Length =l
Height = h
Area function = l * h = 924
Perimeter function = 2i + 2h = 122
Divide by 2
I + h = 61.
Plug in I or h for the other variable
I * (61 - I) = 924
61i - i^2 = 924
Factor the function
(-I + 28)(I - 33) = 0
l = 33 as l cannot be negative
61 - 33 = 28
h = 28
Difference between h and l is 33-28=5
Find the missing ? Explanation need it
Answer:
37°
Step-by-step explanation:
that is the procedure above
Consider rolling a fair die twice and tossing a fair coin nineteen times. Assume that all the tosses and rolls are independent.
The chance that the total number of heads in all the coin tosses equals 9 is(Q)_____ , and the chance that the total number of spots showing in all the die rolls equals 9 is(Q)__________ The number of heads in all the tosses of the coin plus the total number of times the die lands with an even number of spots showing on top (Q)______(Choose A~E)
a. has a Binomial distribution with n=31 and p=50%
b. does not have a Binomial distribution
c. has a Binomial distribution with n=21 and p=50%
d. has a Binomial distribution with n=21 and p=1/6
e. has a Binomial distribution with n=31 and p=1/6
Answer:
Hence the correct option is option c has a Binomial distribution with n=21 and p=50%.
Step-by-step explanation:
1)
A coin is tossed 19 times,
P(Head)=0.5
P(Tail)=0.5
We have to find the probability of a total number of heads in all the coin tosses equals 9.
This can be solved using the binomial distribution. For binomial distribution,
P(X=x)=C(n,x)px(1-p)n-x
where n is the number of trials, x is the number of successes, p is the probability of success, C(n,x) is a number of ways of choosing x from n.
P(X=9)=C(19,9)(0.5)9(0.5)10
P(X=9)=0.1762
2)
A fair die is rolled twice.
Total number of outcomes=36
Possibilities of getting sum as 9
S9={(3,6),(4,5)(5,4),(6,3)}
The total number of spots showing in all the die rolls equals 9 =4/36=0.1111
3)
The event of getting a good number of spots on a die roll is actually no different from the event of heads on a coin toss since the probability of a good number of spots is 3/6 = 1/2, which is additionally the probability of heads. the entire number of heads altogether the tosses of the coin plus the entire number of times the die lands with a good number of spots has an equivalent distribution because the total number of heads in 19+2= 21 tosses of the coin. The distribution is binomial with n=21 and p=50%.
If a and b are positive numbers, find the maximum value of f(x) = x^a(2 − x)^b on the interval 0 ≤ x ≤ 2.
Answer:
The maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = x^a (2-x)^b \text{ where } a, b >0[/tex]
And we want to find the maximum value of f(x) on the interval [0, 2].
First, let's evaluate the endpoints of the interval:
[tex]\displaystyle f(0) = (0)^a(2-(0))^b = 0[/tex]
And:
[tex]\displaystyle f(2) = (2)^a(2-(2))^b = 0[/tex]
Recall that extrema occurs at a function's critical points. The critical points of a function at the points where its derivative is either zero or undefined. Thus, find the derivative of the function:
[tex]\displaystyle f'(x) = \frac{d}{dx} \left[ x^a\left(2-x\right)^b\right][/tex]
By the Product Rule:
[tex]\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[x^a\right] (2-x)^b + x^a\frac{d}{dx}\left[(2-x)^b\right]\\ \\ &=\left(ax^{a-1}\right)\left(2-x\right)^b + x^a\left(b(2-x)^{b-1}\cdot -1\right) \\ \\ &= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right] \end{aligned}[/tex]
Set the derivative equal to zero and solve for x:
[tex]\displaystyle 0= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right][/tex]
By the Zero Product Property:
[tex]\displaystyle x^a (2-x)^b = 0\text{ or } \frac{a}{x} - \frac{b}{2-x} = 0[/tex]
The solutions to the first equation are x = 0 and x = 2.
First, for the second equation, note that it is undefined when x = 0 and x = 2.
To solve for x, we can multiply both sides by the denominators.
[tex]\displaystyle\left( \frac{a}{x} - \frac{b}{2-x} \right)\left((x(2-x)\right) = 0(x(2-x))[/tex]
Simplify:
[tex]\displaystyle a(2-x) - b(x) = 0[/tex]
And solve for x:
[tex]\displaystyle \begin{aligned} 2a-ax-bx &= 0 \\ 2a &= ax+bx \\ 2a&= x(a+b) \\ \frac{2a}{a+b} &= x \end{aligned}[/tex]
So, our critical points are:
[tex]\displaystyle x = 0 , 2 , \text{ and } \frac{2a}{a+b}[/tex]
We already know that f(0) = f(2) = 0.
For the third point, we can see that:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(2- \frac{2a}{a+b}\right)^b[/tex]
This can be simplified to:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Since a and b > 0, both factors must be positive. Thus, f(2a / (a + b)) > 0. So, this must be the maximum value.
To confirm that this is indeed a maximum, we can select values to test. Let a = 2 and b = 3. Then:
[tex]\displaystyle f'(x) = x^2(2-x)^3\left(\frac{2}{x} - \frac{3}{2-x}\right)[/tex]
The critical point will be at:
[tex]\displaystyle x= \frac{2(2)}{(2)+(3)} = \frac{4}{5}=0.8[/tex]
Testing x = 0.5 and x = 1 yields that:
[tex]\displaystyle f'(0.5) >0\text{ and } f'(1) <0[/tex]
Since the derivative is positive and then negative, we can conclude that the point is indeed a maximum.
Therefore, the maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Which of the following is a polynomial?
A. X4- 2
B. 1/x+ 2
c. x-2-1
D.(x - 4)/(x + 1)
Answer:
ok um last person was rude but your answer is A
Step-by-step explanation:
We are given a jar full of thousands of red and blue marbles. We want to estimate the unknown proportion pof red marbles in the jar. To do this, we randomly draw 100 marbles and count reds: it so happens we drew 45 reds. Enter values in decimal form, rounded to four decimal places (or more).
We estimate the proportion of reds in the jar to be
Attach a give-or-take value to this estimate. (That is, estimate the standard error.)
For a 96% confidence interval, about how many standard errors should be added to and subtracted from the estimate?
Set up an approximate 96% confidence interval for the unknown proportion of reds in the jar.
Answer:
(0.3478, 0.5522)
Step-by-step explanation:
Given:
Total number of red marbles, x = 45
Total number of marbles, n = 100
Phat = x / n = 45 / 100 = 0.45
The confidence interval, C.I is given by :
Phat ± Zcritical * standard error
Phat ± Zcritical * √Phat(1 - Phat) / n
Zcritical at 96% = 2.0537
The standard error = √Phat(1 - Phat) / n
S.E = √(0.45 * 0.55) / 100 = 0.0497493
C.I = 0.45 ± (2.0537 * 0.0497493)
C.I = 0.45 ± 0.10217013741
C. I = (0.3478, 0.5522)
Find the missing length indicated
Answer:
what's the question? ke
Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. That tree can be seen when one walks 14 bu from the south gate, turns west and walks 1775 bu. Find the length of each side of the city.
Answer:
The length of each side of the city is 250b
Step-by-step explanation:
Given
[tex]a = 20[/tex] --- tree distance from north gate
[tex]b =14[/tex] --- movement from south gate
[tex]c = 1775[/tex] --- movement in west direction from (b)
See attachment for illustration
Required
Find x
To do this, we have:
[tex]\triangle ADE \sim \triangle ACB[/tex] --- similar triangles
So, we have the following equivalent ratios
[tex]AE:DE = AB:CB[/tex]
Where:
[tex]AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775[/tex]
Substitute these in the above equation
[tex]20:x/2 = 20 + x + 14: 1775[/tex]
[tex]20:x/2 = x + 34: 1775[/tex]
Express as fraction
[tex]\frac{20}{x/2} = \frac{x + 34}{1775}[/tex]
[tex]\frac{40}{x} = \frac{x + 34}{1775}[/tex]
Cross multiply
[tex]x *(x + 34) = 1775 * 40[/tex]
Open bracket
[tex]x^2 + 34x = 71000[/tex]
Rewrite as:
[tex]x^2 + 34x - 71000 = 0[/tex]
Expand
[tex]x^2 + 284x -250x - 71000 = 0[/tex]
Factorize
[tex]x(x + 284) -250(x + 284)= 0[/tex]
Factor out x + 284
[tex](x - 250)(x + 284)= 0[/tex]
Split
[tex]x - 250 = 0 \ or\ x + 284= 0[/tex]
Solve for x
[tex]x = 250 \ or\ x =- 284[/tex]
x can't be negative;
So:
[tex]x = 250[/tex]
Question
Express all real numbers less than -2 or greater than or equal to 3 in interval notation.
Real numbers can be expressed using the following interval,
[tex]\mathbb{R}=(-\infty,\infty)[/tex]
Of course infinities are not just normal infinities but thats out of the scope of this question.
Real numbers less than two can be expressed with,
[tex](-\infty,\infty)\cap(-\infty,-2)=\boxed{(-\infty,-2)}[/tex]
The [tex]\cap[/tex] is called intersection ie. where are both intervals valid. First we took real numbers then we intersected them with real numbers valued less than -2 and we got real numbers which are less than -2.
Similarly we can perform with "greater than or equal to 3" real numbers,
[tex](-\infty,\infty)\cap[3,\infty)=\boxed{[3,\infty)}[/tex]
So we have one interval stretching from negative infinity to (but not including) -2, and another interval stretching from including 3 to positive infinity.
If we want numbers in both intervals we can express this two ways,
First way is to use [tex]\cup[/tex] union operator to denote we want numbers from two intervals,
[tex]\boxed{(-\infty,2)\cup[3,\infty)}[/tex]
The second way is to specify which numbers we do not want, we do not want -2 and everything up to but not including 3, which is expressed with the following interval
[tex][-2,3)[/tex]
Now we just take out the not wanted interval from real numbers and we will remain with all wanted numbers,
[tex]\boxed{(-\infty,\infty)-[-2,3)}[/tex]
Hope this helps.
Use the graph to complete the statement. O is the origin. Ry−axis ο Ry=x: (-1,2)
A. (2, -1)
B. (-2, -1)
C. (-1, -2)
D. (1, -2)
Answer:
[tex](x,y) = (1,2)[/tex] -------- [tex]R_{y-axis}[/tex]
[tex](x,y)=(2,-1)[/tex] --------- [tex]R_{y=x}[/tex]
Step-by-step explanation:
Given
[tex](x,y) = (-1,2)[/tex]
Required
[tex]R_{y-axis}[/tex]
[tex]R_{y=x}[/tex]
[tex]R_{y-axis}[/tex] implies that:
[tex](x,y) = (-x,y)[/tex]
So, we have: (-1,2) becomes
[tex](x,y) = (1,2)[/tex]
[tex]R_{y=x}[/tex] implies that
[tex](x,y) = (y,x)[/tex]
So, we have: (-1,2) becomes
[tex](x,y)=(2,-1)[/tex]
A large soda-pop manufacturer wants to introduce a new design for the label on one of its signature soda-pop drinks. The manufacturer selects a random sample of 150 customers from people who purchase the drink at a large sporting event. Each selected customer is asked whether or not he or she prefers the new design. If the manufacturer were to take a second random sample of 150 customers at the sporting event, the two samples would give somewhat different results in the proportion who prefer the new design. This variation is a source of
Answer:
This variation is a source of
response error.
Step-by-step explanation:
A response error shows the lack of accuracy in the customer responses to the survey questions. A response error can be caused by a questionnaire that requires framing improvements, misinterpretation of questions by interviewers or respondents, and errors in respondents' statements. Some responses are influenced by the answers provided to previous questions, which introduces response bias.
Tom and Jerry make separate investments at the same time. Tom invests $2000 at an annual interest rate of 2% compounded continuously. Jerry invests $1800 at an annual rate of 2.5% compounded monthly.
a.) Who has the most money after 15 years? Clearly show all work to support your answer.
b.) How long will it take for Tom’s investment to triple in value?
Answer:
Step-by-step explanation:
TOM / 6.02 years
~~~~~~~~~~~~~~~~~~~~~~
Tom: 2000(1.02)^15 = $2,691.74
Jerry: 1800(1.025)^15 = $2,606.94
TOM has more money after 15 years...
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
6000 = 2000(1.02)^t
3=(1.02)^t
ln(3) = t * ln(1.02)
t = ln(3)/ln(1.2)
t = 6.02 years
I purchased a new Apple iPad on Amazon for $249.00. The tax rate is 8.625%. What is the total purchase price of the iPad?
Answer:
270.47625
Step-by-step explanation:
249 is the original price
(249/100) · 8.625 = 21.47625 the tax total
249 + 21.47625 = 270.47625
Find the area of a rectangle that is 4-inches-wide and 15-inches-long.
Answer:
the area of a rectangle that is 4-inches-wide and 15-inches-long =15*4=60 square inches
[tex]\\ \sf\longmapsto Area=Length\times width[/tex]
[tex]\\ \sf\longmapsto Area=4(15)[/tex]
[tex]\\ \sf\longmapsto Area=60in^2[/tex]
(Kind of urgent!) Using the figure below, find the value of a. Enter your answer as a simplified radical or improper fraction (if necessary)
Answer:
15/4
Step-by-step explanation:
sin60 =z/15
z=15sin60 =(15√3)/2
cos30 =b/z
b = zcos30 = (15√3)/2 * √3/2 = 45/4
a = 15-b = 15-45/4 = 15/4
The value of a is 15/4
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
According to the given figure,
Here is a right triangle
Let, The hypotenuse = 15
perpendicular = z and base = 15 = a + b
⇒ sin60 = perpendicular/hypotenuse = z/15
⇒ z = 15sin60 = (15√3)/2
⇒ cos30 = base/hypotenuse = b/z
⇒ b = zcos30 = (15√3)/2 * √3/2 = 45/4
⇒ a + b = 15
Substitute the value of b in the above equation,
⇒ a = 15-b = 15-45/4 = 15/4
Hence, the value of a is 15/4.
Learn more about the right triangle here:
brainly.com/question/6322314
#SPJ6
Solve this equation for x. Round your answer to the nearest hundredth.
8 = In(x + 3)
Answer:
2977.96 =x
Step-by-step explanation:
8 = In(x + 3)
Raise each side to the base of e
e^8 = e^ ln(x+3)
e^8 = x+3
Subtract 3 from each side
e^8 -3 = x+3-3
e^8 -3= x
2977.95798 = x
Rounding to the nearest hundredth
2977.96 =x
Answer:
[tex]\displaystyle x = 2977.96[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra II
Natural logarithms ln and Euler's number eStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 8 = ln(x + 3)[/tex]
Step 2: Solve for x
[Equality Properties] e both sides: [tex]\displaystyle e^8 = e^{ln(x + 3)}[/tex]Simplify: [tex]\displaystyle x + 3 = e^8[/tex][Equality Property] Subtract 3 on both sides: [tex]\displaystyle x = e^8 - 3[/tex]Evaluate: [tex]\displaystyle x = 2977.96[/tex]find the slope of the line
answer choices: 4, 5, 20, 25
Answer: Third Choice. 20
Concept:
Here, we need to know the idea of a slope.
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Slope = Rise / Run = Δy / Δx = (y₂ - y₁) / (x₂ - x₁)
Solve:
STEP ONE: Select two points on the line that intersects with the grids
A (0, 5)
B (1, 25)
STEP TWO: Apply the formula
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = (25 - 5) / (1 - 0)
Slope = 20 / 1
Slope = 20
Hope this helps!! :)
Please let me know if you have any questions
Answer:
20
Step-by-step explanation:
We can find the slope of the line by using the slope formula
Slope = (y2 - y1)/(x2-x1)
Where the x and y values are derived from points chosen on the line
The points chosen may vary but I have chosen (1,25) and (2,45)
Now that we have chosen the points let's define our variables ( our variables are x1 x2 y1 and y2 )
x1 is the x value of the first point chosen.The x value of the first point chosen is 1 so x1 = 1
x2 is the x value of the second point chosen. The x value of the second point chosen is 2 so x2 = 2
y1 is the y value of the second point chosen. The y value of the first point chosen is 25 so y1 = 25
y2 is the y value of the second point chosen. The y value of the second point chosen is 45 so y2 = 45
Now to find the slope we simply plug in the values of the variables into the formula
Formula: (y2 - y1)/(x2-x1)
Variables: x1 = 1, x2 = 2, y1 = 25, y2 = 45
Plug in values
(45-25)/(2-1)
Subtract top numbers
(20)/(2-1)
Subtract bottom numbers
20/1
Simplify
The slope is 20
Solve for x
X-8 = -10
A) X = 2
B) X = -2
C) X = 18
D) X = -18
Answer:
x=–2
Step-by-step explanation:
x-8=-10
x=-10-8
x=–2
Answer:
-8= -10
, = -10+8
, = -2
The length L of the base of a rectangle is 5 less than twice its height H. Write the algebraic expression to model the area of the rectangle.
Answer:
Area of rectangle = 2H² - 5H
Step-by-step explanation:
Let the length be L.Let the height be H.Translating the word problem into an algebraic expression, we have;
Length =2H - 5
To write the algebraic expression to model the area of the rectangle;
Mathematically, the area of a rectangle is given by the formula;
Area of rectangle = L * H
Where;
L is the Length.H is the Height.Substituting the values into the formula, we have;
Area of rectangle = (2H - 5)*H
Area of rectangle = 2H² - 5H
What is the equation of the line that passes through (-3,-1) and has a slope of 2/5? Put your answer in slope-intercept form
A: y= 2/5x -1/5
B: y= 2/5x +1/5
C: y= -2/5x -1/5
Answer:
y = 2/5x + 1/5
Step-by-step explanation:
y = 2/5x + b
-1 = 2/5(-3) + b
-1 = -6/5 + b
1/5 = b
***URGENT***
PLEASE HELP ME ASAP, ITS DUE TODAY!!!
............................................................
T is the point on AB such that AT:TB = 5: 1. Show that ot is parallel to the vector a + 2b.
Step-by-step explanation:
SO, OT is parallel to the vector a+2b
the mean if 5 numbers is 19 what is the sum of the number?
Answer:
95
Step-by-step explanation:
Use the mean formula: mean = sum of elements / number of elements
Plug in the mean and number of elements, then solve for the sum of the numbers:
mean = sum of elements / number of elements
19 = sum of elements / 5
95 = sum of elements
So, the sum of the numbers is 95.
Emily, Yani and Joyce have a total of 3209 stickers. Yani has 2 times
as many stickers as Joyce. Emily has 279 more stickers than Yani. How
many more stickers does Emily have than Joyce?
Answer:
279+x
Step-by-step explanation:
Emily + Yani + Joyce=3209 stickers
if Yani has 2 times as many stickers as Joyce:this statement states that Joyce has x stickers and Yani has 2x stickers because x multiplied by 2"Emily has 279 more stickers than Yani":therefore the equation for Emily will be ;279+2xhow many stickers does Emily have than Joyce:
(279+2x)-(x)
279+2x-x
=279+x
Mason conducted a survey of his class to determine if they prefer to use pens or pencils for their math homework. Out of the 30 students in his class, 12 of them are male. A total of 21 students said they prefer pencils, and 12 of those students are female.
Fill in the missing joint and marginal frequencies in the table.
Pencils Pens Total
Male
% 10% 40%
Female
% 20%
%
Total 70%
% 100%
Answer:
Step-by-step explanation:
-Total column
30 students in the class
12 male , so 30-12 = 18 female
-Pencils column
21 students prefer pencils
12 female that prefer pencils , 21-12 = 9 male that prefer pencils
-Total row
21 students prefer pencils
30 students total, 30-21 = 9 students prefer pens
-Pens column
12 students male -9 students male prefer pencil =3 students male prefer pens
18 students female -12 students female prefer pencil =6 students female prefer pens
-to calculate the % always find the equivalent fraction of
30 students/ 100% = number of students you have / ?%
example: for male that prefer pencils we have 30/100 = 9/? so
? = 100*9 /30 =30%
PLEASE HELP!!!
Evaluate each expression.
(252) =
Answer:
1/5
Step-by-step explanation:
what is the least common factor between 9 8 and 7
Answer:
504
Step-by-step explanation:
Using LCM the common multiple is 504 as shown in the image above.
find the slope of the line that passes through these two points
Answer:
Step-by-step explanation:
PLEASE ANSWER
Triangle ABC is similar to triangle DEF. find the length of median CP
A. 12
B. 16
C. 24
D.48
12/16 = (3x-12)/(2x+8)
16(3x-12)=12(2x+8)
48x-192=24x+96
48x-24x=192+96
24x=288
X=288/24
X=12
3x-12
=(12x3)-12
=36-12
=24
C is the answer
Hope this helps!
Answer:
48
Step-by-step explanation:
2x+8=3x-12(ABCP ~FDQE)
2x-3x= -8-12
-x= -20
x=20
now,
CP=3x-12
3*20-12
48
9+1+10+6×5+9+8×9+8+8+7+6+6+9+6+8+69+85+86+86+97+86+87+86+68
Step-by-step explanation:
hope it will help u
hope it will help u please mark me as brillient...
Answer:
939 is the answer
Step-by-step explanation:
plz Mark me as the brainlist
Please help explanation need it
Step-by-step explanation:
jejejebe. s shs sjs sibskkw
QUESTION 2
A board is 86 cm. in lenght and must be cut so that one piece is 20 cm. longer than the other piece
Find the lenght of each piece.
A26 cm and 60 cm
b. 33 cm and 53 cm
C 30 cm and 56 cm
d. 70 cm and 16 cm
One piece will be length x and the other piece will be 20 cm longer, so it will be x + 20 cm long.
Added together the length of these two boards will equal 86 cm. So you can write an equation:
x + (x + 20) = 86
Remove the parentheses and add the two x's together to get:
2x + 20 = 86
Subtract 20 from both sides:
2x = 66
Divide both sides by 2 and you have:
x = 33
The short piece is 33 cm and the other piece is 20 cm longer or 33 + 20 = 53 cm.
