The given data shows that in 2000, the population of a country was approximately 6.19 million, and by 2050, it is projected to grow to 10 million. The exponential growth model can be represented as:
A = A0e^{kt}
Where A0 = 6.19 (initial population in 2000), A = 10 (projected population in 2050), T = 50 - 00 = 50 years (time period between 2000 and 2050).
Substituting the values in the formula, we get:
10 = 6.19 e^{k × 50}
Solving for k:
e^{k × 50} = 10/6.19
k × 50 = ln(10/6.19)
k = ln(10/6.19) / 50
k = 0.0169
Therefore, the population of the country will be given by A = 6.19 e^{0.0169t} where t represents the time in years after 2000.
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A box has a base area of 1.1 m2.
The box is placed on the ground and exerts a force of 4.5 kN.
What pressure is the force applied with?
Give your answer in kN/m2 and rounded to 2 dp.
Answer:
To find the pressure that the box exerts on the ground, we need to divide the force by the area of the base:
pressure = force / area
We are given that the force is 4.5 kN and the area is 1.1 m². However, we need to convert the force from kilonewtons to newtons before we can divide by the area:
force = 4.5 kN = 4,500 N
Now we can plug in the values:
pressure = 4,500 N / 1.1 m² = 4,090.91 N/m²
To express the pressure in kilonewtons per square meter, we need to divide by 1,000:
pressure = 4.09091 kN/m²
Rounding to 2 decimal places, we get:
pressure ≈ 4.09 kN/m²
Therefore, the pressure exerted by the box on the ground is approximately 4.09 kN/m².
Monthly salary Is $2332. It is given an Increase of 6. 9%. After the first increase, It rece/ves a second increase of 15%. What Is the
new monthly salary after both increases? Round to the nearest dollar.
The new monthly salary after two increases of 6.9% and 15% is 2867.
The new monthly salary after two increases is calculated as follows:
First Increase:
The initial salary of 2332 increases by 6.9%. This is calculated by multiplying the salary by the percentage increase, i.e. 2332 x 0.069 = 160.68. The new salary after the first increase is 2332 + 160.68 = 2492.68.
Second Increase:
The salary after the first increase of 2492.68 is further increased by 15%. This is calculated by multiplying the salary by the percentage increase, i.e. 2492.68 x 0.15 = 373.90. The new salary after both increases is 2492.68 + 373.90 = 2866.58.
Rounded to the nearest dollar, the new monthly salary after both increases is 2867.
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HELP PLEASE THIS WAS DUE YESTERDAY
MONEY Hans opens a savings account by depositing $1200. The account earns 0.2 percent interest compounded weekly. How much will be in the account in 10 years if he makes no more deposits? Assume that there are exactly 52 weeks in a year, and round your answer to the nearest cent.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1200\\ r=rate\to 0.2\%\to \frac{0.2}{100}\dotfill &0.002\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty two} \end{array}\dotfill &52\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 1200\left(1+\frac{0.002}{52}\right)^{52\cdot 10}\implies A \approx 1224.24[/tex]
Answer: $1248 in compound interest for 10 years
Step-by-step explanation:
The population in the United States between 1930 and 1975 had parameters B = 0. 00004 and c = 1. 9. Use this information to determine an explicit formula for this period
The explicit formula for the population in the United States between 1930 and 1975 is [tex]P(t) = 0.00004t^1.9 + 1[/tex], where t is the number of years after 1930.
To calculate the population for any year between 1930 and 1975, we can simply substitute the corresponding year for t in the equation. For example, if we want to calculate the population in 1950, we can substitute t = 1950 in the equation.
Therefore, [tex]P(1950) = 0.00004(1950)^1.9 + 1 = 0.0035 + 1 = 1.0035[/tex].
This is the population in 1950. In conclusion, the explicit formula for the population in the United States between 1930 and 1975 is [tex]P(t) = 0.00004t^1.9 + 1[/tex], where t is the number of years after 1930.
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the prescriber orders medication f 150 mcg po q.12h. the pharmacy sends a bottle labeled: medication f 0.05 mg/ml. how many milliliters will the nurse administer with each dose?
The nurse will have to administer 3 milliliters with each dose.
When the prescriber orders medication f 150 mcg po q.12h, the pharmacy sends a bottle labeled:
medication f 0.05 mg/ml.
Milliliters will the nurse administer with each dose :
The conversion factor from mcg to mg is 1/1000.
Therefore, 150 mcg = 150/1000 = 0.15 mg.
The nurse has to administer 0.15 mg of medication f per dose.
The medication f available with the pharmacy is 0.05 mg/ml.
So, the nurse has to administer 0.15 mg in a single dose, which is equal to three times the quantity of medication f available in the bottle (0.05 mg/ml).
Therefore, the nurse has to administer 3 ml (0.05 mg/ml × 3 ml) of medication f with each dose.
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2x+ 5y=7
solve for x and y
Answer:
x = 0 y = 7/5
A textbook store sold a combined total of 288 history and chemistry textbooks in a week. The number of chemistry textbooks sold was 72 less than the number of history textbooks sold. How many textbooks of each type were sold?
The number οf histοry bοοks is 180 that sοld in a week. The number οf chemistry textbοοks is 108 sοld in a week.
What is an equatiοn?There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical declaratiοn that illustrates the equality οf twο mathematical expressiοns.
Given that the tοtal number οf bοοks that sοld in a week is 288.
The number οf chemistry textbοοks sοld was 72 less than the number οf histοry textbοοks sοld.
Assume that the number οf histοry textbοοks sοld was x.
The number οf chemistry textbοοks sοld was (x-72)
The tοtal number οf bοοks sοld was x + (x-72) = 2x - 72.
Accοrding tο the questiοn:
2x - 72 = 288
Add 72 frοm bοth sides:
2x - 72 + 72 = 288 + 72
2x = 360
Divide bοth sides by 2:
x = 360/2
x = 180
The number οf histοry textbοοks sοld was 180.
The number οf chemistry textbοοks sοld was (180-72) = 108.
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When the litres are 16 how many litres are 3/4 of the tank capacity?
Answer:
16 litres = 100% of the tank capacity
x litres = 75% of the tank capacity (since 3/4 is equivalent to 75%)
To solve for x, we can cross-multiply and simplify:
16 * 75 = 100x
1200 = 100x
x = 12
Therefore, 3/4 of the tank capacity when the tank holds 16 litres is 12 litres.
Answer:
= 12 liters.
Step-by-step explanation:
16*3/4 =48/4.
= 12
The quantity y varies directly with the square of x and inversely with z. When x is 9 and z is 27, y is 6. What is the constant of variation?
2
9
18
54
y varies directly as x means
[tex]y=kx[/tex]
y varies inversely with z means
[tex]y=k\div z[/tex]
therefore
[tex]y=(kx^2)\div z[/tex]
k=constant of variation
[tex]6=(k9^2)\div 27[/tex]
[tex]6=(k81)\div27[/tex]
[tex]6=3k[/tex]
divide both sides by 3
[tex]2=k[/tex]
the constant of variation is 2
If the quantity y varies directly with the square of x and inversely with z, then we can write the following equation:
What is equation ?
A assertion that two mathematical expressions are equal is known as an equation. It typically consists of variables, constants, and mathematical operations, and it may also include functions, exponents, and other mathematical symbols. Equations are used to represent relationships between quantities in mathematics and to solve problems in various fields such as physics, engineering, and economics.
y = k * (x^2) / z
where k is the constant of variation.
We are given that when x is 9, z is 27, and y is 6. Substituting these values into the equation, we get:
6 = k * (9^2) / 27
Simplifying, we get:
6 = k * 3
k = 6 / 3
k = 2
Therefore, the constant of variation is 2.
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Here is a diagram of a person standing next to a lorry.
The diagram shows two centimetre rulers.
The person and the lorry are drawn to the same scale.
The lorry is approximately 11.2 m in length.
Using the scale diagram, estimate the height of the person in metres.
By using the scale diagram, the height of this person in meters is equal to 1.6 meter.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)
Based on the information provided about the lorry, the lorry is approximately 11.2 m in length and 14 cm on a scale diagram. Therefore, the height of the person in meters can be calculated as follows;
1 centimeter = 11.2/14
1 centimeter = 0.8 meter.
Height of the person in meters = 0.8 meter × 2
Height of the person in meters = 1.6 meter.
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Question 4, please help
4/10
Option (a) is correct Mr. Reynolds walks 2000 feet per minute for 8 minute. Here it is the condition of speed.
What is Speed?Speed is define as the distance covered by a person in a given interval or time. It is generally denotes in Km/h or m/sec.
[tex]Speed\ (S)= Distance\ (d) * Time\ (t)[/tex]
Distance, It is an area cover by a person to complete his journey.
Distance is generally denoted by km, m etc,
Time, It is an interval in which generally person complete it task.
It is generally denoted by hour (h), Minute (min) or Second (Sec).
The correct is (a) Mr. Reynolds walks 2000 feet per minute for 8 minute. Here it is the condition of speed.
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(-3+4)2 distributive property and it needs to have work shown
Answer:
2
Step-by-step explanation:
PEMDAS
(-3+4)2
(1)2
2x1=2
Find the surface area of water tower that is 40 feet tall and has a diameter of 30 feet. DO NOT ROUND YOUR ANSWER!
Answer: SA=5183.62788
Step-by-step explanation:
A=2πrh+2πr2=2·π·15·40+2·π·152≈ 5183.62788
~Find the radius- 30 divided by 2= 15 so radius =15
En un salón de clase de 60 alumnos, se tomaron 3 exámenes para aprobar un curso y se
observó que los que aprobaron un solo examen es el quíntuple de los que aprobaron los
3 exámenes y los que aprobaron sólo 2 exámenes es el triple de los que desaprobaron
los 3 exámenes. Si el número de los que desaprobaron los 3 exámenes es igual al número
de los que aprobaron los 3 exámenes, cuántos aprobaron el curso si para aprobarlo es
necesario que aprueben por lo menos 2 exámenes?
Translate: In a classroom of 60 students, 3 exams were taken to pass a course and
He noted that those who passed a single exam were five times those who passed the
3 exams and those who passed only 2 exams is triple those who failed
the 3 exams. If the number of those who failed the 3 exams is equal to the number
Of those who passed the 3 exams, how many passed the course if to pass it is
Do they need to pass at least 2 exams?
The number of students who passed the course is x + 3y, where x is smallest integer greater than or equal to[tex](180 - 3z)/53[/tex], and y = [tex](60 - 7x)/3[/tex] for equal things.
Let's use some variables to represent the number of students who passed each exam:
Let's call the number of students who passed all 3 exams "x".
Let's call the number of students who passed exactly 2 exams "3y" (since it's given that this number is triple the number who failed all 3 exams).
Let's call the number of students who passed exactly 1 exam "5x" (since it's given that this number is five times the number who passed all 3 exams).
Finally, let's call the number of students who failed all 3 exams "x".
We can use this information to set up a system of equations:
x + 3y + 5x + x = 60 (since there are 60 students in total)
x = x (since the number who failed all 3 exams is equal to itself)
Simplify:
7x + 3y = 60
Now we need to use the fact that passing at least 2 exams is required to pass the course. This means we need to find the number of students who passed at least 2 exams, which is the sum of the number who passed all 3 exams and the number who passed exactly 2 exams:
x + 3y
We know that this number needs to be greater than or equal to the number of students who pass the course. So we set up another equation:
x + 3y >= z (where z is the number of students who pass the course)
Now we can solve for x and y in terms of z. We'll start with y:
7x + 3y = 60
3y = 60 - 7x
y = (60 - 7x)/3
Next, we'll use the fact that the number who failed all 3 exams is equal to the number who passed all 3 exams:
x = x
Finally, we'll use this information to solve for x in terms of z:
x + 3y >= z
x + 3((60 - 7x)/3) >= z
x + (60 - 7x) >= 3z
53x >= 180 - 3z
x >= (180 - 3z)/53
Since x represents the number of students who passed all 3 exams, we want to round it up to the nearest integer (since we can't have a fractional number of students). So the final answer is:
The number of students who passed the course is x + 3y, where x is the smallest integer greater than or equal to (180 - 3z)/53, and y is given by y = (60 - 7x)/3.
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How to write the correct solution of 5a^2-25b^×
The correct solution of the expression 5a² -25bˣ is 5(a² - 5bˣ)
How to determine the correct solution of the expressionFrom the question, we have the following parameters that can be used in our computation:
5a² -25bˣ
The expression is already in its simplest form in terms of combining like terms.
However, we can still look into factoring the expression
To do this, we can factor out the greatest common factor of 5 and rewrite the expression as follows:
5a² -25bˣ = 5(a² - 5bˣ)
This is the factored form of the expression, where the greatest common factor of 5 has been factored out.
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i was wondering if someone could help me with this problem I would appreciate it greatly
The median increases by 0.5 and the mean decreases by 4.375
What are median and mean?
Median and mean are measures of central tendency that are commonly used in statistics. The median is the middle value in a sorted list of numbers. To find the median, you need to arrange the numbers in order from lowest to highest (or highest to lowest) and then find the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers. The mean is the average of all the numbers in a list. To find the mean, you need to add up all the numbers in the list and then divide by the total number of values. It is calculated by summing up all the values and dividing the result by the total number of values. The mean is influenced by outliers and extreme values in the data.
(a) The median is the middle value in a sorted list of numbers. In the original list, the median is 547. If the number 605 is changed to 549, then the new list becomes:
381, 465, 496, 537, 547, 589, 604, 549
Now the median is the average of the two middle values, which are 547 and 549. Therefore, the median increases by:
(549 + 547)/2 - 547 = 0.5
So, the median increases by 0.5.
(b) The mean is the average of all the numbers in a list. In the original list, the mean is:
(381 + 465 + 496 + 537 + 547 + 589 + 604 + 605) / 8 = 527.5
If the number 605 is changed to 549, then the new list becomes:
381, 465, 496, 537, 547, 589, 604, 549
The mean of this new list is:
(381 + 465 + 496 + 537 + 547 + 589 + 604 + 549) / 8 = 523.125
Therefore, the mean decreases by:
527.5 - 523.125 = 4.375
So, the mean decreases by 4.375
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(d) Find the value of k for which the vertex of the parabola y=x2+kx+9 lies on the line x=−3. (e) Find the value of k for which the vertex of the parabola y=kx2+3x+4 lies on the line x=3
(d) The value of k for which the vertex of the parabola y=x2+kx+9 lies on the line x=−3 is 6. (e) The value of k for which the vertex of the parabola y=kx2+3x+4 lies on the line x=3 is -2.
(d) k=6 (e) k=-2
The vertex form of a quadratic function is given as;
f(x) = a(x-h)² + kf(x) = a(x−h)²+k, with vertex (h, k)
∴ for the quadratic equation y=x²+kx+9, the vertex is given by;
x = -b/2a = -k/2 ∴ k = -2x, using x=-3k = -2x = 6,
thus the vertex of the parabola y=x²+6x+9 lies on line x = -3
(e) Similarly, for the quadratic equation y=kx²+3x+4, the vertex is given by;
x = -b/2a = -3/2k ∴ k = -2x/3, using x=3k = -2x/3 = -2(3)/3 = -2,
thus the vertex of the parabola y=-2x²+3x+4 lies on the line x = 3
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A graph comparing the points (x) to the amount of money earned (y) in a minor football league is given by y=200x+500. What is the gradient?
The gradient of the line is 200, hence that is the answer.
What does the word "point" actually mean?
A point is a dot on a sheet of paper or in a plane. There are no lengths, widths, or heights in a point. It establishes a plane's position or location. To make a point, mark a dot on a piece of paper with an A or another capital letter.
The slope-intercept version of the equations y = 200x + 500 is y = mx + b, wherein m is the line's gradient and b is its y-intercept.
The value of x, which really is 200, acts as the gradient (or gradient) in this equation. As a result, the line's gradient is 200.
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The range of values of x for which the inequality 0 less than or equal to x less than 6
The range of values of x that satisfy the inequality 0 ≤ x < 6 is the set of all real numbers between 0 (inclusive) and 6 (exclusive), i.e., the interval [0, 6).
The inequality 0 ≤ x < 6 can be interpreted as follows: x can take on any value between 0 and 6, including 0 but not including 6. This means that x can be any number greater than or equal to 0 and less than 6. In other words, the range of values for x that satisfy this inequality is the set of all real numbers in the interval [0, 6), where the square bracket indicates that 0 is included in the interval (i.e., 0 is a valid value of x) and the round bracket indicates that 6 is excluded from the interval (i.e., 6 is not a valid value of x). This interval can be visualized as a number line with a closed circle at 0 and an open circle at 6, indicating that 0 is included in the range of values for x but 6 is not.
Therefore, any value of x between 0 and 6 (excluding 6) satisfies the inequality 0 ≤ x < 6.
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find the probability of selecting a black checker from a bag of 6 black and 4 red checkers, replacing it and selecting another black
The probability of selecting a black checker from a bag of 6 black and 4 red checkers, replacing it, and selecting another black is 9/25.
To find the probability follow these-
Determine the probability of selecting a black checker on the first draw.
There are 6 black checkers and a total of 10 checkers (6 black + 4 red).
So, the probability of selecting a black checker on the first draw is 6/10,
which can be simplified to 3/5.
Since the black checker is replaced, there are still 6 black checkers and
a total of 10 checkers in the bag. Therefore, the probability of selecting a
black checker on the second draw is also 3/5.
To find the probability of both events occurring, multiply the probabilities together: (3/5) × (3/5) = 9/25.
So, the probability of selecting a black checker from a bag of 6 black and
4 red checkers, replacing it, and selecting another black is 9/25.
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PLEASE HELP THANK YOU The cuboid-shaped container below is partly filled with water. What percentage of the container is filled with water? Give your answer to 1 d.p. please see attachment!
Answer:
The volume of the container is 1872 cubic cm. The volume of the water is 672 cubic cm.
Therefore, 672/1872 = 0.36 or 36%
A carpet is placed in the middle of a room 15m long and 12m broad so that it leaves a uniform width of 1m around it . find the area and the cost of the carpet at Rupee 500 square meter
Answer:
[tex]130m^{2}[/tex] , [tex]65.000 rs[/tex]
Step-by-step explanation:
Given Length = 15m
Given Breadth = 12m
Since there is a 1m gap between the sides,
Actual Length = 15 - 2 = 13m
Actual Breadth = 12 - 2 = 10m
From here find the Area:
L * B = AR of a cuboid , so
13 x 10 = [tex]130m^{2}[/tex] is the Area
for every [tex]m^{2}[/tex] it is 500 rupees, so for [tex]130m^{2}[/tex] ,
130 * 500 = 65,000 rupees.
st Common Factor and Factoring Find the greatest common factor for the list of monomials. x^(3)y^(5)z^(3),y^(3)z^(3),xy^(3)z^(2) The GCF is
[tex]y^(3)z^(2)[/tex] is the greatest common factor for the given set of monomials.
The highest power of each variable that is shared by all of the given monomials must be identified in order to calculate the greatest common factor (GCF) for the given list of monomials. To put it another way, we must first determine the prime factors of each monomial before determining the factors that are shared by all the monomials.
Prime factorization for each monomial:
[tex]x^(3)y^(5)z^(3) = (x * x * x) * (y * y * y * y * y) * (z * z * z)y^(3)z^(3) = (y * y * y) * (z * z * z)xy^(3)z^(2) = (x) * (y * y * y) * (z * z)[/tex]
Factors are common to all monomials are [tex]y^(3), z^(2)[/tex]. The GCF is [tex]y^(3)z^(2)[/tex].
This is appropriate GCF by dividing each monomial by [tex]y^(3)z^(2)[/tex] and verify that result is whole number. For eg:
[tex]x^(3)y^(5)z^(3) / (y^(3)z^(2)) = x^(3)y^(2)zy^(3)z^(3) / (y^(3)z^(2)) = yzxy^(3)z^(2) / (y^(3)z^(2)) = x/y[/tex]
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A+B=25, A^2+B^2= 225 FIND AB
Answer:200
Step-by-step explanation:
A+B=25
A^2+B^2= 225
we use short multiplication formulas:
(A+B)^2=A^2+B^2+2AB
and solve the equation
25^2=225+2AB
625=225+2AB
625-225=2AB
400=2AB
AB=200
Speed, Velocity, and Acceleration Escape Room.
Enter the correct 4 digit code (no spaces level 4
Based on the information in the image, we can infer that the correct four-digit code is: 4321
How to find the four-digit secret code?To find the four-digit secret code we must observe the image carefully, especially the intertwined lines. What we must do is follow the direction of the lines in the order from A to D to identify which number the line of each letter matches.
According to the above we can infer that the lines of each letter coincide in the following way with the numbers:
A-4B-3C-2D-1So according to the image, the four-digit secret code would be 4321.
Note: This question is incomplete. Here is the complete information:
Attached image
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Please help me on this
The criteria that we could use to prove the congruency that ΔABC ≅ ΔDEC is;
Vertical Angles are Congruent. We could then use AAS to prove that ΔABC ≅ ΔDEC
How to find the Triangle Congruence Postulate?There are different triangle congruency postulates namely:
SSS: Side Side Side Congruency Postulate
SAS: Side Angle Side Congruency Postulate
ASA: Angle Side Angle Congruency Postulate
AAS: Angle Angle Side Congruency Postulate
HL: Hypotenuse Leg Congruency Postulate
We want to prove that ΔABC ≅ ΔDEC
Now, from the given image, we see that we are given 2 congruent sides.
However, angle ECD is congruent to angle DCA because they are vertically opposite angles and vertical angles are congruent.
Thus, the triangles are congruent by AAS Congruency postulate.
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Now imagine the quadrilateral is the base of a prism that has a height of h
units. What is the volume of this prism compared to the one with a height of 1
unit? The volume of the prism is Bh, which is h times the volume
V of the
original prism.
right prism
The volume of the prism with height h is h times the volume of the prism with height 1 unit.
If the original prism has a volume of V and a height of 1 unit, then the volume of the prism with height h is given by:
Bh = (V)(h)
where B is the area of the quadrilateral base.
The volume of the prism with height h is h times the volume of the original prism. So, we can compare the volume of the two prisms by looking at their volume ratios:
Volume ratio = Volume of prism with height h / Volume of original prism
= Bh / (V)(1)
= Bh / V
= h
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The following table shows the dirstribution of marks in mathematics
Marks (less than) No.of students
10 7
20 28
30 54
40 71
50 84
60 105
70 147
80 180
With the help of the graph paper, taking 2cm=10units
along one axis and 2cm=20units along the other axis, plot an ogive for the above distribution and use it to find the
a)Median
b)Number of students who scared distinction marks (75% and above)
c)Number of students who passed the examination if pass mark is 35%
The number of students who passed the examination is 152.
How to solveGiven: Marks distribution in Mathematics
To Find: Plot an ogive, the median, the number of students who scored distinction marks (75% and above), and the number of students who passed the examination if the pass marks are 35%.
Solution:
Marks Number of students
Less than 10 7
Less than 20 28
Less than 30 54
Less than 40 71
Less than 50 84
Less than 60 105
Less than 70 147
Less than 80 180
Ogive:
An ogive is a graph that represents the cumulative frequency distribution of a set of data. To plot an ogive, we plot the upper limits of each class on the x-axis and the corresponding cumulative frequency on the y-axis. We then join the points with a free-hand smooth curve to obtain the ogive.
Median:
To find the median from the graph, we draw a line from the value of 50 on the y-axis to the ogive curve and then drop it down to the x-axis. The point where the line intersects the x-axis gives us the median. In this case, the approximate median value from the graph is 52.
The number of students who scored distinction marks:
To find the number of students who scored distinction marks (75% and above), we first calculate 75% of the total number of students, which is 0.75 x 180 = 135.
From the ogive graph, we see that the number of students who scored less than 75% marks is 105.
Therefore, the number of students who scored 75% or more marks is 180 - 105 = 75.
The number of students who passed the examination:
To find the number of students who passed the examination if the pass marks are 35%, we first calculate 35% of the total number of students, which is 0.35 x 180 = 63.
From the ogive graph, we see that the number of students who scored less than 35% marks is 28.
Therefore, the number of students who passed the examination is 180 - 28 = 152.
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5. Diego is building a fence for a rectangular garden. It needs to be at least 10 feet
wide and at least 8 feet long. The fencing he uses costs $3 per foot. His budget is
$120. He wrote some inequalities to represent the constraints in this situation:
1) f = 2x + 2y
2) x ≥ 10
3) y ≥ 8
4) 3f ≤ 120
a. Explain what each equation or inequality represents.
The following items were bought on sale.Complete the missing information in the table.Be sure to specify which answer box you are answering.Also show how you got to these numbers.
1) In the first line item - the Sales Price, Percent Saved and Percent Paid are given.
To work out the Original Price, we can state that: if 20% off the value of x = 800 what is x, (where x is the Original Price)?
If 20% is taken off the value of x, we need to find the original value of x before the discount was applied. We can set up the following equation:
x - 20% of x = 800
Simplifying by factoring out x on the left side, we get:
x * (1 - 20%) = 800
Converting 20% to a decimal, we get:
x * (1 - 0.20) = 800
Simplifying, we get:
x * 0.80 = 800
Dividing both sides by 0.80, we get:
x = 1000
Therefore, the original value of x before the 20% discount was applied is $1000.
Since the Original price is $1000, and the Sales price is $800, that means the Amount of Discount ($) is:
Original Price - Sales Price
= $1,000 - $800
= $200
Thus, the discount value for the Television is $200and the original price is $1000.
2) With regard to the sneakers, Original Price was $80 and the percent saved is 25%.The percentage saved is 75%.
Thus, the Sales Price = Original Price - (Original Price * Percent Saved)
Sales Price = 80 - (80 * 25%)
Sales Price = 80 - 20
Sales Price = $60
Since $20 was removed form the Original Price, that means the Amount of Discount ($) is $20.
3)
For the Video Game, we know the Sales Price and the Percent Paid, which is 90%.
That means $54 = 90% of x, where x is the Original Price.
To find x,
54 = 0.9x
x = 54/0.9
x (Original Price) = $60
Thus, the Original Price of the Video Game is $60.
Since Original Price = $60; and
Sales Price = $54
Amount discounted = Original Price - Sales Price
Amount discounted = 60-54
Amount discounted = $6
As a percentage of the Original Price $6 is: 6/60 * 100
= 10%
4) For the MP3 player, we know that that the Sales Price = $51.60 which is 60% (Percent Paid) of the Original Price. We also know that the Percent saved is 40% of the Original price.
Thus, if $51.6 is 60% of the original price, we can use the following proportion to find the original price:
60% = $51.6 / original price
To solve for the original price, we can isolate it by multiplying both sides by the reciprocal of 60%, which is 100% / 60%, or 5 / 3:
original price = $51.6 / (60%)
original price = $51.6 / (0.60)
original price = $86
Therefore, the original price before the 60% reduction was $86.
Amount of Discount = Original Price - Sales Price
= 86 - 51.6
= $34.4
Thus, Original Price and Amount of Discount for the MP3 Player are $86.00 and $34.40 respectively.
5)
For the book, we know that the Amount of Discount is $2.60 which is 80% (Percent Paid) of the Original Price.
If $2.6 is 20% of the original price, we can use the following proportion to find the original price:
20% = $2.6 / original price
To solve for the original price, we can isolate it by multiplying both sides by the reciprocal of 20%, which is 100% / 20%, or 5:
original price = $2.6 / (20%)
original price = $2.6 / (0.20)
original price = $13
Therefore, the original price before the 20% reduction was $13.
Since Original price = $13 and Discount given is $2.60, Thus,
Sales Price = Original Price - Discount Given
Sales Price = 13- 2.60
Sales Price = $ 10.40
Note that the percentage saved (discount) =
2.6/13 * 100
= 20%
Thus, the Percentage Saved = 20%.
6)
For the Snack Bar, we know that the Sales Price is $1.70 and the Amount of Discount is $0.30. This means that the Original Price =
Sales Price + Discount Given = 1.7 + 0.3
Original Price = $2.00
To find what percent 0.3 is of 2, we can use the following proportion:
x/100 = 0.3/2
where x is the percent we want to find.
To solve for x, we can cross-multiply and simplify:
2x = 30
x = 15
Therefore, $0.3 is 15% of $2 which is the percent saved.
If the percent saved is 15%, then the percent paid is:
100 - 15
= 85%
Thus, the percent paid is 85% of the Original Price.
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