Solve each absolute value inequality and show its solution set.
|2y+3|<19
|2s-6|\(\leq\)6
|5-x|\(\leq\)4
|5t-1|>21
|-2x-5|\(\leq\)5
Please answer fast!
Answers
Answer:
|-2x - 5| > 5 is x < -5 or x > 0
Step-by-step explanation:
|2y + 3| < 19:
To solve this inequality, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: 2y + 3 > 0
In this case, the absolute value simplifies to 2y + 3 < 19.
Solving this inequality, we get 2y < 16 and y < 8.
Case 2: 2y + 3 < 0
In this case, the absolute value simplifies to -(2y + 3) < 19.
Solving this inequality, we get -2y < 22 and y > -11.
Therefore, the solution set for the inequality |2y + 3| < 19 is -11 < y < 8.
|2s - 6| < 6:
Again, we'll consider two cases based on the sign of the expression inside the absolute value.
Case 1: 2s - 6 > 0
In this case, the absolute value simplifies to 2s - 6 < 6.
Solving this inequality, we get 2s < 12 and s < 6.
Case 2: 2s - 6 < 0
In this case, the absolute value simplifies to -(2s - 6) < 6.
Solving this inequality, we get -2s < 12 and s > -6.
Therefore, the solution set for the inequality |2s - 6| < 6 is -6 < s < 6.
|5 - x| < 4:
Case 1: 5 - x > 0
In this case, the absolute value simplifies to 5 - x < 4.
Solving this inequality, we get -x < -1 and x > 1.
Case 2: 5 - x < 0
In this case, the absolute value simplifies to -(5 - x) < 4.
Solving this inequality, we get x < 9 and x < 5.
Therefore, the solution set for the inequality |5 - x| < 4 is 1 < x < 5.
|5t - 1| > 21:
Case 1: 5t - 1 > 0
In this case, the absolute value simplifies to 5t - 1 > 21.
Solving this inequality, we get 5t > 22 and t > 4.4.
Case 2: 5t - 1 < 0
In this case, the absolute value simplifies to -(5t - 1) > 21.
Solving this inequality, we get -5t > 20 and t < -4.
Therefore, the solution set for the inequality |5t - 1| > 21 is t < -4 or t > 4.4.
|-2x - 5| > 5:
Case 1: -2x - 5 > 0
In this case, the absolute value simplifies to -2x - 5 > 5.
Solving this inequality, we get -2x > 10 and x < -5.
Case 2: -2x - 5 < 0
In this case, the absolute value simplifies to -(-2x - 5) > 5.
Solving this inequality, we get 2x > 0 and x > 0.
Therefore, the solution set for the inequality |-2x - 5| > 5 is x < -5 or x > 0.
Related Questions
graph the function
y=4(2^x+3)-1
and
y=-2(3^x-4)+1
Answers
The graphs of the functions y = 4(2ˣ + 3) - 1 and y = - 2(3ˣ - 4) + 1 are plotted on the graph.
What is function?A function is a relation between a dependent and a independent variable, such that the dependent variable depends upon the independent one for its existence.
Given are the following functions -
y = 4(2ˣ + 3) - 1
y = - 2(3ˣ - 4) + 1
We have the following functions -
y = 4(2ˣ + 3) - 1
y = - 2(3ˣ - 4) + 1
Refer to the graph attached. The graph of red color represents the function y = 4(2ˣ + 3) - 1 and the graph of blue color represents the function y = - 2(3ˣ - 4) + 1. It can be seen that the graphs are symmetrical about the line y = 10.
Therefore, the graphs of the functions y = 4(2ˣ + 3) - 1 and y = - 2(3ˣ - 4) + 1 are plotted on the graph.
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HELP ME PLEASE IM HAVING SO MUCH TROUBLE....
A company offers a nut mixture with 7 peanuts for every 4 almonds. The company changed the mixture to have 8 peanuts for every 5 almonds, but the number of nuts per container does not change.
a. Create a ratio table for each mixture. How many nuts are in the smallest possible container?
b. Graph the ordered pairs from the tables. What could you conclude?
c. Almonds cost more than peanuts. Should the company charge more or less for the new mixture? Explain your reasoning.
Answers
The position of an open-water swimmer is shown in the graph. The shortest route to the shoreline is one that is perpendicular to the shoreline. Write an equation that represents this path.
Answers
Answer:
Step-by-step explanation:
To define the perpendicular line we need to first know the slope of the reference line graphed.
m=(y2-y1)/(x2-x1) we have points (0,5) and (2,1)
m=(1-5)/(2-0)
m=-4/2
m=-2
For lines to be perpendicular their slopes must satisfy
m1m2=-1, we have a line with a slope of -2 so
-2m=-1
m=1/2, so our perpendicular line is so far
y=x/2+b, it must have point (3,2) so we can solve for b
2=3/2+b
b=1/2, so the swimmer will travel along the line
y=x/2+1/2
The submarine is descending at a rate of 4.2 feet per minute. How many feet below sea level is the submarine at after 5 minutes.
But the multiplication problem below.
Answers
Answer:
21
Step-by-step explanation:
4.2*5=21 hope this helps
Which expression is equivalent to (m^-2n^-4)^-4
Answers
Answer:
m^8 n^16
Step-by-step explanation:
Simplify the following:
(1/(m^2 n^4))^(-4)
Multiply exponents. (1/(m^2 n^4))^(-4) = (m^2 n^4)^4:
(m^2 n^4)^4
Multiply each exponent in m^2 n^4 by 4:
m^(4×2) n^(4×4)
4×4 = 16:
m^(4×2) n^16
4×2 = 8:
Answer: m^8 n^16
what is the equstion of s line with a y-intercept of -5 and a slope of 8
Answers
Answer:
y = 8x - 5
Step-by-step explanation:
Given:
Slope: 8Y-intercept: -5To find:
Equation.How to find:
The slope is always known as "constant of variation" or "rate of change", but it's basically the increase of both y and x axes in simple terms. The decrease or increase in two points together and then found with the formula of rise/run (increase and decrease) (horizontal line/vertical line).
The y-intercept is always on the y-axis and is the beginning of what is learned in pre-algebra as a "story" which helps students practice finding the slope which again, is the change with "per" or "each".
Make sure to use the formula:
y = mx + b
Now we insert.
y = 8x <---------- slope
y = 8x - 5 <------ y-intercept and completed slope-intercept equation.
The reason it has a negative is because it started out as a negative y-intercept and is increasing by 8 through ordered pairs.
Answer:
y = 8x - 5
Step-by-step explanation:
because if its has a slope of 8 then m is 8
if the y intercept is -5 the b is -5
y = mx + b
y = 8x -5
Use the slope-intercept form to write a equation of the line that passes through the given points. Use function notation where y = f(x).
(10, 2) and (8, 10)
The slope of a line is given.
a. Determine the slope of a line parallel to the given line, if possible.
b. Determine the slope of a line perpendicular to the given line, if possible.
Answers
the equation of the line is f(x) = -4x + 42.
To find the equation of the line that passes through the points (10, 2) and (8, 10) using the slope-intercept form, we first need to determine the slope of the line.
a. To determine the slope of a line parallel to the given line, we can use the fact that parallel lines have the same slope. So, we need to find the slope of the given line passing through (10, 2) and (8, 10).
Slope (m) = (y2 - y1) / (x2 - x1)
= (10 - 2) / (8 - 10)
= 8 / (-2)
= -4
Therefore, the slope of any line parallel to the given line is also -4.
b. To determine the slope of a line perpendicular to the given line, we can use the fact that perpendicular lines have negative reciprocal slopes. So, the perpendicular slope would be the negative inverse of the given slope.
Perpendicular slope = -1 / (-4)
= 1/4
Therefore, the slope of any line perpendicular to the given line is 1/4.
The equation of the line passing through the points (10, 2) and (8, 10) using the slope-intercept form (y = f(x)) can be found using the point-slope form:
y - y1 = m(x - x1)
Taking (10, 2) as (x1, y1), we have:
y - 2 = -4(x - 10)
y - 2 = -4x + 40
y = -4x + 42
Hence, the equation of the line is f(x) = -4x + 42.
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stock can justify a p/e ratio of 24. assume the underwriting spread is 15 percent.
Answers
A stock with a price-to-earnings (P/E) ratio of 24 can be justified considering the underwriting spread of 15 percent.
The P/E ratio is a commonly used valuation metric that compares the price of a stock to its earnings per share (EPS). A higher P/E ratio indicates that investors are willing to pay a premium for each dollar of earnings. In this case, a P/E ratio of 24 suggests that investors are valuing the stock at 24 times its earnings.
The underwriting spread, which is typically a percentage of the offering price, represents the compensation received by underwriters for their services in distributing and selling the stock. Assuming an underwriting spread of 15 percent, it implies that the offering price is 15 percent higher than the price at which the underwriters acquire the stock.
When considering the underwriting spread, it can have an impact on the valuation of the stock. The spread effectively increases the offering price and, therefore, the P/E ratio. In this scenario, if the underwriting spread is 15 percent, it means that the actual purchase price for investors would be 15 percent lower than the offering price. Thus, the P/E ratio of 24 can be justified by factoring in the underwriting spread, as it adjusts the purchase price and aligns the valuation with market conditions and investor sentiment.
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What is the unit price of $6.80 for 8
Answers
Answer:
$0.85
Step-by-step explanation:
6.8/8 which is 0.85.
Hope this helps plz mark brainliest :D
Answer:
Step-by-step explanation:
divide 6.80 by 8 to get the unit price.
6.80/8= 0.85 a piece
A construction company has to complete a project no later than three months from now or there will be significant cost overruns. The manager of the construction company believes that there are four possible values for the random variable X, the number of months from now it will take to complete this project: 2, 2.5, 3, and 3.5. The manager currently thinks that the probabilities of these four possibilities are in the ratio 1 to 2 to 4 to 2. That is, X = 2.5 is twice as likely as X = 2, X = 3 is twice as likely as X = 2.5, and X = 3.5 is half as likely as X = 3. a. Find the probability distribution of X. b. What is the probability that this project will be completed in less than three months from now? c. What is the probability that this project will not be completed on time? d. What is the expected completion time (in months) of this project from now? e. How much variability (in months) exists around the expected value you found in part d?
Answers
The probabilities are:
The expected completion time is 2.83 months with a variability of 0.6301 months.
a. Probability distribution of X:
P(X=2) = 1/9
P(X=2.5) = 2/9
P(X=3) = 4/9
P(X=3.5) = 2/9
b. Probability of completing the project in less than three months:
P(X<3) = P(X=2) + P(X=2.5) + P(X=3) = 7/9
c. Probability of not completing the project on time:
P(X>=3) = P(X=3) + P(X=3.5) = 6/9
d. Expected completion time:
E(X) = 2P(X=2) + 2.5P(X=2.5) + 3P(X=3) + 3.5P(X=3.5) = 2.83 months
e. Variability around the expected completion time:
To calculate variability, we need to find the variance of the distribution. Variance is the average of the squared deviations from the mean. The formula for variance is:
Var(X) = E(X^2) - [E(X)]^2
E(X^2) = 2^2P(X=2) + 2.5^2P(X=2.5) + 3^2P(X=3) + 3.5^2P(X=3.5) = 9.075
Var(X) = 9.075 - (2.83)^2 = 0.3969
The standard deviation is the square root of the variance:
SD(X) = sqrt(0.3969) = 0.6301 months
In this scenario, a construction company must complete a project within three months to avoid cost overruns. The manager believes that the completion time follows a specific probability distribution.
This problem requires finding the probability distribution, calculating the probability of completing the project on time, the probability of not completing it on time, the expected completion time, and the variability around the expected value.
The problem statement specifies four possible values for the completion time: 2, 2.5, 3, and 3.5 months. The manager believes that the probabilities of these values are in the ratio of 1:2:4:2. To find the probability of each value, divide the ratio by the sum of the ratio:
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determine the inteerval on which the following function is convave upor concave down. identify any inflection points. f(x)= x^4 - 4x^3 – 6 x^2 -x -7
Answers
The function is concave down on the interval ((2 -√(2))/2, (2 + √(2))/2), and concave up on the other two intervals. The inflection points are at x = (2 - √(2))/2 and x = (2 + √(2))/2.
To determine where the function is concave up or concave down, we need to find the second derivative and check its sign:
f(x) = x⁴ - 4x³ - 6x² - x - 7
f'(x) = 4x³ - 12x² - 12x - 1
f''(x) = 12x² - 24x - 12 = 12(x² - 2x - 1)
To find the intervals of concavity, we need to solve the inequality 12(x² - 2x - 1) > 0:
x² - 2x - 1 > 0
Using the quadratic formula, we find the roots of the quadratic equation:
x = (2 ± √(2))/2
These are the critical points where the concavity changes, so we can use them to divide the real line into three intervals:
(-∞, (2 - √(2))/2), ((2 - √(2))/2, (2 + √(2))/2), ((2 + √(2))/2, +∞)
Now we can test any value in each interval to determine the sign of the second derivative and any inflection points, and thus the concavity:
For x < (2 - √(2))/2:
f''(x) > 0, so f(x) is concave up.
For (2 - √(2))/2 < x < (2 + √(2))/2:
f''(x) < 0, so f(x) is concave down.
For x > (2 + √(2))/2:
f''(x) > 0, so f(x) is concave up.
Therefore, on the intervals((2 -√(2))/2, (2 + √(2))/2), the function is concave down, whereas on the other two intervals, it is concave up. Both at x = (2 - √(2))/2 and x = (2 + √(2))/2.
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HELP - 100 POINTS AND BRAINLIEST!! Find the area and volume - a square has a side length of 6.25 Please show your work! Thank you!
Answers
Step-by-step explanation:
Area: bh
The shape is a square in which the side lengths are the same, so we multiply the number squared.
A = 6.25(6.25)
A = 39.06
Volume: lwh
6.25^3 = V
V = 244.14
Hope this helps:)
Step-by-step explanation:
Area: bh
The shape is a square in which the side lengths are the same, so we multiply the number squared.
A = 6.25(6.25)
A = 39.06
Volume: lwh
6.25^3 = V
V = 244.14
I hope I contributed
hello need ASAP please help due tommorow
Answers
Answer:
28×4/7=16
Step-by-step explanation:
well it seems as the most logical answer but it also seems the realist one to pick for me personally but I would think it is better to see mixed opinions but I think it's the 2nd one
the two dice are rolled and the sum of the results is calculated. what is the probability of the sum equaling 5?
Answers
The probability of the sum equaling 5 is 1/9
How to determine the probability of the sum equaling 5?From the question, we have the following parameters that can be used in our computation:
Rolling two dice
When two dice are rolled, we have
Outcomes = 36
Sum of 5 = 4
using the above as a guide, we have the following:
P = Sum of 5/Outcomes
substitute the known values in the above equation, so, we have the following representation
P = 4/36
Evaluate
P = 1/9
Hence, the probability is 1/9
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Please I'm serious no time for nonsense
Draw (3) Convex Polygons & (3) Non- polygons .
Answers
Answer & step-by-step explanation:
Convex: Triangle, Square, Pentagon. (Has to be equal sided and angled)
Non-Convex: Draw a weird shape, such as a deformed star, a 5 sided shape with no equal sides, such as these listed below:
They do not need equal sides or symmetry but all regular polygons are convex.
The interior angles all need to be less than 180 degrees.
Non-convex polygons have one or more vertices pushed inside the shape.
The interior angle at those vertices will be greater than 180 degrees
The function h(x) is a transformation of the square root parent function, f(x) = \( \sqrt{x} \)
![The function h(x) is a transformation of the square root parent function, f(x) = [tex] \sqrt{x} [/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/4VcmtmLr543oilxUEki5Cf3NTIvbAhoD.jpeg)
Answers
Here we want to know the expression in the new funtion
Let s look at the difference between the two functions so as to be clear with the situation.
The funtion f(x) starts at the origin.
Looking at the function h(x), we can see that it starts out at the point x = -6
We can use these starting point to actually predict what the function will look like
In this case, the function h(x) has its expression as
\(h(x)\text{ = }\sqrt[]{x\text{ + 6}}\)Option B is the correct option for the function h(x)
Carl deposited P dollars into a savings account that earned 8 percent annual interest, compounded semiannually. Carl made no additional deposits to or withdrawals from the account. After one year, the account had a total value of $10,816. What was the value of P?
Answers
Carl deposited 10,000 into the savings account.
We can use the formula for compound interest to solve this problem:
\(A = P(1 + r/n)^{(nt)}\)
Where:
A = the final amount
P = the initial principal (what Carl deposited)
r = the annual interest rate (8%)
n = the number of times interest is compounded per year (2 for semiannual compounding)
t = the number of years (1)
Plugging in the given values and solving for P:
\(10,816 = P(1 + 0.08/2)^{(2\times 1)}\)
\(10,816 = P(1.04)^2\)
10,816 = 1.0816P
P = 10,000
Therefore, Carl deposited 10,000 into the savings account.
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question the random variable x is exponentially distributed, where x represents the time it takes for a whale watcher to spot a whale. if x has an average value of 45 minutes, what is the probability that x is less than 45 minutes? round the final answer to three decimal places.
Answers
0.368 .
The probability that a random variable x is exponentially distributed and less than 45 minutes,
given that the average value is 45 minutes, is 0.368.
This can be calculated by taking the negative of the natural logarithm of 1/2 (i.e. -ln(0.5)) and dividing it by the average value of 45 minutes.
The result, -ln(0.5)/45, equals 0.368, rounded to three decimal places.
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Help plz I just need the answer
Answers
Answer:
x = 7
Step-by-step explanation:
4 packages of blueberries cost $9. How many packages of blueberries can you buy for $63?
Answers
Answer:
28
Step-by-step explanation:
Answer:
9 divided by 3= 6. You can buy 6 packages of blueberries for $9 dollars.
Step-by-step explanation:
i need help with this: (photo below)
Answers
Answer: middle
Step-by-step explanation:
Michael is on page 28 of a 315-page book. He must finish the book within the next 14 days. He solved the inequality 28+ 14p = 315 He did not use the correct value as the coefficient of p and should have solved 14 + 28p <= 315
Answers
Answer:
yes you're right it is 14 + 28p = 315
Answer:
C
Step-by-step explanation:
I had this question edge 2021
14. Which of the following is equivalent to y= x^2 – 18x + 70?
y = (x – 9)^2 - 11
y = (x + 9)^2 +11
y = (x - 9)^2 +11
y = (x + 9)^2 - 11
Answers
Answer:
I believe that the answer is C
if a = b and b = c then a = c. true or false
Answers
Answer: true
Step-by-step explanation:
Answer: True
Step-by-step explanation: Has to be true if a b and c are all numbers
Solve and check the equation. X +2 2/5 = 4
Answers
Answer:
x= 8/5 . or 1.6 in decimal form or 1 and 3/5 in a mixed number .
Step-by-step explanation:
Please help and thank you
Answers
Answer:
A. \(4^3*6^3\)
Step-by-step explanation:
First, you solve the given equation.
\((4*6)^3\\\\=24^3\\=13824\)
You solve the multiple choice afterwards. Since choice A was given first, we managed to find the answer.
\(4^3 * 6^3\\\\=64 * 216\\=13824\)
Choice A has the same answer as the given equation, making them equivalent.
Find the circumference of the circle
Answers
Answer:
Formula for circumference;
C = 2πr
replace those values
C = 2 x 3.14 x 9
C = 56.52 inches, C
Answer:
The circumference would be 56.52
Step-by-step explanation:
Place your radius into the formula for circumference (C=2πr)
C = 2 × 3.14 × 9
C = 56.52
3(2 + f) = -15
A. 3
B. 7
C. -3
D. -7
Answers
Answer:
D. (-7)
Step-by-step explanation:
3(2 + f) = (-15)
(3 . 2) + (3 . f) = (-15)
6 + 3f = (-15)
3f = (-15) - 6
3f = (-21)
f = (-21)/3
f = (-7)
Step-by-step explanation:
6+3f=-15
subtract 6
3f=-21
then divide
f=-7
6. Which equation represents: "Seven times the difference of a number and tenis
equal to the same number increased by 2.
Answers
Answer:
12
Step-by-step explanation:
let the number=x
7(x-10)=x+2
7x-70=x+2
7x-x=2+70
6x=72
x=72/6=12
Which is not true about the degrees of freedom (df) of a chi-square distribution?
Answers
Option (A): "As the degrees of freedom increases the shape of the Chi-Square Distribution becomes more skewed" is a false statement.
What is Chi-Square Distribution?The Chi-Square Distribution is a type of probability distribution that is skewed rightward. The Chi-Square Distribution is used for both the confidence interval and hypothesis testing. The confidence interval is used mainly for variances and the hypothesis testing is used for the goodness of fit test and the test of independence.Now, amongst the considered options, "As the degrees of freedom increases the shape of the Chi-Square Distribution becomes more skewed." (Option A) is not true, because:
As the degrees of freedom increases, the shape of the Chi-Square Distribution approaches a normal distribution and the graph of the Chi-Square Distribution looks more symmetrical.
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