Answer:
First angle: 48°
Second angle: 36°
Third angle: 96°
Step-by-step explanation:
The sum of the three angles of a triangle = 180°
Let the measure of the first angle be a°
Then second angle measure = (a - 12)°
Third angle measure = 2a°
Adding up all these should equal 180°
⇒ a + a - 12 + 2a = 180
⇒ 4a - 12 = 180
⇒ 4a = 180 -+ 12
⇒ 4a = 192
⇒ a = 192/4 = 48°
Thus the first angle is 48°
Second angle = 48 - 12 = 36°
Third angle = 2 x 48 = 96°
let x1,x2,...,xn be a random sample of size n from the exponential dis- tribution with rate λ. find a 97% confidence interval (using explicitly computed critical values) for λ based on the x(1), the minimum of the sample. (hint: consider the distribution of nλx(1).
For given[tex]$\mathrm{n}$[/tex] and [tex]$\mathrm{X}_{(1)}$[/tex], we can obtain the confidence interval [tex]$(\mathrm{a}, \mathrm{b})$[/tex].
Let[tex]$\mathrm{X}_1, \mathrm{X}_2, \ldots, \mathrm{X}_{\mathrm{n}}$[/tex] be a sequence of size [tex]$\mathrm{n}$[/tex] from the exponential distribution with rate[tex]$\lambda$.[/tex] Then the probability density function of the random is a given [tex]$\mathrm{f}\left(\mathrm{x}_{\mathrm{i}}, \lambda\right)=\lambda \exp (-\lambda \mathrm{x}) ; \quad 0 \leq \mathrm{x} < \infty$[/tex]
Let us consider a ordered random sample of size [tex]$\mathrm{n}$[/tex] as [tex]$\mathrm{X}_{(1)}, \mathrm{X}_{(2)}, \ldots, \mathrm{X}_{(\mathrm{n})}$[/tex]. Then [tex]$\mathrm{X}_{(1)}$[/tex] is the smallest of the sample. The density function of the smallest sample [tex]$\mathrm{X}_{(1)}$[/tex] is give by
[tex]$$\mathrm{f}\left(\mathrm{X}_{(1)}, \lambda\right)=\mathrm{n}\left[1-\mathrm{F}_{\mathrm{x}}(\mathrm{x}, \lambda)\right]^{\mathrm{n}-1} \times \mathrm{f}(\mathrm{x}, \lambda)$$[/tex]
As the cumulative density is given by
[tex]=\int_0^{\mathrm{x}} \mathrm{f}(\mathrm{x}, \lambda) \mathrm{dx} \\&=\int_0^{\mathrm{x}} \lambda \times \exp (-\lambda \mathrm{x}) \mathrm{dx} \\&=1-\exp (-\lambda \mathrm{x})\end{aligned}$$[/tex]
The density of the minimum of the sample is given by
[tex]=\mathrm{n} \times[1-(1-\exp (-\lambda \mathrm{x}))]^{\mathrm{n}-1} \times \lambda \times \exp (-\lambda \mathrm{x})$[/tex]
[tex]$$\begin{aligned}&=\mathrm{n} \times[\exp (-\lambda \mathrm{x})]^{\mathrm{n}-1} \times \lambda \times \exp (-\lambda \mathrm{x}) . \\&=\mathrm{n} \lambda \times \exp (-\mathrm{n} \lambda \mathrm{x})\end{aligned}$$[/tex]
Thus, here [tex]$\mathrm{X}_{(1)}$[/tex] follows gamma distribution with parameter [tex]$\alpha=1 \quad$[/tex] and [tex]$\beta=\frac{1}{n \lambda}$[/tex].
We make use of the condition that if Y follows Gamma distribution with parameter with parameter [tex]$\alpha$[/tex]and [tex]$\beta$[/tex]. Then, we have
[tex]$\frac{2 \mathrm{Y}}{\beta} \sim \chi^2(2 \alpha, \mathrm{n}-1)$[/tex]
Thus we have that
[tex]\mathrm{T}=\frac{2 \mathrm{X}_{(1)}}{\frac{1}{\mathrm{n} \lambda}} \sim \chi^2(2, \mathrm{n}-1)$$[/tex]
[tex]$$\begin{aligned}\mathrm{b} &=\frac{\chi^2\left(1-\frac{\alpha}{2}, \mathrm{n}-1\right)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\&=\frac{\chi^2\left(1-\frac{0.03}{2}, \mathrm{n}-1\right)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\&=\frac{\chi^2(0.985, \mathrm{n}-1)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\\mathrm{a} &=\frac{\chi^2\left(\frac{0.03}{2}, \mathrm{n}-1\right)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\&=\frac{\chi^2(0.015, \mathrm{n}-1)}{2 \mathrm{X}_{(1)} \times \mathrm{n}}\end{aligned}$$[/tex]
Therefore for given[tex]$\mathrm{n}$[/tex] and [tex]$\mathrm{X}_{(1)}$[/tex], we can obtain the confidence interval [tex]$(\mathrm{a}, \mathrm{b})$[/tex].
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8. Kim made a pitcher of
lemonade. The pitcher already
contained 1 5/6 cups of
lemonade, and she added 2 2/3
more cups. How many cups
were in the pitcher when Kim
was finished?
Answer:
4 1/2
Step-by-step explanation:
Add the fractions:
11/6+8/3
11/6+16/6
27/6
27/6=4.5
You need a 70% alcohol solution. On hand, you have a 150 mL of a 15% alcohol mixture. How much pure alcohol will you need to add to obtain the desired solution?
Answer: you have to add 60 mL of the 70% solution.
Step-by-step explanation:
If you have 180 mL of a 30% alcohol mixture, then (180mL)(0.30) = 54mL of that solution is alcohol.
Similarly, if you have x mL of a 70% alcohol mixture, then (x mL)(0.70) = 0.70x mL of that solution is alcohol.
When you combine these two liquids, you will have (180 + x) mL of liquid and you want it to be 40% alcohol.
So, you simply need to solve the equation:
180(0.30) + x(0.70) = (180 + x)(0.40)
54 + 0.70x = 72 + 0.40x (distribute the 0.40)
0.30x = 18 (subtract 54 from both sides and subtract 0.40x from both sides)
x = 60
So, you have to add 60 mL of the 70% solution.
Hope this helps! :)
is -70 a integer or rational number
Answer:
all integers are rational numbers
Step-by-step explanation:
Find the 63rd term of the following arithmetic sequence.
17, 21, 25, 29, ...
Answer:
265
Step-by-step explanation:
the nth term of an arithmetic progression is given by
[a+(n-1)d]
where "a" is the first term, "d" is the common difference and "n" is the term you're looking for
from the question, a= 17
d=4
n=63
substituting, [17+(63-1)4]=[17+248]=265
HELP URGENT!!!!! WILL MARK BRAINLIEST!!!!
Which equation best fits the graph given?
a. f(x)=(x-1)^3 (x+2)^2
b. f(x)=(x+1)^2(x-2)^3
c. f(x)=(x-1)^2 (x+2)^3
d. f(x)=(x+1)^3(x-2)^2
e. None of the above
Briefly explain how you decided on the equation.
Answer:
D
Step-by-step explanation:
first find the zeros on the graph and their multiplicity.
zeros: -1, 2
mult: 3, 2
the equation that fits is f(x)=(x+1)^3(x-2)^2
Which mixed number is the GREATEST?
Brain pop btw
A 3 5/8
B 8 1/2
C 7 1/5
D 1 7/5
Answer: 8 1/2
I can't give an explanation though
A gym offers a 12-month membership for $125 or an 8-month membership for $90. Which option has the lesser price per month?
Answer:
12-month option is cheaper per month
Step-by-step explanation:
A gym offers a 12-month membership for $125 or an 8-month membership for $90. Which option has the lesser price per month?
12-month option:
125/12 = $10.42
8-month option:
90/8 = $11.25
12-month option is cheaper per month.
Which of the following values are solutions to the
inequality 9 3x + 4?
I. 7 II. 8
III. 2
On solving the inequality we get that values 7 and 8 are solutions to the inequality, hence, option 3.
Here, we are given an inequality as follows-
9 < 3x + 4
Inequalities are solved in a similar manner as we solve equations.
Subtracting 4 from both sides of the inequality we get-
9 - 4 < 3x + 4 - 4
5 < 3x
dividing both sides by 3, we get-
5/3 < 3x/3
5/3 < x
x > 5/3
5/3 in decimal can be written as 1.66
Thus,
x > 1.66
From the given options only 7 and 8 are greater than 1.66.
Thus, on solving the inequality we get that values 7 and 8 are solutions to the inequality, hence, option 3.
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Find the solution for −0.4x − 4.15 = x − 1.6 − 2.97.
x = −3.3
x = 3.3
x = −0.3
x = 0.3
Answer:
x=0.3
Step-by-step explanation:
-0.4x-4.15=x-1.6-2.97
-0.4x-x=-(1.6-2.97)+4.15
-1.4x=0.42
x=0.3
Answer:
x=0.3
Step-by-step explanation:
Hannah is the oldest of four siblings whose ages are consecutive integers. If the sum
of their ages is 86, find Hannah's age.
Four siblings whose ages are consecutive integers. If the sum of their ages is 86 then The eldest sibling is 20, followed by siblings 21, 22, and 23.
What is consecutive integers ?Consecutive means in order. Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.
Let x = the one sibling
Let x + 1 = the second sibling
Let x + 2 = the third sibling
Let x+4 = the fourth sibling.
If you add the four siblings together they equal 86
(x) + (x +1) + (x + 2) + (x+3) = 86 I put the parentheses in so that you can see each sibling, but it is not needed.
x + x+ 1 +x + 2 + x+ 3 = 86 Combine like terms
4x + 6 = 86 Subtract 6 from both sides
4x = 80
x = 20
The eldest sibling is 20, followed by siblings 21, 22, and 23.
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whats the co-ordinates of the midpoint of (3,11) and (7,21)
The coordinates of the mid- point are (5, 16)
Given,
The midpoint of the line, given any points A (x₁, y₁) and B(x₂, y₂) .
In the question, we are given that the midpoint is (3, 11) and (7, 21).
and, to find the co- ordinates of the line.
Now, We know that the Formula of mid point
M = ({(x₁ + x₂)/2},{(y₁ + y₂)/2}).
Here, the points are (3, 11) and (7, 21)
Therefore,
(x, y) = ({(x₁ + x₂)/2},{(y₁ + y₂)/2}).
=> (x, y) = [( [tex]\frac{3+7}{2}[/tex]) , ([tex]\frac{11 + 21}{2}[/tex]) ]
=> (x , y) = (10/2 , 32/ 2)
=> (x ,y) = (5 , 16)
Hence, The coordinates of the mid- point are (5, 16)
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5. Roger put down carpet in half of his bedroom, which is shown below. Which answer shows the area of his bedroom that has carpet?
Option(A) i.e, 60 sq. feet is an answer.
Define Area of rectangleThe area of a rectangle is the number of unit squares that its perimeter includes. A rectangle's area is the area it takes up within the confines of its four sides. The area of a rectangle is determined by its dimensions. A rectangle's area is essentially equal to the product of its length and breadth. A shape's area is defined as the "space enclosed within the perimeter or the boundary" of the given shape.
The area of a rectangle can be calculated using the formula Area of rectangle = length × width.
Given, length = 15 feet, width = 4 feet
put these values in given formula,
Area of rectangle = 15 * 4
= 60 square feet
Hence, the answer is option(A) i.e, 60 sq. feet.
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I need help solving this math problem
Answer: y=15, AQ=31, QX=14
Step-by-step explanation:
2y+1+y+1=45
3y=45
•1/3 to both sides
y=15
then substitute 15 for y in the other equations to get the result
pls help have to turn this in by midnight
Answer:
Point-slope form: y - 6 = -1/3(x + 6)
Slope-intercept form: y = -1/3x + 4
Write the equation of a line with slope=2/3 and passes through the point (15/6, -4/11)
Answer: y=2/3x-2.03
Step-by-step explanation: This may not be exactly correct, and I don't know if you're using standard form, but I used demos the graphing calculator to make a graph, and that matches down to the 0.03 of the line.
I hope this helps, brainliest would be appreciated <3
7. The temperature has been changing at the rate of -1.5° each hour. The starting
reading is 0°. What was the temperature 7 hours ago? Justify your answer.
Hello,
The temperature changes at rate of -1.5 degree celsius every hours and the reading of temperatures starts at 0 degree celsius which can be modeled into the linear equation of f(t) = -1.5t where f(t) is the temperature function and t is time.
The problem then asks, “what was the temperature 7 hours ago?” This question asks for the temperature 7 hours ago which means t = -7 in this case since we are solving for temperature 7 hours ago, not next 7 hours.
Time being negative in this scenario means in past or hours ago, generally time cannot be negative as it’s scalar quantity.
Substitute t = -7 in the temperature function, this’ll result in:
f(-7) = -1.5(-7)f(-7) = 10.5Therefore, 7 hours ago, the temperature was at 10.5 degree celsius. Please let me know if you have any questions!
Evaluate the numerical expression open parentheses 3 to the power of 2 close parentheses to the power of one third. 3 cube root of 9 cube root of 128 square root of 9
The simplified expression for this problem is given as follows:
(3²)^(1/3) = 3^(2/3) = [tex]\sqrt[3]{9}[/tex]
What is the power of a power rule?The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
The exponents for this problem are given as follows:
2 and 1/3.
Hence the product is of:
2 x 1/3 = 2/3.
Converting the fractional exponent to a rational expression, we have that:
3^(2/3) = [tex]\sqrt[3]{3^2} = \sqrt[3]{9}[/tex]
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You are ordering shirts for a club at your school. The function f(x)=12x+25 represents the cost of ordered x shirts. How much would it cost to buy 68 shirts?
The Cost of 68 shirts is 841. The total cost formula is used to calculate a total by combining the variable and fixed costs of providing goods.
What is meant by total cost?Total cost = (average fixed cost x average variable cost) x number of units produced is the formula. To use this formula, you must first determine your fixed and variable costs. Total cost refers to the total cost of making an investment, which includes the investment cost as well as any broker commissions, taxes, licenses, and fees associated with the transaction. When calculating the return on investment, all of these costs should be considered. Total fixed costs are the sum of all a company's consistent, non-variable expenses.How to find Cost :
f(x) = 12x+25where f(x) is the cost of the shirt.X represents the number of shirts.Substitute x=68 in the above equation
so , f(x) = 12 (68)+25
f(x) = 841
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Alex bought 6 books for 8 dollars. He had 20% off the total cost ($8) how much did he pay for the books? It’s asking to write it up in 2 decimal places
SOLUTION
The total cost of the books is $8
Calculating 20% off gives
[tex]\begin{gathered} 8-20\%\times8 \\ =8-1.6 \\ =6.4 \end{gathered}[/tex]Therefore the amount paid is $6.40
Question 12 of 25
Which of these terms does not describe polygon A'B'C'D?
Polygons A'B'C'D' are not described by the rem preimage. The initial form before a change is known as the preimage. The transformation in the example below involves both a rotation and a dilation.
What are polygons?When three or more line segments are connected to one another, a polygon is created, which is a closed, two-dimensional, plane shape. Most frequently, when learning about geometry, we run into polygons.
A closed two-dimensional figure with three or more straight lines is what a polygon is defined as in geometry. Poly means "many" and gon means "angle" in Greek, making up the word "Polygon." We are surrounded by a wide variety of polygons.
An illustration of this is the hexagonal shape of a honeycomb. Every polygon has a unique structure, and they are all divided into different groups according to how many sides they have and other factors. This means that all polygons are closed plane shapes.
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Please please answer the questions in the photo! ( will mark brainliest )
The reason for the required step using the property of equality are as follow:
7. Addition property of equality.
8. Symmetric property of equality.
9. Reflexive property of equality.
10.Symmetric property of equality.
As given,
The reason for the required step using the property of equality are as follow:
7. 4x - 10 = 7 - 2x
4x+2x - 10 = 7
6x -10 = 7
Here
Addition Property of Equality is applied.
If x, y, and z are real numbers, and x=y
then
x+ z=y+ z
8. 6 = x
x = 6
Here Symmetric Property of Equality is applied.
If x and y are real numbers, then
x = y
y = x
9. 4 = 4
Here Reflexive Property of Equality is applied.
If x is a real number, then
x = x
10. -3 = x
x = -3
Here Symmetric Property of Equality is applied.
If a is a and b are real numbers then,
a = b
b = a
Therefore, The reason for the required step using the property of equality are as follow:
7. Addition property of equality.
8. Symmetric property of equality.
9. Reflexive property of equality.
10.Symmetric property of equality.
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malik is younger than daniel. their ages are consecutive integers. find malik’s age if the product of their ages is 42.
Answer:
go to gogle
Step-by-step explanation:
The consecutive age is 6 and 7 and Malik is 6 years old.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let their Consecutive age be x, x+1
So, x(x+ 1)= 42
x²+ x - 42 = 0
x² + 7x- 6x - 42=0
x( x+ 7)- 6 ( x+ 7)= 0
(x+ 7)( x-6)= 0
x = 6, -7
Hence, the consecutive age is 6 and 7.
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An exponent is always smaller in value than the base. true/false
False. Exponent can be as big as it wants
8.
Mixed Practice: Simplify the expressions and express as a polynomial in standard form:
4. -3x(9x-4)
5.x(2x^2+x) 6. -5x^2-4x+1) 7. (3x-5y+z)-(2x-4y-z)
Answer:
4 = -27x^2+12x
5 = 2x^3+x^2
6 = -5x^2+4x-1
7 = x-y+2z
Step-by-step explanation:
Simple collecting like terms and distributive properties.
10. Which expression is equivalent to
(7.9x + 2)(0.5x)?
A. 3.95x² + 1
B. 3.95x2 + X
C. 7.9x² + 1
D. 7.9x² + 0.5x
Answer:
a.3.95x^2+1
9999999999999999999999999
"Here are some values of sequence D"
n | D(n)
1 | 13
5 | 7
7 | 4
A) "Write a recursive definition for the sequence"
B) "Write a definition for this sequence for the nth term"
Answer:
See below
Step-by-step explanation:
A) Recursive Definition
The value of each term in a sequence that starts at 13 is reduced by 1.5 for each step in the sequence.
B) Definition for nth Term
D(n) = D(1)+(n-1)(-1.5)
D(1) = 13
D(n) = 13+(n-1)(-1.5)
Examples:
D(5) = 13 + (5-1)*(-1.5)
D(5) = 13 + (4)*(-1.5)
D(5) = 13 - 6, or 7
------------------
D(7) = 13 + (7-1)*(-1.5)
D(7) = 13 + (6)*(-1.5)
D(7) = 4
Solving Inequalities with One Variable
Show work
21+21<63
Answer: infinitely many solutions
Step-by-step explanation:
21 + 21 < 63
Calculate
42 < 63
infinitely many solutions
Bryce wrote the linear regression equation y = 1.123 x minus 6.443 to predict the armspan, y, of a person who is x inches tall. riley has an armspan of 67.5 inches. which is the best prediction of riley’s height? 54.36 inches 65.84 inches 66.55 inches 69.36 inches
Finding the numeric value of the regression equation, the best prediction of Riley's height is given by:
65.84 inches.
Finding the numeric value of a function or of an expressionTo find the numeric value of a function, we replace each instance of the variable in the function or in the expression by the desired value.
The regression equation in this problem gives the armspan of a person, represented by y, as a function of the height x as follows:
y = 1.123x - 6.443.
Riley has an armspan of 67.5 inches, hence y = 67.5, and we can find the best prediction for his height replacing the lone instance of y in the equation by 67.5 and solving for x, as follows:
67.5 = 1.123x - 6.443.
1.123x = 67.5 + 6.443
x = (67.5 + 6.443)/1.123
x = 65.84 inches, which is the best prediction.
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Answer:
It’s B
Step-by-step explanation:I did it on edge 2022 got it right!
Hello could you please help me with question number 10?
Exponential Model
Some phenomena can be modeled as an exponential function of the form:
[tex]P=P_o(1+r)^t[/tex]Where Po is the initial value, r is the rate of change, and t is the time.
If the value of P decreases in time (decaying function), then r is negative. If the value of P increases in time (growth), then r is positive.
We know an investment of Po=$4500 has been losing value (decay) at a rate of r = -2.5% = -0.025 each year.
The value of the investment when t = 5 years is:
[tex]P=4500(1-0.025)^5[/tex]Calculating:
[tex]\begin{gathered} P=4500(0.975)^5 \\ P=4500\cdot0.8810957 \\ P=3964.93 \end{gathered}[/tex]The investment will be worth $3964.93 in 5 years
