The height of Jamie's plant on the twenty-first day is 82.5 feet.
Here we have to find the height of Jamie's plant on the twenty-first day.
Data given:
First-day increase in the plant = 2.5 inches
On the fourth day increase in the plant = 14.5 inches
We can find the slope of the line:
m = (y2 - y1) / ( x2 - x1)
= (14.5 - 2.5) / (4 - 1)
= 12/3
= 4
Now we will find the equation of a line:
(y - y1) = m( x - x1)
( y - 2.5) = 4( x - 1)
y - 2.5 = 4x - 4
y = 4x - 1.5
Now substitute x = 21 in our equation.
y = 4(21) - 1.5
y = 84 - 1.5
= 82.5
Therefore we get the height of the plant as 82.5 feet.
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A car corporation produced 940
fewer cars this month than last.
Write a signed number to represent this month's change in production
The signed number to represent ''A car corporation produced 940 fewer cars this month than last'' is - 940.
What is meant by signed number representations ?Negative integers in binary number systems must be encoded in computation using signed number representations.In mathematics, negative integers in any base are denoted by a minus sign ("-") before them. However, numbers are solely represented as bit sequences, without any additional symbols, in RAM or CPU registers. The four most popular ways to express signed integers using the binary numeral system are offset binary, ones' complement, two's complement, and sign-magnitude. Some of the other techniques, such negative binary with the base 2, employ implicit signs rather than explicit ones. For different bases, whether positive, negative, fractional, or other elaborations on such themes, corresponding algorithms can be developed.Learn more about signed number refer to :
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Triangle abc is defined by the points a(2,9), b(8,4), and c(-3,-2). Complete the following equation for a line passing through point c and perpendicular ab. Y = x +.
When triangle ABC is defined by the coordinates a(2,9), b(8,4), and c, the equation for the line is 5y=6x+8 (-3,-2).
What is equation of line?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical phrase with two equal sides and an equal sign is called an equation. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations. Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation. Equal treatment should be given to each side.
Here,
A=(2,9)
B=(8,4)
C=(-3,-2)
The slope of line AB,
m=(y2-y1)/(x2-x1)
=(4-9)/(8-2)
=-5/6
Slope of line perpendicular to AB,
m1=-1/m
=-1/(-5/6)
=6/5
This line pass through (-3,-2).
y=mx+c
-2=6/5*(-3)+c
c=-2+18/5
c=8/5
The equation of line,
y=6/5x+8/5
5y=6x+8
The equation of line is 5y=6x+8 when triangle ABC is defined by the points a(2,9), b(8,4), and c(-3,-2).
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Who now what is egal 8+8-8×8÷8
Answer:
8+8-8×1
8+8-8
16-8
8 Ans.
The mean of 11 numbers is 7 one of the numbers, 13, is deleted. What is the mean of the remaining 10 numbers?.
If mean of 11 numbers is 7 one of the numbers, 13, is deleted then the mean of remaining 10 numbers is 6.4
The mean of 7 numbers = 11
We know,
Mean = Sum of the terms / Number of terms
Substitute the values in the equation
11 = Sum of the terms / 7
The sum of the terms = 11 × 7
= 77
Number 13 is deleted
Sum of the terms = 77 - 13
= 64
Number of terms = 11 - 1
= 10
The mean = Sum of the terms / Number of terms
Substitute the values in the equation
= 64 / 10
= 6.4
Hence, the mean of the remaining 10 numbers is 6.4
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A triangle has side lengths of n, n – 3, and 2(n − 2). If the perimeter of the triangle is at least 37 units, what is the value of n?
OA.
n> 11
OB
n> 8
O C.
n > 10. 5
OD
n > 7. 5
Answer:
A. n ≥ 11
Step-by-step explanation:
You have a triangle with sides (n), (n-3), and 2(n-2). Its perimeter is at least 37 units, and you want to know the value of n.
PerimeterThe perimeter is the sum of the side lengths:
P = (n) +(n -3) +2(n -2)
P = n + n -3 +2n -4
P = 4n -7
ConstraintThe perimeter is at least 37, so we have ...
P ≥ 37
4n -7 ≥ 37
4n ≥ 44 . . . . . . . add 7
n ≥ 11 . . . . . . . divide by 4
The value of n is at least 11.
A vehicle uses 1\frac{1}{8} gallons of gasoline to travel 13\frac{1}{2} miles. Create a rate to represent the miles the vehicle can travel per gallon of gasoline.
The vehicle can travel 12 miles per gallon of gasoline.
What is the Mixed fraction ?
A mixed fraction is one that is represented by both its remainder and quotient. Consequently, a mixed fraction is created by combining a whole number and a proper fraction.
What is the Rate ?
A rate is the comparison of two comparable amounts expressed in different units. If the ratio's denominator is written as a single unit of one of these quantities, and if it is assumed that this quantity can be modified systematically (i.e., is an independent variable), then the numerator of the ratio indicates the comparable rate of change in the other (dependent) variable.
The vehicle travels 13\frac{1}{2} by using 1\frac{1}{8} gallons of gasoline.
since the units are in mixed fraction, we can simplify it to simple fraction,
distance travelled= 13\frac{1}{2} = [(13 × 2) + 1] / 2 = 27/2 miles.
gasoline used= 1\frac{1}{8} = [(1×8)+1] /8 = 9/8 gallons.
∴ Miles per gallon of gasoline = distance travelled ÷ gasoline used
= 27/2 miles ÷ 9/8 gallons
= 12 miles per gallon of gasoline.
Hence, The rate of miles per gallon of gasoline is 12 miles/gallon of gasoline.
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Find the sum of (8 + 2 − 4) and (3 − 5).
Answer:
4
Step-by-step explanation:
(8+2-4)+(3-5)
(10-4)+(-2)
6-2
4
Hopes this helps please mark brainliest
find the value of the constant c which makes fx|y (x, y) a valid conditional probability mass function.
c=1/2 which makes fx|y (x, y) a valid conditional probability mass function.
What is conditional probability?
The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is determined by multiplying the likelihood of the earlier event by the increased likelihood of the later, or conditional, event.
Given that;
p(x) = [tex]c (\frac{2}{3} )^n[/tex] where x = 1,2,3,........
for getting value of c we are using the expression :
[tex]\sum_{n=1}^{\infty} c(\frac{2}{3})^n = 1[/tex]
[tex]c\sum_{n=1}^{\infty} (\frac{2}{3})^n = 1[/tex]
Since we want p(x) to be a Probability Mass Function, your approach is correct, since for any such function
fX:A→[0,1],X:S→A⊆R, it is :
[tex]\sum _{x\in A} \ fX(x)=1[/tex]
As long as you've correctly understood that condition, you can proceed with your specific exercise as follows:
[tex]\sum_{n=1}^{\infty} c(\frac{2}{3})^n = 1[/tex]
⇔ [tex]c\sum_{n=1}^{\infty} (\frac{2}{3})^n = 1[/tex]
⇔2c = 1
⇔c = 1/2
Hence c = 1/2 is the valid conditional probability mass function.
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HELP ME PLEASE! IM SO CONFUSED
Answer:
299,792 km599,585 km899,377 km1,199,170 km1,498,962 kmStep-by-step explanation:
You want to find the distance traveled by light in km for periods of 1–5 seconds at a speed of 299,792,458 m/s.
UnitsThe speed is given in meters per second, and the table values are wanted in kilometers. There are 1000 meters in 1 km, so it can be convenient to convert the speed to km/s before doing other calculations.
(299,792,458 m/s) / (1000 m/km) = 299,792.458 km/s
DistanceThe distance is found by multiplying the speed by time:
d = 299,792.458t
It is convenient to let a calculator do the multiplication (and rounding). The attachment shows the result of using t = {1, 2, 3, 4, 5}.
The distances are, respectively, {299792, 599585, 899377, 1199170, 1498962} km.
chapter 17 review questions how does a b-tree differ from a b -tree? why is a b -tree usually preferred as an access structure to a data file?
The difference in b-tree and b +tree, b -tree is a self balancing tree data structure that maintains sorted data and b +tree is a modified version of b -tree.
b -tree is used to sort the data with various pieces facilities such as insertion ,deletion and search etc whereas b +tree is a modified version of b -tree providing all the functions smoothly and quickly .
In b -tree, both internal nodes and leaf nodes are used to store records and keys whereas in b +tree keys are stored in internal nodes whereas records are storing leaf nodes
In b +tree, no duplication is allowed but in b +tree duplication may occur
A b +tree usually preferred as an access structure to a data file as as the height of the tree remains balanced and less as compared to b -tree . We can assess the data stored in b +tree sequentially as well as directly . keys are used for indexing . Faster search queries as the data is stored only on a leaf nodes.
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Tell whether the expression is positive or negative without evaluating it. -3/10 X (-8/15)
The expression -3/10 X (-8/15) is positive
Expression
Expression in mathematics has two or more variables, terms and constants. Also, arithmetic expression contains only numbers and mathematical operators and algebraic expression
The expression has negative sign and from mathematical calculation we already know the following relation:
+ x + = +
positive multiply by positive equals Positive
- x - = +
Negative multiply by Negative equals Positive
+ x - = -
Positive multiply by Negative equal Negative
hence, - [tex]\frac{3}{10}[/tex] x - [tex]\frac{8}{15}[/tex]
The negative sign multiply by -3/10 X (-8/15) sign will give positive.
Therefore, the expression -3/10 X (-8/15) is positive.
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Find the exact value of sin(u + v) given that sinu = 5/3 and cos v =-4/5. (Both u and v are in Quadrant I.)
The exact value of sin(u + v), obtained using trigonometric identities is for sine and cosine is 16/65
What are trigonometric identities?Trigonometric identities are equations that involve trigonometric functions that are valid for all values of the input variable.
The possible value of sin(u) obtained from a similar question posted online is; sin(u) = 5/13
Both u and v are in quadrant II
The trigonometric identity of the addition formula for the sine of the sum of two angles, indicates;
sin(u + v) = sin(u)·cos(v) + sin(v)·cos(u)
sin(u) = 5/13
cos(v) = -4/5
sin(v) = √(1 - (cos(v))²)
Therefore;
sin(v) = √(1 - (-4/5)²) = 3/5
cos(u) = √(1 - (sin(v))²)
Therefore;
cos(u) = √(1 - (5/13)²) = 12/13
Therefore;
sin(u + v) = (5/13) × (-4/5) + (3/5) × (12/13) = 16/65
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The mean cost of a five pound bag of shrimp is 42 dollars with a variance of 49. If a sample of 54 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than 43.4 dollars? Round your answer to four decimal places.
The probability that the sample mean would be less than 43.4 dollars is 0.9292.
What is a probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.
From the information, the mean cost of a five pound bag of shrimp is 42 dollars with a variance of 49 and a sample of 54 bags of shrimp is randomly selected.
Therefore, the probability will be:
P(x < 43.4)
Using normal distribution
= P(z < 43.4 - Mean( / 7/✓54)
= P(z < 43.4 - 42( / 7/✓54)
= P(z < 1.4697)
= 0.9292
The probability is 0.9292.
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For questions 7-9, factor each polynomial completely over the set of complex
numbers.
7. a(x)=2x²-3x³-24x² +13x+12
8. b(x) = x² − 2x³ −17x² +4x+30
9. c(x)=2x³-5x² +12x-5
PLEASE SHOW WORK
Answer:
answers attached int he files below all in order
HELP QUICKLY THANK YOU!
The values are;
⇒ F ∩ H = Ф
⇒ F ∪ H = (- ∞, 7]
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
F and H are defined as;
F = {v | v < 4 }
H = {v | v ≥ 7 }
Now,
Since, F and H are defined as;
F = {v | v < 4 }
H = {v | v ≥ 7 }
Hence, The values are;
F ∩ H = {v | v < 4 } ∩ {v | v ≥ 7 }
= Ф
And, F ∪ H = {v | v < 4 } ∪ {v | v ≥ 7 }
= (- ∞, 7]
Thus, The values are;
⇒ F ∩ H = Ф
⇒ F ∪ H = (- ∞, 7]
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Jorge wants to buy a drink. Which option is cheaper per ounce: one 24-ounce cup for $1.92 or two 12-ounce cups for $0.96 each?
The 24-ounce cup costs $0.08 per ounce, and the 12-ounce cups cost $0.085 per ounce. The 24-ounce cup is the cheaper option.
The 24-ounce cup costs $0.08 per ounce, and the 12-ounce cups cost $0.085 per ounce. The two 12-ounce cups are the cheaper option.
The 24-ounce cup costs $0.085 per ounce, and the 12-ounce cups cost $0.08 per ounce. The two 12-ounce cups are the cheaper option.
The cost per ounce in both options is the same.
The cost per ounce in both options is the same. Then the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The rate is the ratio of the amount of something to the unit.
Jorge wants to buy a drink.
Choice 1: 24-ounce cup for $1.92
Choice 2: 12-ounce cups for $0.96 each
The cost per ounce in choice 1 is calculated as,
⇒ $1.92 / 24
⇒ $0.08 per ounce
The cost per ounce in choice 2 is calculated as,
⇒ $0.96 / 12
⇒ $0.08 per ounce
The cost per ounce in both options is the same. Then the correct option is D.
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I need help to get these answers
The quadratic function, f(x) = 3·x² + 6·x, has the following values;
1. The function has a minimum value
2. The y-intercept of the function is (0, 0)
The axis of symmetry is; x = -1
The x-coordinate of the vertex is; x = -1
3. The table of values can be presented as follows;
x [tex]{}[/tex]-2 -1 0
f(x) [tex]{}[/tex]0 -3 0
The vertex is (-1, -3)
4. Please find attached the graph of the function
What is a quadratic function?A quadratic function is a function that has 2 as the highest power of the variables.
The specified function is; f(x) = 3·x² + 6·x
1. The coefficient of x² in the specified quadratic function, which indicates the existence of a minimum or maximum value is positive, therefore, the function has a minimum value
2. The y-intercept is the value of the function when x = 0, therefore;
f(0) = 3 × 0² + 6 × 0 = 0
Therefore, at the y-intercept, x = 0, and f(x) = 0
The y-intercept is (0, 0)
The axis of symmetry is a line that passes through the vertex
A the vertex, we get, f'(x) = 6·x + 6 = 0
Therefore; 6·x + 6 = 0
6·x = -6
x = -6/6 = -1
f(-1) = 3·(-1)² + 6 × (-1) = -3
The vertex is (-1, -3)
Therefore, the axis of symmetry is the line x = -1
The x-coordinate of the vertex of the function is; x = -1
3. A table of values for the function can be presented as follows;
x [tex]{}[/tex] f(x)
-6 [tex]{}[/tex] 72
-5 [tex]{}[/tex] 45
-4 [tex]{}[/tex] 24
-3 [tex]{}[/tex] 9
-2 [tex]{}[/tex] 0
-1 [tex]{}[/tex] -3
0 [tex]{}[/tex] 0
1 [tex]{}[/tex] 9
2 [tex]{}[/tex] 24
3 [tex]{}[/tex] 45
4 [tex]{}[/tex] 72
5 [tex]{}[/tex] 105
4. . Please find attached the graph of the function created with MS Excel
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When would you calculate an expected value? a. When your data points occur on different datesb. When your data points have various probabilities of occurringc. When you need to know the exact outcome of a future, unknown eventd. When you only have one data point
We calculate an expected value when the given data points have various probabilities of occurrence .
The expected value , applies best when we are performing the test or experiment many times. For example, EV applies well to gambling situations to describe expected results for thousands of gamblers per day, repeated day after day after day. However, the EV does not very accurately predict one particular outcome on one specific test.
For example, when drawing a playing card from a standard deck, on one specific draw, the likelihood of drawing a 2 is equal to the likelihood of drawing a 6 or 7 or 8 or any other numbered card.Over many many draws, the theoretical value to expect is 6.538. Obviously, there is no “6.538” card in the deck. But if you were gambling, you would expect to draw a card higher than 6 more often than not.To learn more about expected value
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solve for x under the assumption that x >0 x-70/x<-3
x under the assumption that x >0 x-70/x<-3, x > -35
WHAT IS INEQUALITY?
Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the quantity of money people get paid) (the amount of wealth people own). There are significant forms of economic inequality among various groups of people in addition to economic inequality between nations or states. Wealth, income, as well as consumption are the three main focuses of significant economic measurements. There are numerous ways to gauge economic inequality, with the Gini coefficient being among the most popular. The Disparities Human Development Index is a statistic composite index which offers another type of measurement by taking inequality into account.
assuming x > 0,
(x-70/x) < 3
= x-70 < 3x = -70 < 2x
= x > -35
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Write the equation of a line that is perpendicular to the line y=1/2x-6 and passes through the point (-1,5)
The equation of the line that is perpendicular to y = 1/2x - 6 and that passes through the point (-4, -5) is y = -2x + 3
Equation of a straight line passing through a given pointFrom the question, we are to determine the equation of the line that is perpendicular to the given line and that passes through the given point.
The given equation is y = 1/2x - 6
The given point is (-1, 5)
NOTE: If two lines are perpendicular, then their slopes are negative reciprocals of each other
First, we will determine the slope of the given line
y = 1/2x - 6
Compare to the general form of an equation of a straight line
y = mx + b
Where m is the slope
and b is the y-intercept
Therefore,
The slope of the line is 1/2
But,
The negative reciprocal of 1/2 is -2
Thus, the slope of the equation we are to determine is -2
Now, we will determine the equation of the line that has a slope of -2 and that passes through the point (-1, 5)
Using the point-slope form of the equation of a straight line
y - y₁ = m(x - x₁)
Then,
y - 5= -2(x - (-1))
y - 5 = -2(x + 1)
y - 5 = -2x -2
Add 5 to both sides of the equation
y - 5 + 5 = -2x - 2 + 5
y = -2x + 3
Hence, the equation of the line is y = -2x + 3
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You have an urn with 6 red, 10 blue and 4 black balls.
What is the probability that you take different colours in two"picks"?
The probability that you take different colors in two"picks" is 31/45.
You could choose one red followed by one blue, one blue followed by one red, one blue followed by one black, one black followed by one blue, one black followed by one red, or one red followed by one black.
P( different colors) = P( one blue followed by one red ) +P( one red followed by one blue) + P( one blue followed by one black ) +P( one black followed by one blue) +P( one black followed by one red ) +P( one red followed by one black)
P(one blue followed by one red) = (10/20)( 6/19) = 3/19
P(one red followed by one blue) = (6/20)( 10/19) = 3/19
P(one blue followed by one black) = (10/20)( 4/19) = 2/19
P(one black followed by one blue) = (4/20)( 10/19) = 2/19
P(one red followed by one black) = (6/20)( 4/19) = 6/95
P(one black followed by one red) = (4/20)( 6/19) = 6/95
P(different colors )= 3/19 + 3/19 + 2/19 + 2/19 + 6/95 + 6/95
= 31/45
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You have saved $2.82 to buy a magazine that costs $7.39. Estimate how much more money you need to buy the magazine
HELPPPPPP MEEEEEEEE Ps. THIS IS DECIMALS AND STUFF
an open box is to be made from a two-foot by three-foot rectangular piece of metal by cutting equal squares from the corners and turning up the sides. find the volume of the largest box that can be made in this manner. round your final answer to the nearest hundredth.
The volume for the largest box will be 1.056 foot³. This can find out by application of differentiation.
What is AOD?
AOD is nothing but application of differentiation. It implies scopes where we can use differentiation to make our calculations easy.
Here, given
Length and breadth = 2,3 foot
Let us consider length of side of square = x
So, after cutting squares left sides of rectangular sheet = 2-2x , 3-2x
So, volume = (2-2x)*(3-2x)*x
v = 4x³ - 10x² + 6x
To find largest volume , [tex]\frac{dv}{dx}[/tex] = 0
[tex]\frac{dv}{dx}[/tex] = 12x² - 20x + 6
12x² - 20x + 6 = 0
x = 0.4 , 1.3
But, for 1.3 volume will be negative i.e. not possible.
So, volume = 2.2*1.2*0.4
= 1.056 foot³
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one thousand independent rolls of a fair die will be made. compute an approximation to the probability that the number 6 will appear between 150 and 200 times inclusively.
The probability that the number 6 will appear between 150 and 200 times inclusively is 0.926.
In the given question, one thousand independent rolls of a fair die will be made.
We have to compute an approximation to the probability that the number 6 will appear between 150 and 200 times inclusively.
Let n=1000 are independent trails.
The probability of success is constant, p=1/6
The probability of success is not constant,
q=1-1/6 = 5/6
let X be the number of times the die shows a 6.
μ = np
μ = 1000*1/6
μ = 166.7
σ=√npq
σ=√1000*1/6*5/6
σ=√5000/36
σ=11.785
Now we used the correlation continuity for finding the probability that number 6 will appear between 150 and 200 times is
P(150≤X≤200)=P(X≤200)-P(X<150)
P(150≤X≤200)=P(Z≤(200+0.5-166.7)/11.785)-P(Z≤(150-0.5-166.7)/11.785)
P(150≤X≤200)=P(Z≤2.87)-P(Z≤-1.46)
P(150≤X≤200)=0.998-0.072
P(150≤X≤200)=0.926
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Compare 160 and 115/9 using <, >, or =.
The correct comparison between the given numbers ; √160 and 115 / 9 is; 115 / 9 > √160.
Which sign correctly compares the given numbers?It follows from the task content that the sign which correctly compares the two numbers as given in the task content be determined.
Since the given numbers in the task content can be evaluated as follows;
√160 = 12.64911064.
115 / 9 = 12.7777777778
From the results of the evaluations as represented above, since 12.7777777778 is greater than 12.64911064, it follows that the 115 / 9 > √160.
Therefore, the required correct comparison is;
115 / 9 > √160
The answer choice which is correct is as represented above.
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In 1980, about 17.7 million households had cable television. This was about 25.8% of the households that had cable in 2000. How many households had cable in 2000?
In 2000, cable was available in 45683700000 homes.
What is percentage?Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
In 1980, 17700000 = 25.8%\s1% = 4566600000
Then, in 2000, there were 45683700000 households (17 700 000 + 4566 600 000).
Comparing two amounts while rebasing the second amount to 100 is the simplest way to use percentages. Let's assume that we are interested in the proportion of employed women who are female.
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Please help.
Solve the inequality show all your work
-4x+5>37
The solution for x in the inequality expression is x < -8
How to determine the solution for x?From the question, we have the following inequality expression that can be used in our computation:
-4x+5>37
Subtract 5 from both sides of the inequality
So, we have
-4x + 5 - 5 >37 - 5
Evaluate the like terms
This gives
-4x > 32
Divide both sides by -4
x < -8
Hence, the solution is x < -8
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Determine the next 4 terms in the sequence. Put commas in between your numbers. If you get marked wrong, simply check to see if your numbers were correct. -0.02 ,0.01, 0.04, 0.07, 0.10, ...
Answer:
0.13, 0.16, 0.19, 0.22
Step-by-step explanation:
You are adding 0.03 each time
Answer:
0.13, 0.16, 0.19, 0.22
Step-by-step explanation:
Add 0.03 to each.
Please help again 10 points again to first one
Answer: it would be 18 candies that are left
Step-by-step explanation:
I did the math
different data sets that have a median of 13
Two different data sets that have a median of 13 are
9, 10, 13, 18, 2010, 13, 13, 18How to determine the datasets?From the question, we have the following parameter
Median =13
The median of a dataset is the number at the middle position
So, we can make use of the following dataset
9, 10, 13, 18, 20
This is so because the middle number is 13
Another possible dataset is
10, 13, 13, 18
Similarly, this is because the middle number is 13
Read more about median at
https://brainly.com/question/14532771
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