Joe has $4.52 in dimes, nickels, and pennies. If he has one more dime than three times the number of nickels and 10 more pennies than nickels, how many of each type of coin does he have?

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.

" 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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Answer:

2 stations with 7 of jugs of water and 10 of sports drink in each station

Step-by-step explanation:

Lets start with the jugs of water, to have the same amount in each station you need have a number of station that divide for 14 the remainder or "left over" equal to 0, or in other words multiple of 14 in the interval 1 to 14

multiples of 14 : 1, 2, 7 and 14

so you can have

1 station with 14 jugs of water

2 stations with 7 jugs of water each

7 stations with 2 jugs of water each

14 station with 1 jugs of water each

Now we need to do the same for the 20 jugs of sports drink

multiple of 20 in the interval 1 to 20: 1,2,4,5,10 and 20

so you can have:

1 station with 20 jugs of sports drink

2 stations with 10 jugs of sports drink

4 stations with 5 jugs of sports drink

5 station with 4 jugs of sports drink

10 station with 2 jugs of sports drink

20 stations with 1 jugs of sports drink

So we have that both cases, water and sport drinks have coincidence of 1 or 2 stations, and the maximum of both is 2 stations with 7 jugs of water and 10 of sports drink each

Final answer:

To determine the greatest number of refreshment stations that can be set up, we find the greatest common divisor (GCD) of 14 jugs of water and 20 jugs of sports drink, which is 2. Therefore, the committee can set up 7 refreshment stations with 1 jug of water and 2 jugs of sports drink at each.

Explanation:

The committee has 14 jugs of water and 20 jugs of sports drink and wants to set up the greatest number of refreshment stations along the marathon course without any beverages left over. To find this solution, we need to determine the greatest common divisor (GCD) of the two quantities of jugs because each station must have the same combination of jugs of water and sports drink.

First, list the factors of each number:

Factors of 14: 1, 2, 7, 14

Factors of 20: 1, 2, 4, 5, 10, 20

The largest common factor is 2, which means the refreshment stations can have a combination of 1 jug of water and 2 jugs of sports drink. So, the committee can set up 7 refreshment stations (14 jugs of water / 2 per station = 7 stations; and 20 jugs of sports drink / 2 per station = 10 stations, but limited by the smaller number of jugs of water).

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

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]

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.

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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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.

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

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.

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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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!

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.

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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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.

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.

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

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

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.

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.

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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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.

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.

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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Answer:

  32 mi @ N77°E

Step-by-step explanation:

The route of travel forms legs of a right triangle, so the final distance (d) from harbor can be found using the Pythagorean theorem:

  d² = 28² +16² = 784 +256 = 1040

  d = √1040 ≈ 32.249 . . . miles

___

The angle (α) added to the original N47°E bearing can be found using the fact that opposite and adjacent sides are given. So, they can tell you the tangent of the angle:

  tan(α) = 16/28

  α = arctan(16/28) ≈ 29.74°

Then the bearing to the final position is ...

  47° +29.74° = 76.74°  . . . . . east of north

Rounded to whole numbers, the final position from harbor is ...

  32 miles @ N 77° E

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.

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

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.

Answer:

Step-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.

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.

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

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

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.

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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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

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]