Kaitlin is riding her bike. The number of revolutions (turns) her wheels make varies directly with the distance she travels. See the graph below.



How far does Kaitlin travel per revolution?

What is the slope of the graph?

The expression equivalent to x(y)^(2/9) is option D.  x [tex]\sqrt[9]{y^{2} }[/tex].

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is x(y)^(2/9).

We have to find the equivalent expressions of this.

We can write the exponent 2/9 as 2 × 1/9.

So, x(y)^(2/9) = x(y)^(2 × 1/9)

We have the power of a power rule,

(xᵃ)ᵇ = xᵃᵇ

Using this rule,

(y)^(2 × 1/9) = (y²)^(1/9)

So, x(y)^(2/9) = x (y²)^(1/9)

Also, we have,

[tex]\sqrt[n]{x}[/tex] = [tex](x)^{\frac{1}{n}}[/tex]

So, (y²)^(1/9) = [tex]\sqrt[9]{y^{2} }[/tex]

x(y)^(2/9) = x [tex]\sqrt[9]{y^{2} }[/tex]

Hence the equivalent expression is  x [tex]\sqrt[9]{y^{2} }[/tex].

Learn more about Expressions here :

https://brainly.com/question/28170201

#SPJ7

Your question is incomplete. The complete question is as follows.

Answer:

Compound interest is $7,037,339.2

Step-by-step explanation:

[tex]{ \boxed{ \bf{A=P(1+ \frac{r}{100} ) {}^{n} }}}[/tex]

substitute:

[tex]{ \sf{ = 50000(1 + \frac{6.4}{100}) {}^{10} }} \\ \\ = { \sf{50000(1.64) {}^{10} }} \\ \\ { = \sf{7037339.2}}[/tex]

Answer:

0.1151 = 11.51% probability of completing the project over 20 days.

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.

Expected completion time of the project = 22 days.

Variance of project completion time = 2.77

This means that [tex]\mu = 22, \sigma = \sqrt{2.77}[/tex]

What is the probability of completing the project over 20 days?

This is the p-value of Z when X = 20, so:

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

[tex]Z = \frac{20 - 22}{\sqrt{2.77}}[/tex]

[tex]Z = -1.2[/tex]

[tex]Z = -1.2[/tex] has a p-value of 0.1151.

0.1151 = 11.51% probability of completing the project over 20 days.

In a unit circle a line reaching from origin to the circle's circumference specifies the trigonometric functions.

A point where the line which comes from origin to the circumference intersecting it has coordinates [tex](\cos\theta,\sin\theta)[/tex].

In our case [tex]\theta=45^\circ[/tex] which lifts the line up by 45 degrees and makes it intersect circumference at [tex](\cos45^\circ,\sin45^\circ)[/tex].

In the upper right quadrant the angle between x and y axis is 90 degrees so a line coming in at angle of 45 degrees would split the quadrant in half, that means sine and cosine 45 degrees will be equal.

As you may noticed a point has coordinates cos, sin which means the distance between 0 and y coordinate where the point on a circle is, is called [tex]\cos\theta=\cos45^\circ[/tex].

Because cosine 45 degrees is so simple in interpretation it has a known value of [tex]\cos45^\circ=\sin45^\circ=\frac{\sqrt{2}}{2}[/tex].

Hope this helps :)

Answer:

3125

Step-by-step explanation:

5* 5* 5* 5 = 3125

Answer:

The decision rule is to Reject H0 if Z ≤ -1.282

Step-by-step explanation:

We are given;

Population mean; μ = 409 g

Sample mean; x¯ = 401 g

Sample size; n = 21

Standard deviation; s = 26

Let's define the hypotheses;

Null hypothesis; H0: μ = 409 g

Alternative hypothesis; Ha : μ ≠ 409 g

Formula for test statistic is;

z = (x¯ - μ)/(s/√n)

z = (401 - 409)/(26/√21)

z = -1.410

z-value is negative and thus this is a lower tail test.

At significance level of 0.1, the critical value is -1.282.

Thus, the decision rule is;

Reject H0 if Z ≤ -1.282

Answer:

Your wrong, it's 65%.

Step-by-step explanation:

The reason why: You can calculate the percentage by dividing the number of accepted students by the total of business students, 65/100 which equals 65%.

yw :)

The probability that a student was accepted is 5.0% since option  b be the correct answer.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1,

We have to find out the probability of the selection of a student applied for the business program.

We know that, Probability= Total number of events occurred÷ Total number of possible outcomes/events

So, Probability that a student applying to the business program got selected= No of accepted students for business program÷Total number of students applied for business program=65÷100=0.65For converting a number into percentage we multiply the number by 100 that is 0.65*100=65%So, probability that a student applying for business program gets selected is 65%.

Learn more about probability here- https://brainly.com/question/11234923

#SPJ2

Answer:

48 m^3

Step-by-step explanation:

If the scale factor of linear dimensions between two solids is k, then the scale factor for areas is k^2, and the scale factor of volumes is k^3.

Let's call the solid with 16 m^2 of area solid A, and the other one solid B.

The scale factor of areas from, A to B is (100 m^2)/(16 m^2) = 25/4

In other words, multiply the area of the solid A by 25/4 to get the area of solid B.

Let's check: 16 m^2 * 25/4 = 16 * 25/4 m^2 = 4 * 25 m^2 = 100 m^2

We do get 100 m^2 for solid B, so the area scale factor of 25/4 is correct.

The area scale factor is k^2, so we have:

k^2 = 25/4

We solve for k:

k = 5/2

Now we cube both sides to get k^3, the scale factor of volumes.

k^3 = 5^3/2^3

k^3 = 125/8

Let V = volume of smaller solid, solid A.

V * 125/8 = 750 m^3

V = 750 * 8/125 m^3

V = 48 m^3

Answer:

by doing the problem and you should get -24

Step-by-step explanation:

Answer:

10/16=5/8

6+6+4=16

The probability is 5/8

Answer:

y= -6x-6, I think, hope it helped

Step-by-step explanation:

Answer:

the speed of the boat is 6.67 ft/s

Step-by-step explanation:

Given;

height of the winch, h = 12 ft

the rate at which the winch pulls, the rope, = 4 ft/s

This form a right triangle problem;

let the height of the right triangle = h

let the base of the triangle = b (this corresponds to the horizontal displacement of the boat)

let the hypotenuse side = c

c² = b² + h²

[tex]2c\frac{dc}{dt} = 2b\frac{db}{dt} + 2h \frac{dh}{dt}\\\\The \ height \ of \ the \ winch \ is \ not \ changing \\\\2c\frac{dc}{dt} = 2b\frac{db}{dt} + 2h (0)\\\\2c\frac{dc}{dt} = 2b\frac{db}{dt} \\\\c\frac{dc}{dt} = b\frac{db}{dt} ----(*) \\\\when;\\\\the\ hypotenuse \ c = 15 \ ft\\\\the \ the \ the \ height, h = 12 \ ft\\\\the \ base, b \ becomes ;\\\\b^2 = c^2 -h^2\\\\b^2 = 15^2 - 12^2\\\\b^2 = 81\\\\b = \sqrt{81} \\\\b = 9 \ ft\\\\\\from \ the \ equation (*) \ above;\\\\[/tex]

[tex]c\frac{dc}{dt} = b \frac{db}{dt} \\\\dc/dt = 4 \ ft/s, \ \ c = 15 \ ft, \ \ b = 9 \ ft\\\\15 (4) = 9\frac{db}{dt} \\\\60 = 9 \frac{db}{dt} \\\\\frac{db}{dt} = \frac{60}{9} = 6.67 \ ft/s[/tex]

Therefore, the speed of the boat is 6.67 ft/s

70 mL=25% alcohol

?mL=90% alcohol

90×70÷25

=252 mL

I think do like this....I'm not sure

Hope this help you

9514 1404 393

Answer:

  420 mL

Step-by-step explanation:

Let x represent the amount of the 95% solution needed in the mixture. The the total amount of alcohol in the mixture is ...

  0.25×70 + 0.95(x) = 0.85(70 +x)

  0.10x = 42 . . . . . . . . subtract 17.5+0.85x

  x = 420 . . . . . . . . divide by 0.10

You will need 420 mL of the 95% solution.

__

Additional comment

There will be 70+420 = 490 mL of solution, of which 85%, or 0.85×490 = 416.5 ml is alcohol. That alcohol is the total of 0.25×70 = 17.5 mL of alcohol from the 25% solution and 0.95×420 = 399 mL of alcohol from the added 95% solution. (17.5 +399 = 416.5)

Answer:

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}x_{1} &x_{2} &x_{3} \\y_{1} &y_{2} &y_{3} \end{array}\right][/tex]  ---------> [tex]\left[\begin{array}{ccc}-x_{1} &-x_{2} &-x_{3} \\y_{1} &y_{2} &y_{3} \end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-3&-6&-3\\-3&3&3\end{array}\right][/tex]

If x = -1, you have

2(-1) + 3 cos(-1) + e ⁻¹ ≈ -0.0112136 < 0

and if x = 0, you have

2(0) + 3 cos(0) + e ⁰ = 4 > 0

The function f(x) = 2x + 3 cos(x) + eˣ is continuous over the real numbers, so the intermediate value theorem applies, and it says that there is some -1 < c < 0 such that f(c) = 0.

Answer:

6x^4−2x^3+26x^2+x+14

Step-by-step explanation:

−x^3+26x^2−7x−13+6x^4−x^3+8x+27

= 6x^4−x^3−x^3+26x^2−7x+8x−13+27

= 6x^4−2x^3+26x^2+x+14

Answer:

Step-by-step explanation:

= -x3+ 26x2- 7x-13+6x4-x3+8x+27

=6x4-2x3+26x2+x+14

Answer:

5 lawns

Step-by-step explanation:

Firstly, the equation is 25x + 10 = 135

Ezri makes $25 for every lawn she mows (25x) and has an automatic $10 per day (10). In order to make $135 we take what she makes each day and set it equal to 135.

To solve, we subtract 10 from both sides to create 25x = 125. We then divide 25 from both sides to get x=5. This means that Ezri needs to mow 5 lawns in order to make $135.

I hope this is helpful to you!

**To anyone out there seeing this - let me know if you think I made a mistake and I will fix it.**

Answer:

A. 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Identify points from graph.

Point (8, 5)

Point (4, 2)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

i need the graph

Step-by-step explanation:

.

Answer:

$1.85 = £1

Step-by-step explanation:

55680/72.50 = 786

55680/128 = 435

435x = (786 + 19.80)

x = 805.8/435

x = 1.85

Answer:

£1 = $1.72

Step-by-step explanation:

55680/72.50=768

55680/128=435

768.00 - 19.80 = 748.20

x = 748.20 / 435

x = $1.72

The angle between the planes is the same as the angle between their normal vectors, which are

n₁ = ⟨1, 1, 1⟩

n₂ = ⟨4, 3, 1⟩

The angle θ between the vectors is such that

⟨1, 1, 1⟩ • ⟨4, 3, 1⟩ = ||⟨1, 1, 1⟩|| ||⟨4, 3, 1⟩|| cos(θ)

Solve for cos(θ) :

4 + 3 + 1 = √(1² + 1² + 1²) √(4² + 3² + 1²) cos(θ)

8 = √3 √26 cos(θ)

cos(θ) = 8/√78

Answer:

Step-by-step explanation:

Never mind the minus for a second. What is the approximate value of sqrt(50)?

Isn't it about 7 or just a tiny bit over?

That's the answer here. Find the square root first, and then add the minus.

<o==o==o==o==o==o==o==o

  -7  -6  -5  -4  - 3  - 2  - 1    0

Answer:

385

Step-by-step explanation:

Answer:

V≈50.27cm³

Step-by-step explanation:

Using the formulas

V=πr2h

3

l=r2+h2

Solving forV

V=1

3πr2l2﹣r2=1

3·π·42·52﹣42≈50.26548cm³

The answer is simply just a+b.

Solution:

log10^6=log10^2+log10^3

Since log10^2=a and log10^3=b,

The answer is a+b.

I think that the answer is a+b.

Answer:

D

Does the answer help you?

Answer:

D

Step-by-step explanation:

Answer: 7x + 9y >_ (more or equal) 314

X + Y <_ ( less or equal) 35

Step-by-step explanation:

Answer:

h+s≤35 and 7h + 9s >_314

Step-by-step explanation:

The best conclusion to make based on the data is: The difference of the means is significant because the re-randomizations show that it is outside the range of what could happen by chance.

Given:

Drug A= Decrease serotonin level by means of 36 nanograms per millimeter

Drug B= Decrease serotonin level by means of 20 nanograms per millimeter

Hence,

When we take a look at the difference of means data that was given, we would see that the different of means is significant  between the means of Drug A and Drug B due to chance or random variation.

Based on the fact that  the re-randomizations indicate that it is outside the range of what could happen by chance.

Therefore the correct option is A.

Learn more about difference of mean here:https://brainly.com/question/6281520

#SPJ1

Answer:

The difference of the means is NOT significant because the rerandomizations show that it is within the range of what likely happens by chance

Step-by-step explanation:

Took the test and this is 100% the answer. Hope it helps.

Answer:

x = 5/2

Step-by-step explanation:

4x-1=9

Add 1 to each side

4x-1+1=9+1

4x = 10

Divide by 4

4x/4 = 10/4

x = 5/2

Answer:

3

Step-by-step explanation:

3 = 9 \:th \\ 1 = 3 \\ 3 \times 3 = 9 \\ 9 \div 3 = 3 \\ so \: that \: answer \: is \: 3