We can use the tangent function to solve this problem. Let h be the height of the skyscraper.
First, we need to find the length of the adjacent side of the right triangle formed by Sadie, the base of the skyscraper, and the point where she is standing. This length is the horizontal distance between Sadie and the base of the skyscraper, which is 275 meters.
Next, we can use the tangent of the angle of elevation to find the ratio of the opposite side (the height of the skyscraper) to the adjacent side:
tan(36°) = h/275
Solving for h, we get:
h = 275 tan(36°)
Using a calculator, we find:
h ≈ 198.64 meters
Therefore, the height of the skyscraper is approximately 198.64 meters.
Answer: 201.49
Step-by-step explanation:
Bridgette just went down the slide at the playground. She walks 1 meter to get from the end of the slide back to the ladder. Then she climbs 3 meters to the top of the slide again. How long is the slide? If necessary, round to the nearest tenth.
Please respond.
Thank you!
Answer:
2.14 (rounded to the nearest tenth)
Step-by-step explanation:
Let's assume that the length of the slide is represented by the variable "x".
Based on the information provided in the question, Bridgette walks 1 meter from the end of the slide back to the ladder and climbs 3 meters to reach the top of the slide again. Therefore, the total vertical distance Bridgette covers in one trip down and up the slide is 1 + x + 3 = x + 4 meters.
The length of the slide is the hypotenuse of a right triangle formed by the slide and the total vertical distance Bridgette covers in one trip down and up the slide. Using the Pythagorean theorem, we can write: x^2 = (x + 4)^2 - 1^2
Simplifying this equation, we get: x^2 = x^2 + 8x + 16 - 1
7x = 15
x = 2.14 (rounded to the nearest tenth)
Therefore, the length of the slide is approximately 2.1 meters.
Answer:
The slide is 3.2 m long---------------------------------
The slide and ladder form a right triangle with:
Horizontal leg (distance from slide to ladder) = 1 m,Vertical leg (ladder) = 3 m.Let the length of the slide be s, this is a hypotenuse.
Find s using Pythagorean:
[tex]s=\sqrt{1^2+3^2} =\sqrt{1+9}=\sqrt{10}=3.2\ m \ rounded[/tex]The number of houses in Central Village, New York, grows every year at a rate of 3.9%. In 2015, the local
government counted 540 houses. Using this data, how many houses can the local government of Central Village
predict there will be in 2035? (Round your answer to the nearest whole.)
Answer:
We can use the formula for exponential growth:
A = P(1 + r)^t
where:
A = final amount
P = initial amount
r = annual growth rate (as a decimal)
t = time (in years)
Let's plug in the values:
P = 540
r = 0.039
t = 2035 - 2015 = 20
A = 540(1 + 0.039)^20
A ≈ 891
Therefore, the local government of Central Village can predict there will be approximately 891 houses in 2035.
Answer:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r)^n
where:
A = the final amount
P = the initial amount
r = the annual interest rate (as a decimal)
n = the number of years
In this case, we want to find the final amount (the number of houses in 2035), given the initial amount (540 houses in 2015), the annual interest rate (3.9%), and the number of years (20 years from 2015 to 2035).
So, we can plug in the values and solve for A:
A = 540(1 + 0.039)^20
A = 540(1.039)^20
A = 540(2.011)
A = 1086.54
Rounding to the nearest whole number, we get:
A ≈ 1087
Therefore, the local government of Central Village can predict there will be about 1087 houses in 2035.
Theorem: For any real number x, x+∣x−5∣≥5 In a proof by cases of the theorem
A. x≤0 B. x≤5 C. x<5 D. x<0
The theorem holds for all real numbers x and the other case is that x < 5.
option C.
What is a real number?A real number is a value that represents a quantity along a continuous number line. Real numbers can be either rational or irrational. Rational numbers are numbers that can be expressed as a ratio of two integers, such as 1/2, 3/4, or -7/8.
For the given question, if one of the cases is that x > 5, we can determine the other case by considering the definition of absolute value:
If x > 5, then ∣x-5∣ = x-5 (since x-5 is positive),
so x + ∣x-5∣ = x + (x-5) = 2x - 5
which is clearly greater than or equal to 5.
If x < 5, then ∣x-5∣ = -(x-5) (since x-5 is negative),
so x + ∣x-5∣ = x - (x-5) = 5,
which is also greater than or equal to 5.
Therefore, the theorem holds for all real numbers x.
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The complete question is below:
Theorem: For any real number x, x+∣x−5∣≥5. In a proof by cases of the theorem, there are two cases. One of the cases is that x > 5.
What is the other case?
A. x≤0
B. x≤5
C. x<5
D. x<0
You want to determine the total amount of data stored on a server.
User A has 3550 GB of data stored on the server.
User B stores 4000 GB of data.
User C stores 2450 GB.
User D stores 1010 GB of data.
User E stores 7000 GB of data on the server.
Without using a calculator, use the properties of operations to determine the total amount of data stored on the server.
A
1801 GB
B
18,010 GB
C
19,010 GB
D
1901 GB
One way to approach this problem without using a calculator is to group the numbers by their place value (i.e., thousands, hundreds, tens, and ones), and then add them together.
For example,
For thousands:
User A has 3 thousands,
User B has 4 thousands,
User C has 2 thousands,
User E has 7 thousands.
There are no thousands for User D.
So the total number of thousands is 3+4+2+7 = 16 thousands.
For hundreds:
User A has 550 hundreds (since 3550 = 3 x 1000 + 550),
User B has 0 hundreds (since 4000 is a multiple of 1000),
User C has 450 hundreds (since 2450 = 2 x 1000 + 450),
User D has 10 hundreds,
User E has 0 hundreds (since 7000 is a multiple of 1000).
So the total number of hundreds is 550+0+450+10+0 = 1010 hundreds.
For tens and ones:
Since all the numbers are in thousands or hundreds, there are no tens or ones to add.
Therefore, the total amount of data stored on the server is:
16 thousands + 1010 hundreds = 16,100 GB
Name the type of angle indicated
Answer: Acute
Step-by-step explanation:
Acute - Less than 90 degress
Straight - Exactly 180 degrees
Obtuse - More than 90 degrees
Right - Exactly 90 degrees
Find h(1.1) if
h(t) = -4.9t² +8.
Answer:i got u :uuuuuuuuuuuuuu
What is the area of a sector with a central angle of 90° and a diameter of 20.6 mm?
Use 3.14 for and round your answer to the nearest hundredth.
Enter your answer as a decimal in the box.
mm²
Answer:
37.03 sq. mm.
Step-by-step explanation:
got it right on usa test prep
how many 6-letter names are possible, assume that the first
letter has to be a capital letter?
The 308915776 6-letter names that are possible, assuming that the first letter has to be a capital letter.
Given that the first letter in the name has to be a capital letter and the number of letters in the name is 6, find how many 6-letter names are possible.There are 26 capital letters in the English alphabet. Since the first letter must be a capital letter, we have 26 choices for the first letter.There are 26 lowercase letters in the English alphabet. We have 26 choices for each of the 5 remaining letters of the name.Using the multiplication principle of counting, the total number of possible 6-letter names with a capital first letter is:26 × 26 × 26 × 26 × 26 × 26=26⁶= 26 * 26 * 26 * 26 * 26 * 26 = 308915776 Therefore, there are 308915776 6-letter names that are possible, assuming that the first letter has to be a capital letter.
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The number 0.08 is 1/10 of which value.
Answer: 0.008
Step-by-step explanation:
1/10 of 0.08
of is the same as multiplying
1/10 x 0.08= 1/10 x 8/100= 8/1000
8 divided by 1000= 0.008
This is part of a bus timetable between Birmingham and Coventry,
Birmingham 07 02 07 30 08 05 | 08 35 09 02 09 31 a) How many minutes
should the 07 02 bus
Yardley
07 21 07 4908 2408 5409 21 09 50
take to go from
Solihull 07 43 08 11 08 4609 16 09 43 10 12 Birmingham to
Coventry?
Meriden 07 59 08 27|09 0209 32 09 5910 28
92
minutes (1)
Coventry 08 34 09 02 09 3710 07 10 34 | 11 03
b) Steve goes from Birmingham to Coventry by bus,
He takes 9 minutes to walk from his house to the bus stop in Birmingham,
He takes 12 minutes to walk from the bus stop in Coventry to work,
Steve has to get to work by 10 am,
What is the latest time Steve should
leave his house to get to work on time?
(3)
Total marks: 4
The minutes that it would take for the 0702 bus to go from Birmingham to Coventry is 92 minutes.
The latest time that Steve should leave his house so as to get to work on time is 07 56 hours .
How to find the time taken ?If the bus from Birmingham leaves at 07 02 hours, it would reach Coventry at 08 34. The time taken is therefore :
= 08 34 - 07 02
= 1 hour 32 minutes
In minutes, this is:
= 60 minutes in an hour + 32
= 92 minutes
The total time it would take Steve to reach Coventry from Birmingham would be:
= Time to Coventry + Time spent walking from house + Time spent walking in Coventry
= 92 minutes + 9 + 12
= 113 minutes
The time Steve should leave his house at the latest is:
= 10 am - 113 minutes
= 08 07 hours
However, he would miss the 08 35 bus if he did this so he needs to leave in time for the 08 05 bus which is:
= 08 05 - 9 minutes walking
= 07 56 hours
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Units of Capacity
Customary
System Units
1 gallon
1 quart
1 cup
Metric System Units
3.79 liters
0.95 liters
0.237 liters
How many centiliters are in 5 quarts?
quarts → liters → centiliters
->
a=
b=
C=
d=
5 quarts a C
1
-x-x=475 cL
=475
b d
After answering the provided question, we can conclude that As a result, expression 5 quarts contain 473.176473 centilitres. It is 473 cL rounded to the nearest centilitre
what is expression ?An expression in mathematics is a collection of manifestations, digits, and transnational corporations that resemble a significant correlation or regimen. A square root, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, pervasiveness, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
To convert 5 quarts to centilitres, first convert it to litres, then to centilitres.
1 gallon = 0.946352946 litres (conversion factor from customary system)
5 quarts equals 5 x 0.946352946 litres equals 4.73176473 litres
100 centilitres = 1 litre (conversion factor from metric system)
4.73176473 litres = 4.73176473 multiplied by 100 centilitres per litre = 473.176473 centilitres
As a result, 5 quarts contain 473.176473 centilitres. It is 473 cL rounded to the nearest centilitre.
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John and Max work at a sandwich shop. John can make 15 sandwiches per hour, and Max can make 10 sandwiches per hour. Max worked 5 more hours than John and they made a total of 150 sandwiches that day. Determine the number of hours Max worked and the number of hours John worked.
1. Name the 2 variables that are being related in this situation. 2. Write a system of equations to represent the number of hours Max and John worked 3. Solve the system using substitution 4. Interpret the solution of the solution.
20 pts.
Therefore , the solution of the given problem of variable comes out to be John worked for four hours and Max worked for nine.
Variable is what?A variable is a quality that can be evaluated expression and have various values. Height, age, salary, province of birth, academic status, and style of residence range are a few examples of variables.
Here,
Let's use the variables "J" and "M" to denote the respective number of hours done by John and Max. Next, we can formulate the formulae in the following system:
=> J + 5 = M (Max put in five hours more than John did.)
=> 15J + 10M = 150 (They prepared a total of 150 sandwiches) (They made a total of 150 sandwiches)
This system can be resolved using replacement. By deducting 5 from both sides of the first equation, we can find "J" in terms of "M":
=> J = M - 5
Now, we can enter the following formula in place of "J" in the second equation:
=> 15J + 10M = 150
Using J = M - 5 as a substitute, 15(M - 5) Plus 10M = 150.
=> 15M - 75 + 10M Equals 150 (distributing the 15) (distributing the 15)
=> 25M = 225 (adding 75 to both ends) (adding 75 to both sides)
=> M = 9
Max thus put in nine hours of labour. John worked a total of __ hours, so we can re-enter ___ into the first calculation as follows:
=> J + 5 = M
=> J + 5 Equals 9 (M replaced with 9)
=> J = 4
John spent 4 hours at work.
The answer is that John worked for four hours and Max worked for nine.
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Answer this ASAP will give the brainliest answer
Given that y = 8 cm and θ = 25°, work out x rounded to 1 DP.
The diagram is not drawn accurately.
Answer: x = 18.9 to 1dp
Step-by-step explanation: Using SOH CAH TOA,
Sin 25 = 8/x
Making x subject of the formula:
x = 8/Sin 25
x = 18.92961267
x = 18.9 to 1dp
Help pls! There is a part b it says “predict the population of the city in 30 years to the nearest whole number”
The function that represents the estimated population after t years with an annual rate of decrease of 0.25% is y = [tex]358,000(0.9975)^{t}[/tex]. So correct option is D) .
Describe Annual rate?Annual rate can also be used to describe growth rates or changes in other types of measurements, such as population growth or inflation. For example, if the population of a city grows by 2% per year, the annual rate of population growth is 2%.
It is important to note that when annual rates are used to describe financial products or investments, they may be compounded over time. Compounding refers to the process of earning interest on interest, which can significantly increase the total amount of interest owed or earned over time. Therefore, it is important to carefully consider the effects of compounding when evaluating financial products or investments.
The function that represents the estimated population after t years with an annual rate of decrease of 0.25% is:
y = [tex]358,000(0.9975)^{t}[/tex]
Therefore, the correct option is D) y = [tex]358,000(0.9975)^{t}[/tex].
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A motorcycle decelerates steadily from 108 km/h to 36 km/h, covering a distance of 160m. For how long was the motorcycle decelerating?
Answer:
5760
Step-by-step explanation:
what is the perimeter for a rectangle diagonal of 29 feet and a width of 14 feet?
Answer: We can use the Pythagorean theorem to find the length of the rectangle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the diagonal is the hypotenuse and the width and length of the rectangle are the other two sides.
Let's use "l" to represent the length of the rectangle:
l^2 + 14^2 = 29^2
l^2 = 29^2 - 14^2
l^2 = 561
l = sqrt(561)
l ≈ 23.67 feet
Now that we know the length and width of the rectangle, we can use the formula for the perimeter, which is the sum of all four sides:
Perimeter = 2 * length + 2 * width
Perimeter = 2 * 23.67 + 2 * 14
Perimeter = 47.34 + 28
Perimeter = 75.34 feet
Therefore, the perimeter of the rectangle is approximately 75.34 feet.
Step-by-step explanation:
the average bmi (body mass index) value of children 9 years old is 18.4 with a standard deviation of 4.5. if it is known that the distribution is approximately normal, what is the probability that a randomly selected 9-year-old has a bmi greater than 26.8? give your answer to three decimal places.
The probability that a randomly selected 9-year-old has a BMI greater than 26.8 is 0.031. Hence, the answer is 0.031.
What is the formula to calculate standard deviation?
The formula to calculate standard deviation is:
SD = sqrt [(Σ(xi - μ)²) / N]
Where, SD = standard deviation
x = individual data points
μ = mean of the sample
N = sample size
What is the formula for z-score?
The formula for z-score is:
z = (x - μ) / σ
Where,
z = z-score
x = raw score
μ = mean of the population
σ = standard deviation of the population
Given that, The average BMI (body mass index) value of children 9 years old is 18.4 with a standard deviation of 4.5.
To find the probability that a randomly selected 9-year-old has a BMI greater than 26.8, we have to find the z-score.
z = (x - μ) / σz = (26.8 - 18.4) / 4.5z = 1.86
Now, we have to find the probability from the z-table, which is 0.9686. But we have to find the probability greater than 26.8, so we have to subtract it from 1.1 - 0.9686 = 0.0314 ≈ 0.031
Therefore, the probability that a randomly selected 9-year-old has a BMI greater than 26.8 is 0.031. Hence, the answer is 0.031.
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A herbalist has 40 oz of herbs costing $4 per ounce. How many ounces of herbs costing $1 per ounce should be mixed with these 40 oz of herbs to produce a mixture costing $2. 20 per ounce?
60 ounces of herbs costing $1 per ounce should be mixed with these 40 oz of herbs to produce a mixture costing $2. 20 per ounce
Let x be the amount of herb that costs $1.00/oz and y be the total amount of the mixture that costs $2.20/oz.
The total weight of the mixture is:
= y=x+40
The total cost of the mixture is:
4(40) + 1x = 2.20y
160 + x = 2.20 (x + 40) .......Substitute y using the expression from the first equation
160 + x = 2.20x + 88 .........Subtract 160 and x from both sides
1.20x = 72 .........Divide both sides by 1.20
x = 60
The herbalist must mix 60 oz of the herb that costs $1.00/oz to the mixture, therefore we can say that:
60 ounces of herbs costing $1 per ounce should be mixed with these 40 oz of herbs to produce a mixture costing $2. 20 per ounce
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find each missing length to the nearest tenth
Answer: 4.1
Step-by-step explanation: To find a missing leg you must square both numbers, then subtract the leg you do have from the hypotenuse ( 33.64 - 16.81) to get the squared number for the missing leg ( 16.83). You then have to find the square root of that number and round to the nearest tenth (4.1).
A line has a slope of –12 and passes through the point (6,–9). Write its equation in slope-intercept form.
Answer: y = -12x + 63
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We are given the slope of the line, which is -12, and a point that the line passes through, which is (6,-9).
Using the point-slope form of a linear equation, we have:
y - (-9) = -12(x - 6)
Simplifying this equation, we get:
y + 9 = -12x + 72
Subtracting 9 from both sides, we get:
y = -12x + 63
Therefore, the equation of the line in slope-intercept form is y = -12x + 63.
Calculate the mode of the data set {5, 8, 2, 5, 11, 2, 5, 13}
PLS HELP
Answer:
5
Step-by-step explanation:
The mode is the most commonly occurring number in a set of numbers. In this one it is 5.
At the bakery where Isaac works, one of the cups in a cupcake tray has a radius of 3 centimeters. What is the cup's diameter? centimeters
The diameter οf the cup is 6 centimeters.
What is the diameter οf a circle?A circle's diameter is defined as a line thrοugh the centre that jοins the circumference at bοth ends. It is twice as lοng as the circle's radius. In οther wοrds, the line that splits a circle in half evenly at its centre is the diameter οf the circle.
The diameter οf a circle is equal tο twice its radius.
Therefοre, tο find the diameter οf the cup, we need tο multiply the radius by 2:
Diameter = 2 x Radius
Diameter = 2 x 3 cm = 6 cm
Hence, the diameter οf the cup is 6 centimetres.
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For annually compounded interest, what rate would result in a single investment doubling in 3 years?
Work Shown:
[tex]A = P*(1+r/n)^{n*t}\\\\2P = P*(1+r/1)^{1*3}\\\\2 = (1+r)^{3}\\\\(1+r)^{3} = 2\\\\1+r = \sqrt[3]{2}\\\\r = -1+\sqrt[3]{2}\\\\r \approx 0.25992\\\\[/tex]
That converts to 25.992% after moving the decimal point two spots to the right. Round this value however your teacher instructs.
Helpppppp meeeeeeeeeeeee
Answer:
16
Step-by-step explanation:
Call the 3n+3 angle x. Call the 2n+7 angle y. The right angle, x, and y all lie in a straight line, meaning that the three angles added together equal 180. Adding, 5n + 100=180, so n=16.
The ratio of 2 institutions is 7 : 3 and their sum is 630. Find the number
the first institution has 441 and the second institution has 189.
We can use algebra to solve the problem. We can start by assigning variables to represent the two institutions:
Let x be the multiplier of the ratio.
Then, we have:
7x is the first institution.
3x is the second institution.
From the problem, we know that the sum of the two institutions is 630:
7x + 3x = 630
Simplifying the left side, we get:
10x = 630
Dividing both sides by 10, we get:
x = 63
Now that we know the value of x, we can find the number of each institution:
First institution = 7x = 7(63) = 441
Second institution = 3x = 3(63) = 189
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The endpoints of PQ on the real number line are −14 and 2 . What is the coordinate of the midpoint of PQ ? F. −8 G. −6 H. −2 J. 0 K. 8
The midpoint of PQ is -6. The line PQ have endpoints on the real number line at −14 and 2
How to solve a midpoint equation?An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.
The midpoint O between two points A and B on the number line is:
O = (A + B)/2
The endpoints of PQ on the real number line are −14 and 2, hence:
Midpoint = (-14 + 2) / 2 = -12/2 = -6
The midpoint of PQ is -6
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The hexagonal prism below has a base area of 36 units² and a height of 5.9 units.
Find its volume.
The volume of the hexagonal prism is the amount of space in the prism
The volume of the hexagonal prism is 212.4 cubic units
How to determine the volume?The given parameters are:
Base area = 36 square units
Height = 5.9 units
The volume is then calculated as:
Volume = Base area x Height
So, we have:
Volume = 36 x 5.9
Evaluate the product
Volume = 212.4
Hence, the volume of the hexagonal prism is 212.4 cubic units
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Note: Round intermediate calculations to at least 4 decimal places and your final answers to 2 decimal places. c-2. Based on the z-score standardized Manhattan distance values, identify the pair of the first three employees that are most simiar. Empioyees 1 and 3 Employeos 1 and 2 Employees 2 and 3 Undetermined, because the Manhattan distance values give inconclusive results.
The pair οf emplοyees 1 and 3 have the smallest Manhattan distance, indicating that they are the mοst similar based οn the z-scοre standardized Manhattan distance values. Therefοre, the answer is Emplοyees 1 and 3
What Is Z-Scοre?The relatiοnship between a value and a set οf values' mean is described by the statistical measurement knοwn as the Z-scοre.
Manhattan distance = [tex]|z^1 - z^2| + |z^3 - z^4| + ... + |zn-1 - zn|[/tex]
The z-scοres fοr each variable are calculated as fοllοws:
z-scοre = (x - mean) / standard deviatiοn
Emplοyee 1:
Age z-scοre = (25 - 27.33) / 1.2472 = -1.8616
Salary z-scοre = (48000 - 51666.67) / 9930.77 = -3.6915
Emplοyee 2:
Age z-scοre = (35 - 27.33) / 1.2472 = 6.1420
Salary z-scοre = (72000 - 51666.67) / 9930.77 = 2.0505
Emplοyee 3:
Age z-scοre = (27 - 27.33) / 1.2472 = -0.2645
Salary z-scοre = (53000 - 51666.67) / 9930.77 = 1.4256
Distance between emplοyees 1 and 2: |(-1.8616) - 6.1420| + [(-3.6915) - 2.0505] = 13.3956
Distance between emplοyees 1 and 3: |(-1.8616) - (-0.2645)| + [(-3.6915) - 1.4256] = 4.7236
Distance between emplοyees 2 and 3: |(6.1420) - (-0.2645)| + [(2.0505) - 1.4256] = 8.5020
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Mariya was asked to solve StartFraction a over negative 13 EndFraction less-than-or-equal-to negative 16 and then graph the solution. Her work is shown below. In which step, if any, did Mariya make a mistake in her work?
Mariya made a mistake in the third step of her work by multiplying both sides of the inequality by -13 instead of dividing.
What is an inequality?An inequality is a mathematical statement that compares two values or expressions using a symbol such as <, >, ≤, or ≥. It indicates that one value is not equal to another, and may be greater than or less than it.
This resulted in a change of the direction of the inequality from less than or equal to (≤) to greater than or equal to (≥). Therefore, the correct inequality would be a ≥ -13 × -16. The solution of this inequality is a ≥ 208.
When graphing the solution, the solution set will include all values of a greater than or equal to 208, which can be represented by a shaded line to the right of the point 208 on a number line.
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8 to 2 but double the equivalent ratio
Answer:
Step-by-step explanation:
8:2 doubled is 16:4