Answer:
A is correctStep-by-step explanation:
The option that is greater than 4 is option (a) 5. This is because 5 is a positive value that is larger than 4. Option (b) -5 is a negative value that is less than 4. Option (c) -1/2 is also negative and less than 4. Option (d) -25 is the most negative option and therefore less than 4. So, the only option that is greater than 4 in this case is 5.
Answer:
a
Step-by-step explanation:
got it right on edge
Michelle had 7 paperback books and 4 hardcover books on the shelf by her bed. Write a ratio to represent the ratio of paperback books to hardcover books
Answer:
7:4 that would be the ratio
if n is even
if n is odd
Yes, repeating two simple arithmetic operations will eventually transform every positive integer into 1.
Checking whether repeating two operations will transform every positive integer into 1.From the question, we have the following parameters that can be used in our computation:
f(n) = n/2 if n%2 = 0
f(n) = 3n + 1 if n%2 = 1
The above definition means that
f(n) = n/2 if n is even
f(n) = 3n + 1 if n is odd
To check if repeating operations would transform to 1, we can set n = 10
and then evaluate the function values
So, we have
f(10) = 10/2 = 5
f(5) = 3(5) + 1 = 16
f(16) = 16/2 = 8
f(8) = 8/2 = 4
f(4) = 4/2 = 2
f(2) = 2/2 = 1
See that the end result of the operations is 1
Hence, repeating two operations will transform every positive integer into 1
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a line has the equation y=6x+19 what are the coordinates of the y intercept
Answer:
The equation of the line is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
From the given equation, we can see that the y-intercept is 19. This means that the line passes through the point (0, 19).
Therefore, the coordinates of the y-intercept are (0, 19).
The y-intercept of the equation y=6x+19 is the value of y when x equals 0, which is at the point (0,19).
Explanation:The y-intercept refers to the point where the line crosses the y-axis. In the equation of a line in slope-intercept form, y=mx+b, 'b' represents the y-intercept.Therefore, in the equation y=6x+19, the y-intercept is at the point (0, 19). Hence, the coordinates of the y-intercept are (0,19).
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The number of international Netflix subscriptions (in millions) can be approximated by the function N(x)=24.9(1.736)^x, where x is the number of years after 2012. (Source: Statista.com) a. How many million international Netflix subscriptions were there in the year 2012? blank1 - Numeric Answer 24.9 You are correct million (Do not round answer.) b. Estimate the number of Netflix subscriptions in the year 2020.
According to the given function.
There were approximately 24.9 million international Netflix subscriptions in the year 2012.
There were approximately 167.7 million international Netflix subscriptions in the year 2020,
We have,
a.
Since the function N(x) gives the number of international Netflix subscriptions x years after 2012, to find the number of Netflix subscriptions in the year 2012,
We need to set x = 0.
So,
N(0) = 24.9(1.736)^0
= 24.9 million
b.
To estimate the number of Netflix subscriptions in the year 2020, we need to set x = 8 (since 2020 is 8 years after 2012).
N(8) = 24.9(1.736)^8
= 167.7 million
Thus,
According to the given function.
There were approximately 24.9 million international Netflix subscriptions in the year 2012.
There were approximately 167.7 million international Netflix subscriptions in the year 2020,
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Water works commission assume population standard deviation is 1.7 gallons. 15.8 gallons a day for sample of 249 families. Construct 80% confidence intervals
The 80% confidence interval for the average water usage of 249 families is (15.42, 16.18) gallons.
To construct an 80% confidence interval for the average water usage of 249 families, we can use the following formula:
CI = X ± t(α/2, df) * (s/√n)
where X is the sample mean (15.8 gallons), t(α/2, df) is the critical t-value from the t-distribution table at the desired confidence level and degrees of freedom (247 in this case), s is the population standard deviation (1.7 gallons), and n is the sample size (249).
At an 80% confidence level and 247 degrees of freedom, the critical t-value is approximately 1.296.
Plugging in the values, we get:
CI = 15.8 ± 1.296 * (1.7/√249)
CI = 15.8 ± 0.38
Therefore, the 80% confidence interval for the average water usage of 249 families is (15.42, 16.18) gallons.
This means that we are 80% confident that the true average water usage of the population lies within this interval.
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6. Roy reviews his purchases over a week. He spent $3.55 on coffee four
times, $10.76 and $15.35 on lunch, $55.27 on groceries, and $16.98 at the
hardware store. What is the average cost of the items he bought? State
what strategy you will use to answer the question, explain your choice,
and then find the answer.
Answer: herefore, the average cost of the items Roy bought is $14.07.
Step-by-step explanation:
To find the average cost of the items Roy bought, we need to add up the total cost of all his purchases and divide by the total number of purchases.
Strategy:
1. Add up the cost of all Roy's purchases.
2. Count the number of purchases.
3. Divide the total cost by the number of purchases to find the average cost.
Explanation:
We will use this strategy because it is a straightforward way to find the average cost of multiple items. We will add up all the costs and divide by the number of purchases to get the average cost.
Calculations:
Total cost = (4 x $3.55) + $10.76 + $15.35 + $55.27 + $16.98
Total cost = $14.20 + $10.76 + $15.35 + $55.27 + $16.98
Total cost = $112.56
Number of purchases = 4 (coffee) + 2 (lunch) + 1 (groceries) + 1 (hardware store)
Number of purchases = 8
Average cost = Total cost / Number of purchases
Average cost = $112.56 / 8
Average cost = $14.07
Therefore, the average cost of the items Roy bought is $14.07.
Which one is correct about the nth term of a geometric sequence?
Answer:
d
Step-by-step explanation:
The first term is 'a'
then for the second term a r
third term = a r^(n-1)
etc
Will give Brainliest for right answer and extra points!!!!
New homeowners hire a painter to paint rooms in their house. The painter pays $100 for supplies and charges the homeowners $25 for each room they want painted.
Which of the following graphs shows the relationship between the amount of money the painter earns, in dollars, and the number of rooms he paints?
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 0
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma negative 100 through the point 4 comma 0
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 200
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma negative 100 through the point 4 comma negative 200
Answer:
The amount of money the painter earns, in dollars, depends on the number of rooms he paints.
For each room painted, the painter charges $25. Therefore, the amount of money earned, y, is given by the equation:
y = 25x + 100
where x is the number of rooms painted and 100 is the cost of supplies.
To graph this equation, we can plot a point on the y-axis where x=0 (the fixed cost of supplies) at (0, 100), and then use the slope of 25 to find additional points. For example, when x=1, y=125; when x=2, y=150; and so on.
With this information, we can eliminate options (b) and (d) because they both show negative slopes, which would mean the painter loses money as he paints more rooms.
Option (c) shows a positive slope, but the line goes through the point (0,100) and (4,200), which means the painter earns $200 after painting 4 rooms, but this contradicts the given information that the painter charges $25 per room. Therefore, option (c) is also incorrect.
Option (a) correctly shows the slope of 25 and goes through the point (0, 100), and the line reaches the x-axis when x=4, indicating that the painter earns $0 after painting 4 rooms. This matches the given information that the painter charges $25 per room. Therefore, the correct answer is option (a).
Therefore, the graph that shows the relationship between the amount of money the painter earns, in dollars, and the number of rooms he paints is:
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 0
Answer:
The correct answer is a C. coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 200.
The painter pays $100 for supplies, so he will only earn money for the rooms he paints after he has recouped that cost. The first room he paints will earn him $25, the second will earn him $50, and so on. After he has painted 4 rooms, he will have earned $200.
The graph of this relationship would be a line that starts at the point (0, 100) and goes up to the point (4, 200).
Step-by-step explanation:
27% of all college students major in STEM (Science, Technology, Engineering, and Math). If 35 college students are randomly selected, find the probability that
a. Exactly 9 of them major in STEM.
b. At most 11 of them major in STEM.
c. At least 11 of them major in STEM
The probability of getting exactly 9 of them major in STEM is 0.139 or 13.9%.
The probability of getting at most 11 of them major in STEM is approximately 0.898 or 89.8%.
The probability of getting at least 11 of them major in STEM is approximately 0.318 or 31.8%.
a. Exactly 9 of them major in STEM.
In this case, the probability of success (a student majoring in STEM) is 0.27, and the number of trials is 35. The probability of exactly 9 students majoring in STEM is then given by the formula:
P(X = 9) = (35 choose 9) x (0.27)⁹ x (0.73)²⁶
where (35 choose 9) is the number of ways to choose 9 students out of 35, and (0.27)⁹ x (0.73)²⁶ is the probability of 9 successes and 26 failures. Evaluating this expression gives a probability of approximately 0.139 or 13.9%.
b. At most 11 of them major in STEM.
To calculate the probability that at most 11 students out of 35 major in STEM, we can use the cumulative binomial probability distribution. This distribution calculates the probability of at most X successes, where X is any number from 0 to the total number of trials.
The probability of at most 11 students majoring in STEM can be calculated as follows:
P(X <= 11) = P(X = 0) + P(X = 1) + ... + P(X = 11) = 0.898 or 89.8%.
c. At least 11 of them major in STEM.
The probability of less than 11 students majoring in STEM can be calculated using the cumulative binomial probability distribution, as in part (b). Specifically:
P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)
Subtracting this probability from 1 gives the probability of at least 11 students majoring in STEM:
P(X >= 11) = 1 - P(X < 11) = 31.8%
Again, we can use the binomial distribution formula from part (a), or a binomial probability calculator or statistical software package to calculate this probability.
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Five sisters shared their father's inheritance equally. There were three houses in the inheritance, and nothing else. Since it is impossible to divide each home into fractional pieces, the three oldest sisters each took one house, and then allocated their own money to the other two: each of the three oldest sisters paid 800 rubles, and the two younger sisters divided the money among themselves. How much, in rubles, did one house cost? Please round to the nearest integer.
This is a word problem, and the cost of one house in rubles is 1200, as the five sisters shared their father's inheritance equally.
How to evaluate for the cost of one house in rublesIf the three oldest sisters each paid 800 rubles, then they collectively paid 2400 rubles (800 rubles x 3 sisters) to the two younger sisters
Each of the the two younger sisters will have a total of 1200 rubles (2400 rubles/2 younger sisters), as they divided the money among themselves.
In conclusion, since the five sisters shared their father's inheritance equally, then 1200 rubles is the cost of one house, which solves the word problem
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Hi, I don't get what to do here I tried using vietas theorem, but I still can't get it. 55 points
Answer:
x^3 - 6x^2 + 12x - 8 = 0
Step-by-step explanation:
Let the roots of the equation x^3 - 8x + 3 = 0 be a, b, and c. Then, we know that the squares of the roots are a^2, b^2, and c^2.
By Vieta's formulas, we know that the sum of the roots of x^3 - 8x + 3 = 0 is 0, since there is no x^2 term:
a + b + c = 0
We also know that the product of the roots is 3/1 = 3:
abc = 3
Using the fact that the squares of the roots are a^2, b^2, and c^2, we can write:
a^2 + b^2 + c^2 = (a + b + c)^2 - 2(ab + ac + bc)
Since a + b + c = 0, this simplifies to:
a^2 + b^2 + c^2 = -2(ab + ac + bc)
Now, let's try to find a cubic equation with roots a^2, b^2, and c^2. We can start with:
(x - a^2)(x - b^2)(x - c^2) = 0
Expanding the left side, we get:
x^3 - (a^2 + b^2 + c^2)x^2 + (a^2b^2 + b^2c^2 + c^2a^2)x - a^2b^2c^2 = 0
Using the identity we found earlier for a^2 + b^2 + c^2, we can simplify this to:
x^3 + 2(ab + ac + bc)x - 3a^2b^2c^2 = 0
Now, we can substitute in the values we know for ab, ac, and bc:
ab = (a + b + c)(ab + ac + bc) - (a^2b + ab^2 + c^2a)
ac = (a + b + c)(ab + ac + bc) - (a^2c + ac^2 + b^2a)
bc = (a + b + c)(ab + ac + bc) - (b^2c + bc^2 + a^2b)
Plugging in these values and simplifying, we get:
x^3 - 6x^2 + 12x - 8 = 0
Therefore, the cubic equation we're looking for is:
x^3 - 6x^2 + 12x - 8 = 0
And the roots of this equation are the squares of the roots of x^3 - 8x + 3 = 0.
what is the simple interest on a sum of money invested at 3% per annum for 212
years is N123, find the principal.
Answer: The simple interest on a sum of money invested at 3% per annum for 2 1/2 years is N9.225, and the principal is N3,000.
Step-by-step explanation:
We can use the formula for simple interest:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Given that the interest is N123, the interest rate is 3% per annum, and the time is 2 1/2 years, we can plug these values into the formula and solve for the principal:
123 = P * 0.03 * 2.5
Simplifying, we get:
123 = 0.075P
P = 123 / 0.075
P ≈ 1,640
Therefore, the principal is approximately N1,640.
However, this principal value does not correspond to the given interest amount of N9.225. To obtain the correct principal, we need to use the correct interest amount:
We can convert the time of 2 1/2 years to 5/2 years, and use the formula for simple interest:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Given that the interest is N9.225, the interest rate is 3% per annum, and the time is 5/2 years, we can plug these values into the formula and solve for the principal:
9.225 = P * 0.03 * 5/2
Simplifying, we get:
9.225 = 0.0375P
P = 9.225 / 0.0375
P = 246
Therefore, the principal is N246.
Kyle sold an antique through an online auction website. The website host charges kyle $15, plus 2.5% of the final selling price of the antique. After selling the antique, kyle had to pay the website host $32. What was the selling price?
The selling price of the antique through an online auction website is $680.
Given that,
Kyle sold an antique through an online auction website.
The website host charges Kyle $15, plus 2.5% of the final selling price of the antique.
After selling the antique, Kyle had to pay the website host $32.
Let x be the selling price of the antique.
We get an equation,
15 + (2.5% × x) = 32
15 + 0.025x = 32
0.025x = 17
x = $680
Hence the selling price is $680.
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What is the sum of the interior angle
measures of a regular hexagon? Show
or explain how you can use the sum
of the interior angles of a triangle to
determine the answer.
Answer:
The sum of the interior angle measures of a regular hexagon is 720°.
Step-by-step explanation:
To find the sum of the interior angle measures of a regular hexagon, we can use the fact that any polygon can be divided into triangles. The formula to find the sum of the interior angles of any polygon with n sides is:
Sum of interior angles = (n - 2) × 180°
In the case of a hexagon, n = 6. So, we can plug this value into the formula:
Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°
The sum of the interior angle measures of a regular hexagon is 720°.
To explain this using triangles, let's divide the hexagon into triangles. A hexagon can be divided into four triangles by drawing three diagonals from one vertex to the three non-adjacent vertices. Since the sum of the interior angles of each triangle is 180°, and we have four triangles:
Sum of interior angles of hexagon = 4 × 180° = 720°
The sum of the interior angle measures of a regular hexagon is 720°.
Use the calculator to find the product.
(1.466 × 10–8)(5.02 × 105)
What is the coefficient of the product?
What is the exponent of the power in the product?
Answer:
7.3593 and -3 is the correct answerStep-by-step explanation:
Using the given calculator, the product of (1.466 × 10–8) and (5.02 × 105) was found to be 7.3593 × 10–3. The coefficient of the product is 7.3593, which is obtained by multiplying the coefficients of the two given numbers. The exponent of the power in the product is –3, which is obtained by adding the exponent of the first number to the exponent of the second number and then subtracting it from the power of 10. Therefore, the final answer is 7.3593 × 10–3.
Answer:
7.3593 and -3Step-by-step explanation:
How to us caculator to find product?Using a calculator to find the product of two or more numbers is a simple process. First, enter the first number into the calculator using the number keys. Then, press the multiplication symbol (usually represented by the "x" key) followed by the second number. If there are more numbers to multiply together, repeat the process until all numbers have been entered. Finally, press the equals sign (often represented by the "=" key) to display the product of all the numbers. Remember to check the order of operations if necessary, and to double-check your input and output to avoid errors.
How to Multiply 2 numbers?To multiply two numbers in scientific notation, we first multiply their coefficients (1.466 x 5.02 = 7.358). Then, we add their exponents together (-8 + 5 = -3). Therefore, (1.466 x 10⁻⁸) multiplied by (5.02 x 10⁵) equals 7.358 x 10⁻³ or 0.007358. The final answer has the exponent of -3, indicating that the answer should be moved 3 decimal places to the left to convert it from scientific notation to standard notation.
Please help answer this question!!!
The solution is the area of triangle ABC is 9.56 square units .
Given:
The objective is to find the area of triangle ABC
Explanation:
The general formula to find the area of a triangle is,
A = 1/2 *b*h
To find the area of triangle ABC:
The height of the triangle DC can be calculated using the Pythagorean theorem of triangle ADC.
DC = √ 9 - 6.25
=1.65
On plugging the given values in equation
Thus, the height of triangle ABC is 2.5
So the base of the triangle CB = 6 + 1.65 = 7.65.
Now, substitute the obtained values in equation
area = 1/2 * 7.65 * 2.5
= 9.56
Hence, the area of triangle ABC is 9.56 square units .
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The box plot below represents some data sets. What percentage of the data values are between 52 and 68?
Answer:
25%
Step-by-step explanation:
The box and whisker plot is broken up into 4 quartiles. Each quartile is 25% of the date. The data range in in the third quartile.
Helping in the name of Jesus.
What is the Recursive relation of 1,1,5,17,71,247…
The recursive relation of the data distribution a(n) = a ( n - 1 ) x n - ( n - 1 ).
How to find the recursive relation ?A sequence of values is defined by a mathematical equation termed as a recursive relation, also known as recursive relation. It derives current value(s) through specified initial value(s) and previous value dependent rule(s). In essence, it generates numeric sequences.
Note that every individual unit can be derived by multiplying the preceding one with a rising integer, and subsequently subtracting a descending integer:
1 x 1 - 0 = 1
1 x 2 - 1 = 1
1 x 3 - 2 = 5
5 x 4 - 3 = 17
17 x 5 - 4 = 71
71 x 6 - 5 = 247
We can deduce the relation of a(n) = a ( n - 1 ) x n - ( n - 1 ).
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Which statement is true about the end behavior of the function represented by the graph
Answer:3
Step-by-step explanation:
Please help me with this question
The surface area of the prism is 112 in²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of a prism is expressed as;
SA = 2B +pH
where h is the height and B is the base area and p is the perimeter of the base
The perimeter of the base = 2(l+b)
= 2(3+4) = 2×7 =14 in
The area of the base = l× b
= 4× 3 = 12 in²
height = 7
Therefore the surface area = 2 × 12 + 14 × 7
= 14+98
= 112 in²
therefore the surface area of the prism is 112 in²
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Two similar octagons have areas of 4 ft2 and 16 ft2. Find their similarity ratio.
1:4
1:2
1:16
1:8
Answer: 1:4
Step-by-step explanation:
In order to do this, we have to know that the octagon has an area which is four times less than the other area. Because of this, it shuld be 1:4
I need help on solving the problems and answers ASAP, please
The volumes of the following shapes include:
728.00 m³.
135.78 yd³.
1260.00 cm³.
452.39 in³.
1344.00 m
How to calculate volume?1. Pyramid:
The formula for the volume of a pyramid is:
V = (1/3) × B × h
where B is the area of the base and h is the height.
For a pyramid with a rectangular base, the area of the base is:
B = l × w
where l and w are the length and width of the base, respectively.
Using the given measurements:
l = 13 m
w = 8 m
h = 21 m
Therefore, the area of the base is:
B = l × w = 13 m × 8 m = 104 m²
And the volume of the pyramid is:
V = (1/3) × B × h = (1/3) × 104 m² × 21 m ≈ 728 m³
Rounded to the nearest hundredth, the volume of the pyramid is 728.00 m³.
2. Cylinder:
The formula for the volume of a cylinder is:
V = πr²h
where r is the radius of the base and h is the height.
Using the given measurements, we have:
r = 3.5 yd / 2 = 1.75 yd
h = 10 yd
Therefore, the volume of the cylinder is:
V = πr²h = π × (1.75 yd)² × 10 yd ≈ 135.78 yd³
Rounded to the nearest hundredth, the volume of the cylinder is 135.78 yd³.
3. Cuboid:
The formula for the volume of a cuboid is:
V = l × w × h
Using the given measurements, we have:
l = 14 cm
w = 18 cm
h = 5 cm
Therefore, the volume of the cuboid is:
V = l × w × h = 14 cm × 18 cm × 5 cm = 1260 cm³
Rounded to the nearest hundredth, the volume of the cuboid is 1260.00 cm³.
4. Cone:
The formula for the volume of a cone is:
V = (1/3) × πr²h
where r is the radius of the base and h is the height.
Using the given measurements:
r = 12 in / 2 = 6 in
h = 37 in
Therefore, the volume of the cone is:
V = (1/3) × πr²h = (1/3) × π × (6 in)² × 37 in ≈ 452.39 in³
Rounded to the nearest hundredth, the volume of the cone is 452.39 in³.
5. Prism:
The formula for the volume of a prism is:
V = Bh
where B is the area of the base and h is the height.
Using the given measurements:
B = 6 m × 16 m = 96 m²
h = 14 m
Therefore, the volume of the prism is:
V = Bh = 96 m² × 14 m = 1344 m³
Rounded to the nearest hundredth, the volume of the prism is `1344.00 m
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Calculate the arc length of the
sector.
147°
7 mm
Give your answer correct to 1
decimal place.
Answer:
Arc length = (147/360) x (2π x 7)
Arc length = (0.40833) x (2 x 3.14159 x 7)
Arc length = 0.40833 x 43.9823
Arc length = 17.9955
2.6y + 14.8 - 7.8x - 9.7y Combine like terms
The simplified expression is -7.1y - 7.8x + 14.8.
The given expression is 2.6y + 14.8 - 7.8x - 9.7y. To combine like terms, we first identify the terms that have the same variable with the same exponent. In this case, we have two terms with y, and they both have the exponent 1. So, we can combine these terms together by adding their coefficients, which are 2.6 and -9.7.
2.6y - 9.7y can be simplified as (2.6 - 9.7)y, which is equal to -7.1y. Therefore, the expression can be written as:
-7.1y - 7.8x + 14.8
We cannot combine any other terms in this expression since they do not have the same variable or exponent.
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Activity 3
Write in increasing order according to their capacity:
HURRY DUE TONIGHT
Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts. What percent of the new mixture if peanuts?
A. 34%
B. 13%
What are the values of a and B
Answer:
a = 48
b = 28
Step-by-step explanation:
b = 0.5 × 56
b = 28
52 = 0.5 × (56 + a)
104 = 56 + a
a = 48
please help me here is screenshot. quick and right answers only. algebra
The slope of f(x) is smaller than the slope of g(x).
Which function has the largest slope?For a linear function that passes through two points (x₁, y₁) and (x₂, y₂) the slope is given by the formula:
a = (y₂ - y₁)/(x₂ - x₁)
Then the slope of g(x) is:
a = (3 - 0)/(0 + 2) = 3/2
And for f(x) the slope is 4/5, then we can see that:
3/2 > 4/5
Thus the slope of g(x) is larger.
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Use the form |x – b | ≤ c or |x – b | ≥ c to write an absolute value
inequality that has the solution set x ≤ –9 or x ≥ –5.
The absolute value inequality that has the solution set x ≤ –9 or x ≥ –5 is
|x + 7| ≤ 2
We have,
To write an absolute value inequality with a solution set x ≤ –9 or x ≥ –5, we first need to find the midpoint of the two given values:
Midpoint of –9 and –5
= (-9 + (-5)) / 2
= -7
We can now use the midpoint and one of the given values to write the absolute value inequality.
Since the solution set includes both values, we need to use the form
|x – b | ≤ c.
We can choose to use either value, let's use x ≤ –9:
|x – (-7)| ≤ |-9 – (-7)|
|x + 7| ≤ 2
Therefore,
The absolute value inequality that has the solution set x ≤ –9 or x ≥ –5 is
|x + 7| ≤ 2
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Look at photo question 1
The inches of water could Rafael have added is less than 3/8 inches
How many inches of water could Rafael have addedGiven that
The water level must be at least 11 inchesThe initial water level is 11 1/2The water decreased by 7/8So, the inequality expression is
Initial water level - The decreased amount + Amount of water added by Rafael < The actual water level
Represent the Amount of water added by Rafael with x
So, we have
11 1/2 - 7/8 + x < 11
So, we have
92 - 7 + 8x < 88
When the like terms are evaluated, we have
8x < 88 + 7 - 92
Evaluate
8x <3
This gives
x < 3/8
Hence, the amount added by Rafael is less than 3/8 inches
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