What is the area of a square

Step-by-step explanation:

T0 = a³+4

T1 = a⁴x a¹ +4

T2= a³ + a³ + 4

T3= a⁴ + a⁴* a² + 4

T4= a⁴ + a⁴ x a¹ + 4

T5= a³ + a³ + a⁴+4

Answer:

hello,

Step-by-step explanation:

c(1)=5

c(2)=9

c(2)-c(1)=9-5=4

c(2)=9

c(3)=13

c(3)-c(2)=13-9=4

c(3)=13

c(4)=17

c(4)-c(3)=17-13=4

c(4)=17

c(5)=21

c(5)-c(4)=21-17=4

for n=1,2,...,k :

c(n+1)-c(n)=4 and c(n+1)=4*(n+1)+1=4n+5

c(1)=1

The relative atomic mass of Interactium is 290.14 amu.


We can calculate the relative atomic mass of Interactium using the following equation:

Ar = (Ab × Mb) + (Ac × Mc) + (Ad × Md) where Ar is the relative atomic mass, Ab is the abundance of Interactium-284, Mb is the mass of Interactium-284, Ac is the abundance of Interactium-289, Mc is the mass of Interactium-289, Ad is the abundance of Interactium-294, and Md is the mass of Interactium-294.  

Substituting the given values in the equation, we get:

Ar = (0.16 × 284) + (0.27 × 289) + (0.57 × 294)
Ar = 45.44 + 77.97 + 167.43
Ar = 290.14 amu

Therefore, the relative atomic mass of Interactium is 290.14 amu.

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Answer:

What is 2x times 3x

6x

Step-by-step explanation:

3•2=6

Answer:

9, -19

Step-by-step explanation:

Given that the distance between point J and point K on a number line is 14, and the coordinate of J is -5, there are two possible coordinates that could represent the location of K.

K can either be located to the right of J, or to the left of J. Either ways, distance between J and K will still equal 14.

To the right we would have K located at: -5 + 14 = 9

To the left we can also have K located at: -5 - 14 = -19

K can be located at either 9 or -19

Answer:

per inch 0.90 cents hhhhhhjjkolllll

Answer:

The speed of Sara is 78.4 km/h.

Step- by-step explanation:

Manuel and Sara travel a certain distance, and the times they use are in the ratio 21/15. Manuel's speed is 56km / h. What is Sara's speed?

Let the distance is d.

speed of Manuel = 56 km/h

time taken by Manuel = 21 t

time taken by Sara =  15 t

Let the speed of Sara is v.

Distance = speed x time

For Manuel:

d = 56 x 21 t ..... (1)

For Sara:

d = v x 15 t ..... (2)

From (1) and (2)

56 x 21 t = v x 15 t

v = 78.4 km/h

Answer:  The box measurements are as follows: Box A: height = 5 inches, length = 18 inches, width = 10. Box B: height = 8 inches, length = 10 inches, ..

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

you divided everything in blankets 3 /-3 is equal to zero

Answer: 220

Step-by-step explanation:

The value of m∠SRT as shown in the circle below is 46.5°.

A circle is a round-shaped figure that has no corners or edges.

To calculate the value of m∠SRT, use the formula below

Formula:

But,

From the diagram,

Given:

Substitute these values into equation 2

Finally we substitute the value m∠SUT into equation 1

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The composite transformation that has happened is defined as follows:

From the triangle ABC to the triangle A'B'C', we have that the figure was reflected over the x-axis, as the orientation of the figure was changed.

From triangle A'B'C' to triangle A''B''C'', the figure was moved 6 units right and 2 units up, which is defined as a translation 6 units right and 2 units up.

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The dosage at which the resulting blood pressure is maximized is x at 0.2 and the maximum dosage is 0.0008.

In the question,

The function is \(B(x) = 0. 06x^2 - 0. 2x^3\)

To find the maximum or minimum, take the derivative and set it equal to zero.

⇒ \(B'(x) = 2(0. 06)x - 3(0. 2)x^{2}\)

Setting it equal to zero, we get

⇒ \(0.12x - 0.6x^{2}=0\)

⇒ 0.6x (0.2-x) = 0

⇒ x = 0 or x = 0.2

Now substitute x = 0.2 in B(x), we get

⇒ \(B(0.2) = 0. 06(0.2)^{2} - 0. 2(0.2)^{3}\)

⇒ B(0.2) = 0.0024 - 0.0016

⇒ B(0.2) = 0.0008

To know B(0.2) is maximum, let us find the values for x = 1 and x = 0.01.

For x = 1,

⇒ \(B(1) = 0. 06(1)^{2} - 0. 2(1)^{3}\)

⇒ B(1) = 0.06-0.2

⇒ B(1) = -1.04

For x = 0.01,

⇒ \(B(0.01) = 0. 06(0.01)^{2} - 0. 2(0.01)^{3}\)

⇒ B(0.01) = 0.000006 - 0.0000002

⇒ B(0.01) = 0.0000058

Thus, x = 0.2 is the maximum.

Hence we can conclude that the dosage at which the resulting blood pressure is maximized is x at 0.2 and the maximum dosage is 0.0008.

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Answer:

It was decently and increase

Step-by-step explanation:

I don't know the percent though?

If we have an angle equal to 175.5°, then its supplementary angle is equal to 4.5°.

To solve this problem we must know that an angle and its supplementary add up to 180º, that is, the following equality must be satisfied:

β + α = 180º

The measure of a supplementary angle is the difference between 180° and the given angle. In this case, the given angle is 175.5°. To find the measure of the supplementary angle, we will subtract 175.5° from 180°.
α = 180° - 175.5° = 4.5°

Therefore, the measure of the supplementary angle is 4.5°.

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Answer:

The area of the rectangle A =  25x² -  20x

Step-by-step explanation:

Given

The width of the rectangle = w = 5x - 4

The length of a rectangle = l = 5x

To determine

The area of the rectangle = ?

Using the Formula to determine the area of the rectangle

\(A = wl\)

substitute w = 5x - 4 and l = 5x in the formula

\(A = (5x-4) (5x)\)

Apply distributive law:  a(b-c) = ab - ac

   \(=\left(5x\right)\cdot \:5x-\left(5x\right)\cdot \:4\)

   \(=5x\left(5x\right)-4\left(5x\right)\)

as 5x(5x) = 25x²  and  4(5x) = 20x, so

    \(=25x^2-20x\)

Therefore, the area of the rectangle A =  25x² -  20x

The unknown angle x in the triangle is 80 degrees

From the question, we have the following parameters that can be used in our computation:

The triangle

The unknown angle x is calculated using the sum of angles in a triangle theorem

So, we have

x + 60 + 40 = 180

Evaluate the like terms

x + 100 = 180

So, we have

x = 80

Hence, the unknown angle x is 80 degrees

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The volume under the graph of f(x,y) over the triangle with vertices (0, 0), (2, 2) and (4, 0) is (3 + e^-5/2) / 5.

To find the volume under the graph of f(x,y) over the triangle with vertices (0, 0), (2, 2) and (4, 0).The triangle with vertices (0, 0), (2, 2) and (4, 0) can be represented as below:

The volume under the graph of f(x,y) over the triangle is given by the double integral over the triangle of f(x,y) dA.i.e.,

V = ∫∫R f(x,y) dA

where R is the given region

We can rewrite this volume using iterated integrals as below:

V = ∫[0,4] ∫[0,y/2] f(x,y) dxdy

Now, f(x,y) = xe^-5y

Thus, V = ∫[0,4] ∫[0,y/2] xe^-5y dx

dy= ∫[0,4] e^-5y/2 [ x^2/2]

dy= [e^-5y/2 x^2/4] 02 + [e^-5y/2 x^2/4] y/2 0= (e^-5/2 2^2 + e^-5 - e^-10/2) / 5= (4e^-5/2 + e^-5 - e^-5/2) / 5= (3e^-5/2 + e^-5) / 5= (3 + e^-5/2) / 5

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Answer: Graph is below

====================================================

Explanation:

If we plugged in x = 0, then we get...

\(y = \sin\left(\frac{\pi x}{4}\right)\\\\y = \sin\left(\frac{\pi*0}{4}\right)\\\\y = \sin\left(\frac{0}{4}\right)\\\\y = \sin\left(0\right)\\\\y = 0\\\\\)

Therefore, this sine curve goes through the origin. More specifically, this point is on the midline y = 0, aka the x axis. This is point A in the diagram below, which I made with GeoGebra (free graphing software).

Now to find another point on this sine curve. We need either a min or max point. Note that the expression \(\frac{\pi x}{4}\) is the same as \(\frac{\pi}{4}x\). We will divide 2pi over the coefficient of pi/4 to get

(2pi) divide (pi/4) = 2pi * 4/pi = 8

This tells us the period of this sine curve is 8 units in the horizontal x axis direction. The distance from midline to the nearest peak or valley is 1/4 of this, so (1/4)*8 = 2 units. Move 2 units to the right to arrive at x = 2. Plug this into the original function to get the following:

\(y = \sin\left(\frac{\pi x}{4}\right)\\\\y = \sin\left(\frac{\pi*2}{4}\right)\\\\y = \sin\left(\frac{\pi}{2}\right)\\\\y = 1\\\\\)

This matches with the fact that sin(x) maxes out at 1. So we've reached a max or highest point here. The location of which is B(2,1).

The first point on the midline is (0, 0), and the second point is either (2, 1) for the maximum or (6, -1) for the minimum.

To graph the function f(x) = sin(πx/4), we need to find the midline and the closest maximum or minimum value. The midline is the horizontal line that the graph oscillates around, which is y = 0 for the sine function.

The sine function's maximum value is 1, and the minimum value is -1. Since the sine function repeats every 2π, we can find the maximum or minimum value closest to the midline by setting the argument (πx/4) equal to π/2 or 3π/2, respectively.

1. For the maximum value:

πx/4 = π/2

x = 2

2. For the minimum value:

πx/4 = 3π/2

x = 6

So, the first point on the midline is (0, 0), and the second point is either (2, 1) for the maximum or (6, -1) for the minimum. Now, we can plot these points and draw the sine graph oscillating between them.

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Answer:

Step-by-step explanation:

\(cos\alpha =\sqrt{1-sin^{2} \alpha } =\sqrt{1-(\frac{5}{13})^{2} } =\sqrt{\frac{144}{169} }\)

=\(\frac{12}{13}\)

\(tan\alpha =\frac{sin\alpha }{cos\alpha } =\frac{\frac{5}{13} }{\frac{12}{13} } = \frac{5}{12}\)

As per the area of rectangle, the required length of rope is 36.66 square meter.

The formula to calculate the area of rectangle is written as,

=> A = l x b

Where l refers the length and b refers the breadth.

Here we have given that a florist want to put a rope around his rectangular garden with the dimensions 7. 8m by 4. 7m.

In order to put the rope we have to find the area of the garden,

The area of the garden is calculated by using the area of rectangle formula, as 7.8 as length and 4.7 as breadth

=> A = 7.8 x 4.7

=> A = 36.66

Therefore, 36.66 square meter is required.

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Answer:

Between -1 and -0 the third marker from zero on the left side

Correct answers -

a.Rate of change of water in the pool at t= 5 hours

b. Total volume of water in the pool at t=10 hours

c. Average rate of change of water in the pool = 389.31 gallons/hour

To answer the given questions, let's go step by step:

a. To find the rate of change of water in the pool at t=5 hours, we need to calculate the difference between the rate of water being pumped into the pool and the rate of water leaking from the pool at that specific time.

Rate of change of water in the pool at t=5 hours = P(5) - L(5)

P(5) = 1170 gal/hour (given)

L(5) = \(0.3e^5\) gal/hour (given)

Substituting the values into the equation:

Rate of change of water in the pool at t= 5 hours = 1170 - \(0.3e^5\)

b. To write an integral expression to calculate the total volume of water in the pool at t=10 hours, we need to integrate the rate of water being pumped into the pool over the time interval [0, 10] and subtract the integral of the rate of water leaking from the pool over the same interval.

Total volume of water in the pool at t=10 hours = ∫[0,10] P(t) - ∫[0,10] L(t) dt

P(t) = 1170 gal/hour (given)

L(t) = \(0.3e^t\) gal/hour (given)

Calculating the integrals:

∫[0,10] P(t) dt = ∫[0,10] 1170 dt = 1170t | [0,10] = 1170 × 10 - 1170 × 0 = 11700 gallons

∫[0,10] L(t) dt = ∫[0,10] 0.3\(e^t\) dt = 0.3 ∫[0,10] \(e^t\)dt = 0.3 (\(e^t\)) | [0,10] = 0.3 × (\(e^{10} - e^0\)) ≈ 0.3 × (22025 - 1) ≈ 6606.9 gallons

Total volume of water in the pool at t=10 hours = 11700 - 6606.9 ≈ 5093.1 gallons

c. To find the average rate of change of water in the pool over the 10 hours, we need to divide the change in volume by the time interval.

Average rate of change of water in the pool = (Change in volume) / (Time interval)

Change in volume = Total volume of water in the pool at t=10 hours - Initial volume of water in the pool

Change in volume = 5093.1 - 1200 = 3893.1 gallons

Time interval = 10 hours

Average rate of change of water in the pool = 3893.1 / 10 = 389.31 gallons/hour

d. To find the absolute maximum volume of water in the pool over the interval [0,10], we need to find the maximum value of the volume function within that interval.

To determine this, we can find the critical points by setting the derivative of the volume function equal to zero and check the endpoints of the interval.

Since the volume function is not provided, we cannot directly find the absolute maximum volume without additional information.

Final answers-

a.Rate of change of water in the pool at t= 5 hours

b. Total volume of water in the pool at t=10 hours

c. Average rate of change of water in the pool = 389.31 gallons/hour

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Answer:

The answer to your problem is, B. Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, grape

Step-by-step explanation:

We are given that, Julia had a bag filled with gumballs. There were 3 lemon-lime, 4 watermelon, and 6 grape gumballs.

There are 3 lemon-lime: Elements in sample space are lemon-lime, lemon-lime, lemon-lime

There are also 4 watermelon: Elements in sample space are watermelon, watermelon, watermelon, watermelon

Lastly there are 6 grape: Elements in sample space are grape, grape, grape, grape, grape, grape

Which can lead to the problem of:

3 + 4 + 6 = 13. Same as option B

Thus the answer to your problem is, B. Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, grape

To find the z-score for a sales associate who earns $37,500, we can use the formula:

z = (x - μ) / σ

Where:

x is the value we want to convert to a z-score (in this case, $37,500),

μ is the mean of the distribution (in this case, $32,500), and

σ is the standard deviation of the distribution (in this case, $2,500).

Substituting the given values into the formula, we have:

z = (37,500 - 32,500) / 2,500

z = 5,000 / 2,500

z = 2

Therefore, the z-score for a sales associate who earns $37,500 is 2.

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The z-score for a sales associate earning $37,500 in a system where the mean salary is $32,500 and the standard deviation is $2,500 has a z-score of 2. This score indicates that the associate's salary is two standard deviations above the mean.

The z-score represents how many standard deviations a value is from the mean. In this case, the value is the salary of a sales associate, the mean is the average salary, and the standard deviation is the average variation in salaries.

We calculate the z-score by subtracting the mean from the value and dividing by the standard deviation, like so:

Z = (Value - Mean) / Standard Deviation

So, the z-score for an associate earning $37,500 would be:

Z = ($37,500 - $32,500) / $2,500

This gives us a z-score of +2, indicating that a salary of $37,500 is two standard deviations above mean.

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Answer:

\(\frac{x+4}{x+3}\)

Step-by-step explanation:

Given

\(\frac{x^2+5x + 4}{x^2+4x+3}\) ← factor numerator and denominator

= \(\frac{(x+1)(x+4)}{(x+1)(x+3)}\) ← cancel common factor (x + 1) on numerator/ denominator

= \(\frac{x+4}{x+3}\)

If she moves at a speed of 1.33 miles per minute while walking 4 miles in 3 minutes, she can cover 20 miles in 15 minutes.

A number is divided in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

Here,

In 3 minutes, she walk 4 miles,

speed=distance/time

=4/3 miles/minute

distance=speed*time

=4/3*15

=20 miles

She can walk 20 miles in 15 minutes if she walks 4 miles in 3 minutes with a speed of 1.33 miles/minute.

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