Answer:
[tex]-\frac{77}{24}[/tex]
Step-by-step explanation:
1. rewrite the equation in standard form: [tex]4\cdot \frac{3}{2}\left(y-\left(-\frac{41}{24}\right)\right)=\left(x-\left(-\frac{3}{2}\right)\right)^2[/tex]
2. find (h,k), the vertex. the vertex is [tex]\left(h,\:k\right)=\left(-\frac{3}{2},\:-\frac{41}{24}\right)[/tex]
3. find the 'focal length' of the parabola - the focal length is the distance between the vertex and the focus. from the vertex we can see that the focal length, p, = 3/2
4. Parabola is symmetric around the y-axis and so the asymptote is a line parallel to the x-axis, a distance p from the [tex]\left(-\frac{3}{2},\:-\frac{41}{24}\right)[/tex] y coordinate which is at [tex]-\frac{41}{24}\right)[/tex]. Set up the equation:
[tex]y=-\frac{41}{24}-p[/tex]
5. substitute and solve:
[tex]y=-\frac{41}{24}-\frac{3}{2}[/tex]
[tex]y = -\frac{77}{24}[/tex]
hope this helps, ask me questions if you still don't understand.
Use cylindrical shells to find the volume of the solid generated when the region
R under y = x2 over the interval (0,2) revolved about the line y = -1
Answer:
[tex]\displaystyle V = \frac{176 \pi}{15}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsExpandingFunctionsFunction NotationGraphingExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Integrals
Definite IntegralsArea under the curveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Shell Method:
[tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]
[Shell Method] x is the radius[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is the volumeStep-by-step explanation:
Step 1: Define
Identify
Graph of region
y = x²
x = 2
y = 4
Axis of Revolution: y = -1
Step 2: Sort
We are revolving around a horizontal line.
[Function] Rewrite in terms of y: x = √y[Graph] Identify bounds of integration: [0, 4]Step 3: Find Volume Pt. 1
[Shell Method] Find distance of radius x: [tex]x = y + 1[/tex][Shell Method] Find circumference variable f(x) [Area]: [tex]\displaystyle f(x) = 2 - \sqrt{y}[/tex][Shell Method] Substitute in variables: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - \sqrt{y})} \, dy[/tex][Integral] Rewrite integrand [Exponential Rule - Root Rewrite]: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - y^\bigg{\frac{1}{2}})} \, dy[/tex][Integral] Expand integrand: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(-y^\bigg{\frac{3}{2}} + 2y - y^\bigg{\frac{1}{2}} + 2)} \, dy[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle V = 2\pi \bigg( \frac{-2y^\bigg{\frac{5}{2}}}{5} + y^2 - \frac{2y^\bigg{\frac{3}{2}}}{3} + 2y \bigg) \bigg| \limits^4_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle V = 2\pi (\frac{88}{15})[/tex]Multiply: [tex]\displaystyle V = \frac{176 \pi}{15}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
suppose you borrow $1000 for 3 years and you owe $200 interest. what is the interest rate?
Answer:
6.67%
Step-by-step explanation:
By question I borrow $1000 for 3 years and I owe $200 interest . We can use the formula of Simple Interest as ,
[tex]\implies SI =\dfrac{ P*R*T}{100}[/tex]
Plug in the values .[tex]\implies \$200 =\dfrac{3*\$1000*R }{100}\\\\\implies R = \dfrac{ \$ 200 * 100}{3*\$ 1000} \\\\\implies\underline{\underline{ R = 6.67 \%}} [/tex]
100 POINTS PLEASE HELP ON HW
Answer:
Solution given:
f(x)=x²
g(x)=x+5
h(x)=4x-6
now
23:
(fog)(x)=f(g(x))=f(x+5)=(x+5)²=x²+10x+25
24:
(gof)(x)=g(f(x))=g(x²)=x²+5
25:
(foh)(x)=f(h(x))=f(4x-6)=(4x-6)²=16x²-48x+36
26:
(hof)(x)=h(f(x))=h(x²)=4x²-6
27;
(goh)(x)=g(h(x))=g(4x-6)=4x-6+5=4x-1
28:
(hog)(x)=h(g(x))=h(x+5)=4(x+5)-6=4x+20-6=4x-14
Answer:
the answer is 4x - 4
Step-by-step explanation:
Mac is about to sue his contractor who promised to install a water tank that holds 260 gallons of water. Mac knows that 260 gallons is the capacity of a tank that
holds 35 cubic feet. The cylindrical tank has a radius of 2 feet and height of 2 feet 6 inches. Does the evidence indicate Mac can win the case against the contractor
if it goes to court
Does the evidence indicate Mac can win the case against the contractor if it goes to court?
Please hello :)
Answer:
Yes
Step-by-step explanation:
volume of cylinder = πr²h
volume = (3.14)(2 ft)²(2.5 ft)
volume = 31.4 ft³
The volume of the cylinder that was built is 31.4 ft³. It should have been 35 ft³. The evidence helps Mac in court.
Assume that there is a 8% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive?
Answer:
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
Step-by-step explanation:
For each disk, there are only two possible outcomes. Either it works, or it does not. The probability of a disk working is independent of any other disk, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Assume that there is a 8% rate of disk drive failure in a year.
So 100 - 8 = 92% probability of working, which means that [tex]p = 0.92[/tex]
Two disks are used:
This means that [tex]n = 2[/tex]
What is the probability that during a year, you can avoid catastrophe with at least one working drive?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.92)^{0}.(0.08)^{2} = 0.0064[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0064 = 0.9936[/tex]
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
expand and simplify (x-2)(x+5)(2x-1)
Answer:
simplified: 2x^3+5x^2-23x+10
Step-by-step explanation:
Sumas y restas
W+y=9
3W-y=11
Answer:
w = 5
y = 4
Step-by-step explanation:
w + y = 9
3w - y = 11 ( + )
________
4w + 0 = 20
4w = 20
w = 20 / 4
w = 5
Substitute w = 5 in eq. w + y = 9,
w + y = 9
5 + y = 9
y = 9 - 5
y = 4
The perimeter of an equilateral triangle is 126mm.
State the length of one of its sides.
Explanation:
Divide 126 over 3. This is because any equilateral triangle has all three sides the same length
126/3 = 42
Each side is 42 mm long
So its perimeter is 3*42 = 126 mm
Side note: if your teacher says a triangle is equiangular, then it's automatically equilateral as well (and vice versa).
The length of one of its sides of an equilateral triangle is 42 mm.
What is equilateral triangle?In geometry, an equilateral triangle exists as a triangle that contains all its sides equivalent in length. Since the three sides stand equivalent therefore the three angles, opposite to the equivalent sides, stand equivalent in measure. Thus, it stands also named an equiangular triangle, where each angle measure 60 degrees.
The perimeter of an equilateral triangle exists 126 mm.
The equilateral triangle contains all three sides of the same length
126/3 = 42
Each side stands 42 mm long
So its perimeter stands 3 [tex]*[/tex] 42 = 126 mm
Therefore, the length of one of its sides = 42 mm.
To learn more about equilateral triangle
https://brainly.com/question/1399707
#SPJ2
The sample mean, x , is a statistic.
True or False
Answer:
True
Step-by-step explanation:
The statistic is a numerical value which describes the characteristic of a particular sample data. The sample is a set of data which represents a smaller subset randomly selected from the population or a larger dataset.
The sample mean, refers to the mean or average value of a sample data, therefore, a sample mean is a numerical characteristic of the sample dataset and it is therefore a statistic. On the other hand, numerical characteristics of a population data is called the parameter.
How do you solve this problem and what did you do to gain the answer 1/64+5/8-3/32=?
Answer:
the answer is 35/64(in fraction) but in decimals it's 0.55
The graph below represents the distance of a dog from a trainer after a command is given.
Which statement could describe the dog’s movement 5 seconds after the command was given?
The dog stopped to lie down and obey the trainer’s command.
The dog was running towards the trainer to receive a treat.
The dog was running away from the trainer to chase a squirrel.
The dog was stopped but began running towards the trainer.
Answer:
.
Step-by-step explanation:
What is the midpoint of the segment shown below?
10
A. (5,-4)
(16,5)
B. (10,-4)
C. (10,-2)
10
15
(-6.-9)
D. (5,-2)
Answer:
D
Step-by-step explanation:
Use the midpoint formula to find the midpoint of the line segment.
if cars A and B are traveling at the speed of 55km/hr and 75km/hr respectively. What is their average speed?
Answer:
65 km/hr
Step-by-step explanation:
The average of numbers can be calculated by adding them up and dividing that by how many numbers there are.
Here, we have two numbers. Therefore, we first add them (55+75 = 130) and then divide by 2 because there are 2 numbers, so 130/2 = 65
9. Mariah has 28 centimeters of reed
and 37/100 meters of reed for weaving
baskets. How many meters of reed
does she have? Write your answer as a
decimal and explain your answer. (The first time time I asked I forgot to put the 37/100)
Answer:
0.65m
Step-by-step explanation:
28cm is equal to 0.28m
37/100 is 37% of a metre so 0.37m
0.28 + 0.37 = 0.65m
What is the volume of a cube that has a side length of 5 centimeters?
A cube with side lengths of 5 centimeters.
Recall the formula Cube volume = s cubed.
Answer:
125
Step-by-step explanation:
We know that the side length is 5, and the formula for the volume of a cube is the side length cubed. Therefore, 5 cubed is equal to the volume.
A value cubed is equal to a value multiplied by itself twice. Therefore, 5 cubed is equal to 5 * 5 * 5. This is equal to 125
Answer:
125
Step-by-step explanation:
If a business borrows $12,600 and repays $23,940 in 5 years, what is the simple interest rate?
Answer:
18%
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Simple Interest Rate Formula: A = P(1 + rt)
P is principle amountr is ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 12600
A = 23940
t = 5
Step 2: Solve for r
Substitute in variables [Simple Interest Rate Formula]: 23940 = 12600(1 + 5r)[Division Property of Equality] Divide 12600 on both sides: 19/10 = 1 + 5r[Subtraction Property of Equality] Subtract 1 on both sides: 9/10 = 5r[Division Property of Equality] Divide 5 on both sides: 9/50 = rRewrite: r = 9/50Evaluate: r = 0.18Convert: r = 18%A plane flies 1.4 hours at 150 mph on a bearing of 10. It then turns and flies hours at the same speed on a bearing of . How far is the plane from its starting point?
Answer:
The answer is "1035.76 miles"
Explanation:
The aircraft flies at 120 mph for 1.5 hours at a [tex]10^{\circ}[/tex] bearing, then flies at the very same speed at [tex]100^{\circ}[/tex] bearings for 8.5 hours.
However an angle of [tex]100-10 = 90^{\circ}[/tex] between displacements
First shifts[tex]= 1.5 \times 120 = 180\ miles.[/tex]
Second shift [tex]= 8.5\times 120 = 1020\ miles.[/tex]
These two shifts are at [tex]90^{\circ}[/tex] and therefore the final shift is:
[tex]\to \sqrt{180^2+1020^2}=1035.76 \ miles[/tex]
Researchers study the mean weight (in pounds) of adults between the ages of 30-40. The researchers form a SRS of adults and build a 90% confidence interval: [160, 180]. Which of the following statements are true about this confidence interval?
a. 90% of intervals built according to the method capture the true mean weight of adults between the ages of 30-40.
b. The intervals margin of error is 20.
c. There is a 90% chance that the mean weight of adults between the ages of 30- 40 is between 160 and 180 pounds.
d. The sample mean used to build this interval was 170 pounds.
Answer:
d. The sample mean used to build this interval was 170 pounds.
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the difference between the two bounds, divided by 2.
In this question:
Bounds 160 and 180, so the sample mean used was (160+180)/2 = 170, and thus the correct answer is given by option d.
Sixty-five percent of men consider themselves knowledgeable soccer fans. If 10 men are randomly selected, find the probability that exactly seven of them will consider themselves knowledgeable fans. Round to the nearest thousandth.
0.700
0.65
0.252
0.021
Answer:
.252
Step-by-step explanation:
[tex]{10\choose7}*.65^7*(1-.65)^3=.252219625[/tex]
Circle O has radius 5 m with an arc AB intercepted by a central angle of π5π5 radians. What is the length of arc AB expressed in terms of ππ?
Answer:
I am assuming that you meant to write π/5.
Step-by-step explanation:
Radius r = 5 meters
Circumference = 2πr = 10π
Central angle θ = π/5 radian
Arc length = 10π × θ/(2π radians)
= 5θ
= π meters
A line has a slope of -2/3 and passes through the point (-3, 8). What is the equation of the line?
y= -2/3x + 6
y= -2/3x + 8
y= 6x- 2/3
y= 8x- 2/3
Answer:
y= -2/3x+6
Step-by-step explanation:
Using slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = -2/3x +b
Substitute the point into the equation
8 = -2/3(-3) +b
8 = 2+b
8-2 =b
6=b
y= -2/3x+6
The heights (in inches) of a sample of eight mother/daughter pairs of subjects were measured. Using a spreadsheet with the paired mother/daughter heights, the linear correlation coefficient is found to be 0.693. Find the critical value, assuming a 0.05 significance level. Is there sufficient evidence to support the claim that there is a linear correlation between the heights of mothers and the heights of their daughters?
A. Critical value = ± 0.666; there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
B. Critical value = ± 0.707; there is sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
C. Critical value =± 0.666; there is sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
D. Critical value =± 0.707; there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
Answer:
D. Critical value =± 0.707; there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
Step-by-step explanation:
Given that :
Correlation Coefficient, r = 0.693
The sample size, n = 8
The degree of freedom used for linear correlation :
df = n - 2
df = 8 - 2 = 6
Using a critical value calculator for correlation Coefficient at α = 0.05
The critical value obtained is : 0.707
The test statistic :
T = r / √(1 - r²) / (n - 2)
T = 0.693 / √(1 - 0.693²) / (8 - 2)
T = 0.693 / 0.2943215
T = 2.354
Since ;
Test statistic < Critical value ; we fail to reject the null and conclude that there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
salve by gauss jueabis method if iteration mothere aitration
4X+0.024x2-0.08x3=8
0.09x1+3x2-0.15x3=9
0.04x1+-0.08x2+4x3=20
GED Academy Practice Test
What is the value of the expression?
4+(-2)
-3+3
Answer:
The first one is 2
The second one is 0
I hope this helps!
Answer:
First:
[tex]{ \tt{ = 4 + ( - 2)}} \\ = 4 - 2 \\ = 2[/tex]
Second:
[tex] - 3 + 3 \\ = 0[/tex]
ora started watching a movie at 2:45 p.m. She watched the movie for hours before stopping the movie for hours to eat dinner. After dinner, Nora finished watching the remaining hours of the movie. At what time did the movie end?
Answer: Movies Average around 1 hour to 2 hours long. 1:30 to 2:30 so id say somewhere around 4-5 pm. Which leaves time for dinner after
Step-by-step explanation:
What is the measure of angle b
Answer:
51 ?
Step-by-step explanation:
90-39= 51. I hope its correct
Answer:
51 degrees
Step-by-step explanation:
Well if you look at the picture angle b and the 39 degrees angle together must make a 90 degree angle
90-39 is 51 so therefor angle b must be 51 degrees
Multiply m and 6. Then, add 8.
Answer:
6m + 8 is the answer.
Step-by-step explanation:
( m x 6 ) + 8
= 6m + 8
Suppose the sales tax rate in Idaho is 6%. If a computer sells for $589, how much is
the sales tax?
what is the factors of p(x)=x^2+7√2x+4
PLEAE HELP!
Answer:
aasha here it is.
Step-by-step explanation:
3x−1)(2x+3)
6x2+7x−3
=6x2+9x−2x−3
=3x(2x+3)−1(2x+3)
=(2x+3)(3x−1)
and hiii
Camille bought a set of kitchen chairs discounted 25% off of the original price of $170. What was the dollar amount of discount of the set of chairs?
Answer:
$42.50
Step-by-step explanation:
All you have to do is simply multiply
170 x 0.25=$42.50
