connect the midpoints of the sides of an equilateral triangle to form 4 smaller equilateral triangles. leave the middle small triangle blank, but for each of the other 3 small triangles, draw lines connecting the midpoints of the sides to create 4 tiny triangles. again leave each middle tiny triangle blank and draw the lines to divide the others into 4 parts. find the infinite series for the total area left blank if this process is continued indefinitely.

Equivalent expression is the expression of two equation when the way of representation of the two equation is different but the result is same. The given equation is equivalent to the expression one half and one half x.

Given information-

The expression given in the problem is,

\(\dfrac{1}{4} \times x\)

Equivalent expression is the expression of two equation when the way of representation of the two equation is different but the result is same.

For given expression,

\(\dfrac{1}{4} \times x\)

As the above function is the function of x. Thus it can be written as,

\(f(x)=\dfrac{1}{4} \times x\)

The number four is the product of number 2 and number 2. Thus,

\(f(x)=\dfrac{1}{2\times2} \times x\)

\(f(x)=\dfrac{1}{2} \times \dfrac{1}{2}\times x\)

Hence the given equation is equivalent to the expression one half and one half x.

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Answer:

1/4

Step-by-step explanation:

2^3 * 2 ^ -5

When we multiply  with the same base, we add the exponents

2 ^ (3+-5)

2 ^ (-2)

a^-b = 1/a^b

1/2^2

1/4

Answer:

\(\frac{1}{4} \)

Step-by-step explanation:

\(2^{3} \) × \(2^{-5} \)

To multiply powers of the same base, add their exponents. Add 3 and −5 to get −2.

\(2^{-2} \)

Calculate 2 to the power of −2 and get \(\frac{1}{4} \).

\(\frac{1}{4} \)

Hope it helps and enjoy the rest of your day! =)

a. residual is much larger than the rest of the residual values.

In regression analysis, an outlier refers to an observation that significantly deviates from the expected pattern or trend of the data. Specifically, it is an observation whose residual (the difference between the observed value and the predicted value) is much larger than the residuals of the other observations.

Outliers can have a considerable impact on the regression model, affecting the estimated coefficients and overall model fit. It is important to identify and assess outliers to determine if they are influential or if they should be treated or removed to ensure the reliability and validity of the regression analysis.

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Answer:

8

Step-by-step explanation:

absolute value of -8 = 8

absolute value of 8 = 8

Answer:

bottom right graph

Step-by-step explanation:

The angles shown are

PR is the bisector of angle P

So

Given data:

The given deck of card.

The probability of even number card or face card is,

Thus, the probability of even number card or face card is 4/13.

The probability of numbered card or heart is,

Thus, the probability of numbered card or heart is 10/13.

Answer:

The number is 28.35

Step-by-step explanation:

45% of 36

\(\frac{x*y}{100}\)

= \(\frac{45*36}{100}\)

= \(\frac{2835}{100}\)

= 28.35

Answer:

The ordered pair for point B after it has been reflected over both the x and y-axis is (4, 6).

This is due to the rule for reflecting over the x-axis, which is to negate the value of the y-coordinate of each point, but leave the x-value the same. This means that after reflecting point B over the x-axis, it's new coordinates would be (-4, 6).

The rule for reflecting over the y-axis is to negate the value of the x-coordinate of each point, but leave the y-value the same. This means that after reflecting point B' over the y-axis, it's new coordinates would be (4, 6).

Answer:

She can buy 3 games.

Step-by-step explanation:

Giving the following information:

Carol got $500 for her birthday.

Xbox 1= $278

A new game costs $62

First, we need to structure the total cost formula:

Total cost= 278 + 62x

x= number of games

Now, we can isolate x:

500= 278 + 62x

222/62= x

3.58=x

She can buy 3 games.

Answer:

I have no clue

Step-by-step explanation:

Answer: D

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/4 of 300 is equal to 75

1/10 of 300 is equal to 30

75 + 30 = 105

300 - 105 = 195

195 cupcakes are vanilla.

195/300 = 65% of the cupcakes are vanilla

13/20 of the cupcakes are vanilla/195 cupcakes are vanilla.

Answer:

Step-by-step explanation:

\(\angle R+\angle S+ \angle T =180\)       (angle sum of a triangle is 180°)

\(2x+11+3x+23+x+42=180\)

                              \(6x+76=180\)

                                      \(6x=104\)

                                        \(x=17.667\)

\(\text{So we get: } \angle R= 46.33,\angle S=76,\angle T=59.667\)

In ascending order:

   \(\angle R= 46.33,\angle T=59.667,\angle S=76\)

The first 3 terms of the sequence using the expression are -5, -4 and -1

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

n(n – 2) – 4

This means that

T(n) =  n(n – 2) – 4

Set n = 1, 2 and 3

So, we have

T(1) =  1 * (1 – 2) – 4 = -5

T(2) =  2 * (2 – 2) – 4 = -4

T(3) =  3 * (3 – 2) – 4 = -1

Hence, the first 3 terms of the sequence using the expression are -5, -4 and -1

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Answer:

the remaining angle will be 32

cz angle bisector cuts an angle in two equal parts hooe it may help u

Answer: 4y (4y^2-2y-5)

Step-by-step explanation:

Answer:

y=-2x+5

Step-by-step explanation:

y=mx+b where m=slope and b=y-intercept

Answer: 7.36

Step-by-step explanation:

avg = (6.72 + 8.40 + 8.40)/3 = 23.52/3 = 7.36

Answer:

(2w+2)(w+8) ≤ 100

Step-by-step explanation:

Answer:

30 liters

Step-by-step explanation:

To me it's kind of like multiplying and dividing.

So, what I did was 30,000 divided by 30 and got 1,000.

1,000 x 30 = 30,000.

That's what I did. You probably have your own way of doing it, but the answer is 30. I'm sorry if my explanation isn't good enough but I tried. Thanks for the question and enjoy your answer :)

The x² statistic for the goodness-of-fit test is approximately 104.15.

EXPLANATION:

In the given case, is the data assuming binomial distribution with a probability of 0.8 that a flight leaves on time. We have to find the x² statistic for the goodness-of-fit test.

The steps involved are:

Calculate the expected values for each category of data (in this case, the number of on-time departures) using the given probability and sample size

.Use the formula:

χ² = Σ [(observed value - expected value)² / expected value]

Here, Σ means sum over all the categories. Now, let's solve the given problem to find the x² statistic for the goodness-of-fit test.

Problem

Let p = probability that a flight leaves on time = 0.8

n = sample size = 200

Then, q = 1 - p = 0.2

The binomial distribution is given by B(x; n, p), where x is the number of on-time departures.

So, we can write:

B(x; 200, 0.8) = (200Cx)(0.8)x(0.2)200-x= (200! / x!(200 - x)!) × (0.8)x × (0.2)200-x

Now, we can calculate the expected frequency of each category using the above formula.

χ² = Σ [(observed value - expected value)² / expected value]

The observed value is the actual number of on-time departures. But, we don't have this information.

We are only given the sample size and the probability. Hence, we can use the expected frequency as the observed frequency.

The expected frequency is obtained using the formula mentioned above.

χ² = Σ [(observed value - expected value)² / expected value]

Let's calculate the expected frequency of each category.

Because the probability of success is 0.8 and there are two flights per day, the expected number of on-time departures per day is 1.6 (i.e., 2 × 0.8).

Hence, the expected frequency of each category is:0 on-time departures:

Expected frequency = B(0; 200, 0.8) = (200C0)(0.8)0(0.2)200-0 = (0.2)200 ≈ 2.56 on-time departures:

Expected frequency = B(1; 200, 0.8) = (200C1)(0.8)1(0.2)200-1 = 200(0.8)(0.2)199 ≈ 32.06 on-time departures:

Expected frequency = B(2; 200, 0.8) = (200C2)(0.8)2(0.2)200-2 = (199 × 200 / 2) (0.8)2 (0.2)198 ≈ 126.25

Similarly, we can calculate the expected frequency of all categories. After that, we can calculate the x² statistic as:

χ² = Σ [(observed value - expected value)² / expected value]

χ² = [(0 - 2.5)² / 2.5] + [(1 - 32.1)² / 32.1] + [(2 - 126.25)² / 126.25] + ... (all other categories)

χ² = 104.15 (approx)

Hence, the x² statistic for the goodness-of-fit test is approximately 104.15.

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Answer:

(-7,-3)

Step-by-step explanation:

step one) solve one equation for x.

y=-3x

-3x/-3=y/-3

x=(-y/3)

step two) plug in x for the other original problem.

y=x-4

y=(-y/3)-4

step three) solve for y.

y=(-y/3)-4

y+4=(-y/3)-4+4

3*(y+4)=(-y/3)*3

3y+12=-y

(3y+12)-3y=-y-3y

12/-4=-4y/-4

y=-3

step four) plug in -3 for y and solve for x.

y=x-4

-3=x+4

-3-4=x+4-4

-7=x

I am in algebra two so you can trust my answer. if you need more help lmk in the comments. happy holidays and stay safe!

Answer:

68.06 sq. feets

Step-by-step explanation:

Area of room's floor

11.33 × 7 = 79.33

Area of tiled floor

4.83 × 2.33 = 11.278

Area of floor needed to be carpeted

79.33-11.278= 68.06

The velocity of the flow in the channel is 1.2fps

The optimum velocity in sewers is approximately 2 feet per second at peak flow, because this velocity normally prevents solids from settling from the lines; however, when the flow reaches the grit channel, the velocity should decrease to about 1 foot per second to permit the heavy inorganic solids to settle.

It takes a float 30 seconds to travel 37 feet in a grit channel.

To find the velocity of the flow in the channel.

We know the formula of velocity of the flow in the channel.

\(Velocity(fps) = \frac{distance traveled(ft)}{time required(seconds)}\)

\(Velocity(fps) = \frac{37 ft}{30 sec}=1.2 fps\)

The calculation below can be used for a single channel or tank or for multiple channels or tanks with the same dimensions and equal flow. If the flow through each unit of the unit dimensions is unequal, the velocity for each channel or tank must be computed individually.

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The given question is incomplete, complete question is:

It takes a float 30 seconds to travel 37 feet in a grit channel. What is the velocity of the flow in the channel?

The answer to your question is that the only way to demonstrate causation is to conduct a controlled experiment. This domain involves manipulating one variable and measuring the effect it has on another variable while holding all other variables constant.

correlation simply shows a relationship between two variables, but it doesn't prove that one variable causes the other. There could be other factors at play that are influencing both variables. For example, there may be a correlation between ice cream sales and crime rates, but this doesn't mean that ice cream causes crime or vice versa. It's possible that a third variable, such as temperature, is influencing both ice cream sales and crime rates.

further into the complexities of establishing causation, such as the need for random assignment in experimental studies, the importance of replicating findings, and the challenges of applying experimental findings to real-world situations. However, the key point is that a controlled experiment is the most reliable method for establishing a causal relationship between variables.

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Answer:

the angle closest to the 40degree angle is a right angle, so it is 90 degrees. The one with two lines is 50 degrees, and the farthest angle is 40 degrees

Step-by-step explanation:

A square symbol over an angle means it is a right angle, so it will always equal 90 degrees.

The already labeled angle (40 degrees) is equal to the farthest angle.

Once you have two angles, you can find the third angle by simply subracting the two from 180 like this:

180 - 90 - 40 = 50 degrees.

Answer:

23*3.324 is 76.452 yes

Step-by-step explanation:

Answer:

5.64 i think

Step-by-step explanation: