The double number line shows the number of children 1 adult supervises on a field trip.




Complete the table to show the same information as the double number line.

Adults Children

8

66

15

If VAR[-4X+5]=13 and E[X]=2.5, so E[(X-3)²] will be 1.06. The correct answer is A

We have VAR[-4X+5] = 13, which means VAR[-4X] = 13 since VAR[c] = 0 for any constant c, and VAR[aX] = a² VAR[X] for any constant a.

So we have:

VAR[-4X] = (-4)² VAR[X] = 16 VAR[X] = 13

Solving for VAR[X], we get:

VAR[X] = 13/16

Now, we want to find E[(X-3)^2]:

E[(X-3)²] = E[X² - 6X + 9]

= E[X²] - 6E[X] + 9 (by linearity of expectation)

We can use the formula VAR[X] = E[X²] - (E[X])² to solve for E[X²]:

VAR[X] = E[X²] - (E[X])²

13/16 = E[X²] - (2.5)²

E[X²] = 13/16 + 6.25

E[X²] = 7.31

Therefore, we have:

E[(X-3)²] = E[X²] - 6E[X] + 9

= 7.31 - 6(2.5) + 9

= 1.06

So the answer is (a) 1.06.

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In general, you would need to know the number of polygons in the original shape and the rule for how the shape is expanded or repeated in each iteration to calculate the number of polygons in a fractal expansion.

A fractal is a geometric shape that has intricate detail at arbitrarily small scales and typically has fractal dimensions that rigorously surpass topological dimensions. Several fractals resemble one another at different scales, as shown in the Mandelbrot set's sequential magnifications. Self-similarity, also known as expanding symmetry or unfolding symmetry, is the display of similar patterns at progressively smaller scales; if this replication is precisely the same at every scale, as in the Menger sponge, the shape is referred to as affine self-similar. The academic field of measure theory includes fractal geometry.

Depending on the particular kind of fractal under consideration, a polygon's fractal expansion can be calculated using a specific algorithm. However, the formula will typically entail iteratively transforming the original polygon with geometric operations.

For instance, by continually removing the central triangle from a larger equilateral triangle, the Sierpinski triangle—a well-known fractal—can be created. The remaining triangle is divided into three smaller replicas, which are then put together to make an equilateral triangle at the end of each iteration. The formula below can be used to determine the amount of triangles in each iteration:

the number of triangles in the nth repetition is represented by

Another illustration is the Koch snowflake, which is created by repeatedly dividing each of an equilateral triangle's three sides into two segments and swapping out the middle segment for two segments that also make an equilateral triangle. The following algorithm can be used to determine how many line segments are used in each iteration:

the number of line segments in the nth cycle is represented by L(n).

Generally speaking, the expansion formula for a fractal will rely on the particular rule or algorithm that was used to create the fractal.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 6000\\ P=\textit{original amount deposited}\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]6000 = P\left(1+\frac{0.12}{4}\right)^{4\cdot 10} \implies 6000=P1.03^{40} \\\\\\ \cfrac{6000}{1.03^{40}}=P\implies 1839.34\approx P[/tex]

The maximum value οf the prοbability οf any event cannοt exceed 1.

The maximum value οf the prοbability οf an event is 1. The prοbability οf an event represents the likelihοοd οr chance that the event will οccur, and it is always expressed as a number between 0 and 1. A prοbability οf 0 means the event is impοssible, while a prοbability οf 1 means the event is certain tο οccur.

Prοbabilities between 0 and 1 represent the degree οf uncertainty οr likelihοοd οf the event. Since the sum οf prοbabilities οf all pοssible οutcοmes is always 1, the maximum value οf the prοbability οf any event cannοt exceed 1.

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Answer:

B

Step-by-step explanation:

The answer is B because for the slope of the first part of the equation, it's 2/3 up 2 over 3. The starting point for that part of the equation is -2, so that's where your starting point is. For the second part of the equation, your starting point is on 1, and the slope is -5, so moving to the right 1 and down 5.

so let's put the prism upright, Check the picture below.

keeping in mind that for a triangular prism the bases are the triangular parts, so le'ts find the area of those guys

[tex]\stackrel{ \textit{\LARGE Lateral} }{\stackrel{ \textit{Area of the three rectangles} }{(7)(5)~~ + ~~(3)(7)~~ + ~~(4)(7)}}\implies \text{\LARGE 84} \\\\\\ \stackrel{ \textit{\LARGE Total} }{\stackrel{ \textit{Area of the bases} }{2\left[\cfrac{1}{2}(\underset{b}{4})(\underset{h}{3}) \right]}~~ + ~~84}\implies \text{\LARGE 96}[/tex]

Therefore , the solution of the given problem of area comes out to be the force of 60 kN applies 5 kN/m2 of pressure to a 12 m² is 5 kN/m².

Calculating how much room is needed to fully cover the outside will reveal its overall size. When calculating a trapezoidal shape's surface, the immediate environs are taken into account. The surface area of something determines its overall measurements. The internal water capability of a cuboid is given by the total of the borders connected to each of its six rectangular edges.

Here,

The following method determines the pressure P that a force F exerts on an area A:

=> P = F/A

Inputting the numbers provided yields:

=> P = 60 kN / 12 m²

If we simplify, we get:

=> P = 5 kN/m²

As a result, the force of 60 kN applies 5 kN/m2 of pressure to a 12 m² is 5 kN/m².

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Therefore , the solution of the given problem of unitary comes out to be each asset class as part of the diversification plan.

By combining the information obtained using this nanosection technique with all variable additional data from two individuals who used a specific strategy, the task can be completed. Simply put, this mean that, if the desired outcome materialises, either the specified entity will be known or, actually, the colour from both enormous processes will be skipped. For forty pens, a refundable charge of Rupees ($1.01) might be required.

Here,

The next two are methods for reducing the danger associated with investing out of the four you offered:

Dollar-cost averaging is the term used to describe this method of spreading investments out over time. Regardless of the investment's price, it entails making a set amount of investments at regular intervals over a length of time.

Spread your investments across various asset classes (such as stocks, bonds, real estate, etc.) and/or various companies within each asset class as part of the diversification plan.

Since currency values can be influenced by a number of variables and are sometimes unpredictable, investing in a particular currency (such as the British pound) is not always a risk management plan.

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bAnswer:

Step-by-step explanation:

The combined volume of the cylinder and cone with diameters of 2 feet and heights of 9 feet is 42.39 ft3.

The volume of the cylinder and cone can be calculated using the formula V=πr2h. The radius of both is 1 foot and the height of both is 9 feet. Therefore, the volume of the cylinder is Vcylinder = π(1)2(9) = 28.26 ft3. The volume of the cone can be calculated using Vcone = π(1)2(4.5) = 14.13 ft3, where 4.5 is the height of the cone. To calculate the combined volume, add the volumes of the cylinder and the cone: Vtotal = 28.26 + 14.13 = 42.39 ft3.

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Using functions we can find that there would be nine roadways for six cities. This is due to the fact that each city must be connected to every other city, and since there are 5 pairs of connected cities, there must be 5 highways.

A function is a statement, concept, or rule that establishes an association between two variables.

Functions in mathematics are required for the development of meaningful relationships. If there are more than one dependent values for a particular independent value, then we are aware of this.

In that situation, the relation is not a function. Nevertheless, if there are multiple dependent values for a given independent value.

The relationship is then a function.

Now as per the question,

The remaining 4 cities must then be connected, which requires building an additional 4 roads, for a total of 9.

There would be 12 roadways for 7 cities.

This is due to the fact that each city must be connected to every other city, and since there are 6 pairs of connected cities, there must be 6 highways.

Then, the final five cities must be connected, which requires five more roads, for a total of twelve.

The number of highways for N cities would be N(N-1)/2.

This is because there are N(N-1)/2 pairs of cities that need to be connected, and each city must be connected to every other city.

For instance, if N = 10, 90 highways or 10× 9 = 90 pairs of cities must be connected.

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The complete question is:

There are five cities in a country, and two are connected with one road that goes straight between them. How many roads would be in this country if there were 6 cities? 7 cities? And N cities?

Answer: To find the value of k(9), we need to substitute x=9 into the given function k(x):

k(9) = 2(9)² - 3√(9)

k(9) = 2(81) - 3(3)

k(9) = 162 - 9

k(9) = 153

Therefore, the value of k(9) is 153.

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All original content anything provided above is not copy and pasted. IT was typed by hand.

Answer:

Step-by-step explanation:

The initial height is the beginning of the graph, or in this case, x=0. So the initial height is 1.5.

Answer:

31/7

Step-by-step explanation:

7 i - 15 = 16

1. add 15 to both sides you will get

7i = 31

2. dividing both sides gives us 31/7

3. i = 31/7

Answer:

Step-by-step explanation:

In order to find a hole, you have to factor the denominator to see if it matches an expression in the numerator and can therefore be crossed out.

The factored form of the denominator is shown below:

[tex]f(x)=\frac{x-1}{(x-3)(x-1)}[/tex]

Because the term x-1 is in both the numerator and the denominator, it is a hole, or removeable discontinuity. To find the hole, we plug in a 1 to the fraction that remains after we cancel the hole:

[tex]f(1)=\frac{1}{1-3}=-\frac{1}{2}[/tex]

The hole is found at (1, -1/2)

Answer:

If 400 ml of squash is made by mixing 50 ml of cordial with water, then the remaining volume is water.

The volume of water used in making the squash = 400 ml - 50 ml = 350 ml

The fraction of the drink that is water is:

Water volume / Total volume = 350 ml / 400 ml = 7/8

Therefore, 7/8 of the drink is water.

Answer:

[tex]\frac{7}{8}[/tex]

Step-by-step explanation:

We know that 400ml squash = 50ml of Cordial With Water.

Therefore in 400ml of squash, amount of water will be 400ml - 50ml = 350ml of water.

In fraction form, this will be [tex]\frac{350}{400} =\frac{7}{8}[/tex]

Hope it helps

Using this formula, we can calculate that the chance that the plane will be overbooked is 35.1%. This means that there is a 35.1% chance that more than 300 passengers will show up for the flight despite the airline only having 300 seats.

The chance that a plane will be overbooked is calculated using a binomial probability formula. The formula is P(x) = nCx * p^x * (1 - p)^(n - x), where n is the number of trials (in this case, 300), x is the number of successes (in this case, 324 reservations), and p is the probability of success (in this case, 90%).

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Answer:

116

Step-by-step explanation:

We can see that the two lines in between the triangle are the same size. This must mean that if we were to move the inner triangle and line it up to the triangle on the edge it must be the same size. We are also told that one of the angles on the side is 116. This means that the value of x must also be 116!

Hope this helps, have a lovely day! :)

Answer:

m = - 6.5

Step-by-step explanation:

the remainder theorem states

if a function f(x) is divide by (x - a) then the remainder is equal to f(a)

given

p(x) is divided by (x - 2) then p(2) = 2 ( the remainder )

then

2[tex](2)^{4}[/tex] - 5(2)² + 2m + 3 = 2

2(16) - 5(4) + 2m + 3 = 2

32 - 20 + 2m + 3 = 2

15 + 2m = 2 ( subtract 15 from both sides )

2m = - 13 ( divide both sides by 2 )

m = - 6.5

Answer:

The reduced answer is 1/4

Answer:

<COA MESURES = 61

<AOH MESURES = 46

<HOG MESURES = 73

<FOE MESURES = 73

Step-by-step explanation:

Answer:

8 Mangoes

Step-by-step explanation:

Since he decides to buy 4 apples, that would cost him: 4 × $1 = $4

That leaves him: $20 - $4 = $16.

So, how many mangoes can Noah possibly buy with $16?

That is: $16/$2 = 8(We divide by $2 because it is the cost of one mango)

Answer: Let's start by representing the number of Blu-Ray discs sold as x.

According to the problem, the store sold 2/3 as many DVDs as Blu-Ray discs. So the number of DVDs sold is 2/3 of x, or (2/3)x.

We also know that the total number of DVDs and Blu-Ray discs sold was 280. So we can set up an equation:

(2/3)x + x = 280

To solve for x, we can simplify the equation by combining like terms:

(5/3)x = 280

Multiplying both sides by 3/5, we get:

x = 168

So the number of Blu-Ray discs sold was 168.

To find the number of DVDs sold, we can use the expression we derived earlier:

(2/3)x = (2/3) * 168 = 112

Therefore, the store sold 112 DVDs on that day.

Step-by-step explanation:

The sale price of the laptop is $414 after the use of the coupon.

Answer:

$385.00

Step-by-step explanation:

Original Price - Discount = Sale price

Since the discount is 30%, we would multiply 0.30(550) to get the amount of the discount.

0.30(550) = 165

550 - 165 = $385

The 95% of the babies born to 22-year-old mothers will weigh between 3308.4 grams and 5665.6 grams.The correct answer is option C) (3051.25, 5408.49).

To get started, let's put the mother's age into the given equation to determine the mean birth weight. Then, we'll use the RMS value to calculate the standard deviation.The equation for predicting baby birth weight in grams given the mother's age is: Y = -1163.45 + 245.15XWhere X is the mother's age, and Y is the baby's birth weight. We are given X=22, so let's use that to find the predicted mean birth weight:Y = -1163.45 + 245.15(22) = 4486.95 gramsThe RMS is given to be 589.3 grams. Because we're told that the distribution is approximately normal, we can use the 68-95-99.7 rule to find the 95% prediction interval. Here are the steps:Subtract the RMS from the mean to find the lower endpoint of the interval:4486.95 - (2 x 589.3) = 3308.35Add the RMS to the mean to find the upper endpoint of the interval:4486.95 + (2 x 589.3) = 5665.55Round both values to four decimal places, as instructed in the problem:3308.35 rounds to 3308.4 grams5665.55 rounds to 5665.6 gramsTherefore, about 95% of the babies born to 22-year-old mothers will weigh between 3308.4 grams and 5665.6 grams.The correct answer is option C) (3051.25, 5408.49).

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Answer:

4*sqrt(2)

Step-by-step explanation:

To find the distance between two points, we use the distance formula, which is the following:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the values for the given points, we get the following:

d = sqrt((1 - (-3))^2 + (-2 - (-6))^2)

= sqrt((1 + 3)^2 + (-2 + 6)^2)

= sqrt(4^2 + 4^2)

= sqrt(32)

= 4*sqrt(2)

Therefore, the distance between the points (-3, -6) and (1, -2) is 4*sqrt(2).

The sample that has a greater mass is given as follows:

The sample of rock.

The sample of rock has a mass that is 5000 times the mass of the sample of dry sponge.

A number in scientific notation is given by the notation presented as follows:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.

To obtain which amount is greater, we must verify the bases when the exponent is the same, hence:

Hence the rock has the greater mass, and the ratio is given as follows:

10/0.002 = 5000.

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Answer:

5 and 13

Step-by-step explanation:

given the first number is x and the second number is y

then x + y = 18 => y = 18 - x

also

x^2 + y^2 = 194

substitute

x^2 + (18 - x)^2 = 194

x^2 + x^2 - 36x + 324 = 194

2x^2 - 36x + 130 = 0

2(x^2 - 18x + 65) = 0

x^2 - 18x + 65 = 0/2

x^2 - 13x - 5x + 65 = 0

x(x - 13) - 5(x - 13) = 0

(x - 13)(x - 5) = 0

=> x - 13 = 0 => x = 13

=> x - 5 = 0 => x = 5

if x = 13, y = 18 - 13 = 5

if x = 5, y = 18 - 5 = 13

so x and y can be either 5 and 13

Step-by-step explanation:

To rewrite (24 + 40) as an integer times the sum of two integers, Gracie first factored out 2, obtaining:

(24 + 40) = 2 × (12 + 20)

We can check that this is true by distributing the 2:

2 × (12 + 20) = 2 × 12 + 2 × 20 = 24 + 40

Now, Gracie is looking for other numbers greater than 2 that she can factor out of (24 + 40) to rewrite the expression as an integer times the sum of two integers.

One way to approach this is to look for other common factors between 24 and 40. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. The common factors of 24 and 40 are 1, 2, 4, 8, and the largest factor is 8.

Therefore, Gracie can factor out 4 or 8 to rewrite the expression as an integer times the sum of two integers. For example:

(24 + 40) = 4 × (6 + 10)

(24 + 40) = 8 × (3 + 5)

Note that we can also factor out 1 or 2, but that would not change the expression in any meaningful way.