = 15
4. Check:
4(y - 3) = 48
4((15) - 3) = 48
4(12) = 48
48 = 48 Correct!
Hope this helped,
Kavitha
Answer:
[tex]y=15\\[/tex]
Step 1:
To find y, we first have to multiply [tex]4(y-3)[/tex]. When we do that (4 * y, 4 * - 3), we get [tex]4y-12[/tex].
Step 2:
Our equation looks like this now:
[tex]4y-12=48[/tex]
To solve this equation, we have to add 12 on both sides so we can cancel out the -12 on the left side of the equation.
[tex]4y-12(+12)=48(+12)[/tex]
[tex]4y=60[/tex]
Now, we can divide 4 on both sides to get y by itself.
[tex]4y/4\\60/4[/tex]
[tex]y=15[/tex]
Find the number of possible outcomes Five books need to be placed on a shelf. You randomly arrange the books on the shelf from left to right.
Answer:
120
Step-by-step explanation:
Let's say you put them on the shelf one by one, from left to right.
You can pick 1 of the 5 for the first position.
5
Now you have 4 books left. You pick one out of those 4 for the second position.
5 * 4
There are 3 choices left for the 3rd position.
5 * 4 * 3
2 left for the 4th position.
5 * 4 * 3 * 2
Finally, there is one book left for the 5th position.
5 * 4 * 3 * 2 * 1
Now we multiply:
5 * 4 * 3 * 2 * 1 = 120
A heating pad takes 3,030 Watts during each time it is turned on. If you only use it for 34 minutes, how much CO2 was created? Round to 1 decimal.
Answer:
1.7kW/hrStep-by-step explanation:
Using the formula for calculating the energy used up during the process;
Energy used up = Amount of CO₂ created.
Energy used up in the process = Power * Time.
Given Parameters:
Power = 3,030Watts
Converting to Kilowatts, power = 3030/1000 kW
Power (in kW) = 3.03kW
Time taken = 34 minutes
Converting to hour;
Since 60 minutes = 1hr
34minutes = (34/60)hr
34minutes = (17/30)hr
Required:
Energy used up = 3.03 * 17/30
Energy used up = 51.51/30
Energy used up = 1.717 kW/hr
Hence, amount of CO₂ created in kW/hr is 1.7 kW/hr to 1 decimal place.
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 95% confidence; n = 349, x = 42
Answer:
0.5705Step-by-step explanation:
Margin of error is expressed as M.E = [tex]z * \sqrt{\frac{\sigma}{n} }[/tex] where;
z is the z score at 95% confidence
[tex]\sigma[/tex] is the standard deviation
n is the sample size
Given n = 349, [tex]\sigma = 42[/tex] and z score at 95% confidence = 1.645
Substituting this values into the formula above we will have;
M.E = [tex]1.645*\sqrt{\frac{42}{349} }[/tex]
[tex]M.E = 1.645*\sqrt{0.1203} \\\\M.E = 1.645*0.3468\\\\M.E = 0.5705 (to\ four\ dp)[/tex]
what is the length of a hypotenuse of a triangle if each of its legs is 4 units
Answer:
[tex]\boxed{c = 5.7 units}[/tex]
Step-by-step explanation:
Using Pythagorean Theorem:
=> [tex]c^2 = a^2+b^2[/tex]
Where c is hypotenuse, a is base and b is perpendicular and ( a, b = 4)
=> [tex]c^2 = 4^2+4^2[/tex]
=> [tex]c^2 = 16+16[/tex]
=> [tex]c^2 = 32[/tex]
Taking sqrt on both sides
=> c = 5.7 units
Answer:
5.65 unitsStep-by-step explanation:
Given,
Base ( b ) = 4 units
Perpendicular ( p ) = 4 units
Hypotenuse ( h ) = ?
Now,
Using Pythagoras theorem to find length of hypotenuse:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
Plugging the values
[tex] {h}^{2} = {4}^{2} + {4}^{2} [/tex]
Evaluate the power
[tex] {h}^{2} = 16 + 16[/tex]
Calculate the sum
[tex] {h}^{2} = 32[/tex]
[tex]h = \sqrt{32} [/tex]
[tex]h = 5.65 \: units[/tex]
Hope this helps..
Best regards !!
which graph represents a function? Please help!
Answer:
The last graph (to the far right).
Step-by-step explanation:
As long as each x-value has one y-value, it is a function. However, the last graph has an x-value at -1 where there are two y-values. So, it does not pass the Vertical Line Test, and it is a relation rather than a function.
Hope this helps!
Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k. A) 2 B) 3 C) 4 D) 5 IF YOU ANSWER IN 5 MINUTES I WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!
Ans k = 4
Step-by-step explanation:
Here g(x) =[tex]\frac{-1}{3}x + 1[/tex] and
f(x) = [tex]\frac{-1}{3} x -3[/tex]
Now, g(x) = f(x) + k
or, [tex]\frac{-1}{3}x + 1[/tex] = [tex]\frac{-1}{3} x -3 + k[/tex]
or, 1 + 3 = k
So, k = 4 Answer.
What is the formula for the area A of a trapezoid with parallel sides of length B and D, nonparallel sides of length A and C and height H?
A. A = 1/2h (a+c)
B. A = 1/2h (b + d)
C. A = a+b + c + d
D. A= abcd
E. A = 1/2h (a+b+c+d)
Answer:
[tex](B) \dfrac12H (B+D)[/tex]
Step-by-step explanation:
[tex]\text{Area of a trapezoid }= \dfrac12 ($Sum of the parallel sides) \times $Height\\Parallel Sides = B and D\\Height =H\\Therefore:\\\text{Area of the trapezoid }= \dfrac12 (B+D) H[/tex]
The correct option is B.
the perimeter of a square flower bed is 100 feet. what is the area of the flower bed in sqaure feet
Answer:
A =625 ft^2
Step-by-step explanation:
The perimeter of a square is
P = 4s where s is the side length
100 =4s
Divide each side by 4
100/4 = 4s/4
25 = s
A = s^2 for a square
A = 25^2
A =625