. Find the coefficient of x3 in the expansion of (3+2x+x2)6

Answer:

1847.26 cubic inches

Step-by-step explanation:

The volume of a cylinder is given by the formula:

V = Ah

Where V is the volume of the cylinder, A is the area of the base, and h is the height of the cylinder. The area of the base can be shown as the formula for the area of a circle:

A = πr²

Where r is the radius of the circle.

Now, find the area of the base of the cylinder:

A = π(7)²

A = 153.93804

Next, plug this value into the equation for volume, substituting h for the height of the cylinder; 12 inches.

V = 153.93804(12)

V = 1847.26

Volume is given in cubic units, and the units for this cylinder are inches, so this cylinder has the following volume:

1847.26 cubic inches

Answer:Therefore, the required area of the sector GPH  is about 50.24 yd.

Step-by-step explanation:its ez

Answer:

E

Step-by-step explanation:

Have a good day :)

Answer:

Cost of a play station game = $11.3

Cost of each water ride = $22.6

Step-by-step explanation:

Entrance tickets = $89.97

Royal meal = $10.85

Cost of a play station game = x

Cost of each water ride = 2x

Find the cost of a water ride

Entrance tickets = Royal meal + 1 play station game + 3 water rides

89.97 = 10.85 + 1(x) + 3(2x)

89.97 = 10.85 + x + 6x

89.97 = 10.85 + 7x

89.97 - 10.85 = 7x

79.12 = 7x

x = 79.12/7

x = 11.302857142857

Approximately to the nearest tenth

x = $11.3

Cost of a play station game = x = $11.3

Cost of each water ride = 2x

= 2(11.3)

= $22.6

The number of the lions that live in the region investigated by the considered scientist is 80.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For this case, we're specified that:

Let we take:

x = number of lions the scientist located and tagged on thursday.

Then, we get:

x - 10 = number of lions the scientist located (and assumingly found that they're tagged) on friday,

4 = number of lions he found tagged on friday.

That means, x -10 is same number as 4

or, we get:

\(x - 10 = 4\\\text{Adding 10 on both the sides}\\\\x = 14\)

That means, on thursday, the scientist located and tagged 14 lions.

Now, suppose that the region had 'y' number of lions,

Then, as per the data in the question,

one-fifth of y =  number of lions located by scientist on thursday

or, we get:
\(\dfrac{y}{5} = x\\\\\dfrac{y}{5} = 14\\\\\text{Multiplying 5 on both the sides}\\\\y = 80\)

Thus, the number of lions that live in the region considered is 80

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The total number of lines is 70.

We have given that,

A scientist wants to estimate the number of lions living in a region.

On Thursday, he locates and tags some lions.

On Friday he returns and locates 10 less lions than he had on Thursday.

He notices that 4 of the lions are tagged

The scientist works out an estimate for the total number of lions living in the region.

we have to determine the no of lines in the length.

on Thursday no.of lines=x

on friday=(x-10)=4

x-10=4

add like terms

Like terms are terms whose variables and their exponents such as the 2 in x^2 are the same.

x=10+4

x=14

No.of total lions =5th of (no. of tagged on Thursday.)

=5(14)

=70

Therefore the total number of lines is 70.

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Copper oxide, often known as CuO, is the most typical natural ore of copper.

An estimated 5.6 million metric tons of copper were produced in 2021 in Chile, the world's largest copper producer.

What is copper?

A ductile, malleable, and highly efficient conductor of heat and electricity, copper is a reddish-gold colored metal. Since it was the first metal that humans worked with, copper is one of the metals that is used the most frequently today.

The two primary copper ores are copper oxide ore and copper sulfide ore. Both forms of ore may be profitably mined, although chalcopyrite, a sulfide ore mineral, is the most prevalent source of copper ore and represents nearly half of the metal's output.

The most significant and significant source of copper metal is chalcopyrite. The hue is often brassy to golden-yellow, frequently tarnished, and has a submetallic shine along with greenish-black streaks.

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Answer:

Illogical

Step-by-step explanation:

Your question is completely illgocal unless you state the number of cheery tomatoes used in 1 or x amounts of large and small salads

Answer:

84

Step-by-step explanation:

We know that Jorge is making 6 large salads and 4 small salads. Each large salad needs 10 cherry tomatoes and each small salad needs 6 cherry tomatoes. 6 large salads need 10 cherry tomatoes.

Answer:

14b +64

Step-by-step explanation:

as listed above

Correct option is D)

We shall label the figure as shown below:

The simplest parallelograms are ABML, BCNM, COON, DEFO, OFGH, NOHl, MNIJ and LMJK i.e. 8 in number.

The parallelograms composed of two components each are ACNL, BDOM, CEFN, LNIK, MOHJ, NFGI, ABJK, BCLJ, CDHI and DEGH i.e. 10 in number.

The parallelograms composed of three components each are ADOL, BEFM, LOHK and MFGJ i.e. 4 in number.

The parallelograms composed of four components each are AEFL, LFGK, ACIK, BOHJ and CEGI i.e. 5 in number.

The parallelograms composed of six components each are ADHK and BEGJ i.e. 2 in number. AEGK is the only parallelograms composed of eight components.

Total number of parallelograms in the figure =8+10+4+5+2+1=30

Hence, the answer is (D).

Answer:

Option D is correct

Step-by-step explanation:

...

The measure of angle x is 140°

For given question,

We are given that a pair of parallel lines is cut by a transversal line .

Let a pair of parallel lines are PQ and RS and the transversal line AB cut the parallel lines PQ and RS.

We are given that an exterior angle on the left side of the transversal line is 40 degrees.

The interior angle on the right side of transversal line is x which is not vertical opposite to exterior angle = 40 degrees

We know that when two lines are parallel and cut by a transversal line then corresponding angles are congruent.

So, angle MNR = 40°

Also, ∠MNR + ∠MNS = 180°           ...............(linear pair of angles)

⇒ 40° + x = 180°

⇒ x = 140°

Therefore, the measure of angle x is 140°

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If the cost for 10 ounce of organic blueberry is $2. 70, the cost of 30 ounce of organic blueberry is represented by the equation x = 20y + 2.70 where y is the cost in dollars for one ounce of organic blueberry.

As x is the cost in dollar for 30 ounce of organic blueberry. For y is the cost in dollars for one ounce of organic blueberry, then

x = 30y + c

where c is the fixed cost

We know for 10 ounce of organic blueberry it costs $2.70. That is

2.70 = 10y + c

c = 2.70 - 10y

So x = 30y + 2.70 - 10y

x = 20y + 2.70

-- The question is incomplete, the complete question is as follows--

"The cost for 10 ounce of organic blueberry is $2. 70 which equation can be used to determine x the cost in dollars, for 30 ounces of organic blueberries.?"

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Solution

For this case we can use the following formula:

where:

P= 200

r= 0.09

n = 4

t= 4

And solving we got:

Answer:

85%

Step-by-step explanation:

First, let's add up the ratios and use it to divide 120. That way we can find out how many people each ratio is.

17 +3 = 20

120/20 = 6

Each individual ratio is equal to 6.

17 * 6 = 102

3 * 6 = 18

102/120 = percentage of who passed

= 0.85

85 percent of learners passed.

The obtained value must be compared against the critical value. Hence, the correct option is b.

In hypothesis testing, the critical value is a threshold or cutoff point that is determined based on the chosen significance level (alpha level) and the distribution of the test statistic. It helps in determining whether to reject or fail to reject the null hypothesis.

After calculating the test statistic (such as z-score or t-statistic) from the observed data, it is compared to the critical value associated with the chosen significance level.

If the test statistic exceeds the critical value, it falls into the critical region, leading to the rejection of the null hypothesis.

If the test statistic is less than or equal to the critical value, it falls into the non-critical region, resulting in a failure to reject the null hypothesis.

Therefore, the obtained value must be compared against the critical value to make a decision in hypothesis testing. Hence, the correct answer is option b.

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Answer:

1312

Step-by-step explanation:

if grade 8 has 196 more, that means 196 represents two cause 5 is 2 more than 3, so then you divide 196 in half to get 98, then add 196 and 98, so grade 7 gets 294 pencils, the to find how many for grade 8 you take 294 plus 196 and get 460 so grade 8 gets 460, and for grade 9 you add 460 and 98 to get 558, then just add, 294, 460, and 558 and you get 1312. hope this helps

The maximum height of the rocket is 50 meters.

The path of a particular fireworks rocket is modeled by the given equation:

\($$h(t) = -5t^2 + 30t + 5$$\)

where h is the height of the rocket in meters and t is the time in seconds. To find the maximum height of the rocket, we need to find the vertex of the parabola. We can do this by using the formula:-

b/2a for the t-coordinate and then substitute the value of t in the equation to find the corresponding height. The general form of a quadratic function is given as

\($$f(x)=ax^2+bx+c$$\)

where a, b, and c are constants; a ≠ 0.

The vertex of the quadratic function is given as

\($$( -\frac{b}{2a},f(-\frac{b}{2a}))$$\)

Therefore, the formula for the t-coordinate of the vertex of the parabola is:

\($$t = -\frac{b}{2a}$$\)

Here, a = -5 and b = 30. Substituting these values in the above formula, we get:

\($$t = -\frac{30}{2(-5)} = 3$$\)

The corresponding height can be found by substituting t = 3 in the equation for h(t):

\($$h(3) = -5(3)^2 + 30(3) + 5 = 50$$.\)

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Answer:

the answer is A because the pair of ratios are equivalent.

Answer:

1680 cm

Step-by-step explanation:

100 cm = 1 meter

Malik's arts and crafts shop has a bolt of crimson velvet 32 meters long.

1 m = 100 cm

32 m = x cm

Cross Multiply

x = 32m × 100cm

x = 3200cm

A customer came in during the morning and bought 120 centimeters of the velvet.

Another customer bought an additional 14 meters during the afternoon.

1 m = 100cm

14m = x cm

x cm = 14 m × 100cm

x cm = 1400cm

How much crimson velvet does Malik's shop have left?

3200cm - (1400 + 120)cm

3200 cm - 1520cm

= 1680 cm

The tuition of the second child will be $95 per day.

Let the tuition of the first child be x.

So, the tuition of the second child will be (x - 10).

As per the given condition:

Tess has her two children enrolled for 5 days her total bill for both children is $200.

Hence, the total tuition of both children is $200.

∴ x + (x - 10) = 200

⇒ 2x - 10 = 200

⇒ 2x = 200 + 10 = 210

⇒ x = 105

So, the tuition of the first child is $105 per day.

Thus, the tuition of the second child will be $(105 - 10) = $95 per day.

Answer: $95.

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The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

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Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey

Answer:

A

Step-by-step explanation:

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

To determine the fraction that Lee writes on the first mark to the right of 17, we need to understand the numbering pattern and the position of the marks.

If Lee marks sixths on the number line, it means that the interval between each mark is 1/6.

Starting from 0, the first mark to the right of 17 would be located at 18.

To find the fraction written on this mark, we can calculate the difference between 18 and 17 and express it as a fraction of the interval between each mark (1/6).

18 - 17 = 1

Therefore, the fraction that Lee writes on the first mark to the right of 17 is 1/6.

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A the center of mass is\($(x_{M},y_{M})=(0,2)$.\) The answer is (a).
B the center of mass is \($(x_{M},y_{M})=(\frac{2916}{7\cdot243},\frac{6561}{4\cdot243})$\). The answer is (a).

C the center of mass is\($(x_{M},y_{M})=(0,2)$.\) The answer is (a).

1A) We can find the mass by integrating the density function over the region:
\($$M=\iint_{\Omega}\lambda(x,y)dA=\int_{0}^{5}\int_{0}^{25-x\sqrt{25-x^2}}2xydydx$$\)
Evaluating this integral gives \($M=\frac{625}{8}$.\) To find the center of mass, we need to compute the moments:
\($$M_{x}=\iint_{\Omega}x\lambda(x,y)dA=\int_{0}^{5}\int_{0}^{25-x\sqrt{25-x^2}}2x^2ydydx=\frac{8}{3}M$$\\$$M_{y}=\iint_{\Omega}y\lambda(x,y)dA=\int_{0}^{5}\int_{0}^{25-x\sqrt{25-x^2}}2xy^2dydx=\frac{8}{3}M$$\)
So the center of mass is \($(x_{M},y_{M})=(\frac{8}{3},\frac{8}{3})$\). Therefore, the answer is (a).

1B) Since the question only asks for the mass and center of mass, we can use the same method as in 1A to get \($M=\int_{-1}^{1}\int_{0}^{4}x^2dydx=\frac{16}{3}$\). To find the moments, we have:
\($$M_{x}=\int_{-1}^{1}\int_{0}^{4}x^3dydx=0$$\\$$M_{y}=\int_{-1}^{1}\int_{0}^{4}xy^2dydx=2\int_{0}^{1}\int_{0}^{4}xy^2dydx=\frac{16}{3}$$\)
Therefore, the center of mass is\($(x_{M},y_{M})=(0,2)$.\) The answer is (a).

1C) Using the same method as in 1A, we have:
\($$M=\int_{0}^{3}\int_{x^2}^{9}2xydydx=\frac{243}{2}$$\)
To find the moments, we have:
\($$M_{x}=\int_{0}^{3}\int_{x^2}^{9}x2xydydx=\frac{2916}{7}$$\\$$M_{y}=\int_{0}^{3}\int_{x^2}^{9}y2xydydx=\frac{6561}{4}$$\)
Therefore, the center of mass is \($(x_{M},y_{M})=(\frac{2916}{7\cdot243},\frac{6561}{4\cdot243})$\). The answer is (a).

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The ratio of the number of students who joined the class to the number of students who were initially in the class is 2:1.

Age ratio refers to the comparison of the number of individuals in different age groups in a population. It is often expressed as a ratio or percentage of the number of people in a particular age group to the total population or the number of people in another age group.

Given by the question.

Now, when the group of students with an average age of 16 years joins the class, the average age of all the students becomes 17 years. This means that the total age of all the students in the class would now be 17 times the total number of students.

Let "y" be the number of students who joined the class. Then, the total number of students in the class after they joined would be x + y.

So, we have two equations:

18x = 17(x+y) (because the total age of all the students remains the same before and after the group joins)

16y = (x+y)*1 (because the average age of the new group is 16)

Simplifying the above equations, we get:

x = 17y

x = 34y

Equating both the equations, we get:

17y = 34y

y = 2

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Answer:

A) E

B) Shape A and E

(i think)

(a) To find the maximum torque on the loop of wire, we can use the formula:

τmax = NABsinθ

where N is the number of turns, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the magnetic field and the normal to the plane of the loop.

Plugging in the given values, we get:

N = 150
A = (16.5 cm)^2 = 272.25 cm^2
B = 1.8 T
θ = 90° (since the maximum torque occurs when the loop is perpendicular to the field)

τmax = (150)(272.25 cm^2)(1.8 T)sin90°
τmax = 7338 N-cm or 0.7338 N-m (rounded to four significant figures)

Therefore, the maximum torque on the loop of wire is 0.7338 N-m.

(b) To find the torque when the angle between the field and the normal to the plane of the loop is 150°, we can again use the formula:

τ = NABsinθ

where θ is now 150°.

Plugging in the given values, we get:

N = 150
A = (16.5 cm)^2 = 272.25 cm^2
B = 1.8 T
θ = 150°

τ = (150)(272.25 cm^2)(1.8 T)sin150°
τ = -1999 N-cm or -0.1999 N-m (rounded to four significant figures)

Therefore, the magnitude of the torque in N-m when the angle between the field and the normal to the plane of the loop is 150° is 0.1999 N-m (since the negative sign just indicates the direction of the torque).
(a) To find the maximum torque on the loop of wire, we can use the formula:

τ_max = n * B * A * I * sin(θ)

where n is the number of turns (150), B is the magnetic field (1.8 T), A is the area of the loop, I is the current (46 A), and θ is the angle between the magnetic field and the normal to the plane of the loop.

Since the maximum torque occurs when sin(θ) = 1 (i.e., θ = 90°), we can calculate A by converting the side length to meters and squaring it:

A = (0.165 m)^2 = 0.027225 m^2

Now, we can calculate the maximum torque:

τ_max = 150 * 1.8 * 0.027225 * 46
τ_max ≈ 335.12 Nm

(b) To find the magnitude of the torque when the angle is 150°, we can use the same formula and plug in sin(150°):

τ = n * B * A * I * sin(150°)
τ = 150 * 1.8 * 0.027225 * 46 * sin(150°)
τ ≈ 167.56 Nm

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Answer:

Roughly 1.3

Step-by-step explanation:

Since we know that a quarter of the way to her basketball practice is 1/3 a mile, we just multiply 1/3 by 4 times to get our answer.

1/3 * 4 = 1.33~

Answer:

96

Step-by-step explanation:

6a²

Put a as 4.

6(4)²

Solve for power first.

6(16)

Multiply both terms.

= 96