Given:
The system of inequalities:
[tex]y\leq \dfrac{1}{2}x+2[/tex]
[tex]y<-2x-3[/tex]
To find:
Whether the points (–3,–2) and (3,2) are in the solution set of the given system of inequalities.
Solution:
A point is in the solution set of the given system of inequalities if it satisfies both inequalities.
Check for the point (-3,-2).
[tex]-2\leq \dfrac{1}{2}(-3)+2[/tex]
[tex]-2\leq -1.5+2[/tex]
[tex]-2\leq 0.5[/tex]
This statement is true.
[tex]-2<-2(-3)-3[/tex]
[tex]-2<6-3[/tex]
[tex]-2<3[/tex]
This statement is also true.
Since the point (-3,-2) satisfies both inequalities, therefore (-3,-2) is in the solution set of the given system of inequalities.
Now, check for the point (3,2).
[tex]2<-2(3)-3[/tex]
[tex]2<-6-3[/tex]
[tex]2<-9[/tex]
This statement is false because [tex]2>-9[/tex].
Since the point (3,2) does not satisfy the second inequality, therefore (3,2) is not in the solution set of the given system of inequalities.
Answer: The point (–3,–2) is in the solution set, and the point (3,2) is not in the solution set.
Please mark Brainliest Thank you :)
the adjacent sides of a parallelogram are (x + 3) and (x + 2). Find the perimeter of the parallelogram
9514 1404 393
Answer:
4x+10
Step-by-step explanation:
For parallelogram adjacent sides a and b, the perimeter is ...
P = 2(a +b)
For the given sides, the perimeter is ...
P = 2((x +3) +(x +2)) = 2(2x +5)
P = 4x +10 . . . perimeter of the parallelogram
The cost of producing a custom-made clock includes an initial set-up fee of $1,200 plus an additional $20 per unit made. Each clock sells for $60. Find the number of clocks that must be produced and sold for the costs to equal the revenue generated. (Enter a numerical value.)
Answer:
30 clocks
Step-by-step explanation:
Set up an equation:
Variable x = number of clocks
1200 + 20x = 60x
Isolate variable x:
1200 = 60x - 20x
1200 = 40x
Divide both sides by 40:
30 = x
Check your work:
1200 + 20(30) = 60(30)
1200 + 600 = 1800
1800 = 1800
Correct!
Suppose the method of tree ring dating gave the following dates A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.
1241 1210 1267 1314 1211 1299 1246 1280 1291
a. Determine if the data meets the initial conditions to construct a confidence interval.
b. Find the sample mean year x and sample standard deviation σ.
c. What is the maximal margin of error when finding a 90 % confidence interval for the mean of all tree-ring dates from this archaeological site?
Answer:
(1238.845 ;1285.376)
Step-by-step explanation:
Conditions for constructing a confidence interval :
Data must be random
Distribution should be normal and independent ;
Based on the conditions above ; data meets initial conditions ;
C. I = sample mean ± margin of error
Given the data :
1241 1210 1267 1314 1211 1299 1246 1280 1291
Mean, xbar = Σx / n = 11359 / 9 = 1262.11
The standard deviation, s = [√Σ(x - xbar)²/n - 1]
Using a calculator ; s = 37.525
The confidence interval :
C.I = xbar ± [Tcritical * s/√n]
Tcritical(0.10 ; df = n - 1 = 9 - 1 = 8)
Tcritical at 90% = 1.860
C. I = 1262.11 ± [1.860 * 37.525/√9]
C.I = 1262.11 ± 23.266
(1238.845 ;1285.376)
± 23.266
The margin of error :
[Tcritical * s/√n]
[1.860 * 37.525/√9]
C.I = ± 23.266
which of the following values could NOT be a probability
Answer:
3/2, -1.1
Step-by-step explanation:
the probability cannot be greater than 1. probability is between 0 and 1
1. In the number 123,546,870, which digit
is in the hundred thousands place?
Answer:
5
Step-by-step explanation:
Suppose a rumor is going around a group of 191 people. Initially, only 38 members of the group have heard the rumor, but 3 days later 68 people have heard it. Using a logistic growth model, how many people are expected to have heard the rumor after 6 days total have passed since it was initially spread? (Round your answer to the nearest whole person.)
Answer:
106 people.
Step-by-step explanation:
Logistic equation:
The logistic equation is given by:
[tex]P(t) = \frac{K}{1+Ae^{-kt}}[/tex]
In which
[tex]A = \frac{K - P_0}{P_0}[/tex]
K is the carrying capacity, k is the growth/decay rate, t is the time and P_0 is the initial value.
Suppose a rumor is going around a group of 191 people. Initially, only 38 members of the group have heard the rumor.
This means that [tex]K = 191, P_0 = 38[/tex], so:
[tex]A = \frac{191 - 38}{38} = 4.03[/tex]
Then
[tex]P(t) = \frac{191}{1+4.03e^{-kt}}[/tex]
3 days later 68 people have heard it.
This means that [tex]P(3) = 68[/tex]. We use this to find k.
[tex]P(t) = \frac{191}{1+4.03e^{-kt}}[/tex]
[tex]68 = \frac{191}{1+4.03e^{-3k}}[/tex]
[tex]68 + 274.04e^{-3k} = 191[/tex]
[tex]e^{-3k} = \frac{191-68}{274.04}[/tex]
[tex]e^{-3k} = 0.4484[/tex]
[tex]\ln{e^{-3k}} = \ln{0.4484}[/tex]
[tex]-3k = \ln{0.4484}[/tex]
[tex]k = -\frac{\ln{0.4484}}{3}[/tex]
[tex]k = 0.2674[/tex]
Then
[tex]P(t) = \frac{191}{1+4.03e^{-0.2674t}}[/tex]
How many people are expected to have heard the rumor after 6 days total have passed since it was initially spread?
This is P(6). So
[tex]P(6) = \frac{191}{1+4.03e^{-0.2674*6}} = 105.52[/tex]
Rounding to the nearest whole number, 106 people.
7b please make the graph look nice and neat and easy to read.
Answer:
Step-by-step explanation:
A website manager has noticed that during the evening hours, about 3.23.2 people per minute check out from their shopping cart and make an online purchase. She believes that each purchase is independent of the others and wants to model the number of purchases per minute.
1. What model might you suggest to model the number of purchases per minute?
a. Binomial
b. Uniform
c. Poisson
d. Geometric
2. What is the probability that in any one minute at least one purchase is made?
3. What is the probability that no one makes a purchase in the next 2 minutes?
Answer:
1. c. Poisson
2. 0.9592 = 95.92% probability that in any one minute at least one purchase is made.
3. 0.0017 = 0.17% probability that no one makes a purchase in the next 2 minutes.
Step-by-step explanation:
We have only the mean, which means that the Poisson distribution is used to solve this question, and thus the answer to question 1 is given by option c.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Mean of 3.2 minutes:
This means that [tex]\mu = 3.2n[/tex], in which n is the number of minutes.
2. What is the probability that in any one minute at least one purchase is made?
[tex]n = 1[/tex], so [tex]\mu = 3.2[/tex].
This probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3.2}*3.2^{0}}{(0)!} = 0.0408[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0408 = 0.9592[/tex]
0.9592 = 95.92% probability that in any one minute at least one purchase is made.
3. What is the probability that no one makes a purchase in the next 2 minutes?
2 minutes, so [tex]n = 2, \mu = 3.2(2) = 6.4[/tex]
This probability is P(X = 0). So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-6.4}*6.4^{0}}{(0)!} = 0.0017[/tex]
0.0017 = 0.17% probability that no one makes a purchase in the next 2 minutes.
convert the following fractions to decimals using a different method for each. explain why you chose that method for that particular example. SHOW ALL WORK!!
9514 1404 393
Answer:
a. 0.28
b. 0.125
Step-by-step explanation:
a) We recognize 25 as a divisor of 100, a power of 10, so we can convert the fraction to one that has 100 as a denominator.
[tex]\dfrac{7}{25}=\dfrac{7}{25}\cdot\dfrac{4}{4}=\dfrac{28}{100}=0.28[/tex]
__
b) We can convert this fraction to a decimal by dividing the numerator by the denominator. The work is shown in the attached.
1/8 = 0.125
Create truth table to determine whether or not the following statements are logically equivalent
The statement is totally false.
[tex]\neg P\lor\neg Q \equiv \neg(P \land Q) \not\equiv P\land Q[/tex]
because (P and ¬P) is a contradiction.
p and q are two numbers.whrite down an expression of. a.) the sum of p and q. b) the product of p and q
Answer:
A. p+q
B. (p)(q)
Step-by-step explanation:
A. The sum of the variables will be p+q, since we are just adding the two variables together.
B. The product of the variables will be (p)(q), or just pq, since you are simply multiplying the two variables.
Hope this Helps!!
y
27
х
10
11
12
In order for the data in the table to represent a linear
, function with a rate of change of -8, what must be the
value of a?
a
11
O a = 2
O a = 3
O a = 19
a = 35
The value of a that would make the data in the table represent a linear function with a rate of change of -8 is a = 19.
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The rate of change of a linear function is also known as the slope of the function.
To determine the slope of the function represented by the given table, we need to calculate the change in Y for a unit change in X.
Using the values given in the table, we can calculate the slope as follows:
Slope = (Change in Y) / (Change in X)
So,
(a - 27) / (11 - 10) = (11 - 27) / (12 - 10) = -8
Setting this equation equal to -8, we get:
= (a - 27) / 1
= -8
Simplifying the equation, we get:
a - 27 = -8
a = 19
Therefore,
The value of a that would make the data in the table represent a linear function with a rate of change of -8 is a = 19.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ7
Determine the domain and range of the graph
Answer:
5 ≤ x ≤ 10 5 ≤ y ≥ -1
Step-by-step explanation:
A consumer electronics company is comparing the brightness of two different types of picture tubes for use in its television sets. Tube type A has mean brightness of 100 and standard deviation of 16, and tube type B has unknown mean brightness, but the standard deviation is assumed to be identical to that for type A. A random sample of tubes of each type is selected, and is computed. If equals or exceeds , the manufacturer would like to adopt type B for use. The observed difference is . a. What is the probability that exceeds by 3.0 or more if and are equal
Answer:
The answer is "0.7794".
Step-by-step explanation:
Please find the complete question in the attached file.
Given:
[tex]\to n_{1}=n_{2}=25\\\\[/tex]
Hypotheses:
[tex]\to H_{0}:\mu_{B}-\mu_{A}\geq 0\\\\\to H_{a}:\mu_{B}-\mu_{A}< 0\\\\[/tex]
Testing statistics:
[tex]\to z=\frac{(\bar{x}_{B}-\bar{x}_{A})-(\mu_{B}-\mu_{A})}{\sqrt{\frac{\sigma^{2}_{B}}{n_{1}}+\frac{\sigma^{2}_{A}}{n_{2}}}}=\frac{3.5-(0)}{\sqrt{\frac{16^{2}}{25}+\frac{16^{2}}{25}}}=0.77[/tex]
The test is done just so the p-value of a test is
[tex]\to p-value = P(z < 0.77) = 0.7794[/tex]
Because the p-value of the management is large, type B can take it.
Cyril has six more than twice as many mangoes as Kubie and half as many mangoes as Maxine. If Kubie has six mangoes, then, in terms of x, how many mangoes do Cyril, Kubie, and Maxine have combined?
Answer:
(7x + 18) or 60 Mangoes
Step-by-step explanation:
Let the no. of mangoes Kubie possesses be x
So,
Cyril has mangoes = 2x + 6 ...(i)
So,
Maxine has = 2 * (2x + 6)
= 4x + 12
Given that,
Kubie has mangoes = 6
∵ The combined mangoes they have in terms of x,
= Cyril + Kubie + Maxine
= (2x + 6) + x + (4x + 12)
= 7x + 18
A.T.Q.
Cyril has = 2x + 6
∵ Cyril has mangoes = 2 * (6) + 6
= 18 mangoes
∵ Maxine has = 2 * Cyril's mangoes
= 2 * 18
= 36
Thus,
Total mangoes = Cyril + Kubie + Maxine
= 18 + 6 + 36
= 60 Mangoes
1 and 2 are supplementary.If m1 = (3x-17) and m2= (5x+21) find the value of x
Answer:
22
Step-by-step explanation:
m1 + m2 = 180
3x - 17 + 5x + 21 = 180
3x + 5x + 21 - 17 = 180
8x + 4 = 180
8x = 180 - 4
8x = 176
x = 176 / 8
x = 22
Chang has 2 shirts: a white one and a black one. He also has 2 pairs of pants, one blue and one tan. What is the probability, if Chang gets dressed in the dark, that
he winds up wearing the white shirt and tan pants? Show your work.
Answer:
1/4
Step-by-step explanation:
White = w
Black = B
Blue = b1
Tan = t
Wb1
Wt
Bbi
Bt
The answer will be 1/4, because there are 4 ways it can work and only 1 way it can be white shirt and tan pants.
Answer:
1/4
Step-by-step explanation:
it would be 1/4 because there are 4 different clothing pieces in total and there is only one way it would work the way the problem says.
Perimeter (numerical) cm
Answer:
101 cm
Step-by-step explanation:
Add all the side lengths up to get 101 cm.
Find x please step by step explanation need it
Answer:
19.27
Step-by-step explanation:
To find :-
The value of x .Answer :-
As we know that ,
→ cos ∅ = b/h
→ cos 33° = 16/x
→ 0.83 = 16/x
→ x = 16/0.83
→ x = 19.27
Anthony read 46 pages of a book in 23 minutes.
To find the unit rate, use
.
Anthony read
pages per minute.
Answer:
2 pages per minute
Step-by-step explanation:
Take the number of pages and divide by the number of minutes
46 pages / 23 minutes
2 pages per minute
2 Pages per Minute
Solutions:46 ÷ 23 = 2
Final Answer:Anthony can read 2 pages per minute.
find and sketch the domain of the function. f(x,y)=√(4-x^2-y^2) +√(1-x^2)
Answer:
Hello
Step-by-step explanation:
The domain is limited with 2 lines parallel: -1 ≤ x ≤ 1
and the disk ? (inside of a circle) of center (0,0) and radius 2
[tex]dom\ f(x,y)=\{(x,y) \in \mathbb{R} ^2 | \ -1\leq x \leq -1\ and \ ( -\sqrt{4-x^2} \leq \ y \leq \sqrt{4-x^2}\ ) \ \}\\[/tex]
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = -x+3
Step-by-step explanation:
Slope intercept form => y = mx+b
To find 'm', the slope, pick 2 coordinates.
(0,3)
(2,1)
Use this equation to find the slope using these 2 coordinates: (y1 - y2)/(x1 - x2)
(3 - 1)/(0 - 2) = -1
m = slope = -1
'b' is the y-intersept, or the point when a line passes through the y-axis. That's (0,3).
b = y-intercept = 3
So the equation will be y = -1x + 3, or y = -x + 3
if 3x=y+z, y=6-7, and z+x=8, what is the value of y/z?
Answer:
-4/25
Step-by-step explanation:
3x=y+z
y=6-7=-1
z+x=8
y/z=?
solution
3x=-1 + z
x= -1 + z\3 ...eq(*)
then, z= 8- x
z= 8 - (-1 +z)\3
z= 8 +(1- z )\3
z= 8+1\3 -z \3
= 24+1\3 - z\3
z=25\3-z\3
z+z\3=25\3
4z\3=25\3
4z=25
z=25/4
then,
25/4 +x = 8
x=8- 25/4
x= 32 - 25/4
x=7/4
so that,
y/z=-1 /25/4
=-4/25
I NEED HELP!! PLEASE
Answer:
Step-by-step explanation:
D is the answer. You shift the function to the left 5 units, hence the term |x+5|, and move it down 1, hence the term -1.
A boxcar contains six complex electronic systems. Two of the six are to be randomly selected for thorough testing and then classified as defective or not defective.
a. If two of the six systems are actually defective, find the probability that at least one of the two systems tested will be defective. Find the probability that both are defective.
b. If four of the six systems are actually defective, find the probabilities indicated in part (a).
Answer:
Step-by-step explanation:
Number of electronic systems = 6
(a) Number of defected systems = 2
Probability of getting at least one system is defective
1 defective and 1 non defective + 2 defective
= (2 C 1 ) x (4 C 1) + (2 C 2) / (6 C 2)
= 3 / 5
(b) four defective
Probability of getting at least one system is defective
2 defective and 2 non defective + 3 defective and 1 non defective + 4 defective
= (4 C 2 ) x (2 C 2) + (4 C 3 )(2 C 1) + (4 C 4) / (6 C 4)
= 1
Answer:
(a)P(At least one defective)[tex]=0.6[/tex]
P(Both are defective)[tex]=0.067[/tex]
(b)P(At least one defective)[tex]=14/15[/tex]
P(Both are defective)[tex]=0.4[/tex]
Step-by-step explanation:
We are given that
Total number of complex electronic system, n=6
(a)Defective items=2
Non-defective items=6-2=4
We have to find the probability that at least one of the two systems tested will be defective.
P(At least one defective)=[tex]\frac{2C_1\times 4C_1}{6C_2}+\frac{2C_2\times 4C_0}{6C_2}[/tex]
Using the formula
[tex]P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}[/tex]
P(At least one defective)[tex]=\frac{\frac{2!}{1!1!}\times \frac{4!}{1!3!} }{\frac{6!}{2!4!}}+\frac{\frac{2!}{0!2!}\times \frac{4!}{4!}}{\frac{6!}{2!4!}}[/tex]
Using the formula
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]
P(At least one defective)[tex]=\frac{2\times \frac{4\times 3!}{3!}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}+\frac{1}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}[/tex]
P(At least one defective)[tex]=\frac{2\times 4}{3\times 5}+\frac{1}{3\times 5}[/tex]
P(At least one defective)[tex]=\frac{8}{15}+\frac{1}{15}=\frac{9}{15}[/tex]
P(At least one defective)[tex]=\frac{3}{5}=0.6[/tex]
Now, the probability that both are defective
P(Both are defective)=[tex]\frac{2C_2\times 4C_0}{6C_2}[/tex]
P(Both are defective)=[tex]\frac{\frac{2!}{0!2!}\times \frac{4!}{4!}}{\frac{6!}{2!4!}}[/tex]
P(Both are defective)[tex]=\frac{1}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}[/tex]
P(Both are defective)[tex]=\frac{1}{3\times 5}[/tex]
P(Both are defective)[tex]=0.067[/tex]
(b)
Defective items=4
Non- defective item=6-4=2
P(At least one defective)=[tex]\frac{4C_1\times 2C_1}{6C_2}+\frac{4C_2\times 2C_0}{6C_2}[/tex]
P(At least one defective)[tex]=\frac{\frac{4!}{1!3!}\times \frac{2!}{1!1!} }{\frac{6!}{2!4!}}+\frac{\frac{4!}{2!2!}\times \frac{2!}{2!}}{\frac{6!}{2!4!}}[/tex]
P(At least one defective)[tex]=\frac{2\times \frac{4\times 3!}{3!}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}+\frac{\frac{4\times 3\times 2!}{2!\times 2\times 1}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}[/tex]
P(At least one defective)[tex]=\frac{2\times 4}{3\times 5}+\frac{2\times 3}{3\times 5}[/tex]
P(At least one defective)[tex]=\frac{8}{15}+\frac{6}{15}=\frac{8+6}{15}[/tex]
P(At least one defective)[tex]=\frac{14}{15}[/tex]
P(Both are defective)[tex]=\frac{4C_2\times 2C_0}{6C_2}[/tex]
P(Both are defective)[tex]=\frac{\frac{4\times 3\times 2!}{2\times 1\times 2!}\times \frac{2!}{2!}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}[/tex]
P(Both are defective)[tex]=\frac{\frac{4\times 3\times 2\times 1}{2\times 1\times 2\times 1}}{3\times 5}[/tex]
P(Both are defective)[tex]=\frac{6}{15}=0.4[/tex]
P(Both are defective)[tex]=0.4[/tex]
A trade magazine routinely checks the drive-through service times of fast-food restaurants. 95% confidence interval that results from examining 609 customers in one fast-food chain's drive-through has a lower bound of 160.8 seconds and an upper bound of 160.8 seconds. What does this mean?
Answer:
z= 1.70 Since the test statistic is less than the critical value, we can conclude that the average length of an online video is not more than 8 minutes
Jack drives 175 miles in 2.5hrs. How far can he go in 4hr
Answer:
280 miles
Step-by-step explanation:
175/2.5
= 70
70 x 4
= 280
what is the discrimination of the polynomial below ?
9x2-18x+9
if p, q, and r are all integers greather than 1 and p*q =27 and q*r =51, then which of the following gives the correct ordering of numbers?
Answer:
Step-by-step explanation:
pq = 27 = 3³
qr = 51 = 3×17
q = 3
p = 9
r = 17
Please help with this question
Answer:
im not too sure but try using a cartesuan plane and measure it precisely using a protractor then key in the measurements. Im not entirely sure its the correct method tho
