Graph the following inequality. Then click to show the correct graph.
3x - 2y ≤ 6
Answers
Answer:
We want to graph the inequality:
3x - 2y ≤ 6
The first step is to write this as a linear equation, to do it, we can isolate y in one side of the inequality.
3x ≤ 6 + 2y
3x - 6 ≤ 2y
(3/2)x - 6/2 ≤ y
(3/2)x - 3 ≤ y
or:
y ≥ (3/2)x - 3
Because we have the symbol ≥
The points on the line are solutions, then the first part is to graph the line:
y = (3/2)*x - 3
Next, we have:
y equal to or larger than (3/2)*x - 3
Then we need to shade all the region above that line.
The graph can be seen below.
Related Questions
The following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean.
Atmospheric Pressure (mb) Wind Speed (knots) Atmospheric Pressure (mb) Wind Speed (knots)
993 50 1006 40
995 60 942 120
994 60 1002 40
Required:
a. Find the y-intercept of the least-squares regression line, treating atmospheric pressure as the explanatory variable (round to four decimal places.)
b. Find the slope of the least-squares regression line, treating atmospheric pressure as the explanatory variable (round to four decimal places.)
c. Is it reasonable to interpret the y-intercept of the least-squares regression line, treating atmospheric pressure as the explanatory variable? Why or why not?
Answers
Answer:
Step-by-step explanation:
X Y X² Y² XY
993 50 986049 2500 49650
995 60 990025 3600 59700
994 60 988036 3600 59640
1006 40 1012036 1600 40240
942 120 887364 14400 113040
1002 40 1004004 1600 40080
[tex]\sum X: 5932[/tex] [tex]\sum Y : 370[/tex] [tex]\sum X^2 : 5867514[/tex] [tex]\sum Y^2 = 27300[/tex] [tex]\sum XY : 362350[/tex]
To determine the regression:
[tex]Mean \ (X) = \dfrac{\sum X }{n} \\ \\ = \dfrac{5932}{6} \\ \\ = 988.67[/tex]
[tex]Mean \ (Y) = \dfrac{\sum Y}{n} \\ \\ = \dfrac{370}{6} \\ \\ = 61.67[/tex]
Intercept [tex]b_o = \dfrac{\sum YX *\sum X^2 - \sum X \sum Y}{n(\sum X^2) - (\sum X)^2}[/tex]
[tex]=\dfrac{370(5867514) -(5932)(370)}{6(5867514) - (5932)^2}[/tex]
= 131760.9563
Slope [tex]b_1 = \dfrac{n(\sum XY) -(\sum X *\sum Y) }{n(\sum X^2)-(\sum X)^2}[/tex]
[tex]b_1 = \dfrac{6(362350) -(5932*370) }{6(5867514)-(5932)^2}[/tex]
[tex]b_1 = -1.2600[/tex]
The regression line equation [tex]Y = b_o +b_1X[/tex]
[tex]Y = 131760.96 -1.2600 X[/tex]
We then make a comparison of the slope of the equation to y = mx+c
slope of the equation = -1.2600
the y-intercept corresponds to when X = 0, thus:
y-intercept = 131760.9563
Yes, it is reasonable to interpret the y-intercept of the regression line, Using atmospheric pressure as an explanatory variable due to the fact that:
X is the independent variable and Y exists as the dependent variable.
The diameter of a pipe is normally distributed, with a mean of 0.8 inch and a variance of 0.0025. What is the probability that the diameter of a randomly selected pipe will exceed 0.9 inch?
Answers
Answer:
0.02275
Step-by-step explanation:
Standard deviation is the square root of variance
Standard deviation= Square(0.0025)= 0.05
Because of the normally distributed, the z- score for 0.9 inches is:
(0.9-0.8)/0.05= 2
-> P(x<= 0.9)= P(2) = 0.97725
-> P (x>= 0.9)= 1-0.97725 = 0.02275
if a line with an angle of inclination 120⁰ and passes trough (√3,1),then what is the equation of a line
Answers
Answer:
The equation of a line, having inclination 120° with positive direction of x-axis, .of x-axis, which is at a distance of 3 units from the origin is. 1. See answer ... where α is the angle with the positive X-axis, made by the perpendicular line drawn Now, from equation the equation of the straight line will be.
Step-by-step explanation:
Find the value of the missing angles in the following figures
Answers
Answer:
ans: ii) 87° and iii) 60°
Step-by-step explanation:
ii)
y° = 180° - ( 56° + 37°)
missing angle on triangle is alternate angle of y° so are equal and sum of angles of triangle is 180°
iii)
x° + 2x° = 180°
sum of co interior angles is 180°
Please help please reply
Answers
Answer:
hypotenuse:15
Step-by-step explanation:
Pythagorean Theorem is a^2 + b^2 = c^2
"a" and "b" are the legs, "c" is the hypotenuse
9^2 + 12^2 = 225
[tex]\sqrt{225\\[/tex]
hypotenuse = 15
Half of a set of the parts are manufactured by machine A and half by machine B. Six percent of all the parts are defective. Three percent of the parts manufactured on machine Are defective. Find the probability that a part was manufactured on machine A, given that the part is defective. (Round your answer to 4 decimal places.) Probability
Answers
Answer:
0.25 = 25% probability that a part was manufactured on machine A, given that the part is defective.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Defective
Event B: Manufactured by machine A.
Six percent of all the parts are defective.
This means that [tex]P(A) = 0.06[/tex]
Probability that a part is defective and was manufactured on machine A
3% of the parts manufactured on machine A are defective, manufacture A is responsible for 50% of the parts. So
[tex]P(A \cap B) = 0.03*0.5 = 0.015[/tex]
Find the probability that a part was manufactured on machine A, given that the part is defective.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.015}{0.06} = 0.25[/tex]
0.25 = 25% probability that a part was manufactured on machine A, given that the part is defective.
A phone manufacturer wants to compete in the touch screen phone market. He understands that the lead product has a battery life of just 5 hours. The manufacturer claims that while the new touch screen phone is more expensive, its battery life is more than twice as long as that of the leading product. In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.a. Select the relevant null and the alternative hypotheses. b-1. Calculate the value of the test statistic.b-2. Find the p-value.
Answers
Answer:
a)
The null hypothesis is [tex]H_0: \mu \leq 10[/tex]
The alternative hypothesis is [tex]H_1: \mu > 10[/tex]
b-1) The value of the test statistic is t = 1.86.
b-2) The p-value is of 0.0348.
Step-by-step explanation:
Question a:
Test if the battery life is more than twice of 5 hours:
Twice of 5 hours = 5*2 = 10 hours.
At the null hypothesis, we test if the battery life is of 10 hours or less, than is:
[tex]H_0: \mu \leq 10[/tex]
At the alternative hypothesis, we test if the battery life is of more than 10 hours, that is:
[tex]H_1: \mu > 10[/tex]
b-1. Calculate the value of the test statistic.
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used to solve this question
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
10 is tested at the null hypothesis:
This means that [tex]\mu = 10[/tex]
In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.
This means that [tex]n = 45, X = 10.5, s = 1.8[/tex]
Then
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{10.5 - 10}{\frac{1.8}{\sqrt{45}}}[/tex]
[tex]t = 1.86[/tex]
The value of the test statistic is t = 1.86.
b-2. Find the p-value.
Testing if the mean is more than a value, so a right-tailed test.
Sample of 45, so 45 - 1 = 44 degrees of freedom.
Test statistic t = 1.86.
Using a t-distribution calculator, the p-value is of 0.0348.
help whats the answer??
Answers
Answer:
2 7/12
Step-by-step explanation:
You have to get all the fractions to a common denominator. Smallest common denominator would be 12.
5 and 3/4 turns to 5 and 9/12
2/3 turns to 8/12
2 and 1/2 turns to 2 and 6/12
8/12 + 2 6/12 = 3 2/12
5 9/12 - 3 2/12 = 2 7/12
2 7/12 being the remaining amount
Payment types vary at the grocery store. Here are the proportions of the leading three payment methods: Payment Method Cash Credit Cards Debit Cards Proportion 0.11 0.43 0.21 If a transaction is selected at random, the probability that the customer did not pay with a Debit Card is .
Answers
Answer:
0.79
Step-by-step explanation:
Given the probability distribution :
Payment Methd: Cash Credit Cards Debit Cards Proportion : ____0.11 ____ 0.43 _____0.21
The probability that a customer did not pay with debit card can be obtained as :
If customer did not pay with debit card, then he would have paid with any of the other payment methods
This Can best be obtained using the complement method
P(not debit card) = 1 - P(debit card)
P(debit card) = 0.21
P(not debit card) = 1 - 0.21
P(not debit card) = 0.79
2. Kayli swam 0.7 kilometers at the school swimming pool. How many meters did she swim?
Kayli swam
meters in the swimming pool.
Answers
Answer:
To convert kilometres to metres, divide the value by 1000.
0.7 ÷ 1000 = 700 metres
Kayli swam 700 meters in the swimming pool
Hope this helps!
a housewife spent 3/7 of her money to buy yams and 1/2 of the remainder to buy rice what is the fraction of her money left
Answers
Answer:
Fraction of money spent on calculator = 2/5
Find the fraction of money left:
1 - 2/5 = 3/5
Find the fraction of money spent on a book:
4/7 x 3/5 = 12/35
Answer: She spent 12/35 of the money on a book
------------------------------------------------------------------------------------------------
To find the fraction of saving:
Fraction of money saved = 1 - calculator - book
Fraction of money saved = 1 - 2/5 - 12/35 = 9/35
Fraction of the money saved = 9/35
Step-by-step explanation:
(x) 3 5 7
(y) 7 11 15
Find x, when y = 21
Answers
Answer:
x = 10
Step-by-step explanation:
y = 2x + 1
21 = 2x + 1
21 - 1 = 2x
2x = 20
x = 10
guys plz help i’m struggling
Answers
Answer:
0.46017
Step-by-step explanation:
Given :
Mean score = 75
Standard deviation, s = 10
Areum's score = 76
Probability of scoring higher than Areum is given by :
P(x > 76)
The standardized score : (x - mean) / standard deviation
P(x > 76) = P[Z > (76 - 75) / 10]
P[(Z > 0.1)] = 0.46017 (Z probability calculator)
= 0.46017
a)Loss is denoted by a negative integer and profit is denoted by a positive integer. A
cement company earns a profit of ₹ 10 per bag of white cement and a loss of ₹ 5 per
bag of grey cement. The company sells 325 bags of white cement and 500 bags of
grey cement. What is its profit or loss?
Answers
Answer:
There was a profit of ₹750.
Step-by-step explanation:
325 bags of white cement
Profit of 10 for each bag of white cement. So
[tex]P = 325*10 = 3250[/tex]
500 bags of grey cement.
Loss of 5 for each bag of grey cement. So
[tex]L = 5*500 = 2500[/tex]
What is its profit or loss?
3250 - 2500 = 750
Positive, so profit. There was a profit of ₹750.
PLS HELPP MEE !!
Use a calculator to find the r-value of these data. Round the value to three decimal places.
Answers
The Answer is -0.985
I just took the test.
find the inverse function of F(x) = 1/2x-6
Answers
Answer:
[tex]F^{-1} (x) = 2x + 12[/tex]
Step-by-step explanation:
Let's assume F(x) = y, then
[tex]y = \frac{1}{2} x - 6[/tex]
Let us solve the equation for x.
[tex]y + 6 = \frac{1}{2} x[/tex]
[tex]2y + 12 = x[/tex]
Next, replace y with x and also replace x with F⁻¹(x)
Answer: [tex]F^{-1} (x) = 2x + 12[/tex]
attendance drop at 7% this year to 1050 what was the attendance before the drop
Answers
Answer:
7% divided by 1050 is basically 73.5 but the fraction of that is 147/2 hope u find my answer reasonable have a great day.
Step-by-step explanation:
Evaluate the given equation for the indicated function values. pls help
Answers
Answer:
The answer in each numeral is:
f(4) = 28f(10) = -19f(-5) = -33f(9) = -9Step-by-step explanation:
To obtain the result in each case, you must replace the variable (n) by the value that appears in the second case, I'll explain it with the first exercise:
1. f(n) = 5n + 8 f(4) = ?As you can see, in the second doesn't appear f(n), but f(4), that means you must replace the "n" in the equation by 4, if we do this, we obtain:
1. f(4) = 5*(4) + 8f(4) = 20 + 8f(4) = 28The first answer is 28, now we'll continue with the next exercises:
2. f(n) = -2n + 1f(10) = -2*(10) + 1f(10) = -20 + 1f(10) = -193. f(n) = 6n - 3f(-5) = 6*(-5) - 3f(-5) = -30 - 3f(-5) = -334. f(n) = -nf(9) = -9In this form, you can prove the answers are: 28, -19, -33, and -9 respectively.
Please answer my question correctly.
Nonsense/Plagiarized = Report
Answers
Find the perimeter or circumference and area of each figure. Round to the nearest tenth.
Solution:-The circumference of a circle with radius r is given by C = 2πr. The radius of the circle is 4 in.
Substitute 4 for r.
[tex]\sf{C=2πr}[/tex]
[tex]\sf{ \: \: \: \: =2π(4)}[/tex]
[tex]\sf{ \: \: \: \: ≈{\color{darkviolet}{25.1}}}[/tex]
Answer:-The circumference of the circle is about 25.1 in.
======================The area of a circle with radius r is given by A = πr².
Substitute 4 for r.
[tex]\sf{A = πr²}[/tex]
[tex]\sf{ \: \: \: \: = π(4)²}[/tex]
[tex]\sf{ \: \: \: \: ≈{\color{magenta}{50.3}}}[/tex]
Answer:-The area of the circle is about 50.3 in².
======================#Hope it helps!
(ノ^_^)ノ
Answer the following and round to one decimal place.
Answers
Step-by-step explanation:
5 1/2% = 5.5% = 5.5/100 = 0.055
0.055 * 68 = 3.74
Answer:
3.74
Step-by-step explanation:
[tex]5\frac{1}{2}%[/tex] of 68
In order to do this you need to convert 5 1/2 into a decimal!
Answer: 5.5
Explanation: 5 is a whole number and half of one unit will be 0.5
5 + 0.5 = 5.5
Then multiply 5.5 and convert 68 into "0.68"
5.5 × 0.68 = 3.74
Answer: 3.74
Passion wants to rent a car to take a trip and has a budget of $75. There is a fixed rental fee of $25 and a daily fee of $10. Write ab inequality that would be used to solve for the maximum number of days for which passion can rent the car on her budget
Answers
Answer:
5 days
Step-by-step explanation:
75 = 10d +25
-25 -25
50 = 10d
/ /
10 10
5 = d
i already have A but I do not have B
Answers
Answer:
-4 , -1 , -2 , 0 , +1 , +3
Step-by-step explanation:
Answer:
the integers -4,-2,-1,0, +1, +3
Step-by-step explanation:
because when you put them in order you find which pairs are located between -5 and +5
-8,-4,-2,-1,0,+3,+8,+9
which tells you that
-4,-2,-1,0, +1, +3 are between -5 and +5
A table is made using the following two patterns.
Pattern 3: Starting number: 5, Rule: add 1
Pattern y: Starting number: 10, Rule: add 2
Complete the table for the given patterns.
Answers
Answer:
x = 6, y = 12
x = 7 y = 14
Step-by-step explanation:
im pretty sure that right, hope this helps!
What is the solution set to this equation? Log2(x - 2) + log2x = 3
Answers
The required, solution set to the given equation is {4}. Option A is correct.
What are logarithmic functions?A logarithmic function is a mathematical function that represents the logarithm of a number with respect to a given base. In other words, it is a function that relates a number to its logarithm. The general form of a logarithmic function is f(x) = logₐ(x).
Using the product rule of logarithms, we can combine the two logarithms on the left-hand side of the equation:
log2(x - 2) + log2x = log2[(x - 2) * x] = log2(x² - 2x)
So the given equation becomes:
log2(x² - 2x) = 3
2³ = x² - 2x
8 = x² - 2x
x² - 2x - 8 = 0
Factor this quadratic equation as:
(x - 4)(x + 2) = 0
x - 4 = 0, which gives x = 4
x + 2 = 0, which gives x = -2
However, the logarithm function is only defined for positive values of x, so the only possible solution is:
x = 4
Therefore, the solution set to the given equation is {4}.
Learn more about logarithmic function here:
https://brainly.com/question/30284289
#SPJ2
Find the inverse of \(\Large h(x) = \frac {3}{2}x + 1 \)
Answers
Answer:
[tex]h(x) = \frac {3}{2}x + 1 \\ { \tt{let \: the \: inverse \: be \: { \bold{m}}}} \\ { \tt{m = \frac{1}{ \frac{3}{2}x + 1 } }} \\ \\ { \tt{m = \frac{2}{3x + 2} }} \\ \\ { \tt{m(3x + 2) = 2}} \\ \\ { \tt{3x + 2 = \frac{2}{m} }} \\ \\ { \tt{x = \frac{2 - 2m}{3m} }} \\ \\ { \tt{x = \frac{2}{3m}(1 - m) }} \\ \\ { \bf{h {}^{ - 1} (x) = \frac{2}{3x}(1 - x) }}[/tex]
a and b are complementary angles and a and c are supplementary angles. If a=xº, (a) express b and c in terms of x
(b) find c - b.
Answers
Step-by-step explanation:
a + b = 90
a + c = 180
a) If a = x, the. we can write
x + b = 90 and x + c = 180
or
b = 90 - x
c = 180 - x
b) c - b = (180 - x) - (90 - x)
= 180 - x - 90 + x
= 90
Which graph shows the solution to this system of inequalities?
y>-1/3x+1
y>2x-3
Answers
Given:
The system of inequalities is:
[tex]y>-\dfrac{1}{3}x+1[/tex]
[tex]y>2x-3[/tex]
To find:
The graph of the given system of inequalities.
Solution:
We have,
[tex]y>-\dfrac{1}{3}x+1[/tex]
[tex]y>2x-3[/tex]
The related equations are:
[tex]y=-\dfrac{1}{3}x+1[/tex]
[tex]y=2x-3[/tex]
Table of values for the given equations is:
[tex]x[/tex] [tex]y=-\dfrac{1}{3}x+1[/tex] [tex]y=2x-3[/tex]
0 1 -3
3 0 3
Plot (0,1) and (3,0) and connect them by a straight line to get the graph of [tex]y=-\dfrac{1}{3}x+1[/tex].
Similarly, plot (0,-3) and (3,3) and connect them by a straight line to get the graph of [tex]y=2x-3[/tex].
The signs of both inequalities are ">". So, the boundary line is a dotted line and the shaded region or each inequality lie above the boundary line.
Therefore, the graph of the given system of inequalities is shown below.
A Little League baseball coach wants to know if his team is representative of other teams in scoring runs. Nationally, the average number of runs scored by a Little League team in a game is 5.7. He chooses five games at random and finds the mean number of runs scored is 7.4 with a sample standard deviation of 2.88.
Required:
Is it likely that his team's scores is different than the national average?
Answers
Answer:
That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average
Step-by-step explanation:
The National average number of runs scored by a LL team is
μ = 5.7
Sample Information:
size sample n = 5
sample average x = 7.4
sample standard deviation s = 2.88
Is required to investigate if that sample average is statistically different from the National average
We will do a test with 95 % of confidence Interval that means
significance level α = 5 % or α = 0.05.
The sample size is 5 then even when we assume normal distribution the sample size indicates that we need to use t-student distribution. Furthermore, as the question is if the sample average is different from the national the test will be a two-tail test.
Then α = 0.05 α/2 = 0.025
df = n - 1 df = 5 - 1 df = 4
Then from t-student table we get t(c) = 2.132
Hypothesis test:
Null Hypothesis H₀ x = μ
Alternative Hypothesis Hₐ x ≠ μ
To calculate t (s)
t(s) = ( x - μ ) / s/√n
t(s) = ( 7.4 - 5.7 )* 2.24 / 2.88
t(s) = 1.7* 2.24 / 2.88
t(s) = 1.32
Comparing t(s) and t(c)
1.32 < 2.132
That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average
Find the radius of a circle in which the central angle, a, intercepts an arc of the given length s.
a = 60°, s = 44 ft
The radius is ft.
(Round to the nearest hundredth as needed.)
Answers
Answer:
42.02 ft
Step-by-step explanation:
60 : 360 = 44 : x
x = 264 ft (length of the circumference)
C = 2 * radius * pi
radius = C / 2 * pi
Radius = 264 / 2 * pi = 42,016905 ft
Given the functions below, find (g•h) (1).
g(x) = х^2 +4+ 2х
h(x) = — 3х + 2
-7
-30
35
7
Answers
Answer:
-7
Step-by-step explanation:
We are given the following functions:
[tex]g(x) = x^2 + 4 + 2x[/tex]
[tex]h(x) = -3x + 2[/tex]
(g•h) (1)
The multiplication is:
[tex](g \times h)(1) = g(1) \times h(1)[/tex]
So
[tex]g(x) = 1^2 + 4 + 2(1) = 7[/tex]
[tex]h(1) = -3(1) + 2 = -3 + 2 = -1[/tex]
Then
[tex]g(1) \times h(1) = 7(-1) = -7[/tex]
So -7 is the answer.