The amount that Josephine will be paid is $644.30.
How much was Josephine paid?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.
In this situation, Josephine earns a salary of $560.00 per week, plus a commission of 10% on all sales and she sold $843 worth of goods.
The amount she'll be paid will be:
= $560 + (10% × $843)
= $560 + $84.3
= $644.30
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Under a translation 2 units to the right on the coordinate plane, point A maps to A’ and point B maps to B’
The correct statement as regards the transformation involving translation is
AB = A'B'What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Transformation is basically of two major divisions
Rigid transformationnon rigid transformationNon rigid transformation are the transformation where the dimension or size of the object will be different from the image, example is dilation
In rigid transformation, the dimensions of the object is maintained through out the transformation examples of rigid transformation are
rotationreflectiontranslationSince the transformation point A and point B made are all translation which is a type of rigid transformation, the dimension of the length will remain same
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Find the:
Domain:
Range:
Local maximum:
Local minimum:
Increasing interval:
Decreasing interval:
Constant interval:
By studying the graph of the function, it can be inferred that -
Domain = [-3, 3]
Range = ([tex]-\infty[/tex], 4]
Local maximum = 0, 4
Local minimum = -0.5
Increasing interval = [-3, -2) [tex]\cup[/tex] (-1, 2)
Decreasing interval = (-2, -1) [tex]\cup[/tex] (2, 3]
There is no constant interval.
What is graph of a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Graph of a function f(x) is the collection of all points of the form (x, f(x)).
Suppose the size of each square of the graph is 1 unit
From the graph, it can be seen that the value on the horizontal axis ranges from -3 to 3
Domain = [-3, 3]
The value on the vertical axis ranges from [tex]-\infty[/tex] to 4
Range = ([tex]-\infty[/tex], 4]
The graph has a local maximum at (2, 4) and (-2, 0)
Local maximum = 0, 4
The graph has local minimum at (-1, -0.5)
Local minimum = -0.5
Increasing interval [-3, -2) [tex]\cup[/tex] (-1, 2)
Decreasing interval = (-2, -1) [tex]\cup[/tex] (2, 3]
There is no constant interval.
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Elian is placing a rectangle in the coordinate plane. He knows that the shorter side of the rectangle is half the length of the longer side. He places the longer side on the x-axis. What coordinates should he assign to the top-left vertex of the rectangle? enter your answer in the boxes. ( , ).
Since the rectangle's shorter side is half as long as its longer side, its top left vertex is (0,a).
What is coordinate?A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y). You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To find the y-coordinate, repeat the previous step while adhering to a horizontal line.
Here,
Let x be the length and y be the width,
y=x/2
x=2a
y=a
The top left vertex=(0,a)
The top left vertex is (0,a) as shorter side of the rectangle is half the length of the longer side.
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someone help me with this equation please
4m^2=45+11m
solve with quadratic formula
m = 5 and m = -9/5 are the roots of the equation.
Factoring 4m²-11m-45
The first term is, 4m² its coefficient is 4 .
The middle term is, -11m its coefficient is -11 .
The last term, "the constant", is -45
Step-1 : Multiply the coefficient of the first term by the constant 4 • -45 = -180
Step-2 : Find two factors of -180 whose sum equals the coefficient of the middle term, which is -11 .
-180 + 1 = -179
-90 + 2 = -88
-60 + 3 = -57
-45 + 4 = -41
-36 + 5 = -31
-30 + 6 = -24
-20 + 9 = -11 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and 9
4m² - 20m + 9m - 45
Step-4 : Add up the first 2 terms, pulling out like factors :
4m • (m-5)
Add up the last 2 terms, pulling out common factors :
9 • (m-5)
Step-5 : Add up the four terms of step 4 :
(4m+9) • (m-5)
Which is the desired factorization
Theory - Roots of a product
A product of several terms equals zero. When a product of two or more terms equals zero, then at least one of the terms must be zero. We shall now solve each term = 0 separately In other words, we are going to solve as many equations as there are terms in the product Any solution of term = 0 solves product = 0 as well.Now ,
1. Solve : m-5 = 0
Add 5 to both sides of the equation :
m = 5
2. Solve : 4m+9 = 0
Subtract 9 from both sides of the equation :
4m = -9
Divide both sides of the equation by 4:
m = -9/4
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In the first week of July, a record
1,020 people went to the local swimming pool. In the second week,
100 fewer people went to the pool than in the first week. In the third week,
130 more people went to the pool than in the second week. In the fourth week,
234 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
20% is the percent decrease in the number of people who went to the pool over these four weeks
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
In the first week of July, a record 1,020 people went to the local swimming pool.
In the second week,100 fewer people went to the pool than in the first week
1020-100=920
In the third week,130 more people went to the pool than in the second week.
920+130=1050
In the fourth week, 234 fewer people went to the pool than in the third week.
1050-234=816
Now we need to find the percent decrease in the number of people who went to the pool over these four weeks
1020-816=204
204/1020=0.2×100=20
Hence, 20% is the percent decrease in the number of people who went to the pool over these four weeks
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On Monday you run on treadmill for one half an hour at X mph on Tuesday you walk the same distance on the treadmill at 2 mph slower and it takes you three fourths an hour how many miles did you run on the treadmill on Monday
The number of miles that you ran on the treadmill on Monday will be 3 miles.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
On Monday you run on the treadmill for thirty minutes at x mph and on Tuesday you walk a similar distance on the treadmill at 2 mph increasingly slow takes you three-fourths 60 minutes.
Then the distance is the same in both cases. Then we have
x × (1/2) = (x - 2) × (3/4)
Simplify the equation, then we have
x × (1/2) = (x - 2) × (3/4)
4x = 6(x - 2)
4x = 6x - 12
2x = 12
x = 6 miles per hour
The number of miles is given as,
D = 6 × 1/2
D = 3 miles
The number of miles that you ran on the treadmill on Monday will be 3 miles.
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What value of x is in the solution set of the inequality 9(2x + 1) < 9x – 18?
Answer: x < -3
Step-by-step explanation: even tho if we solve you will get a big number number then you reduce the number to a smaller number
what is the answer i need answers now I'm am going to fail
Answer:
D
Step-by-step explanation:
2 times 5x is 10x, and 2 x 1 is 2
Answer:
655
Step-by-step explanation:
A school is arranging a field trip to the zoo. The school spends 746.34 dollars on passes for 40 students and 2 teachers. The school also spends 352.40 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Each pass costs $17.77 and each student's lunch costs $8.81
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The school spends 746.34 dollars on passes for 40 students and 2 teachers.
So, Each pass costs = 746. 34/ 42 = $17.77
Now, The school also spends 352.40 dollars on lunch for just the students.
= 352.40/ 40
= $8.81
Hence, Each pass costs $17.77 and each student's lunch costs $8.81
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If it takes 5 hours to drive 62 miles how fast are you going
Answer:
12.40mph
Step-by-step explanation:
Please help me I’m so sad
Answer:
Sym
Step-by-step explanation:
4.) Describe a series of transformations
(translate, rotate, reflect and dilate) that
takes triangle ABC to triangle CEF. Give all specific details.
The series of transformations of triangle ABC to triangle CEF is shown.
Explain the term transformation?A point, line, or geometry figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.For the given transformations from triangle ABC to triangle CEF are-
Translation:
1 unit to the right2 units upward.Rotation: There is no rotation taken place.
Reflection: There is no reflection of the given triangle ABC.
Dilation: The dilation of the 2 times the original coordinates is taken place.
Thus, the series of transformations of triangle ABC to triangle CEF is shown.
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PLEASE HELP!!!
Evaluate the expression.
-0.08 ÷ (-0.29 - -0.39)²
Write your answer as an integer or a decimal. Do not round.
Answer:
Step-by-step explanation:
-0.17301038
Pls Help ASAP) Willing to give 25 points) Pls show your work) If you don't know pls don't answer.
From the given statements about the linear graph, the correct ones are statements 1, 2 and 3 while the incorrect one is statement 4
How to interpret Linear Graphs?The slope of a linear graph is simply the change in the y-values divided change in the corresponding x-values.
Now, from the graph, if we take two coordinates, we can easily say that;
Slope = (18 - 16)/(0 - 100)
Slope = -2/10 = -1/5
Statement 1; From the graph, the y-intercept is $18. This means that this is the cost of the book as that is where the cost starts decreasing for each weed she pulls. Thus, it is true.
Statement 2; The slope as we saw earlier was -1/5. Thus, it means that her grandma pays $1 for every 5 weed she pulls.
Statement 3; The x-intercept is 90 and it means after 90 weeds pulled, she no longer has to use her own money at all for the book. This is correct.
Statement 4; This is wrong because she needs to pull at least 90 weeds for her not to use her money.
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The last time Barry checked, his dog weighed 30 kilograms. Barry just measured his dog again and found out that it weighs 10% less now. How much does the dog weigh now?
27kg is the weight of Barrys dog now,
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The weight of dog last time when Barry checked is 30kilograms.
Barry just measured his dog again and found out that it weighs 10% less now.
We need to find the weight of Barrys dog.
Convert 10% to decimal value
10/100=0.1
0.1×30=3
Now subtract 3 from 30
30-3
27
Hence, currently Barrys dog weight is 27kg.
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a sports team has 99 jerseys numbered 1, 2, 3, . . . , 99. show your work for each part. (a) (2 points) how many ways are there to choose 2 different jerseys, without order, such that their numbers sum to 100?
a sports team has 99 jerseys numbered 1, 2, 3, . . . , 99. show your work for each part, 49 pairs many ways are there to choose 2 different jerseys, without order, such that their numbers sum to 100, using the concept of combination formula.
What is combination formula?The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.
The formula becomes: [tex]^nC_r[/tex]
Where, n = total number of objects
r = number of choosing objects.
Sports team has 99 jerseys. So, 49 pairs will be possible to have their sum is 100.
Example - (1+99), (2+98),......,(49+51)
Thus, there are 49 ways to choose two different jerseys.
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A suit is being sold for 194.49, discount is 73% from the original price.
What’s the original price?
The original price is $720.33 .
What is original price ?
Convert the percent discount to a decimal by dividing by 100% . Step 2: Set up the equation P=(1−d)x P = ( 1 − d ) x to find the original price of the item where P is the sale price, d is the discount as a decimal, and x is the original price of the item.You need to be aware of the selling price as well as the discount % in order to determine the item's original cost. The calculations contain a straightforward method that divides the sale price by the percentage-based result of 1 minus the discount. To determine an item's original or list price, use this formula.
SInce $194.49, is what is owed after the discount you will want to subtract 73 from 100 to get the percent of what is owed. Then you will set it up like a percent equation. 27/100 = 194.49/X where X = the original price. You will then multiply 194.49 by 100 and divide that answer by 1.9449. This equals $720.33 as the original price.
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Find f(1), f(2), f(3), f(4), and f(5) if fen) i defined recurively by f(O) = 3 and for n 0,1,2,. A) fen I) = -2f(n). B) fen I) = 3f(n) 7. C) fen I) = f(n)2 2f(n) 2. D) fen 1) = )f(n)/3
Given recursion function in options we have calculated values of f(1),f(2),f(3),f(4),f(5).
Find f(1), f(2), f(3), f(4), f(5) if f(0) = 3.
First recursive Function is given as
a) f(n+1) = -2*f(n)
f(1) = -2*f(0) = -2*3 = -6
f(2) = -2*f(1) = -2*(-6) = 12
f(3) = -2*f(2) = -2*12 = -24
f(4) = -2*f(1) = -2*(-24) = 48
f(5) = -2*f(4) = -2*(48) = -96
Second recursive Function is given as
b) f(n+1) = 3*f(n)+7
f(1) = 3*f(0)+7 = 3*3+7 = 16
f(2) = 3*f(1)+7 = 3*16+7= 55
f(3) = 3*f(2)+7 = 3*55+7 = 172
f(4) = 3*f(3)+7 = 3*172+7 = 523
f(5) = 3*f(4)+7 = 3*523+7 = 1576
Third recursive Function is given as
c) f(n+1) = [tex]f(n)^2-2*f(n)-2[/tex]
f(1) = f(0)*f(0)-2*f(0)-2 =3*3 - 2*3 - 2 = 1
f(2) = f(1)*f(1) - 2*f(1) - 2 = 1*1 - 2*1 - 2 = -3
f(3) = f(2)*f(2) -2*f(2)- 2 =-3*(-3) - 2*(-3) - 2 = 13
f(4) = f(3)*f(3) -2*f(3)- 2 = 13*13 - 2*13 - 2 = 141
f(5) = f(4)*f(4) -2*f(4)-2 = 141*141 - 2*141 - 2 = 19597
Fourth recursive Function is given as
d) f(n+1) = [tex]3^(f(n)/3)[/tex]
f(1) = 3^((f(0)/3) = 3^1 = 3
f(2) = 3^((f(1)/3) = 3^1 = 3
f(3) = 3^((f(2)/3) = 3^1 = 3
f(4) = 3^((f(3)/3) = 3^1 = 3
f(5) = 3^((f(4)/3) = 3^1 = 3
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Predict the cost of a meal for a family of four between $55 and $100. Be sure to include dollars and cents.
Part A: If the family has a 15% off coupon, calculate the new price of the meal. Show all work or explain your steps. (6 points)
Part B: Calculate a 22% tip using the new price. What is the final cost of the meal? Show all work or explain your steps. (6 points)
The final cost is lie between the amount $46.00 and $92.00.
What is an equation?
When two expressions are connected with both the equals sign (=) in a mathematical formula, it expresses this same equality of the two expressions. The meanings of the word equation as well as its cognates in those other languages can vary slightly. For instance, an equation in French is defined as having one or maybe more variables, whereas in English, an equation is any properly formed formula that consists of two expressions linked by the equals sign.
The coupon is given = 15% off
New price = Cost of meal (1 - coupon)
Now Substitute the known values in the equation;
New price = between 55(1 - 15%) and 100.00 (1 - 15%)
Evaluate;
The final cost of the meal is between $40.00 and $80.00
Tip = 22%
Thus Final cost = New price (1 + tip)
Now Substitute the known values in the equation
Final cost = Between 40.00 (1 + 22%) and 80.00 (1 + 22%)
The Final cost is Between $46.00 and $92.00
Hence, the final cost is lie between the amount $46.00 and $92.00
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Help me find the measure of m
The values of the angles for the given figure are m ∠M=76°,
m ∠N=76°.
What is meant by an angle?An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are located in the plane where the rays are located. The meeting of two planes can also create an angle. These are referred to as dihedral angles. The angle formed by the rays lying perpendicular to the two intersecting curves at their point of intersection can likewise be used to establish an angle between two intersecting curves.
Given,
In ΔLMN,
m ∠L=28°
As we know that,
Angle sum in a triangle=180°
m ∠L+ m ∠M+ m ∠N=180°
From the figure,
m ∠M= m ∠N
So, m ∠L+ m ∠M+ m ∠M=180°
28°+ 2 m ∠M=180°
2 m ∠M=180°-28°
2 m ∠M=152°
m ∠M=76°
So, m ∠N=76°
Therefore, the values of the angles for the given figure are m ∠M=76°,
m ∠N=76°.
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In this triangle, what is the value of x?
The value of x in the triangle is 26.1°
What is a triangle?A triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.
Types of Triangles
Acute triangle - all three angles are less than 90°
Right triangle - one angle is 90°
Obtuse triangle - one angle is greater than 90°
Equilateral triangle - all three sides are the same length
Isosceles triangle - two sides are the same length
Scalene triangle - all three sides are different lengths
Since the triangle is right-angled
tan x = opposite/adjacent
tan x = 26/53
tan x = 0.4905
x = arc(tan) 0.4905
x = 26.1°
In conclusion x = 26.1°
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CA bisects angle BAD and CA bisects angle BCD. Prove ABC congruent to ADC
The triangles are then congruent according to the SAS congruence criteria for triangles.
What is congruence?Congruent triangles are those with the same size and form. This signifies that the respective sides are equal, as are the corresponding angles. We can determine if two triangles are congruent without evaluating all of their sides and angles. The phrase "congruent" refers to having exactly the same form and dimension. Even if we flip, turn, or rotate the forms, the shape and size should remain the same. In terms of shape and size, the adjective "congruent" implies "absolutely equal." The forms remain equal even when we spin, flip, or rotate them. Draw two circles with the same radius, then cut them out and stack them on top of each other.
Here,
If I understood correctly, then first let's call the angle BAC = CAD = α. From the statement we have angle ABC = 90° (AB ⊥ BC) and also angle ADC = 90° (AD ⊥ DC).
Then we have: angle BCA = ACD = 90 - α
We the have that:
AC = AC (the triangles share this size)
angle BCA = ACD
angle BAC = CAD
Then the triangles are congruent due to SAS criterion of congruence for triangle.
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What’s true mean if mid value are 37.5 42.5 47.5 52.5 57.5 and number of students are 30,20,15,13,22 respectively
The true mean of the data-set is given as follows:
46.35.
How to obtain the mean of a data-set?
The mean of a data-set is calculated as the sum of all observations divided by the number of observations.
In this problem, the sum is given by the multiplication of the mid-values by the number of students with each value, as follows:
S = 37.5 x 30 + 42.5 x 20 + 47.5 x 15 + 52.5 x 13 + 57.5 x 22 = 4635.
The total number of students is given as follows:
30 + 20 + 15 + 13 + 22 = 100.
Hence the mean is calculated as follows:
Mean = 4635/100 = 46.35.
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OMG PLS HELP ME!!!!!! I NEED THIS ASAP!!! 100 PTS!!!!!!!
(its in the pic)
By algebra properties we find the following relationships between each pair of algebraic expressions:
First equation: Case 4Second equation: Case 1Third equation: Case 2Fourth equation: Case 5Fifth equation: Case 3How to determine pairs of equivalent equations
In this we must determine the equivalent algebraic expression related to given expressions, this can be done by applying algebra properties on equations from the second column until equivalent expression is found. Now we proceed to find for each case:
First equation
(7 - 2 · x) + (3 · x - 11)
(7 - 11) + (- 2 · x + 3 · x)
- 4 + (- 2 + 3) · x
- 4 + (1) · x
- 4 + (5 - 4) · x
- 4 - 4 · x + 5 · x
- 4 · (x + 1) + 5 · x → Case 4
Second equation
- 7 + 6 · x - 4 · x + 3
(6 · x - 4 · x) + (- 7 + 3)
(6 - 4) · x - 4
2 · x - 4
2 · (x - 2) → Case 1
Third equation
9 · x - 2 · (3 · x - 3)
9 · x - 6 · x + 6
3 · x + 6
(2 + 1) · x + (14 - 8)
[1 - (- 2)] · x + (14 - 8)
(x + 14) - (8 - 2 · x) → Case 2
Fourth equation
- 3 · x + 6 + 4 · x
x + 6
(5 - 4) · x + (7 - 1)
(7 + 5 · x) + (- 4 · x - 1) → Case 5
Fifth equation
- 2 · x + 9 + 5 · x + 6
3 · x + 15
3 · (x + 5) → Case 3
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12 pencils cost 1.80$ . How many pencils can be bought for 6$ ?
pls help me with this
Bisector of the segment (3.5 , 5)
What is bisector?A line known as a bisector divides an angle or a line into two equally sized segments. A segment's midpoint is always contained in the segment's bisector.
A line segment's midpoint was crossed by the perpendicular bisector of the segment.
If C is the point on AB, through which its perpendicular bisector passes, then C = mid point of AB.
Mid x1 +x2/2 ,y1+y2/2
7+-2/2, 5+5/2
5/2,5
(3.5,5)
The angle bisector theorem states that PQ/PR = QS/RS or a/b = x/y. A line or ray that divides an angle in a triangle into two equal parts is known as an angle bisector.
Measuring the length of the line segment you need to bisect is an easy approach to discover a perpendicular bisector. Find the midpoint of the measured length by dividing it by two. From this midpoint, extend a line at a 90° angle.
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NEED HELP! 50 POINTS!
If you move the quadratic parent function, f(x) = x2, left 3 units, what is the equation of the new function?
g(x) = x2 - 3
g(x) = (x - 3)2
g(x) = (x + 3)2
g(x) = 3x2
Answer: [tex]g(x)=(x+3)^2[/tex]
Step-by-step explanation:
When shifting a function left [tex]3[/tex] units, [tex]f(x) \to f(x+3)[/tex].
Therefore, [tex]g(x)=(x+3)^2[/tex].
what is the solution to the problem expressed to the correct number of significant figures? 2.13 1
The solution to the problem expressed to the correct number of significant figures is, 2.13 + 1 = 3
Given that,
The solution to the problem expressed to the correct number of significant figures,
2.13 + 1 = ?
Unit is a quantity of constant magnitude which is used to measure the magnitudes of other quantities of the same manner.
Unit can be defined as the rightmost position in a number or the one's place. Here, 3 is the unit's number in the number 6713. A unit may also mean the standard units used for measurement.
You must round your answer to the same "place" when adding values as the measurement with the last significant figure that is farthest to the left.
= 2.13
= +1
= 3.13
The “1” has its last significant figure furthest to the left, so you round off the number to the “units" place. That's the last column that the measurements share.
3.13 → 3 (rounded to the "units" place)
Therefore,
The solution to the problem expressed to the correct number of significant figures is, 2.13 + 1 = 3
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a probability experiment consists of rolling a fair 10-sided die. Find the probability of the event below.
rolling a number greater than 3
The probability of getting a number larger than 3 is P = 0.7
How to find the probability?The probability is equal to the quotient between the number of outcomes that meet the condition, and the total number of outcomes.
The 10-sided die has the outcomes {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} so 10 outcomes.
The outcomes that are greater than 3 are {4, 5, 6, 7, 8, 9, 10} so there are 7 outcomes, then the probability is:
P = 7/10 = 0.7
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Graph y=2x-3-5. Algebra 2 connection unit 2 test
Answer: Slope: 2, y-intercept: (0,-8)
Step-by-step explanation:
x | y
0 -8
1 -6