Answer:
Domain: -6,-1,4,6,7
Range: -5,3,6,8,9
Step-by-step explanation:
The domain is the first element in each ordered pair. It is the x value. The range is the second element in each ordered pair. It is the y values.
The diagram below shows an equilateral triangle ABC, with each side 3 cm long. The side [BC] is extended to D so that CD = 4 cm.What is the length of side AD?Round your answer to two decimal places.
The triangle ABC is an equilateral triangle. This means that each angle equals 60°. Hence, the angle at B is 60°.
The length of each side of ABC is given to be 3 cm long.
We can get the length of side AD by solving the triangle ABD using the Cosine Rule given to be:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]Since we're considering triangle ABD, and we have the measure of angle B, we can use the relationship:
[tex]b^2=a^2+d^2-2ad\cos B[/tex]Note that a, b, and d are the sides, such that:
[tex]\begin{gathered} a=BD=BC+CD=3+4=7\operatorname{cm} \\ b=AD \\ d=AB=3\operatorname{cm} \end{gathered}[/tex]Substituting these values, we have:
[tex]\begin{gathered} AD^2=7^2+3^2-2(7\times3\times\cos 60) \\ AD^2=49+9-42\cos 60 \\ AD^2=37 \\ AD=\sqrt[]{37} \\ AD=6.08\operatorname{cm} \end{gathered}[/tex]The length of AD is 6.08 cm to 2 decimal places.
a communication system consists of n components, each of which will, independently, function with probability p. the total system will be able to operate effectively if at least one-half of its components function. (a) let x denote the number of functioning components out of the n components. what is the distribution of x? (b) what is the probability that a 5-component system will function? (c) for what values of p is a 5-component system more likely to operate effectively than a 3-component system?
A Communication system consists of n components.
a) Binomial distribution,
P(X=x) = ⁿC ₓ p ˣ (1-p) ⁽ⁿ⁻ˣ⁾
b) For 5-component system,
P(X= 5) = ⁵Cₓ pˣ (1-p)⁵⁻ˣ , x= 3,4,5
c) 5-component system is effectively than a 3-component system if 0.5<p<1 where p is probability of functioning components.
Communication system consists of n components and functions with probability p . Then the probability of components which are not function from n components is q = 1-p .
(a) Let x denotes number of functioning components i.e., their probability value is p . And system is effectively operate when atleast one half of components are function. So, the distribution of x is binomial distribution P (X=x) = ⁿCₓ pˣ (1-p)⁽ⁿ⁻ˣ⁾ where n is total number of components, x numbers of functioning components, p is probability of functioning components.
(b) Now , 5-component system is function . That is n=5
Probability that 5-components system will function is P(X= 5)
= ⁵C ₓ p ˣ(1-p)⁽⁵⁻ˣ⁾ , x= 3,4 ,5 ( because one half of components are function)
(c) Because the number of functioning components is a binomial random variable with parameters (n, p), it follows that the probability that a 5-component system will be effective is
⁵ C₃ p³(1-p)² + ⁵C₄ p⁴ (1-p)¹+ ⁵C ₅ p⁵ (1-p)⁰ = 10 p³ (1-p)² + 5 p⁴(1-p) + p⁵
Whereas the corresponding probability for a 3-components system
³ C ₓ p ˣ ( 1-p)⁽ⁿ⁻ˣ⁾ , x= 2,3
³ C₂ p²(1-p)¹ + ³C₃p³(1-p)⁰ = 3 p² 1-p) + p³
5-Component system is better than 3-Components system if
10 p³ (1-p)² + 5p⁴ (1-p) + p⁵= 3p²(1-p) + p³
=> 10 p⁵ + 10 p³– 20 p⁴+ 5 p⁴ – 5p⁵ + p⁵ = 3p² + p³ – 3p²
Which reduce to
3( 2p -1) (1-p) 2 > 0 , either (2p-1) > 0 or 3(1-p) 2>0
either p> ½ or p <1
=> p belongs to ( 0.5, 1)
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You had $21 to spend on five notebooks after buying them u had $6 dollars how much did each notebook cost.
Let x be the cost of each notebook. We know that we bought 5 of them, then the total cost of the notebooks is:
[tex]5x[/tex]We had 21 dollars and we spent 5x on the notebooks, this can be express as:
[tex]21-5x[/tex]Finally we know that this is equal to the six dollars we had at the end, then we have the equations:
[tex]21-5x=6[/tex]Solving for x we have:
[tex]\begin{gathered} 21-5x=6 \\ 21-6=5x \\ 5x=15 \\ x=\frac{15}{5} \\ x=3 \end{gathered}[/tex]Therefore each notebook cost $3
find the number of terms in the sequence 1,-4,16,...,65536
Answer:
9 terms
Step-by-step explanation:
The sequence given is a geometric sequence
In a geometric sequence, the nth term of the sequence can be found by the formula
[tex]a_n = a_1r^{n-1}[/tex]
[tex]\text{where }\\\\ a_n = \text {nth term}\\\\\text{$a_1 = $ first term}\\\\\text{$r = $ common ratio}[/tex]
In the given sequence,
a₁ = 1
r = -4
aₙ = 65536
So we get the relation:
65536 = 1· (-4)ⁿ⁻¹
65536 = (-4)ⁿ⁻¹
It is clear that n-1 has to be even so that the power of 4 is positive.
Substituting x = n -1 where x is even gives us
4ˣ = 65536
If we take logarithms to the base 4 on both sides we get
=> x = [tex]\log_465536 = 8\\\\[/tex]
Since x = n - 1 and x = 8, n = 9
So the 9th term in the series is 65536
Please help me I don’t know it
Answer:
angle 4 and 5 are interior angles, and 3 and 6 as well
a=3,k=12,z=6,h=4 Evaluate the algebraic expression z+15=?
since z=6, so z+15 is equal to 21
or a+k+z=21
question 8 a large hotel chain sees about 500 customers per week. a data analyst working there is gathering data through customer satisfaction surveys. they are anxious to begin analysis, so they start analyzing the data as soon as they receive 50 survey responses. this is an example of what? select all that apply.
The sampling strategy used in this problem is an example of:
Failing to include diverse perspectives in the collection.Failing to choose a large enough sample size.What is sampling?Sampling is when a subset of an entire population is studied, to verify whether characteristics of the sample can be expanded to the entire population.
The sample has to be representative of the population, that is, large enough, hence it should contain all the subsets of the population.;
In the context of this problem, the chain sees about 500 customers a week and they receive the responses from 50 of them. This is a not large enough sample size, hence it could cause biased results, meaning that the perspective of the entire population will not be considered.
In the context of this problem, the survey are anonymous, and the objective of a survey is generally not to reward the participants, hence the last two options are false.
What is the missing information?The options are given as follows:
Failing to include diverse perspectives in the collection.Failing to choose a large enough sample size.Failing to reward customers for participating in the survey.Failing to collect data anonymously.More can be learned about sampling at https://brainly.com/question/9910540
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The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
Answer:
A) there are no outliers in this distribution.
Assume the given function is one to one.Find the indicated values
To solve this question, you have to look for the answers in the table.
Let's analise each part of the question to solve it:
(a) f(1) =
f(1) means the output of the function [f(x)] when x = 1.
Looking for x =1 in the table, you can see that f(x) = 0.
f(1) = 0.
(b) f(x) = 3, x =
Now, you have to find the input (x) when the outpout [f(x)] is 3.
Looking for f(x) = 3, you can see that x = 7.
f(x) = 3, x = 7.
(c) f⁻¹(0) =
Now, you have to evaluate the inverse function.
To look for the values of the inverse function, x will be the output and f⁻¹ will be the input.
To look for f⁻¹(0), look for f(x) = 0 (input) and the output will be 1
f⁻¹(0) = 1.
(d) f⁻¹(x) = 7; x =
Again, you have an inverse function. So, 7 will be the input in the table (x). x is 7 (output).
f⁻¹(x) = 7; x = 3.
karem drives his car 96 miles per hour 1 1/2 hours how many miles will he drive in 2 1/2 hours
NEEd HELP 9th grade asp
Answer:175/48
Step-by-step explanation:
helpppppp math its hard for me
Step-by-step explanation:
You would start off with solving inside, the parenthesis, and you would get -8/27.
Then, your would solve the 1 1/4 - 3/4 and get 1/2.
You then have to multiply -8/27*1/2, which is -4/27.
Lastly, you divide by negative 4.
-4/27 divided by -4.
You have to flip it to multiply the reciprocal, and you get -4/27*-1/4.
Since negative times negative is positive, the answer would be 1/27.
Answer:
1/27
Hope this helped! :)
Taylor and Emily are painting banners for their Halloween Party. Taylor’s banner is 8 inches tall and 564 inches wide. The area of Emily’s banner is 10 times as large as the area of Taylor’s banner. What is the area of Emily’s banner, in square inches?
Answer:
[tex]45120 in^2[/tex]
Step-by-step explanation:
Area of Taylor's Banner (AT): [tex]A_T = 8*564=4512 in^2[/tex]
Area of Emily's Banner (AE): [tex]A_E=10*A_T[/tex]
Plugging in AT: [tex]A_E = 10 * 4512 = 45120 in^2[/tex]
The Area of Emily's Banner is 45120 inch²
What is Area of rectangle?The Area of rectangle is the product of its length to its width.
i.e., Area of rectangle= length x width
Given:
Taylor’s banner : 8 inches tall and 564 inches wide.
Area of Taylor's Banner= l x w
= 8 x 564
= 4512 inch²
and, area of Emily’s banner is 10 times as large as the area of Taylor’s banner.
So, Area of Emil's Banner= 10 x 4512
= 45120 inch²
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Santiago's car used 15 gallons to travel 525 miles. How far can he travel on 19 gallons?
Answer:
665
Step-by-step explanation:
the reasoning is because you divide 525/15 and you get 35 with that you multiply by 19 because you are seeing how far you can get with 19 gallons of gas .
665 miles Santiago can travel on 19 gallons of fuel.
What is the ratio?A ratio in mathematics demonstrates how many times one number is present in another.
Given, Santiago's car used 15 gallons to travel 525 miles. Since,
Santiago travels in 15 gallons = 525 miles
Santiago travels in 1 gallons = 525/ 15 = 35
Santiago travels in 19 gallons = 35* 19 = 665
Therefore, Santiago can travel 665 miles on 19 gallons of fuel.
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The line perpendicular to y=-3x+4 that passes through the point (-3,-7)
Answer:
Step-by-step explanation:
A perpendicular line will have a sope that is the negative inverse of the reference line. The reference line is y = -3 + 4, with a slope of -3. The negative inverse would be -(-1/3) or (1/3).
The new line will take the form of y = (1/3)x + b, where b is the y-intercept (the value of y when x=0). We want the new line to go through point (-3,-7). We;ll need a value of b that will make that happen. To find b, enter the given data point and solve for b:
y = (1/3)x + b for (-3,-7).
-7 = (1/3)(-3) + b
-7 = -1 + b
b = -6
The new equation is y = (1/3)x - 6
See the attached graph.
What is the slope of the line that passes through the points (-6, 1) and (-6,-4)?
Write your answer in simplest form.
Answer:
The slope is undefined
Step-by-step explanation:
Which of the following best estimates the sum 1 1 2 3 B 0.5 0.8
we have
1/2 +1/3
Remember that
1/2=0.5
1/3=0.33 -----> rounded 0.3
so
0.5+0.3=0.80
Answer: please help
Step-by-step explanation: I don’t know what the answer is I need help
what is the probability that a card drawn randomly from a standard deck of 52 cards is a red three? express your answer as a fraction in lowest terms or a decimal number rounded to three decimal places, if necessary.
Answer:
1/26
Step-by-step explanation:
If the cards are all there, you can count there are 2 red threes. And there are 52 cards. The fraction is 2/52 or 1/26
PLEASE HELP
what is the value of x? justify each step
AC= 32
Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. For illustration: If we take 45 into account. Here, the fourth digit is in the tens column.
Explain about the value?Value in mathematics is a number that represents the outcome of a computation or function. In the aforementioned example, you may inform your teacher that 5 + 6 Equals 30 or that x + y = 9 if x = 6 and y = 3. A variable or constant can also be referred to as a value.
X has a value of 3. The following is a list of the arguments made for each step.
Adding more line segments
Rule of substitution (b)
c) Simplifying by incorporating related terms
d) Compiling terms for lies
e) Multiplying each side by 8
AB = 2x
BC = 6x + 8
AC = 32
AB plus BC equals AC. (Extension rule)
addition of a line's individual segments
2x + 6x + 8 = 32 (Substitution rule) (Substitution rule)
replacing AB, BC, and AC in the formula AB + BC = AC
8x + 8 = 32 (Simplification) (Simplification)
2x + 6x + 8 = 32, simplified adding comparable terms
8x = 24 (Assembling similar terms)
8x = 32 - 8
8x = 24
x = 3 (Divide both sides by 8) (Divide both sides by 8)
8x / 8 = 24/8
x = 3
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Draw the preimage and image of the polygon with the vertices X(-1,4), Y (2,2), and Z(0,-1) translated using the vector <2,-37>
Answer:
12
Step-by-step explanation:
find the product
6x/(-2)
Answer:
-12xy
The result of the expression given as 6x/(-2) is -3x
How to determine the product?From the question, the expression is given as
6x/(-2)
The above expression is a quotient expression
So, we start by rewritting it as a product
This is represented as
6x/(-2) = 6x * 1/(-2)
Remove the bracket
So, we have the following equation
6x/(-2) = 6x * 1/-2
Evaluate the product
6x/(-2) = -3x
Hence, the value of the expression is -3x
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find the volume of a cone with a height of 100 feet and a radius of its base 100 feet use 3.14 for pi
The volume of a cone is given as follows;
[tex]\begin{gathered} \text{Vol}=\frac{1}{3}(\pi\times r^2\times h) \\ \text{The radius of the base r=100, h=100} \\ \text{Vol}=\frac{1}{3}\times3.14\times100^2\times100 \\ \text{Vol}=\frac{3.14\times10000\times100}{3} \\ \text{Vol}=1046666.67 \\ \text{Vol}\approx1046666.67ft^3\text{ (rounded to the nearest hundredth)} \end{gathered}[/tex]The volume of the cone with the given dimensions is
1,046,666.67 cubic feet (rounded to the nearest hundredth)
Without approximation, the answer would be,
1,046,666.6666 cubic feet
Given that f(x)=x^2-3x-54and g(x)=x-9 find (x)(f⋅g)(x)
Answer: [tex]x^4 - 12x^3 - 27x^2 +486x[/tex]
Step-by-step explanation:
[tex](f \cdot g)(x)=f(x)g(x)\\\\=(x^2 -3x-54)(x-9)\\\\=x^3 - 9x^2 - 3x^2 + 27x - 54x + 486\\\\=x^3 -12x^2 -27x+486\\\\\therefore x(f \cdot g)(x)=x(x^3 -12x^2 -27x+486)\\\\=x^4 - 12x^3 - 27x^2 +486x[/tex]
help me answer this question please
Answer:
sum = -15/2
Step-by-step explanation:
Given the formula for the n-th term of a sequence is n(n-8)/√(n+3), you want the sum of the 1st and 6th terms.
First termThe first term is found by substituting 1 for n:
1(1 -8)/√(1 +3) = 1(-7)/√4 = -7/2
Sixth termThe sixth term is found by substituting 6 for n:
6(6 -8)/√(6 +3) = 6(-2)/√9 = -12/3 = -4
SumThe sum of the first and sixth terms is ...
-7/2 +(-4) = -(7/2 +8/2) = -15/2
sum = -7 1/2
Please help me do my Math Homework ASAP, it is attached.
Answer:
Step-by-step explanation:
Pleas help me !!!! Please!!!
The most appropriate choice for domain of a functions will be given by -
What is a domain of a function
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
The set of values for which the function is defined is called domain of the function.
Here, from the graph, the set of values of x axis for which the graph is drawn is [tex]-6\leq x \leq 6[/tex].
And values of x - axis represents the domain.
So domain of function is {x ∈ [tex]\mathbb{R}[/tex], [tex]-6 \leq x \leq 6[/tex]}
Third option is correct.
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Given the image Q’(33, 36) and preimage Q(11, 12), by what scale factor was the point dilated?
22
3
24
1/3
Answer:
22
Step-by-step explanation:
Use spinner and color key to find the indicated probabilities. Landing on green or a vowelNot landing on yellow or a constant
Solution:
The spinner has a total of 8 sections.
There are two green sections and 4 four vowel sections where one of the vowels is also green.
Then, the probability of landing on green or a vowel is;
[tex]\frac{5}{8}=0.625[/tex]Which expression is equivalent to the given expression? (+2+6)-(- 2+3) x +9 O A I O B. - } +3 O C. x+3 OD. - *+9
Answer:
The equivalent expression is;
[tex]\frac{5}{7}x+3[/tex]Explanation:
We want to simplify the expression;
[tex](\frac{1}{7}x+6)-(-\frac{4}{7}x+3)[/tex]we will first multiply the negative by every term in the bracket, then simplify by collecting the like terms.
[tex]\begin{gathered} \frac{1}{7}x+6-(-\frac{4}{7}x)-(+3) \\ \frac{1}{7}x+6+\frac{4}{7}x-3 \\ \text{collecting the like terms we have;} \\ \frac{1}{7}x+\frac{4}{7}x+6-3 \\ \frac{5}{7}x+3 \end{gathered}[/tex]Therefore, the equivalent expression is;
[tex]\frac{5}{7}x+3[/tex]Find the measure of the complement for the angle 1 degree
89 degrees
Explanations:
The sum of an angle and its complement is equal to 90 degrees.
Let the measure of the complement be "x"
Given the information below:
Angle = 1 degrees
Taking the sum of the angle and its complement will give:
[tex]x+1^0=90^0[/tex]Subtract 1 from both sides
[tex]\begin{gathered} x+1-1=90-1 \\ x+0=90-1 \\ x=89^0 \end{gathered}[/tex]Therefore the measure of the complement for the angle given is 89 degrees