Answer:
A. Kelley uses 2 parts blue for every 3 parts yellow.
Step-by-step explanation:
Given equation that shows the amount of blue food coloring,
[tex]b=\frac{2}{3}y[/tex]
Where,
y = amount of yellow food coloring,
If y = 2,
[tex]b=\frac{2}{3}\times 2=\frac{4}{3}[/tex]
i.e. [tex]\frac{4}{3}[/tex] parts of blue for every 2 parts yellow.
If y = 3,
[tex]b=\frac{2}{3}\times 3=2[/tex]
i.e. 2 parts of blue for every 3 parts yellow.
If y = 5,
[tex]b=\frac{2}{3}\times 5=\frac{10}{3}[/tex]
i.e. [tex]\frac{10}{3}[/tex] parts of blue for every 5 parts yellow.
Hence, OPTION A is correct.
PLZ HELP Describe the end behavior and determine whether the graph represents an odd-degree or an even-degree polynomial function. Then state the number of real zeros. simple answer
Answer:
x=8
Step-by-step explanation:
6. an odd-degree polynomial function.
f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞
Step by step explanation;
6. The graph represent an odd-degree polynomial function.
The graph enters the graphing box from the bottom and goes up leaving through the top of the graphing box.This is a positive polynomial whose limiting behavior is given by;
f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞
Answer:
End behavior: [tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty[/tex] and [tex]f(x)\rightarrow \infty\text{ as }x\rightarrow \infty[/tex]
The function has odd-degree.
The number of real zeros in 5.
Step-by-step explanation:
From the given graph it is clear that the graph approaches towards negative infinite as x approaches towards negative infinite.
[tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty[/tex]
The graph approaches towards positive infinite as x approaches towards positive infinite.
[tex]f(x)\rightarrow \infty\text{ as }x\rightarrow \infty[/tex]
For even-degree the polynomial has same end behavior.
For odd-degree the polynomial has different end behavior.
Since the given functions has different end behavior, therefore the graph represents an odd-degree polynomial function.
If the graph of a function intersects the x-axis at a point then it is a zero of the function.
If the graph of a function touch the x-axis at a point and return then it is a zero of the function with multiplicity 2. It means, the function has 2 equal zeros.
The graph intersect the x -axis at 3 points and it touch the x-axis at origin. So, the number of zeros is
[tex]N=3+2=5[/tex]
The number of real zeros is 5.
Charles is going camping with his family. Their campsite is 7/8 miles away. They walk a steady speed of 1 1/4 mi/h. How many minutes will it take them to get at the campsite
Answer:
42 minutes
Step-by-step explanation:
time = distance / speed
time = (7/8 mi)/((1 1/4 mi)/(60 min)) = 60×(4/5)(7/8) min = 42 min
Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.
(4 square root of 2, 45°), (-4 square root of 2, 225°)
(4 square root of 2, 135°), (-4 square root of 2, 315°)
(4 square root of 2, 225°), (-4 square root of 2, 45°)
(4 square root of 2, 315°), (-4 square root of 2, 135°)
Answer:
D
Step-by-step explanation:
[tex]4=r cos \theta\\-4=r sin \theta\\square ~and~add\\16+16=r^2(cos^2 \theta+sin^2\theta)\\r^2=32\\ r=4\sqrt{2} \\divide \\tan \theta=-1\\as x is positive ,y is negative ,so \theta lies in 4th quadrant.\\tan \theta=-1=-tan 45=tan(360-45)=tan 315\\\theta=315°\\\\co-ordinates~ are~(r,theta) ~or~(-r,\theta+ -180°)\\hence ~co-ordinates~are(4\sqrt{2} ,315°),(-4\sqrt{2} ,135°)[/tex]
In regional spelling bee, the 8 finalists consist of 3 boys and 5 girls. Find the number of sample point the sample space S for the number of possible orders at the conclusion of the contest for:
- All 8 finalist
- The fist 3 positions
Answer:
i) There are 40320 possible orders
ii) There are 336 possible orders for the first 3 positions.
Step-by-step explanation:
Given: The number of finalists = 8
The number of boys = 3
The number of girls = 5
To find the number of sample point the sample space S for the number of possible orders, we need to find factorial of 8!
The number of possible orders = 8!
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
= 40320
ii) From all 8 finalist, we need to choose first 3 position. Here the order is important. So we use permutation.
nPr =[tex]\frac{n!}{(n - r)!}[/tex]
Here n = 8 and r = 3
Plug in n =8 and r = 3 in the above formula, we get
8P3 = [tex]\frac{8!}{(8 - 3)!}[/tex]
= [tex]\frac{8!}{5!} \\= \frac{1.2.3.4.5.6.7.8}{1.2.3.4.5}[/tex]
= 6.7.8
= 336
So there are 336 possible orders for the first 3 positions.
How do you solve this? 5/14 divided by 4/7??
Answer:
The answer to your question is: 5/8
Step-by-step explanation:
data
5/14 divided by 4/7
Process
[tex]\frac{5}{14\\}[/tex]
[tex]\frac{4}{7}[/tex]
multiply 5 and 7 and the result is the numerator
multiply 14 and 4 and the result is the denominator
(5 x 7) / ( 14 x 4)
35 / 56
5 / 8 simplify both numerator and denominator
Noah earned w dollars over the summer. Mai earned x dollars, which is y dollars
more than Noah did.
The question revolves around basic algebra and setting up an equality equation based on the given information. In this case, from the facts given, we can state Mai's earnings (x) in terms of Noah's earnings plus an additional amount (y), resulting in the equation x = w + y.
Explanation:The subject of this problem is algebra, specifically involving variables and the concept of equality. In this problem, Noah earned an amount we will denote as w dollars over the summer. Mai, on the other hand, earned x dollars, and it's said that this is an amount of y dollars more than Noah did.
We can express Mai's earnings in terms of Noah's earnings by adding the extra amount to what Noah earned, which gives us the following equality equation:
x = w + y
This equation means that Mai's earnings (x) are equal to the sum of Noah's earnings (w) and the additional amount (y).
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Suppose that 0 < c < π/2. For what value of c is the area of the region enclosed by the curves y = cos(x), y = cos(x − c), and x = 0 equal to the area of the region enclosed by the curves y = cos(x − c), x = π, and y = 0? (Note: These areas are in the interval 0 ≤ x ≤ π.)
Answer:
[tex]c = \cfrac{\pi}{3}[/tex]
Step-by-step explanation:
We can see in the first figure that area enclosed between the curves is a triangle like shape that is between the x= 0 axis and the two cosine curves, whose top vertex is the point (0,1) . We can calculate its area by integration, but first we must find the intersection between cos(x) and cos (x-c)
We can check easily that the intersection between these curves will always be [tex]x= \cfrac{c}{2}[/tex] because cos is an even function.
[tex]\cos\Big(\cfrac{c}{2}-c\, \Big) = \cos\Big(-\cfrac{c}{2}\, \Big) = \cos\Big( \cfrac{c}{2}\, \Big)[/tex]
Where the last step is justified because cosine is an even function.
now, to find the area we will integrate the difference between these functions as follows:
[tex]A= \int\limits^{\frac{c}{2}}_0 {\cos(x) - \cos(x-c)} \, dx \\\\A= \Big[ \sin(x) - sin (x-c) \, \Big]^{c/2 }_0\\ \\A= \sin(c/2) - \sin (-c/2) - \big( sin (0) - sin (-c) \big) \\\\A= 2 \sin (c/2) - \sin (c)[/tex]
Where we have used the property that sine is an odd function.
Now we must find the area for the other region, which is shown on the bottom right in the second figure.
Now, we have to find for which value of x will the cos(x-c) intersect the y=0 axis. We can see tho that as the function cos(x-c) is just the cosine function displaced to the right by c units, its root will shift aswell. Therefore we see that when [tex]x= \cfrac{\pi}{2} + c[/tex] we will have that: [tex]\cos(x-c) = 0[/tex]
Now, to find the second area, (let's call it B) we integrate the difference between the top and bottom curves, in this case y= 0 and y= cos(x-c) up until [tex]x= \pi[/tex]
[tex]B=\int\limits^{\pi}_{\pi/2+c} {0-\cos(x-c)} \, dx \\\\B= \Big[ - \sin(x-c)\Big]^\pi_{\pi/2+c}\\\\B= \sin(\pi/2)-\sin(\pi-c)[/tex]
And finally we set A = B:
[tex]2 \sin (c/2) - sin (c) = 1 - \sin(c)\\\\2 \sin (c/2)= 1\\\\ \sin (c/2) = \cfrac{1}{2} \implies c/2 = \pi /6 \\\\\implies c = \cfrac{\pi}{3}[/tex]
This problem involves finding the value of 'c' such that two areas under different curves are equal. This requires setting up and solving two integral equations, which involves knowledge of trigonometric functions and calculus. This is a challenging problem.
Explanation:The question asks for the value of c when the first region enclosed by the curves y = cos(x), y = cos(x - c), and x = 0 has equal area to the second region enclosed by the curves y = cos(x - c), x = π, and y = 0. To solve this, you need knowledge about trigonometric functions and properties. This is less about probability and more about areas under curves and integral calculus.
Generally, if you're asked to find areas under curves, the area between the x-axis (in this case, y=0) and the curve from x=a to x=b is given by the definite integral ∫ from a to b of f(x) dx, where f(x) is the equation of the curve. If you have not studied calculus, you might struggle with this problem because it essentially asks you to set up and solve two different integral equations and then to equate those two areas in order to solve for c.
Please seek additional help in setting up and solving these integrals if you need it. This is a challenging problem!
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If DE = 5x EF = 3x and DF = 32 what is the length of DE?
Answer:
15
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
Combine like terms: 5x + 3x = 8x
Divide both sides by 8: 8x/4; 32/8
Solve for x: x = 4
Plug it in: DE = 5(4) = 20
Check: 5(4) + 3(4) = 32; 20 + 12 = 32
Estefani‘s house is at point E (3,-2) and Jasmin's house is at point J (-5,3). Jasmin's house is the Mid-point of Estefani's house and Preston's house. Give the y-coordinate of Preston's house.
Answer:
8
Step-by-step explanation:
The coordinates of Preston's house are ...
2J -E = P = 2(-5, 3) -(3, -2) = (-13, 8)
The y-coordinate of P is 8.
Colton and Gage were building a castle together. Colton was 5 times as fast at building the castle than Gage. If it takes 120 blocks to build the castle, how many blocks did Colton build on the castle?
Answer:
100 blocks.
Step-by-step explanation:
Let x represent number of blocks built by Gage.
We have been given that Colton was 5 times as fast at building the castle than Gage, so number of blocks built by Colton would be [tex]5x[/tex].
We are also told that it takes 120 blocks to build the castle. Since Colton and Gage were building a castle together, so number of blocks built by both will be equal to 120.
[tex]x+5x=120[/tex]
[tex]6x=120[/tex]
[tex]\frac{6x}{6}=\frac{120}{6}[/tex]
[tex]x=20[/tex]
Number of blocks built by Colton: [tex]5x=5\cdot 20=100[/tex].
Therefore, Colton had build 100 blocks.
An urn contains 10 balls: 7 red and 3 blue. A second urn contains 25 red balls and an unknown number of blue balls. A single ball is drawn at random from each urn. The probability that the balls are the same color is ________
Answer:
The probability that the balls are the same color is [tex]\frac{175-7x}{250}[/tex] where x is the number of blue balls in the second urn
Step-by-step explanation:
Let's call x the number of blue balls in the second urn. Since there are 25 ball in this urn, the number of red balls would be 25 - x.
Now, we're looking for the probability that the balls are the same color, this means, that both balls are either blue OR red. (since we're using "or", this gives us the clue that we will sum up both probabilities.
1) P(both balls are the same color) = P(both balls are blue) + P( both balls are red).
2) Now we will find what is the probability that both balls are blue (this will be a multiplication since we need that ball 1 is blue AND ball 2 is blue:
P(both balls are blue) = P(ball 1 is blue) x P(ball 2 is blue)
P(both balls are blue) = [tex](\frac{3}{10} )(\frac{x}{25} )[/tex] = [tex]\frac{3x}{250}[/tex]
3) To find what is the probability that both balls are red, the process is similar than when both are blue.
P(both balls are red) = P(ball 1 is red) x P(ball 2 is red)
P(both balls are red) = [tex](\frac{7}{10} )(\frac{25-x}{25} )[/tex]= [tex]\frac{175-7x}{250}[/tex]
4) Going back to 1) and substituting:
P(both balls are the same color) = [tex]\frac{3x}{250} +\frac{175-7x}{250} \\ \\ = \frac{3x-7x+175}{250} \\ \\=\frac{175-4x}{250}[/tex]
Final answer:
The probability that the balls are the same color is 17/40.
Explanation:
The probability that the balls are the same color is 17/40.
To calculate this, we need to find the probabilities of both balls being red and both balls being blue and then add them together.
Probability of both balls being red: (7/10) * (26/35) = 182/350
Probability of both balls being blue: (3/10) * (9/35) = 27/350
Finally, add the two probabilities: 182/350 + 27/350 = 209/350 = 17/40
Find the length of the diagonal Bd rectangle ABCD drawn on the coordinate plane
Answer:
The answer to your question is letter: c) √106 units
Step-by-step explanation:
data
B (5, 3)
D (-4 , -2)
Formula
d = √((x2-x1)² + (y2-y1)²)
dBD = √(-4-5)² + (-2-3)²)
dBD = √(-9)² + (-5)²
dBD = √81 +25
dBD = √106 units
A quality control specialist for a restaurant chain takes a random sample of size 12 to check the amount of soda served in the 16 oz. serving size. The sample mean is 13.80 with a sample standard deviation of 1.57. Assume the underlying population is normally distributed. Find the 95% Confidence Interval for the true population mean for the amount of soda served.
a. (12.42, 14.18)
b. (12.32, 14.29)
c. (12.50, 14.10)
d. None of the above
e. Impossible to determine
Answer:
The answer is E. Impossible to determine
Step-by-step explanation:
Normally, you would find the Confidence interval of a normal sample by using
X(-+) Z* Sigma/n
Where x is the mean, sigma the standard deviation n the size of the sample and z the value determined by your confidence interval size of 95%
.However, this approximation of a confidence interval may only be used for a sample if the number of observations is at least 30 or above. When we have less observations than 30 we must use the standard deviation of the populations. But we only have a sample standard deviation so its not adequate or possible to determine CI the true mean of the population with such a small sample size.
1.Solve for t.
3t + 35=6
Enter your answer in the box.
t =
Answer:
3t + 35 = 6
subtract 35 from both the sides of the equation
3t + 35 - 35 = 6-35
3t = -29
t = - 29/3
Step-by-step explanation:
Answer:
-29/3
Step-by-step explanation:
3t+35=6
3t=6-35
3t=-29
t=-29/3
If we have the curve y = sqrt(x), find the y value and the slope of the curve when x = 36. y = 6 Correct: Your answer is correct. slope = 1/12 Correct: Your answer is correct. Hence, find the equation of the tangent line to the curve at x = 36, writing your answer in the form y = mx + c. What are the values of m and c?
m =
c =
Answer:
Equation of tangent of curve at x = 36:
1)[tex]y = \frac{x}{12} + 3[/tex]
2[tex]y = \frac{-x}{12} - 3[/tex]
Step-by-step explanation:
We are given the following information:
[tex]y = \sqrt{x}[/tex]
Value of curve when x = 36:
[tex]y = \sqrt{36} = \pm 6[/tex]
Thus, [tex]y = \pm6[/tex], when x = 6.
Slope of curve, m =
[tex]\frac{dy}{dx} =\frac{d(\sqrt{x})}{dx}=\frac{1}{2\sqrt{x}}[/tex]
At x = 36,
slope of curve =
[tex]\frac{1}{2\times \sqrt{36}}\\\\m=\frac{1}{12},\frac{-1}{12}[/tex]
Equation of tangent of curve at x = 36:
[tex](y-y_1) = m(x-x_1)[/tex]
[tex]= (y-(\pm 6)) = (\pm\frac{1}{12} )(x - 36)[/tex]
Thus, equation of tangents are:
1)
[tex](y-6) = \frac{1}{12}(x-36)\\12(y-6) = x-36\\y = \frac{x}{12} + 3[/tex]
Comparing to [tex]y = mx + c[/tex], we get [tex]m = \frac{1}{12}[/tex] and [tex]c =3[/tex]
2)
[tex](y+6) = \frac{-1}{12}(x-36)\\12(y+6) = -x+36\\y = \frac{-x}{12} - 3[/tex]
Comparing to [tex]y = mx + c[/tex], we get [tex]m = \frac{-1}{12}[/tex] and [tex]c =-3[/tex]
Final answer:
The equation of the tangent line at x = 36 for the curve y = sqrt(x) is y = 1/12x + 3, found by using the slope of 1/12 and solving for the y-intercept c, which is 3.
m = 1/12
c = 3
Explanation:
To find the equation of the tangent line at x = 36 for the curve y = sqrt(x), we first identified that y = 6 when x = 36 and computed the slope of the curve, which is 1/12 at x = 36.
Using the slope-intercept form of a line, y = mx + c, where m is the slope, and c is the y-intercept, we can substitute m = 1/12 and the point (36, 6) to solve for c.
Substituting into the slope-intercept equation gives us 6 = (1/12)\(36) + c.
Solving for c, we find that the y-intercept c = 3.
Thus, the equation of the tangent line is y = 1/12x + 3.
YO I FR NeED HELP DUE TOMMOrow
Andrew drew a plan of a courtyard at a scale of 1 cm to 60 in. On his drawing, one side of the courtyard measures 2.75. What is the actual measurement of that side of the courtyard in inches?
Answer:
The answer to your question is: 165 in
Step-by-step explanation:
Data
1 cm --------------- 60 inches
If 1 side of the courtyard measures 2.75, what is the actual size of that side?
We can solve this problem with a rule of three
1 cm -------------------- 60 inches
2.75 --------------------- x
[tex]\frac{2.75(60)}{1}[/tex]
= 165 inches
The back of Alisha's property is a creek. Alisha would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 600 feet of fencing available, what is the maximum possible area of the pasture?
A square has all 4 sides equal, so divide the amount of fence available by 4 to get the length of one side of the square
600/4 = 150
Now since the creek is being used for one side, add one side of the square to the other side to get a rectagle 150 by 300 feet.
Area = 150 x 300 = 45,000 square feet.
The maximum possible area of the pasture is;
A_max = 45000 ft²
We are given;Available fencing; Perimeter = 600 feet
Number of sides to fence; 3 sides of rectangle
Since we are dealing with rectangle, let L be the length and W be the width.
Perimeter of rectangle; P = 2L + 2W
But we are told one of the edges is the creek.
Thus, New perimeter = L + 2W
thus, we have; L + 2W = 600
L = 600 - 2W
Formula for Area of a rectangle is; A = LW
Let's put 600 - 2W for L in the area equation to get;
A = (600 - 2W)W
A = 600W - 2W²
We can maximize this area by finding the value of W when dA/dW = 0
Thus;
dA/dW = 600 - 4W
At dA/dW = 0, we have;
600 - 4W = 0
4W = 600
W = 600/4
W = 150 ft
Let's put 150 for W in L = 600 - 2W
L = 600 - 2(150)
L = 600 - 300
L = 300 ft
Therefore, Maximum possible area of pasture = 300 × 150 = 45000 ft²
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Elvira and Aletheia live 3.1 miles apart on the same street. They are in a study group that meets at a coffee shop between their houses. It took Elvira 12 hour and Aletheia 23 hour to walk to the coffee shop. Aletheia's speed is 0.6 miles per hour slower than Elvira's speed. Find both women's walking speeds.
Answer:
Elvira's speed: 3.0 mphAletheia's speed: 2.4 mphStep-by-step explanation:
Let "e" and "a" represent the speeds of Elvira and Aletheia, respectively. Then the total distance they cover is ...
distance = speed × time
(1/2)e + (2/3)a = 3.1
And the relationship between their speeds is ...
e - a = 0.6
__
To solve this system, we can double the first equation and subtract the second to get ...
2(1/2e +2/3a) -(e -a) = 2(3.1) -(0.6)
7/3a = 5.6 . . . . . . . . . . simplify
a = (3/7)(5.6) = 2.4 . . . multiply by 3/7
e = a +0.6 = 3.0 . . . . . Elvira's speed is 0.6 mph more than Aletheia's
Elvira's walking speed is 3.0 miles per hour; Aletheia's is 2.4 miles per hour.
Simplify the expressions by combining like terms
1. 6n^2 - 2n - 3 + 5n^2 - 9n - 6
2. 8c^2 - c + 3 + 2c^2-c + 2
Hey!
---------------------------------------------------------
Question #1:
= 6n^2 - 2n - 3 + 5n^2 - 9n - 6
= 6n^2 + (-2n) + (-3) + 5n^2 + (-9n) + (-6)
= (6n^2 + 5n^2) + (-2n + -9n) + (-3 + -6)
= (11n^2) + (-11n) + (-9)
Answer: 11n² + (-11n) + (-9)
---------------------------------------------------------
Question #2:
= 8c^2 - c + 3 + 2c^2 - c + 2
= 8c^2 + (-c) + 3 + 2c^2 + (-c) + 2
= (8c^2 + 2c^2) + (-c + -c) + (3 + 2)
= (10c^2) + (-2c) + (5)
Answer: 10c² + (-2c) + 5
---------------------------------------------------------
Hope This Helped! Good Luck!
Answer:
1. 11n^2-11n-9
2. 10c^2-2c+5
Step-by-step explanation:
1. 6n^2+5n^2 = 11n^2
-2n-9n = -11n
-3-6=-9
2. 8c^2+2c^2 = 10c^2
-c-c= -2c
3+2=5
In a sample of 1,600 registered voters, 912, or 57%, approve of the way the President is doing his job.
A political pollster states: "Fifty-seven percent of all voters approve of the President." This statement is an example of
a) A Sample
b) Descriptive Statistics
c) Statistical Inference
d) A Population
Answer:
This statement is an example of - statistical inference
Step-by-step explanation:.
A political pollster states: "Fifty-seven percent of all voters approve of the President."
This statement is an example of - statistical inference
Statistical inference is defined as the process of drawing conclusions about populations by using data analysis.
There are two types of statistical inference - statistical estimation and statistical hypothesis testing.
A clothesline is tied between two poles, 10 m apart. The line is quite taut and has negligible sag. When a wet shirt with a weight of 0.5 kg is hung at the middle of the line, the midpoint is pulled down 10 cm. Find the tension in each half of the clothesline. (Use g = 9.8 m/s2 for the acceleration due to gravity. Enter your answers from smallest to largest value of the coefficient of i.)
Answer:
Tension in each half of the clothesline is 25 kg
Step-by-step explanation:
When the middle of the line is pulled down a right triangle is formed in each half of the rope whose legs measure 0.1 m and 5 m respectively.
Since the rope has an insignificant sag, the measure of the hypotenuse of the triangle is approximately equal to that of the longer leg.
The value of the rope tension is equal to the value of the force applied divided by the sine value of the angle of the rope with the horizontal.
So,
[tex]Sin (a)=\frac{0.1}{5} = 0.02[/tex]
T=[tex]\frac{0.5 kg}{0.02}=25kg[/tex]
a linear system in three variables has no solution. Your friend concludes that it is not possible for two of the three equations to have any points in common. is your friend correct? Explain your reasoning.
Answer:
He is correct.
Step-by-step explanation:
Because a linear system in three variables means that they have solutions if the all three have points in common in R3 space. But, in the case that they don't have any solution mean the opposite, they don't have points in common in R3 space.
In a linear system, variables must be related through common points. So, graphically, you should draw intersecting geometrical places in order to show the intersections, wich are the common results or points that are the solutions of the linear system.
A linear system of equation in three variables has no solution is the correct statement.
What is linear equation?" Linear equation is defined as the equation whose variables with highest degree one."
According to the question,
Given statement,
A linear system of equation in three variables has no solution.
Verification:
Consider a example of linear system of equation with three variables
[tex]2x-4y +z=3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)[/tex]
[tex]8x-2y+ 4z=7 \ \ \ \ \ \ \ \ \ \ \ \ \ (2)[/tex]
[tex]-4x+y -2z=-14\ \ \ \ \ \ \ \ \ \ (3)[/tex]
Solve linear equation to get the solution
Multiply [tex](3)[/tex] by [tex]2[/tex] and add it to [tex](2)[/tex],
[tex]\ \ 8x-2y+ 4z=7\\\\-8x+2y-4z =-28[/tex]
we get,
[tex]0x+0y + 0z = -21[/tex] which is not possible and has no solution.
Hence, linear system of equation has no solution is the correct statement.
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Isaiah helped pick 72 bananas on the weekend. There were a total of 6 people picking bananas. If they each picked an equal number of bananas, how many bananas did each person pick?
Answer:
Step-by-step explanation:
72/6=13
Answer:
Each person picked 12 bananas.
Step-by-step explanation:
Given,
Total numbers of banana = 72,
The number of persons = 6,
If each person picks equal number of bananas,
Then,
[tex]\text{Total bananas picked by each person}=\frac{\text{Total bananas}}{\text{Total persons}}[/tex]
[tex]=\frac{72}{6}[/tex]
= 12
point b is the midpoint of ac-. if ab= 4x+2 and ac=10x-6, find the length of ac
let's bear in mind that B is the midpoint and thus it cuts a segment into two equal halves.
[tex]\bf \underset{\leftarrow \qquad \textit{\large 10x-6}\qquad \to }{\boxed{A}\stackrel{4x+2}{\rule[0.35em]{10em}{0.25pt}} B\stackrel{\underline{4x+2}}{\rule[0.35em]{10em}{0.25pt}\boxed{C}}} \\\\\\ AC=AB+BC\implies 10x-6=(4x+2)+(4x+2)\implies 10x-6=8x+4 \\\\\\ 2x-6=4\implies 2x=10\implies x=\cfrac{10}{2}\implies x= 5 \\\\[-0.35em] ~\dotfill\\\\ AC=(4x+2)+(4x+2)\implies AC=[4(5)+2]+[4(5)+2] \\\\\\ AC=22+22\implies AC=44[/tex]
This is a geometry problem, specifically involving the calculation of lengths using the properties of midpoints. A midpoint divides a line into two equal lengths. The problem is solved by equating the length of AB to half of AC to determine the value of x, which is then substituted back into the equation for AC to find its length.
Explanation:The solution to your problem involves understanding that Point B is the midpoint of AC. A midpoint essentially divides a line into two equal lengths. Therefore, AB is equal to BC which can also be referred to as (AC/2). If AB = 4x+2 and AC = 10x-6, then to solve for the value of x, you would need to equate (4x+2) to (10x-6)/2. After solving this equation, the value of x can then be substituted back into the equation of AC to get the length of AC.
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Jim Murray and Phyllis Lowe received a total of $52,000 from a deceased relative's estate. They decided to put $10,400 in a trust for their nephew and divide the remainder. Phyllis received 45 of the remainder; Jim received 15. How much did Jim and Phyllis receive?
Answer:
Phyllis will get $33280.
Jim will get $8320.
Step-by-step explanation:
Jim Murray and Phyllis Lowe received a total of $52,000 from a deceased relative's estate. They decided to put $10,400 in a trust for their nephew and divide the remainder.
The remainder = [tex]52000-10400=41600[/tex] dollars
Phyllis received 4/5 of the remainder; = [tex]0.8 \times41600=33280[/tex] dollars
Jim received 1/5 ; =[tex]0.2\times41600=8320[/tex] dollars
So, Phyllis will get $33280.
Jim will get $8320.
Phyllis received $18,720, which was 45% of the remaining estate, while Jim received $6,240, which was 15% of the remaining estate.
Jim Murray and Phyllis Lowe received a total of $52,000 from a deceased relative's estate. They first put $10,400 in a trust for their nephew. This leaves $52,000 - $10,400 = $41,600 remaining to divide between Jim and Phyllis. Phyllis received 45% of the remainder and Jim received 15% of the remainder.
To find out how much Phyllis received, calculate 45% of $41,600, which is $41,600 x 0.45 = $18,720. To find out how much Jim received, calculate 15% of $41,600, which is $41,600 x 0.15 = $6,240. Therefore, Phyllis received $18,720 and Jim received $6,240 from the remaining estate after the trust was funded.
Jon’s picture frame is 6 inches high by 5 inches wide. He wants to know what other size frames he can use if he enlarges the photo by using the same relative proportions for length and width.
How can Jon find the sizes of other frames?
Jon can plot the ratio of 5 to 6 on a graph (5, 6), then move up 6 and left 5 to find the next frame size, and then keep the same rate to find other points.
Jon can plot the ratio of 5 to 6 on a graph (5, 6), then move up 6 and right 5 to find the next frame size, and then keep the same rate to find other points.
Jon can plot the ratio of 6 to 5 on a graph (6, 5), then move right 6 and down 5 to find the next frame size, and then keep the same rate to find other points.
Jon can plot the ratio of 6 to 5 on a graph (6, 5), then move right 5 and up 6 to find the next frame size, and then keep the same rate to find other points.
Answer:
Jon can plot the ratio of 5 to 6 on a graph (5, 6), then move up 6 and right 5 to find the next frame size, and then keep the same rate to find other points.
Step-by-step explanation:
A line from the origin to the point (5, 6) has a slope of 6/5. To find other points on the same line, one would need to continue to rise 6 units for each run of 5 units to the right.
The only answer choice that appropriately matches (x, y) values to rise/run values is the one shown above.
_____
Comment on this answer
The slope of the line described in this answer is 6/5, which seems appropriate for a frame that is 6 inches high and 5 inches wide. However, I would call this a plot of the ratio 6 to 5, rather than the ratio 5 to 6.
Answer:
Jon can plot the ratio of 5 to 6 on a graph (5, 6), then move up 6 and right 5 to find the next frame size, and then keep the same rate to find other points.
i hope this helps!
what is the area of the composite figure 262 264 266 268
Answer:
264cm2
Step-by-step explanation:
the length of line in green = 5 cm
the length of line in yellow = 3 cm
the length of line in red = 6 cm
the length of line in white = 16 cm
the total area = 100 + 12 + 12 + 20 + 24 + 96 = 264 cm2
The area of the composite figure is 262 cm².
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is side².
We have,
The composite figure has:
- 3 squares of 10 cm, 4 cm, and 6 cm.
- 1 rectangle of 3cm x 10 cm
- 1 trapezium of two paralel sides (10 cm and 6 cm) and height of 7 cm.
- 1 rectangle with 4cm x 6cm.
Now,
Area of the squares.
= 10² + 4² + 6²
= 100 + 16 + 36
= 100 + 52
= 152 cm²
Area of the rectangle.
= 3 x 10
= 30 cm²
Area of trapezium.
= 1/2 x (10 + 6) x 7
= 1/2 x 16 x 7
= 56 cm²
Area of the rectangle.
= 4 x 6
= 24 cm²
Now,
Area of the composite figure.
= 152 + 30 + 56 + 24
= 262 cm²
Thus,
262 cm² is the area.
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Which of the following correlation coefficients would generate the most benefit in terms of risk reduction for a 2-asset portfolio that consists of 40% in Asset A and 60% in Asset B?
Answer:
Asset B generate most benefit.
Step-by-step explanation:
Correlation shows the strength of relation between two variables.
Greater the correlation coefficient greater the strength between two variables.
Since here It is given that Correlation Coefficient between risk reduction and Asset B is higher (i.e. 60%) than the Correlation Coefficient between risk reduction and Asset A (i.e. 40%).
Thus, Asset B generate most benefit.
For risk reduction in a 2-asset portfolio, a lower correlation coefficient would be most beneficial, specifically one closer to -1. This is due to the fact that negative correlation allows for diversification, where one asset rises as the other falls, reducing overall volatility and risk.
Explanation:In terms of reducing risk for a 2-asset portfolio, a lower correlation coefficient would generate the most benefit. This means two assets that tend not to move in the same direction at the same time. In other words, a negative correlation between Asset A and Asset B would be most beneficial for risk diversification. If Asset A goes up when Asset B goes down, and vice versa, these movements could cancel out and reduce the overall volatility of the portfolio.
Correlation coefficients range from -1 to +1. A coefficient of +1 indicates that the two assets move perfectly together, i.e., they have a perfect positive correlation. A coefficient of -1 means that the two assets move perfectly oppositely, i.e., they have a perfect negative correlation. A coefficient near zero indicates little or no correlation between the assets.
Therefore, the most useful correlation coefficient for risk reduction would be the one closer to -1. This is because the negative correlation coefficients allow for diversification – one asset zigging while the other is zagging – and this helps to provide a safety net against significant loss in the portfolio.
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Analyze each graph and determine which of the provided scenarios it models, then, for each graph, label the x- and y-axis with the appropriate quantity and unit of measure. Finally, label each tick mark with the correct intervals.
Could not do the 2nd one, but will update if I figure it out
To analyze each graph and determine the scenario it models, first, understand the variables on the axes. Label the x- and y-axis with the appropriate quantity and unit of measure. Finally, label each tick mark with the correct intervals based on the scale of the graph.
Explanation:In order to analyze each graph and determine the scenario it models, we need to understand the information represented on the axes. The x-axis typically represents the independent variable, while the y-axis represents the dependent variable. For example, in a graph showing time on the x-axis and distance on the y-axis, we can determine if the scenario is representing a moving object and measure the time intervals along the x-axis and the distance intervals along the y-axis.
Once we understand the variables represented on the axes, we can label them accordingly. For instance, if the x-axis represents time, we would label it as 'Time (seconds)' or 'Time (minutes)', depending on the unit of measure. Similarly, if the y-axis represents distance, we would label it as 'Distance (meters)' or 'Distance (kilometers)', again depending on the unit of measure.
We would then label each tick mark with the correct intervals based on the scale of the graph. For example, if the x-axis represents time and each tick mark represents 1 second, we would label each tick mark as '1s', '2s', '3s', etc. The same applies to the y-axis based on the unit of measure.
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