A scatter plot shows the association between two variables.
If the variables tend to increase and decrease together, the association is positive. If one variable tends to increase as the other decreases, the association is negative. If there is no pattern, the association is zero.
From the graph we notice that in this case both variables increcase together, therefore the scatter plot has a positive association.
Please show me how to solve this step by step im really confused
Given
[tex]-16t^2+v_0t+h_0[/tex]initial velocity = 60 feet per second
initial height = 95 feet
Find
Maximum height attained by the ball
Explanation
we have given
[tex]\begin{gathered} h(t)=-16t^2+60t+95 \\ h^{\prime}(t)=-32t+60 \end{gathered}[/tex]put h'(t) = 0
[tex]\begin{gathered} -32t+60=0 \\ -32t=-60 \\ t=\frac{60}{32}=1.875sec \end{gathered}[/tex]to find the maximum height find the value of h(1.875)
[tex]\begin{gathered} h(1.875)=-16(1.875)^2+60(1.875)+95 \\ h(1.875)=-56.25+112.5+95 \\ h(1.875)=-56.25+207.5 \\ h(1.875)=151.25 \end{gathered}[/tex]Final Answer
Therefore , the maximum height attained by the ball is 151.25 feet
lily ordered a set of green and brown pin.she received 35 pins, and 80% of them were green.How many green pins did lily receive?
In total there are 35 pins so that correspound to the 100%, so we can use a rule of 3 to solve it so:
[tex]\begin{gathered} 35\to100 \\ x\to80 \end{gathered}[/tex]So the equation is:
[tex]x=\frac{35\cdot80}{100}=28[/tex]So there are 28 green pins
May I please get help with this. For I have tried many times but still could not get the rotation correct
Let us write out the coordinates of the parent image given
Let us name the triangle ABC
[tex]\begin{gathered} A\rightarrow(1,5) \\ B\rightarrow(-3,2) \\ C\rightarrow(-5,4) \end{gathered}[/tex]Therefore, the rule for the rotation 90 degrees counterclockwise about the origin is,
[tex]A(x,y)\rightarrow A^{\prime}(-y,x)[/tex]Let us now obtain the coordinates of the transformed image
[tex]\begin{gathered} A(1,5)\rightarrow A^{\prime}(-5,1) \\ B(-3,2)\rightarrow B^{\prime}(-2,-3) \\ C(-5,4)\rightarrow C^{\prime}(-4,-5) \end{gathered}[/tex]Hence, the coordinates of the transformed image are
[tex]\begin{gathered} A^{\prime}(-5,1) \\ B^{\prime}(-2,-3) \\ C^{\prime}(-4,-5) \end{gathered}[/tex]Let us now plot the transformed image
1 point Esther thinks she understands how to find the midpoint of a segment on a graph. "I always look for the middle of the line segment. But what should I do if the coordinates are not easy to graph?" she asks. Find the midpoint of KL if (2.125) and L(98, 15). *
In this case, we can write out the parameters
[tex]\begin{gathered} x_1=2,_{}y_1=125, \\ x_2=98,y_2=15 \end{gathered}[/tex]Thus, substitute the coordinates in the mid-point formula and simplify
[tex]\begin{gathered} x_m=\frac{98+2}{2}=\frac{100}{2}=50 \\ y_m=\frac{125+15}{2}=\frac{140}{2}=70 \end{gathered}[/tex]Hence, the coordinate of the mid-point is (50, 70)
Find the time it would take for the general level of prices in the economy to double at an average annual inflation rate of 4%. The doubling time is aboutyears.
The doubling time for the general price levels in the eonomy given the average annual inflation rate is 18 years.
What is the doubling time?Inflation is a period where the general price levels in an economy rise persistently. When there is an inflation, the prices of goods and services increase. Inflation can either be as a result of an increase in the cost of production or an increase in the demand of a good.
The rule of 72 can be used to determine the doubling time. The rule of 72 is a rule of thumb that determines the number of years it would take an investment to double given its rate of growth.
The rule of 72 = 72 / inflation rate
72 / 4 = 18 years
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Quadrilateral PQRS is plotted in the coordinate plane. The quadrilateral is dilated by a scale factor of 3/4. What are the new ordered pairs for P'Q'R'S'?
Explanation:
The first thing is to state the coordinates of Quadrilateral PQRS
P (5, 5), Q (3, 5), R (3, 1), S (5, 1)
Then we find the distance between two points using the distance formula
[tex]dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex][tex]\begin{gathered} P(5,5),Q(3,5)\text{ = (x1, y1) and (x2, y2)} \\ \text{distance PQ = }\sqrt[]{(5-5)^2+(3-5)^2}\text{ = }\sqrt[]{0+(-2)^2}\text{ =}\sqrt[]{4} \\ \text{distance PQ = }2 \end{gathered}[/tex][tex]\begin{gathered} Q(3,5),R(3,1)\text{= (x1, y1) and (x2, y2)} \\ \text{distance QR = }\sqrt[]{(1-5)^2+(3-3)^2}\text{ = }\sqrt[]{(-4)^2+0}\text{ = }\sqrt[]{16} \\ \text{distance QR = 4} \end{gathered}[/tex]It is a quadrilateral, meaning the two lengths are equal. Like wise the two widths are equal.
length PQ = length SR = 2
Length QR = length PS = 4
Scale factor = 3/4
Scale factor = corresponding side of new image/ corresponding side of original image
PQRS = original image, P'Q'R'S' = new image
3/4 = P'Q'/PQ
3/4 = P'Q'/2
P'Q' = 2(3/4) = 6/4 = 3/2
Since P'Q' = S'R'
S'R' = 3/2
3/4 = Q'R'/QR
3/4 = Q'R'/4
Q'R' = 3/4 (4) = 12/4 = 3
Since Q'R' = P'S
P (5, 5), Q (3, 5), R (3, 1), S (5, 1)
PQRS to P'Q'R'S' = 3/4(
P' = 3/4 (5, 5) = (15/4, 15/4)
Q' = 3/4 (3, 5) = (9/4, 15/4)
R' = 3/4 (3, 1) = (9/4, 3/4)
S' = 3/4 (5, 1)
A local road has a grade of 5%. The grade of a road is its slope expressed as a percent. What is the slope? What is the rise? What is the run?
a) Since the grade is given by the slope, and the grade has a 5%.
We can rewrite it as a fraction, like this:
[tex]\frac{5}{100}=\frac{1}{20}[/tex]Note that we have simplified this to 1/20 by dividing the numerator and the denominator (bottom number) by 5
So, the slope is:
[tex]\frac{1}{20}[/tex]b) The "rise" is the difference between two coordinates on the y-axis and the "run" is the subtraction between two coordinates on the x-axis. Let's remember the slope formula and the Cartesian plane:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{1}{20}[/tex]So the "rise" for this grade is 1 foot and the run is 20 feet.
3) Hence, the answers are:
[tex]\begin{gathered} a)\text{ }\frac{1}{20} \\ b)\text{ }Rise\colon\text{ }1\text{ Run: 20} \end{gathered}[/tex]Is y-x+wz=5 linear? And not, why and if so, can you put it in slope intercept form?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of this kind of equation is given by:
[tex]Ax+By=C[/tex]For the equation:
[tex]y-x+wz=5[/tex]We can conclude is not a linear equation since there is a product between two variables.
Reba is playing on the slide. Over and over, she climbs the 9-foot ladder, goes down the slide, and walks 3 feet to get back to the ladder. How far does Reba travel each time she repeats this process? If necessary, round to the nearest tenth.
we have
then find c
[tex]\begin{gathered} c^2=3^2+9^2 \\ c^2=9+81 \\ c^2=90 \\ c=\sqrt[]{90} \\ c=3\sqrt[]{10} \end{gathered}[/tex]therefore the distance is:
[tex]9+3\sqrt[]{10}+3=21.5[/tex]answer: 21.5 ft
Express the interval using inequality notation(1,6)
The interval (1, 6) contains all the real numbers between 1 and 6, not including any of the endpoints.
This can be written in inequality notation as:
x >1 AND x < 6
But there is a shorter way to write the interval by combining both inequalities:
1 < x < 6
Multiply.(2x + 4)(2x - 4)A. 4x2 + 16x- 16B. 4x2 - 16C. 4x2 - 16x - 16D. 4x2 + 16
We have to multiply the expression (2x + 4)(2x - 4):
[tex]\begin{gathered} \left(2x+4\right)\left(2x-4\right) \\ 2x\cdot2x+2x\cdot(-4)+4\cdot2x+4\cdot(-4) \\ 4x^2-8x+8x-16 \\ 4x^2+(8-8)x-16 \\ 4x^2-16 \end{gathered}[/tex]The answer is:
B. 4x^2 - 16
I got 4089 for the answer but it was incorrect
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
50 gramos de pechuga de un pollo contiene 10.4 g de proteínas, 0.5 g de carbohidratos y 1.6 g de grasas. Los valores medios de energía alimentaria de esas sustancias son de 4.0 kcal/g para las proteínas y los carbohidratos, y de 9.0 kcal/g para las grasas. a) Al jugar baloncesto, una persona representativa consume energía a una potencia de 420 kcal/h. ¿Cuánto tiempo debe jugar para “quemar” esa pechuga?
Tenemos lo siguiente:
Lo primero es calcular las kilocalorías para las proteínas y para los carbohidratos y grasas, de la siguiente día:
[tex]\begin{gathered} \text{Protenas} \\ 10.4\text{ g}\cdot4\frac{\text{ kcal}}{g}=41.6\text{kcal} \\ \text{Carbohidratos} \\ 0.5\text{ g}\cdot4\frac{\text{ kcal}}{g}=2\text{kcal} \\ \text{Grasas} \\ 1.6\text{ g}\cdot9\frac{\text{ kcal}}{g}=14.4\text{kcal} \end{gathered}[/tex]Ahora sumamos todas las kilocalorías y nos queda lo siguiente:
[tex]41.6+2+14.4=58[/tex]Es decir que en total en los 50 gramos de pechuga hay en total de 58 kilocalorías, ahora debemos calcular el tiempo dividiendo el numero de kilocalorías por la cantidad de consumo de kilocalorías al jugar baloncesto
[tex]\frac{58\text{ kcal}}{420\text{ kcal/h}}=0.138\text{ h}[/tex]Es decir que debe jugar 0.138 horas o un total de:
[tex]0.138\text{ h}\cdot\frac{60\text{ min}}{1\text{ h}}=8.28\text{ min}[/tex]Es decir que debe jugar 8.28 minutos
Suppose you want to have $ 749,791 for retirement in 13 years. Your account earns 9.5 % interest monthly. How much interest will you earn?$_________ (Round to the nearest DOLLAR)
ANSWER
$530,663
EXPLANATION
The amount the account will have in t years is given by,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where n = 12, t = 13 years, r = 0.095 and A = 749,791. We have to find P,
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Replace with the values and solve,
[tex]P=\frac{749,791}{(1+\frac{0.095}{12})^{12\cdot13}}\approx219,128[/tex]The interest earned is the difference between the initial deposit P and the final amount A,
[tex]i=A-P=749,791-219,128=530,663[/tex]Hence, the interest earned would be $530,663.
Charlene and Gary want to make perfume. In order to get the right balance of ingredients for their tastes they bought 2ounces of rose oil at $4.36 per ounce, 5 ounces of ginger essence for $2.15 per ounce, and 4 ounces of black currant essence for $2.27 per ounce. Determine the cost per ounce of the perfume.
First, lets calculate how much the expended in the perfume:
[tex]2\times(4.36)+5\times(2.15)_{}+4\times(2.27)=28.55[/tex]So, for 11 ounces of perfume, they need $28.55, so the minimum that the perfume need to cost per ounce is:
[tex]\frac{28.55}{11}=2.5954\cong2.6[/tex]So, about $2.6 per ounce of perfume.
Find the domain of the function. Write the domain in interval notation.
The domain of a function is the possible values of "t" that the given function can take.
Since the variable "t" is in the denominator, the denominator cannot be equal to zero because it would make the function undefined.
Hence, t - 4 must be greater than zero. For t - 4 to be greater than zero, the value of t must be greater than 4.
In addition, since the variable is inside the radical sign, then the function itself cannot be negative.
Hence, the domain of this function must be greater than 4. In interval notation, it is (4, ∞).
Identify the type(s) of symmetry for the graph below.Select all that apply. aSymmetry with respect to the line \small \theta=\frac{\pi}{2} bSymmetry with respect to the polar axis cSymmetry with respect to the pole
The line θ=π/2 is the vertical line in the polar grid, the polar axis is the horizontal line and the pole is the center of coordinates. Now let's analyze the symmetries:
If the grpah is symmetric with respect to θ=π/2 then the graph at the left of this line has to be the mirrored image of the graph at the right side. This is the case of this graph so it does have symmetry with respect to θ=π/2.
For the polar axis is the same, the graph above the axis has to be the mirrored image of that below the axis. However in this case we have two "petals" above the polar axis and one below so the upper part is not the mirrored version of the lower part so it has no symmetry with respect to this axis.
For the pole we must rotate the graph 180°. If the graph remains unchanged then it is symmetric with respect to it. In this case if we rotate the graph 180° the lower petal ends up in the opposite direction so the graph changes after a 180° rotation and it has no symmetry with respect to the pole.
Then the only type of symmetry is with respect to the line θ=π/2 and the answer is option a.
Kuta Software - Infinite Precalculus Angles and Angle Measure Find the measure of each angle.
Explanation:
We are to draw the angle that is equivalent to 5pi/4
First we need to convert the radian value to degree
Since pi rad = 180degrees
5pi/4 = x
Cross multiply
pi * x = 5pi/4 * 180
x = 5/4 * 180
x = 5 * 45
x = 225 degrees
This can also be written as 225 = 180 + 45
225degrees = 180 + pi/4
Note that 180degrees is an angle on a straight line. Find the digaram attached
The remaining angle which is pi/4 is the reason for the angle extensionon for the angle extension
5pi/4 = x
Cross multiply
pi * x = 5pi/4 * 180
x =
Problem Solving: Fraction Division For exercises 1 and 2, write three problem situations for each division 56÷1/3 and 6/1/2÷1/2/3
56÷1/3
We have to model a problem where the solution is 56÷1/3.
So, we take something that is 56 and we have to divide it by 1/3rd.
So, we can say:
George had 56 large cakes.
Giving 1/3rd of each cake to each person is enough.
If George used all of the cake, how many person could he feed?
-14.4 + x = -8.2what does x equal?I NEED ANSWERS ASAPi will give brainliest
the given expression is,
-14.4 + x = -8.2
x = 14.4 - 8.2
x = 6.2
thus, the answer is x = 6.2
Bill Jensen deposits $8500 with Bank of America in an investment paying 5% compounded semiannually. Find the interest in 6 years
Amount deposited = $8500
Rate = 5%
time for interest = 6years
Compounded semiannually
The formula for semiannually is
[tex]A=P(1+\frac{r}{100n})^{nt}[/tex]From the given information
P = $8500
r = 5
t = 6
Since the investment was compounded semiannually then
n = 2
Substitute the values into the formula
This gives
[tex]A=8500(1+\frac{5}{100\times2})^{6\times2}[/tex]Solve for A
[tex]\begin{gathered} A=8500(1+0.025)^{12} \\ A=8500(1.025)^{12} \\ A=11431.56 \end{gathered}[/tex]To find the interest
Recall
[tex]I=A-P[/tex]Where I, is the interest
Hence
[tex]\begin{gathered} I=\text{\$}11431.56-\text{\$}8500 \\ I=\text{\$}2931.56 \end{gathered}[/tex]is H less than 9?[tex]h \leqslant 9[/tex]
3) The given inequality is
[tex]h\text{ }\leq\text{ 9}[/tex]The inequality symbol is that of less than. Since it has an equal to sign attached, then, the meaning is h is less than or equal to 9. In words, h is at most 9, no more than 9.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representations of the inequality -3(2x-5)<5(2-x) are -6x + 15 < 10 - 5x and "an open circle is at 5 and a bold line that starts at 5 and is pointing to the right" , the correct option is (c) and (d) .
In the question ;
it is given that
the inequality -3(2x-5)<5(2-x)
on solving this inequality further , we get
-3(2x-5)<5(2-x)
-6x+15<10-5x
which is option (c) .
Further solving
Subtracting 15 from both the sides of the inequality , we get
-6x + 15 -15 < 10 -5x -15
-6x < -5 -5x
-6x +5x < -5
-x < -5
multiplying both sides by (-1) ,
we get
x > 5 .
x> 5 on number line means an open circle is at 5 and a bold line starts at 5 and is pointing to the right .
Therefore , the correct representations of the inequality -3(2x-5)<5(2-x) are -6x + 15 < 10 - 5x and "an open circle is at 5 and a bold line that starts at 5 and is pointing to the right" , the correct option is (c) and (d) .
The given question is incomplete , the complete question is
Which are correct representations of the inequality -3(2x - 5) < 5(2 - x)? Select two options.
(a) x < 5
(b) –6x – 5 < 10 – x
(c) –6x + 15 < 10 – 5x
(d) A number line from negative 3 to 7 in increments of 1 , An open circle is at 5 and a bold line that starts at 5 and is pointing to the right.
(e) A number line from negative 7 to 3 in increments of 1, An open circle is at negative 5 and a bold line that starts at negative 5 and is pointing to the left.
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Dr Taylor just started an experiment he will collect data for 5 days how many hours is this
In one day the total number of hours is 24 hours.
So, in 5 days the number of hours is,
[tex]24\times5=120\text{ hours}[/tex]So, the required number of hours is 120 hours.
What number is 75% of 96?
The number 96 is equivalent to the 100%. So we can state the following rule of three:
[tex]\begin{gathered} 96\text{ ------ 100 \%} \\ x\text{ -------- 75 \%} \end{gathered}[/tex]By cross-multiplying these numbers, we have
[tex]\text{ (100\%)}\times x=(96)\times\text{ (75 \%)}[/tex]So, x is given by
[tex]\begin{gathered} x=\frac{(96)\times\text{ (75 \%)}}{\text{ 100\%}} \\ x=72 \end{gathered}[/tex]Therefore, the answer is 72
The Hughes family and the Gonzalez family each used their sprinklers last summer. The Hughes family's sprinkler was used for 15 hours. The Gonzalez family's sprinkler was used for 35 hours. There was a combined total output of 1475 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 65 L per hour?
Answer:
Hughes Family: 40 L/ hour
Gonzalez family: 25L/hour
Step-by-step explanation:
Let us use the following variables to denote the output rates for each sprinkler.
Let H = water output rate for the Hughes family
Let G = water output rate for the Gonzalez family
(I am using H ang G rather than the traditionally used X and Y to easily identify which rate belongs to which family)
The general equation for the volume of water outputted, V, in time h hours at a rate of r per hour is
V = r x h
Given r
Using this fact
Water Output for Hughes family at rate H for 15 hours = 15H
Water Output for Gonzalez family at rate G for 35 hours = 35 G
The total of both outputs = 1475
That gives us one equation
15H + 35G = 1475 [1]
We are given the combined rate as 65 L per hour
Sum of the two rates = combined rate
H + G = 65 [2]
Let's write down these two equations and solve for H and G7 x 5f = 7070
HELPPPP PLEASE
f = 202
Step-by-step explanation:
[tex]7 \times 5f = 7070[/tex]
[tex]5f = \frac{7070}{7} [/tex]
[tex]5f = 1010[/tex]
[tex]f = \frac{1010}{5} [/tex]
[tex]f = 202[/tex]
Verification to check the given answer is correct, then put the value of f in the given question.
[tex]7 \times 5(202) = 7070[/tex]
[tex]35(202) = 7070[/tex]
[tex]7070 = 7070[/tex]
L.H.S. = R.H.S
[tex]{ \green { \boxed{ \red{ \sf{f = 202}}}}}[/tex]
Step-by-step explanation:
The given Eqⁿ is, [tex]{ \purple{ \sf{7 \times 5f = 7070}}}[/tex]
We need to find the value of f. So, let us cancel the numbers one by one.
First, let us cancel 7 by dividing both the sides by 7 in the given Eqⁿ.
[tex]{ \purple{ \sf \frac{ \cancel7 \times 5f}{ \cancel7}}} = { \purple{ \sf{ \frac{ \cancel{7070} ^{ \green{ \tt{1010}}} }{ \cancel 7_{ \green{ \tt{1}}}}}}}[/tex]
[tex]{ \purple{ \sf{5f = 1010}}}[/tex]
Now, let us cancel 5 by dividing both the sides by 5. then,
[tex]{ \purple{ \sf{ \frac{ \cancel5}{ \cancel5}f}}} = { \purple{ \sf{ \frac{ \cancel{1010^{ \red{ \tt{ \: \:202}}}}}{ \cancel 5_{ \red{ \tt{1}}}}}}}[/tex]
[tex]{ \boxed{ \blue{ \sf{f = 202}}}}[/tex]
Set up the system of equations:The cost of 4 bananas and 6 pears is $1.68. Nine bananas and 2 pears cost $1.48. Set up thesystem of equations to find the cost of each banana and pear.4B + 6P = 1.689B - 2P = 1.484B + 6P + 1.689B + 2P + 1.484B + 6P = 1.689B + 2P = 1484B = 6P + 1.689B = 2P + 148
Solution:
Let b represent the cost of 1 banana
Let p represent the cost of 1 pear
From the first statement, The cost of 4 bananas and 6 pears is $1.68
4b + 6p = 1.68 ----------------------------equation (1)
From the second statement, Nine bananas and 2 pears cost $1.48
9b + 2p = 1.48 -----------------------------equation (2)
Solve both equations simultaneously
4b + 6p = 1.68 ----------------------------equation (1)
9b + 2p = 1.48 -----------------------------equation (2)
Multiply equation (2) by 3 to eliminate p
27b + 6p = 4.44
4b + 6p = 1.68
Subtract both equatuions above
23b = 2.76
b = 2.76/23
b= 0.12
Substitute b = 0.12 into equation (1)
9b + 2p = 1.48
9(0.12) + 2p = 1.48
1.08 + 2p = 1.48
2p = 1.48 - 1.08
2p = 0.4
p = 0.4/2
p = 0.2
Hence, the cost of each banana is $0.12 while the cost of each pear is $0.2
please help me with this. four potential solutions.450, 780, 647, 354
So first of all let's take:
[tex]x_1=x\text{ and }x_2=y[/tex]Then we get:
[tex]\begin{gathered} \text{Min}z=1.5x+2y \\ x+y\ge300 \\ 2x+y\ge400 \\ 2x+5y\leq750 \\ x,y\ge0 \end{gathered}[/tex]The next step would be operate with the inequalities and the equation so we end up having only the term y at the left side of each:
[tex]\begin{gathered} \text{Min}z=1.5x+2y \\ 1.5x+2y=\text{Min}z \\ 2y=\text{Min}z-1.5x \\ y=\frac{\text{Min}z}{2}-0.75x \end{gathered}[/tex][tex]\begin{gathered} x+y\ge300 \\ y\ge300-x \end{gathered}[/tex][tex]\begin{gathered} 2x+y\ge400 \\ y\ge400-2x \end{gathered}[/tex][tex]\begin{gathered} 2x+5y\leq750 \\ y\leq150-\frac{2}{5}x \end{gathered}[/tex]So now we have the following inequalities and equality:
[tex]\begin{gathered} y=\frac{\text{Min}z}{2}-0.75x \\ y\ge300-x \\ y\ge400-2x \\ y\leq150-\frac{2}{5}x \end{gathered}[/tex]If we take the three inequalities and replace their symbols by "=' we'll have three equations of a line:
[tex]\begin{gathered} y=300-x \\ y=400-2x \\ y=150-\frac{2}{5}x \end{gathered}[/tex]The following step is graphing these three lines and delimitating a zone in the grid that meets the inequalities:
Where the blue area is under the graph of y=150-(2/5)x which means that it meets:
[tex]y\leq150-\frac{2}{5}x[/tex]And it is also above the x-axis, y=400-2x and y=300-x which means that it also meets:
[tex]\begin{gathered} x\ge0 \\ y\ge0 \\ y\ge400-2x \\ y\ge300-x \end{gathered}[/tex]All of this means that the values of x and y that give us the correct minimum of z are given by the coordinates of a point inside the blue area. The next thing to do is take the four possible values for Min(z) and use them to graph four lines using this equation:
[tex]y=\frac{\text{Min}z}{2}-0.75x[/tex]Then we have four equations of a line:
[tex]\begin{gathered} y=\frac{450}{2}-0.75x \\ y=\frac{780}{2}-0.75x \\ y=\frac{647}{2}-0.75x \\ y=\frac{354}{2}-0.75x \end{gathered}[/tex]The line that has more points inside the blue area is the one made with the closest value to Min(z). Then we have the following graph:
As you can see there are two lines that have points inside the blue area. These are:
[tex]\begin{gathered} y=-\frac{3}{4}x+\frac{450}{2} \\ y=-\frac{3}{4}x+\frac{354}{2} \end{gathered}[/tex]That where made using:
[tex]\begin{gathered} \text{Min }z=450 \\ \text{Min }z=354 \end{gathered}[/tex]Taking a closer look you can see that the part of the orange line inside the blue area is larger than that of the red line. Then the value used to make the orange line would be a better aproximation for the Min z. The orange line is -(3/4)x+450/2 which means that the answer to this problem is the first option, 450.
Nguyen deposited $35 in a bank account earning 14% interest, compounded annually. How much interest will he earn in 72 months?
Given:
a.) Nguyen deposited $35 in a bank account.
b.) It earns 14% interest.
To be able to determine how much interest will he earn in 72 months, the following formula will be used for Compound Interest:
[tex]\text{ Interest Earned = P(1 + }\frac{\frac{r}{100}}{n})^{nt}\text{ - P}[/tex]Where,
P = Principal amount
r = Interest rate
n = No. of times the interest is compounded = annually = 1
t = Time in years = 72 months = 72/12 = 6 Years
We get,
[tex]\text{ Intereset Earned = (35)(1 + }\frac{\frac{14}{100}}{1})^{(1)(6)}\text{ - 35}[/tex][tex]\text{ = (35)(1 + }0.14)^6\text{ - 35}[/tex][tex]\text{ = (35)(}1.14)^6\text{ - 35}[/tex][tex]\text{ = (35)(}2.19497262394)^{}\text{ - 35}[/tex][tex]\text{ = 76.82404183776 - 35}[/tex][tex]\text{ = 41.82404183776 }\approx\text{ 41.82}[/tex][tex]\text{ Interest Earned = \$41.82}[/tex]Therefore, the interest he will be earning is $41.82