Ben starts walking along a path at 3 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 7 mi/h. How long (in hours) will it be before Amanda catches up to Ben?



Enter the exact answer.
Hint: The distance formula is that distance = rate * time, so for example in one and a half hours, Ben has walked 3 * 1.5 miles.

Amanda catches up to Ben in ____________ hours.

Answer:

-00

OKAY

OKAY

OK

OK

DGSOTSITS6EUEYEYTITUTUTIT

Answer:

[tex]\displaystyle V = \frac{6561 \pi}{2}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Shell Method:                                                                                                         [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

y = x²

y = 0

x = 9

Step 2: Identify

Find other information from graph.

See attachment.

Bounds of Integration: [0, 9]

Step 3: Find Volume

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Applications of Integration

Book: College Calculus 10e

Answer:

RM 1200 kalau ada gambar cuba insert

9514 1404 393

Answer:

Step-by-step explanation:

Rewriting the equations to make x the subject, we have ...

  x = y² -1 . . . . . [eq1]

  x = 1 - y . . . . . .[eq2]

At the points of intersection, the difference will be zero.

  y² -1 -(1 -y) = 0

  y² +y -2 = 0

  (y -1)(y +2) = 0

The y-coordinates of points A and B are 1 and -2.

The corresponding x-coordinates are ...

  x = 1 -{1, -2} = {1 -1, 1+2} = {0, 3}

Then A = (0, 1) and B = (3, -2).

__

A differential of area can be written ...

  (x2 -x1)dy = ((1 -y) -(y² -1))dy = (2 -y -y²)dy

Integrating this over the interval y = [-2, 1] gives the area.

  [tex]\displaystyle A=\int_{-2}^1(2-y-y^2)\,dy=\left.(2y-\dfrac{1}{2}y^2-\dfrac{1}{3}y^3)\right|_{-2}^1\\\\=\left(2-\dfrac{1}{2}-\dfrac{1}{3}\right)-\left(2(-2)-\dfrac{(-2)^2}{2}-\dfrac{(-2)^3}{3}\right)=\dfrac{7}{6}+4+2-\dfrac{8}{3}\\\\=\boxed{4.5}[/tex]

The area of the shaded region is 4.5 square units.

Answer:

[tex]{19}C_1=19[/tex]

Step-by-step explanation:

We need to find the value of [tex]{19}C_1[/tex].

C stands for combination.

The formula of combination is as follows :

[tex]nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Here,

n = 19 and r = 1

So,

[tex]nC_r=\dfrac{19!}{1!(19-1)!}\\\\nC_r=\dfrac{19!}{1!\times 18!}\\\\nC_r=\dfrac{19\times 18!}{1!\times 18!}\\\\nC_r=19[/tex]

So, the value of [tex]{19}C_1[/tex] is 19.

Answer:

Your answer will be 19C1 =19

Answer:

0.0668 = 6.68% probability a randomly selected year will have an average snowfall above 200 inches.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set 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]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a average of 170 inches, and a standard deviation of 20 inches.

This means that [tex]\mu = 170, \sigma = 20[/tex]

What is the probability a randomly selected year will have an average snowfall above 200 inches?

This is 1 subtracted by the p-value of Z when X = 200. So

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

[tex]Z = \frac{200 - 170}{20}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a p-value of 0.9332.

1 - 0.9332 = 0.0668

0.0668 = 6.68% probability a randomly selected year will have an average snowfall above 200 inches.

Answer:

[tex]A=603.18\ cm^2[/tex]

Step-by-step explanation:

The length of a blade, r = 24 cm

The sweeping angle is 120°.

We need to find the total area cleaned at one sweep of the blade. The area of sector is given by :

[tex]A=\dfrac{\theta}{360}\times \pi r^2[/tex]

[tex]A=\dfrac{120}{360}\times \pi \times 24^2\\\\=603.18\ cm^2[/tex]

So, the total area cleaned at one sweep of the blade is [tex]603.18\ cm^2[/tex].

Answer:

1/2 or 50-50

Step-by-step explanation:

1/4 +1/4 = 1/2 or 50-50

Answer:

24% or 0.24

Step-by-step explanation:

100% or 1 minus 76% or 0.76. That makes 24% or 0.24.

To answer the question you should prob just put in 0.24.

Answer:

The probability that you get an even card or a spade is P = 0.596

Step-by-step explanation:

In a deck of 52 cards, all the cards have the exact same probability of being drawn.

So, the probability of drawing an even card of a spade, will be equal to the quotient between the number of even cards and spades, and the total number of cards (52).

First, let's found the number of even cards and spades.

There are 13 spades.

For each set, the even cards are:

{2. 4, 6, 8, 10}

(not counting the queen as a "12")

Then for each set, there are 6 even cards.

(there are four sets but we already counted the 6 even cards from the spade set, so we ignore that set)

Then there are 3 sets with 6 even cards each, there are:

3*6 = 18 even cards

So we have:

13 spades + 18 even cards = 31 cards that meet the condition.

The probability is then:

P = 31/52 = 0.596

The probability that you get an even card or a spade is P = 0.596

Answer:

3z+3x=2

Step-by-step explanation:

3z+8=12+3x-2

collecting like terms

3z-3x=12-2-8

3z-3x=2

3z=2+3x

divide through by three

z= ⅔+x

Answer:

[tex]z + 4 = 15 \\ z + 4 - 4 = 15 \\ z = 15 - 4 \\ z = 11[/tex]

z>11

Answer:

y=0

Step-by-step explanation:

1. Make variable y as subject for the first equation, which is y= -2x +10

2. substitute the first eq to the second one

3. x - (-2x+10) -5=0

4. solve x, which x = 5

5. substitute in eq 1 which is y= -2x +10

6. solve the eq, the possible solution is y=0

Answer:

I don't really understand the question

Step-by-step explanation:

c

Answer:

D)

[tex]an = -6 \times {( \frac{1}{4} )}^{n - 1} [/tex]

Step-by-step explanation:

(See the picture)

The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]

The general explicit formula for a geometric sequence is expressed as:

Given the following recursive functions:

[tex]a_1=-6\\ a_n=a_{n-1}\cdot\frac{1}{4} [/tex]

Get the next two terms:

[tex]a_2=a_{1}\cdot\frac{1}{4} \\ a_2=-6\cdot\frac{1}{4} \\ a_2=\frac{-3}{2} [/tex]

For the third term:

[tex]a_3=a_{2}\cdot\frac{1}{4} \\ a_3=\frac{-3}{2} \cdot\frac{1}{4} \\ a_3=\frac{-3}{8} [/tex]

The common ratio for the sequence will be [tex]\frac{1}{4} [/tex]

The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]

Learn more on explicit functions here: https://brainly.com/question/10308651

Answer:

Grey's Anatomy

Step-by-step explanation:

Answer:

They can buy up to 240 drinks.

Step-by-step explanation:

Let x = number of drinks

The price of 1 drink is 75¢ = $0.75

The price of x drinks is 0.75x

The store gives a discount of $100.

The rice of x drinks is

0.75x - 100

The total price of the drinks must be less than or equal to $80.

0.75x - 100 ≤ 80

Add 100 to both sides.

0.75x ≤ 180

Divide both sides by 0.75

x ≤ 240

Answer: They can buy up to 240 drinks.

Answer:

69.6

Step-by-step explanation:

sin 55 = x / 85

0.8191520443 = x / 85

x = 69.6

Answer:

D is the correct answer.

Step-by-step explanation:

You can get every y value by multiplying the x value by 3/2. This value never changes and there are no extra limitations.

Answer:

your answer is 18

Step-by-step explanation:

if one bar is shaped into 1/3 of strip.

know,

9 bars =3 × 9

=18

Answer:

(-5,2)

Step-by-step explanation:

A function is a relation where each y-value has a unique x-value. That means that x's can never repeat. Therefore, to solve find the ordered pair that does not have the same x-value as one of the points on the graph. The x-values currently represented on the graph are -4, -2, 2, 3. So, the only coordinate pair that does not repeat an x-value is the last option, (-5, 2).

Answer: You will never reach a sum of 2. You would need infinitely many terms to sum up.

============================================================

Explanation:

We have this sequence

1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, ...

which is geometric with the following properties

Notice how we multiply each term by 1/2 to get the next term. Eg: (1/4)*(1/2) = 1/8 or (1/16)*(1/2) = 1/32.

Since r = 0.5 is between -1 and 1, i.e. -1 < r < 1 is true, this means that adding infinite terms of this form will get us to approach some finite sum which we'll call S. This is because the new terms added on get smaller and smaller.

That infinite sum is

S = a/(1-r)

S = 1/(1-0.5)

S = 1/0.5

S = 2

So if we keep going with that pattern 1+1/2+1/4+... and do so forever, then we'll reach a sum of 2. However, we cannot go on forever since it's asking when we'll reach that specific sum. In other words, your teacher wants finitely many terms to be added.

In short, we'll never actually reach the sum 2 itself. We'll just get closer and closer.

Here's a list of partial sums

We can see that we're getting closer to 2, but we'll never actually get there. We'd need to add infinitely many terms to get to exactly 2.

Answer:

Following are the response to the given choice.

Step-by-step explanation:

Please find the complete question in the attached file.

Subjective opinion = Question of opinion.

Therefore this requires only just opinion and we don't have to do any actual calculations.

Does this seem like a great number of girls, a little number of girls, or a decent number of girls to you but if 1,300 babies were born, 5 of whom were females?

This is a small number of beautiful gals, in my honest opinion. We anticipate boys and girls to be produced about the very same frequency, thus I expect some half of them to be females if there are 1 300 newborns. You should have roughly 650 girls if 50% of the infants are girls, but now we only have five. That appears to me to be considerably low. which is your own opinion.

Answer:

Step-by-step explanation:

we are given  the angles ∠5 , ∠4 , ∠3 , but with one variable,  "X"  :)

also we are told ∠AOC is bisected by OB , meaning that ∠1 = ∠2

and the EC is perpendicular to OD ,  so ∠4+∠5=90°

since we are given ∠4 & ∠5,  lets use that to solve for "X"

:)

90= x-6 + 2x+4

90= 3x -2

92 =3x

30[tex]\frac{2}{3}[/tex] ° = x

30.6666666666666666 ° = x

Incurring a budget surplus and allowing that surplus to accumulate as idle Treasury balances. Then the correct option is B.

A span of transitory negative growth marked by a drop in Income in four quarters.

The negative effects of a recession would be reduced by the fiscal policy decision will be

Incurring a budget surplus and allowing that surplus to accumulate as idle Treasury balances

Then the correct option is B.

More about the Recession link is given below.

https://brainly.com/question/18075358

#SPJ1

9514 1404 393

Answer:

  4.1

Step-by-step explanation:

x is the short leg of a right triangle with hypotenuse 8.8 cm and longer leg 7.8 cm. Its measure is found using the Pythagorean theorem:

  x^2 +7.8^2 = 8.8^2

  x^2 = 77.44 -60.84 = 16.60

  x = √16.6

  x ≈ 4.1

Answer:

A. TRUE

Step-by-step explanation:

To determine if two triangles are congruent, we need to establish the facts that the three angles and three side lengths of one is congruent to corresponding angles and side lengths of the other triangle.

The diagram given only tells us the angle measure of the two triangles which are congruent to each other. The side length wasn't given. Therefore, the triangles may not be congruent.

The probability of winning at least one prize is 0.40951.

Probability is the likelihood that an event will occur.

The following information can be deduced:

P = probability of winning = 1/10

q = probability of not winning = 1- (1/10) = 9/10

x = no. of winning

then, p (x ≥ 1) = 1 - p (x < 1)

= 1 - p (x=0)

= 1 - ⁵C₀ (1/10)^⁰ (9/10)^(5-0)

= 1 - (1) (1) (9/10)^5

=  1 - (9/10)^5

= 1 - 0.59049

= 0.40951

Therefore, the probability is 0.40951.

Learn more about probability on:

https://brainly.com/question/24756209

#SPJ1

Answer:

42%

Step-by-step explanation:

to find percentages, you move the decimal point twice to the right