given that g ( u ) = 4 u 7 4 17 where g ( u ) = v , define a function rule for g − 1 .

Answer: w = -238

Step-by-step explanation:

\(34=\frac{-w}{7}\)

Switch sides

\(\frac{-w}{7} =34\)

Multiply both sides by 7

\(\frac{7\left(-w\right)}{7} =34\cdot \:7\)

Simplify

-w = 238

Divide both sides by -1

\(\frac{-w}{-1}=\frac{238}{-1}\)

Simplify

w = -238

If I made any mistakes, please let me know!

 I hope this helped :)

Answer:

x ≥  4

Step-by-step explanation:

cross-multiply:

3x - 1 ≥ 1(2x + 3)

3x - 1 ≥  2x + 3

subtract 2x from boths sides and add 1 to both sides:

3x - 2x ≥  3 + 1

x ≥  4

our domain is x ≥  4.

we can check if we're correct by inputting 4, 3.9 and 4.1 into the equation.

[3(4) - 1] / [2(4) + 3]

= 11/11

= 1

[3(3.9) - 1] / [2(3.9) + 3]

= 107/108 < 1

[3(4.1) - 1] / [2(4.1) + 3]

= 113/112 > 1

Answer: look at the image for the answer and solution

Step-by-step explanation:

Using the concept of probability, the probability that the first experiment is successful is 70.97%

To calculate the probability that the first experiment is successful, we use the relation thus :

Inserting the values into the formula :

Therefore, the probability value is 70.97%

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Answer:

\(The\ brother's\ present\ age= 4\ years\\The\ sister's\ present\ age=8\ years\)

Step-by-step explanation:

\(Let\ the\ brother's\ present\ age\ be\ x\\Hence\ we\ are\ given,\\His\ sister's\ present\ age=(2x)\\Now,\\The\ brother's\ age\ before\ two\ years=(x-2)\\The\ sister's\ age\ before\ two\ years=3(x-2)\\Also,\\His\ sisters\ age\ before\ two\ years=2x-2\\Hence,\\3(x-2)=2x-2\\3x-6=2x-2\\3x-2x=6-2\\x=4\\Hence,\\The\ brother's\ present\ age= 4\ years\\The\ sister's\ present\ age=2x=2*4=8\ years\)

Answer:

The sister's present age is 8 years old, and the brother's present age is 4 years old.

Step-by-step explanation:

Let \(b =\) present age of the brother, \(s =\) present age of the sister

\(s-2 = (b-2)\) × \(3\)

\(s-2\) = \(3b - 6\)

\(s = 3b - 4\)

\(s = b\) × \(2\)

\(= 2b\)

\(sb-4 = 2b\)  (proved from above equations)

\(b = 4\)

\(\because s = 3b - 4\)

\(\therefore\)\(s = 3\)×\(4 - 4\)

\(= 8\)

\(\therefore\) the brother's present age is 4 years old, and the sister's present age is 8 years old.

Hope this helps :)

Answer:

3, 13

Step-by-step explanation:

(3,13)

Answer: (3,13)

Step-by-step explanation:

The surface area obtained by rotating about the y -axis is 168.159.

In mathematics, integration is a technique for combining or adding the parts to arrive at the total. It is a form of differentiation in reverse where we break down functions into their component elements. This technique is employed to determine the summation on a sizable scale.

We have the function y=1+5x² from x=0 to x=2 about the y -axis.

So, the Surface are is

S = 2π ∫ R(x) √ (1+ f'(x)²}

Then, f'(x) = 10x

Then, S = 2π ∫ R(x) √ (1+ f'(x)²}

= 2π ∫ (1+5x²) √ (1+100x²)

= 1/150 (401 (√401-1)) π

= 168.159

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A) Current (I)= 4A and power dissipated is 24W

B) The energy delivers to the water in 350 sec is 2009.57 cal.

We have, Resistance of the resistor, R = 1.5 ohm

The voltage across the resistor, V = 6.00 V

Let the current in the resistor be 'I'

By using Ohms' Law

I = V/R ⇒ 6.00 V / 1.5 ohm ⇒ 4 A

Therefore, the current in the resistor is 4 A.

The power dissipated by the resistor,

P = I²R ⇒ (4 A)² × 1.5 ohm ⇒ 24 W

Therefore, the power dissipated by the resistor is 24 W.

B) The energy delivered to the water by the resistor can be calculated using the formula:

E = P × t,

Where P = Power of the resistor = 24 W

t = Time = 350 seconds

Therefore, the energy delivered to the water by the resistor is:

E = Pt ⇒ 24 W × 350 s ⇒ 8400 J

Now, convert it to calories:

1 calorie = 4.18 J

Therefore, Energy in calories = Energy in joules / 4.18

⇒ 8400 J / 4.18

⇒ 2009.57 cal

Hence, the energy delivered to the water in 350 seconds is 8400 J or 2009.57 cal.

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The sum or the compound interest were Rs. 10,089 & Rs. 2589, respectively, according to the supplied statement.

Per year, as used in contracts, is used to describe ongoing duties, or those that take place continuously during the course of an agreement. For instance, if a customer pays 3% interest on a loan annually, it indicates that you will have to pay 3% more of the loan's principle each year until the deal is through.

Given : Initial principle amount (P) = Rs. 7500

      Rate of interest (R) = 16% per annum

To find : Compound interest (C.I.) = ?

Solution :

It is given that Initial principle amount (P) = Rs. 7500

Rate of interest (R) = 16% per annum

      Time (t) = 1 year = 2 ( ∵ Half Yearly)

We know the formula for Compound Interest,

       Compound Interest (A) = \(P\left(1+\frac{R}{100}\right)^{n t}\)

\(\begin{aligned}& =7500\left(1+\frac{16}{100}\right)^2 \\& =7500\left(\frac{100+16}{100}\right)^2 \\& =7500\left(\frac{116}{100}\right)^2\end{aligned}\)

= 7500 * 1.345

= Rs. 10,089

Now, Compound interest = A - P

= 10,089 - 7500

= Rs. 2589

∴ Final amount = Rs. 10,089

Compound Interest = Rs. 2589

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The complete question is-

Calculate the amount and the compound interest on Rs. 7500 for 1 year at 16% p.a compounded half yearly​

the upper sum for f(x) = 17 - \(x^{2}\) on the interval [3, 4] using four subintervals is approximately 6.46875.

To calculate the upper sum, we divide the interval [3, 4] into four subintervals of equal width. The width of each subinterval is (4 - 3) / 4 = 1/4.

Next, we evaluate the function at the right endpoint of each subinterval and multiply it by the width of the subinterval. For this function, we need to find the maximum value within each subinterval. Since the function f(x) = 17 - \(x^{2}\) is a downward-opening parabola, the maximum value within each subinterval occurs at the left endpoint.

Using four subintervals, the right endpoints are: 3 + (1/4), 3 + (2/4), 3 + (3/4), and 3 + (4/4), which are 3.25, 3.5, 3.75, and 4 respectively.

Evaluating the function at these right endpoints, we get: f(3.25) = 8.5625, f(3.5) = 10.75, f(3.75) = 13.5625, and f(4) = 13.

Finally, we calculate the upper sum by summing the products of each function value and the subinterval width: (1/4) × (8.5625 + 10.75 + 13.5625 + 13) = 6.46875.

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Answer:

21 cm^2

Step-by-step explanation:

A = 1/2 x 3 cm (5 cm + 9 cm)

A = 1/2 x 3 cm x 14 cm

A = 21 cm^2

To reach your fundraising goal of $75, you will need to sell 150 pencils for $0.50 each and 0 bracelets for $1.00 each.

To reach your fundraising goal of $75, you can sell pencils for $0.50 and bracelets for $1.00.

1. Calculate the total amount of money needed to reach the goal:
  Goal amount = $75

2. Determine the number of pencils and bracelets you need to sell to reach the goal:
  Let's assume you sell x number of pencils and y number of bracelets.

  The amount raised from selling pencils = x * $0.50
  The amount raised from selling bracelets = y * $1.00

  The total amount raised from both items should be equal to the goal amount:
  x * $0.50 + y * $1.00 = $75

3. Simplify the equation:
  0.50x + 1.00y = 75

4. Solve for one variable in terms of the other:
  Let's solve for x in terms of y:
  0.50x = 75 - 1.00y
  x = (75 - 1.00y) / 0.50

5. Substitute the value of x into the equation:
  (75 - 1.00y) / 0.50 * 0.50 + y * $1.00 = $75
  75 - 2y + y = 75
  -y = 0
  y = 0

6. Find the value of x:
  x = (75 - 1.00 * 0) / 0.50
  x = 75 / 0.50
  x = 150

To reach your fundraising goal of $75, you will need to sell 150 pencils for $0.50 each and 0 bracelets for $1.00 each.

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Answer:

Step-by-step explanation:

Part A

The units on 9500 must be miles. So if x is time, then 55 must be the rate at which she travels ie 55 miles per hour. So the answer must be A.

Part B

The trip began when the time was zero. Therefore x is zero. What remains is the mileage on the odometer when x = 0.  The answer must be 1950.

Answer:

This suggests that as the distance of a house from the ocean increases by 1 km, the number of people willing to buy it decreases by 0.231.

What is regression line?

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True. Recursion is often necessary to solve certain types of problems that exhibit a recursive structure or require repeated subproblem solving.

Recursion is a programming technique where a function calls itself in its own definition. It allows for the decomposition of complex problems into smaller, more manageable subproblems that can be solved recursively. Recursion is particularly useful when problems exhibit a recursive structure, such as tree traversal, backtracking, or divide-and-conquer algorithms.

For example, problems like computing the factorial of a number, calculating Fibonacci numbers, or traversing a binary tree can be elegantly and efficiently solved using recursion. These problems can be broken down into smaller instances of the same problem until a base case is reached, and then the solutions are combined to solve the original problem.

However, it's worth noting that not all problems require recursion for their solution. There are alternative approaches, such as iterative loops or dynamic programming, which can be used depending on the problem's characteristics and requirements.

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Answer:

The bike path

Step-by-step explanation:

A right triangle has a hypotenuse that can be found using the formula

a^2 + b^2 = c^2 where c is the hypotenuse

The street sign is obviously not correct because a hypotenuse is longer than the sides. The bathroom tile isn't correct either because 6^2 + 8^2 = 100, or 10 after you take the square root. That leaves the bike path.

Checking to make sure:

5^2 + 12^2 = c^2

25 + 144 = √169

√169 = 13

The scenario from the given scenarios involving a right triangle is: "A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles", as the sides satisfy the Pythagoras theorem.

Any three line segments can form a right triangle only when they satisfy the Pythagoras Theorem, according to which, the square of the largest side in a right triangle is equal to the sum of the squares of the other two sides, that is, a² = b² + c², where a is the largest side, and b and c are the two other sides.

In the question, we are asked to identify from the given scenarios, the case that involves a right triangle.

We know that for three segments to be a right triangle, they need to satisfy the Pythagoras Theorem. So we check every scenario with the theorem:

∴ The scenario from the given scenarios involving a right triangle is: "A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles", as the sides satisfy the Pythagoras theorem.

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Answer:

None of those are the correct answer. The answer is 10.3625

Step-by-step explanation:

So, yes there is a 3625 but it is only in the decimal places such as the tenths, the hundreths and the thousandths.

Three consecutive odd integers are -3, -1, and 1.

A detailed explanation of the answer.

To find 3 consecutive odd integers such that 3 times the sum of the first and second equals 13 less than the third, we can follow these steps:

Therefore, the three consecutive odd integers are -3, -1, and 1.

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Answer:

√[(5-1)² + (5-5)²]

√[16+0]

√(16)

+4 or -4 units

I hope this helped :D

Step-by-step explanation: for your other question

((

−

4

,

7

)

(

−

4

,

5

)

Answer:

4

Step-by-step explanation:

p=?

r=8

i=816

t=2years

we know that

p=I×100/t×r

p=816×100/8×2

p=81600/16

p=5100

it the answer

She will earn $924 if she works 38.5 hours this week

The function is given as

w(h) = 24h, if h < 40

w(h) = (36(h-40)+960 h> 40

If she works 38.5 hours this week, then

h < 40

So, we use

w(h) = 24h

This gives

w(38.5) = 24 * 38.5

Evaluate

w(38.5) = 924

Hence, she will earn $924 if she works 38.5 hours this week

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The function that represents the relationship between x and y is y = (2/3)x.

The function that represents the relationship between x and y when y varies directly with x is of the form y = kx, where k is the constant of proportionality. In this case, we are given that y = 6 when x = 9, which means that k = y/x = 6/9 = 2/3. Therefore, the function that represents the relationship between x and y is y = (2/3)x.

This means that for any given value of x, y will be equal to 2/3 times that value of x. For example, if x = 12, then y = (2/3) x 12 = 8. This relationship is called direct variation because as x increases, y also increases in proportional level.

Overall, the answer is function that represents the relationship between x and y when y = 6 and x = 9 is y = (2/3)x.

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The point shown on the number line is: 3.1.

A number line can be described a line that shows graduated marks indicating different points that are marked. It shows the position of real numbers and how they are ordered.

In the diagram given, a number line is shown having different equal number of intervals between each number.

From point 1 to 2, therefore are 10 equal intervals. The point that is marked after 3, is therefore 3.1 on the number line.

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Answer: 440

1200 - 760 = 440

Answer: 440 pounds

Step-by-step explanation:

(a) The greatest common divisor of \(x^3\) - 6x - 7 and \(x^4\) is 1.

(b) The greatest common divisor of \(x^2\)- 1 and 2\(x^7\) - 4x\(^5\) + 2 is 1.

(a) To find the greatest common divisor (GCD) of the polynomials, we can use polynomial long division.

Dividing \(x^3\) - 6x - 7 by \(x^4\), we get a remainder of \(x^3\) - 6x - 7.

Since the remainder is non-zero, the GCD of \(x^3\) - 6x - 7 and \(x^4\) is 1.

(b) To find the GCD of \(x^2\) - 1 and 2\(x^7\) - 4\(x^5\) + 2, we can again use polynomial long division.

Dividing 2\(x^7\) - 4\(x^5\) + 2 by \(x^2\) - 1, we get a remainder of 2\(x^5\) + 2.

Since the remainder is non-zero, the GCD of \(x^2\) - 1 and 2\(x^7\) - 4\(x^5\) + 2 is 1.

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Answer:

225.6 feet

Step-by-step explanation:

It should be pretty simple, you need to multiply 75.2 times 3. In result your answer is 225.6 feet or rather more simply (225 feet 7 13/64 inches.)