A thief steals a number of rare plants from a nursery. On the way out, the thief meets three security guards, one after
another. To each security guard, the thief is forced to give one-half the plants that he still has, plus 2 more. Finally, the
thief leaves the nursery with 0 plants. How many plants were originally stolen?

The correct answer is : c) As the number of experiments increases, the mean of the observations will approach the mean of the random variable.

Mean of random Variable x :

The expected value of a discrete random variable X, symbolized as E(X), is often called the long-term average or mean (symbolized as μ). This means that if you run the experiment many times over time, you would expect this average. For example, let X = the number of heads you get when you toss 3 fair coins. If we repeat this experiment (tossing 3 fair coins) many times, the expected value of X will be the expected average number of heads per 3 tosses.

Standard Deviation of Random Variable:

A measure of the variance of a random variable distribution that determines how for a value is from its expected value.

The standard deviation of a random variable X is often written as σ or σₓ.

For discrete random variables, the standard deviation is computed by taking the square of the difference between the value of the random variable and the expected value multiplied by the associated probability of the value of the random variable. Calculate the value of a random variable and finally take the square root.

In symbols σ = √ (x - μ)² P(X =x)

The equivalent formula is σ = [tex]\sqrt{E(x^{2}) - [{E(x^2)]}[/tex]

The square of the standard deviation equals the variance Var(X) = σ².

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Answer:It will cost Mrs. Wu $44.5 to fill the gas tank.

Step-by-step explanation: 3.56x12.5= 44.5

The value of p is -5

Simply use cross multiplication :

The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equal symbol. Cross multiplication is a method for comparing fractions.

Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.

[tex]14p-8=22+20p\\or, 14p-20p=22+8\\or, -6p=30\\or, p=-\frac{30}{6} \\or, p= -5[/tex]

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The function depicted in the table has the following slope-intercept form:

y = -3x + 4

For such equation of every straight line, the slope-intercept form is provided by:

y = mx +c

where:

Choose 2 points from the provided table, such as (2,-2) and (3,-5) and to use the evidence that the slope is, to determine the line's slope.

m = (y2 - y1)/(x2 - x1)

m = -5 + 2 / 3 - 2

m = -3

You can use the point (2,-2) or other point listed in the table along with this relation, to determine the y-intercept b.

b = y1 - mx1

b = (-2) -(-3 + 2)

b = 4

Consequently, is the function represented by the table's slope-intercept form: y -3x + 4.

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Applying the exterior angles theorem, the measure of angle GHI is: 29°.

The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

In other words, if a triangle, for example triangle GHI, has angles G, H, and I, and angle HIJ is the exterior angle formed by extending side GI through point I to point J, then the measure of angle HIJ is equal to the sum of the measures of angles IGH and GHI.

Given the following:

m<IGH = (x+16)°,

m<HIJ = (4x – 12)°,

m<GHI= (x +10)°

Therefore:

m<HIJ = m<IGH + m<GHI

Substitute:

4x - 12 = x + 16 + x + 10

4x - 12 = 2x + 26

4x - 2x = 12 + 26

2x = 38

2x/2 = 38/2

x = 19

m<GHI= (x +10)° = 19 + 10 = 29°

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The function f(x) = −16x² + 48x + 64 represents the height of an object above the ground in feet, x seconds after being launched.

To find f(-1), we plug -1 into the function:

f(-1) = −16(-1)² + 48(-1) + 64

= 16 - 48 + 64

= 32

This means that 1 second after the object was launched, it was 32 feet above the ground.

To find f(0.5), we plug 0.5 into the function:

f(0.5) = −16(0.5)² + 48(0.5) + 64

= −16(0.25) + 24 + 64

= −4 + 24 + 64

= 84

This means that 0.5 seconds after the object was launched, it was 84 feet above the ground.

Since the function represents the height of the object above the ground, the domain of the function would be the set of all real numbers x such that x represents the number of seconds after the object was launched.

This would include all positive and negative values of x, since the object could have been launched at any time in the past or future. However, if the problem specifies a specific range of time, then the domain would be limited to that range.

Therefore, the correct answer is as given above

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Therefore, there are 4 x 1128 = 4512 possible 5 card poker hands with at least 3 aces that can be dealt from a standard deck of 52 cards.

1. There are 4 aces in a standard deck of 52 cards, so the maximum number of aces in a 5-card poker hand is 3.

2. There are C(4,3) = 4 ways to choose 3 aces out of the 4 aces in the deck.

3. For the remaining 2 cards, there are C(48,2) = 1128 ways to choose them from the 48 non-ace cards.

4. Therefore, there are 4 x 1128 = 4512 possible 5 card poker hands with at least 3 aces that can be dealt from a standard deck of 52 cards.

There are 4 aces in a standard deck of 52 cards, so the maximum number of aces in a 5-card poker hand is 3. There are C(4,3) = 4 ways to choose 3 aces out of the 4 aces in the deck. For the remaining 2 cards, there are C(48,2) = 1128 ways to choose them from the 48 non-ace cards.

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Answer:

52%

Step-by-step explanation:

What percent of 200 is 104?

104/200 = 0.52

0.52 = 52%

Answer: T=25

Step-by-step explanation:

T=4m^2 -11

We know that m= -3

-3^2 = 9

So the equation is T=4 (9) -11

T = 36 -11

T= 25

Option b is correct.

Therefore, the probability that a state highway inspector would choose a sample of 49 trucks and discover that the sample mean was 14.3 tons or less is equal to  0.3758

Given: The population mean and standard deviation for the weight of trucks moving on a given stretch of I-475 are both tons.

n=49 sample size

Consider x to be the random variable that represents the truck weight.

z-score: z  = x - μ ÷ σ/[tex]\sqrt{n}[/tex]

When x=14.3 tons

z = [tex]\frac{14.3 - 15.8}{\frac{4.2}{\sqrt{49} } }[/tex]  ≈ -2.5

The likelihood that a state highway inspector will choose 49 trucks as a sample and discover that the sample mean is 14.3 tons or less is as follows:

P(X ≤ 14.3) = P(z < -2.5) = 0.3758

Therefore, the probability that a state highway inspector would choose a sample of 49 trucks and discover that the sample mean was 14.3 tons or less is equal to  0.3758

option b is correct.

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The relative maxima and minima of the function g(x) are at the point (-4, 22) at the local maxima and at point (4,-124) at the local minima.

Given:

Function g(x) = x^3 - 48x + 4

Take the derivative and set it equal to zero

3x^2 - 48 = 0

x^2 = 48/3 = 16

x = sqr16 = ±4

At x=+4, y = (4)^3 -48(4) + 4 = 64 -192+4 = -124

Point (4,-124) is a local or relative minimum

At x-4 y=(-4)^3 -48(-4)+4 = -64 + 192 + 4 = 122

The point (-4, 22) is a local or relative maximum

Refer to this complete question:

Find the relative maxima and minima, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = x3 − 48x + 4 relative maximum (x, y) = relative minimum (x, y) =?

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Answer:

  57.8

Step-by-step explanation:

You have quadrilateral JKLM similar to quadrilateral NOPQ with given sides JK = 9, LM = 13.7, NO = 38, and you want the measure of PQ.

Corresponding sides in similar figures are proportional in length:

  PQ/LM = NO/JK

  PQ/13.7 = 38/9

  PQ = 13.7(38/9) = 2603/45 ≈ 57.8

The measure of PQ is approximately 57.8 units.

Answer:

Step-by-step explanation:

andrea lb: 164.5cm

andrea ub: 165.5 cm

joel lb: 165

joel ub: 175

According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

It is given to us that -

Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving

Company now advertises that its new small cars average more than 45 miles per gallon in highway driving

52 automobiles were tested

Sample average is 46.1 miles per gallon

Sample standard deviation is 5.3 miles per gallon

Significance level is 0.01

We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.

Let us assume that -

p = population of average gasoline of new small cars in highway driving

According to the given information,

Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -

[tex]H_{0}[/tex] : [tex]p\leq 45[/tex] miles per gallon

Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -

[tex]H_{A}[/tex] : [tex]p > 45[/tex] miles per gallon

For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.

According to one sample z test, the value of test statistic is given as -

[tex]T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }[/tex] ------ (1)

where,

[tex]X_{avg}[/tex] = Sample mean

p = hypothesized population mean

S = Sample standard deviation

n = Sample size

According to the given information, we have

[tex]X_{avg}[/tex] = 46.1 miles per gallon

p = 45 miles per gallon

S = 5.3 miles per gallon

n = 52

Substituting the above values in equation (1), we have

[tex]T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }\\= > T = \frac{(46.1 -45)}{\frac{5.3}{\sqrt{52} } }\\= > T = \frac{1.1}{0.735}\\ = > T = 0.634[/tex]

It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.

But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,

0.634 < 2.58

This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.

Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

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According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

It is given to us that -

Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving

Company now advertises that its new small cars average more than 45 miles per gallon in highway driving

52 automobiles were tested

Sample average is 46.1 miles per gallon

Sample standard deviation is 5.3 miles per gallon

Significance level is 0.01

We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.

Let us assume that -

p = population of average gasoline of new small cars in highway driving

According to the given information,

Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -

H0 = p<= 45 :  miles per gallon

Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -

HA : p > 45 :  miles per gallon

For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.

According to one sample z test, the value of test statistic is given as -

T = (X - p)/(SD/√n)

where,

X = Sample mean

p = hypothesized population mean

S = Sample standard deviation

n = Sample size

According to the given information, we have

X = 46.1 miles per gallon

p = 45 miles per gallon

S = 5.3 miles per gallon

n = 52

Substituting the above values in equation (1), we have

T = 46.1-45/(5.2/√52)

T = 1.1/0.735

T = 0.634

It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.

But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,

0.634 < 2.58

This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.

Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

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Answer:

x∈(−∞,−22)∪(12,+∞)

Step-by-step explanation:

Evaluate

−∣x+5∣<−17

Calculate

∣x+5∣>17

Separate the inequality into 2 possible cases

​x+5>17x+5<−17​

Solve the inequality for x

​x>12x+5<−17​

Solve the inequality for x

​x>12x<−22​

Solution

x∈(−∞,−22)∪(12,+∞)

The linear equation that passes through the points (0,-8) and (5,-5) is:

y = (3/5)*x - 8

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

a = (y2 - y1)/(x2 - x1)

Here we have the two points: (0,-8) and (5,-5)

Then the slope is:

a = (-5 + 8)/(5 - 0) = 3/5

And because of the point (0, -8) we know that the y-intercept is -8, then the linear equation is:

y = (3/5)*x - 8

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An inequality representing c, the total number of 40-kilogram crates that can be loaded into the shipping container is; 7700 + (40c) ≤ 27500

The maximum number of 40 kg crate is 380.

We are given;

Weight of the crate = 40 kg

Greatest weight that the container can load = 27500 kg

Weight of the other shipments on the container = 7700 kg

The greatest number of 40 kg crates is represented by the letter "c".

Thus;

The weight of the other shipment + weight of crate x number of crates ≤ greatest weight of the container

Plugging in the relevant values gives;

7700 + (40c) ≤ 27500

7700 + 40c ≤ 23000

40c ≤ 27500 - 7700

40c ≤ 19800

c ≤ 19800/40

c ≤ 495

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The average rate of change to the function is (d) 3/2

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

g(x) = 3/2x + 1

Also, we have the interval to be

-2 < x < 8

This interval can be expressed as

a = -2 and b = 8

So, we start by calculating g(-2) and g(8)

Substitute the known values in the above equation, so, we have the following representation

g(-2) = 3/2 * (-2) + 1

g(-2) = -2

Also, we have

g(8) = 3/2 * (8) + 1

g(8) = 13

The average rate of change to the function is then calculated as

Rate = [g(8) - g(-2)]/[8 + 2]

So, we have

Rate = (13 + 2)/(8 + 2)

Evaluate

Rate = 3/2

Hence, the average rate is 3/2

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Answer: $164

Step-by-step explanation:

25*7=175

175+12.5

226.50-187.50

5*25=125+39

Jones family payed $164

The Maclaurin series expansion of f(x) = 1/(1-x)² is

1 + 2x + 6x² + 24x³ +......

The general expression for the Maclaurin series is given by the formula:

f(x) = f(0) + xf'(0) + x²f''(0) + ..... + xⁿf⁽ⁿ⁾(0)+...

= ∑ f⁽ⁿ⁾ (0)xⁿ/n!

n= 0 to infinity

Specifying the convergence region completes the Maclaurin series formulation. Detailed five steps for determining the Maclaurin series of

f(x) = 1/(1-x)²

Step 1 : Find Derivatives for f(x)

f(x) = 1/(1-x)²

f'(x) = -2(1-x)⁽⁻²⁻¹⁾ (-1) = 2/(1-x)³

The second derivative of f(x) is the derivative of f''(x) :

f"(x) = 2(-3)(1-x)⁽⁻³⁻¹⁾(-1) = 6/(1-x)⁴

Differentiating again, f"'(x) = 6(-4)(1-x)⁽⁻⁴⁻¹⁾(-1)

= 24/(1-x)⁵

Thus, the nᵗʰ derivative is ,

f⁽ⁿ⁾(x) = (n+1)!/(1-x)⁽ⁿ⁻¹⁾

Step 2: Evaluate These Derivatives and f(x) at x=0 let x = 0 , f(0) = 1

f'(0) = 2 , f"(0) = 6 , ....... , f⁽ⁿ⁾(0) = (n+1)!

Step 3 : Now, the Sum of Products :

f(x) = f(0) + xf'(0) + x²f''(0) + ..... + xⁿf⁽ⁿ⁾(0)+...

xf'(0) = 2x

x²f"(0) = 6x²

x³f"'(0) = 24 x³

----------------------------

xⁿf⁽ⁿ⁾(0)= (n+1)!

Thus, the Maclaurin series for ln(1 + x) is this:

f(x) = (1−x)⁻² = 1 + 2x + 6x² + 24x³ +......

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[tex]6x^2=6[/tex]

Divide both sides by 6:

[tex]\dfrac{6x^2}{6} =\dfrac{6}{6}[/tex]

[tex]x^2=1[/tex]

Take square root:

[tex]x=\pm\sqrt{1}[/tex]

[tex]\fbox{x = 1 or x = -1}[/tex]

To find the circumference of a circle with a radius of 7 cm, Erin should use 2×7×π. This is because the circumference of a circle is calculated by the formula 2×π×r.

The circumference is the measure of the perimeter of a circle. Since we know that from every point on the circle to its center has an equal length and is said to be its radius, the perimeter of the circle we can write as

Circumference = 2 × π × r units.

Here r is the radius of the circle.

It is given that Erin wants to find the circumference of a circle with a radius of 7 cm.

So, first, she has to know the formula for finding the circumference.

Here the radius is given as 7 cm i.e., r = 7 cm

Then, the circumference of the given circle is

= 2 × π × r

On substituting the radius value into the above formula, we get

Circumference = 2 × π × 7 cm

⇒ 14π cm

So, she needs to use option A. 2 × 7 × π  for finding the required circumference. This is the first step for finding the circumference of a circle.

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By using logarithm principles, log₇t in base 2 logarithm equals log₂t/log₂7.

The most frequent logarithms are common logarithms with a base of 10, binary logarithms with a base of 2, and natural logarithms with a base of e 2.71828. A logarithm is the number of powers that a number must be raised to in order to acquire another number (see Section 3 of this Math Review for more about exponents). The base ten logarithm of 100, for example, is 2, because ten raised to the power of two equals 100: log 100 = 2.

Here,

logₓy=logₐy/logₐx

log₇t=log₂t/log₂7

log₇t in base 2 logarithm is log₂t/log₂7 by the help of properties of logarithm applied.

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Answer:

Below

Step-by-step explanation:

The area is just the two side lengths multiplied together

area = (4x+13)(5x-2) = 20x^2 +57x -26   units^2

Answer: $96.25

Step-by-step explanation:

Take 89.75 divided by 100% = 0.8975

Then times 7.25% = $6.5

Total is 89.75 + 6.5 = $96.25

Answer: x=500,000

Step-by-step explanation:

60,000=.12x

60,000/.12=x/.12

500,000=x

2 - 2i can be written in polar form as [tex]2\sqrt{2} \ cis\frac {-3\pi}{4}[/tex]

To convert a complex number in Cartesian form (such as 2 - 2i) to polar form, you can use the following steps:

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Answer:

Answer Option A: AA Postulate

201 numbers are less than 2017

If and only if it is odd, a number is the sum of two successive integers.

Only if it is a multiple of 5 is a number considered to be the sum of 5 consecutive integers. If you have any doubts, remember that the product of five consecutive integers equals five times the integer in the middle (this remains true if instead of 5 you put in any odd positive integer).

Consequently, you are seeking odd multiples of 5 below 2017. There are 403 multiples of 5 immediately below 2017, or 2015/5. Of those, 202 are odd. It is necessary to eliminate the number 5 because it is not completely positive when expressed as the sum of its successive integers, which is (-1)+0+1+2+3.

There are 201 numbers left.

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Answer:

9/100

Step-by-step explanation:

numerator = whole number

denominator = 100

9/100