G is the centroid of triangle ABC.

What is the value of x?
22

What is the length of segment DG?
units

What is the length of segment AG?
units

What is the length of segment AD?
unit

In a geometric sequence, the ratio between two consecutive terms remains the same. In this case, this common ratio (r) is:

Therefore, the sequence is geometric.

Geometric sequence explicit formula

where aₙ is the nth term, a₁ is the first term, and r is the common ratio.

In this case, the first term is a₁ = 4, and the common ratio is r = 2. Substituting these values into the formula, we get:

Answer:

Assuming that the triangle is isosceles, V = 39 and W = 39 as well

Step-by-step explanation:

180 - 102 = 78

78 ÷ 2 = 39

U=102

V=39

W=39

102 + 39 + 39 = 180

Using the Central Limit Theorem, it is found that the measures are given by:

a) 2,500,000.

b) 88,388.35.

c) 2,500,000.

By the Central Limit Theorem, the sampling distribution of sample means of size n for a population of mean \(\mu\) and standard deviation \(\sigma\) has the same mean as the population, but with standard deviation \(s = \frac{\sigma}{\sqrt{n}}\)

Hence, we have that for options a and c, the mean is of 2,500,000 users, while for option b, the standard deviation is given by:

\(s = \frac{\sigma}{\sqrt{n}} = \frac{625000}{\sqrt{50}} = 88,388.35.\)

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Answer:

A

Step-by-step explanation:

\(\sqrt{x^3}\) = \(x\sqrt{x}\)

\(\sqrt{16x^3}\) = \(4x\sqrt{x}\)

\(x\sqrt{x}\) + \(4x\sqrt{x}\)  \(-3x\sqrt{x}\)

= \(5x\sqrt{x}\) \(-3x\sqrt{x}\)

= \(2x\sqrt{x}\)

Answer:

Every combination of atoms is a molecule. A compound is a molecule made of atoms from different elements. All compounds are molecules, but not all molecules are compounds. Hydrogen gas (H2) is a molecule, but not a compound because it is made of only one element.

Step-by-step explanation:

Answer

Every combination of atoms is a molecule. A compound is a molecule made of atoms from different elements. All compounds are molecules, but not all molecules are compounds.  For example : Hydrogen gas (H2) is a molecule, but not a compound because it is made of only one element.

Hope that helps :)

The zeroes of any function are where the function touches or passes through the x-axis.

To find these zeroes, we can factor, and set each part equal to 0.

y = (x - 4)(x^2 - 12x + 36)

It looks like some of the factoring was already done for us! All we have to do is factor the quadratic. To do so, we need two numbers that multiply to equal (a * c) and add up to b. In this case those two numbers are -6 and -6.

y = (x - 4)(x - 6)(x - 6)

Finally, set each part equal to 0!

x - 4 = 0

x = 4

x - 6 = 0

x = 6

x - 6 = 0

x = 6

Therefore, the zeroes of the function are 4 and 6, option B.

Hope this helps!! :)

Answer: it's = 1

Step-by-step explanation:

The probability that in 650 games 0, 1, 2, or 3 no-hitters will be pitched:

No-hitters    probability

     0             0.5944

     1             0.3093

     2             0.0804

     3             0.0139

In this question, we have been given  the probability that a major league pitcher pitches a no-hitter in a game is about 1/1300.

We need to determine the probability that in 650 games 0, 1, 2, or 3 no-hitters will be pitched.

Here, p = 1/1300

            = 0.0008

q = 1 - p

  = 1 - 1/1300

  = 1299/1300

  = 0.9992

And n = 650

We know that the binomial distribution formula.

P(x) = nCx * p^(x) * q^(n - x)

Using binomial distribution we find required probability.

For x = 0,

P(x = 0) = 650C0 * (1/1300)^0 * (1299/1300)^(650 - 0)

P(x = 0) = 1 * 1 * (0.9992)^650

P(x = 0) = 0.5944

For x = 1,

P(x = 1) = 650C1 * (1/1300)^1 * (1299/1300)^(650 - 1)

P(x = 1) = 650 * (0.0008) * (0.9992)^649

P(x = 1) = 0.52  * 0.5948

P(x = 1) = 0.3093

For x = 2,

P(x = 2) = 650C2 * (1/1300)^2 * (1299/1300)^(650 - 2)

P(x = 2) = 210925 * (0.0008)^2 * (0.9992)^648

P(x = 2) = 0.0804

For x = 3,

P(x = 3) = 650C3 * (1/1300)^3 * (1299/1300)^(650 - 3)

P(x = 3) = 45559800 * (0.0008)^3 * (0.9992)^647

P(x = 3) = 0.0139

Therefore, the probability that in 650 games 0, 1, 2, or 3 no-hitters will be pitched are 0.5944, 0.3093, 0.0804, and 0.0139 respectively.

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Answer:

Step-by-step explanation:

You want to identify the x-intercepts on the graph.

An "x-intercept" is a point where the graph crosses or touches (intercepts) the x-axis. The y-value there is always 0.

The given graph crosses the x-axis where x = -2 and x = 3. This means the x-intercept points are ...

  (-2, 0) and (3, 0)

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Answer:

18 napkins

Step-by-step explanation:

If the restaurant gives 3 napkins for every 5 items ordered, and there's 30 items... you must divide 30 by 5 which is 6. Then, multiply 6 by 3. Therefore the answer is 18.

\(30 \div 5 = 6\)

\(6 \times 3 = 18\)

Hope this helped:)

Answer:

18 napkins

Step-by-step explanation:

The zeroes of the quadratic function f(x) = 6x² + 12x – 7 will be given below. Then the correct option is A.

The quadratic function is given as ax² + bx + c = f(x).

For finding the zeroes of the polynomial we have to find the roots of the polynomial , The value of f(x) = 0

The given function is f(x) = 6x² + 12x – 7

Then the zeroes of the quadratic function will be

\(roots = \dfrac {-b \pm \sqrt{b^2 -4ac}}{2a}\\\\\)

Here a =6 , b = 12 ,c = -7

Therefore the zeroes are

\(\rm roots = \dfrac {-12 \pm \sqrt{12^2 -4 * 6 * (-7)}}{2 *6}\\\\\)

\(\rm root_1 = -1 + \sqrt{\dfrac {13}{6}}\\\\\rm root_2 = -1 - \sqrt{\dfrac {13}{6}}\)

Therefore the correct option is A.

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Answer:

10%

Step-by-step explanation:

the difference between 260 and 286 is 26, which is 10% of 260 so 10%

The coat of the dress based on the percentage is $66.

From the information, it was stated that Tonya spends 55% of her savings on a new dress and that she saved $120.

Let the cost of the dress be represented as x

Therefore, the appropriate information given I'll be expressed as:

= 55% × 120 = x

0.55 × 120 = x

Multiply

x = 66

The amount spent is $66.

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Answer:

to make it perpendicular the slope as to be -5 (opposite reciprocal of the original)

Your conclusion would equal

x = 5

Fraction, A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Blue t-shirts that are on sale and are in the medium size make up 1/8 of the speakers in the store.

Let T represent the quantity of T-shirts in the store.

In a store selling t-shirts, blue dominates by three to one.

3/5 of the blue T-shirts were worn.

These blue t-shirts, 5/8 of them, are on sale.

The amount of blue T-shirts for sale is equal to 5/8 × 3/5 T, or 3/8 T.

The majority of the blue t-shirts for sale are size medium,

The number of medium-sized blue t-shirts available for purchase is equal to 1/3 × 3/8 T = 1/8 T.

Blue t-shirts in size medium that are on sale make up 1/8 of the store's speakers.

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Answer: B (4/5)

Step-by-step explanation:

SOH CAH TOA

T = opposite/hypotenuse

Opposite = 32

Hypotenuse = 40

Simplify 32/40 = 4/5

The differentiation of \(e\x^{x}\) is \(e\x^{x}\) proved using the first law of differentiation or limit law.

A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.

Differentiation is the ratio of a slight change in one quantity to a little change in another that depends on the first quantity. Calculus' major emphasis on the differentiation of a function makes it one of the subject's key ideas. Differentiation is the process of determining the maximum or lowest value of a function, the speed and acceleration of moving objects, and the tangent of a curve. If y = f(x) and f(x) is differentiable, then f'(x) or dy/dx is used to indicate the differentiation.

\(\frac{d}{dx}e\x^{x}\) using first order or limits to differentiate we get

for \(\lim_{h \to0} \frac{f(x+h) - f(x)}{h} = \frac{d}{dx}f(x)\)

therefore,

\(\lim_{h \to 0} \frac{e\x^{(x +h)}- e\x^{x} }{h} \\\) = \(\lim_{h \to 0} \frac{e\x^{x}(e\x^{h}-1 ) }{h}\) = \(\lim_{h \to 0} \frac{e\x^{x}*e\x^{h} }{1} \\\) ( using L-Hospital)

\(\lim_{h \to 0} e\x^{x} * e\x^{h} = e\x^{x} (proved)\)

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The larger bucket paint contains roughly the same amount of thermal energy as each of the smaller buckets of paint.

Thermal energy is the energy possessed by a substance or system as a result of particle movement within the object or system.

As, the thermal energy is due to the kinetic energy.

Thus, the kinetic energy of an object is directly proportional to its mass; thus, doubling the mass doubles the kinetic energy.

In, the given case, the paint contained in the two buckets are combined.

Thus, the mass is remained constant.

The larger bucket also have the the same temperature. thus, the thermal energy will not change.

Therefore, the amount of thermal energy with in larger bucket of paint is roughly equal to the amount of thermal energy in all of the smaller buckets of paint.

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The statement that is true about the function is:

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

The minimum value of the curve = (1.9, -5.7),

The maximum value = (0, 2)

The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)

The point the function crosses the y-axis (the y-intercept) = (0, 2)

The given points can be plotted using MS Excel, from which we have:

F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5.

Hence, the correct option is A.

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The binomial theorem states that: \((x + y)^n = \sum_{k=0}^n{n\choose k} x^{n-k}y^k\). So, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).

Now, let's use the Binomial Theorem to find the binomial expansion of (2x - 3y)⁵. We will have to find the coefficients for each term. So, let's get started. n = 5x = 2xy = -3[nCr = n! / (r! * (n-r)!)]

Term k = 0: \( {5 \choose 0} (2x)^5 (-3y)^0\) = 32x⁵

Term k = 1: \({5 \choose 1} (2x)^4 (-3y)^1\) = -240x⁴y

Term k = 2: \({5 \choose 2} (2x)^3 (-3y)^2\) = 720x³y²

Term k = 3: \({5 \choose 3} (2x)^2 (-3y)^3\) = -1080x²y³

Term k = 4: \({5 \choose 4} (2x)^1 (-3y)^4\) = 810xy⁴

Term k = 5: \({5 \choose 5} (2x)^0 (-3y)^5\) = -243y⁵

Now we can combine all of these terms to form the binomial expansion of (2x - 3y)⁵:\((2x - 3y)^5 = 32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\)

Therefore, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).

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Answer:

B. x < 6 and x > -28

Step-by-step explanation:

|x + 11| < 17

-17 < x + 11 < 17

Subtract 11 from all 3 sides.

-28 < x < 6

x > -28 and x < 6

Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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Eestimating the expression 5.8324 ÷ 0.1 will be 58.

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, estimating the expression 5.8324 ÷ 0.1 will be:

= 5.8324 ÷ 0.1

= 58

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Complete question

Estimate the expression 5.8324 ÷ 0.1

Answer:

D

Step-by-step explanation:

Answer:

To be honest it has to be d

Step-by-step explanation:

Number of ways that the representative can be chosen = 12

The number of women = 2

The number of men = 3

Since the president must be a woman

Number of ways of choosing the president = 2C1

Number of ways of choosing the president = 2

The secretary and treasurer must be men

Let us first choose the secretary out of all the three men

Number of ways of choosing the secretary = 3C1

Number of ways of choosing the secretary = 3

After the secretary has been selected, there are 2 men left

Number of ways of selecting the treasurer = 2C1

Number of ways of choosing the treasurer = 2

Number of ways that the representative can be chosen = 2 x 3 x 2

Number of ways that the representative can be chosen = 12

Answer:

-1 - 4 and 4 - (-1).

Step-by-step explanation:

.

Answer:

1

Step-by-step explanation:

→ If we know that 3 numbers need to multiply to make -1, it must be

1, 1 and -1

→ Then we just substitute this into a³ + b³ + c³

1³ + 1³ + (-1)³ = 2 - 1 = 1