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The probability distribution for bn is:

n | P(bn)

1 | 1/6

2 | (5/6)(1/6)

3 | (5/6)^2(1/6)

4 | (5/6)^3*(1/6)

... | ...

k | (5/6)^(k-1)*(1/6)

... | ...

where k can be any positive integer. Note that this is a geometric distribution with p=1/6.

The sample space for this experiment consists of the sequence of rolls required to obtain the first 6. For example, if a 6 appears on the first roll, then the sample space consists of the single element {6}. If a 6 does not appear on the first roll, then the sample space consists of all possible sequences of rolls that do not include a 6 until the final roll, which is a 6.

More formally, we can represent the sample space as follows:

S = {6, (not 6)(6), (not 6)(not 6)(6), (not 6)(not 6)(not 6)(6), ...}

where (not 6) represents any roll that is not a 6, and each element of the sample space consists of a sequence of (not 6) rolls followed by a 6.

Now, let bn denote the event that n rolls are required to complete the experiment, i.e., the experiment ends with a 6 on the nth roll. The probability of success on any roll is 1/6, and the probability of failure (i.e., rolling a number other than 6) is 5/6. Therefore, the probability of requiring exactly n rolls to obtain the first 6 is:

P(bn) = (5/6)^(n-1) * (1/6)

This is because we must roll a non-6 number on the first n-1 rolls (with probability 5/6 for each roll), and then roll a 6 on the nth roll (with probability 1/6).

Therefore, the probability distribution for bn is:

n | P(bn)

1 | 1/6

2 | (5/6)(1/6)

3 | (5/6)^2(1/6)

4 | (5/6)^3*(1/6)

... | ...

k | (5/6)^(k-1)*(1/6)

... | ...

where k can be any positive integer. Note that this is a geometric distribution with p=1/6.

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The only thing that can be determined is that the difference in height between the two sunflowers is 1.75 feet.

If the difference in heights of the two sunflowers is 1.75 feet, then the heights of the sunflowers cannot be 1.75 feet.

Sunflowers have the ability to grow up to 12 feet tall, depending on the species and growing conditions. The height of a sunflower is influenced by various factors such as the species, availability of sunlight, and soil nutrients.

Sunflowers have a fast growth rate, which means that they can grow rapidly within a few weeks. If two sunflowers are grown under different conditions, it's possible that one of them will grow taller than the other. This can be due to factors such as exposure to sunlight, soil nutrients, and water availability.In summary, it's impossible to determine the height of the sunflowers based on the information given. The only thing that can be determined is that the difference in height between the two sunflowers is 1.75 feet.

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Answer:

3x^2+10x

Step-by-step explanation:

Answer:

(4.25*H)+10

H=hours used

Step-by-step explanation:

samules age = (cousins age * 2) -2

Step-by-step explanation:

1) 10+4.25x

the variable represents the time so in this case it would be per a hour so we know the cost changes based on the hour

The sample standard deviation is approximately 0.83.

Sample size \(($n$)\) = 36

Population mean \(($\mu$)\) = 50

Population standard deviation \(($\sigma$)\) = 5

The sample standard deviation, denoted as \($s$\) can be estimated using the formula:

\(\[ s = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}} \]\)

where:

\($x_i$\) represents the individual data points in the sample

\($\bar{x}$\) is the sample mean

In this case, since we don't have individual data points, we can use the population standard deviation as an estimate for the sample standard deviation when the sample size is relatively large (as in this case \($n = 36$\)). This approximation is known as the standard error of the mean.

Therefore, the sample standard deviation can be approximated as:

\(\[ s \approx \frac{\sigma}{\sqrt{n}} \]\)

Substituting the given values:

\(\[ s \approx \frac{5}{\sqrt{36}} = \frac{5}{6} \] = 0.83\)

Hence, the sample standard deviation is approximately 0.83.

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The comparison of two quantities with different units is called a ratio and proportion. A ratio that specifically compares two quantities measured in different units.

Comparing amounts is done using a ratio. A ratio demonstrates how many times one amount fits inside another or how much larger one amount is than another.

If I need to mix some cement, I would add two parts cement to four parts sand. The two numbers are both portions of the entire. Hence, the 2:4 ratio (6 parts in total). The written version is crucial; 4:2 would produce a different blend.

Ratios are expressed in their most basic form. There are five green and fifteen red dots in the figure on the right. The ratio is 15:5, but like with fractions, this can be boiled down to its most basic form.

If you look at the relationship between the numbers 15:5 as is 3:1, you can see that 3 is multiplied by 5 to obtain 15 and that 1 is multiplied by 1 to get 5. The ratio, as we can see in the image, is also 3:1.

Therefore,

The comparison of two quantities with different units is called a ratio and proportion. A ratio that specifically compares two quantities measured in different units.

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Answer:

d

Step-by-step explanation:

Answer:

drum roll please

Step-by-step explanation:

The coordinate plane was developed centuries ago and refined by the French mathematician René Descartes. In his honor, the system is sometimes called the Cartesian coordinate system. The coordinate plane can be used to plot points and graph lines. This system allows us to describe algebraic relationships in a visual sense, and also helps us create and interpret algebraic concepts.

Answer:

Step-by-step explanation:

You want to know the intercepts and slope of the line whose equation is ...

  14x +y = 140

Each intercept is the solution to the equation when the other variable is set to zero.

To find the y-intercept, use x=0: y = 140.

To find the x-intercept, use y=0: 14x = 140   ⇒   x = 10

The slope is the coefficient of x when the equation is solved for y:

  14x +y = 140

  y = -14x +140 . . . . . the x-coefficient is -14

The y-intercept is 140; the slope is -14; the x-intercept is 10.

__

Additional comment

As you can see, when the equation is in standard form:

  ax +by = c

The intercepts are ...

  x-intercept = c/a

  y-intercept = c/b

and the slope is ...

  slope = -a/b

Part III: Note reduction for payment 2 = Payment Amount - Interest Due = $1055.69 - $758.68 = $297.01.

Part I: The payment amount for payment number 2 is $1055.69 (same as the first payment).

Part II: Interest due for payment number 2 = (Unpaid Balance after payment 1) * (Monthly Interest Rate) = $189,671.31 * (4.8% / 12) = $758.68.

Part III: Note reduction for payment 2 = Payment Amount - Interest Due = $1055.69 - $758.68 = $297.01.

Part IV: Unpaid balance for payment number 2 = (Unpaid Balance after payment 1) - (Note Reduction for payment 2) = $189,671.31 - $297.01 = $189,374.30.

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Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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Answer:this is the order of the things to put them

number of bouquets: 5

mass of bouquets: 3d+4t+v

mass of the tulips in one bouquet: 4t

mass of the daffodils in one bouquet: 3d

Step-by-step explanation:

Answer:

Step-by-step explanation:

x - y² = -1     ⇒   - y² = - x - 1    ⇒    y² = x + 1   {x≥-1}

4x² + 9y² = 72

4x² + 9(x + 1)² = 72

4x² + 9(x² + 2x + 1) = 72

4x² + 9x² + 18x + 9 - 72 = 0

13x² + 18x - 63 = 0     ⇒   a = 13,  b = 18,  c = -63

\(x=\dfrac{-18\pm\sqrt{18^2-4\cdot13\cdot(-63)}}{2\cdot13}=\dfrac{-18\pm\sqrt{324+252}}{26}=\dfrac{-18\pm\sqrt{576}}{26}\\\\x=\dfrac{-18+24}{26}=\dfrac3{13}\qquad\vee\qquad x=\dfrac{-18-24}{26}=-\dfrac{21}{13}\\\\ y^2= x + 1\quad\iff\quad x\ge-1\\\\y^2=\dfrac3{13}+1\\\\ y^2=\dfrac{16}{13}\\\\y=\dfrac{4}{\sqrt{13}}=\dfrac{4\sqrt{13}}{13}\qquad\vee\qquad y=-\dfrac{4\sqrt{13}}{13}\)

Check the picture below.

so firstly let's find side "a"

\(\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ a = \sqrt{7^2+12^2~-~2(7)(12)\cos(55^o)} \implies a = \sqrt{ 193 - 14112 \cos(55^o) } \\\\\\ a \approx \sqrt{ 193 - (96.3608) } \implies a \approx \sqrt{ 96.6392 } \implies a \approx 9.8305\)

now, let's use "a" to get angle C

\(\textit{Law of Sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin( C )}{7}\approx\cfrac{\sin( 55^o )}{9.8305}\implies 9.8305\sin(C)\approx7\sin(55^o) \implies \sin(C)\approx\cfrac{7\sin(55^o)}{9.8305} \\\\\\ C\approx\sin^{-1}\left( ~~ \cfrac{7\sin( 55^o)}{9.8305} ~~\right)\implies \boxed{C\approx 35.7^o}\)

Make sure your calculator is in Degree mode.

Answer:

-7 + 3 = -4

-5 + 1 = -4

-3 + (-1) = -4

Step-by-step explanation:

Answer:

45%

Step-by-step explanation:

There are 450 people with over 3 people in their family. There are 1000 total people. 450/1000 is 45%

Lowes Depot uses a (Q, R) policy to manage its stock levels for a popular mini drill with a replacement lead time of 14 weeks. Historical demand during the replacement lead time is normally distributed with a mean of 90.4616 and a standard deviation of 14.3795. Each drill costs $6, and backorders result in a loss of goodwill of $10. The supplier charges $15 per order, and holding costs are based on a 30% annual interest rate.

To determine the optimal order quantity Q and reorder point R, we need to use the (Q, R) policy. The policy specifies that when the inventory level reaches the reorder point R, an order of size Q is placed. We need to determine Q and R such that the total annual cost is minimized.

The total annual cost consists of three components: ordering costs, holding costs, and shortage costs. Ordering costs are the costs associated with placing an order, which is given by (number of orders per year) x (ordering cost per order). The number of orders per year is the annual demand divided by the order quantity, which is Q. The ordering cost per order is $15. Therefore, the ordering cost is 15 X (Demand rate/Q).

Holding costs are the costs associated with holding inventory, which is given by (inventory level) x (holding cost per unit per year). The holding cost per unit per year is 30% of the unit cost, which is 0.3 x $6 = $1.8.

Shortage costs are the costs associated with backordering, which is given by (expected shortage per year) x (shortage cost per unit). The expected shortage per year is the probability of a stockout during the lead time multiplied by the expected demand

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Answer:

Volume of prism = 4000 cm cubed

Step-by-step explanation:

Given that:

Height of rectangular prism = 5 meters

Converting into centimeters as the area of base is in centimeters.

1 meter = 100 centimeter

5 meters = 500 cm

Area of the base = 8 cm squared

Volume of prism = Area of base * Height

Volume of prism = 8 * 500

Volume of prism = 4000 cm cubed

Hence,

Volume of prism = 4000 cm cubed

So Reena has ran a distance of 5 kilometers while only covering one-sixth of the distance.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

If Reena has completed one sixth of the 30 km run,

30 km / 6 = 5 km.

So, Reena has run a distance of 5 km so far when she had run one sixth of the distance.

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The slope of the tangent to the curve is -5/14.

Apply implicit differentiation and the product rule to the curve:

\(3y^{2} \frac{dy}{dx} x + y^{3} + 2y\frac{dy}{dx} x^{2} + y^{2}2x = 0\)

Do some rewriting

\(3xy^{2}\frac{dy}{dx} + 2x^{2}y\frac{dy}{dx} + y^{3} + 2xy^{2} = 0\)

Factor and move terms without a  \(\frac{dy}{dx}\)  factor to the right side

\(\frac{dy}{dx}(3xy^{2}+2x^{2}y) = -y^{3} - 2xy^{2}\)

Now divide both sides by  \(3xy^{2}+2x^{2}y\)  and factor where you can

\(\frac{dy}{dx} = \frac{-y^{2}(y+2x)}{yx(3y+2x)}\)

\(\frac{dy}{dx} = \frac{-y(y+2x)}{x(3y+2x)}\)

Now evaluate the given point \((2,1)\)

\(\frac{dy}{dx} = \frac{-1(1 + 2(2))}{2(3(1) + 2(2))} = \frac{-1(5)}{2(7)} = \frac{-5}{14}\)

Therefore, the slope of the tangent to the curve is -5/14.

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The resulting cross-section of a cylinder intersected by a plane parallel to the bases is a circle.

When a plane passes through a cylinder parallel to the bases, it creates a cross-section that is congruent to the bases of the cylinder. Since the bases of a cylinder are circles, the resulting cross-section is also a circle. The circle formed will have the same diameter as the bases of the cylinder and will be parallel to them. This is because the plane slices through the cylinder at a constant distance from the bases, resulting in a circular shape that is perpendicular to the axis of the cylinder. This characteristic holds true for any position of the plane parallel to the bases, resulting in circular cross-sections.

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The value of the variable is 4√5. Then the correct option is C.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The similar triangles are shown in the diagram.

16 / x = x / 5

    x² = 16 × 5

      x = 4 √5

Then the value of the variable is 4√5.

Then the correct option is C.

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Answer:

284 u^3

Step-by-step explanation:

a b c d e f g h i j k l m n o p q r s t u v w x y z

Answer:

5.76106287

Step-by-step explanation:

Answer: 5.76106287488

Step-by-step explanation: