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Answer:

if its easy do it

Step-by-step explanation:

Answer:

7.5/15 or something because yes

The zeros of the function of the graph lies at 0 and 2.

And the function of the graph is a polynomial of degree 4.

The probability that all 7 graduates selected at random received a starting salary of $60,000 or more is , 0.0065

This is a binomial probability problem where we have a sample of size 7 and want to find the probability that all 7 graduates received a starting salary of $60,000 or more.

We know that 40% of mathematics graduates received a starting salary of $60,000 or more,

So, the probability of any one graduate receiving a salary of $60,000 or more is 0.4.

Using the binomial probability formula, we can calculate the probability as follows:

P(X = 7) = (n choose X) pˣ (1-p)ⁿ⁻ˣ

where n is the sample size, x is the number of graduates who received a starting salary of $60,000 or more, p is the probability of success (i.e., receiving a salary of $60,000 or more), and (n choose X) is the number of ways to select X graduates out of n.

So in this case, we have:

n = 7, X = 7 and p = 0.4

Plugging into the formula, we get:

P(X = 7) = (7 choose 7) 0.4⁷ (1-0.4)⁷⁻⁷

P(X = 7) = (1) 0.4⁷ (0.6)⁰

P(X = 7) = 0.0065

Therefore, the probability that all 7 graduates selected at random received a starting salary of $60,000 or more is , 0.0065

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A garrison has provision for 30 days for certain men. if 2/3 of them do not attend the mess, then the food will last for 45 days. So, the correct option is (a).

Given that the provision for certain men in the garrison is for 30 days. Also, given that 2/3 of them do not attend the mess, then we have to find the number of days the food will last.

The food will last longer if the number of people attending the mess is less because the same amount of food will have to be shared between fewer people. Therefore, the food will last for more than 30 days.

Let the total number of men be x, then the number of men attending the mess is (1/3)x

And the number of men not attending the mess is (2/3)x.

Therefore, the food will last for (30 × x) / (2/3)x = 45 days

Hence, the answer of the question is 46 days.

Your question is incomplete but most probably your full question was:

A garrison has provision for 30 days for certain men. if 2/3 of them do not attend the mess, then the food will last for?

(a) 45 days

(b) 65 days

(c) 50 days

(d) none of above

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Answer:

g(x)=f(x+6)

Step-by-step explanation:

it was translated backward by 6 units

Using the Algebra operation,

Radon have 2 dimes and 2 quaters .

We have given that,

Radon has a cup of quarters and dimes .

total value of dimes and quaters = $4.90

let total number of quarters and number of dimes be x and y respectively.

numbers of quaters are 2 less than 2 times the number of dimes

i.e., x = 2y - 2 ---(1)

total values of quaters and dimes in dollars

=> y/10 + 25x/6 = $4.90

from equation (1) put value of x in equation 2

=> y/10 + 25 ( 2y-2)/6 = $4.90

=> y/10 + 50y/6 - 50/6 = 4.90

=> 253y/30 = 4.90 + 50/6 = 13.233

=> 253y = 397 => y = 1.6 ~ 2

put this value in equation (1)

=> x = 2×2 -2 = 2

Hence, randon has 2 dimes and 2 quaters .

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Answer: Her neighbors paid her 28 dollars

Step-by-step explanation: if you add 4, 16, and 8 then you get 28

The value of the function g(x) = x^3 + 6x^2 + 12x + 8 when x = -1 is 1

The equation of the function is given as:

g(x) = x^3 + 6x^2 + 12x + 8

When x = -1, we have:

g(-1) = (-1)^3 + 6(-1)^2 + 12(-1) + 8

Evaluate the expression

g(-1) = 1

Hence, the value of the function g(x) = x^3 + 6x^2 + 12x + 8 when x = -1 is 1

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Answer:

g(-1) = 1

Step-by-step explanation:

Let A(t) denote the amount of salt (in ounces, oz) in the tank at time t (in minutes, min).

Salt flows in at a rate of

\(\dfrac{dA}{dt}_{\rm in} = \left(17 (1 + 15 \sin(t)) \dfrac{\rm oz}{\rm gal}\right) \left(8\dfrac{\rm gal}{\rm min}\right) = 136 (1 + 15 \sin(t)) \dfrac{\rm oz}{\min}\)

and flows out at a rate of

\(\dfrac{dA}{dt}_{\rm out} = \left(\dfrac{A(t) \, \mathrm{oz}}{180 \,\mathrm{gal} + \left(8\frac{\rm gal}{\rm min} - 8\frac{\rm gal}{\rm min}\right) (t \, \mathrm{min})}\right) \left(8 \dfrac{\rm gal}{\rm min}\right) = \dfrac{A(t)}{180} \dfrac{\rm oz}{\rm min}\)

so that the net rate of change in the amount of salt in the tank is given by the linear differential equation

\(\dfrac{dA}{dt} = \dfrac{dA}{dt}_{\rm in} - \dfrac{dA}{dt}_{\rm out} \iff \dfrac{dA}{dt} + \dfrac{A(t)}{180} = 136 (1 + 15 \sin(t))\)

Multiply both sides by the integrating factor, \(e^{t/180}\), and rewrite the left side as the derivative of a product.

\(e^{t/180} \dfrac{dA}{dt} + e^{t/180} \dfrac{A(t)}{180} = 136 e^{t/180} (1 + 15 \sin(t))\)

\(\dfrac d{dt}\left[e^{t/180} A(t)\right] = 136 e^{t/180} (1 + 15 \sin(t))\)

Integrate both sides with respect to t (integrate the right side by parts):

\(\displaystyle \int \frac d{dt}\left[e^{t/180} A(t)\right] \, dt = 136 \int e^{t/180} (1 + 15 \sin(t)) \, dt\)

\(\displaystyle e^{t/180} A(t) = \left(24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t)\right) e^{t/180} + C\)

Solve for A(t) :

\(\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) + C e^{-t/180}\)

The tank starts with A(0) = 15 oz of salt; use this to solve for the constant C.

\(\displaystyle 15 = 24,480 - \frac{66,096,000}{32,401} + C \implies C = -\dfrac{726,594,465}{32,401}\)

So,

\(\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) - \frac{726,594,465}{32,401} e^{-t/180}\)

Recall the angle-sum identity for cosine:

\(R \cos(x-\theta) = R \cos(\theta) \cos(x) + R \sin(\theta) \sin(x)\)

so that we can condense the trigonometric terms in A(t). Solve for R and θ :

\(R \cos(\theta) = -\dfrac{66,096,000}{32,401}\)

\(R \sin(\theta) = \dfrac{367,200}{32,401}\)

Recall the Pythagorean identity and definition of tangent,

\(\cos^2(x) + \sin^2(x) = 1\)

\(\tan(x) = \dfrac{\sin(x)}{\cos(x)}\)

Then

\(R^2 \cos^2(\theta) + R^2 \sin^2(\theta) = R^2 = \dfrac{134,835,840,000}{32,401} \implies R = \dfrac{367,200}{\sqrt{32,401}}\)

and

\(\dfrac{R \sin(\theta)}{R \cos(\theta)} = \tan(\theta) = -\dfrac{367,200}{66,096,000} = -\dfrac1{180} \\\\ \implies \theta = -\tan^{-1}\left(\dfrac1{180}\right) = -\cot^{-1}(180)\)

so we can rewrite A(t) as

\(\displaystyle A(t) = 24,480 + \frac{367,200}{\sqrt{32,401}} \cos\left(t + \cot^{-1}(180)\right) - \frac{726,594,465}{32,401} e^{-t/180}\)

As t goes to infinity, the exponential term will converge to zero. Meanwhile the cosine term will oscillate between -1 and 1, so that A(t) will oscillate about the constant level of 24,480 oz between the extreme values of

\(24,480 - \dfrac{267,200}{\sqrt{32,401}} \approx 22,995.6 \,\mathrm{oz}\)

and

\(24,480 + \dfrac{267,200}{\sqrt{32,401}} \approx 25,964.4 \,\mathrm{oz}\)

which is to say, with amplitude

\(2 \times \dfrac{267,200}{\sqrt{32,401}} \approx \mathbf{2,968.84 \,oz}\)

Answer:

Equation: x+x+6=20

x=7

Andy completed 16 problems

Step-by-step explanation:

Volume of a right cone with base radius r cm and height h cm :

V = 1/3 π r² h cm³

Surface area :

A = (π r² + π r √(h² + r²)) cm²

Volume of a sphere with radius r cm :

V = 4/3 π r³ cm³

Surface area :

A = 4 π r² cm²

Volume of a cuboid with dimensions r cm × r cm × h cm :

V = r² h cm³

Surface area :

A = 2 r² + 4 r h

a. If the cone and sphere have the same volume, then

1/3 π r² h = 4/3 π r³   ⇒   h = 4r

b. If the area of the cuboid is 98 cm², then

2 r² + 4 r h = 98   ⇒   r (r + 2 h) = 49

c. Since h = 4r, substituting this into the equation from (b) gives

r (r + 8 r) = 9 r² = 49   ⇒   r² = 49/9   ⇒   r = 7/3

d. With r = 7/3, we have

h = 4 × 7/3 = 28/3

and so the volume of the cuboid is

V = (7/3 cm)² (28/3 cm) = 1372/27 cm³

Answer:

\(a_{n} = 12 -3(n-1)\)

Step-by-step explanation:

\(a_{1} = 12\\a_{n} = a_{n-1} - 3\)

we have to find formula for nth term of series for this problem

\(a_{1} = 12\\a_{2} = a_{2-1} - 3 = a_{1} -3 = 12 -3 = 9\\a_{3} = a_{3-1} - 3 = a_{2} -3 = 9 -3 = 6\)

Thus, we see series is 12, 9 ,6

Thus, we can see that series is decreasing by unit of 3.

and we know that when there is in increase or decrease in series by a a constant number then series is arithmetic progression series.

Hence, this is a decreasing AP series

In AP

nth term is given

nth term = a+(n-1)d

where a is the first term

d is the common difference

common difference is given by = nth term - (n-)th term

lets take 2nd and 1st term to get common difference.

d = 9-12 = -3

(note: this was obvious by looking at series itself that d is -3 as series was decreasing by 3 unit)

a = 12

thus, nth term = a +(n-1)d

nth term = 12 +(n-1)(-3)

nth term = 12 -3(n-1)

writing this in form of \(a_{n}\)

\(a_{n} = 12 -3(n-1)\)  Answer

Answer:

length=48cm

Step-by-step explanation:

a²+14²=50²

a²+196=2500

a²=2304

a=48

Answer:

D

Step-by-step explanation:

I hope this is correct and have a great day

The derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).

a) To find f'(x) for f(x) = x*sin(x), we can use the product rule and the derivative of the sine function.

Using the product rule, we have:

f'(x) = (xsin(x))' = xsin'(x) + sin(x)*x'

The derivative of sin(x) is cos(x), and the derivative of x with respect to x is 1. Therefore:

f'(x) = x*cos(x) + sin(x)

So, the derivative of f(x) = xsin(x) is f'(x) = xcos(x) + sin(x).

(b) To find f'(x) for f(x) = sech^(-1)(x^2), we can use the chain rule and the derivative of the inverse hyperbolic secant function.

Let u = x^2. Then, f(x) can be rewritten as f(u) = sech^(-1)(u).

Using the chain rule, we have:

f'(x) = f'(u) * u'

The derivative of sech^(-1)(u) can be found using the derivative of the inverse hyperbolic secant function:

(sech^(-1)(u))' = 1/sqrt(1 - u^2)

Since u = x^2, we have:

f'(x) = 1/sqrt(1 - (x^2)^2) * (x^2)'

Simplifying:

f'(x) = 1/sqrt(1 - x^4) * 2x

So, the derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).

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Answer:

Umm nine ways?

Step-by-step explanation:

Answer:

1260

Step-by-step explanation:

35x36

Answer:

-12,27

Step-by-step explanation:

\( {x}^{8} + {x}^{4} + 1\)

factorise

\( {x}^{8} + {x}^{4} + 1\)

\( = x ^{8} + 2 {x}^{4} + 1 - {x}^{4} \)

\( = ( {x}^{4} + 1 {)}^{2} - ( {x}^{2} {)}^{2} \)

\( = ({x}^{4 } + 1 + {x}^{2}) ( {x}^{4} + 1 - {x}^{2} )\)

\( = ( {x}^{4} + 2 {x}^{2} + 1 - {x}^{2} )( {x}^{4} - {x}^{2} + 1)\)

\( = (( {x}^{2} + 1 {)}^{2} - {x}^{2} )( {x}^{4} - {x}^{2} + 1)\)

\( = ( {x}^{2} + 1 + x)( {x}^{2} + 1 - x)\)

\( = ( {x}^{4} - {x}^{2} + 1)\)

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x + 2 ← is in slope- intercept form

Thus its graph is a straight line

crosses the y- axis at (0, 2 ) , that is c = 2

the 4 in 4x is the slope m of the line

Compound amount = $8867.39

compound interest = $1867.39

EXPLANATION

Given:

Principal(p) = $7000 Rate(r) = 0.12 Time(t) = 2 n= 4

We can calculate the compound amount(A) using the formula below:

Substitute the values and evaluate.

Hence, the compound amount = $8867.39

We proceed to find the compound interest.

A = P + I

⇒ I = A - P

= 8867.39 - 7000

=1867. 39

Therefore, the compound interest = $1867.39

Answer:

y=-1/3x + 4/3

Step-by-step explanation:

Answer:

6.25 weeks

Step-by-step explanation:

Take 18.75 and divide it by 3, since the crew is finishing 3 km per week. You get 6.25, so it took the crew 6.25 weeks to finish the road.

Hopefully this helps- let me know if you have any questions!

Answer:

the answer should be 30

Step-by-step explanation:

since you can divided 15 by 5 to get 3, you can multiply 10 x 3 to get 30

Answer:

3.5 un

Step-by-step explanation:

to find the new length of the square using a scale factor of 1/7 you can just multiply 24.5 by 1/7

this is basically dividing 24.5 by 7

24.5 / 7 = 3.5

that is your answer

According to the US Geological Survey (USGS), the total copper contained in world reserves as of 2018 was estimated to be approximately 830 million metric tons.

The USGS gathers and analyzes data on global mineral reserves, including copper. In their 2018 report, they estimated that the total identified copper resources worldwide were approximately 2.2 billion metric tons. However, not all of these resources are economically recoverable. To determine the amount of copper in world reserves, the USGS considers factors such as geology, mining methods, and economic viability.

Based on their analysis, the USGS estimated that around 38% of the identified copper resources were classified as reserves in 2018. Therefore, the calculated amount of copper in world reserves was approximately 830 million metric tons (2.2 billion metric tons x 38%).

In 2018, the USGS estimated that the world's copper reserves contained approximately 830 million metric tons. It is important to note that these estimates are subject to change as new discoveries are made, mining technologies evolve, and economic factors fluctuate. The USGS plays a crucial role in providing reliable and up-to-date information on global mineral resources to aid in resource planning and decision-making.

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Answer:

C

Step-by-step explanation:

It's C because i majored in mathmatics in college and ended with a A

The Lagrangian for a damped harmonic oscillator is given by L = (1/2) * m * (dx/dt)² - (1/2) * w² * x².

To show that a damped harmonic oscillator can be described by a Lagrangian, we need to derive the Lagrangian function for the system.

Let's consider a one-dimensional damped harmonic oscillator with position x(t) and damping coefficient a. The equation of motion for this system is given by:

m * ä + a * ä + w² * x = 0,

where m is the mass of the oscillator and w is the angular frequency.

We can rewrite the above equation as:

( m + a ) * ä + w² * x = 0.

Now, let's define the Lagrangian function L as the kinetic energy minus the potential energy:

L = T - V,

where T is the kinetic energy and V is the potential energy.

The kinetic energy T is given by:

T = (1/2) * m * v²,

where v = dx/dt is the velocity of the oscillator.

The potential energy V is given by:

V = (1/2) * w² * x².

Now, we can calculate the Lagrangian function:

L = T - V = (1/2) * m * v² - (1/2) * w² * x².

Next, we need to express the Lagrangian in terms of the generalized coordinates and their derivatives. In this case, the generalized coordinate is the position x.

The derivative of the position with respect to time is:

v = dx/dt.

Substituting this into the Lagrangian, we have:

L = (1/2) * m * (dx/dt)² - (1/2) * w² * x².

Now, let's calculate the Euler-Lagrange equation:

d/dt * (∂L/∂(dx/dt)) - ∂L/∂x = 0.

Taking the derivatives, we have:

d/dt * (m * (dx/dt)) - (-w² * x) = 0,

m * d²x/dt² + w² * x = 0,

which is the equation of motion for the damped harmonic oscillator.

Therefore, we have shown that the damped harmonic oscillator can be described by a Lagrangian, given by:

L = (1/2) * m * (dx/dt)² - (1/2) * w² * x².

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The equation representing total fraction strip is  ³/₃ + ¹/₃ = ⁴/₃.

option B.

A fraction is a mathematical representation of a part of a whole or a ratio between two numbers. It consists of a numerator, which represents the number of parts being considered, and a denominator, which represents the total number of parts in the whole.

For this case, 1 is divided into, and 1 divide into 3.

To obtain the total fractions, we will add the individual fractions as shown below;

For this first fraction = ¹/₃ + ¹/₃ + ¹/₃

For the second fraction = ¹/₃

Total fraction = 3(¹/₃ + ¹/₃ + ¹/₃) + ¹/₃

Total fraction = ³/₃ + ¹/₃ = ⁴/₃

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