Factorise the expression:21x+3xy+6x²​

The average period of the trials that were conducted with an amplitude of 10 degrees is 1.694 seconds.

What is amplitude ?

In mathematics, amplitude refers to the maximum displacement or distance from the equilibrium position of a periodic function, such as a sine or cosine wave. In other words, if a periodic function oscillates back and forth between two extreme values, the amplitude is the maximum distance from the average value or midpoint of the oscillation to one of the extreme values.

To calculate the average period of the trials that were conducted with an amplitude of 10 degrees, we simply add up all the periods and divide by the total number of trials.

10 degrees: 1.66 s, 1.700 s, 1.71 s, 1.68 s, 1.72 s

Average period = (1.66 + 1.700 + 1.71 + 1.68 + 1.72) / 5 = 1.694 seconds

Therefore, the average period of the trials that were conducted with an amplitude of 10 degrees is 1.694 seconds.

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The cοrrect answer is: The pοpulatiοn must be apprοximately nοrmal οr the sample size must be greater than 30.

The standard deviatiοn is a statistical measure οf the vοlatility οr dispersiοn οf a grοup οf numerical values. The values are mοre likely tο fall within a narrοw range, alsο knοwn as the expected value, when the standard deviatiοn is lοw, whereas when it is high, the values tend tο be clοser tο the mean.

Standard deviatiοn is mοst usually represented in mathematical equatiοns and literature by the lοwercase Greek symbοl sigma, which represents fοr the pοpulatiοn standard deviatiοn, οr by the Rοman letter s, which stands fοr the sample standard deviatiοn. Sοmetimes, standard deviatiοn (SD) is used tο refer tο it.

Tο cοnstruct a cοnfidence interval fοr a pοpulatiοn mean, the sample must be selected randοmly frοm a pοpulatiοn that is apprοximately nοrmal οr the sample size must be sufficiently large (greater than οr equal tο 30) regardless οf the pοpulatiοn distributiοn. Additiοnally, the sample standard deviatiοn shοuld be used tο estimate the pοpulatiοn standard deviatiοn if the pοpulatiοn standard deviatiοn is unknοwn.

Sο, the cοrrect answer is: The pοpulatiοn must be apprοximately nοrmal οr the sample size must be greater than 30.

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Answer:

h=0

Step-by-step explanation:

Let's solve your equation step-by-step.

2h−(6−5)=−1

Answer:

5,386,830

Step-by-step explanation:

the points of horizontal tangency on the curve are \(\((9, -2)\)\)and\(\((12, 2)\).\)

To find the points of horizontal tangency to the curve represented by the equations\(\(x = t^2 - t + 9\)\) and \(\(y = t^3 - 3t\),\) we need to find the values of \(\(t\)\)where the tangent line is horizontal. These points will have zero slope, meaning the derivative of \(\(y\)\) with respect to \(\(x\)\)will be zero.

First, let's find the derivative of \(\(y\)\) with respect to \(\(x\).\)We can differentiate \(\(y\)\) with respect to \(\(t\)\)using the power rule:

\(\(\frac{dy}{dt} = 3t^2 - 3\)\)

Next, we can find \(\(\frac{dt}{dx}\)\)by expressing \(\(t\)\) in terms of\(\(x\)\)from the equation\(\(x = t^2 - t + 9\).\)Rearranging the equation, we get:

\(\(t^2 - t + (9 - x) = 0\)\)

Solving this quadratic equation for \(\(t\)\) using the quadratic formula, we have:

\(\(t = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(1)(9-x)}}{2(1)}\)\)

Simplifying further, we get:

\(\(t = \frac{1 \pm \sqrt{1 - 36 + 4x}}{2}\)\)

To find the points of horizontal tangency, we set \(\(\frac{dy}{dt}\)\)equal to zero:

\(\(3t^2 - 3 = 0\)\)

This equation is satisfied when\(\(t = \pm 1\).\)

Substituting\(\(t = 1\)\)back into the equation \(\(x = t^2 - t + 9\)\), we find:

\(\(x = 1^2 - 1 + 9 = 9\)\)

Substituting\(\(t = -1\)\), we get:

\(\(x = (-1)^2 - (-1) + 9 = 12\)\)

Now we substitute these values of \(\(t\)\)into the equation\(\(y = t^3 - 3t\):\)

For\(\(t = 1\),\)we have:

\(\(y = 1^3 - 3(1) = -2\)\)

For\(\(t = -1\),\) we get:

\(\(y = (-1)^3 - 3(-1) = 2\)\)

Therefore, the points of horizontal tangency on the curve are \(\((9, -2)\)\)and\(\((12, 2)\).\)

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Answer:

2/27

Step-by-step explanation:

Step one:

given data

Sample space

2 red sections,

3 blue sections, and

4 green sections

Sample size

2+3+4= 9

Required

The probability of Basha spinning a red on her first spin and a blue on her second spin

Step two:

On the first spin, spinning a red= 2/9

On the second spini, spinning a blue= 3/9= 1/3

Hence, The probability of Basha spinning a red on her first spin and a blue on her second spin= 2/9*1/3= 2/27

Answer:

Go to the bottom of that problem and click save for later

The Extreme Value Theorem states that if a function f(x) is continuous on a closed interval [a, b], then f(x) has both a minimum value and a maximum value on that interval.

Therefore, we can find the absolute maximum or minimum value of a continuous function on a closed interval by evaluating the function at the critical points and at the endpoints of the interval.Since the given function f(x) = x² - 4 is continuous on the closed interval [–3, 0] and the open interval (0, 2], we need to evaluate the function at the critical points and endpoints of these intervals and then compare the values to determine the absolute maximum value.

Let's begin by finding the critical points of the function f(x) = x² - 4. To do this, we will need to find the values of x for which the derivative of the function is zero.f'(x) = 2xSetting f'(x) = 0, we get:2x = 0x = 0Therefore, the only critical point of the function is x = 0.Now, let's evaluate the function at the critical point and endpoints of the intervals to find the absolute maximum value:f(–3) = (–3)² – 4 = 5f(0) = 0² – 4 = –4f(2) = 2² – 4 = 0The absolute maximum value is 5, which occurs at x = –3.

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The total surface area of North America is approximately 9.54 × 10^6 square miles in scientific notation. The signal from a certain satellite takes approximately 0.0013 seconds to reach Earth in standard notation.

To convert a number into scientific notation, we express it as a product of a decimal number greater than or equal to 1 but less than 10, and a power of 10. In this case, we move the decimal point to the left until there is only one nonzero digit to the left of the decimal point, resulting in 9.54. The exponent represents the number of places the decimal point was moved, which is 6 in this case since the original number had six digits.

Regarding the signal from a certain satellite taking approximately 1.3 × 10^(-3) seconds to reach Earth, we can write this number in standard notation as 0.0013 seconds.

To convert a number from scientific notation to standard notation, we multiply the decimal number by 10 raised to the power of the exponent. In this case, multiplying 1.3 by 10 raised to the power of -3 gives us 0.0013.

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Answer:

reflection

Step-by-step explanation:

its flipping over the y axis therefore a reflection

sorry if this is wrong :)

(1) The integral evaluation is  (25/2) - (5√24)/2..

(2) The value of indefinite integral is  (-x/64) cos(8x) + (1/512) sin(8x) + C

(1) The value of the integral ∫_0^1 5x^3/(√(x^4+24)) dx, evaluated over the interval [0, 1], can be written in the simplest fractional form as (5√5 - 5)/4.

To evaluate the integral ∫[0,1] 5x^3/(√(x^4+24)) dx, we can use substitution to simplify the expression.

Let's substitute u = x^2 + 24, then du = 2x dx.

To convert the limits of integration, when x = 0, u = (0^2 + 24) = 24, and when x = 1, u = (1^2 + 24) = 25.

Now, let's rewrite the integral in terms of u:

∫[0,1] 5x^3/(√(x^4+24)) dx = ∫[24,25] 5x^3/(√u) * (1/2x) du

Simplifying further:

= (5/2) ∫[24,25] (x^2)/(√u) du

= (5/2) ∫[24,25] (1/2) u^(-1/2) du

Using the power rule for integration, we can integrate u^(-1/2):

= (5/2) * (1/2) * 2 * u^(1/2) evaluated from 24 to 25

= (5/2) * (1/2) * 2 * (25^(1/2) - 24^(1/2))

= (5/2) * (1/2) * 2 * (√25 - √24)

= (5/2) * (1/2) * 2 * (5 - √24)

= (5/2) * (5 - √24)

= (25/2) - (5√24)/2

Therefore, the value of the integral ∫[0,1] 5x^3/(√(x^4+24)) dx is  (25/2) - (5√24)/2.

(2) To evaluate the integral ∫x sin(8x) dx, we can use integration by parts. Integration by parts is a technique based on the product rule for differentiation, which allows us to rewrite the integral in a different form.

The integration by parts formula is given by:

∫u dv = uv - ∫v du

Let's choose u = x and dv = sin(8x) dx. Then, du = dx and v can be found by integrating dv:

v = ∫sin(8x) dx = -(1/8) cos(8x)

Using the integration by parts formula, we have:

∫x sin(8x) dx = uv - ∫v du

= x * (-(1/8) cos(8x)) - ∫(-(1/8) cos(8x)) dx

Simplifying further:

= -(1/8) x cos(8x) + (1/8) ∫cos(8x) dx

To find the integral of cos(8x), we can integrate term-by-term:

= -(1/8) x cos(8x) + (1/64) sin(8x) + C

Therefore, the indefinite integral of x sin(8x) dx is -(1/8) x cos(8x) + (1/64) sin(8x) + C, where C is the constant of integration.

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Given:

IE || GH

EF ≅ HF

we need to prove

Δ EFI ≅ ΔHFG

The proof will be as follows:

Statements Reason

IE || GH Given

m∠ I = m∠G

IE

The expected winning and the value of that prize, which gives an expected winning is c. $3.13 per ticket.

The expected winnings per ticket in the raffle can be calculated by adding the products of the probability of the expected value of winning each prize. The predicted wins per ticket may be computed as the total of each prize's value multiplied by its probability of winning, i.e.

Expected winnings per ticket

= (1/800) × $400 + (4/800) × $200 + (12/800) × $125 + (30/800) × $60 + (753/800) × $0

If we condense the equation, we obtain:

Calculating the total wins anticipated per ticket

= $0.50 + $1.00 + $1.88 + $0.75 + $0

Expected winnings per ticket = $3.13

Therefore, if you buy a ticket, the expected winnings per ticket are $3.13.

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Complete question:

For a fundraiser, there is a raffle with 800 tickets, each costing $15. 1 ticket will win a $400 prize, 4 tickets will win a $200 prize, 12 tickets will win a $125 prize, 30 tickets will win a $60 prize, and the remaining tickets will win nothing. if you buy a ticket, what are the expected winnings per ticket? question options:

a) $5.36

b) $5.63

c) $5.33

d) $5.66

I think this might helpful

The correct choice is (e) All of the above is a property for all LP problems.

All Linear Programming (LP) problems have a linear objective function that is to be maximized or minimized (property a), a set of linear constraints (property b), and decision variables (property c). Additionally, LP problems require variables that are all restricted to nonnegative values (property d). Therefore, all of the given properties are true for all LP problems, making option (e) the correct choice.

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Answer:

C

Step-by-step explanation:

The formula for the volume of a cylinder is \(\pi r^2 h\), since you are multiplying the area of the base (a circle) by the height of the cylinder to find the volume. Therefore, the volume of this cylinder is:

\(\pi r^2 h= \\\\3.14 \cdot 8^2 \cdot 15=\\\\3.14 \cdot 960=\\\\3014.4\)

Hope this helps!

Answer:

\(3014.4ft^3\)

even though this is not the most precise answer, ths is the answer you will be looking for

Step-by-step explanation:

To find the volume of a cylinder you use the formula \(V=\pi r^2h\\=\pi *8^2*15\\=3015.93ft^3\)

It will take the golf ball 12 seconds to hit the ground using the kinematic equation for vertical motion.

To determine the time it takes for the golf ball to hit the ground, we can use the kinematic equation for vertical motion:

\(h = ut + (1/2)gt^2\)

Where:

h is the height (0 feet, as the ball is on the ground)

u is the initial velocity (192 feet per second)

g is the acceleration due to gravity (-32 feet per second squared, considering downward direction)

t is the time we want to find

Plugging in the given values, we get:

\(0 = (192)t + (1/2)(-32)t^2\)

Simplifying the equation, we have:

\(-16t^2 + 192t = 0\)

Factoring out t, we get:

t(-16t + 192) = 0

Setting each factor equal to zero, we have:

t = 0 (not applicable in this case)

-16t + 192 = 0

Solving for t, we get:

-16t = -192

t = 12

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The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

The time it takes for the golf ball to hit the ground can be determined using the equation of motion. We can use the formula:

h0 = 0

v0 = 192

g = 32.2

a = 16.1

b = 192

t1 = 0

t2 = -b / a

t(-16t + 192) = 0

Setting each factor equal to zero, we have:

t = 0 (not applicable in this case)

-16t + 192 = 0

Solving for t, we get:

-16t = -192

t = 12

t2 >= 0:

   time_to_hit_ground = t2

   time_to_hit_ground = t1

The time it takes for the golf ball to hit the ground is approximately", round(time_to_hit_ground, 2 seconds.

The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

Since time cannot be negative in this context, we discard the negative solution. Therefore, the time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

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Send a better cropped

photo

Based on the above, we need a little less than two cupcakes (1.99) to have the amount of cupcakes everyone wants.

To identify the amount of cupcake that each one wants, we must make the divisions of the fractions as shown below:

1/3 = 0.33

1/3 = 0.33

4/3 = 1.33

Based on the above, me and my sister require 0.33 from a cupcake, while our cousin requires 1.33. To know how many cupcakes we need to meet everyone's need, we must add these values as shown below:

0.33 + 0.33 + 1.33 = 1.99

So 1.99 cupcakes would be needed so it would be better to buy 2 cupcakes to give everyone the portion they need.

Note: This question is incomplete because there is some information missing. Here is the complete information:

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Answer:

y = -9/5x + 9/5

Step-by-step explanation:

From this points, we can determine the slope and the y-intercept.

First, we do:   y/x  -  y1/x1

=> 0/3 - (3 - 2)

=> 0-3/ 3 + 2

=> -3/5

So the slope of the equation is -3/5.

The equation is: y = mx + b

In this equation "m" = slope.

=>  b = constant

Now we take the x and y points from the above numbers.

=> Let's take 3 as x and 0 as y.

=> 0 = -3/5 *3 + b

=> 0 = -9/5 + b

=> Take the -9/5 to the other side

=> 9/5 = b

So, the constant number which is not multiplied by the x is 9/5

Now, our equation looks like:

y = -9/5x + 9/5

If you have any doubts about this question, ask me the comments and I will answer it as soon as possible.

Answer:

85-6=79

STU=79

Step-by-step explanation:

Step-by-step explanation:

To calculate the minimum number of days required to finish this project, we need to use the critical path method (CPM), which involves identifying the longest sequence of dependent tasks and their durations.

First, we need to draw the network diagram for the project:

```

|---(T1-8)---(T3-10)---|

(T2-6) (T5-12)

| / |

|---(T4-7)---(T6-15)---|

```

Next, we need to calculate the earliest start time (EST), earliest finish time (EFT), latest start time (LST), and latest finish time (LFT) for each task. For the starting task, EST = 0 and EFT = 0.

```

EST EFT LST LFT

T1 (8 days) 0 8 22 30

T2 (6 days) 0 6 6 12

T3 (10 days) 8 18 22 32

T4 (7 days) 18 25 25 32

T5 (12 days) 18 30 32 44

T6 (15 days) 32 47 32 47

```

The critical path is the longest sequence of dependent tasks that have no slack (i.e., the difference between LST and EST, or LFT and EFT, is zero). In this case, the critical path is T1-T3-T5-T6.

Therefore, the minimum number of days to finish this project is the sum of the durations of tasks on the critical path:

8 + 10 + 12 + 15 = 45 days

Therefore, the minimum number of days required to finish this project is 45 days.

In the long run, new technology can have a significant impact on the long-run average total cost (LRATC) of a company.

The LRATC curve represents the lowest possible average cost at which a company can produce a particular level of output in the long run. New technology can reduce the costs of production by improving efficiency, reducing waste, and increasing productivity, leading to lower LRATC. This can lead to a shift in the LRATC curve downward, indicating that the company can now produce the same output at a lower cost than before. This can make the company more competitive and increase its profitability.

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The direction of vector D is perpendicular to vector A, and it makes an angle of 90 degrees with vector A.

We are given that:

vector A + vector B = vector C

vector A - vector B = vector D

To find the direction of vector C,

we can use the fact that the tangent of the angle between vector A and vector C is equal to the ratio of their magnitudes.

That is:

tan(theta) = |vector C| / |vector A|

where theta is the angle between vector A and vector C.

Similarly, to find the direction of vector D,

we can use the fact that the tangent of the angle between vector A and vector D is equal to the ratio of their magnitudes.

That is:

tan(phi) = |vector D| / |vector A|

where phi is the angle between vector A and vector D.

We want to find the angle between vector A and vector D, which is equal to the supplement of the angle between vector A and vector C.

That is:

theta + phi = 180 degrees

Rearranging, we get:

phi = 180 degrees - theta

Substituting the equations for theta and phi, we get:

tan(180 degrees - phi) = |vector D| / |vector A| = tan(phi)

Simplifying, we get:

tan(180 degrees - phi) = tan(phi)

Using the identity tan(180 degrees - theta) = -tan(theta), we can rewrite this as:

-tan(phi) = tan(phi)

Solving for phi, we get:

2*phi = 180 degrees

phi = 90 degrees

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Complete question may be:

If, vector A + vector B = vector Cvector A - vector B = vector D, then find the direction of vector D is perpendicular to vector A?

Answer: 1,000 milliliters = 1 litter

Step-by-step explanation: 1 milliliter = 0.001 litter so 1,000 milliliters= 1 litter

Answer:

1,000milliliters =

one liters

The 'x' coordinate is negative and 'y' coordinate is positive.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

We know that :

π = 180

Therefore,

3π/4 = (3×180)/4 = 3 × 45

3π/4 = 135

In second quadrant, we have negative value if x coordinate and positive value of y coordinate.

Hence, the angle lies in the second quadrant. Second quadrant is enclosed by the negative x axis and positive y axis.

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Answer:

x is negative, and y is positive.

Step-by-step explanation:

The answer above is correct.

Answer:

She spends 111 minutes doing cardio workouts and 39 minutes doing weight training

Step-by-step explanation:

Call the time she spend on cardio workouts : a
And the time she spend on weight training : b

We have : a + b = 150
                 a - b = 72
Add them together, we get : a + b + (a-b) -> a+ b + a - b = 150 + 72 = 222
                                                                      = 2a
=> 2a = 222, and we have a = 111
=> b = 150 - 111 = 39

Hope this helps :)

Answer:

1.25 words per minute

Step-by-step explanation:

Divide 40 by 40 to get 1 minute

Divide 50 by 40 to get 1.25 words