Answer:
x = 1/25
Step-by-step explanation:
2/5x+1/x=35
[tex]2/5x+1/x=35[/tex]
taking 1/x common
[tex]1/x(2/5+1)=35[/tex]
[tex](2+5)/5=35x\\7/5 = 35x\\x = 7/(5*35) = 1/(5*5) = 1/25[/tex]
Thus, value of x is 1/25
Let p0, p1, and p2 be the orthogonal polynomials described below, where the inner product on P4 is given by evaluation at -2, -1, 0, 1, 2. Find the othogonal projection of 3t^(3) onto Span{p0,p1,p2}.
p0(t) = 4
p1(t) = 3t
p2(t) = t^(2) -2
Answer:
[tex]$\frac{51}{5}t$[/tex]
Step-by-step explanation:
Let W = [tex]$(p_0, p_1, p_2)$[/tex] be orthogonal polynomials which is equal to [tex]$(4, 3t, t^2 -2)$[/tex], which defines the inner products as
[tex]$(f,g)=f(-2)g(-2)+f(-1)g(-1)+f(0)g(0)+f(1)g(1)+f(2)g(2)$[/tex]
Now, we find the orthogonal projection of [tex]$p=3t^3$[/tex] on W.
So the projection is
[tex]$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$[/tex]
[tex]$(p_0,p)=p_0(-2)p(-2)+p_0(-1)p(-1)+p_0(0)p(0)+p_0(1)p(1)+p_0(2)p(2)$[/tex]
[tex]$=4(-24)+4(-3)+4(0)+4(3)+4(24)=0$[/tex]
[tex]$(p_0,p_0)=p_0(-2)p_0(-2)+p_0(-1)p_0(-1)+p_0(0)p_0(0)+p_0(1)p_0(1)+p_0(2)p_0(2)$[/tex]
[tex]$=4(4)+4(4)+4(4)+4(4)+4(4)=80$[/tex]
[tex]$(p_1,p)=p_1(-2)p(-2)+p_1(-1)p(-1)+p_1(0)p(0)+p_1(1)p(1)+p_1(2)p(2)$[/tex]
[tex]$=(-6)(-24)+(-3)(-3)+0(0)+3(3)+6(24)=306$[/tex]
[tex]$(p_1,p_1)=p_1(-2)p_1(-2)+p_1(-1)p_1(-1)+p_1(0)p_1(0)+p_1(1)p_1(1)+p_1(2)p_1(2)$[/tex]
[tex]$=(-6)(-6)+(-3)(-3)+0(0)+3(3)+6(6)=90$[/tex]
[tex]$(p_2,p)=p_2(-2)p(-2)+p_2(-1)p(-1)+p_2(0)p(0)+p_2(1)p(1)+p_2(2)p(2)$[/tex]
[tex]$=2(-24)+(-1)(-3)+(-2)(0)+(-1)(3)+2(24)=0$[/tex]
[tex]$(p_2,p_2)=p_2(-2)p_2(-2)+p_2(-1)p_2(-1)+p_2(0)p_2(0)+p_2(1)p_2(1)+p_2(2)p_2(2)$[/tex]
[tex]$=(2)(2)+(-1)(-1)+(-2)(-2)+(-1)(-1)+2(2)=14$[/tex]
Therefore,
[tex]$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$[/tex]
[tex]$=\frac{0}{80}(4)+\frac{306}{90}(3t)+\frac{0}{14}(t^2-2)$[/tex]
[tex]$=\frac{51}{5}t$[/tex]
How do I graph this? Also how do identify which values of c for which
lim f(x) exist?
x -> c
Answer:
Step-by-step explanation:
Hello, I attached the graph.
This is a parabola, then a line and finally an horizontal line.
The vertex of the parabola is (0,0) and (2,4) is on the graph.
For the second part, draw a line which is passing by (2,4) and (0,4)
Finally, draw the line y = 4
You can see that f is continuous everywhere except in x = 4.
So, for any c real different from 4 the limit of f(x) exists.
Thank you
Distribute a negative -(5.5q+7)
Hi there! :)
Answer:
[tex]\huge\boxed{-5.5q - 7}[/tex]
-(5.5q + 7)
Distribute:
-(5.5q) -(7)
-5.5q - 7
Answer:
Z≥0 = {0, 1, 2, .
Step-by-step explanation:
Just took test
After a shipwreck, 120 rats manage to swim from the wreckage to a deserted island. The rat population on the island grows exponentially, and after 15 months, there are 280 rats on the island.
A. Find a function that models the population t months after the arrival of the rats.
B. What will the population be 3 years after the shipwreck?
C. When will the population reach 2000 rats?
Answer:
a. [tex]X(T) = 120 (1.058)^T[/tex]
b. Population after 3 years is 142
c. 50 years
Step-by-step explanation:
Given
Type of growth: Exponential
Initial number of rats = 120
Number of rats (15months) = 280
Solving (a)
Since the growth type is exponential, we make use of the following exponential progression
[tex]X_T = X_0 (1 + R)^T[/tex]
Where Xo is the initial population;
Xo = 125
[tex]X_T[/tex] is the current population at T month
So;
[tex]X_T = 280[/tex]; when [tex]T = 15[/tex]
Substitute these values in the above formula
[tex]280 =120 * (1 + R)^{15}[/tex]
Divide both sides by 120
[tex]\frac{280}{120} =(1 + R)^{15}[/tex]
[tex]2.3333 =(1 + R)^{15}[/tex]
Take 15th root of both sides
[tex]\sqrt[15]{2.3333} =1 + R[/tex]
[tex]1.05811235561 = 1 + R[/tex]
Subtract 1 from both sides
[tex]R = 1.05811235561 - 1[/tex]
[tex]R = 0.05811235561[/tex]
[tex]R = 0.058[/tex] (Approximated)
Plug in values of R and Xo in [tex]X_T = X_0 (1 + R)^T[/tex]
[tex]X_T = 120 (1 + 0.058)^T[/tex]
[tex]X_T = 120 (1.058)^T[/tex]
Write as a function
[tex]X(T) = 120 (1.058)^T[/tex]
Hence, the function is [tex]X(T) = 120 (1.058)^T[/tex]
Solving (b):
Population after 3 years
In this case, T = 3
So:
[tex]X(T) = 120 (1.058)^T[/tex]
[tex]X(3) = 120 (1.058)^3[/tex]
[tex]X(3) = 120 * 1.18466445254[/tex]
[tex]X(3) = 142.159734305[/tex]
[tex]X(3) = 142[/tex] (Approximated)
Solving (c): When population will reach 2000
Here: X(T) = 2000
So:
So:
[tex]2000 = 120 (1.058)^T[/tex]
Divide both sides by 120
[tex]\frac{2000}{120} = 1.058^T[/tex]
[tex]16.667 = 1.058^T[/tex]
Take Log of both sides
[tex]Log(16.667) = Log(1.058^T)[/tex]
Apply law of logarithm
[tex]Log(16.667) = TLog(1.058)[/tex]
Divide both sides by Log(1.058)
[tex]T = \frac{Log(16.667)}{Log(1.058)}[/tex]
[tex]T = 49.9009236926[/tex]
Approximate
[tex]T = 50\ years[/tex]
can someone please help me???
a is 3/4
b is -8
c is -2
d is 3
Answer:
-b[a + (c-d)^2]
-(-8)[3/4 + (-2 -3)^2]
8 [3/4 + (-5)^2]
8 [3/4 + 25]
8 [25.75]
206
=======================================
Work Shown:
a = 3/4
b = -8
c = -2
d = 3
----------------
c-d = -2-3 = -5
(c-d)^2 = (-5)^2 = 25
a+(c-d)^2 = 3/4 + 25 = 3/4 + 100/4 = 103/4
-b * [ a + (c-d)^2 ] = -(-8)*103/4 = 8*103/4 = (8/4)*103 = 2*103 = 206
----------------
Another way to show the steps could be
[tex]-b[a+(c-d)^2]\\\\-(-8)\left[\frac{3}{4}+(-2-3)^2\right]\\\\8\left[\frac{3}{4}+(-5)^2\right]\\\\8\left(\frac{3}{4}+25\right)\\\\8\left(\frac{3}{4}+\frac{100}{4}\right)\\\\8\left(\frac{3+100}{4}\right)\\\\8\left(\frac{103}{4}\right)\\\\\frac{8}{4}*103\\\\2*103\\\\206\\\\[/tex]
Which is more or less the same thing as the previous section.
----------------
So ultimately,
[tex]-b[a+(c-d)^2] = 206[/tex]
when a = 3/4, b = -8, c = -2, and d = 3.
Solve the inequalities (i) 5 ≤ 2x − 4 ≤ 8 (ii) −10 < 4 −3y/− 5 ≤ 4
Step-by-step explanation:
(i) 5 ≤ 2x − 4 ≤ 8 add 4 to all three expressions
9 ≤ 2x ≤ 12 divide by 2
9/2 ≤ x ≤ 6
(ii) −10 < (4 −3y)/− 5 ≤ 4 multiply all sides by -5
-20 ≤ 4 - 3y < 50 subtract 4
-24 ≤ -3y < 46 divide with -3
-46/3 < y ≤ 8
Damien worked at a grocery store earning $9.00 an hour. He worked 30 hours a week and was paid every two weeks. He paid $62 in taxes and had a $50 savings account deduction. What was Damien's gross income?
Answer:
$540
Step-by-step explanation:
We know Damien earned $9 per hour, worked 30 hours a week and was paid every 2 weeks.
We can write an expression to something like this:
(9 x 30) x 2
Which would give us 540
The question asks for the Gross income (the total income, before any taxes or deductions)
Which means that his gross income was $540
Eddie Lange earns $11.50 per hour. He worked 40 hours, plus time and a half
for 7 hours.
Answer:580
Step-by-step explanation:
What are the distances from the point (x,y) to the focus of the parabola and the directrix? Select two answers. A.distance to the directrix: |y+6| B.distance to the focus: (x+4)2+(y−2)2√ C.distance to the directrix: |y−6| D.distance to the focus: (x−2)2+(y+4)2√ E.distance to the directrix: |x+6| F.distance to the focus: (x−2)2+(y+5)2√
Answer:
Option (A) and Option (D)
Step-by-step explanation:
Point on the parabola is (x, y).
Focus given as (2, -4) and directrix of the parabola is y = -6
Therefore, distance of the point from the directrix will be,
d = |(y + 6)|
Similarly, distance of the point (x, y) from the focus will be,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(x-2)^2+(y+4)^2}[/tex]
Therefore, Option (A) and Option (D) will be the correct options.
which of the following is not a factor in becoming a money smart?
Answer:
Its learning how to read credit card statements
Step-by-step explanation:
Learn how to read your credit card statements and control the way you process them
The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the systolic reading be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 146 . Is the predicted value close to 91.0 , which was the actual diastolicreading? Use a significance level of 0.05.Systolic 117 134 150 113 138 113 144 145Diastolic 85 74 86 55 75 80 106 841. What is the regression equation? (Round to two decimal places as needed.)2. What is the best predicted diastolic pressure for a person with a systolic reading of 146 ?3. Is the predicted value close to 91.0 , which was the actual diastolic reading?A. The predicted value is very close to the actual diastolic reading.B. The predicted value is not close to the actual diastolic reading.C. The predicted value is close to the actual diastolic reading.D. The predicted value is exactly the same as the actual diastolic reading.
Answer:
ŷ = 6.69X - 706.18 ; 270.56; B. The predicted value is not close to the actual diastolic reading.
Step-by-step explanation:
Given the data below :
Systolic reading(x) :
117
134
150
113
138
113
144
145
Diastolic (y) :
85
74
86
55
75
80
106
841
A) Find the regression equation, letting the systolic reading be the independent (x) variable:
Using the online regression calculator :
The regression equation obtained is ;
ŷ = 6.69X - 706.18
Where ;
ŷ = dependent variable
6.69 is the gradient or slope
-706.18 is the intercept, where the line crosses the y - axis.
X - the independent variable (Systolic reading)
B.) Find the best predicted diastolic pressure for a person with a systolic reading of 146 .
ŷ = 6.69X - 706.18
ŷ = 6.69(146) - 706.18
ŷ = 270.56
Is the predicted value close to 91.0
B. The predicted value is not close to the actual diastolic reading.
In 2000, the total number of employees working for
U.S. airlines was 679,967. Round this number to the
nearest thousand. (Source: The Air Transport Asso-
ciation of America, Inc.)
Answer:
680,000
679,967 rounded to the nearest thousand is 680,000.
So, there are around 680,000 employees working for US Airlines. Hope it helps!
Answer:
680,000
Step-by-step explanation:
Look at the hundreds place if it's 5 or higher you round up the thousands place by one. Every place to the right of the hundreds place turns into a zero.
If f(x) = -1x + 4 then what is f(-2)?
Answer:
[tex]\huge \boxed{f(-2)=6}[/tex]
Step-by-step explanation:
[tex]\sf f(x)=-1x+4[/tex]
Switching x variable with -2.
[tex]\sf f(-2)=-1(-2)+4[/tex]
Evaluating.
[tex]\sf f(-2)=2+4[/tex]
[tex]\sf f(-2)=6[/tex]
Answer:
6Step-by-step explanation:
[tex]f(x) = -1x + 4\\\\f(-2) =?\\\\f(-2) = -1(-2) +4\\f(-2) = 2+4\\f(-2) = 6[/tex]
Use the Method of Lagrange Multipliers to find the Minimum and Maximum of f(x,y) = xy subject to x^2+y^2-xy = 9 g
Answer: The Max fun is 9, and the Min fun is -3
Step-by-step explanation:
Please follow the steps carefully;
Let us consider the function f(x,y) = xy -------------- (1)
We will apply the Lagrange multipliers to maximize the function f(x,y) subject to the constraint g(x,y) = x^2+y^2-xy = 9
By differentiating (1) w.r.t x, we get fx(x,y) = y
By differentiating (1) w.r.t y, we get fy(x,y) = x
By differentiating g(x,y) w.r.t x, we get gx(x,y) = 2x - y
Also By differentiating g(x,y) w.r.t y, we get gy(x,y) = 2y - x
let us take
fx = λgx
where y = λ(2x - y)
y/2x - y = λ ----------- (2)
fy = λgy
where x = λ(2y - x)
λ = x/2y -x ----------- (2)
Let us equate (2) and (3)
y/2x - y = x/2y -x
2y² - xy = 2x² - xy
2y² = 2x² after cancelling like terms
y² = x²
So y = ±x
Now let us substitute y = x into the given constraint
x² + y² - xy = 9
x² + x² - x(x) = 9
x² = 9
therefore x = ± 3
We can conclude that when x = ±3, ⇒ y = ±3
The corresponding points are (3,3), (-3,-3)
Substitue y = -x in the given constraint gives
x² + y² - xy = 9
x² + (-x)² -x(-x) = 9
3x² = 9
x² = 3
x = ±√3
The corresponding points are (√3,-√3), (-√3,√3)
The function value is
f(x,y) = xy
f (√3,-√3) = (√3)(-√3) = -3
f (-√3,√3) = (-√3)(√3) = -3
we get;
f(3,3) = (3)(3) = 9
and
f (-3,-3) = (-3)(-3) = 9
We can conclusively say that ;
The Maximum value of the function is 9
The Minimum value of the function is -3
cheers i hope this helped
Simplify. Answer and explanation if you can
Hi there! Hopefully this helps!
--------------------------------------------------------------------------------------------------
Answer: 6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Calculate 36 to the power of [tex]\frac{1}{2}[/tex].
[tex]\frac{1}{2} = 0.5[/tex]
[tex]36^{0.5} = 6[/tex].
Simplify the following expression as much as possible.
4^10/4^10 x 7^O=?
Answer:
1
Step-by-step explanation:
4^10/4^10 x 7^O =
= 4^(10 - 10) * 1
= 4^0 * 1
= 1 * 1
= 1
Answer:
1
Step-by-step explanation:
4^10/4^10 = 1
7^0 = 1
1 x 1 = 1
Help me please thank y’all
Answer:
125°
Step-by-step explanation:
Sum of angles of triangle equals 180°:
x + 25° + 30° = 180°x + 55° = 180°x = 180° -55°x = 125°Answer:
x=125
Step-by-step explanation:
because sum of interior angles of a triangle is 180
1 lb = 16 oz. How many lbs (pounds) are in 14 oz (ounces)?
Answer:
0.875
Step-by-step explanation:
14÷16= 0.875
divide the mass value by 16
Convert 0.00001 to a power of 10
Answer:
1 * 10 ^ -7
Step-by-step explanation:
calculate 65 L to quarts. Final answer round two places
Step-by-step explanation:
The approximate equation to convert from liters to quarts is : x • 1.056688.
We enter 65 for x and multiply.
65 • 1.056688 = 68.68472
We round that to the nearest 100th to get our final answer.
Our final answer: 68.68 liters
If a new movie is selling for $20, and the local city charges 8% sales tax, how much tax will be charged? $_____
Answer: $1.6
Step-by-step explanation:
price × percentage of tax=amount of tax
$20 × 8%=20 × 0.08= $1.6
Hope this helps!! :)
order the following numbers from least (top) to greatest number( bottom) . 0.40 , 0.489 , 0.430 , 0.480
Answer:
[tex]\Large \boxed{0.40 < 0.430 < 0.480 < 0.489}[/tex]
Step-by-step explanation:
First you have to see the decimal places.
Than the number of digits there is.
So this is how we make it from least to greatest!
Since there is 3 numbers after the decimals in almost all of them...
Than let’s make ‘0.40’ into 3 numbers after the decimal too.
I am sure you have heard that if you add a ‘0’ to a decimal nothing will change right?
So let’s make 0.40 into 3 numbers after the decimal just like the other numbers!
Okay so first let’s add a zero to ‘0.40’... which now this turns into ‘0.400’
Now it will be more easier to compare least to greatest!
0.400 is the least, than comes 0.430, & than would be 0.480, & finally the greatest would be 0.489
Therefore the answer is 0.40 < 0.430 < 0.480 < 0.489.
A local diner has started selling cupcakes and is using the bar chart given below to keep track of how many are sold each day. How many cupcakes will be sold on day n?
Answer:
a + (n-1)*4
Step-by-step explanation:
Day n could be any particular day located on the x-axis of the bar chart. Each bar represents the amount of cupcakes sold on each of the four days numbered from 1 to 4. The height of each bar marks the number of cupcakes sold. According to the chart attached, the number of cupcakes sold on each day is listed below:
Day 1 : 1 cupcake sold
Day 2 : 5 cupckaes sold
Day 3: 9 cupcakes sold
Day 4: 13 cupckaes sold
Studying the graph carefully fully, it will be observed that the number of cupcakes sold increases by a margin of 4 after day one.
As such the number of cupcakes sold in n days can be modeled by:
Using the Arithmetic progression formula:
Tn = a + (n-1)d
d = common difference, = 4
a = first term = 1
n = number of days
Hence, number sold in day n:
a + (n-1)*4
Arithmetic progressio
Answer:
3n−1 cupcakes
Step-by-step explanation:
3. Dr. Potter provides vaccinations against polio and measles. Each polio vaccination consists of 5
doses, and each measles vaccination consists of 3 doses. Last year, Dr. Potter gave a total of 60
vaccinations that consisted of a total of 225 doses. How many more measles vaccines did Mr.
Potter give than polio?
Please explain the process. THX
Answer:
There are 15 more measles vaccines than polio vaccines
Step-by-step explanation:
Represent Polio with P and Measles with M
Given
5P + 3M = 225
P + M = 60
Required
How much is M greater than P; M - P
Make M the subject of formula in the second equation
[tex]M = 60 - P[/tex]
Substitute this in the first equation
[tex]5P + 3M = 225[/tex] becomes
[tex]5P + 3(60 - P) = 225[/tex]
Open the bracket
[tex]5P + 180 - 3P = 225[/tex]
Collect Like Terms
[tex]5P - 3P = 225 - 180[/tex]
[tex]2P = 45[/tex]
Divide both sides by 2
[tex]P = 22.5[/tex]
Substitute 22.5 for P in [tex]M = 60 - P[/tex]
[tex]M = 60 - 22.5[/tex]
[tex]M = 37.5[/tex]
Calculate the difference; M - P
[tex]M - P = 37.5 - 22.5[/tex]
[tex]M - P = 15[/tex]
Hence, there are 15 more measles vaccines than polio vaccines
Which shows a true math fact? A 18.7×3.47=58.157 B 86.128−29.473=56.655 C 37.561+28.94=40.455 D 36.26÷0.50=725.2
Answer:
The correct answer is B.
Explanation:
Putting it into your calculator as you see it gives you the correct answer.
Have a good day! :)
A company issues 10% Irredeemable preference shares. The face value per share is RO 10, but the issue price is RO 9.5. what is the cost of preference share?
Answer:
The answer of the question is 10.53%.
Help please I would appreciate it !
Answer/Step-by-step explanation:
Given:
Line equation => [tex] 2.1x + 9.9y - 9.2 = 0 [/tex]
Required:
x-intercept and y-intercept of the line.
SOLUTION:
The x-intercept is the point where the line intercepts the x-axis. To find the x-intercept of the line for which the equation is given above, set y = 0 and solve for x.
[tex] 2.1x + 9.9(0) - 9.2 = 0 [/tex]
[tex] 2.1x + 0 - 9.2 = 0 [/tex]
[tex] 2.1x - 9.2 = 0 [/tex]
[tex] 2.1x - 9.2 + 9.2 = 0 + 9.2 [/tex]
[tex] 2.1x = 9.2 [/tex]
[tex] \frac{2.1x}{2.1} = \frac{9.2}{2.1} [/tex]
[tex] x = 4.4 [/tex] (approximated)
The y-intercept is the point where the line intercepts the y-axis. At this point, x = 0. Set x = 0 and solve for y to find the y intercept.
[tex] 2.1(0) + 9.9y - 9.2 = 0 [/tex]
[tex] 9.9y - 9.2 = 0 [/tex]
[tex] 9.9y - 9.2 + 9.2 = 0 + 9.2 [/tex]
[tex] 9.9y = 9.2 [/tex]
[tex] y = \frac{9.2}{9.9} [/tex]
[tex] y = 0.9 [/tex] (approximated)
Simplify the following polynomial, then evaluate for x = -2 . 2x^2-4x+3x^2+x-7
Answer:
19
Step-by-step explanation:
first you would combine like terms to get 5x^2-3x-7. plug in -2 into the x's and you will get 19!
A computers is on on sale for $1085. if the original price was reduced by 30%, what was the original price of the Computer ?
Answer:
1.131,5
Step-by-step explanation:
What is the slope of the line that contains these points? x,12,13,14,,15. y,-4, 2,8,14.
Answer:
[tex]\huge \boxed{{m=6}}[/tex]
Step-by-step explanation:
Let's take two points,
(12, -4) and (13, 2).
slope = (difference of y) / (difference of x)
m = (2 - - 4) / (13 - 12)
m = (2 + 4) / 1
m = 6 / 1 = 6
The slope of the line is 6.
Answer:
6
Step-by-step explanation:
The slope is the change in y over the change in x
m = ( y2-y1)/(x2-x1)
= (14-8)/(15-14)
= 6/1