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The final step coincides with option 4
Related Questions
Latoya, Josh, and Alonzo have a total of $82 in their wallets. Josh has 2 times what Alonzo has. Latoya has $6 less than Alonzo. How much does each have?Amount in Latoya's wallet:Amount in Josh's wallet:Amount in Alonzo's wallet:
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As per given by the question,
There are given that Latoya, Josh, and Alonzo have a total of $82 in their wallets.
now,
Let L, J, and A be the amounts that each person has.
So,
[tex]L+J+A=82\ldots\text{ (1)}[/tex]Now,
According to the question,
Jos has 2 times what Alonzo has,
So,
[tex]L+2A+A=82\ldots\text{. (2)}[/tex]Now,
Latoya has $6 less than Alonzo,
So,
[tex](A-6)+2A+A=82_{}\ldots\ldots\text{.}(3)[/tex]Then,
From the equation (3),
[tex]\begin{gathered} (A-6)+2A+A=82 \\ A-6+3A=82 \\ 4A-6=82 \\ 4A=82+6 \\ 4A=88 \\ A=\frac{88}{4} \\ A=22 \end{gathered}[/tex]Now,
From the question,
Jose has 2 times what Alonzo has,
So,
[tex]\begin{gathered} A(\text{Alonzo)}=22 \\ J(\text{Jose)}=22\times2 \\ =44 \end{gathered}[/tex]Now,
Latoya has 6 less than Alonzo,
So,
[tex]\begin{gathered} A=22 \\ L=22-6 \\ L=16 \end{gathered}[/tex]Then,
From the equation (1).
[tex]\begin{gathered} L+J+A=82 \\ 16+44+22=82 \\ 82=82. \end{gathered}[/tex]Hence,
Amount in Latoya wallets is$16.
Amounts in Jose's wallets is $44.
Amount in Alonzo wallet's is $22.
Perform the indicated calculation.(Round to the nearest thousandth as needed.)
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By definition,
[tex]\text{nCr}=\frac{n!}{(n-r)!r!}[/tex]Using this, we have:
[tex]\begin{gathered} 8C4=\frac{8!}{(8-4)!4!}=\frac{40320}{576}=70 \\ \\ \\ 11C4=\frac{11!}{(11-4)!4!}=\frac{39916800}{120960}=330 \\ \\ \frac{8C4}{11C4}=\frac{70}{330}=\frac{7}{33}=0.212 \end{gathered}[/tex]Solving a distance rate time problem using a system of linear equations
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ANSWER
[tex]\begin{gathered} \text{ Rate of the boat in still water }=36mi\/hr \\ \text{ Rate of the current }=9mi\/hr \end{gathered}[/tex]EXPLANATION
We want to find the rate of the boat in still water and the rate of the current.
Let the boat's rate be x.
Let the rate of the current be y.
When the boat is traveling upstream, it means that it is traveling against the current. This implies that its rate traveling upstream is:
[tex]x-y[/tex]Using the relationship between speed (rate) and distance, we can write that for the upstream travel:
[tex]\begin{gathered} s=\frac{d}{t} \\ \Rightarrow x-y=\frac{108}{3} \\ x-y=36 \end{gathered}[/tex]When the boat is traveling downstream, it means that it is traveling along with the current. This implies that its rate traveling downstream is:
[tex]x+y[/tex]and:
[tex]\begin{gathered} x+y=\frac{108}{2} \\ x+y=54 \end{gathered}[/tex]Now, we have two simultaneous linear equations:
[tex]\begin{gathered} x-y=36 \\ x+y=54 \end{gathered}[/tex]Solve for x by elimination. To do this, add the two equations and simplify:
[tex]\begin{gathered} x-y+x+y=36+54 \\ 2x=90 \\ x=\frac{90}{2} \\ x=45mi\/hr \end{gathered}[/tex]Solve for y by substituting x into the second equation:
[tex]\begin{gathered} 45+y=54 \\ \Rightarrow y=54-45 \\ y=9mi\/hr \end{gathered}[/tex]Hence, the rate of the boat in still water is 36 mi/hr and the rate of the current is 9 mi/hr.
Assume the average amount of caffeine consumed daily by adults is normally distributed with a mean of 250 mg and a standard deviation of 46 mg. In a random sample of 300 adults, how many consume at least 310 mg of caffeine dally?Click here to view page 1 of the standard normal distribution tableClick here to view page 2 of the standard normal distribution tabloof the 300 adults, approximately adults consume at least 310 mg of caffeine daily(Round to the nearest whole number as needed.)
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so we have that the amount of adults that consume at least 310mg is
[tex]300\cdot0.0961=28.83\approx29[/tex]
The length of a rectangle is (x+8) inches long and the width is 7 4/5 inches. if the area is 37 7/10 square inches. write an equation that could be used to find the length of the rectangle
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Area of a rectangle = width x length
Width = 7 4/5
Length = x+8
Area = 37 7/10
Replacing:
Area = width x length
Lenght = Area / width
x+8 = (37 7/10 ) / (7 4/5)
Solve for x:
x = [(37 7/10 ) / (7 4/5)] -8
Lenght = x+8 = ( [(37 7/10 ) / (7 4/5)] -8)+8 = [(area/ width)-8]+8
Sarah can edge a large lawn in 3 hours. Jesse can edge a similar lawn in 2.5 hours. How long would it take Sarah and Jesse if they worked together?
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It takes sarah 3 hours to edge the lawn
so her rate = 1 lawn/ 3 hours
Jesse takes 2.5 hours, so his rate = 1 lawn / 2.5 hours
Together they will take a combined rate of sarah + Jesse
= 1/3 lawn/hour + 1/2.5 lawn/hour
= 1/3 + 1/5/2
= 1/3 + (1 x 2/5)
= 1/3 + 2/5 = 11/15 lawn/hour = 1/r
r = 1/11/15 = 15/11
The time = 15/11 =1 4/11 hours
[tex]\text{The time = 1}\frac{4}{11}hours[/tex]
Answer:
The time = 15/11 =1 4/11 hours
Step-by-step explanation:
Select One 3^6/3^3 ↑ Select One Add Subtract Multiply can you help me with this please?[tex] {3}^{6} {3}^{3} [/tex]thats supposed to be a fraction
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Find 3^6 / 3^3
Operation is SUBSTRACT
Let 3 equal base
and SUBSTRACT (6-3) = 3
THEN result is
3^(6-3) = 3^3
ANSWER IS SUBSTRACT
then Multiply 3x3x3 = 27
use the rule (x,y) (x-2, y-4) to graph the image of the rectangle. Then describe the transformation.The coordinates of the vertices of the rectagle before the tansformation, are:A (1,1)B (4,1)C (4,-2)D(1, -2)
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Use the given rule to find the coordinates of the transformed vertices:
[tex]\begin{gathered} (x,y)\rightarrow(x-2,y-4) \\ \Rightarrow A(1,1)\rightarrow A^{\prime}(1-2,1-4)=A^{\prime}(-1,-3) \\ \Rightarrow B(4,1)\rightarrow B^{\prime}(4-2,1-4)=B^{\prime}(2,-3) \\ \Rightarrow C(4,-2)\rightarrow C^{\prime}(4-2,-2-4)=C^{\prime}(2,-6) \\ \Rightarrow D(1,-2)\rightarrow D^{\prime}(1-2,-2-4)=D^{\prime}(-1,-6) \end{gathered}[/tex]Plot the points A,B,C,D,A',B',C' and D':
Identify that the transformation corresponds to a translation two units to the left and four units downwards:
Determine the amount of the ordinary annuity at the end of the given period. (Round your final answer to two decimal places.)$200 deposited quarterly at 6.9 for 6 years
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For solving this question it is necessary to apply the formula
[tex]FV=P\cdot(\frac{(1+r)^n-1}{r})[/tex]Where:
FV = future value of the account;
P= deposit = $200
r = quarterly percentage - use decimal=0.069
n = number of deposits = 4* 6=24
[tex]\begin{gathered} FV=P\cdot(\frac{(1+r)^n-1}{r}) \\ FV=200\cdot(\frac{(1+\frac{0.069}{4})^{24}-1}{\frac{0.069}{4}}) \\ FV=200\cdot(\frac{(1+0.01725)^{24}-1}{0.01725}) \\ FV=200\cdot(\frac{(1.01725)^{24}-1}{0.01725}) \\ FV=200\cdot\frac{0.5075}{0.01725}=5884.38 \\ FV=5884.38 \end{gathered}[/tex]FV=$5884.38
I need help with these 3 questions on this math problem
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The table represents Monte's savings
The rate of change is 8. This means that he earns 8 dollars per hour
The graph represents Ramon's savings
The rate of change is 6. This means that he earns 6 dollars per hour
The answers to the questions are shown below
1) The rates of change represent the amount that each person earns per hour.
2) The rate of change of Monte's is greater. It means that he earns more per hour than Ramon.
3) We would find the equation in slope intercept form representing each person's savings. The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The y intercept is the value of y when x = 0. On the graph, it is the value of y at the point where the line cuts the vertical axis. We have
For the table,
when x = 0, y = 3
Thus, c = 3
m = 8
The equation for Monte's total savings is
y = 8x + 3
After 8 working hours, x = 8. We would substitute x = 8 into the equation. We have
y = 8 * 8 + 3 = 64 + 3
y = 67
Monte's total savings after 8 hours is $67
For the graph, c = 6
m = 6
The equation for Ramon's total savings is
y = 6x + 6
After 8 working hours, x = 8. We would substitute x = 8 into the equation. We have
y = 6 * 8 + 6 = 48 + 6
y = 54
Ramon's total savings after 8 hours is $54
Match the following items.1.(-4, -2)D2.(2, -4)H3.(4, -2)G4.(2, 5)B5.(-1, 1)A6.(-5, 0)F7.(4, 2)E8.(0, -5)CNEXT
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From the graph, we can conclude:
[tex]A=(-4,-2)[/tex][tex]B=(2,-4)[/tex][tex]C=(4,-2)[/tex][tex]D=(2,5)[/tex][tex]E=(-1,1)[/tex][tex]F=(-5,0)[/tex][tex]G=(4,2)[/tex][tex]H=(0,-5)[/tex]Therefore:
Answer:
(-4,-2)----------------->A
(2,-4)------------------>B
(4,-2)------------------>C
(2,5)------------------>D
(-1,1)------------------>E
(-5,0)------------------>F
(4,2)------------------>G
(0,-5)------------------>H
I need help with this practice I attempted this practice previously and my attempt is in the picture
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We will draw a sketch for the given triangle to find its area
The area of the triangle will be
[tex]A=\frac{1}{2}\times XY\times ZM[/tex]Since ZX = ZY = 7, then the triangle is isosceles
Then the height ZM will bisect the base XY
Then we can find ZM by using Pythagoras Theorem
[tex]\begin{gathered} ZM=\sqrt[]{7^2-3^2} \\ ZM=\sqrt[]{49-9} \\ ZM=\sqrt[]{40} \\ ZM=2\sqrt[]{10} \end{gathered}[/tex]Since XY = 6, then
The area of the triangle is
[tex]\begin{gathered} A=\frac{1}{2}\times6\times2\sqrt[]{10} \\ A=6\sqrt[]{10}\text{ square units} \end{gathered}[/tex]There are five performers who represent the Kami access weekend at a comedy club how many different ways are there to schedule this appearances
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SOLUTION
Given the question in the image, the following is the solution to the problem
Step 1: Scheduling n performers is found by n! ways...so five performers gives 5! The different number of ways for 5 performers therefore mean:
[tex]\begin{gathered} 5!=5\times4\times3\times2\times1 \\ =120\text{ ways} \end{gathered}[/tex]Hence, there are 120 different ways of scheduling these appearances.
Point A is located at (-3,5). Find its new coordinates after it is reflected along the x-axis then dilated using a scale factor of 4 with center of dilation at the origin.
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We have (-3,5)
The rule for reflection around the x-axis is
[tex](x,y)\rightarrow(x,-y)[/tex]so the point after the reflection is around x-axis
[tex](-3,5)=(-3,-5)[/tex]for the dilatation we need to multiply the point find above by 4
[tex]A^{\prime}=(-3(4),-5(4))=(-12,-20)[/tex]The table below summarizes the birth weights to the nearest pound of a sample of 36 newborn babies find the mean birth weight of these 36 babies round your answer to the nearest tenth
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To determine the mean, divide the sum of the products of the number of babies and the birth weight of each by the total number of sample.
Thus, we have the following:
[tex]\bar{x}=\frac{6(5)+7(6)+16(7)+7(8)}{36}[/tex]Simplifying the numerator, we have the following.
[tex]\begin{gathered} \bar{x}=\frac{30+42+112+56}{36} \\ \bar{x}=\frac{240}{36} \end{gathered}[/tex]Therefore, the mean is as follows.
[tex]\bar{x}=6.\bar{6}\approx6.7[/tex]-6 5 4 3 2 1 AC 2 5 Move options to the blanks to show that N ABC=A DEF using transformations, given the corresponding angles and sides are congruent. The first transformation is a of N ABC The second transformation is a of N ABC The transformations map AB onto BConto CA onto ZA onto 2B onto and 2C onto This demonstrates that I ABG A DEF. reflection rotation translation up 2 units down 2 units across the x-axis across the y-axis 90 91 clockwise about the origin 90° counter-clockwise about the origin EF DE ZF LE D
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Solution
For this case the solution would be:
The first transformation is a rotation of ABC clockwise about the origin
The second transformation is a translation of ABC up 2 units
The transformations map AB onto DK, BC onto KF. CA onto FD. < A onto
that demonstrates that ABC is similar to DEF
Bonnie deposits $250 into a new savings account. The account earns 3.5% simple interest per year No money is added or removed from the savings account for 6 years. What is the total amount of money in her savings account at the end of the 6 years?
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Let's begin by identifying key information given to us:
Principal (p) = $250
Interest rate (r) = 3.5% = 3.5/100 = 0.035
Time (t) = 6 years
The simple interest is given by:
[tex]\begin{gathered} A=p(1+rt) \\ A=250(1+0.035\cdot6) \\ A=259(1+0.21) \\ A=250(1.21) \\ A=\text{\$}302.50 \end{gathered}[/tex]I need help on question 4 and if possible question 8 please
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Given:
Diagram is given.
Pair of opposite rays are:
[tex]\begin{gathered} XA\text{ and }XD \\ XB\text{ and XE} \end{gathered}[/tex]Select the correct answer. Using a table of values, determine the solution to the equation below to the nearest fourth of a unit. 2^(-x)+1=5^x+2
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I'm trying to graph the equation:y=1/4x + 3y=2x +10please help
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To graph the equation, the easiest way to get its coordinates is when x = 0 and y = 0.
Let's apply these conditions to get the coordinates of the equation.
a.) y = 1/4x + 3
when,
x = 0 y = 0
y = 1/4(0) + 3 (0) = 1/4x + 3
y = 3 0 - 3 = 1/4x + 3 - 3
-3 = 1/4x
-3(4) = x
-12 = x or x = -12
Thus, the coordinates for equation y = 1/4x + 3 are (0,3) and (-12,0).
Let's now plot the graph of the equation,
The same steps will also be applied to make a graph of equation y = 2x + 10.
6 Use elimination to solve eachsystem of equations3x + 5y = -23x - 2y = - 16
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Answer:
x = -4
y = 2
Step-by-step Explanation:
Given the below system of equations;
[tex]\begin{gathered} 3x+5y=-2\ldots.\ldots\ldots\text{.Equation 1} \\ 3x-2y=-16\ldots\ldots\ldots\text{.}\mathrm{}\text{Equation 2} \end{gathered}[/tex]We'll go ahead and solve the above system of equations using the elimination method following the below steps;
Step 1: Subtract Equation 2 from Equation 1;
[tex]\begin{gathered} (3x-3x)+\lbrack5y-(-2y)\rbrack=\lbrack-2-(-16)\rbrack \\ 0+(5y+2y)=-2+16 \\ 7y=14 \end{gathered}[/tex]Step 2: Divide both sides by 7;
[tex]\begin{gathered} \frac{7y}{7}=\frac{14}{7} \\ y=2 \end{gathered}[/tex]Step 3: Substitute y in Equation 1 with 2
[tex]\begin{gathered} 3x+5(2)=-2 \\ 3x=-2-10 \\ \frac{3x}{3}=-\frac{12}{3} \\ x=-4 \end{gathered}[/tex]So the solution to the given system of equation is x = -4 and y = 2
Adding and subtracting mixed fractions-2/9 - (-3)
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( - 8 - 3) + ( - 12 - 3)withFinding the Slope from Points
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P1 = (-8, -3)
P2 = (-12, -3)
slope = m = (y2 - y1) / (x2 - x1)
Substitution
m = (-3 + 3 ) / (-12 + 8)
Simplification
m = 0 / -4
Result
m = 0
P1 = (7, -9)
P2 = (15, -29)
slope = m = (-29 + 9) / (15 - 7)
m = -20/8
m = -10/4
m = -5/2
This is the graph
ok
2x + 2y = 4
2y = -2x + 4
y = -2/2x + 4/2
y = -x + 2
A ____?____ diagram is a visual representation of a set of data points represented as ordered pairs.
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Recall that:
A scatter diagram is a graph of ordered pairs of numerical data, with one variable on each axis.
Answer: Option C.
Help! This problem is way too difficult if you can solve it your a lightsaber!
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Solution
For what value of x is the polynomial above x-axis:
The roots of the graph passes through -3 and 3
so the value of x above will be:
[tex](-3,3)\text{ }U\text{ \lparen3,}\infty)[/tex]The reason why the polynomial is having imaginary roots is
Fundamental Theorem of Algebra we explain that a polynomial will have exactly as many roots as its degree (the degree is the highest exponent of the polynomial). So we know one more thing: the degree is 5 so there are 5 roots in total.
The Fundamental Theorem of Algebra assures us that any polynomial with real number coefficients can be factored completely over the field of complex numbers .
A high school basketball coach counted the number of points her team scored each game. Number of points Number of games 12 3 49 6 55 4 63 5 82 2. 95 5 X is the number of points that a randomly chosen game had. What is the expected value of X? Write your answer as a decimal.
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the total number of games = 3 + 6 + 4 + 5 + 2 = 20
[tex]P(x)=\frac{\text{ number of games}}{\text{ total number of games}}[/tex]number of points(x) | Number of games | P(x) = | xP(x)
---------------------------------------------------------------------------------------------------------------------
12 | 3 | 0.15 | 1.8
49 | 6 | 0.30.3 | 14.7
7. Solve the system of linear equations. - 3x + 5y = 4 x + y = -4 A. (1, -5) B. (0, -4) C. (-3,-1) D. (-5, 1)
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To solve this system of equations, we can use the substitution method. In this way, we can solve the system for one of the unknowns. Then, we need to substitute the resulting value in one of the equations to find the other value for the other unknown. We can proceed as follows:
[tex]x+y=-4\Rightarrow x=-4-y[/tex]We can substitute this in the other equation as follows:
[tex]-3(-4-y)+5y=4[/tex]Now, we need to apply the distributive property:
[tex]12+3y+5y=4\Rightarrow12+8y=4[/tex]Subtracting by 12 to both sides of the equation:
[tex]12-12+8y=4-12\Rightarrow8y=-8[/tex]Dividing both sides by 8, we have:
[tex]\frac{8y}{8}=-\frac{8}{8}\Rightarrow y=-1[/tex]Now, with a value of y = -1, we can substitute this one into the easiest equation to find the value of x:
[tex]x+(-1)=-4\Rightarrow x=-4+1\Rightarrow x=-3[/tex]Therefore, we have that the solution for this system is:
• x = -3
,• y = -1, or
,• (-3, -1) (option C).
In an experiment involving a treatment applied to 5 test subjects, researchers plan to use a simple random sample of 5 subjects selected from a pool of 7 available subjects. How many different random samples are possible?
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Solution:
The number of ways to select 5 from 7 (when order does not matter) is;
[tex]\begin{gathered} ^7C_5=\frac{7!}{(7-5)!5!} \\ \\ ^7C_5=\frac{7\times6\times5!}{2!\times5!} \\ \\ ^7C_5=21 \end{gathered}[/tex]ANSWER: 21 ways
Find the length of the missing side on the triangle shown to the right using the Pythagorean theorem.
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The length of the missing side is 68
EXPLANATION
Given:
opposite= 60
Adjacent = 32
Let x be the missing length (hypotenuse)
Using the Pythogaras theorem,
opposite² + adjacent² = hypotenuse²
Substitute the values and evaluate.
60² + 32² = x²
3600 + 1024 = x²
4624 = x²
Take the square root of both-side
√4624 = x
68=x
Hence, the missing side is of length 68.
Graph the line that has a slope of 1/7 and includes the point (0,5)
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Given the slope 1/7 and point (0,5) we are asked to graph a line.
To do this, the first thing we need to do is to plot the given data.
Plot the given point (0,5)
Next, since we know that the slope of a line is rise/run, given the slope 1/7, it means that from the point (0,5) we will "rise" 1 unit or move 1 unit up, and then "run" 7 units, or move 7 units to the right.
And then, we just connect the two points to form a line