You deposit $4000 in an account earning 8% interest compounding monthly. How much will you have in the next 10 years
.
In this case:
[tex]\begin{gathered} P=\$4000 \\ r=8\%=0.08 \\ t=10 \\ n=12 \end{gathered}[/tex]Applying the formula, the compound interest can be calculated as follows:
[tex]\begin{gathered} A=4000(1+\frac{0.08}{12})^{(12\times10)} \\ A=8878.56 \end{gathered}[/tex]The amount in the account will be $8,878.56.
UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each additional pound. How many pounds will it take for UPS and FedEx to cost the same? Define your variable, Write the equation, Solution
UPS charges are:
$ 7 for the firsr pound
+ $0.20
FedEx charges are:
$ 5 for the first pound
+ $ 0.30 for each additional pound
Let x to represent the amount of additional pounds
Equation:
7 + 0.20x = 5 + 0.30x
Like terms:
0.20x - 0.30x = 5 - 7
-0.10x = -2
Dividing by -0.10
-0.10x/- 0.10 = -2/-0.10
x = 20
Interpretation
It will take 21 pounds to cost the same: (the first plus 20 additional)
What is the solution to × + 9 = 24A. × = 9 B. × = 18C. × = 15D. × = 33
if x is a solution to the equation 2x-5=15, select all the equations that also have x as a solution
Answer:
x=10
Step-by-step explanation:
2x-5=15
+5 +5
2x=20
2x/2=20/2
x=10
help meeeeeeeeeeeeeeeeeeeeeee
thank you
The amount of coffee imported into the country in the year 1997 is approximately 1.344 million pounds.
The amount of coffee imported into the country in the year 2002 is approximately 39.3176 million pounds.
The amount of coffee imported into the country in the year 2007 is approximately 85.8966 million pounds.
What is a polynomial function?A polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as:
Multiplication (product)AdditionSubtractionNext, we would determine the amount of coffee imported into the country by using the given polynomial function as follows:
At 1997, we have the following:
x = 0
P(x) = 0.7166x² + 6.627x + 1.344
P(0) = 0.7166(0)² + 6.627(0) + 1.344
P(0) = 1.344 million pounds.
At 2002, we have the following:
x = 4
P(x) = 0.7166x² + 6.627x + 1.344
P(4) = 0.7166(4)² + 6.627(4) + 1.344
P(4) = 0.7166(16) + 26.508 + 1.344
P(4) = 11.4656 + 26.508 + 1.344
P(4) = 39.3176 million pounds.
At 2002, we have the following:
x = 9
P(x) = 0.7166x² + 6.627x + 1.344
P(9) = 0.7166(9)² + 6.627(9) + 1.344
P(9) = 0.7166(81) + 59.643 + 1.344
P(9) = 58.0446 + 26.508 + 1.344
P(9) = 85.8966 million pounds.
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A cylindrical vase has a circumference of about 62.8 centimeters and a height of 33 centimeters. To the nearest cubic centimeter, how much water will the vase hold?
The volume of water that the cylindrical vase can hold is 10362 cm³.
Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.
The circumference of a cylindrical vase is 62.8 centimeters.
The height of the cylindrical vase is 33 centimeters.
Let r be the radius of the cylinder.
The circumference of the cylinder is given as:
C = 2πr
62.8 cm = 2 × 3.14 × r
r = 10 cm
The volume of a cylinder is given as:
V = πr²h where r is the radius and h is the height of the cylinder
Then,
V = 3.14 × ( 10 )² × 33
V = 10362 cm³
Hence, the cylindrical vase can hold 10362 cm³ of water.
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Answer: Bro above is wrong it's 10,367 cm3 PLATO
Step-by-step explanation: mad maths skills
Identify two similar triangles in the figure below, and complete the explanation of why they are similar. Then find AB. B А C 21 D ZA = (select) and ZABD = (select), so ABD - ACB by the (select)y Triangle Similarity Theorem. AB =
Answer:
∠A ≅ ∠A and ∠ABD ≅ ∠ACB, so ΔABD ≅ ΔACB by the AA (Angle - Angle) Triangle Similarity Theorem.
AB = 10
Explanation:
An angle is congruent to itself, so ∠A ≅ ∠A
On the other hand, taking into account the representation of the angles, we can say that: ∠ABD ≅ ∠ACB
Then, the triangles ABD and ACB are congruent by the AA (Angle-Angle) triangle similarity theorem because we have two congruent angles:
∠A ≅ ∠A
∠ABD ≅ ∠ACB
Now, if two triangles are similar their corresponding sides are proportional.
So, we can formulate the following equation:
[tex]\frac{AB}{AC}=\frac{AD}{AB}[/tex]Then, replacing AC by (21 + 4), AD by 4, and solving for AB, we get:
[tex]\begin{gathered} \frac{AB}{21+4}=\frac{4}{AB} \\ AB\times AB=4(21+4) \\ AB^2=4(25) \\ AB^2=100 \\ AB=\sqrt[]{100} \\ AB=10 \end{gathered}[/tex]Therefore, the answers are:
∠A ≅ ∠A and ∠ABD ≅ ∠ACB, so ΔABD ≅ ΔACB by the AA (Angle - Angle) Triangle Similarity Theorem.
AB = 10
Solve the following equations for x and y. Any method can be used.
This is a 2 x 2 equation system: (First, let's put all variables on one side)
[tex]2x-3y=13x-4y\Rightarrow2x-13x=-4y+3y\Rightarrow-11x=-y[/tex][tex]\begin{gathered} y=11x \\ y=\frac{-3}{2}x \end{gathered}[/tex]So, to solve this problem is to find the point (xo,yo) that satisfies both equations, this means a point that intersects those two lines. In this case, we are going to use a visual help:
As you can see, the lines are intersected in the point (0,0). lines are intersected in the point (0,0). Finally, the answer is x=0, y = 0
signed numbers pls help !1) 15-(-2) a) -15+2 b) 15-2 c) 15+22) -18+(-4) a) -18-4 b) -18+4 c) 18-43) -7-(-12) a) -7 - 12 b) -7+12 c) 7+124) -8 - (+15) a) -8+15 b) 8-15 c) -8 -155) 9+(-16) a) 9-16 b) 9+16 c) -9+16
Solution:
Given:
Signed numbers consist of negative numbers and positive numbers.
Rules of multiplication in signed numbers.
If the signs are the same the result is positive. If the signs are different the result is negative.
This means;
[tex]\begin{gathered} -\times-=+ \\ +\times+=+ \\ \\ -\times+=- \\ +\times-=- \end{gathered}[/tex]To solve these questions, we expand the brackets by multiplying the signs together using the rule of multiplying signed numbers.
Question 1:
[tex]\begin{gathered} 15-(-2)=15-\times-2 \\ =15+2 \end{gathered}[/tex]Therefore, the correct answer is OPTION C.
Question 2:
[tex]\begin{gathered} -18+(-4)=-18+\times-4 \\ =-18-4 \end{gathered}[/tex]Therefore, the correct answer is OPTION A.
Question 3:
[tex]\begin{gathered} -7-(-12)=-7-\times-12 \\ =-7+12 \end{gathered}[/tex]Therefore, the correct answer is OPTION B.
Question 4:
[tex]\begin{gathered} -8-(+15)=-8-\times+15 \\ =-8-15 \end{gathered}[/tex]Therefore, the correct answer is OPTION C.
Question 5:
[tex]\begin{gathered} 9+(-16)=9+\times-16 \\ =9-16 \end{gathered}[/tex]Therefore, the correct answer is OPTION A.
Which of these strategies would eliminate a variable in the system of equations?
6z+5y = 1
6z-5y=7
Choose all answers that apply:
!
Required information
Problem 8-63 (LO 8-1) (LO 8-3) (Static)
[The following information applies to the questions displayed below.]
Henrich is a single taxpayer. In 2021, his taxable income is $450,000. What is his income tax and net investment income
tax liability in each of the following alternative scenarios? Use Tax Rate Schedule. Dividends and Capital Gains Tax Rates
for reference. (Do not round intermediate calculations. Leave no answer blank. Enter zero if applicable. Round your
final answers to 2 decimal places.)
Problem 8-63 Part-b (Static)
b. His $450,000 of taxable income includes $2,000 of long-term capital gain that is taxed at preferential rates.
Income tax
Net investment income tax
Total tax liability
Amount
Total income & net investment income tax $ 124,556.00
Tax on preferentially taxed income $ 9,022.50
Given :
In 2021, his taxable income is $450,000.
Use Tax Rate Schedule.
His $450,000 of taxable income includes $2,000 of long-term capital gain that is taxed at preferential rates.
Income tax
Final answer is
Total income & net investment income tax $ 124,556.00
Tax on preferentially taxed income $ 9,022.50
For more explanation i have attached a pictures
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Brad is deciding if he should buy six flags season pass. A pass costs $120 and $6 for food each day. Without the pass, the costs is $18. How many days does Brad need to go to break even?
Answer:
10 times
Step-by-step explanation:
Subtract the price of food per day from the daily cost and divide the season pass price by the daily cost without food.
120+(6•x) x=days 120+(6•x)=18•x
The illustration below shows the graph of yyy as a function of xxx.
Complete the following sentences based on the graph of the function.
This is the graph of a
function.
The yyy-intercept of the graph is the function value y=\:y=y, equals
.
The smallest positive xxx-intercept of the graph is located at x=\:x=x, equals
.
The greatest value of yyy is y=\:y=y, equals
, and it occurs when x=\:x=x, equals
.
For xxx between x=\pix=πx, equals, pi and x=2\pix=2πx, equals, 2, pi, the function value y\:yy
\:000.
Based on the graph (see attachment) of this function, the sentences should be completed as follows:
This is the graph of a nonlinear functionThe y-intercept of the graph is the function value y = 1.The smallest positive x-intercept of the graph is located at x = π.The greatest value of y is y = 1 and it occurs when x = 0.For x between x = π and x = 2π, the function value y ≤ 0.What is y-intercept?In Mathematics, the y-intercept of any graph such as a trigonometric function, generally occurs at the point where the value of "x" is equal to zero (x = 0).
By critically observing the graph (see attachment), the coordinates of the y-intercept of the parabola is given by y-intercept = (0, 1). Additionally, the greatest value of y is equal to 1 (y = 0) and it occurs when x is equal to 0 (x = 0).
What is y-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-axis and the value of "y" is equal to zero (0).
From the graph (see attachment), the smallest positive coordinate of the x-intercept of the parabola is given by:
x-intercept = (π, 0).
In conclusion, when x is between x is equal to π (x = π) and x is equal to 2π (x = 2π), the range of the function is given by y ≤ 0.
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Giselle works as a carpenter and as
a
blacksmith.
She earns $20 per hour as a carpenter and $25
per hour as a blacksmith. Last week, Giselle
worked both jobs for a total of 30 hours, and
earned a total of $690.
How long did Giselle work as a carpenter
last week, and how long did she work as a
blacksmith?
Answer:
Step-by-step explanation:
$20/hr carpenter pay
$25/hr blacksmith pay
Let c = hours working carpentry
Let b = hours working as blacksmith
c + b = 30 {equation 1}
20c + 25b = 690 {equation 2}
In equation 1 solve for one variable in terms of the other.
c = 30-b
Substitute that into equation 2:
20(30-b) + 25b = 690
600 - 20b + 25b = 690
5b = 90
b = 90/5
b = 18 hours working as a blacksmith
c = 30-b = 30-18 = 12 hours as a carpenter
Answer:
she worked as a carpenter for 12 hours
And a blacksmith for 18 hours
Step-by-step explanation:
B=hours as blacksmith
C=hours as carpenter
20c+25b=690
b+c=30
c=30-b
So we substitute this into the first equation
20(30-b)+25b=690
600-20b+25b=690
5b=90
B= 18
18+c=30
C=12
Write an equation of the line that is perpendicular to the line
2x+5y=-15 and contains the point (-8,3)
Welcome to Gboard clipboard, any text you copy will be saved here.Welcome to Gboard clipboard, any text you copy will be saved here.Welcome to Gboard clipboard, any text you copy will be saved here.Welcome to Gboard clipboard, any text you copy will be saved here.
Solve this equation: 80 = 3y + 2y + 4 + 1. O A. y = ¹1/5 O B. y = 75 O C. y = 15 O D.y = -15
Answer:
C. y= 15
Step-by-step explanation:
Add 3y +2y = 5y
Add 4+1=5
Subtract 80 -5 =75
Then divide by 5y on both sides to get
y=15
Given vector u equals open angled bracket 8 comma negative 6 close angled bracket and vector v equals open angled bracket negative 5 comma 2 close angled bracket comma what is v − u?
Answer:
<-13, 8>
Explanation:
Given vectors u and v below:
[tex]\begin{gathered} u=\langle8,-6\rangle \\ v=\langle-5,2\rangle \end{gathered}[/tex]In order to evaluate v-u, subtract the corresponding elements as follows:
[tex]\begin{gathered} v-u=\langle-5,2\rangle-\langle8,-6\rangle \\ =\langle-5-8,2-(-6)\rangle \\ =\langle-13,2+6\rangle \\ v-u=\langle-13,8\rangle \end{gathered}[/tex]The third option is correct.
$Write the following phrase as an algebraic expression. Use y for theunknown."A number times 9"
Given the following phrase:
[tex]\text{A number times 9}[/tex]Let the number = y
The word times means to use the product process
So, the algebraic expression will be as follows:
[tex]9y[/tex]#3 list the angles of each triangle in order from smallest to biggest
Statement Problem: (3)
List the angles of the triangle in order from smallest to largest.
Solution:
First, let's use the Cosine Rule to find the angle B;
[tex]\begin{gathered} b^2=a^2+c^2-2ac\cos B \\ 2ac\cos B=a^2+c^2-b^2 \\ \cos B=\frac{a^2+c^2-b^2}{2ac} \end{gathered}[/tex]Where;
[tex]\begin{gathered} a=3,b=2.9,c=3.1 \\ \cos B=\frac{3^2+3.1^2-2.9^2}{2(3)(3.1)} \\ \cos B=\frac{9+9.61-8.41}{18.6} \\ \cos B=\frac{10.2}{18.6} \\ \cos B=0.5484 \\ B=\cos ^{-1}(0.5484) \\ B=56.74 \\ B=57^o \end{gathered}[/tex]Also, let's use the Cosine Rule to find the angle A;
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ \cos A=\frac{b^2+c^2-a^2}{2bc} \end{gathered}[/tex][tex]\begin{gathered} \cos A=\frac{2.9^2+3.1^2-3^2}{2(2.9)(3.1)} \\ \cos A=\frac{8.41+9.61-9}{17.98} \\ \cos A=\frac{9.02}{17.68} \\ A=\cos ^{-1}(0.5102) \\ A=59.32 \\ A=59^o \end{gathered}[/tex]Lastly, let's use the sum of angles in a triangle theorem to get the third angle, Angle C;
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^o \\ \angle C=180^o-59^o-57^o \\ \angle C=64^o \end{gathered}[/tex]Hence, the angles of the triangle from the smallest to the largest are;
[tex]\angle B,\angle A,\angle C[/tex]Angle B,
Angle A,
Angle C
Damin works 32 hours per week and earns 10.75 per hour
Answer:
32 • 10.75 = $344
Step-by-step explanation:
IF the question is asking how much they earned in 32 hours then your answer is $344. Its simple really, they already gave you the "unit rate" so you're all good 2 go. Good luck
(6.8 x 10^4)+(2.3 x 10^4) as a scientific notation?
We have the fortune that the power of ten is equal in both adding up. So
[tex]6.8\cdot10^4+2.3\cdot10^4=9.1\cdot10^4[/tex]Because the integer before the dot is less than 10, we need not do modifications and our answer is 9.1x10^4.
Let f(x) = 2x-1, g(x) = 1
Find (gof) (-3)
The value of gof(-3) is 1.
How are composite functions defined and what are they?
When two functions, f and g, are combined to produce a new function, h, such that h(x) = g(f(x)), this is known as composition in mathematics. In this instance, the function of x is being applied to the function of g. So, in essence, a function is an application of the result of another function.
Mathematically, the composition of g and h indicated by hog: A→C provided by hog(x) = h(g(x)) for every x ∈ A; let g: A→B and h: B→C signify two functions.
Given, f(x) = 2x - 1 and g(x) = 1
Thus, following the available literature,
gof(x) = g(f(x)) = g(2x - 1) = 1
Therefore, gof(-3) = 1 (∵ No variable is present in gof(x))
Therefore, the required value of gof(-3) is gof(-3)=1
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. (15 points) You work at a canning factory that's producing cans for a new brand of soup. You needto decide what size the cans should be. The soup cans can have a radius of either 2 in, 2.5 in, 3 in, or3.5 in. The cans need to hold a volume of exactly 90 in. The company wants the cans to be no morethan 5 inches tall, and it wants the cans to have the greatest lateral surface area possible so it canprint more information on the side of the cans.To solve this problem, you will fill in this table with the surface area and volume of each cylinder:
A can is shaped like a cylinder. The formula to find the volume of a cylinder is
[tex]\begin{gathered} V=\pi r^2h \\ \text{ Where} \\ \text{ V is the Volume} \\ r\text{ is the radius and} \\ h\text{ is the height of the cylinder} \end{gathered}[/tex]Now, you calculate the height that each can should be, given the radius and the volume. For this you can clear at once, the height of the formula shown:
[tex]\begin{gathered} V=\pi r^2h \\ \text{ Divide by }\pi r^2\text{ from both sides of the equation} \\ \frac{V}{\text{ }\pi r^2}=\frac{\pi r^2h}{\text{ }\pi r^2} \\ \frac{V}{\text{ }\pi r^2}=h \end{gathered}[/tex]Then, you have
*Radius = 2in
[tex]\begin{gathered} \frac{V}{\text{ }\pi r^2}=h \\ \frac{90in^3}{\text{ }\pi(2in)^2}=h \\ \frac{90in^3}{\text{ }\pi\cdot4in^2}=h \\ \frac{90in^3}{4\pi in^2}=h \\ \frac{90}{4\pi^{}}in=h \\ 7.2^{}in=h \end{gathered}[/tex]*Radius = 2.5 in
[tex]\begin{gathered} \frac{V}{\text{ }\pi r^2}=h \\ \frac{90in^3}{\text{ }\pi(2.5in)^2}=h \\ \frac{90in^3}{\text{ }\pi\cdot6.25in^2}=h \\ \frac{90in^3}{6.25\pi in^2}=h \\ \frac{90^{}}{6.25\pi}in=h \\ 4.6in=h \end{gathered}[/tex]*Radius = 3 in
[tex]\begin{gathered} \frac{V}{\text{ }\pi r^2}=h \\ \frac{90in^3}{\text{ }\pi(3in)^2}=h \\ \frac{90in^3}{\text{ }\pi9in^2}=h \\ \frac{90in^3}{9\pi in^2}=h \\ \frac{90}{9\pi}in=h \\ 3.2in=h \end{gathered}[/tex]*Radius = 3.5 in
[tex]\begin{gathered} \frac{V}{\text{ }\pi r^2}=h \\ \frac{90in^3}{\text{ }\pi(3.5in)^2}=h \\ \frac{90in^3}{\text{ }\pi12.25in^2}=h \\ \frac{90in^3}{\text{ }12.25\pi in^2}=h \\ \frac{90}{\text{ }12.25\pi}in=h \\ 2.3in=h \end{gathered}[/tex]Then, the table filled out with the radii, heights, and volumes of the cans would be:
Now, you can calculate the lateral surface area of each can using this formula:
[tex]\begin{gathered} \text{ Lateral Surface Area }=2\pi rh \\ \text{ Where} \\ r\text{ is the radius and} \\ h\text{ is the height of the cylinder} \end{gathered}[/tex]Then, you have
*2 in radius can:
[tex]\begin{gathered} r=2in \\ h=7.2in \\ \text{ Lateral Surface Area }=2\pi rh \\ \text{ Lateral Surface Area }=2\pi(2in)(7.2in) \\ \text{ Lateral Surface Area }=2\pi\cdot14.4in^2 \\ \text{ Lateral Surface Area }=90.5in^2 \end{gathered}[/tex]*2.5 in radius can:
[tex]\begin{gathered} r=2.5in \\ h=4.6in \\ \text{ Lateral Surface Area }=2\pi rh \\ \text{ Lateral Surface Area }=2\pi(2.5in)(4.6in) \\ \text{ Lateral Surface Area }=2\pi\cdot11.5in^2 \\ \text{ Lateral Surface Area }=72.3in^2 \end{gathered}[/tex]*3 in radius can:
[tex]\begin{gathered} r=3in \\ h=3.2in \\ \text{ Lateral Surface Area }=2\pi rh \\ \text{ Lateral Surface Area }=2\pi(3in)(3.2in) \\ \text{ Lateral Surface Area }=2\pi\cdot9.6in^2 \\ \text{ Lateral Surface Area }=60.3in^2 \end{gathered}[/tex]*3.5 in radius can:
[tex]\begin{gathered} r=3.5in \\ h=2.3in \\ \text{ Lateral Surface Area }=2\pi rh \\ \text{ Lateral Surface Area }=2\pi(3.5in)(2.3in) \\ \text{ Lateral Surface Area }=2\pi\cdot8.1in^2 \\ \text{ Lateral Surface Area }=50.6in^2 \end{gathered}[/tex]Then, the table filled out with the radii, heights, lateral surface areas, and volumes of the cans will be:
Therefore, the cans must have a radius of 2.5 inches and a height of 4.6 inches, since they will have a volume of 90 cubic inches, will not exceed 5 inches in height, and will have the maximum possible lateral surface.
Question 20 of 25If AABC is similar to ADEF, the sides of AABC must be congruent to thecorresponding sides of ADEF.OA. TrueOB. False
Given: If triangle ABC is similar to triangle DEF, the sides of triangle ABC must be congruent to the corresponding sides of triangle DEF.
Required: To determine if the given statement is true or false.
Explanation: If two triangles are similar, then their corresponding sides are in equal proportion. So, if triangle ABC is similar to triangle DEF then
[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}[/tex]Final Answer: Option B, False is correct.
Find the equation for the line with slope-= -4 and passing through (-9,40) write your equation in the form y=mx+b
Slope m = Y/X
m = -4
Now find b
b = y - mx
replace now by (-9,40)
b = 40 - (-4)•(-9) = 40 - 36 = 4
Then finally write whole equation
y = -4x + 4
Write the expression with positive exponents only. Then simplify, if possible.
Given:
2^-3
3^-2
By making the expression into positive exponents:
= 1/2^3
1/3^2
The simplifying:
= 1/8
1/9
lets make division into multiplication by turning the numerator
= 1/8 x 9
= 9/8
= 1 1/8 (Being simplified)
PLEASE HURRY ILL GIVE BRAINALIEST!!!
Almost 7 over 16 of the total water supplied to a household is wasted because of leaky faucets. Determine the decimal equivalent of 7 over 16 .
Use words to explain if the decimal terminates or repeats.
Answer:
0.4375
Step-by-step explanation:
Fractions, when the numerator is divided by the denominator, will give the decimal form. Therefore, 7 divided by 16 is 0.4375. It is not a repeating number because the equation doesn't give a repeating number as an answer.
Answer:
0.4375
Step-by-step explanation:
observe
7/16=(((7/2)/2)/2)/2
=((3.5)/2)/2)/2
=(1.75/2)/2
=0.875/2
=0.4375
Sylvia is organizing a small concert as a charity event at her school. She has done a little research and found the expression -10x + 180 represents the number of tickets that will sell at an event given that X represents the price of the ticket. Explain why the income of the event can be represented by the expression -10x^(squared) + 180x. If all the expenses add up to $150, explain why the expression -10x^ +180x-150 represents the profit. Please help. Thank you in advance and I can't make a number squares on this device so ^ is the symbol I used for squares
The income of the event is given by the product of the number of tickets and the price of a ticket.
Hence, the income of the event can be represented by
[tex]\text{ income of the event }=x(-10x+180)=-10x^2+180x[/tex]The income of the event represented by -10x² + 180x
The profit is given by
[tex]\text{ the profit }=(\text{ income of the event) - ( the expenses)}[/tex]Therefore,
[tex]\text{ the profit}=-10x^2+180x-150[/tex]The profit is given by -10x² + 180x - 150
Which are correct representations of the inequality 6x >= 3+ 4(2x - 1)?
First we get rid of the parenthesis on the right side by using the distributive property:
[tex]4\cdot(2x-1)=4\cdot2x-4\cdot1=8x-4[/tex]then, we would have the following equivalent expression:
[tex]\begin{gathered} 6x\ge3+4\cdot(2x-1) \\ \equiv6x\ge3+8x-4 \end{gathered}[/tex]Now we solve for x. First we get all the terms with an 'x' to one side of the inequaility. In this case, we will pass the 8x to the other side with its sign changed:
[tex]\begin{gathered} 6x\ge3+8x-4 \\ \Rightarrow6x-8x\ge3-4 \\ \Rightarrow-2x\ge-1 \end{gathered}[/tex]Since the -2 is multiplying the x, we have to pass it to the other side dividing the -1 but since it's negative, the inequality sign will change:
[tex]\begin{gathered} -2x\ge-1 \\ \Rightarrow x\leq\frac{-1}{-2}=\frac{1}{2} \\ x\leq\frac{1}{2} \end{gathered}[/tex]We have that x <= 1/2, then, the correct representation of the inequality is:
Peaches cost $4 for a 7-pound bag. If grapes cost 15% less per pound and oranges cost 35% more per pound than peaches, which of the following could be the price per pound of grapes and oranges?
A. Grapes are $0.43 per pound and oranges are $0.82 per pound
B. Grapes are $0.48 per pound and oranges are $0.77 per pound
C. Grapes are $0.57 per pound and oranges are $0.77 per pound
D. Grapes are $0.38 per pound and oranges are $0.87 per pound
C. Grapes are $0.48 per pound and oranges are $0.77 per pound.
The cost of grapes and oranges are 0.48 and 0.77 respectively.
Cost word problem
Evaluating cost of solution is simple: You determine the time and money you need to develop and implement it. You're looking at the resources needed. Cost of problem, however, equals the price of doing nothing. That is, for what I know, an important economic principle known from cost-benefit analyses.
Given that Peaches cost $4 for a 7-pound bag, grapes cost 15% less per pound than peaches, oranges cost 35% more per pound than peaches.
Cost of 7 pounds of peaches = 4
Therefore cost of 1 pound of peaches = 4/7 = 0.57
Cost of one pound of grapes = 0.57 - 15% of 0.57
= 0.57 - 0.0855
= 0.4845
= 0.48
Cost of one pound of oranges = 0.57 + 35% of 0.57
= 0.57 + 0.1995
= 0.7695
= 0.77
Therefore Grapes are $0.48 per pound and oranges are $0.77 per pound.
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