42 -3²= 2x
(42-9)/2= x
35/2=x
17.5=x

The sum of the first four terms of the given sequence which is aₙ = (aₙ ₋ ₁)² is gotten as; 278

We are given the arithmetic sequence as;

a₁ = 2

aₙ = (aₙ ₋ ₁)²

We already have the first term. Thus;

Second Term;

a₂ = (a₂ ₋ ₁)²

a₂ = 2² = 4

Third Term;

a₃ = 4²

a₃ = 16

Fourth Term;

a₄ = 16²

a₄ = 256

Thus;

Sum of first four terms is;

S₄ = 2 + 4 + 16 + 256

S₄ = 278

Read more about Arithmetic Sequence at; https://brainly.com/question/6561461

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Answer:

a1=2 an-(an-1)2 = 256

Step-by-step explanation:

Answer:

1e+18

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

It's been a while since I did this but here we go:

So to find if the triangle lengths are possible, we take the shorter two lengths and we add them.

Those shorter two lengths sum have to be greater than the longest length.

I hope this helps.

Answer: 2x^2 + 7x + 3

Step-by-step explanation:

(x+3)(2x+1)

(2x^2+1x+6x+3)

2x^2 + 7x + 3

Answer:

b

Step-by-step explanation:

Step-by-step explanation:

area of triangle = 1/2 × base × height

= 1/2 × 6×4

= 12 cm²

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you.

thankyou.

I think it’s 12cm but I am not sure sorry dude

Answer:

72 o de 7 y 2

Step-by-step explanation:

7: 7 y 1

2:2y1

72:1 2 3 4 5 6 8 9 12 24 36 y 72

Answer:

72.06

Step-by-step explanation:

Given that :

Side Lenght, a = 10

Edge length, b = 17

Using Pythagoras :

h = height of pyramid

h = sqrt (b² - 1/2a²)

h = sqrt(17^2 - 10^2/2)

h = sqrt(289 - 50)

h = 15.46

Slant height :

L = sqrt(h² + a²/4)

L = sqrt(15.46² + 25)

L = sqrt(239 + 25)

L = sqrt(264)

L = 16.25

Sinα = h/L

α = sin^-1 (15.46/16.25)

α = 72.060933

= 72.06

The approximate value of the angle formed between the base and a triangular face is 72.0775°.

Let [tex]h[/tex] be the distance between the center of the square base and the midpoint of the side of the square and let [tex]H[/tex] the height of the triangular face of the pyramid. By properties of the square and the Pythagorean theorem we derive expressions for [tex]h[/tex] and [tex]H[/tex], respectively:

Square base

[tex]h = 0.5\cdot L[/tex] (1)

Triangular face

[tex]H = \sqrt{l^{2}-0.25\cdot L^{2}}[/tex] (2)

Where:

Finally, by trigonometry we can derive an expression for the angle between the base and a triangular face ([tex]\theta[/tex]), in sexagesimal degrees:

[tex]\theta = \cos^{-1} \frac{h}{H}[/tex] (3)

If we know that [tex]L = 10\,km[/tex] and [tex]l = 17\,km[/tex], then the angle between the base and a triangular face is:

[tex]h = 5\,km[/tex]

[tex]H = \sqrt{17^{2}-5^{2}}[/tex]

[tex]H \approx 16.248\,km[/tex]

[tex]\theta = \cos^{-1} \frac{5\,km}{16.248\,km}[/tex]

[tex]\theta \approx 72.0775^{\circ}[/tex]

The approximate value of the angle formed between the base and a triangular face is 72.0775°.

We kindly invite to check this question on pyramids: https://brainly.com/question/16303112

Answer:

The proportion of faculty that earns more than $25,250 but less than $38,750 is 0.8025.

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

In this question, we have that:

Mean of 32000, Standard deviation of 3000.

Using Chebyshev's Theorem, what is the proportion of faculty that earns more than $25,250 but less than $38,750

This is within 38,750 - 32,000 = 32,000 - 25,250 = $6,750 of the mean.

Value of k:

This is k standard deviations from the mean. k is given by:

[tex]k = \frac{6750}{3000} = 2.25[/tex]

Proportion:

The percentage is:

[tex]p = 100(1 - \frac{1}{(2.25)^{2}}) = 80.25[/tex].

So the proportion is 0.8025

Answer:

Answer is 10/12 , 15/18 , 20/24 , 25/30 .

Step-by-step explanation:

1. 5/6 { Multiply both numerator and denominator with 2 }

5/6 = 10/12

2. 5/6 { Multiply both numerator and denominator with 3 }

5/6 = 15/18

3. 5/6 { Multiply both numerator and denominator with 4 }

5/6 = 20/24

4. 5/6 { Multiply both numerator and denominator with 5}

5/6 = 25/30

Answer:

0.873 = 87.3% probability that an athlete tests negative and is not a user of an illegal drug

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Not a user of an illegal drug.

Event B: Tests negative.

The test for this drug is 90% accurate for non-drug users (this means there is a 90% chance the test comes back negative if the person is a non-user)

This means that [tex]P(B|A) = 0.9[/tex]

It is estimated that 3% of the athletes competing in a large tournament are users of an illegal drug to enhance performance.

So 100 - 3 = 97% probability that the athlete does not use the drug, so [tex]P(A) = 0.97[/tex]

What is the probability that an athlete tests negative and is not a user of an illegal drug

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = 0.9*0.97 = 0.873[/tex]

0.873 = 87.3% probability that an athlete tests negative and is not a user of an illegal drug

Answer:

Greater than.

1 1/27 or 28/27.

Step-by-step explanation:

You're multiplying more than 2/3, so it is greater than.

2/3 x 1 5/9 is the same as 2/3 x 14/9. The answer to this is 28/27. Simplify to a mixed number which is 1 1/27.

Hope it helps!

Answer:

2/3 is less than and the answer is 28/27 = 1  1/27 = 2/3 x 1  5/9

Step-by-step explanation:

2/3 x 1  5/9 = 28/27 = 2/3 x 14/9 = 1  1/27

2/3  ≤ 28/27 = 1  5/9

Answer:

a.+37 b.-19 c.+130 d.+43

Step-by-step explanation:

a.72-35 b.21-40 c.250-120 d,68-15

Answer:

4x

Step-by-step explanation:

2x(-1+3)

distributive property: -2x+6x

-2x+6x=4x

Answer:

H

Step-by-step explanation:

Answer:

a.) 48m

b.) 158m

m<B.) 73 degrees

Step-by-step explanation:

Answer:

6.10 for 1 and 4.50 . for 2

Step-by-step explanation:

Answer:

option C : 3 units

Step-by-step explanation:

radius of circle is 3 units

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you .

Answer:

Step-by-step explanation:

[tex]V=h\pi r^2\\ \\ h=7\ and\ r=3\\ \\ V=8(3^2)\pi\\ \\ V=72\pi cm^3\\ \\ V\approx 226.2cm^3[/tex]

Answer:

cant see the choices what the graph is a function

Step-by-step explanation:

Answer:

i need to know the answer choices

Step-by-step explanation:

Answer:

-25 is correct I think

Step-by-step explanation:

Answer:

the slope is 3 because y2-y1/x2-x1 is equal to your slope.

5-2 is 3 and 2-1 is 1, 3/1 is equal to 3.

Step-by-step explanation:

Answer:

The answer is 3

Step-by-step explanation:

Have a great Thursday!

:)

Answer:

a. [tex]m(t) = 26.67 - 26.67e^{-0.03t}[/tex] b. 7.44 s

Step-by-step explanation:

a. If the concentration of salt in the brine entering the tank is 0.2 kg/L, determine the mass of salt in the tank after t min.

Let m(t) be the mass of salt in the tank at any time, t.

Now, since a brine solution flows in at a rate of 4 L/min and has a concentration of 0.2 kg/L, the mass flowing in per minute is m' = 4 L/min × 0.2 kg/L = 0.8 kg/min

Now, the concentration in the tank of volume 100 L at any time, t is m(t)/100 L. Since water flows out at a rate of 3 L/min, the mass flowing out per minute is

m(t)/100 × 3 L/min = 3m(t)/100 kg/min

Now the net rate of change of mass of salt in the tank per minute dm/dt = mass flowing in -mass flowing out

dm/dt = 0.8 kg/min - 3m(t)/100 kg/min

So, dm/dt = 0.8 - 0.03m(t)

The initial mass of salt entering m(0) = 0 kg

dm/dt = 0.8 - 0.03m(t)

separating the variables, we have

dm/[0.8 - 0.03m(t)] = dt

Integrating, we have

∫dm/[0.8 - 0.03m(t)] = ∫dt

-0.03/-0.03 × ∫dm/[0.8 - 0.03m(t)] = ∫dt

1/(-0.03)∫-0.03dm/[0.8 - 0.03m(t)] = ∫dt

-1/0.03㏑[0.8 - 0.03m(t)] = t + C

㏑[0.8 - 0.03m(t)] = -0.03t - 0.03C

㏑[0.8 - 0.03m(t)] = -0.03t + C'  (C'= -0.03C)

taking exponents of both sides, we have

[tex]0.8 - 0.03m(t) = e^{-0.03t + C'} \\0.8 - 0.03m(t) = e^{-0.03t}e^{C'}\\0.8 - 0.03m(t) = Ae^{-0.03t} A = e^{C'}\\0.03m(t) = 0.8 - Ae^{-0.03t}\\m(t) = 26.67 - \frac{A}{0.03} e^{-0.03t}\\when t = 0 \\m(0) = 0\\m(0) = 26.67 - \frac{A}{0.03} e^{-0.03(0)}\\\\0 = 26.67 - \frac{A}{0.03} e^{0}\\26.67 = \frac{A}{0.03} \\\frac{A}{0.03} = 26.67\\\frac{A}{0.03} = 6.67\\A = 26.67 X 0.03\\A = 0.8\\m(t) = 26.67 - \frac{A}{0.03} e^{-0.03t}\\\\m(t) = 26.67 - \frac{0.8}{0.03} e^{-0.03t}\\[/tex]

So, the mass of the salt after t min is

[tex]m(t) = 26.67 - 26.67e^{-0.03t}[/tex]

b. When will the concentration of salt in the tank reach 0.1 kg/L?

When the concentration of the salt reaches 0.1 kg/L, m(t) = 0.1 kg/L

Solving the equation for t,

[tex]m(t) = 26.67 - 6.67e^{-0.03t}\\0.1 = 26.67 - 26.67e^{-0.03t}\\26.67e^{-0.03t} = 26.67 - 0.1\\26.67e^{-0.03t} = 26.57\\e^{-0.03t} = 26.56/26.67\\e^{-0.03t} = 0.9963\\[/tex]

taking natural logarithm of both sides, we have

-0.03t = ㏑0.9963

-0.03t = -0.0038

t = -0.0038/-0.03

t = 0.124 min

t = 0.124 × 60 s

t = 7.44 s

Answer:

0.2y+10

Step-by-step explanation:

Answer:

We have this equation:

0.4y - 0.2y + 10 = 11.8

You can simplify

0.2y + 10 = 11.8

Then, you can substract 10 in both sides:

0.2y = 11.8 - 10

0.2y = 1.8

You can now divide right and left side by 0.2 and get y:

0.2y/0.2 = 1.8/0.2

y =  14