The dimensions and the weight of several solids are given. Use the density information to determine what element is the solid made up of.
Answers
Given:
Dimensions and weight of a solid is given.
Height (h) of a cylinder (in cm) =
[tex]h=5[/tex]Radius (r) of a cylinder (in cm) =
[tex]r=5[/tex]Mass (m) of solid (in grams)=
[tex]m=3090.5[/tex]Density of several elements is given.
Cobalt=8.86, Copper=8.96, Gold=19.3, Iron=7.87, Lead 11.3, Platinum=21.5, Silver=10.5, Nickel=8.90.
Required:
What element is the solid made up of.
Answer:
Let us find the volume (V) of cylinder (in cubic cm).
[tex]\begin{gathered} V=\pi\times r^2\times h \\ V=3.14\times\left(5\right)^2\times5 \\ V=3.14\times25\times5 \\ V=392.5 \end{gathered}[/tex]Using formula of density (D), we get,
[tex]\begin{gathered} D=\frac{m}{V} \\ D=\frac{3090.5}{392.5} \\ D=7.87 \end{gathered}[/tex]Hence, the density of the solid is 7.87 grams per cubic cm.
From the given information of density of several elements, we see that the solid is made up of Iron.
Final Answer:
The solid is made up of Iron.
Related Questions
There is a bag with 7 red buttons, 4 green buttons, 2 blue buttons, and 5 orange buttons. You are drawing thebuttons one at a time. Each time you draw a button, you keep it.P(red then green) =Show Your Work
Answers
7 red buttons, 4 green buttons, 2 blue buttons, and 5 orange buttons
In total there are
= 7 + 4 + 2 + 5
= 18 buttons
P (red) = 7/18
P(green) = 4/18
P(red then green) = 7/18 * 4/18
=7/81
Part A. 150% of what number is 156 Part B. 4.4 is 5.5% of what number
Answers
EXPLANATION
Since 150% represents a percentage bigger than 156, the appropiate relationship would be as follows:
[tex]Part\text{=}\frac{\text{Percentage}}{100}\cdot\text{Whole}[/tex]Where the whole number is 156 and the percentage is 150%:
[tex]\text{Part}=\frac{150}{100}\cdot156[/tex][tex]\text{Part}=1.5\cdot156=234[/tex]In conclusion, the solution is 234
A circular path 4 feet wide has an inner diameter of 650 feet. How much farther is it around the outer edge of the path than around the inner edge? Round to the nearest hundredth. Use 3.14 for pie
Answers
step 1
Find out the circumference of the outer edge
Find out the radius
r=(650/2)+4
r=329 ft
so
[tex]\begin{gathered} C=2\pi\cdot r \\ C=2\cdot3.14\cdot329 \\ C=2,066.12\text{ ft} \end{gathered}[/tex]step 2
Find out the circumference of the inner edge
r=650/2=325 ft
substitute
[tex]\begin{gathered} C=2\cdot3.14\cdot325 \\ C=2,041\text{ ft} \end{gathered}[/tex]Find out the difference
2,066.12-2,041=25.12 ft
therefore
the answer is 25.12 ftTranslate the description below as an algebraic expression:The product of v and the difference of c and 10
Answers
We have to translate the expression "The product of v and the difference of c and 10".
We know that the expression is a product of two factors: v and a difference. The difference is between the terms c and 10, so it can be written as (c-10).
Then, the product can be written as:
[tex]v\cdot(c-10)[/tex]Answer: the expression is v*(c-10)
one box of strawberries cost $5 what equation can be used to calculate the most number of boxes a person can buy with $30
Answers
Answer
The maximum number of boxes that one can buy with 30 dollars is 6 boxes of strawberries.
Explanation
One box of strawberries cost 5 dollars.
If one buys x boxes of strawberries, the cost would be (5x) dollars.
So, if one has 30 dollars, we want to find the maximum number of boxes that the person can buy, that is, the maximum value of x
5x ≤ 30
Divide both sides by 5
(5x/5) ≤ (30/5)
x ≤ 6
The number of boxes that one can buy is less than or equal to 6.
Hence, the maximum number of boxes that one can buy with 30 dollars is 6 boxes of strawberries.
Hope this Helps!!!
Evaluate.
34+(12+14)2⋅2
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answers
Answer:
=1.875
Step-by-step explanation:
Add: 1/
2
+ 1/
4
= 1 · 2/
2 · 2
+ 1/
4
= 2/
4
+ 1/
4
= 2 + 1/
4
= 3/
4
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 4) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 4 = 8. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one half plus one quarter is three quarters.
Exponentiation: No. 1 ^ 2 = 3/
4
^ 2 = 32/
42
= 9/
16
In other words - three quarters raised to the power of squared is nine sixteenths.
Multiple: No. 2 * 2 = 9/
16
* 2 = 9 · 2/
16 · 1
= 18/
16
= 9 · 2/
8 · 2
= 9/
8
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(18, 16) = 2. In the following intermediate step, cancel by a common factor of 2 gives 9/
8
.
In other words - nine sixteenths multiplied by two is nine eighths.
Add: 3/
4
+ the result of step No. 3 = 3/
4
+ 9/
8
= 3 · 2/
4 · 2
+ 9/
8
= 6/
8
+ 9/
8
= 6 + 9/
8
= 15/
8
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators
In 2000, there were 750 cell phone subscribers in a small town. The number of subscribers increased by 80% per year after 2000. How many cell phone subscribers were in 2010? Round off the answer to the nearest whole number.
Answers
This is an exponential growth. We would apply the exponential growth formula which is expressed as
y = a(1 + r)^t
Where
a represents the imitial number of subscribers
r represents the growth rate
t represents the number of years
y represents the number of subscribers after t years
From the information given,
a = 750
r = 80/100 = 0.8
t = 9 (number of years between 2000 and 2010)
Thus,
y = 750(1 + 0.8)^9
y = 750(1.8)^9
y = 148769.48
Rounding to the nearest whole number, the number of cell phone subscribers in 2010 is
148769
Maya bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $400 less than the desktop. She paid for the computers using two different financing plans. For the desktop the interest rate was 7.5 % per year and for the laptop it was 8% per year. The total finance charges for one year were $371. How much did each computer cost before finance charges? Desktop: $Laptop: $
Answers
1. Let D be price of desktop
let L be price of a Laptop
• we know that the laptop cost $400 less than the desktop
L = D -400
• for desktop D, Maya paid interest of 7.5% per year: 7.5/100 = 0.075
,• For Laptop L , Maya paid interest of 8 % per year : 8/100 = 0.08
,• We know that total charges for finance was $ 371,
therefore :
0.075 D + 0.08L = 371, (remember from the above , L = D-400 , lets substitute this value for L)
0.075 D + 0.08( D-400) = 371
0.075D + 0.08 D -32 = 371
0.155D = (371 +32)=403
D = 403/0.0155
D = $26 000
and L = D-400
= 26000-400
= $25600
• This means that Desktopcost $26000 and Laptop cost $25600,
james harmon pays 850.80 per year for his life insurance. if he where to the premiums quarterly, the payments would would be 221.21 what percentage more is mr hamrmon paying for the year using yhe quarterly rate
Answers
Percent is given by the expression:
[tex]\begin{gathered} \text{Total}\cdot\frac{\text{percent}}{100}=\text{Equivalent number to the percent} \\ 850.8\cdot\frac{x}{100}=221.21 \\ x=\frac{221.21\cdot100}{850.8} \\ x=26\text{ percent} \end{gathered}[/tex]So, he is paying 74% more using the quarterly rate
Can the three segments below form a triangle? Explain how you will change the length of one or two of these segments to form each kind of triangle. If no changes needed enter the original length or state that no changes needed. scalene triangleAB=… BC=…. AC=… equilateral triangleAB = … BC = … AC = …isosceles triangleAB = … BC = … AC = …
Answers
ANSWERS
• They cannot form a triangle
,• Scalene triangle: ,AB = 7
,• Equilateral triangle: ,BC = 5, AC = 5
,• Isosceles triangle: ,AB = 8
EXPLANATION
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side,
[tex]\begin{gathered} 14+8>5\Rightarrow true \\ 14+5>8\Rightarrow true \\ 5+8>14\Rightarrow false \end{gathered}[/tex]Hence, these side lengths cannot form a triangle.
To form a scalene triangle one of the shortest sides must be larger, for example, AB should be 7, instead of 5. Other combinations are possible as well.
To form an equilateral triangle all sides must have the same length, for example, AB = BC = AC = 5
To form an isosceles triangle, two of the sides must have the same length, while the third side has a different length, for example, AB = 8
To form all three kinds of triangles, the first rule must be valid as well.
The local appliance store is advertising a 17% off sale on a new flat-screen TV. If the saleprice is $664, what was the original price of the flat-screen TV? Use X in the equation
Answers
Let's assume X is the original price of the flat-screen TV
The store is advertising a 17% off sale in that price, so the real sale price should be less than the original price
To calculate a % discount, we proceed as follows:
Compute the discount:
discount = 17% of X
Recall a percentage can be expressed as the number divided by 100, that is:
discount = 17 / 100 * X = 0.17X
Now we have the discount, we calculate the actual or sale price, which is the original price minus the discount:
sale price = original price - discount
sale price = X - 0.17X
We apply simple algebra to simplify the expression, just subtracting 1-0.17=0.83
sale price = 0.83X
We know the sale price is $664, thus:
0.83X = 664
Finally, we solve for X
[tex]X=\frac{664}{0.83}=800[/tex]This means that the original price of the TV was $800. Let's verify our result
9. Solve the system of equations algebraically. Show your reasoning.2y = x -44x + 3y = 5
Answers
I) 2y = x - 4
II) 4x + 3y = 5
First, we put all the variables on the same side subtracting x from both sides of equation I:
I) 2y - x = -4
II) 3y + 4x = 5
Now, we multiply equation I by 4:
I) 8y - 4x = -16
II) 3y + 4x = 5
Then, we add equation I to equation II:
I) 8y - 4x = -16
II) 11y = -11
Therefore, we got from equation II:
y = -11/11 = -1
Applying this result on equation I, we got:
-8 - 4x = -16
4x = 8
x = 8/4 = 2
Final answer: (x,y) = (2,-1)
Sally deposits $2,500 at 8% interest for 3 years . How much can she withdraw at the end of that period
Answers
ANSWER
$3100
EXPLANATION
Sally deposits $2500 at 8% interest for 3 years.
We want to find the amount she can withdraw at the end of the period.
To know this, we have to first find the interest.
Simple Interest is given as:
[tex]\begin{gathered} SI\text{ = }\frac{P\cdot\text{ R }\cdot\text{ T}}{100} \\ \text{where P = principal = \$2500} \\ R\text{ = rate = 8\%} \\ T\text{ = 3 years} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} SI\text{ = }\frac{2500\cdot\text{ 8 }\cdot\text{ 3}}{100} \\ SI\text{ = }\frac{60000}{100} \\ SI\text{ = \$600} \end{gathered}[/tex]Therefore, after 3 years the interest will be $600.
The amount she can withdraw after this period is therefore the sum of the principal and the interest:
$2500 + $600 = $3100
She can withdraw $3100 at the end of the period.
Leeds Company produced the following number of maps during the first five weeks of last year. Prepare a bar graph. Week Maps 1 800 2 600 3 400 4 700 5 300
Answers
The bar graph is attached below.
The heights of the rectangular bars in a bar graph, which displays complete data, are proportionate to the values they indicate. The graph's bars can be displayed either vertically or horizontally. Bar graphs, commonly referred to as bar charts, are a visual depiction of groups of data. It is one method of processing data. A bar graph is a great tool for representing data that are unrelated to one another and do not need to be displayed in any particular sequence. The bars provide a visual representation for comparing amounts in several categories. The x and y axes, commonly known as the horizontal and vertical axes, the title, labels, and a bar graph are all included.
Hence we frame the desired bar graph.
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Valentina opened a savings account and deposited 1,000.00 as principal the account earns 3%interest compounded monthly what is the balance after 8 years
Answers
According to the problem, the principal is $1,000, the interest is 3% compounded monthly and the time is 8 years.
We have to use the compounded interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Replacing the given information, we have
[tex]A=1,000\cdot(1+\frac{0.03}{12})^{12\cdot8}[/tex]Now, we solve for A
[tex]\begin{gathered} A=1,000(1+0.0025)^{96} \\ A=1,000(1.0025)^{96} \\ A\approx1,270.87 \end{gathered}[/tex]Hence, she will have $1,270.87 after 8 years.What is 3 +4.3+45?A4늘OB.B. 7O. 8○ D. 12
Answers
solution
[tex]3+4\frac{1}{3}=7\frac{1}{3}[/tex]answer: B
A company has net sales revenue of $175000 reporting period and $148000 in the next. using horizontal analysis, it has experienced a decrease of what percentage?A. 15%B. 18%C. 8%D. 12%
Answers
ANSWER:
A. 15%
STEP-BY-STEP EXPLANATION:
We can determine the percentage using the following formula:
[tex]\begin{gathered} r=\frac{\text{ fiinal value - initial value}}{\text{ initial value}}\cdot100 \\ \\ \text{ we replacing} \\ \\ r=\frac{148000-175000}{175000}\cdot100 \\ \\ r=-15.42\%=15\% \end{gathered}[/tex]Therefore, the correct answer is A. 15%
Find the tangent of each angle that is not the right angle. Drag and drop the numbers into the boxes to show the tangent of each angle. B 76 tan ZA tan ZB 2.45 0.38 0.93
Answers
From the trignometric ratio of right angle triangle :
The ratio for the tangent of any angle of right angle triangle is the ratio of the side Opposite to that angle to the adjacent side of that angle :
[tex]\tan \theta=\frac{Opposite\text{ Side}}{Adjacent\text{ Side}}[/tex]In the given triangle :The side opposite to the angle A is BC and the adjacent side AC
So,
[tex]\begin{gathered} \tan \theta=\frac{Opposite\text{ Side}}{Adjacent\text{ Side}} \\ \tan A=\frac{BC}{AC} \end{gathered}[/tex]In the figure : we have AC = 76, BC = 31 and AB = 82.1
Substitute the value and simplify :
[tex]\begin{gathered} \tan A=\frac{BC}{AC} \\ \tan A=\frac{31}{76} \\ \tan A=0.407 \\ \tan A=0.41 \end{gathered}[/tex]Thus, tan A = 0.41
Now, the side opposite to the angle B is AC and the adjacent side is BC
thus :
[tex]\begin{gathered} \tan \theta=\frac{Opposite\text{ Side}}{Adjacent\text{ Side}} \\ \tan B=\frac{AC}{BC} \end{gathered}[/tex]In the figure : we have AC = 76, BC = 31 and AB = 82.1
Substitute the value and simplify :
[tex]\begin{gathered} \tan B=\frac{AC}{BC} \\ \tan B=\frac{76}{31} \\ \tan B=2.451 \end{gathered}[/tex]tan B = 2.451
Answer :
tanA = 0.41
tanB = 2.45
Which expression can be used to find the nth term in this sequence position: 1 2 3 4 5 nvalue of term: 2 5 10 17 26 ?
Answers
n²+1 where n is the position of the sequence
1) Considering the sequence (2,5,10,17,26,...) corresponding to 1,2,3,4,5,...
Let's figure out how that sequence grows:
5 -2 = 3
10 -5 = 5
17-10= 7
26-17= 9
And examining the differences from each difference we have:
5-3 =2
7-5 = 2
9-7 =2
2) So we can write the following table, where the first line is the sequence, then the positions, then the subtraction between them.
As it is a quadratic formula, we can write in the general form and then plug x=0
[tex]\begin{gathered} a_n=n^2 \\ 2\text{ 5 10 17 26} \\ 1\text{ 2 3 4 5 6 } \\ 1\text{ 4 9 25 36} \\ a_n=n^2+0n+1 \\ a_n=n^2+1 \end{gathered}[/tex]3) Hence, to find the 6th term, for instance, we plug n=6 so
6²+1 = 31. So the formula to find the nth term is n² +1
3) Finally, the sequence is given by n² +1 where n is the position of the term.
I got 4089 for the answer but it was incorrect
Answers
Let A be the event "person under 18" and B be the event "employed part-time". So, we need to find the following probability
[tex]P(A\text{ or B) =P(A}\cup B)[/tex]which is given by
[tex]P(A\text{ or B) =P(A}\cup B)=P(A)+P(B)-P(A\cap B)[/tex]Since the total number od people in the table is equal to n=4089, we have that
[tex]P(A)=\frac{28+174+395}{4089}=\frac{597}{4089}[/tex]and
[tex]P(B)=\frac{174+194+71+179+173}{4089}=\frac{791}{{4089}}[/tex]and
[tex]P(A\cap B)=\frac{174}{4089}[/tex]we have that
[tex]P(A\text{ or B) =}\frac{597}{4089}+\frac{791}{{4089}}-\frac{174}{4089}[/tex]which gives
[tex]P(A\text{ or B) =}\frac{597+791-174}{4089}=\frac{1214}{4089}=0.29689[/tex]Therefore, the answer the searched probability is: 0.296
covert 6\10 into decimal number and then see if it's a repeating or terminating
Answers
We are asked to determine wheater 6/10 in decimal form is repeating or terminating. To do that we need to divide 6 over 10. To do that, we proceed as follows:
We need to find a number that when multiplied by 10 gives 6. That number is 0.6, because:
[tex]0.6\times10=6[/tex]Therefore 6/10=0.6 Since the numbers after the radix point do not repeat, this is a terminating decimal.
I have to create a graph but I need some help and clarification
Answers
To complete the table you evaluate the equation by the given value of x to find the corresponding value of y:
[tex]y=x+4[/tex][tex]\begin{gathered} x=4 \\ \\ y=4+4 \\ y=8 \\ \\ (4,8) \end{gathered}[/tex][tex]\begin{gathered} x=8 \\ \\ y=8+4 \\ y=12 \\ \\ (8,12) \end{gathered}[/tex][tex]\begin{gathered} x=12 \\ \\ y=12+4 \\ y=16 \\ \\ (12,16) \end{gathered}[/tex][tex]\begin{gathered} x=16 \\ \\ y=16+4 \\ y=20 \\ \\ (16,20) \end{gathered}[/tex]To put those (x,y) points in the plane;
the frist coordinate x is the number of units you move to the left (if x is negative) or to the right (if x is positive)
the second coordinate y is the number of units you move down (if y is negative) or up (if y is positive)
Then, using the points (0,4), (4,8), (8,12), (12,16) and (16,20) you get the next graph for y=x+4:
Original amount: 25End amount: 18
Answers
The formula to calculate the percentage change is given as
[tex]\text{Percentage Change = }\frac{Original\text{ Amount}-\text{Final Amount}}{Original\text{ Amount}}\times100[/tex]The question gives us:
Original amount: 25
End amount: 18
Substituting, we have
[tex]\begin{gathered} C=\frac{25-18}{25}\times100 \\ =\frac{7}{25}\times100 \\ =28 \end{gathered}[/tex]The percentage change is a 28% decrease.
Is the function y= –10x10–10 linear or nonlinear?
Answers
The function y = -10*x¹⁰ - 10
Is not a linear function, as we can see the exponent is 10.
Is the function linear or non-linear?Remember that a linear function is of the form:
y = m*x + b
Where x is the variable.
So a linear function is a polynomial of degree 1.
Particularly, here we have the function:
y = -10*x¹⁰ - 10
So we have an exponent of 10, which means that this is not a linear function.
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Need to find the domain, range, x-intercept, y-intercept, and rate of change from the graph
Answers
Explanation
Step 1
Domain:The domain of a function is the complete set of possible values of the independent variable, by the graph is it a continuous line, so the domain is
[tex](-\infty,\infty),[/tex]Step 2
Range:The range is the set of all second elements of ordered pairs (y-coordinates), by the graph is it a continuous line, so the range is
[tex](-\infty,\infty),[/tex]Step 3
x-intercept
it is when y= 0 , by the graph :
[tex](-2,0)[/tex]Step 4
y-intercept
it is when x= 0 m by the graph:
[tex](0,4)[/tex]Step 5
rate of change
Let
P1(-2,0) P2(0,4)
[tex]\begin{gathered} rate\text{ of change=}\frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{0-(-2)}=\frac{4}{2}=2 \\ \end{gathered}[/tex]rate of change:2
F(x) = -3x,x<0 4,x=0 x^2, x>0 given the piece wide functions shown below select all of the statements that are true
Answers
The correct statements regarding the numeric values of the piece-wise function are given as follows:
B. f(3) = 9.
D. f(2) = 4.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
A piece-wise function means that the definition of the input is different based on the input of the function. In this problem, all the numeric values we are calculating are for positive numbers, hence the definition of the function is given by:
f(x) = x².
Then the numeric values of the function are given as follows:
f(1) = 1² = 1.f(2) = 2² = 4.f(3) = 3² = 9.f(4) = 4² = 16.Meaning that options B and D are correct.
Missing informationThe options are given by the image at the end of the answer.
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A committee of three people is selected at random from a set containing of seven teachers, six parents of students, and four alumni. • What is the probability the committee consists of all teachers? • What is the probability of the even that the committee consists of no teachers?
Answers
Step 1
State the expression for the probability of an event
[tex]\text{Probability of an event = }\frac{Number\text{ of required events}}{\text{Total number of events}}[/tex]Total number of events = 7+6+4 = 17
Step 2
Find the probability for selection of 3 teachers
[tex]\text{The probability to select a teacher at the first selection = }\frac{7}{17}[/tex][tex]\text{The probability to select a teacher at the second selection=}\frac{6}{16}=\frac{3}{8}[/tex][tex]\text{The probability to select a teacher at the third selection = }\frac{5}{15}=\frac{1}{3}[/tex]Therefore
[tex]The\text{ probability the committ}ee\text{ consists of all teachers = }\frac{7}{17}\times\frac{3}{8}\times\frac{1}{3}=\frac{7}{136}[/tex]Step 3
Find the probability the committee consists of no teachers
Total number of non-teachers in the population = 6 + 4=10
Therefore,
[tex]\text{The probability the committee consists of no teachers on the 1st selection = }\frac{10}{17}[/tex][tex]\text{The probability the committee consists of no teachers on the 2nd selection= }\frac{9}{16}\text{ }[/tex][tex]\text{The probability the committee consists of no teachers on the 3rd selection }=\frac{8}{15^{}}[/tex]Therefore,
[tex]\text{The probability the committe consists of no teacher = }\frac{10}{17}\times\frac{9}{16}\times\frac{8}{15}=\frac{3}{17}[/tex]Laney can finish 17 math problems in 51 minutes while Hayden can finish 6 problems in 18 minutes. Is this a proportional relationship.
Answers
Given data:
The 17 maths problem finish by Laney in 51 minutes.
The 6 maths problem finish by Hayden in 18 minutes.
The time taken by Laney to finish 1 problem is,
17 prob=51 minutes
1 prob=3 minute.
Simmiarly, the time taken by Hayden to finish 1 problem is,
6 prob=18 minutes
1 prob=3 minute.
As, the time taken by the Laney and Hayden to solve one problem is same .
Thus, the given relationship is proportional one.
I need to make 500$ per week after tax in order to pay all my bills. The income tax is 20% What is the smallest pre-tax weekly salary I can earn and still be able to pay my bills after I pay my income tax?
Answers
I must earn at least $625 (or more) per week before tax to pay my bills.
Given,
To make $500 per week after tax in order to pay all my bills.
and, The income tax is 20%
To find the smallest pre-tax weekly .
Now, According to the question:
Let x be the amount to earn pre - tax.
The income tax is 20% = 20/100 = 0.2
Set up an inequality:
x - 0.2x > = 500
0.8 > = 500
x >= 500/0.8
x >= 625
Hence, I must earn at least $625 (or more) per week before tax to pay my bills.
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6. Point A (-16,8) is one of the verticesof a rectangle. After a dilation of 1/2, arotation of 90 degrees clockwise, and areflection over the x-axis, what are thecoordinates of A"'?
Answers
Given the coordinate: A(-16, 8), let's perform the following:
First step:
A dilation with a scale factor of 1/2.
Here, we are to multiply the coordinates by 1/2.
A(-16, 8) ==> A'(-16*½, 8*½) = A'(-8, 4)
Second step:
Perform a rotation of 90 degrees clockwise.
(x, y) will change to (y, -x)
A'(-8, 4) ==> A''(4, 8)
Third step:
A reflection over the x axis.
To perform a reflection over the x axis, (x, y) becomes (x, -y)
A''(4, -8) ==> A'''(4, -8)
Therefore, the coordinates of A''' are:
A'''(4, -8)
