Rational exponents of 2161/3?​

Let x be the first number in the sequence. Then the first three numbers are

{x, x + 3, x + 6}

The next sentence says that the sequence

{x + 1, x + 9, x + 25}

is geometric, which means there is some fixed number r for which

x + 9 = r (x + 1)

x + 25 = r (x + 9)

Solve for r :

r = (x + 9)/(x + 1) = (x + 25)/(x + 9)

Solve for x :

(x + 9)² = (x + 25) (x + 1)

x ² + 18x + 81 = x ² + 26x + 25

8x = 56

x = 7

Then the three numbers are

{7, 10, 13}

(3x +2)(x -3)

FOIL method

3x^2 -9x + 2x -6

3x^2 -7x -6

Your answer: 3x^2 -7x -6

Answer:

[tex]- \frac{\pi}{3}[/tex]

Step-by-step explanation:

Given

[tex]y = -3\cos(3x - \pi) + 5[/tex]

Required

The phase

We have:

[tex]y = -3\cos(3x - \pi) + 5[/tex]

Rewrite as:

[tex]y = -3\cos(3(x - \frac{\pi}{3})) + 5[/tex]

A cosine function is represented as:

[tex]y = A\cos(B(x + C)) + D[/tex]

Where:

[tex]C \to[/tex] Phase

By comparison:

[tex]C = - \frac{\pi}{3}[/tex]

Hence, the phase is: [tex]- \frac{\pi}{3}[/tex]

Answer: y = 3x + 6

Step-by-step explanation:

(x-intercept of -2: (-2,0))

(slope = m)

y = mx + b, (-2,0), m = 3

[tex]y=mx+b\\0=3(-2)+b\\0=-6+b\\b=6\\y=3x+6[/tex]

Answer:

m∠1 = 105°

m∠2 = 75°

Step-by-step explanation:

From the picture attached,

Two lines 'a' and 'b' are parallel and a transversal 't' is intersecting these lines at two distinct lines.

Therefore, m∠2 = 75° [Corresponding angles measure the same]

m∠1 + m∠2 = 180° [Linear pair of angles are supplementary]

m∠1 + 75° = 180°

m∠1 = 105°

[tex]\\ \sf\longmapsto y=(6x-5)\sqrt{8x-3}[/tex]

[tex]\\ \sf\longmapsto y=6(-4)-5\sqrt{8(-4)-3}[/tex]

[tex]\\ \sf\longmapsto y=-24-5\sqrt{-32-3}[/tex]

[tex]\\ \sf\longmapsto y=-29\sqrt{-35}[/tex]

[tex]\\ \sf\longmapsto y=-29\times 35i[/tex]

[tex]\\ \sf\longmapsto y=-1015i[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

The expression written is interpreted according to the order of operations as ...

  sin(x) -(1/x) -1

As x approaches 0 from the left, this approaches +∞. As x approaches 0 from the right, this approaches -∞. These values are different, so the limit does not exist.

__

Maybe you intend ...

  sin(x -1)/(x -1)

This can be evaluated directly at x=0 to give sin(-1)/-1 = sin(1). The argument is interpreted to be radians, so sin(1) ≈ 0.84147098...

The limit is about 0.841 at x=0.

0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.

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For each student, there are only two possible outcomes. Either they score an A, or they do not. The probability of a student scoring an A is independent of any other student, which means that the binomial probability distribution is used to solve this question.

Additionally, to find the proportion of students who scored an A, the normal distribution is used.

----------------

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which  is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of a success.

----------------

Normal Probability Distribution

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

In a set with mean and standard deviation , 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.

----------------

Proportion of students that scored an A:

Scores have a mean of 79 and a standard deviation of 11.3, which means that [tex]\mu = 79, \sigma = 11.3[/tex]

Scores of 90 or higher are graded an A, which means that the proportion is 1 subtracted by the p-value of Z when X = 90, so:

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

[tex]Z = \frac{90 - 79}{11.3}[/tex]

[tex]Z = 0.97[/tex]

[tex]Z = 0.97[/tex] has a p-value of 0.8340.

1 - 0.8340 = 0.166

The proportion of students that scored an A is 0.166.

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Probability that 6 students or more will score an "A" on the final exam:

Binomial distribution.

22 students, which means that [tex]n = 22[/tex]

The proportion of students that scored an A is 0.166, which means that [tex]p = 0.166[/tex]

The probability is:

[tex]P(X \geq 6) = 1 - P(X < 6)[/tex]

In which

[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]

Then

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{22,0}.(0.166)^{0}.(0.834)^{22} = 0.0184[/tex]

[tex]P(X = 1) = C_{22,1}.(0.166)^{1}.(0.834)^{21} = 0.0807[/tex]

[tex]P(X = 2) = C_{22,2}.(0.166)^{2}.(0.834)^{20} = 0.1687[/tex]

[tex]P(X = 3) = C_{22,3}.(0.166)^{3}.(0.834)^{19} = 0.2239[/tex]

[tex]P(X = 4) = C_{22,4}.(0.166)^{4}.(0.834)^{18} = 0.2117[/tex]

[tex]P(X = 5) = C_{22,5}.(0.166)^{5}.(0.834)^{17} = 0.1517[/tex]

Then

[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0184 + 0.0807 + 0.1687 + 0.2239 + 0.2117 + 0.1517 = 0.8551[/tex]

[tex]P(X \geq 6) = 1 - P(X < 6) = 1 - 0.8551 = 0.1449[/tex]

Thus

0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.

For a problem that used the normal distribution, you can check https://brainly.com/question/15181104, and for a problem that used the binomial distribution, you can check https://brainly.com/question/15557838

Answer:

Area = 240 cm²

Perimeter = 80 cm

Step-by-step explanation:

✔️ Area of the triangle = ½*base*height

base of the triangle = 24 cm

height = 20 cm

Plug in the known values

Area = ½*24*20

= 12*20

Area = 240 cm²

✔️Perimeter of the triangle = sum of all the three sides that make up the triangle

Perimeter = 22 + 24 + 34

= 80 cm

Answer:

z = √3

Step-by-step explanation:

sin (30°) = z / 2√3

z = sin (30°) 2√3

z = √3

Answer:

First, find two points on the graph:

Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{8-2}{2-0} =\frac{6}{2}=3[/tex]

16 + (-3) = 16 - 3 = 13

Answer:

the ans is 252................

9514 1404 393

Answer:

  Yes, that distance is the hypotenuse of a right triangle whose sides are known

Step-by-step explanation:

The diagram seems to show the path of the ball as being two segments that are at right angles to each other. Then the direct-line distance to the hole from the tee is the hypotenuse (part A) of the triangle.

Since the leg lengths are known, the Pythagorean theorem can be used (part B) to find the length of the hypotenuse. (The answer to Part B is also the answer to Part C.)

Answer:

605 boys.

Step-by-step explanation:

5:7 means 5 parts consists of boys and 7 parts consist of girls.

Since 7 parts = 847, 1 part = 121 and 5 parts = 605

Hence there are 605 boys.

Hope you have a nice day :)

Answer:

b) Y =5.73X +4.36

C)  =5.73225*(21)X +4.359

    124.73625

D) 163.728 = 5.73X +4.36  

     X = (163.728 - 4.36)/5.73

     X = 27.81291449

  Year would be 2027

Step-by-step explanation:

x1 y1  x2 y2

4 27.288  16 96.075

(Y2-Y1) (96.075)-(27.288)=   68.787  ΔY 68.787

(X2-X1) (16)-(4)=    12  ΔX 12

slope= 5 41/56    

B= 4 14/39    

Y =5.73X +4.36      

Answer:

Step-by-step explanation:

The decay rate of strontium-90 is -.0244 as given.

For b., we have to use the formula to find out how much is left after 30 years. This will be important for part d.

[tex]A(t)=400e^{-.0244(30)}[/tex] which simplifies a bit to

A(t) = 400(.4809461353) so

A(t) = 192.4 g

For c., we have to find out how long it takes for the initial amount of 400 g to decay to 100:

[tex]100=400e^{-.0244t}[/tex]. Begin by dividing both sides by 400:

[tex].25=e^{-.0244t[/tex] and then take the natural log of both sides:

[tex]ln(.25)=lne^{-.0244t[/tex] . The natural log and the e cancel each other out since they are inverses of one another, leaving us with:

ln(.25) = -.0244t and divide by -.0244:

61.8 years = t

For d., we figured in b that after 30 years, 192.4 g of the element was left, so we can use that to solve for the half-life in a different formula:

[tex]A(t)=A_0(.5)^{\frac{t}{H}[/tex] and we are solving for H. Filling in:

[tex]192.4=400(.5)^{\frac{30}{H}[/tex] and begin by dividing both sides by 400:

[tex].481=(.5)^{\frac{30}{H}[/tex] and take the natural log of both sides, which allows us to pull the exponent out front. I'm going to include that step in with this one:

ln(.481) = [tex]\frac{30}{H}[/tex] ln(.5) and then divide both sides by ln(.5):

[tex]\frac{ln(.481)}{ln(.5)}=\frac{30}{H}[/tex] and cross multiply and isolate the H to get:

[tex]H=\frac{30ln(.5)}{ln(.481)}[/tex] and

H = 28.4 years

The general solution of [tex]\tan bx = 2[/tex] and [tex]x = 0.3[/tex] is [tex]x = 0.095\pi \mp 0.271\pi\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].

From Trigonometry we remember that Tangent is a Transcendental Function that is positive both in 1st and 3rd Quadrants and have a periodicity of [tex]\pi[/tex] radians.  The procedure consists in using concepts of Direct and Inverse Trigonometric Functions as well as characteristics related to the behavior of the tangent function in order to derive a General Formula for every value of [tex]x[/tex], measured in radians.

First, we solve the following system of equations for [tex]b[/tex]:

[tex]\tan bx = 2[/tex] (1)

[tex]x = 0.3[/tex] (2)

Please notice that angles are measured in radians.

(2) in (1):

[tex]\tan 0.3b = 2[/tex]

[tex]0.3\cdot b = \tan^{-1} 2[/tex]

[tex]b = \frac{10}{3}\cdot \tan^{-1}2[/tex]

[tex]b\approx 3.690[/tex]

Under the assumption of periodicity, we know that:

[tex]y = \tan bx[/tex]

[tex]b\cdot x \pm \pi\cdot i = \tan^{-1} y[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]

[tex]b\cdot x = \tan^{-1}y \mp \pi\cdot i[/tex]

[tex]x = \frac{\tan^{-1}y \mp \pi\cdot i}{b}[/tex]

If we know that [tex]y = 2[/tex] and [tex]b \approx 3.690[/tex], then the general solution of this trigonometric function is:

[tex]x = \frac{0.352\pi \mp \pi\cdot i}{3.690}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]

[tex]x = 0.095\pi \mp 0.271\pi\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]

The general solution of [tex]\tan bx = 2[/tex] and [tex]x = 0.3[/tex] is [tex]x = 0.095\pi \mp 0.271\pi\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].

For further information, you can see the following outcomes from another users:

https://brainly.com/question/3056589

https://brainly.com/question/11526967

Answer:

c: 21/205

Step-by-step explanation:

The probability of choosing a yellow marble first is 12/41 bc there are 12 yellow marbles and 41 marbles to choose from.

The probability of choosing a red marble is 14/40 bc there are 14 red marbles and 40 marbles to choose from( since you have removed the marble you first chose so there are 40 marbles left).

Multiplying these two together, 12/41 * 14/40 = 168/1640, simplified it's 21/205.

Answer:

dv = surface area * dh

so

dv/dt = surface area * dh/dt

width at surface = 40 + (80-40)(30/40)

= 40 + 30 = 70 cm = 0.70 m

so

surface area = 9 * .7 = 6.3 m^2

so

.3 m^3/min = 6.3 m^2 * dh/dt

and

dh/dt = .047 meters/min or 4.7 cm/min

Step-by-step explanation:

Answer:

$240

Step-by-step explanation:

A year has 12 month in it so lets multiply the 10 by 12 which is $120,Mean a year is $120 so 2years will be $120×2 which is $240

Answer:

x+1/5x

Step-by-step explanation:

Because the eqaution would be x+10%=x+1/10+10%=1/5+x

Then the equation equals x+1/5

Answer:

184.22

Step-by-step explanation:

Distance Formula: [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

Point 1: (9,0)

Point 2: (5,-8)

D = sqrt[ (5 - 9)^2 + (-8 - 0)^2 ]

D = sqrt[ (-4)^2 + (-8)^2 ]

D = sqrt[ 16 + 64]

D = sqrt(80)

Hope this helps!

Answer:

2) Add 21 to both sides

Step-by-step explanation:

When solving [tex]16x-21=52[/tex] for [tex]x[/tex], our goal to isolate [tex]x[/tex] such that we have [tex]x[/tex] set equal to something.

Therefore, we want to start by adding 21 to both sides. This leaves us with [tex]16x=73[/tex] and we are one step closer to isolating [tex]x[/tex].

Answer: 150 degrees

Step-by-step explanation: 10+ 20 = 30

180-30 = 150 degrees.

Answer:

I believe the answer is 4 37/50!