(2π)^(-1)E[∫▒〖e^(-√(-1) xy)]dy〗
The characteristic function of a random variable X is defined as ∅(t) = E[e^(√(-1)tx)]. To show that (2π)^(-1) ∫▒〖e^(-√(-1) xt)∅(t)dt〗 is the Lebesgue density of X, we need to demonstrate that it is a probability density function.
We first calculate the integral to obtain (2π)^(-1) ∫▒〖e^(-√(-1) xt)∅(t)dt〗 = (2π)^(-1) ∫▒〖E[e^(-√(-1) xt +√(-1) tx)]dt〗.
Since the expectation is a constant, we can pull it out of the integral to get (2π)^(-1)E[∫▒〖e^(-√(-1) xt +√(-1) tx)]dt〗.
Now, if we substitute t = y-x and rewrite the integral, we obtain (2π)^(-1)E[∫▒〖e^(-√(-1) x(y-x))e^(√(-1) xy)]dy〗.
This simplifies to (2π)^(-1)E[∫▒〖e^(-√(-1) xy)]dy〗.
Because the integrand is 1, the integral is simply y. Then, the expectation becomes E[y] which is the mean of the random variable X. Thus, the Lebesgue density of X is (2π)^(-1)E[y], which is the probability density function of X.
Learn more about Lebesgue density
brainly.com/question/30848086
#SPJ11
A recipe uses 2 cups of milk to make 6 servings. If the same amount of milk is used for each serving, how many servings can be made from one gallon?
1 gallon
=
1 gallon=
4 quarts
4 quarts
1 quart
=
1 quart=
2 pints
2 pints
1 pint
=
1 pint=
2 cups
2 cups
1 cup
=
1 cup=
8 fluid ounces
8 fluid ounces
Before you try that problem, answer the question below.
How many cups will you need to find the number of servings for?
Answer:
48 servings
Step-by-step explanation:
since there are 16 cups in a gallon and 2 cups makes 6 servings, then to find the number of servings a gallon makes we divide the amount of cups in a gallon (16) by how many you need to make the recipe (2), and 16/2=8 so now we multiply how many times we can make the recipe with a gallon (8) by how many servings the recipe makes (6) to get 8x6=48 servings
Sketch the least positive angle and find the values of the six trigonometric functions
3x+5y=0 , x≥0
The least positive angle is 180 - θ.
To sketch the least positive angle and find the values of the six trigonometric functions for the given equation 3x + 5y = 0, x ≥ 0, we need to first find the slope and y-intercept of the equation.
The slope of the equation is -3/5 and the y-intercept is 0. This means that the line passes through the origin and has a negative slope.
To sketch the least positive angle, we need to find the angle between the x-axis and the line. Since the slope is negative, the angle will be in the second quadrant. The least positive angle is the reference angle in the second quadrant, which is 180 - θ.
To find the values of the six trigonometric functions, we can use the slope and y-intercept to find the coordinates of a point on the line. One such point is (5, -3).
Using these coordinates, we can find the values of the trigonometric functions:
sin θ = -3/√(5^2 + (-3)^2) = -3/√34
cos θ = 5/√(5^2 + (-3)^2) = 5/√34
tan θ = -3/5
csc θ = √34/-3
sec θ = √34/5
cot θ = -5/3
Therefore, the least positive angle is 180 - θ and the values of the six trigonometric functions are as follows:
sin θ = -3/√34
cos θ = 5/√34
tan θ = -3/5
csc θ = √34/-3
sec θ = √34/5
cot θ = -5/3
Learn more about trigonometric
brainly.com/question/29156330
#SPJ11
SLOVE RN ITS DUE IN ONE HOUR
The part of the mural that Trevor has completed is 6/20 square meter.
The correct answer choice is option C.
What part of the mural has Trevor completed?Area of a rectangle is the measure of the extent of a surface. it is measured in square units.
Total area of the mural = 1 square meter
Rectangular part of the mural:
Length = 2/5 meter
Width = 3/4 meter
Area of the rectangular part of the mural = length × width
= 2/5 × 3/4
= 6/20 square meter
Ultimately, Trevor has completed 6/20 of the mural.
Read more on area of rectangle:
https://brainly.com/question/25292087
#SPJ1
I neeeed help plssssssssssssssssssssssss
Answer:
I AINT SOLVING ALL THAT
2. What is the product of (-3x3 + 2x – 5) and (2x4 – 4x2 – 3)?
(a) Show your work
(b) Is the product of (-3x3 + 2x – 5) and (2x4 – 4x2 – 3) equal to the product of (2x4 –
4x2 – 3) and (-3x3 + 2x – 5) Explain your answer.
The answer is that the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3) is the same as the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3)
What is expressiοn?An expressiοn in mathematics is made up οf different numbers, variables, and mathematical prοcesses, such as expοnents, lοgarithms, trigοnοmetric functiοns, and arithmetic. It can symbοlise a number οr a fοrmula, but it lacks an equals sign (=) and cannοt be evaluated οr sοlved withοut being cοmbined οr simplified. Expressiοns can be straightfοrward, like 3x + 4, οr they can be cοmplicated, like (2x - 1)/(x + 3).
given:
(a) We must multiply each term in the first expressiοn by each term in the secοnd expressiοn befοre cοmbining like terms tο determine the prοduct οf (-3x³ + 2x - 5) and (2x4 - 4x² - 3). The distributive principle allοws us tο write:
= (-3x³ + 2x - 5) * (2x⁴ - 4x² - 3) * (3x³ + 2x - 5) * = 3x³ * 2x⁴ + (-3x³) * (-4x²) * (-3)
= 2x * 2x⁴ + 2x * (-4x²) + 2x * (-3)
= -6x⁷ + 12x⁵ + 9x³ + 4x⁵ - 8x³ - 6x - 10x⁴ + 20x² + 15 = 5 * 2x⁴ - 5 * (-4x²) - 5 * (-3)
The result οf the οperatiοns (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3) is as fοllοws: -6x⁷ + 10x⁴ + 16x⁵ - 17x³ - 6x + 15
(b) The answer is that the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3) is the same as the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3). Due tο the fact that multiplicatiοn is cοmmutative, changing the οrder οf the variables has nο effect οn the οutcοme οf the prοduct. Cοnsequently, we can write:
(2x⁴ - 4x² - 3) * (-3x³ + 2x - 5) = (-3x³ + 2x - 5) * (2x⁴ - 4x² - 3)
The answer is that the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3) is the same as the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3)
To know more about expressions visit :-
brainly.com/question/14083225
#SPJ1
Two friends share a sum of money in the ratio 4:3. If the friend who received the larger
amount received R19,60, what was the total amount of money they had to share???
The total amount of money two friends had is $3430.
What is ratio?
When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.
Here the ratio of the money of friends = 4:3.
Let us take shares of money as 4x and 3x.
Here larger amount 4x=R1960
=> 4x=1960
=> x= 1960/4= $490
Then Total amount = 4x+3x=7x
=> Total amount = 7*490=$3430
Hence the total amount of money two friends had is $3430.
To learn more about ratio refer the below link
https://brainly.com/question/12024093
#SPJ1
Find i (the rate per period) and n (the number of periods) for the following annuity.
Annual deposits of $1,800 are made for 6 years into an annuity that pays 5.1% compounded annually.
i=enter your response here
(Type an integer or a decimal.)
So, the answer to the question is:
i = 0.051
n = 6
The annuity in question is an ordinary annuity, which means that the deposits are made at the end of each period. In this case, the period is one year, so the rate per period (i) is simply the annual interest rate of 5.1%. Therefore, i = 0.051.
The number of periods (n) is the number of years that the deposits are made, which is 6. Therefore, n = 6.
So, the answer to the question is:
i = 0.051
n = 6
It is important to note that the terms "period" and "annuity" are used in the context of this question to refer to the time frame and the type of investment, respectively. The term "pays" is used to describe the interest rate that the annuity pays on the deposits.
Learn more about annual interest
brainly.com/question/29845806
#SPJ11
WILL GIVE BRAINLIST TO BEST ANSWER
Given the recursive formula for a geometric sequence find the common ratio, the first five terms, the term named in the problem, and the explicit formula.
Show work
12) f(n) = f(n - 1) * (- 3)
f(1) = - 1
Find f(12)
[tex]f(n) = f(n - 1) * (- 3)[/tex]
[tex]f(2) = f(2 - 1) * (- 3) = \boxed{f(1) * (- 3)} = (-1)*(-3) = \bf 3\\[/tex]
[tex]f(3) = f(3 - 1) * (- 3) = f(2) * (- 3) = f(1) * (-3) * (- 3) = \boxed{f(1) * (-3)^{2}} = (-1)*3^{2} =-3^{2} = \bf -9\\[/tex]
[tex]f(4) = f(4 - 1) * (- 3) = f(3) * (- 3) = f(1) * (-3)^{2} * (- 3) = \boxed{f(1) * (-3)^{3}} = (-1)*(-3^{3}) = 3^{3} = \bf 27\\[/tex]
[tex]f(5) = f(5 - 1) * (- 3) = f(4) * (- 3) = f(1) * (-3)^{3} * (- 3) = \boxed{f(1) * (-3)^{4}} = (-1)*3^{4} =-3^{4} = \bf -64\\[/tex]
[tex]f(12) = f(12 - 1) * (- 3) = f(1) * (-3)^{10} * (- 3) = \boxed{f(1) * (-3)^{11}} = (-1)* (-3)^{11} = -(-3^{11}) = 3^{11} \\[/tex]
⇒
[tex]\boxed{f(n) = (-1)^{n} * 3^{n - 1}}[/tex]
A principle ideal is an ideal generated by a single
element. That is I is a principle
ideal if there exists an element a of I such that
I = (a) = {ar : r ∈ I}.
This means that there exists an element a of the ideal I, such that all other elements in the ideal can be written as a multiple of a. In other words, the ideal I can be written as I = (a) = {ar : r ∈ I}, where r is any element of the ideal I.
A principle ideal is an ideal that is generated by a single element. This means that there exists an element a of the ideal I, such that all other elements in the ideal can be written as a multiple of a. In other words, the ideal I can be written as I = (a) = {ar : r ∈ I}, where r is any element of the ideal I. This is an important concept in the study of rings and algebraic structures, as it allows us to understand how ideals are generated and how they relate to other ideals in the same ring.
Learn about Principle ideal
brainly.com/question/2599243
#SPJ11
An L-shaped polygon is shown on the coordinate grid. Draw the dilation
of this polygon after multiplying each coordinate by 3. Upload your
picture. (I need help with finding out the original coordinates so I can multiply it by 3 and draw the dilation)
Answer:
Step-by-step explanation:
ypi ,tfr
al numbers that could be zeros of the polynomial accordir P(v)=14v^(5)+6v^(4)+5v^(3)-4v^(2)+2v
The only possible rational zero of the polynomial is 0
The possible zeros of the polynomial P(v) = 14v^5 + 6v^4 + 5v^3 - 4v^2 + 2v can be found by using the Rational Root Theorem. This theorem states that if a polynomial has rational zeros, they will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In this case, the constant term is 0 and the leading coefficient is 14. The factors of 0 are just 0, and the factors of 14 are 1, 2, 7, and 14. Therefore, the possible rational zeros of the polynomial are 0/1, 0/2, 0/7, and 0/14, which all simplify to just 0.
This means that the only possible rational zero of the polynomial is 0. However, there may also be irrational or complex zeros. To find these, we would need to use other methods, such as synthetic division or the quadratic formula.
In conclusion, the possible zeros of the polynomial P(v) = 14v^5 + 6v^4 + 5v^3 - 4v^2 + 2v are 0 and any irrational or complex numbers that satisfy the equation.
Learn more about polynomial
brainly.com/question/11536910
#SPJ11
Do not use L'Hospital's Rule.
Prove
A. show that 1(x) = {(sin(x) A. Show × EQ (x) XER-Q
X= zkπ, K 6 z
is continuous only at.
B. Prove that lim x=2 by & definition X-8
A. we can observe that 1(x) is continuous at x = kπ- for any integer k, and hence, it is continuous only at x = kπ, where k is an integer.
B. We have proved that limx → 2 (x2 - 1) = 3 using the definition of a limit.
How to proveA. To prove that 1(x) = {(sin(x) × EQ (x) XER-Q, X = zkπ, K 6 z is continuous only at x = kπ, where k is an integer without using L'Hospital's Rule, we can use the concept of limits.Let's consider the left limit of the function at x = kπ+ (where ε > 0 is a small value).
Here, we can observe that:
lim x → kπ+ 1(x) = lim x → kπ+ sin(x)/x > 0 since sin(x) > 0 when x is in (kπ, kπ + ε/2) and x is in (kπ - ε/2, kπ)
So, 1(x) = {(sin(x) × EQ (x) XER-Q, X = zkπ, K 6 z is continuous at x = kπ+ for any integer k.
Similarly, we can observe that 1(x) is continuous at x = kπ- for any integer k, and hence, it is continuous only at x = kπ, where k is an integer.
B. To prove that limx → 2 f(x) = 3, we can use the following definition of a limit:
For any ε > 0, there exists a δ > 0 such that |f(x) - 3| < ε for all 0 < |x - 2| < δ.
Here, f(x) = x2 - 1, and we need to prove that limx → 2 (x2 - 1) = 3.
Using algebraic manipulation, we can write x2 - 1 - 3 = (x + 2)(x - 2).Now, |(x + 2)(x - 2)| = |x + 2||x - 2|.
Therefore, we need to find δ such that |(x + 2)(x - 2)| < ε whenever 0 < |x - 2| < δ.
In order to ensure this, we can put an upper bound on |x + 2| and |x - 2|:|x + 2| < 4 (since x is close to 2)|x - 2| < δ
From the above inequalities, we can say that |(x + 2)(x - 2)| < 4δ.
Then, we can say that |(x2 - 1) - 3| = |(x + 2)(x - 2)| < 4δ < ε.
So, we can choose δ = ε/4.
Hence, we have proved that limx → 2 (x2 - 1) = 3 using the definition of a limit.
Learn more about integer at
https://brainly.com/question/15276410
#SPJ11
1.Solve log2x=log218 showing steps as done in the exam 2. 2.Solve log2×2=log2(4x−4) showing steps as done in the 3. Solve logb(x2−56)=logbx showing steps as done in the e
x = 2logb(x2 + 56)/2
1. log2x = log218
log2x = 3
x = 23 = 8
2. log2×2 = log2(4x−4)
log2×2 = log2(4x)−log2(4)
log2×2 = log2(4x)−2
log2×2 + 2 = log2(4x)
log2(2×2) + 2 = log2(4x)
log2(4) + 2 = log2(4x)
4 + 2 = log2(4x)
6 = log2(4x)
26 = 4x
x = 23 = 8
3. logb(x2−56)=logbx
logb(x2−56) = logbx
logb(x2)−logb(56) = logbx
logbx2−logb56 = logbx
logbx2−logb56 + logbx = logbx + logbx
2logbx = logbx2 + logb56
2logbx − logbx2 = logb56
2logbx − logb(x2−56) = logb56
2logbx − logb(x2) + logb(56) = logb56
2logbx−logbx2 + logb(56) = logb56
2logbx = logb(x2 + 56)
2logbx = logb(x2 + 56)
logbx = logb(x2 + 56)/2
x = 2logb(x2 + 56)/2
Learn more about logarithm
brainly.com/question/30085872
#SPJ11
3.
The box-and-whisker plot shown below represents
600 scores on a district geometry te
150 students scored between 42 and 56 on the district geometry test.
What is box whisker plot?Box whisker plots are used to abstract a collection of data that has been approximated using an interval scale. Just a box plot is another name for it. They are mostly employed while interpreting data. It is one of the graphical approaches that shows how the dataset's data varies from one another. The histogram may be used to display the data as well. Yet a histogram offers a useful presentation. Box and whisker plots are preferable to histograms because they may exhibit numerous sets of data on a single graph, which adds more information.
From the box whisker plot we see that the lower quartile is 42 and the median is 56.
The median represents the 50th percentile whereas lower quartile is 75%.
The difference is:
75 - 50 = 25%.
Now, for 600 scores we have:
25% of 600
= 25/100 (600) = 150
Hence, 150 students scored between 42 and 56 on the district geometry test.
Learn more about box-whisker plot here:
https://brainly.com/question/2742784
#SPJ1
-2(-3)+27÷ (-3) +3=calculate without using a calculator
the value of the expression is 0.
To solve this expression, we can use the PEMDAS order of operations:
since there are no Parentheses and Exponents we move to multiplication and division
-2(-3) + 27 ÷ (-3) + 3 = 6 + (-9) + 3
6 + (-9) + 3 = 0
As a result, the equation has a value of 0.
What are equations?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Here,
5 and 13 are expressions for 2x.
These two expressions are joined together by the sign "=".
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality. The two most well-known groups of equations in algebra are linear equations and polynomial equations. P(x) = 0 can be used to represent polynomial equations with a single variable. P is a polynomial, and axe + b = 0 is the standard form for linear equations. Here, are the parameters a and b.
to know more about equations visit:
https://brainly.com/question/10413253
#SPJ1
What is the y-intercept
Answer:
y-intercept: 3
equation: y = -x + 3
Step-by-step explanation:
For problem #6: (-2,5) and (2,1)
Slope m = (y2 - y1)/(x2 - x1)
=>m = (1 - 5)/(2 - -2) = -4/4 = -1
Slope-intercept form is y = mx + b
Given m = -1, y = 1, x = 2
=> 1 = -1(2) + b
=> 1 = -2 + b
=> b = 1 + 2 = 3
equation: y = -x + 3
since b is the y-intercept => 3
Big ideas 7.5 question
None of the options are sufficient to prove that ABCD quadrilateral is a kite.
what are quadrilaterals ?
Quadrilaterals are closed two-dimensional shapes with four straight sides and four angles. The word "quadrilateral" comes from the Latin words "quadri" which means "four" and "latus" which means "side". Some common examples of quadrilaterals include squares, rectangles, parallelograms, rhombuses, and trapezoids.
Each type of quadrilateral has its own unique set of properties and characteristics. For example, a rectangle has four right angles and opposite sides that are parallel and congruent. A parallelogram has opposite sides that are parallel and congruent, and opposite angles that are congruent. A rhombus has four congruent sides and opposite angles that are congruent.
According to the question:
Option A: OBC and DC being congruent only tells us that OBDC is a parallelogram, but it does not tell us anything about the other pair of adjacent sides, AB and BC.
Option B: OAC and DC being congruent only tells us that OACD is an isosceles trapezoid, but it does not tell us anything about the other pair of adjacent sides, AB and BC.
Option C: OAC and BC being congruent only tells us that OABC is a kite, but it does not tell us anything about the other pair of adjacent sides, AD and DC.
None of the options given are sufficient to prove that ABCD is a kite. To prove that ABCD is a kite that we need to show that two pairs of adjacent sides are congruent.
Therefore, none of the options are sufficient to prove that ABCD is a kite.
To know more about quadrilaterals visit:
https://brainly.com/question/29755822
#SPJ1
The table below shows the relationship between the perimeter and area of four squares.
Squares
Area, A
(square units) Perimeter, P
(units)
1 4
4 8
9 12
16 16
Which equation can be used to find A, the area of a square that has a perimeter of P units?
A.A = (P ÷ 4) x (P ÷ 4)
B.A = (P– 4)
C.A = (P + 4) x (P + 4)
D.A = P
Equation A = (P ÷ 4)*(P ÷ 4) can be used to find area of a square.
What exactly is a square?A square is a geometrical shape that has four equal sides and four equal angles (90-degree angles or right angles). It is a type of rectangle where all sides have the same length. A square is a two-dimensional shape, meaning it only has length and width, and all of its sides are parallel to each other. The opposite sides of a square are parallel and equal in length, and its diagonals bisect each other at 90-degree angles. Squares are used in mathematics, geometry, and various other fields.
Now,
As Area =a² where a=side of square
and perimeter=4a⇒a=p/4
then area=(p/4)²
Hence, The equation that can be used to find A, the area of a square that has a perimeter of P units is:
A = (P ÷ 4)*(P ÷ 4)
Therefore, the correct option is A.
To know more about squares visit the link
https://brainly.com/question/28776767
#SPJ1
The table below shows how much Eloise spent on ribbon at two different shops. What is the difference in the price of 300cm of ribbon between shop A and shop B? Give your answer in pounds (£).
The difference in price of both the shops is £0.25.
What is price?
Price is the amount of money one pays for a good or service. It is determined by a variety of factors, such as supply and demand, the cost of production, and the availability of resources. Prices are also affected by government regulations, taxes, inflation, and other economic and market forces. The price of a product or service is an important factor in determining whether consumers will purchase it or not.
Shop A | Shop B
200 cm | £0.50 | 300 cm | £0.75
The difference in the price of 300cm of ribbon between shop A and shop B is £0.25. Eloise spent £0.50 on 200cm of ribbon at shop A, and £0.75 on 300cm of ribbon at shop B. Therefore, the difference in price is £0.25.
To know more about price
https://brainly.com/question/19104371
#SPJ1
Nick is 64 years younger than Madelyn. 4 years ago, Madelyn's age was 3 times Nick's age. How old is Nick now?
Nick is 36 years old now.
To solve the problem, we can use the following steps:
Step 1: Let Nick's age be x and Madelyn's age be y.
Step 2: We are given that Nick is 64 years younger than Madelyn, so we can write an equation: x = y - 64
Step 3: We are also given that 4 years ago, Madelyn's age was 3 times Nick's age, so we can write another equation: y - 4 = 3(x - 4)
Step 4: Substitute the first equation into the second equation to get: y - 4 = 3(y - 64 - 4)
Step 5: Simplify the equation to get: y - 4 = 3y - 204
Step 6: Solve for y to get: y = 100
Step 7: Substitute the value of y back into the first equation to get: x = 100 - 64 = 36
Therefore, Nick is 36 years old now.
To know more about age click here:
https://brainly.com/question/29963980
#SPJ11
There are 657 students at Fairview Elementary. All the students in the
school need to sit in the auditorium for an awards ceremony. Each
row in the auditorium seats exactly 24 students. How many rows will
be needed to seat all students?
The instructions are
DRAW A
MODEL
MAKE AN
ESTIMATION
ORGANIZE
THE INFO
LOOK FOR
A PATTERN
WORK
BACKWARDS
WRITE AN
EQUATION
a) A drawn model to illustrate the number of rows that will be needed is as follows:
Rows = 28Number of students per row = 24Total number of students = 657.b) An estimated number of rows is 30, which will seat about 720 students.
c) The information organization is as follows:
The total number of students at Fairview Elementary = 657The number of students per row of auditorium = 24Let the number of rows required = x.d) The pattern shows that each row will seat no more 24 students.
e) Working backwards indicates that only between 27 and 28 rows are required.
f) Using an equation, the number of rows that will be needed to seat all students is 28 rows.
What is an equation?An equation is a mathematical statement depicting the equality of two or more algebraic expressions.
An equation is more than an algebraic or mathematical expression because it uses all the elements in an expression, and includes the equal symbol (=).
The total number of students at Fairview Elementary = 657
The number of students per row of auditorium = 24
Let the number of rows required = x
Equation:x = 657/24
= 27.375
≈ 28 rows.
Thus, 28 rows must be arranged to accommodate 24 students per row.
Learn more about equations at https://brainly.com/question/2972832.
#SPJ1
Tangents. of a circle
The required,
19. AB is tangent to circle C.
20. AB is not tangent.
In a right-angled triangle, its sides, such as the hypotenuse, are perpendicular and the base is Pythagorean triplets.
Here,
Form figure 19.
Applying the Pythagorean theorem,
BS² = AS² + AB²
Substitute the value in the above expression.
12² = 7.2² + [2*4.8]² [radius = diameter /2]
144 = 51.84+92.16
144 = 144
Thus, the required AB is tangent to circle C.
Similarly,
In figure 20 AB is not tangent because,
BC² ≠ AB² + AC²
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
#SPJ1
What is the exact value of x?
Answer:
x= 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Liam opens a savings account with $400 deposit and a simple interest rate of 7. 5%. Of the balance of the account is not $760 and there were no deposits or withdrawals, how long ago did he open the account?
Liam opened the savings account 4 years ago based on the given condition of a $400 deposit.
The formula for simple interest is I = Prt, where I is the interest earned, P is the principal amount, r is the interest rate per year, and t is the time in years.
We are given that Liam deposited $400 and the interest rate is 7.5%. Let's first calculate the interest earned:
I = Prt = 4000.075t = 30t
After some time t, the balance of the account is $760, which means the total amount in the account is the principal plus the interest earned:
400 + 30t = 760
Simplifying this equation, we get:
30t = 360
t = 12
Therefore, Liam opened the savings account 12/3 = 4 years ago.
Learn more about Simple Interest:
https://brainly.com/question/25793394
#SPJ4
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What type of polynomial is: −2/3b*3
A. quadratic
B. linear
C. quartic
D. cubic
The type of polynomial that - 2 / 3 x b³ is D. Cubic polynomial.
What is a cubic polynomial ?A cubic polynomial is a type of polynomial function in algebra that has a degree of three. Cubic polynomials can take many different forms and can have multiple real roots, complex roots, or no real roots at all.
A quadratic polynomial contains a degree of 2, a linear polynomial contains a degree of 1, and a quartic polynomial contains a degree of 4. In this case, the highest degree of the variable b is 3, which makes it a cubic polynomial.
Find out more on polynomials at https://brainly.com/question/14779377
#SPJ1
The dashed triangle is the image of the solid triangle for a dilation with center at the origin. What is the scale factor?
The scale factor using in that dilation of the dashed triangle would be = 3:1
What is a scale factor?A scale factor is defined as the ratio that exists between an original size of an object and the new formed size of the same object.
The formula that can be used to calculate the scale factor ;
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
Using the base of the triangle from the centre of origin in the graph;
The dimension of the new shape = 18
The dimension of the original shape = 6
scale factor = 18/6 =3
That is, the scale factor = 3:1
Learn more about scale factor here ;
https://brainly.com/question/28339205
#SPJ1
Identify the area of the figure rounded to the nearest tenth
Answer:
118.7 inches squared.
Step-by-step explanation:
What is the area?The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.
What is diameter?Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.
The expression for solving the area of a circle is A = π × [tex]r^{2}[/tex].
To solve for the semicircle above, we can divide the diameter into 2 to get the radius.
12 ÷ 2 = 6So, the radius of the upper semicircle is 6 inches.
If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.
A = π × [tex]6^{2}[/tex]This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.
To solve for the lower semicircle, we can do the same this as we did above.
A = π × [tex]r^{2}[/tex]But wait, we don't know the radius or diameter!
No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.
To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.
6 ÷ 2 = 3So, the radius of the circle is 3.
Now we can insert 3 into the expression.
A = π × [tex]3^{2}[/tex]This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.
Adding the two semicircles together:
18π + 4.5π = 22.5π22.5 × π ≈ 70.6858So, the area of both semicircles is approximately 70.6858 square inches.
To solve for the area of a rectangle we use the expression:
A = length × widthInserting the dimensions of the rectangle:
8 × 6 = 48So, the area of the rectangle is 48 square inches.
Adding the two areas together:
70.6858 + 48 = 118.6858 ≈ 118.7Therefore, the area of the entire figure, rounded to the nearest tenth is [tex]118.7[/tex] [tex]in^{2}[/tex].
The isosceles trapezoid ABDE is part of an isosceles triangle ACE. Find the measure of the vertex angle of triangle ACE.
The measure of the vertex angle of triangle ACE is 50°. The solution has been obtained by using properties of angles.
What is an angle?
An angle is a figure in plane geometry that is created when two rays or lines share an endpoint.
We are given an isosceles triangle ACE which means that AC = CE.
We are given ∠BDE = 115°
Since, angles on a straight line form a linear pair, therefore
⇒∠BDE + ∠BDC = 180°
⇒115° + ∠BDC = 180°
⇒∠BDC = 65°
Since, BD║AE so,
∠BDC = ∠AEC
So, ∠AEC = 65°
Since, AC = CE so,
∠AEC = ∠CAE
So, ∠CAE = 65°
Now, using angle sum property, we get
⇒∠AEC + ∠CAE + ∠ACE = 180°
⇒65° + 65° + ∠ACE = 180°
⇒130° + ∠ACE = 180°
⇒∠ACE = 50°
Hence, the measure of the vertex angle of triangle ACE is 50°.
Learn more about angle from the given link
https://brainly.com/question/25770607
#SPJ1
The right rectangular prism is made up of 48 cubes. Each cube has an edge length of 14 inch. Image_30414 What is the volume of this prism? Responses 14 cubic inch 1 fourth, cubic inch 12 cubic inch 1 half, cubic inch 34 cubic inch 3 fourths, cubic inch 1 cubic inch
The right rectangle prism contains 48 cubes, which results in a volume of 131,712 cubic inches.
what is prism ?A prism is a solid geometric form with two parallel bases that are congruent and typically shaped like polygons, as well as parallelogram-shaped sides that connect the bases. Prisms come in different shapes, such as hexagonal, triangular, and rectangle.
given
The 48 blocks that make up the right rectangular prism each have an edge length of 14 inches. By dividing the quantity of cubes by the sum of their individual volumes, one can determine the volume of the prism.
Each cube has a volume of (14 in.)3 = 2744 cubic inches.
Cube count is 48.
48 squares at 2744 cubic inches each equals 131,712 cubic inches of volume for the prism.
The right rectangle prism contains 48 cubes, which results in a volume of 131,712 cubic inches.
To know more about prism visit:
https://brainly.com/question/27914026
#SPJ1
Evaluate. Write your answer as a fraction or whole number without exponents.
2^–2 =
Answer:
1/4
Step-by-step explanation:
you can plug it into a calculator