Answer:
question 1
if you want x to stand alone
you will take the -3 off by crossing it to the other side
NB when a negative number crosses the equal sign it becomes positive
x =10+3= ×=13 is the final answer
Step-by-step explanation:
question 2
you will divide both sides by 2(because we want x to stand alone)
so final answer is ×=4
Use the procedures developed to find the general solution of the differential equation. (Let x be the independent variable.)
2y''' + 15y'' + 24y' + 11y= 0
Solution :
Given :
2y''' + 15y'' + 24y' + 11y= 0
Let x = independent variable
[tex](a_0D^n + a_1D^{n-1}+a_2D^{n-2} + ....+ a_n) y) = Q(x)[/tex] is a differential equation.
If [tex]Q(x) \neq 0[/tex]
It is non homogeneous then,
The general solution = complementary solution + particular integral
If Q(x) = 0
It is called the homogeneous then the general solution = complementary solution.
2y''' + 15y'' + 24y' + 11y= 0
[tex]$(2D^3+15D^2+24D+11)y=0$[/tex]
Auxiliary equation,
[tex]$2m^3+15m^2+24m +11 = 0$[/tex]
-1 | 2 15 24 11
| 0 -2 - 13 -11
2 13 11 0
∴ [tex]2m^2+13m+11=0[/tex]
The roots are
[tex]$=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$[/tex]
[tex]$=\frac{-13\pm \sqrt{13^2-4(11)(2)}}{2(2)}$[/tex]
[tex]$=\frac{-13\pm9}{4}$[/tex]
[tex]$=-5.5, -1$[/tex]
So, [tex]m_1, m_2, m_3 = -1, -1, -5.5[/tex]
Then the general solution is :
[tex]$= (c_1+c_2 x)e^{-x} + c_3 \ e^{-5.5x}$[/tex]
What is the area of the figure
Answer:
72 in. sq.
Step-by-step explanation:
6 x 6 = 36
6 x 6 = 36 / 2 = 18
6 x 6 = 36 / 2 = 18
18 + 18 + 36 = 72.
Hope this helps!
If there is something wrong just let me know.
Find the values of c such that the area of the region bounded by the parabolas y = 4x2 − c2 and y = c2 − 4x2 is 32/3. (Enter your answers as a comma-separated list.)
Answer:
-2,2
Step-by-step explanation:
Let
[tex]y_1=4x^2-c^2[/tex]
[tex]y_2=c^2-4x^2[/tex]
We have to find the value of c such that the are of the region bounded by the parabolas =32/3
[tex]y_1=y_2[/tex]
[tex]4x^2-c^2=c^2-4x^2[/tex]
[tex]4x^2+4x^2=c^2+c^2[/tex]
[tex]8x^2=2c^2[/tex]
[tex]x^2=c^2/4[/tex]
[tex]x=\pm \frac{c}{2}[/tex]
Now, the area bounded by two curves
[tex]A=\int_{a}^{b}(y_2-y_1)dx[/tex]
[tex]A=\int_{-c/2}^{c/2}(c^2-4x^2-4x^2+c^2)dx[/tex]
[tex]\frac{32}{3}=\int_{-c/2}^{c/2}(2c^2-8x^2)dx[/tex]
[tex]\frac{32}{3}=2\int_{-c/2}^{c/2}(c^2-4x^2)dx[/tex]
[tex]\frac{32}{3}=2[c^2x-\frac{4}{3}x^3]^{c/2}_{-c/2}[/tex]
[tex]\frac{32}{3}=2(c^2(c/2+c/2)-4/3(c^3/8+c^3/28))[/tex]
[tex]\frac{32}{3}=2(c^3-\frac{4}{3}(\frac{c^3}{4}))[/tex]
[tex]\frac{32}{3}=2(c^3-\frac{c^3}{3})[/tex]
[tex]\frac{32}{3}=2(\frac{2}{3}c^3)[/tex]
[tex]c^3=\frac{32\times 3}{4\times 3}[/tex]
[tex]c^3=8[/tex]
[tex]c=\sqrt[3]{8}=2[/tex]
When c=2 and when c=-2 then the given parabolas gives the same answer.
Therefore, value of c=-2, 2
What is the measurement of N?
Answer:
the measurement of N is D, 81.
Step-by-step explanation:
The angle measurement of a Right Angled Triangle is 90 degrees. And based off the angle dimension given in the image above ( 9 degrees ), you need to subtract 90 ( the angle dimension of the triangle) with the angle dimension given (9 degrees) which gets you to an answer of 81 degrees.
If you have time plz help me
Answer:
option 2 4x²- 8x -4 ghhhhhhhhhhj8
17. What is the solution to -7s=-35? (1 point)
Os=-6
Os=-5
Os = 5
Os=6
Answer:
(+5)=S , be the correct answer
Answer: s = +5
Step-by-step explanation: Since s is being multiplied by -7, to get s by itself, we need to divide by -7 on both sides of the equation.
So we get s = +5 which is the solution to our equation.
Student scores on exams given by a certain instructor have mean 74 and standard deviation 14. This instructor is about to give two exams, one to a class of size 25 and the other to a class of size 64.
Required:
a. Approximate the probability that the average test score in the class of size 25 exceeds 80.
b. Repeat part (a) for the class of size 64.
c. Approximate the probability that the average test score in the larger class exceeds that of the other class by over 2.2 points.
Answer:
a) Hence the probability that the average test score in the class of size 25 exceeds 80.
P ( X > 74) = 0.9838
P ( Z > 2.14) = 0.0162
b) Hence the probability that the average test score for the class of size 64
P ( X > 74) = 0.9838
P ( Z > 2.14) = 0.0003
c) Probability of the difference exceeding 2.2 = 0.9936
P (Z < 2.49) = 0.0064
Step-by-step explanation:
Let's assume a normal distribution.
Now,
a) For a class of 25
[tex]P ( X > 74) = P (Z > 80 - 74/ 14\sqrt(25) )\\\\= P (Z < 6 / 2.8)\\\\= P ( Z < 2.14)\\= 0.9838\\[/tex]
[tex]P ( Z > 2.14) = 1- 0.9838\\= 0.0162[/tex]
b)
Similarly:
For the class of 64
[tex]P ( X > 74) = P (Z > 80 - 74/ 14\sqrt(64) )\\\\= P (Z < 6 / 1.75)= P ( Z < 3.428)\\= 0.9838\\[/tex]
[tex]P ( Z > 2.14) = 1- 0.9997\\= 0.0003[/tex]
c) Probability of the difference exceeding 2.2
[tex]= P (Z > 2.2/\sqrt{14 * {(1/25) + (1/64}\\[/tex]
[tex]= P (Z > 2.49)\\= 0.9936[/tex]
P (Z < 2.49)
= 1 - 0.9936
= 0.0064
Betty received $ 500,000 from a life insurance policy to be distributed to her as an annuity certain in 10 equal annual installments with the first payment made immediately. On the day she receives her third payment, she is offered a monthly perpetuity of X in lieu of the future annual payments. The first payment will be made in exactly one month. The effective annual rate of interest is 8 %. Determine the value of X.
9514 1404 393
Answer:
annual payment: $68,995.13monthly payment in perpetuity: X = $2394.76Step-by-step explanation:
a) For payments made at the beginning of the period, the annuity is called an "annuity due." The formula in the first attachment tells how to compute the payment for a given present value ($500,000), number of periods (N=10), and interest rate (i=0.08).
pmt = $500,000/(1 +(1 -(1 +i)^(-N+1))/i) = $500,000/(1 +(1 -(1.08^-9))/.08)
pmt ≈ $68,995.13 . . . . annual payment
__
b) After the first payment, the account balance is ...
$500,000 -68,995.13 = $431,004.87
After subsequent payments, the account balance will be ...
$431,004.87×1.08 -68,995.13 = $396,490.13 . . . after 2nd payment
$396,490.13×1.08 -68,995.13 = $359,214.21 . . . after 3rd payment
The payment amount that can be made in perpetuity is the amount of the monthly interest on this balance:
X = $359,214.21 × (0.08/12) = $2394.76
whats 2 plus 2
*just trying to help someone get points* :)
Answer:4 ma boi
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
because I am god at meth and very smart
The winter group provides tax advice
what? ;-;.............
ASAP PLSSS!!!!!!!!!!1!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: i think its the last one bc if you multiply 9 and 3 in its gets you 18
Step-by-step explanation:
Answer:
V=(1/3)πr²h
v=
[tex] \frac{1}{3} \times {3}^{2} \times 9 \times \pi \\ = 27\pi[/tex]
27pi in³
27pi in³First option
Brainliest please~
If h(x) = −3x − 10, find h(−3). (1 point)
Answer:
h(- 3) = - 1
Step-by-step explanation:
Substitute x = - 3 into h(x) , that is
h(- 3) = - 3(- 3) - 10 = 9 - 10 = - 1
Regarding the violation of multicollinearity, which of the following description is wrong?
Complete question is;
Regarding the violation of multicollinearity, which of the following description is wrong?
a. It changes the intercept of the regression line.
b. It changes the sign of the slope.
c. It changes the slope of the regression line.
d. It changes the value of F-tests.
e. It changes the value of T-tests
Answer:
a. It changes the intercept of the regression line
Step-by-step explanation:
Multicollinearity is a term used in multiple regression analysis to show a high correlation between independent variables of a study.
Since it deals with independent variables correlation, it means it must be found before getting the regression equation.
Now, looking at the options, the one that doesn't relate with multicollinearity is option A because the intercept of the regression line is the value of y that is predicted when x is 0. Meanwhile, multicollinearity from definition above does in no way change the intercept of the regression line because it doesn't predict the y-value when x is zero.
Please helpppppp me!!!!!!!!
Answer:
A --> y=cot(x)
Step-by-step explanation:
if you graph tan(x), it has a period of just PI, because tan(x) is just sin(x)/cos(), and cot(x) is the same because it is just sec(x)/csc(x).
a rice cooker was sold for $60 after a discount of 60% waht was the usual price of the rice cooker with explaination simple method for class 5
Answer:
$150
Step-by-step explanation:
So, 60 dollars is 40% of the original price. So 30 dollars is 20% of the original price, and 150 dollars is 100% of the original price. So, the original value of the rice cooker is 150 dollars.
Answer:
The price of the Rice Cooker was 150$.
Step-by-step explanation:
So if you buy an item at $150 with 60% discounts, you will pay $60 and get 90 cashback rewards ... interest per annum, dollars, pounds, coupons,60% off, 60% of price or something, we ... For example 5% of 20, which is the same thing as fraction x/100 * 20=5%. ... Formula and equation for % of something or whole numbers.
.
you invested $
7000
7000
between two accounts payin
6
%
6
%
and
8
%
8
%
annual interet, respectively. if the total interest earned for the year was $
480
,
480
,
how much was invested at each rate
9514 1404 393
Answer:
$3000 at 8%$4000 at 6%Step-by-step explanation:
Let x represent the amount invested at 8%. Then the total interest earned is ...
0.06(7000 -x) +0.08x = 480
420 +0.02x = 480 . . . . . . . . . eliminate parentheses
0.02x = 60 . . . . . . . . . . subtract 420
x = 60/0.02 = 3000 . . . . . divide by the coefficient of x
$3000 was invested at 8%; $4000 was invested at 6%.
How does the rate of change of f(x)=3x+5 compare to the rate of change of g(x)=2x+5 ?
HELP I NEED ANSWERS
Answer:
The rate of change of f(x) is faster than the rate of change of g(x).
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
*Note:
Rate of Change is determined by slope.
Step 1: Define
f(x) = 3x + 5
↓ Compare to y = mx + b
Slope m = 3
g(x) = 2x + 5
↓ Compare to y = mx + b
Slope m = 2
Step 2: Answer
We can see that the slope of f(x) is greater than g(x).
∴ the rate of change of f(x) would be greater than g(x).
A humanities professor assigns letter grades on a test according to the following scheme.
A: Top 8% of scores
B: Scores below the top 8% and above the bottom 62%
C: Scores below the top 38% and above the bottom 18%
D: Scores below the top 82% and above the bottom 9%
E: Bottom 9% of scores Scores on the test are normally distributed with a mean of 67 and a standard deviation of 7.3.
Find the numerical limits for a C grade.
Answer:
The numerical limits for a C grade are 60.6 and 69.1.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Scores on the test are normally distributed with a mean of 67 and a standard deviation of 7.3.
This means that [tex]\mu = 67, \sigma = 7.3[/tex]
Find the numerical limits for a C grade.
Below the 100 - 38 = 62th percentile and above the 18th percentile.
18th percentile:
X when Z has a p-value of 0.18, so X when Z = -0.915.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.915 = \frac{X - 67}{7.3}[/tex]
[tex]X - 67 = -0.915*7[/tex]
[tex]X = 60.6[/tex]
62th percentile:
X when Z has a p-value of 0.62, so X when Z = 0.305.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.305 = \frac{X - 67}{7.3}[/tex]
[tex]X - 67 = 0.305*7[/tex]
[tex]X = 69.1[/tex]
The numerical limits for a C grade are 60.6 and 69.1.
what is the percent decrease on a Tv that has been marked down from $550 to $420? round to the nearest tenth
The percent decrease on a TV after the markdown to the nearest tenth is 23.6%.
What is the percent decrease on the TV after the markdown?The percent decrease formula can be expressed as:
Percent decrease = [( original value - new value ) / original value ] × 100%
Given the data in the question:
The original value of the TV = $550
New value after markdown = $420
Percent decrease =?
Plug the given values into the above formula and solve for the percent decrease.
Percent decrease = [( original value - new value ) / original value ] × 100%
Percent decrease = [( 550 - 420 ) / 550 ] × 100%
Percent decrease = [ 130 / 550 ] × 100%
Percent decrease = 0.2363 × 100%
Percent decrease = 23.6%
Therefore, the percent decrease is 23.6%.
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According to the scale drawing, how wide will the actual patio be?
m
Garden
Patio
7 cm
Scale 1 cm: 2 m
The width of the actual garden patio according to the scale drawing is 14 meters.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.
Given the scale of 1 cm : 2 m
For a patio of 7 cm, then:
Actual patio = 7 cm / (1 cm/ 2m) = 14 m
The width of the actual garden patio according to the scale drawing is 14 meters.
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For the rational function f(x)=5−xx2+5x+6, find the points on the graph at the function value f(x)=3.
Given:
The rational function is:
[tex]f(x)=\dfrac{5-x}{x^2+5x+6}[/tex]
To find:
The points on the graph at the function value [tex]f(x)=3[/tex].
Solution:
We have,
[tex]f(x)=\dfrac{5-x}{x^2+5x+6}[/tex]
Substituting [tex]f(x)=3[/tex], we get
[tex]3=\dfrac{5-x}{x^2+5x+6}[/tex]
[tex]3(x^2+5x+6)=5-x[/tex]
[tex]3x^2+15x+18=5-x[/tex]
Moving all the terms on one side, we get
[tex]3x^2+15x+18-5+x=0[/tex]
[tex]3x^2+16x+13=0[/tex]
Splitting the middle term, we get
[tex]3x^2+3x+13x+13=0[/tex]
[tex]3x(x+1)+13(x+1)=0[/tex]
[tex](3x+13)(x+1)=0[/tex]
Using zero product property, we get
[tex](3x+13)=0\text{ or }(x+1)=0[/tex]
[tex]x=-\dfrac{13}{3}\text{ or }x=-1[/tex]
Therefore, the required values are [tex]-\dfrac{13}{3},-1[/tex].
Find the x and y intercepts and graph 2x − y = −8
Answer:
-2
Step-by-step explanation:
2x-y=-8-1equation
2x=-8+y
x=-8+y -2equation
2
then, taking 1st equation;
2x-y=-8
2(-8+y/2)-y=-8
-16+2y-y=-8
4
-16+2y-4y=-8
4
-16-2y=-8*4
-2y=-32+16
y=-16/-2
y=4
for x
x=-8+y
2
x=-8+4
2
x=-4
2
x=-2
Find the measure for rus
Answer:
90
Step-by-step explanation:
39+23+28=90
180-90=90
what is the area of this whole shape
Answer:
104 m²
Step-by-step explanation:
Area of the whole shape = area of the triangle + area of the rectangle
= ½*b*h + L*W
Where,
b = 8 m
h = 6 m
L = 10 m
W = 8 m
Plug in the values into the equation
Area of the whole shape = ½*8*6 + 10*8
= 24 + 80
= 104 m²
Find the probability of a couple having at least 1 girl among 4 children. Assume that boys and girls are
equally likely and that the gender of a child is independent of the gender of any brothers or sisters.
Answer:
15/16 (93.75%)
Step-by-step explanation:
List of Possible Combinations:
BBBB, BBBG, BBGB, BBGG, BGBB, BGBG, BGGB, BGGG, GBBB, GBBG, GBGB, GBGG, GGBB, GGBG, GGGB, GGGG
As you can see, only 1 out of 16 of the possible combinations is all boys. This means that the chance of at least 1 girl among the 4 children is 15 out of 16 (15/16) or 93.75%
Solve 5 to x-4 power =7
Answer:The value of x is 4.
Step-by-step explanation:
Given : Expression .
To find : Solve for x ?
Solution :
Applying exponential property,
Comparing the base,
Step-by-step explanation:
Directions: Use the figure to write the symbol for each.
1. I ray
2. a plane
А
3. 3 points
4. 2 lines
5. 3 angles
6. 3 line segments
D
Geometry
156
Total Math Grade 6
I need help ASAP please due tomorrow 6th grade geometry
5 = –6x2 + 24x
5 = –6(x2 – 4x)
inside the parentheses and
.
–19 = –6(x – 2)2
StartFraction 19 Over 6 EndFraction = (x – 2)2
Plus or minus StartRoot StartFraction 19 Over 6 EndFraction EndRoot = x – 2
The two solutions are
Plus or minus StartRoot StartFraction 19 Over 6 EndFraction EndRoot.
Answer:
x = 2 - sqrt(19/6)
x = 2 + sqrt(19/6)
Step-by-step explanation:
Answer:
add 4
subtract 24 from 5
2
Step-by-step explanation:
The work done by a machine in 2 minutes is 480J. Calculate the power of the machine
Answer:
I think the power is 4
Step-by-step explanation:
480J / 120 = 4
Put 2 mins into seconds which is 120 seconds
Sorry if it is wrong :)
Answer:
[tex]4\text{ watts}[/tex]
Step-by-step explanation:
In physics, the power of a machine is given by [tex]P=\frac{W}{\Delta t}[/tex], where [tex]W[/tex] is work in Joules and [tex]\Delta t[/tex] is time in seconds.
Convert 2 minutes into seconds:
2 minutes = 120 seconds.
Substitute [tex]W=480[/tex] and [tex]\Delta t=120[/tex] to solve for [tex]P[/tex]:
[tex]P=\frac{480}{120}=\boxed{4\text{ watts}}[/tex]
I need help i don't get it !!!!!
Answer:
4
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 30 = x/8
8 sin 30 =x
8 (1/2) = x
4
Answer:
The answet is A. 4
Step-by-step explanation: