Randy can run six-tenths of a mile every 4 minutes, but it takes Julie 5 minutes. By the time Julie has run for 20 minutes, how far has Randy run?

A
1.8 miles

B
2.4 miles

C
2.6 miles

D
3 miles

(a) It looks like you're saying

[tex]\displaystyle F(x) = \int_0^x (t - 3t^2 + 7) \, dt[/tex]

Find the critical points of F(x). By the fundamental theorem of calculus,

F'(x) = x - 3x² + 7

The critical points are where the derivative vanishes. Using the quadratic formula,

x - 3x² + 7 = 0   ⇒   x = (1 ± √85)/6

Compute the second derivative of F :

F''(x) = 1 - 6x

Check the sign of the second derivative at each critical point.

• x = (1 + √85)/6 ≈ 1.703   ⇒   F''(x) < 0

• x = (1 - √85)/6 ≈ -1.370   ⇒   F''(x) > 0

This tells us F attains a minimum of

[tex]F\left(\dfrac{1-\sqrt{85}}6\right) \approx \boxed{-6.080}[/tex]

(b) Split up the domain of F at the critical points, and check the sign of F'(x) over each subinterval.

• over (-∞, -1.370), consider x = -2; then F'(x) = -7 < 0

• over (-1.370, 1.703), consider x = 0; then F'(x) = 7 > 0

• over (1.703, ∞), consider x = 2; then F'(x) = -3 < 0

This tells us that

• F(x) is increasing over ((1 - √85)/6, (1 + √85)/6)

• F(x) is decreasing over (-∞, (1 - √85)/6) and ((1 + √85)/6, ∞)

(c) Solve F''(x) = 0 to find the possible inflection points of F(x) :

F''(x) = 1 - 6x = 0   ⇒   6x = 1   ⇒   x = 1/6

Split up the domain at the inflection point and check the sign of F''(x) over each subinterval.

• over (-∞, 1/6), consider x = 0; then F''(x) = 1 > 0

• over (1/6, ∞), consider x = 2; then F''(x) = -11 < 0

This tells us that

• F(x) is concave up over (-∞, 1/6)

• F(x) is concave down over (1/6, ∞)

Answer:

84

Step-by-step explanation:

7 Sizes * 3 Lengths * 4 Colors = 84

Th e correct equation will be y = 5x

Ratios is a way dividing two integers. For instance, the ratio of a to b is written as a:b.

Given the ratios expressed as x:y = 1:5

Since ratio means division hence;

x:y = 1:5

x/y = 1/5

Cross multiply

1 * y = 5 * x

y = 5x

Hence the correct equation will be y = 5x

Learn more on ratios here: https://brainly.com/question/2914376

Answer:

Y would equal X on Day 65

Step-by-step explanation:

Im guessing by looking at the chart

Answer:

One line represents something getting heavier over time, while the line pointing down represents something getting lighter over time at a slightly slower rate.

Answer:

x-1

correct me if im wrong

Step-by-step explanation:

9(-7 + 6) = 9(-7) + 9(6)

Hope it help !

Using the normal distribution and the central limit theorem, it is found that there is a:

a) 0.281 = 28.1% probability that the sample mean is above 500.

b) 0.0003 = 0.03% probability that the sample mean is above 500.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item a:

The probability is the p-value of Z when X = 500, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{500 - 430}{120}[/tex]

[tex]Z = 0.58[/tex]

[tex]Z = 0.58[/tex] has a p-value of 0.719.

1 - 0.719 = 0.281

0.281 = 28.1% probability that the sample mean is above 500.

Item b:

Sample of 35, hence [tex]n = 35, s = \frac{120}{\sqrt{35}}[/tex]

Then:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{500 - 430}{\frac{120}{\sqrt{35}}}[/tex]

[tex]Z = 3.45[/tex]

[tex]Z = 3.45[/tex] has a p-value of 0.9997.

1 - 0.9997 = 0.0003

0.0003 = 0.03% probability that the sample mean is above 500.

To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213

Answer:

i think x = -5, y = -7 is a other solution set

Answer:

104-5/9

Step-by-step explanation:

just divided ND SUBTRACT

Answer is below in the picture:-

(From the problem, we know (triangle)ABC (round of equal of) (triangle)A'B'C'. So, <A'B'C' = <ABC {the properties of congruent triangles}. So, ray BC is the angle, bisector of angle ABA')

I hope it helps.

It is proved that the ray BC is the angle bisector of angle ABA'.

Angle bisectors are lines who bisect the considered angle. Bisect refers to splitting in two equal parts. Therefore, the bisected parts of the considered angle are half of the original angle.

When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if it in a mirror.

We will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.

From the given problem, we know Triangle A'B'C' is a reflection of triangle ABC across line BC.

Therefore, <A'B'C' = <ABC

By the properties of congruent triangles. Means if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Hence, the ray BC is the angle, bisector of angle ABA'.

Learn more about reflection here;

https://brainly.com/question/28186407

#SPJ5

The perimeter of the triangle is 10.47 units

The distance between two points is given by:

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Given the points R(2,1), S (2,5), and T(4,  1). Hence:

[tex]RS=\sqrt{(5-1)^2+(2-2)^2}=4\ units[/tex]

[tex]RT=\sqrt{(1-1)^2+(4-2)^2}=2\ units\\\\ST=\sqrt{(4-2)^2+(1-5)^2}=4.47\ units[/tex]

The perimeter of the triangle = 4 + 2 + 4.47 = 10.47 units

Find out more on triangle at: https://brainly.com/question/17335144

[tex]\mathfrak{5x + 15 = 28} [/tex]

[tex]\mathfrak{5x = 28-15} [/tex]

[tex]\mathfrak{5x = 13} [/tex]

[tex]\boxed{\mathfrak{x = \dfrac{13}{5}}} [/tex] → option B.

[tex]\mathbb{MIREU} [/tex]

Answer:

B

Step-by-step explanation:

The first thing you need to do is,

28 - 15

which is 13.

Now look at the answer choices and multiply them by 5.

It cannot be C or D because it would not fit the equation.

If anyone of them equal 13 then it is the answer.

Now lets try it.

43/5 = 8.6

13/5 = 2.6

8.6 times 5 is way to big so A is not it.

2.6 times 5 is 13.

So it is B.

Answer:

Wes

Step-by-step explanation:

This represents a positive correlation, meaning that when x increases, so does y. Because of x, y increases meaning that Wes is correct

Answer:

10,485,760

Step-by-step explanation:

Multiply -4

Answer:

  $189.48

Step-by-step explanation:

  $145.75 + 30% × 145.75 = $145.75×1.30 ≈ $189.48

Answer:

Answer:

night.....

Step-by-step explanation:

..............

Compound inequalities are used to combine several inequalities

The solution as a compound inequality is [tex]374<x <404[/tex]

Assume the correct amount of jelly beans in the jar is x.

15 away from x can be represented as 15 - x or x - 15

The correct number of jelly beans is given as 389.

So, when the statement is represented as an absolute inequality, we have:

[tex]|x - 15| < 389[/tex]

Express as compound inequality:

[tex]389 - 15<x <389 + 15[/tex]

Evaluate like terms

[tex]374<x <404[/tex]

Hence, the solution as a compound inequality is [tex]374<x <404[/tex]

Read more about compound inequalities at:

https://brainly.com/question/1851664

Answer:

B,C,D,F, those are yhe right answer

Answer:

6

Step-by-step explanation:

→ Do the 8.2 × 5

41

→ Minus the answer from the sum of the values

41 - ( 6 + 10 + 7 + 12 ) = 6

Answer:

Step-by-step explanation:

100 %/ 20 % = 5 servings

100 %/ 30 % = 3⅓ servings

He must consume 5 servings to get 100% of Vitamin A

In those servings he will consume 150% of Vitamin C

[tex]\cfrac{\underline{4}}{5}-\cfrac{1}{4}\implies \cfrac{(4)(\underline{4})~~ - ~~(5)(1)}{\underset{\textit{using this LCD}}{20}}\implies \cfrac{16-5}{20}\implies \cfrac{11}{20}[/tex]

Answer:

the answer is

[tex] {3}^{5} [/tex]

nCx⋅px⋅(1−p)n−x

llllllllllllllllllllllllllllllllllllll

Answer:

C

Step-by-step explanation:

because write in standard form hope it helps to you

Answer:

1.

m= 1; b= 4

m= -4; b= 2

m= 1; b= 0

m= 3/2; b= -9

m= -7; b= 4/5

2. C

Step-by-step explanation:

Question 1.

Your slope equation is

y=mx+b

The number before the x is your slope. The number added or subtracted after is your b.

Question 2.

Slope is rise over run.