Let R = {(x, y)|0 ≤ x ≤ 2,0 ≤ y ≤ 1}. Evaluate ∫∫ R x √1-y dA.

Answer:

(1, 7)

Step-by-step explanation:

y = 3x + 4

y = 6x + 1

6x + 1 = 3x + 4 ⇒ x = 1

y = 3(1) + 4 = 7

(1, 7)

Answer:

(1, 7)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define systems

y = 3x + 4

y = 6x + 1

Step 2: Solve for x

Step 3: Solve for y

Answer:

$0.45.

Step-by-step explanation:

Total amount of money held by all 5 children

= 5 * 0.50 = $2.50.

After 0.25 is lost the total = $2.25.

So the new average = 2.25 / 5

= $0.45.

The set of values for Rents lesser than $700. So, rent 700 <y<0

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What is remainder R when the polynomial p(x) is divided by (2x - 1)? is (2x - 1) factor of p(x)?

p(x) = 2x² + 3x + 1

Answer :

R = 3

and (2x - 1) not factor of p(x) because, if (2x - 1) factor of p(x) remainder R when the polynomial p(x) divided by (2x - 1) is R = 0

∴ so the answer is option A

« Attached »

As S = {f in C[a, b] | f(a) - 2f (b) = 0} is a subspace of C[a, b] or not.

To determine whether S = {f in C[a, b] | f(a) - 2f(b) = 0} is a subspace of the vector space C[a, b] (the set of all continuous real-valued functions defined on a closed interval [a, b]), we must check if it satisfies the following three conditions:

1. The zero vector is in S.
2. S is closed under vector addition.
3. S is closed under scalar multiplication.

1. The zero vector in C[a, b] is the function f(x) = 0 for all x in [a, b]. For this function, f(a) - 2f(b) = 0 - 2(0) = 0, so the zero vector is in S.

2. Let f and g be two functions in S. Then, f(a) - 2f(b) = 0 and g(a) - 2g(b) = 0. We need to check if their sum, (f + g), is also in S. For the sum, we have (f + g)(a) - 2(f + g)(b) = f(a) + g(a) - 2[f(b) + g(b)] = (f(a) - 2f(b)) + (g(a) - 2g(b)) = 0 + 0 = 0. Thus, S is closed under vector addition.

3. Let f be a function in S, and let c be a scalar. We need to check if cf is in S. For the scalar multiplication, we have (cf)(a) - 2(cf)(b) = c[f(a) - 2f(b)] = c(0) = 0. Thus, S is closed under scalar multiplication.

Since S satisfies all three conditions, it is a subspace of the vector space C[a, b] of continuous real-valued functions defined on a closed interval [a, b].

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Answer:

Step-by-step explanation:

If P, Q and S are collinear, then the three points lies on the same straight line.

If the Straight <P Q S is divided into 2 angles, <P Q R and <R Q S, by ray Q R, then;

<P Q R + <R Q S = 180

Given

<R Q S =x+1

<P Q R = 3x-5

Substitute the given expression into the formula and calculate x;

3x-5+x+1 = 180

collect like terms

3x+x - 5+1 = 180

4x-4 = 180

4x = 180+4

4x = 184

divide both sides by 4

4x/4 = 184/4

x = 46°

To get m∠PQR, we will substitute x = 46 into the expression for m∠PQR.

m∠PQR = 3x-5

m∠PQR = 3(46) - 5

m∠PQR = 138 - 5

m∠PQR = 133°

Hence the measure of angle m∠PQR is 133°

The measure of angle m∠PQR is 133° and the measure of angle m∠RQS is 47° on straight angle ∠PQS.

Given that, points P, Q and S are collinear, then the three points lies on the same straight line.

The straight ∠PQS is divided into 2 angles as ∠PQR and ∠RQS, by ray QR, then ∠PQR + ∠RQS = 180°

Here, ∠PQR = (3x-5)° and ∠RQS =(x+1)°

So, (3x-5)°+(x+1)°=180°

4x-4=180

4x=184

x=184/4

x=46

Now,

∠PQR = (3x-5)°

= 3×46-5

= 138-5

= 133°

Hence, the measure of angle m∠PQR is 133° and the measure of angle m∠RQS is 47° on straight angle ∠PQS.

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\( \large{f(x) = g(x)} \\ \large{ {x}^{2} + 3x = x + 3}\)

Since we are solving the quadratic equation because the highest degree in the equation is second. We arrange in the form of ax²+bx+c = 0.

\( \large{ {x}^{2} + 3x - x - 3 = 0}\)

Combine like terms.

\( \large{ {x}^{2} + 2x - 3 = 0}\)

Solve the equation by factoring.

\( \large{(x + 3)(x - 1) = 0} \\ \large{x = - 3,1}\)

Hence the values of x that make f(x) = g(x) are -3 and 1.

Answer

Let me know if you have any doubts!

Answer:

hello!!

i like ur pfp! :)

Answer:

  16°

Step-by-step explanation:

The trig function tangent relates an acute angle of a right triangle to the measures of the adjacent and opposites sides. Those are the sides given here, so the relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(?) = 14/49 = 2/7

When the tangent of the angle is known, the inverse tangent function can be used to find the angle:

  ? = arctan(2/7) ≈ 16°

The value of "?" is about 16°.

Answer: 76

Step-by-step explanation:

Answer:

Step-by-step explanation:

extend the line on the 5ft side to create a triangle and a rectangle.

Area of a rectangle is l x b

10 x 4 = 40ft^2

Area of a triangle is 1/2 base x height

the height of the triangle will be 10 - 5 = 5ft

the base of the triangle will be 12 - 4 = 8

1/2 (8) x (5)

20ft^2

Total area = area of triangle + area of rectangle

Total area  = 20ft^2 + 40ft^2

Total area = 60 ft^2

Answer:

14+19=33 33 divided by 23=?

Step-by-step explanation:

triangle with the given side is a right triangle;14mm, 19mm, 23mm ... Use the Pythagorean theorem that only works for right triangles.

Answer:

6/12 or 1/2

Step-by-step explanation:

there ya go i think its right

Answer:

Step-by-step explanation:

8. 7.5 Goes up by 2.5.

9. 7.3 Goes down by 2.1

10. 116/3

Answer:

8- 7.5

9-7.3

10-38 \(\frac{2}{3}\)

Step-by-step explanation:

Thus, the length of a side of the regular hexagon is 8 centimeters using the Pythagorean theorem.

The key to solving this problem is to realize that the perpendiculars drawn from the interior point to the sides of the hexagon form a right triangle with one leg being the perpendicular and the other leg being a side of the hexagon. We also know that the hexagon is regular, meaning all sides have the same length.

Let's label the length of the side of the hexagon as "x". We can use the Pythagorean theorem to find the length of each perpendicular as follows:

- For the perpendicular that is 4 cm long, we have x^2 = 4^2 + (x/2)^2
- For the perpendicular that is 5 cm long, we have x^2 = 5^2 + (x/2)^2
- For the perpendicular that is 6 cm long, we have x^2 = 6^2 + (x/2)^2
- For the perpendicular that is 8 cm long, we have x^2 = 8^2 + (x/2)^2
- For the perpendicular that is 9 cm long, we have x^2 = 9^2 + (x/2)^2
- For the perpendicular that is 10 cm long, we have x^2 = 10^2 + (x/2)^2

Simplifying each equation and using a bit of algebra, we get:

- 3x^2 = 16^2
- 7x^2 = 25^2
- 12x^2 = 36^2
- 24x^2 = 64^2
- 33x^2 = 81^2
- 40x^2 = 100^2

Solving for x in each equation, we find that x = 8 cm. Therefore, the length of a side of the regular hexagon is 8 centimeters.

In summary, we used the fact that the perpendiculars from an interior point to the sides of a regular hexagon form right triangles to set up equations using the Pythagorean theorem. Solving for the length of a side of the hexagon in each equation, we found that it is 8 cm long.

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Answer:

\(\huge\boxed{\sf 3x^2-4x+12}\)

Step-by-step explanation:

\(=x(2x+3)+(x-3)(x-4)\\\\Using \ distributive \ property\\\\=(x)(2x)+(x)(3)+x(x-4)-3(x-4)\\\\=2x^2+3x+x^2-4x-3x+12\\\\Combining \ like \ terms\\\\= 2x^2+x^2+3x-3x-4x+12\\\\= 3x^2-4x+12\\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

I believe the answer is 2

Step-by-step explanation:

For a normal distribution curve where 90 -th percentile is at 12 and the 40 -th percentile is at 8 there is no solution for μ and σ that satisfies the given percentiles.

To find the mean, μ, and the standard deviation, σ, of a normal distribution given the percentiles, we can use the properties of the standard normal distribution.

The standard normal distribution has a mean of 0 and a standard deviation of 1. We can use this information to standardize the given percentiles.

Let Z be a standard normal random variable. To find the values of Z corresponding to the given percentiles, we use the inverse standard normal cumulative distribution function (also known as the Z-score).

The Z-score corresponding to the 90th percentile is denoted as Z_90 and is equal to 1.28 (approximately). Similarly, the Z-score corresponding to the 40th percentile is denoted as Z_40 and is equal to -0.25 (approximately).

We can use these Z-scores to calculate the mean and standard deviation of the distribution as follows:

a) μ = Z_90 * σ + μ

12 = 1.28 * σ + μ

b) σ = (Z_90 - Z_40) * σ

σ = (1.28 - (-0.25)) * σ

σ = 1.53 * σ

Now, we have a system of equations involving μ and σ:

12 = 1.28 * σ + μ

σ = 1.53 * σ

We can solve this system to find the values of μ and σ.

From the second equation, we have:

1 = 1.53

This equation is not possible since 1 does not equal 1.53. Therefore, there is no solution for μ and σ that satisfies the given percentiles.

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Answer:

it is a

Step-by-step explanation:

Answer: it’s A because Richards Park charges an admission fee of $10 plus hourly which is the unit rate which stays at a constant price C=h the hours ($10+$5) is the correct answer. Hope this helps!

Step-by-step explanation:

The learning rate in gradient descent determines the step size and should be not too small or too large, as it can cause the algorithm to converge slowly or overshoot the minimum; adjusting the value of the learning rate can fix the problem, but the optimal value depends on the problem and data set.

According to the given information:

When running gradient descent,

The learning rate α determines the step size taken in each iteration toward the optimal solution.

If α is too small, the algorithm will take small steps and will converge slowly, or may even get stuck in a local minimum.

If α is too large, the algorithm may overshoot the minimum and diverge, or bounce back and forth without converging.

In the scenario described, the learning rate α of 0.5 appears too large, causing J(θ) to increase over time.

This suggests that the algorithm is not converging and is overshooting the minimum.

To fix this,
The value of α can be adjusted by reducing it to a smaller value,

Such as 0.1 or 0.01.

This should allow the algorithm to take smaller steps towards the minimum and eventually converge to a lower value of J(θ).

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Answer:

For number 1, -1.125 and -9/8. For number 2, -46.

Step-by-step explanation:

We can fit 25 notebooks on the space.

Now, According to the question:

The width of the notebook is 2/5

The length of the space is 10 inches.

To find the number of the notebooks can put there divide 30 by 2/3

Number of the books : \(\frac{10}{\frac{2}{5} }\) = 10 × \(\frac{5}{2}\)

=> 50/2 = 25

The number of the notebook is 25

We can fit 25 notebooks on the space.

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%, a relative figure signifying hundredths of any amount. Before the raise, I was making $45,000.

A percentage that represents a tenth of a quantity. In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).

Calculating a percentage involves dividing an item by its sum and multiplying the result by 100.

Considering the query

It was $52,200 after a 16% raise in my pay.

In light of the conditions stated, come up with

\($=\frac{52200}{1+16 \%}$$=\frac{52200}{1+0.16}$$=\frac{52200}{1.16}$$=\frac{5220000}{116}$\)

= $45000

Before the raise, I was making $45,000.

Therefore, the answer is $45,000.

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let x as the total sales

26 250 = 14 250 + 0.06x

26 250 - 14 250 = 14 250 - 14 250 + 0.06x  (subtract 14 250 both sides)

12 000 = 0.06x

x = 200 000

26 250 = 14 250 + 0.06(200 000)

26 250 = 14 250 + 12 000

26 250 = 26 250

Therefore, Peter have total sales of RS 200 000.

Step-by-step explanation:

The formula for the exponential function that passes through the two given points is: f(x) = 4^x

Step-by-step explanation:

An exponential function has the form f(x) = a^x, where a is a constant base.

We can use the two points given to find the value of a.

Using the first point (0, 4), we get:

f(0) = a^0 = 1a = 4

So, a = 4.

Now, we can write the exponential function as:

f(x) = 4^x

To check if this function passes through the second point (3, 256), we substitute x = 3:

f(3) = 4^3 = 64 * 4 = 256

So, the function passes through both points (0, 4) and (3, 256).

Therefore, the formula for the exponential function that passes through the two given points is:

f(x) = 4^x

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Answer:

a

Step-by-step explanation:

the complement of R is 90 - R , then

R = 5(90 - R) - 6

R = 450 - 5R - 6

R = 444 - 5R ( add 5R to both sides )

6R = 444 ( divide both sides by 6 )

R = 74°

complement = 90° - 74° = 16°

Option(a) 16 is correct option, the measure of the complement of R is 16

Two angles are complementary if their sum is 90°.

Let x be an angle and y be its complement of x then x + y = 90°.

Let the measure of the complement of R be x

Given that the measure of angle R is 6 less than 5 times its complement

Then 5 times the complement of R = 5x

And 6 less than 5 times the complement of R  = 5x-6

Thus, R = 5x -6

∴ R + complement of R = 90°

⇒5x-6 + x = 90

⇒6x = 96

⇒x = 96/6 = 16

Therefore, the measure of the complement of angle R is 16 and option (a) is correct option.

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Answer:

4 11/12 feet tall

Answer:

1/6

Step-by-step explanation:

Answer:

0.16666666

repeated

or≈0.17

Step-by-step explanation:

Answer:

Step-by-step explanation:

The function  has a domain x ≥ 5.

This is because the function remains real for (x - 5) ≥ 0 as negative within the square root is imaginary.

Hence, (x - 5) ≥ 0

⇒ x ≥ 5

Now, for all x values that are greater than equal to 5 the value of  will be negative.

So,  

⇒  

⇒ y ≤ 3

Therefore, the range of the function is y ≤ 3. (Answer)

Note: Thanks rani