Answer: 1.49 x [tex]10^{-5}[/tex]
Step-by-step explanation:
7.1.1 use the results of section 3.7 to show that each member of isom (r2) is either a translation or a rotation. 7.1.2 why does an isometry map any circle to a circle? we took care to write the inverse of the isometry r1r2r3 as r3r2r1 because only this ordering of terms will always give the correct result. 7.1.3 give an example of two reflections r1 and r2 such that r1r2
Every isometry can be expressed as composition of reflection and translation only. Also the composition of isometries is isometry. each member of ISOM+R² is either a translation or rotation.
Given that,
Show that each component of isom (r²) is either a translation or a rotation using the findings from section 3.7.
An isometry of R² is a mapping T:R²⇒R² which preserves distance.
The formula for the distance between x and y is
d(x,y)=|y-x|=√(y₂-x₂)²+(y₁-x₁)²
The preservice means,
d(x,y)=d(T(x),T(y))
A translation is an isometry.
Since,
d(Tv(x),Tv(y))=|(xv)-(y-v)|=d(x,y)
The rotation matrix, for rotating by an angle Θ, is defined as,
cosΘ -sinΘ
sinΘ cosΘ
Therefore, every isometry can be expressed as composition of reflection and translation only. Also the composition of isometries is isometry. each member of ISOM+R² is either a translation or rotation.
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an exploring ship is pulling up a diver at the rate of 25 feet per minute. The diver is currently 100 feet below the sea level. How deep was the diver 15 minutes ago?
GIVING BRAINLIEST!!!
What fraction is shown on the number line?
A. 2 over 3
B. 1 over 3
C. 2 over 4
D. 3 over 4
Answer:
a
Step-by-step explanation:
Answer:a
Step-by-step explanation:
Given: KM and JN bisect each other
Prove: JK || MN
Answer:
JN
Step-by-step explanation:
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Based on the information in the fragment, it can be inferred that Josiah's mistake is that he did not multiply the numerator and denominator by the correct number to equal 1,500 (option B). So, the correct statements are A, C, and D.
How to find the ratio?To find the proportion in this problem we have to do the following procedure:
The first step is multiply both sides by 1500.The second step is to evaluate the expression on the right-hand side.The third step is multiply 10 by 1500 on the left-hand side.The fourth step is divide 15000 by 20 on the left-hand side.Once we have carried out the previous steps we must continue the procedure rewriting the equation with the data obtained previously. With this information we can conclude that Josian had the necessary information to discover how many songs of each genre were played during an hour on his MP3, however he performed the wrong procedure so his result was wrong.
According to the above, we can infer that the products are not well carried out. So, Josiah's mistake is no multiplying the numerator and denominator by the correct number to equal 1,500 (option B).
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Let f : Z -> Z be defined by f(x) = x^2 + 1, and let C = {1, 2, 3}.
Find f(C), f^-1(C), f^-1 (f(C)) and f(f^-1 (C)).
We take the inverses of the function and get the results as follows:
[tex]f(1)=1+1=2\\f^{-1}(1)=\sqrt{1-1}=0\\f^{-1}(f(1))=\frac{\sqrt{\sqrt{4(1)+1} -3}}{\sqrt{2} } \\f(f^{-1} (1))=1[/tex], [tex]f(2)=4+1=5\\f^{-1}(2)=\sqrt{2-1}=1\\f^{-1}(f(2))=\frac{\sqrt{\sqrt{4(2)+1} -3}}{\sqrt{2} } \\f(f^{-1} (2))=2[/tex], [tex]f(3)=9+1=\sqrt{10} \\f^{-1}(3)=\sqrt{3-1}=\sqrt{2} \\f^{-1}(f(3))=\frac{\sqrt{\sqrt{4(3)+1} -3}}{\sqrt{2} } \\f(f^{-1} (3))=3[/tex]
What are the inverses of a function?
A function that can change into another function is referred to as being inverse or anti. In other words, the inverse of any function "f" will take y to x if it takes x to y in the first place. The inverse function is indicated by F^-1 if the function is denoted by F.
Given C={1,2,3}, and
[tex]f(x)=x^{2} +1\\ f^{-1}(x)=\sqrt{x-1} \\f^{-1}(f(x))=\frac{\sqrt{\sqrt{4(x)+1} -3}}{\sqrt{2} } \\f(f^{-1} (x))=x[/tex]
Now,
For C=1,
[tex]f(1)=1+1=2\\f^{-1}(1)=\sqrt{1-1}=0\\f^{-1}(f(1))=\frac{\sqrt{\sqrt{4(1)+1} -3}}{\sqrt{2} } \\f(f^{-1} (1))=1[/tex]
For C=2
[tex]f(2)=4+1=5\\f^{-1}(2)=\sqrt{2-1}=1\\f^{-1}(f(2))=\frac{\sqrt{\sqrt{4(2)+1} -3}}{\sqrt{2} } \\f(f^{-1} (2))=2[/tex]
For C=3
[tex]f(3)=9+1=\sqrt{10} \\f^{-1}(3)=\sqrt{3-1}=\sqrt{2} \\f^{-1}(f(3))=\frac{\sqrt{\sqrt{4(3)+1} -3}}{\sqrt{2} } \\f(f^{-1} (3))=3[/tex]
Hence, the solution is provided.
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Use elimination to solve the system of equations.
4y+3z=-6
y12=15
How can you eliminate the z-terms in this system?
4y+3z=-6
y-z=-5 +
Multiply by ? on both sides.
2
3
4
5
The solution to the system of equations is (y,z) = (-23/11, 33/11).
What is the system of equations?
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied in other words, the locations at which all of these equations intersect.
To eliminate the z-terms in this system, you can multiply the first equation by 3 and the second equation by -1 and then add the resulting equations together. This will give you an equation in terms of only y, which you can then solve for y.
The resulting equation will be:
(4y + 3z) * 3 + (y - z) * -1 = (-6) * 3 + (-5) * -1
12y - 3z - y + z = -18 - 5
Combining like terms, we get:
11y = -23
Dividing both sides by 11, we get:
y = -23/11
Now that we have solved for y, we can substitute this value back into one of the original equations to solve for z. For example, substituting -23/11 for y in the first equation gives us:
4(-23/11) + 3z = -6
Solving for z, we get:
z = 33/11
Hence, the solution to the system of equations is (y, z) = (-23/11, 33/11).
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if you use a 0.05 level of significance in a two-tail hypothesis test, what decision will you make if ZSTAT- -1.71?
Determine the decision rule. Select the correct choice below and fill in the answer box(es) within your choice.
(Round to two decimal places as needed.)
A.
Reject H0
enter your response hereZSTAT
enter your response here.
B.
Reject H0 if ZSTAT
enter your response here.
C.
Reject H0 if ZSTAT
enter your response here.
D.
Reject H0 if ZSTAT
enter your response here or ZSTAT
enter your response here.
A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.
What is the relation between the p-value and the conclusion of the test hypothesis?A hypothesis expresses your predictions about what your research will uncover. It is an untested preliminary answer to your research question. For some research projects, you may be required to write several hypotheses that address different aspects of your research question. It depends on whether the p-value is less or greater than the significance level.According to the statement, the value of Z-Stat is +2.10. And we must find the P value when H0 is rejected only in the upper tail. The Z-stat is defined as the Z-score, which indicates how much a given value differs from the standard deviation.
The Z-score, also known as the standard score, is the number of standard deviations a given data point is above or below the mean.
And we know that the P-Value is calculated by converting your statistic into a Z-Score.
As a result, the p value is 0.0179.
So, When ZSTAT = +2.10, the resulting P-Value is 0.0179.
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Question 12 (1 point) In order for this ratio of volumes to be true, what measurements would have to be equal in all 3 solids?
the three solids are cylinder, cone, and sphere
a The radius and the surface area
b The volume and the height
c The surface area and the base
d The radius and the height
Answer:
Step-by-step explanation:
In order for the ratio of volumes of a cylinder, cone, and sphere to be true, the radius of each solid would have to be equal. This is because the radius is a factor in the volume formulas for all three solids:
Volume of cylinder: πr^2h
Volume of cone: (1/3)πr^2h
Volume of sphere: (4/3)πr^3
If the radius is equal in all three solids, then the volumes will be in the same ratio as the given ratio, regardless of the values of h or the surface area. Therefore, the correct answer is : The radius and the height.
Courtney made 3 withdrawals of equal amount from her savings account. The equation below can be used to determine x the amount in dollars of each withdrawal. What was the amount in dollars of each of Courtney’s withdrawals?
By solving the given equation, we know that Courtney withdrawals $25.75 each time from her bank account.
What are equations?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance.
When this equation is solved, we discover that the value of the variable x is 7.
So, we have the equation:
400-3x=322.75
Now, solve the equation for x to get the amount Courtney withdrawals each time:
400-3x=322.75
-3x = 322.75 - 400
-3x = -77.25
x = -77.25/-3
x = $25.75
Therefore, by solving the given equation, we know that Courtney withdrawals $25.75 each time from her bank account.
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Complete question:
Courtney made 3 withdrawals of equal amounts from her savings account. The equation below can be used to determine x, the amount in dollars of each withdrawal.
400-3x=322.75
What was the amount in dollars of each of Courtney's withdrawals?
answer choices
a. $24.09
b. $25.75
c. $74.25
d. $77.25
Solve the following inequality and graph the solution:
(x-4)(x-5)<0
Choose test values and indicate whether the inequality is true or false in each region.
Enter the test values from smallest to largest.
The smallest to largest test values of the inequality (x-4)(x-5)<0 are
(-infinity,4) , (4,5) & (5,+infinity)
What is a inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.
A difference between two values indicates whether one is smaller, larger, or simply not equal to the other.
"A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">," "," "," or "."
(x-4)(x-5)<0
x-4<0 or x-5<0
x<4 or x<5
1)
for False the test values of the inequality (x-4)(x-5)<0 from smallest to largest Lies in between (-infinity,4)
2)
for True the test values of the inequality (x-4)(x-5)<0 from smallest to largest Lies in between (4,5)
3)
for True the test values of the inequality (x-4)(x-5)<0 from smallest to largest Lies in between (5,+infinity)
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Judy wants to buy a sandwich platter. Every 6 inches of sandwich costs $2.50. What is the total
cost in dollars if Judy buys 18 inches?
Answer:
[tex]\huge\boxed{\sf \$ 7.50}[/tex]
Step-by-step explanation:
Given that,
6 inches of sandwich = $2.50
Multiply 3 to both sides
6 × 3 inches of sandwich = $2.50 × 3
18 inches of sandwich = $7.50[tex]\rule[225]{225}{2}[/tex]
In right triangle ABC, altitude CD with length h is drawn to its
We also know AD=2 and DB=8. What is the length of
hypotenuse.
AC?
The length of the hypotenuse AC is √(h² + 4).
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
Right triangle ACD.
AC² = CD² + AD²
AC² = h² + 2²
AC² = h² + 4
AC = √(h² + 4)
Thus,
AC is √(h² + 4).
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A cable company offers its customers two plans.
- Plan A costs $135 per month plus $15 for each premium channel.
- Plan B uses the equation C=5 p+180 to determine the cost, where C represents the total cost and p represents the number of premium channels.
If a customer wants 5 premium channels, which statement comparing the cost of Plan A and Plan B is true?
A. Plan A will cost $5 less than Plan B.
B. Plan A will cost $10 less than Plan B.
C. Plan A will cost $5 more than Plan B.
D. Plan A will cost $10 more than Plan B.
After solving the equation we can say that Plan A will cost $10 more than Plan B. So, D is the Correct answer
What is an Equation?
A statement that affirms the equality of two expressions connected by the equals sign "=" is known as an equation.
For illustration, 2x - 5 = 13.
The two most well-known groups of equations in algebra are the linear
equations and the polynomial equations.
P(x) = 0 can be used to represent polynomial equations with a single variable. P is a polynomial, and axe + b = 0 is the standard form for linear equations.
Here, the parameters a and b. To solve these equations, we can use geometric or computational techniques from linear algebra or mathematical analysis. There are several sorts of equations
as well, including:
linear algebra quadratic formulas cube-based equations linear equations Equations that differ Statistical equations
Plan A:- $135 + $15(no. of premium channel)
Plan A for 5 premium channels will be
=$135 + $15(5)
= $135 + $75
=$210
Plan B:-
equation
C=$(5p+180)
p = no. of premium channel
Plan B for 5 premium channels will be equation
C = $25 + $180
= $205
Thus,
Plan A will cost $5 more than Plan B
As Plan A cost $210 and Plan B cost $205
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To celebrate Ripton's bicentennial fireworks are launched off a dam 36 ft above Lake Marley. The height of a display t seconds after it has been launched is given by h 16 64 36. After how long will the shell from the fireworks reach the water?
The shell from the fireworks will reach the water after 0.75 seconds or -0.625 seconds. Since the time cannot be negative, the shell will reach the water after 0.75 seconds.
How to find time ?To find the time it takes for the shell from the fireworks to reach the water, we need to solve the equation h = 0 for t.
The given equation for h is h = -16t^2 + 64t + 36, so we can substitute this into the equation h = 0 to get:
0 = -16t^2 + 64t + 36
To solve this equation, we can use the quadratic formula, which is:
t = (-b +/- sqrt(b^2 - 4ac)) / (2a)
In this case, a = -16, b = 64, and c = 36, so the formula becomes:
t = (-64 +/- sqrt(64^2 - 4(-16)(36))) / (-32)
Simplifying this gives us:
t = (-64 +/- sqrt(4096 - 2304)) / (-32)
which simplifies to:
t = (-64 +/- sqrt(1792)) / (-32)
Finally, simplifying gives us:
t = (-64 +/- 44) / (-32)
t = (-20 or 24) / (-32)
t = -0.625 or 0.75
Thus, the shell from the fireworks will reach the water after 0.75 seconds or -0.625 seconds. Since the time cannot be negative, the shell will reach the water after 0.75 seconds.
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{ (-3, 4), (7,5), (13, — 7), (15, 4) }
Answer:
Step-by-step explanation:
0
.........10 points.....
The value of angle a is 45, the value of angle b is 135, the value of angle c is 135 and d is 135.
What are lines and angles?Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines. A figure called an angle is one in which two rays originate from the same point. In this area, you might also encounter contrasting and related viewpoints.
Given that the line cutting the two parallel lines. The value of the angles will be calculated as,
Angle a will be,
a + 135 = 180
a = 180 - 135
a = 45
Angle b = 135
Angle c = 135
Angle d = 135
Therefore, the value of angle a is 45, the value of angle b is 135, the value of angle c is 135 and d is 135.
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Find h as indicated in the figure.
The indicated side of the right angle triangle is 183.
How to find the side of a right triangle?A right triangle is a triangle that has one of it's angles as 90 degrees. A right triangle sides are named according to the position of the angles.
The sides name are as follows:
opposite sideadjacent sidehypotenuse sidelet's find the value of side h using the trigonometric ratios as follows
tan ∅ = opposite / adjacent
Therefore,
tan 18.8 = h / x + 423
cross multiply
(x + 423) tan 18.8 = h
h = x tan 18.8 + 423 tan 18.8
h = 0.34042776856x + 144.000946101
tan 57.8 = h / x
cross multiply
x tan 57.8 = h
h = 1.58797305139x
Therefore,
1.58797305139x = 0.34042776856x + 144.000946101
1.58797305139x - 0.34042776856x = 144.000946101
1.24755305139x = 144.000946101
x = 144.000946101 / 1.24755305139
x = 115.426674549
Therefore,
h = 1.58797305139(115.426674549)
h = 183.294448434
h = 183
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Anybody good at statistics that’s can help outside of here?
I'm here trying to help my 12 yr old
I know, the answer is A.
I need some help, explaining how the answer is A although, I have a bit of a rational mind when it comes to explaining stuff unfortunately.
On solving the question, by the help of angle sum property of triangle, we got that x= 14
What is Triangle?Having three edges and three vertices, a triangle has three sides. The most significant characteristic of triangles is the fact that their interior angles add up to 180 degrees.
According to sides, what are the three different types of triangles?Scalene, isosceles, and equilateral triangles are the three types of triangles that can have three sides.
Now, value of x is -
(x+27)° + 70° + (x + 55)° = 180° ( Sum of al angles in a triangle is 180°)
2x + 152 = 180°
2x = 28
x=14
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help please no need to do alot of steps
[tex]x = \sqrt{\frac{z-3y^{2}+9 }{3} }[/tex] , [tex]x = -\sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]
Step-by-step explanation:
[tex]z= -9+3x^{2} +3y^{2} : x= \sqrt{\frac{z-3y^{2}+9 }{3} } ,x = - \sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]
[tex]z= -9+3x^{2} +3y^{2}[/tex] : [tex]-9+3x^{2} +3y^{2} =z[/tex]
[tex]-9+3x^{2} = z- 3y^{2}[/tex]
[tex]3x^{2} = z - 3y^{2} +9[/tex]
[tex]\frac{3x^{2} }{3} = \frac{z}{3} - \frac{3y^{2} }{3} + \frac{9}{3}[/tex]
[tex]x^{2} = \frac{z-3y^{2}+9 }{3}[/tex]
for [tex]x^{2} =[/tex][tex]f(a)[/tex] the solutions are [tex]x= \sqrt{f(a)} , -\sqrt{f(a)}[/tex]
[tex]x = \sqrt{\frac{z-3y^{2}+9 }{3} }[/tex] , [tex]x = -\sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]
[tex]x = i \sqrt{\frac{z+2y^{2}-5 }{2} } , x = -i \sqrt{\frac{z+2y^{2}-5 }{2} }[/tex]
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Dontrell bought 51/2 pounds of potatoes for $3.52. What equation can be used to represent the total amount he paid, y, for x pounds of potatoes?
Enter the correct equation in the box.
The equation that represents the the total amount he paid, y, for x pounds of potatoes is y = 0.64x.
How to use equation to represent the total amount paid?Dontrelle bought [tex]5\frac{1}{2}[/tex] pounds of potatoes for $3.52.
The equation that can be used to represent the the total amount he paid, y, for x pounds of potatoes is as follows:
rate = amount paid / weight in pounds
amount paid = $3.52
weight of potatoes = 11 / 2 pounds
rate = 3.52 ÷11 / 2
rate = 3.52 × 2 / 11
rate = 7.04 / 11
rate = 0.64 dollars per pound.
Therefore, the equation is y = 0.64x
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The fraction 5/7 is equivalent to what percent? Round your percent to the nearest tenth.
Answer:
the fraction 5/7 is equivalent to approximately 71.4%
Step-by-step explanation:
if you divide 5/7, you'll get an answer like 0.71428
to convert decimals to fractions, you have to multiply by 100 to get 71.428
to round to the nearest tenth, round the 2 up to 3
71.43
and then, round 4 down
71.4%
hope this helped!
To allow last minute christmas shopping silverburn shopping centre is opening from 8am till midnight on Monday to Saturdays and 8am till 10pm on sundays. How many hours is it open in one week
There were 500 sweets in a box and Mrs. Miller has given out 35% as prizes. How many are left in
the box?
Answer: 325
Step-by-step explanation:
Lets rewrite this.
35% of sweets are given out of 500.
35% of 500.
35% = 0.35
0.35 x 500 = 175
This means 175 prizes were given. Now we have to subtract.
500 - 175 = 325
(-4)³·7⁰
_____ this a fraction!
(-1³)
Match each system on the left with all words that describe the system on the right. Choices on the right can be used
more than once.
2x = y + 3
y = - 2x + 1
2x = y + 3
2y - 4x = -6
2x = y + 3
2y - 4x = 6
inconsistent
consistent
independent
dependent
Matching the equation to choices
equation classifications
2x = y + 3 and y = - 2x + 1 consistent and independent
2x = y + 3 and 2y - 4x = -6 consistent and dependent
2x = y + 3 and 2y - 4x = 6 inconsistent
What are inconsistent equations?A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.
2x - y = 3... equation * 2
4x - 2y = 6
-4x + 2y = 6
subtracting gives
8x - 4y = 0
no solution
What are consistent and independent equations?A system is deemed consistent if it has at least one solution.
A consistent system is independent if it only has one solution.
y = 2x - 3
y = -2x + 1
subtracting gives
0 = 4x - 4
x = 1
substituting x to get y
y = -1
What are consistent and dependent equations?A consistent system is dependent if there are an endless number of possible solutions. The two equations represent the same line when you graph them.
-y + 2x = 3 .... equation * 2
-2y + 4x = 6
2y - 4x = -6
subtracting gives
-4y + 8x = 12 - none cancels out meaning infinite number of possible solutions
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Please help!
A basketball has the radius of 13 inches
What is the volume?
Answer:
9203 in.³
Step-by-step explanation:
V = (4/3)πr³
V = (4/3) × 3.14159 × (13 in.)³
V = 9203 in.³
Sarah and her friends are going blueberry picking. Sarah picks $b$ blueberries. Michael picks $3$ more than half as many as Sarah, and David picks $5$ more than Michael. In addition, Kaycee picks $10$ less than $3$ times as many as David, and Hannah picks twice as many as Kaycee. Find an expression in terms of $b$ for the number of blueberries that Hannah picked.
Answer:
~ Sarah = b
!!!Michael = 1/2*b + 3
~~David = b/2 + 8
!!!Hannah = 3b + 28
~~~~~Sarah = 3b/2 + 14
a wireless network predicts that sales will increase 110% this upcoming year. if the sales are projected to be $16000 in the future, what are they in the past?
A 1600
B 7619
C 14400
D 14545
SHOW WORK
Answer:
Step-by-step explanation:
14545
Make a basic proportion
16,000/x=110/100
Cross multiply
1,600,000=110x
Divide
x=14545