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Jonah runs 3/5 mile on Sunday and 7/10 mile on Monday . He uses the model to find that he ran a total of 1 mile. What mistake does Jonah make? I NEED ANSWERS ASAP

Answers

Answer 1

Answer:

Answer:

see below

Step-by-step explanation:

3/5 + 7/10

We did not get a common denominator

He added the numerators and got 10/10 = 1

He should get a common denominator

3/5 * 2/2 + 7/10

6/10 + 7/10

13/10

10/10 + 3/10

1 3/10 miles

Answer 2

Answer:

Answer:

His mistake was adding the numerators together without converting the fractions to have a common denominator

Step-by-step explanation:

3/5 + 7/10

convert fractions to have common denominator

6/10 + 7/10 = 13/10

convert improper fraction to mixed number

1 3/10

He ran a total of 1.3 miles

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Minimizing Construction Costs The management of the UNICO department store has decided to enclose a 945 ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. If the pine board fencing costs $7/running foot and the steel fencing costs $4/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (Round your answers to one decimal place.)

Answers

Answer:

Pine board side = 16.4 ft

Steel fencing side = 57.5 ft

Step-by-step explanation:

Let 'B' be the length of each side constructed of pine boards, and 'S' be the length of the side with the steel fencing, the area (A) and cost (C) functions are:

$945 = B*S\nB=(945)/(S) \nC= 4*S+7*2B\nC=4S+(13,230)/(S)$

The value of S for which the derivate of the cost function is zero, minimizes cost:

$C'=0=4+(-13,230)/(S^2)\n S=√(3,307.5) \nS=57.5 ft$

The value of B is:

$B=(945)/(57.5)\nB=16.4 \ ft$

Pine board side = 16.4 ft

Steel fencing side = 57.5 ft

Final answer:

To minimize the construction costs for the enclosure, the dimensions should be calculated using the calculus optimization technique. By incorporating the cost and area requirements into calculated equations and solving, you will find x = 2 times y. This is how you minimize the cost.

Explanation:

This problem involves the application of calculus and optimization techniques. Given that the area of the enclosure needs to be 945 ft2, and that it is adjacent to an external wall of the department store, we can infer that its shape is rectangular.

Let the width of the enclosure parallel to the department store be x (feet), and its length perpendicular to the store be y (feet). According to the area requirement, we have the equation x*y = 945 ft2.

The cost of the enclosure is the sum of the cost of the pine board fences and the steel fence. Since 2 sides are made of pine boards, and 1 side made of steel, the cost can be expressed as C = 2xy p + y s, where 'p' is the cost of pine board per foot ($7), and 's' is the cost of steel per foot ($4).

Since we are looking for the minimum cost, we derive this equation and set it equal to zero to find the dimensions x and y. After substituting and simplifying, we find that the minimum cost is obtained when x = 2 y. By substituting this into the area equation, we can solve for the dimensions of the enclosure.

Learn more about Calculus Optimization here:

brainly.com/question/30795449

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A Ferris wheel has a diameter of 40 feet. What is its circumference?Round to the nearest tenth. Use 3.14 for .

Answers

Answer:125.6 feet

Step-by-step explanation:

diameter=40 feet

π=3.14

Circumference= π x diameter

Circumference=3.14 x 40

Circumference=125.6

Measure the amgle of ced

Answers

Answer:

The measure of angle CED is 58˚

Step-by-step explanation:

CED + AED = 180˚ (straight line)

AED = 122˚ (given)

CED + (122˚) = 180˚ (substitute)

CED = 58˚ (subtract 122˚ from both sides)

as the angle is on a straight line so it is equal to 180°so subtract 122 from 180

Heeeeellllllppppppp meeeeeeeeeee

Answers

Answer:x=13

Step-by-step explanation:

Since they are both corresponding angles you can create the equation

5x+21=86

Subtract 21 from each side

5x=65

Divide each side by 5

X=13

We must use substitution to do this second integral. We can use the substitution t = 7x, which will give dx = Correct: Your answer is correct. dt. Ignoring the constant of integration, we have sin(7x) dx =

Answers

Answer:

Therefore, the solution is:

$\boxed{\int \sin 7x\, dx=-(\cos 7x)/(7)}$

Step-by-step explanation:

We calculate the given integral. We use the substitution t = 7x.

$\int \sin 7x\, dx=\begin{vmatrix} 7x=t\n 7\, dx=dt\n dx=(dt)/(7) \end{vmatrix}\n\n=\int \sin t \cdot (1)/(7)\, dt\n\n=(1)/(7)\cdot (-\cos t)\n\n=-(\cos 7x)/(7)$

Therefore, the solution is:

$\boxed{\int \sin 7x\, dx=-(\cos 7x)/(7)}$

Quadrilateral STRW is inscribed inside a circle as shown below. Write a proof showing that angles T and R are supplementary.

Answers

Minor point: the quadrilateral is STWR, not STRW. Vertices are named in order.

The measure of angle T is half the measure of arc WRS. The measure of angle R is half the measure of arc STW. The sum of the measures of the two arcs is the measure of a circle, 360°, so you have

... T + R = (WRS)/2 + (STW)/2

... ... = (WRS + STW)/2

... ... = 360°/2 = 180°

Since the sum of T and R is 180°, they are supplementary.

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