Solving inequalities |2x - 2|≤ 6
Answers
Answer:
-2 ≤ x ≤ 4
Step-by-step explanation:
|2x - 2| ≤ 6
2x - 2 ≤ 6 or 2x - 2 ≥ -6
2x - 2 ≤ 6
2x ≤ 8
x ≤ 4
2x - 2 ≥ -6
2x ≥ -4
x ≥ -2
Related Questions
Exercise 3
John spends half of his pocket money, then a third of the rest.
1) What proportion of the starting money does he have left?
2) Since he has 5 dollars left, how much did he initially have?
Answers
Answer:
1/2 - 1/3
3/6- 2/6 = 1/6
he has 1/6 left
6 X 5 = 30
he initially had $30
Hello! I got this answer but I am unsure as to how I got the answer.
Answers
Given a quadratic equation: y = ax² + bx + c, "a", "b" and "c" are the coefficients of the regression and can be estimated using the formulas below.
a = {[Σ x²y * Σ xx ] - [Σ xy * Σ xx² ] } / { [ Σ xx * Σ x²x²] - [Σ xx² ]²}
b = {[Σ xy * Σ x²x² ] - [Σ x²y * Σ xx² ] } / { [ Σ xx * Σ x²x²] - [Σ xx² ]²}
c = [Σ y / n ] - { b * [ Σ x / n ] } - { a * [ Σ x² / n ]}
Where:
Σ xx = [Σ x²] - [ ( Σ x )² / n]
Σ xy = [Σ x y] - [ ( Σ x * Σ y ) / n]
Σ xx² = [Σ x³] - [ ( Σ x² * Σ x ) / n]
Σ x²y = [Σ x²y] - [ ( Σ x² * Σ y ) / n]
Σ x²x² = [Σ x⁴] - [ ( Σ x² )² / n]
And:
x and y are the Variables.
n = Number of Values or Elements
Σ x = Sum of x Scores
Σ y = Sum of y Scores
Σ x² = Sum of Square of x
Σ x³ = Sum of Cube of x
Σ x⁴ = Sum of Power Four of x
Σ xy= Sum of the Product of x and y
Σ x²y = Sum of Square of x and y
To solve the problem, follow the steps below.
Step 01: Find n and the values of x and y.
n = 6.
x = 8, 10, 12, 14, 16, 18
y = 45.94, 56.84, 63.88, 67.07, 66.4, 61.87
Step 02: Find Σ x, Σ y, Σ x², Σx³, Σ x⁴, Σ xy, Σ x²y
* (,) represents a decimal point.
Step 03: Find Σ xx, Σ xy, Σ xx², Σ x²y, Σ x²x²
Substitute the values above in the equations for each variable:
Σ xx = [Σ x²] - [ ( Σ x )² / n]
Σ xy = [Σ x y] - [ ( Σ x * Σ y ) / n]
Σ xx² = [Σ x³] - [ ( Σ x² * Σ x ) / n]
Σ x²y = [Σ x²y] - [ ( Σ x² * Σ y ) / n]
Σ x²x² = [Σ x⁴] - [ ( Σ x² )² / n]
\(\begin{gathered} \sum_^xx=\operatorname{\sum}_^x^2-\frac{(\operatorname{\sum}_^x)^2}{n} \\ \sum_^xx=1084-\frac{78^2}{6} \\ \sum_^xx=1084-\frac{6084}{6} \\ \sum_^xx=1084-1014 \\ \sum_^xx=70 \end{gathered}\)Doing the same for the other variables, you have the results:
* (,) represents a decimal point.
Step 03: Find "a".
a = {[Σ x²y * Σ xx ] - [Σ xy * Σ xx² ] } / { [ Σ xx * Σ x²x²] - [Σ xx² ]²}
\(\begin{gathered} a=\frac{2611.55*70-111.52*1820}{70*47917.3-1820^2} \\ a=-0.482 \end{gathered}\)Step 04: Find "b".
b = {[Σ xy * Σ x²x² ] - [Σ x²y * Σ xx² ] } / { [ Σ xx * Σ x²x²] - [Σ xx² ]²}
\(\begin{gathered} b=\frac{111.52*47917.3-2611.55*1820}{70*47917.3-1820^2} \\ b=14.125 \end{gathered}\)Step 05: Find "c".
c = [Σ y / n ] - { b * [ Σ x / n ] } - { a * [ Σ x² / n ]}
\(\begin{gathered} c=\frac{362}{6}-14.125*\frac{78}{6}-(-0.482)*\frac{1084}{6} \\ c=-36.209 \end{gathered}\)Answer:
The equation is:
\(-0.482x^2+14.125x-36.209\)
Angle 1 and Angle 2 form a linear pair. If the measure of angle is 113°, find the measure of angle 2.
Answers
Answer:
<2 =67
Step-by-step explanation:
A linear pair adds to 180 degrees
<1 + <2 =180
113+ <2 = 180
<2 = 180-113
<2 =67
The Wolverine Worldwide (a shoe company in Rockford) improperly disposed of chemicals (PFAS) which leaked into groundwater. The state of Michigan says that if more than 7% of households in a city exceed the safe limit, the city needs to switch to bottled water. A concerned citizen takes a random sample of 100 households and finds that 12 have unsafe water. Do the data provide convincing evidence that Rockford should switch to bottled water?
1. State appropriate hypotheses for performing a significance test. Use.
2. (a) After conducting a significance test, a P-value of 0. 025 is found. Interpret this value.
(b) Reject H0 or fail to reject H0? Keep the current water or switch to bottled water? Explain.
(c) Let’s suppose this decision is wrong. What would be a consequence of this error?
(d) If the water is safe, what is the probability that this error will occur?
3 (a) Now suppose the P-value was 0. 217. Reject H0 or fail to reject H0? Keep the current water or switch to bottled water? Explain.
(b) Let’s suppose this decision is wrong. What would be a consequence of this error?
4 Are the consequences in question #2 or question #3 more serious? Explain
Answers
1) H0: percentage of households with unsafe water <= 7%, Ha: percentage of households with unsafe water > 7%.
2) (a) obtained P-value suggests the percentage of households with unsafe water in Rockford is greater than 7%, (b) Reject H0, and switch to bottled water as there is evidence to suggest the water is unsafe, (c) switching to bottled water when it is not necessary could result in unnecessary expenses for the city, (d) if the water is safe, the probability of making a Type I error is 0.05.
3) (a) P-value of 0.217 suggests that there is no evidence to suggest the water is unsafe, (b) if the decision to keep the current water is wrong, it could lead to health problems for residents exposed to unsafe water.
4) The consequences of a Type II error in question 3 are more severe than those of a Type I error in question 2 as the former could result in adverse health effects.
1) The Hypotheses in the given statements are,
Null hypothesis (H0): The percentage of households in Rockford with unsafe water is less than or equal to 7%.
Alternative hypothesis (Ha): The percentage of households in Rockford with unsafe water is greater than 7%.
2) (a) The P-value of 0.025 indicates that if the null hypothesis were true (i.e., if the percentage of households with unsafe water were less than or equal to 7%), we would observe a sample proportion of 12/100 or more extreme in only 2.5% of samples.
(b) With a significance level of 0.05, we reject the null hypothesis since the P-value is less than the significance level. This means we have evidence to suggest that the percentage of households with unsafe water in Rockford is greater than 7%. Therefore, Rockford should switch to bottled water to ensure safe drinking water.
(c) If the decision to switch to bottled water is wrong, it could result in unnecessary expenses for the city and inconvenience for its residents.
(d) If the water is safe, the probability of making a Type I error (incorrectly rejecting the null hypothesis) is equal to the significance level, which is 0.05.
3) (a) With a P-value of 0.217, we fail to reject the null hypothesis since the P-value is greater than the significance level. This means we do not have sufficient evidence to suggest that the percentage of households with unsafe water in Rockford is greater than 7%, and therefore, there is no need to switch to bottled water.
(b) If the decision to keep the current water is wrong, it could lead to health problems for the residents who are exposed to unsafe water.
4) The consequences in question 3 are more serious because if we make a Type II error (incorrectly failing to reject the null hypothesis), we are essentially allowing households to continue consuming unsafe water, which could have adverse health effects. On the other hand, if we make a Type I error in question 2, we may incur some unnecessary expenses, but it is less severe than putting people's health at risk.
Therefore, the null hypothesis is that the percentage of households with unsafe water in Rockford is less than or equal to 7%, while the alternative hypothesis is that it is greater than 7%. With a sample proportion of 12/100 households having unsafe water, a significance test is performed with a P-value of 0.025, leading to the rejection of the null hypothesis, and the recommendation to switch to bottled water. The consequences of making an incorrect decision could result in unnecessary expenses or adverse health effects.
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how much 44f to celcius ?
Answers
44 °F was found out to be equivalent to approximately 6.67 °C using conversion formula of Fahrenheit to Celsius.
To convert a temperature from Fahrenheit to Celsius, you can use the following formula:
°C = (°F - 32) x 5/9
where °C is the temperature in Celsius, and °F is the temperature in Fahrenheit.
Using this formula, we can convert 44 °F to Celsius as follows:
°C = (44 - 32) x 5/9
= 12 x 5/9
= 6.67 °C (rounded to two decimal places)
Therefore, 44 °F is equivalent to approximately 6.67 °C.
On the Fahrenheit scale, water freezes at 32 degrees Fahrenheit (°F) and boils at 212 °F, at standard atmospheric pressure.
On the Celsius scale, the freezing point of water is defined as 0 degrees Celsius (°C), and the boiling point of water is defined as 100 °C, at standard atmospheric pressure.
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select the points that are solutions to the system of inequalities. Select all that apply.
Answers
The solution to the graph of the linear inequality is the point of intersection which is (-5, 3)
Graph of System of Linear InequalityA system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system
In this problem, to find the solution to the system of linear inequality, we have to find the point of intersection. This gives the exact solution to the graph.
Looking at this graph, the point of intersection is (-5, 3)
The solution to the graph is (-5, 3)
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an important quality characteristic of water is the concentration of suspended solid material in mg/l. twelve measurements on suspended solids from a certain lake are as follows: 42.4, 65.7, 29.8, 58.7, 52.1, 55.8, 57.0, 68.7, 67.3, 67.3, 54.3, and 54.0. calculate the sample average and sample standard deviation. construct a dot diagram of the data.
Answers
Sample average: To calculate the sample average, add up all the measurements and divide by the number of measurements.
42.4 + 65.7 + 29.8 + 58.7 + 52.1 + 55.8 + 57.0 + 68.7 + 67.3 + 67.3 + 54.3 + 54.0 = 751.4
Sample average = 751.4 / 12 = 62.62
Sample standard deviation steps:
Subtract the sample average from each measurement to find the deviations.
Square each deviation.
Add up the squared deviations.
Divide the sum by the number of measurements minus one (n-1).
Take the square root of the result.
Sample standard deviation = sqrt(sum of squared deviations / (n-1))
Dot diagram: A dot diagram, also known as a dot plot, is a simple graphical representation of a set of data where each data point is represented by a dot on a number line. To create a dot diagram, plot each measurement as a dot on a number line with the corresponding value.
This is a useful tool to visualize the distribution of the data and to see the general pattern, such as the presence of outliers, skewness, or clusters.
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Find sets of parametric equations and symmetric equations of the line that passes through the two points. (For the line, write the direction numbers as integers.) (−1,6,3),(10,11,8)
Find sets of parametric equations. (Enter your answer as a comma-separated list of equations in terms of x,y,z, and t.)
Answers
The inverse function of f(x) = -5x + 2 is f^(-1)(x) = (-1/5)x + 2/5.
The parametric equations of the line passing through (-1, 6, 3) and (10, 11, 8) are:
x = -1 + 11t
y = 6 + 5t
z = 3 + 5t
The symmetric equations of the line are:
(x + 1) / 11 = (y - 6) / 5 = (z - 3) / 5
The inverse of the function f(x) = -5x + 2 can be found by interchanging the roles of x and y and solving for y. Let's proceed with the steps:
Start with the original function: f(x) = -5x + 2.
Interchange x and y: x = -5y + 2.
Solve for y: -5y = x - 2.
Divide by -5: y = (x - 2) / -5.
Simplify: y = (-1/5)x + 2/5.
Therefore, the inverse function of f(x) = -5x + 2 is f^(-1)(x) = (-1/5)x + 2/5.
For the line passing through the points (-1, 6, 3) and (10, 11, 8), we can find sets of parametric equations, symmetric equations, and direction numbers. Let's proceed step by step:
Parametric equations:
Choose a parameter, let's say t.
Express x, y, and z in terms of t using the given points and a direction vector of the line. We can choose the vector between the two points as the direction vector, which is (10 - (-1), 11 - 6, 8 - 3) = (11, 5, 5).
Set up the parametric equations:
x = -1 + 11t
y = 6 + 5t
z = 3 + 5t
Symmetric equations:
Determine the direction numbers of the line using the direction vector (11, 5, 5).
Set up the symmetric equations using the point (-1, 6, 3):
(x + 1) / 11 = (y - 6) / 5 = (z - 3) / 5
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What is the product?
Answers
Answer:
2x^2 +5x-3
Step-by-step explanation:
(x+3)(2x-1)
FOIL
first :(x*2x) = 2x^2
outer: x*-1 = -x
inner: 3*2x = 6x
last: -1 *3 = -3
Add together
2x^2 -x+6x-3
Combine like terms
2x^2 +5x-3
Answer:
The third option. 2x^2+5x-3.
Step-by-step explanation:
The product means to multiply them.
(x+3)(2x-1)
You don't multiply x to 2x and 3 and -1.
That is not the product and say it is 2x^2-3.
You have to multiply x to both 2x and -1.
You don't only multiply the terms that correspond with each other.
You have to do x times 2x and x times -1.
2x times x is 2x squared or 2x^2.
x times -1 is -x.
So you have 2x^2-x.
Leave that there for now.
Now, you have to multiply 3 with 2x and -1.
3 times 2x is 6x and 3 times -1 is -3.
Then you have 6x-3.
Bring back the 2x^2-x with the 6x-3.
Now you have 2x^2-x+6x-3.
You always have to simplify.
Combine like terms. -x plus 6x is 5x.
Therefore, you are left with 2x^2+5x-3.
That is the product of (x+3)(2x-1).
you can check by dividing the polynomials as well.
I hope this clarifies things!
QUICKLYYY
Which situation below has the lowest constant of proportionality?
A) 40 ounces of fabric softener cost $20.00.
B) 20 ounces of powder laundry detergent costs $4.00.
C) 30 ounces of laundry scent boosters cost $12.12.
D) 90 ounces of liquid laundry detergent cost $36.00.
Answers
Answer: D
Step-by-step explanation:
Because I can math
Is (–39, 42) a solution to the equation y = x + 81?
Answers
Answer:
Yes
Step-by-step explanation:
Yes because if you insert -39 for x and 42 for y then your equation is:
42 = -39 + 81
If you were to solve this equation it would be true.
Which amount is largest?
1 kg
1 dg
100 g
1,000 mg
Answers
Answer:
1 kg here you go this is the answer
Q2. Use Stoke’s theorem to evaluate CF.
dr , where
F=sinx-yi-cosx j and C is the
boundary of the triangle whose vertices are 0,0,
π2, 0,
π2, 1.
Answers
Bad Bunny o Darell??
Freę points
Answers
Answer:
ok
Step-by-step explanation:
PLEASE HELP IVE BEEN TRYING TO GET PPL TO ANSWER BUT NO ONE HAS: Order from least to greatest
Answers
Solve |y + 2| > 6
Need answer please
Answers
Answer:
y is greater or less then 4
Step-by-step explanation:
Im jesus
Calculate the total number of milligrams in 60 kg
Answers
Answer:
60 000 000 milligrams
Step-by-step explanation:
1kg =1000000milligrams
60kg :????
60/1×1000000
=60 000 000milligrams
Helppp me Please!! i beg
Answers
Answer:
The answer would be -16
Step-by-step explanation:
Add
5
What is the simplified value of the expression below?
StartFraction 4.5 minus 5.9 over 0.2 times 3 minus 0.2 EndFraction
–3.5
–2.4
2.4
3.5
Answers
The simplified value of the expression StartFraction 4.5 minus 5.9 over 0.2 times 3 minus 0.2 EndFraction is -3.5.
The correct answer choice is option A
What is the simplified value of the expression?Using PEMDAS
P = parenthesis
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
(4.5 - 5.9) / (0.2 × 3) - 0.2
= -1.4 / (0.6 - 0.2)
= -1.4 / 0.4
= -3.5
Complete question:
What is the simplified value of the expression below? 4.5 - 5.9 divided by 0.2 x 3 - 0.2
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Answer:
yo
Step-by-step explanation:
the answers A
i took the test
2 cubed x what x 5 = 120
please i really need help
Answers
Answer:
2x3x5=120
Step-by-step explanation:
Answer:
30 is the missing number.
Step-by-step explanation:
The equation is,
→ 2³ × x × 5 = 120
Then the value of x will be,
→ 2³ × x × 5 = 120
→ 8 × x × 5 = 120
→ x × 40 = 120
→ x = 120/40
→ [ x = 30 ]
Hence, the value of x is 30.
I’ll give brainliest if u help
It’s 19 and 20
Answers
Answer:
19. 20 questions total
20. 84.61538461538
Rounded: 85%
Step-by-step explanation:
Using proportion:
a= part
b= whole
a/b=a/b
Answer: Answer for 19 is 20 and answer for 20 is 85%
Hope this helps!
help I suck at math lol
Answers
So that it becomes 7/4, which is 1 3/4
For 48/9, divide both numbers by 3
So that it becomes 16/3 which is 5 1/3
Answer:
14/8 = 1 3/4
48/9 = 5 1/3
Step-by-step explanation:
14/8 = 1 6/8
6/8 = 3/4
14/8 = 1 3/4
48/9 = 5 3/9
3/9 = 1/3
48/9 = 5 1/3
Identify the factors of 6ab − 8a 21b − 28. (2a 4)(3b − 7) (2a − 4)(3b 7) (2a 7)(3b − 4) (2a − 7)(3b 4)
Answers
Answer: ) (2a+7)(3b- 4)
Step-by-step explanation:
Complete the equation so that it is
true for no values of x (no solutions).
3x + 6 = 3 (x + _)
Answers
Answer:
Any number other than 2
Step-by-step explanation:
Well if we plug in any number other than 2 like 1 for the blank and distribute,
the right side becomes,
3x + 6 = 3x + a number other than 6
Parallel lines have the same slope but different y intercept.
Look at the image below ↓
Thus,
to make the equation have no solution the blank has to be any number other than 2.
Hope this helps :)
Can someone help on this question from khanademy geometry. Finding the equation for the circle
Answers
The equation of the circle graphed in this problem is:
(x - 5)² + y² = 16.
What is the equation of a circle?The equation of a circle of center \((x_0, y_0)\) and radius r is given by:
\((x - x_0)^2 + (y - y_0)^2 = r^2\)
For the circle graphed, we have that:
The center is at point (5,0), hence \(x_0 = 5, y_0 = 0\).The radius is of 4 units.Hence the equation of the circle graphed is:
(x - 5)² + y² = 16.
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A fisherman is observing a trout swimming in a stream. When the trout swims along with the stream, the fisherman determines that it travels 21.3 m in 13.4 s. The trout then turns around and swims upstream against the current, now taking 29.8 s to travel the same distance as before (21.3 m). Assuming the stream's current is steady so that the water's velocity relative to the ground is constant, what must be the trout's velocity relative to the water (in meters per second)
Answers
The trout's velocity relative to the water is 1.59 m/s.
To determine the trout's velocity relative to the water, we can analyze its motion in both downstream and upstream scenarios.
Given:
Distance traveled downstream = 21.3 m
Time taken downstream = 13.4 s
Time taken upstream = 29.8 s
When the trout swims downstream, it benefits from the stream's current, which adds to its own velocity. The trout's velocity relative to the water (v_trout) can be calculated by dividing the distance traveled downstream by the time taken downstream:
v_trout = Distance traveled downstream / Time taken downstream
v_trout = 21.3 m / 13.4 s
v_trout ≈ 1.59 m/s
Therefore, the trout's velocity relative to the water is approximately 1.59 m/s.
When the trout swims downstream, the water's velocity relative to the ground is added to the trout's velocity relative to the water. This results in a faster speed for the trout compared to when it swims upstream against the current.
In the downstream scenario, the distance traveled (21.3 m) divided by the time taken (13.4 s) gives us the average velocity of the trout relative to the water during that period. This average velocity takes into account the combined effect of the trout's own swimming speed and the stream's current, resulting in a value of approximately 1.59 m/s.
By swimming upstream, the trout is now swimming against the current. This causes a decrease in its overall speed. The time taken to cover the same distance (21.3 m) upstream is longer (29.8 s) compared to downstream. This indicates that the trout's velocity relative to the water is slower when swimming against the current.
In summary, the trout's velocity relative to the water is 1.59 m/s when swimming in the stream. This velocity represents the trout's own swimming speed, accounting for the stream's current, and is determined by dividing the distance traveled by the time taken in the downstream scenario.
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-x + 3y = -23
-8x - 3y = -22
using elimination
Answers
A building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground. Could you use lines and text to draw and label a diagram that represents this situation?
Answers
Greetings from Brasil...
Its attached the diagram of the situation.....
The ground is 8 feet from the bottom edge of the window
How far up from the ground is the bottom edge of the window?We start by representing the building, the ladder and the ground in a sketch.
See attachment for diagram
From the diagram, the distance (d) from ground to the bottom edge of the window is calculated using Pythagoras theorem:
10^2 = d^2 + 6^2
Evaluate the squares
100 = d^2 + 36
Evaluate the like terms
d^2 = 64
Take the square root of both sides
d = 8
Hence, the ground is 8 feet from the bottom edge of the window
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Find the product using suitable property and also mention the property used.
(- 542) × 45 + (-542) × 55
Answers
Answer:
\(( - 542) \times 45 + ( - 542) \times 55 \\ = ( - 24390) + ( - 29810) \\ = ( - 54200)\)
a flight of stairs in a 10 storey building has 15 steps. what is the total number of steps from the 1st floor to the 6th floor?
Answers
The total number of steps from the 1st floor to the 6th floor in a 10-story building with 15 steps in a flight of stairs is 60.
In a 10-story building, a flight of stairs has 15 steps.
What is the total number of steps from the 1st floor to the 6th floor.
The total number of steps from the 1st floor to the 6th floor in a 10-story building with 15 steps in a flight of stairs is as follows:
Take into consideration the following:
Given that a flight of stairs in a 10-story building has 15 steps, therefore a total number of steps on 10th floor would be;N1 = 10 * 15N1 = 150.
Similarly, the total number of steps on the 6th floor would be;
N2 = 6 * 15N2 = 90
Finally, the total number of steps from the 1st floor to the 6th floor will be;
Total number of steps = N1 – N2
Total number of steps = 150 – 90
Total number of steps = 60
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