Answer:
x< -3 and 0 < x < 4
Step-by-step explanation:
x^3 – x² <12x
Subtract 12x from each side
x^3 -x^2 - 12x< 0
Factor
x( x^2 -x-12) <0
Factor
x( x-4) ( x+3) < 0
Using the zero product property
x=0 x=4 x=-3
We have to check the signs regions
x < -3
-( -) (-) < 0 True
-3 to 0
-( -) (+) < 0 False
0 to 4
+( -) (+) < 0 True
x>4
+( +) (+) < 0 False
The regions this is valid is
x< -3 and 0 < x < 4
Find the surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder x225+y29=1
Correct question is;
Find the surface area of that part of the plane 10x + 7y + z = 4 that lies inside the elliptic cylinder x²/25 + y²/9 = 1
Answer:
A(S) = 15π√150
Step-by-step explanation:
We are given;
10x + 7y + z = 4
Making z the subject, we have;
z = 4 - 10x - 7y
Now, area of the surface as part of z = f(x, y) is;
A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA
From z = 4 - 10x - 7y,
∂f/∂x = -10
∂f/∂y = -7
Thus;
A(S) = ∫∫√[(-10)² + (-7)² + 1]dA
A(S) = √150 ∫∫dA
Where ∫∫dA is the elliptical cylinder
From the general form of an area enclosed by an ellipse with the formula;
x²/a² + y²/b² = 1 and comparing with
x²/25 + y²/9 = 1, we have;
a = 5 and b = 3
So, area of elliptical cylinder = πab
Thus;
A(S) = √150 × π(5 × 3)
A(S) = 15π√150
The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder [tex]\dfrac{x^2}{25}+\dfrac{y^2}{9}=1[/tex] is [tex]15\pi\sqrt{150}[/tex] and this can be determined by using the given data.
Given :
10x + 7y + z = 4 ---- (1)[tex]\dfrac{x^2}{25}+\dfrac{y^2}{9}=1[/tex] --- (2)Equation (1) can also be written as:
z = 4 - 10x - 7y ---- (3)
The surface area is given by the equation:
[tex]\rm A(s) = \int \int \sqrt{(\dfrac{\delta f}{\delta x})^2+(\dfrac{\delta f}{\delta y})^2+1}\;dA[/tex] --- (4)
[tex]\dfrac{\delta f}{\delta x} = -10[/tex]
[tex]\dfrac{\delta f}{\delta y} = -7[/tex]
Now, substitute the known values in the equation (4).
[tex]\rm A(s) = \int \int \sqrt{(10)^2+(7)^2+1}\;dA[/tex]
[tex]\rm A(s) = \sqrt{150} \int \int\;dA[/tex]
Now the area enclosed by an ellipse is given by:
[tex]\dfrac{x^2}{25}+\dfrac{y^2}{9}=1[/tex]
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
By comparing the above equation:
a = 5
b = 3
The area is given by:
[tex]\rm A(s)=\sqrt{150}\times \pi(5\times 3)[/tex]
[tex]\rm A(s) = 15\pi \sqrt{150}[/tex]
For more information, refer to the link given below:
https://brainly.com/question/11952845
What does the tape measure say Measurement # 3 is? *
Answer:
5 and 3/32 of an inch.
Solve the following equation using the square root property.
9x2 + 10 = 5
Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance using the given sample statistics.
Claim: p>0.12; α=0.05; Sample statistics: Modifying above p with caret equals 0.08, n is equal to 250
Answer:
There is no sufficient evidence to support the claim
Step-by-step explanation:
From the question we are told that
The level of significance is [tex]\alpha = 0.05[/tex]
The sample proportion is [tex]\r p = 0.08[/tex]
The sample size is [tex]n = 250[/tex]
Generally for normal sampling distribution can be used
[tex]n * p > 5[/tex]
So
[tex]n* p = 250 * 0.12 = 30[/tex]
Since
[tex]n * p > 5[/tex] then normal sampling distribution can be used
The null hypothesis is [tex]H_o : p = 0.12[/tex]
The alternative hypothesis is [tex]H_a : p > 0.12[/tex]
The test statistic is evaluated as
[tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1- p)}{n} } }[/tex]
substituting values
[tex]t = \frac{0.08 - 0.12 }{ \sqrt{ \frac{0.12 (1- 0.12)}{250 } } }[/tex]
[tex]t = -1.946[/tex]
The p-value is obtained from the z table and the value is
[tex]p-value = P(t > -1.9462) =0.97512[/tex]
Since the [tex]p-value > \alpha[/tex]
Then we fail to reject the null hypothesis
Hence it means there is no sufficient evidence to support the claim
solve 2root3+7root3
Answer:
(2+7) root 3 equals 9 root 3
Which geometric sequence has a first term equal to 55 and a common ratio of -5? {-55, 11, -2.2, 0.44, …} {55; 275; 1,375; 6,875; …} {55, 11, 2.2, 0.44, …} {55; -275; 1,375; -6,875; …}
Answer:
The answer is 55, -275, 1375, -6875......
Step-by-step explanation:
What is the measure of B, in degrees?
Answer:
B = 32
Step-by-step explanation:
Since this is an isosceles triangle, C is also equal to 74 degrees
the angles of a triangle add to 180
A + B+ C = 180
74+ B + 74 = 180
148 + B = 180
B = 180-148
B =32
A study was conducted to explore the effects of ethanol on sleep time. Fifteen rats were randomized to one of three treatments. Treatment 1 got only water (control). Treatment 2 got 1g of ethanol per kg of body weight, and treatment 3 got 2g/kg. The amount of REM sleep in a 24hr period was recorded, in minutes: Treatment 1: 63, 54, 69, 50, 72 Treatment 2: 45, 60, 40, 56 Treatment 3: 31, 40, 45, 25, 23, 28
A) Graph the data. Why did you choose the graph that you did and what does it tell you?B) Create an ANOVA table for the data using the formulas provided in class. C) Evaluate the ANOVA assumptions graphically. Was ANOVA appropriate here?D) Based on the ANOVA table, make a conclusion in the context of the problem.E) Create 95% CIs for all pairwise comparisons of means using the Tukey method.
Answer: Find answer in the attachment
Step-by-step explanation:
A laboratory tested n = 98 chicken eggs and found that the mean amount of cholesterol was LaTeX: \bar{x}x ¯ = 86 milligrams with σ = 7 milligrams. Find the margin of error E corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs.
Answer:
1.3859
Step-by-step explanation:
The formula for Margin of Error is given as:
Margin of Error = Critical value × Standard Error
Critical value = z score
In the question, we are given a confidence interval of 95%.
Z score for a 95% confidence level is given as: 1.96
Hence, critical value = 1.96
Standard Error = σ / √n
Where n = number of samples = 98 chicken eggs
σ = Standard deviation = 7 milligrams
Standard Error = 7/√98
Standard Error = 0.7071067812
Hence, Margin of Error = Critical value × Standard Error
Margin of Error = 1.96 × 0.7071067812
Margin of Error = 1.3859292911
Therefore, the margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is approximately 1.3859
What is the critical F value when the sample size for the numerator is seven and the sample size for the denominator is six
Answer:
Critical F value = 4.9503
Step-by-step explanation:
Given that:
The sample size of the numerator = 7
The sample size of the denominator = 6
The degree of freedom for the numerator df = n -1
The degree of freedom for the numerator df = 7 - 1
The degree of freedom for the numerator df = 6
The degree of freedom for the denominator df = n - 1
The degree of freedom for the denominator df = 6 - 1
The degree of freedom for the denominator df = 5
The assume that the test is two tailed and using a level of significance of ∝ = 0.10
The significance level for the two tailed test = 0.10/2 = 0.05
From the standard normal F table at the level of significance of 0.05
Critical F value = 4.9503
Write the expression (x4)8 in simplest form.
Answer:
the 4 and 8 are exponents
Step-by-step explanation:
Find the 14th term in the sequence 1, 1/3, 1/9, … Find the sum of the first 10 terms of the sequence above.
Answer:
This is a geometric progresion that begins with 1 and each term is 1/3 the preceeding term
Let Pn represent the nth term in the sequence
Then Pn = (1/3)^n-1
From this P14 = (1/3)^13 = 1/1594323
5. The sum of the first n terms of a GP beginning a with ratio r is given by
Sn = a* (r^n+1 - 1)/(r - 1)
With n = 10, a = 1 and r = 1/3, S10 = ((1/3)^11 - 1)/(1/3 - 1) = 1.500
(12x^(2)+x-35)-:(4x+17)
Answer:
(3x-5)(4x+7) / 4x + 17
Step-by-step explanation:
Rewrite the division as a fraction
12 x ^2 + x-35 / 4x+17
Factor by grouping
(3x-5)(4x+7) / 4x + 17
Hope this was the answer you were looking for
ASAP
Which of the following factors determine a plane? A. line and a point on the line B. two lines C. a straight line D. a line and a point not on that line
Answer:
D. a line and a point not on that line
Step-by-step explanation:
That is how you determine a plane.
The factors which determine a plane are a line and a point not on that line.
What is plane ?
In geometry, a plane is a flat surface that extends into infinity.
In a three dimensional space, a plane can be defined by three points it contains, as long as those points are not on the same line.
Therefore, the factors which determine a plane are a line and a point not on that line.
Hence, option D is correct.
Learn more about plane here:
https://brainly.com/question/17458011
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Two numbers, if the first one increases by 1, and the second one decreases by 1, then their product increases by 2020. If the first number decreases by 1, and the second one increases by 1, what value does the product decrease?
Answer:
The product decreases 2022.
Step-by-step explanation:
(x + 1)(y - 1) = xy + 2020
xy - x + y - 1 = xy + 2020
-x + y = 2021
(x - 1)(y + 1) = xy + x - y - 1
+ 2021 = -x + y
----------------------------------
(x - 1)(y + 1) + 2021 = xy - 1
(x - 1)(y + 1) = xy - 2022
The product decreases 2022.
Please help me with this question
Answer:
0 ≤ x ≤ 10
Step-by-step explanation:
The domain of f(x) is the set of values of x for which the function is defined. Here, the square root function is only defined for non-negative arguments, so we require ...
-x^2 +10x ≥ 0
x(10 -x) ≥ 0
The two factors in this product will both be positive only for values ...
0 ≤ x ≤ 10 . . . . the domain of f(x)
Please Help! The point (8, -2) satisfies the equation of which line? (1) y+2=2(x+8) (2) y-2=2(x-8) (3) y+2=2(x-8) (4) y-2=2(x+8)
Answer:
(3) y+2=2(x-8)
Step-by-step explanation:
Substitute the point into the equation and see if it is true
(8,-2)
(1) y+2=2(x+8)
-2+2 = 2(8+8)
0 = 2(16)
False
(2) y-2=2(x-8)
-2-2 = 2(8-8)
-4 =2 (0)
False
(3) y+2=2(x-8)
-2+2 = 2( 8-8)
0 = 2(0)
True
(4) y-2=2(x+8)
-2-2 = 2(8+8)
-4 = 2(16)
False
Answer:
[tex]\boxed{y+2=2(x-8) }[/tex]
Step-by-step explanation:
[tex]x=8[/tex]
[tex]y=-2[/tex]
[tex]\sf Check \ the \ third \ option.[/tex]
[tex]-2+2=2(8-8)[/tex]
[tex]\sf Both \ sides \ must \ be \ equal.[/tex]
[tex]0=2(0)[/tex]
[tex]0=0[/tex]
7 1/4 x−x=9 3/8 HELLLLPPPPP PLLSSSS
-1.5
Step-by-step explanation:
So, you do 7.25 - 1 (because it is) and you get 6.25. Make it a fraction inton 25/4 and divide bu 75/8 (9 3/8 simplified) and you get -1.5 voila.
Answer:
x = 3/2
Step-by-step explanation:
7 1/4 = 7 + 1/4 = 28/4 + 1/4 = 29/4
9 3/8 = 9 + 3/8 = 72/8 + 3/8 = 75/8
then:
7 1/4 x = 29x/4
29x/4 - x = 75/8
29x/4 - 4x/4 = 75/8
25x/4 = 75/8
x = (75/8)/(25/4)
x = (75*4)/(8*25)
x = 300/200
x = 3/2
Checking:
(29/4)(3/2) = (29*3)(4*2) = 87/8
87/8 - 3/2 = 75/8
3/2 = 12/8
then:
87/( - 12/8 = 75/8
find the derivative by using product rule and distribution
pls help quickly and show work
Answer:
Below
Step-by-step explanation:
First method:
● f(x)= (x^3-2x+1)×(x-3)
● f'(x)= (x^3-2x+1)' ×(x-3) + (x^3-2x+1)×(x-3)'
●f'(x)= (3x^2-2)×(x-3) + (x^3-2x+1) × 1
●f'(x) = 3x^3-9x^2-2x+6 + x^3-2x+1
● f'(x)= 4x^3-9x^2-4x+7
■■■■■■■■■■■■■■■■■■■■■■■■■■
Second method:
●f(x) = (x^3-2x+1)×(x-3)
●f(x) = x^4-3x^3 -2x^2+6x+x-3
●f(x) = x^4-3x^3-2x^2+7x-3
●f'(x) = 4x^3-9x^2-4x+7
We got the same result using both methods.
How to simplify this expression??
Answer :
[tex] \frac{2 {x}^{3} + 7 {x}^{2} + 3x - 4}{ {x}^{3} + 3 {x}^{2} + x - 1} [/tex]
Step-by-step-explanation :
I did the explanation in the picture.
Use Lagrange multipliers to find three numbers whose sum is 30 and the product P = x3y4z is a maximum. Choose the answer for the smallest of the three values. Question 20 options: a) 21/4 b) 5 c) 15/4 d) 3
We want to maximize [tex]x^3y^4z[/tex] subject to the constraint [tex]x+y+z=30[/tex].
The Lagrangian is
[tex]L(x,y,z,\lambda)=x^3y^4z-\lambda(x+y+z-30)[/tex]
with critical points where the derivatives vanish:
[tex]L_x=3x^2y^4z-\lambda=0[/tex]
[tex]L_y=4x^3y^3z-\lambda=0[/tex]
[tex]L_z=x^3y^4-\lambda=0[/tex]
[tex]L_\lambda=x+y+z-30=0[/tex]
[tex]\implies\lambda=3x^2y^4z=4x^3y^3z=x^3y^4[/tex]
We have
[tex]3x^2y^4z-4x^3y^3z=x^2y^3z(3y-4x)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}\\z=0,\text{ or}\\3y=4x\end{cases}[/tex]
[tex]3x^2y^4z-x^3y^4=x^2y^4(3z-x)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}\\3z=x\end{cases}[/tex]
[tex]4x^3y^3z-x^3y^4=x^3y^3(4z-y)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}4z=y\end{cases}[/tex]
Let's work with [tex]x=3z[/tex] and [tex]y=4z[/tex], for which we have
[tex]x+y+z=8z=30\implies z=\dfrac{15}4\implies\begin{cases}x=\frac{45}4\\y=15\end{cases}[/tex]
The smallest of these is C. 15/4.
Hi Mathies, Help with this vectors excercise pls. Givan that OA (segment) = 13x+7y , OB = 5x+12y and CO = -15+12y write down each of the following vectors in its simplest form a) BA = 8x+ 5y (l got it, i ve done it) b) AC= ?? i cant find vector AC thanks in advance
Answer:
AC = 2x-19yStep-by-step explanation:
Given vector the following vector equations OA = 13x+7y , OB = 5x+12y and CO = -15x+12y, the following expression is true about vector OA, OB and OC;
OA+OB = CO (CO is the resultant since its is moving in the opposite direction compare to OA and OB)
Also BO+OA = BA and AO+OC = AC
If OB = 5x+12y, then BO = -(5x+12y)
BO = -5x-12y (BO = -OB)
Since BO+OA = BA
BA = -5x-12y + 13x+7y
BA = -5x+13x-12y+7y
BA = 8x-5y
Similarly AO+OC = AC
Since AO = -OA and OC = -CO
-OA-CO = AC
AC = -(13x+7y)-(-15x+12y)
AC = -13x-7y+15x-12y
AC = -13x+15x-7y-12y
AC = 2x-19y
Please help. I’ll mark you as brainliest if correct!
Answer:
Children = 150
Students = 98
Adults = 75
Step-by-step explanation:
C + S + A = 323
5C + 7S + 12A = 2336
A = 1/2C
C = 150
S = 98
A = 75
In a certain state 22% of secondary school students study a foreign language. A group of 100 students were selected in random sample and 24 of them study a foreign language. In this example: a: What is population? b: What is the value of the proportion p1? c: What is the value of the sample proportion p2？
Answer: a. population = "All Students"
b. 0.22
c. 0.24
Step-by-step explanation:
a. Population is the largest group of individuals having same characteristics by the researcher's point of view.
Here , the interest is "Students study foreign language"
So, population = "All Students"
b. Let p be the pro[portion of secondary school students study a foreign language.
In a certain state 22% of secondary school students study a foreign language.
The value of proportion [tex]p_1[/tex] =- 0.22
c. A group of 100 students were selected in random sample and 24 of them study a foreign language.
The value of proportion [tex]p_2=\dfrac{24}{100}=0.24[/tex]
The letters x and y represent rectangular coordinates. Write the given equation using polar coordinates (r,θ) . Select the correct equation in polar coordinates below.
x2+y2−4x=0
a. r=4 sinθ
b. r=4 cosθ
c. r cos2θ=4 sinθ
d. r sin2θ=4 cosθ
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
PLEASE ANSWER ASAP!!!
Equation in the picture
Solve for r in the equation in the picture. You must use the LCD (Least Common Denominator) to simplify. You can also use cross products to solve.
Must show work
A. r = 19
B. r = 21
C. r = 25
D. r = 30
any unrelated answer will be reported
Answer:
r = 19
Step-by-step explanation:
( r-5) /2 = ( r+2) /3
The least common denominator is 6
3/3 *( r-5) /2 = ( r+2) /3 * 2/2
3( r-5) /6 = 2( r+2) /6
Since the denominators are the same, the numerators are the same
3( r-5) = 2(r+2)
Distribute
3r -15 = 2r+4
Subtract 2r from each side
3r-2r -15 = 2r+4-2r
r-15 =4
Add 15 to each side
r-15+15 = 4+15
r = 19
On a class trip with 40 students, 14 are male. What percentage of the class is female?
66%
60%
65%
58%
Answer:
65%
Step-by-step explanation:
If 14 are male, then 26 are female.
To find the percent female, divide the number of females by the total.
26/40 = 0.65
So, the percentage of the class that is female is 65%
Answer:
C. 65%
Step-by-step explanation:
We know that of the 40 total students, 14 are male, which means the remaining students are female.
To find how many are female, we subtract 14 from 40:
40 - 14 = 26 females
Percentage is simply a part divided by a whole, multiplied by 100. Here, the "part" is the number of females, which is 26. The "whole" is the total number of students, which is 40. So, we have:
(26 / 40) * 100 = 65
The answer is thus C, 65%.
~ an aesthetics lover
What is meant by the term "90% confident" when constructing a confidence interval for a mean? Group of answer choices
Answer:
The question is not complete, below is the complete question:
What is meant by the term 90% confident? when constructing a confidence interval for a mean?
a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.
b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.
c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.
d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.
Answer:
The correct answer is:
If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean. (c)
Step-by-step explanation:
a 90% confidence level means that if repeated samples were taken, 9 out of 10 times, the confidence intervals of the sample chosen will be close to the mean (true value), which is a true representation of the population parameter. when using confidence intervals, there are always margins of allowable accuracy, and this is suggested by using standard diviations snd variances.
I attached a simple document to this answer that will give you more insight into confidence intervals used in statistics.
Working together, it takes two computers 10 minutes to send out a company's email. If it takes the slower computer 50 minutes to do the job on its own, how long will it take the faster computer to do the job on its own? don't round
Answer:
12.5 minutes
Step-by-step explanation:
When working together,It takes two computers 10 minutes to send out an email
It takes the slower computer 50 minutes to send out an email
Let x represent the time taken by the faster computer to do the job in its own
Therefore, the time required by the faster computer can be calculated as follows
1/x + 1/50= 1/10
Collect the like terms
1/x= 1/10-1/50
1/x= 4/50
Cross multiply both sides
4 × x = 50×1
4x=50
Divide both sides by the coefficient of x which is 4
4x/4=50/4
x= 12.5
Hence the time taken by the faster computer to finish the job on its own is 12.5 minutes
Today only, a suit is being sold at a 26% discount. The sale price is $259.
What was the price yesterday?
Answer:
$350
Step-by-step explanation:
1. Set up the equation. The sale price of $259 is 74% of the original price.
[tex]\frac{74}{100}[/tex] = [tex]\frac{259}{x}[/tex]
2. Cross multiply
74x = 25900
3. Solve
x = 350
