Which series of transformations shows that trapezoid E’F’G’H is similar to trapezoid EFGH? Assume all dilations are centered at the origin

The probability that less than 9 but more than 7 bulbs from the sample are defective is 0.8944.

The formula to find the probability of x number of defective bulbs in a sample of n bulbs is as follows:

P(x) = [[tex]n \choose x[/tex] * p^x * (1-p)^(n-x)], where [tex]n \choose x[/tex] is the combination of n and x.

So, The probability of x < 9 defective bulbs in a sample of 14 bulbs is given as follows:

P(x<9) = P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4) + P(x=5) + P(x=6) + P(x=7)

Therefore, the probability that less than 9 bulbs from the sample are defective is

P(x<9) = [[tex]14 \choose0[/tex] * (0.2)^0 * (0.8)^14] + [[tex]14 \choose1[/tex] * (0.2)^1 * (0.8)^13] + [[tex]14 \choose2[/tex] * (0.2)^2 * (0.8)^12] + [[tex]14 \choose3[/tex] * (0.2)^3 * (0.8)^11] + [[tex]14 \choose4[/tex] * (0.2)^4 * (0.8)^10] + [[tex]14 \choose5[/tex] * (0.2)^5 * (0.8)^9] + [[tex]14 \choose6[/tex] * (0.2)^6 * (0.8)^8] + [[tex]14 \choose7[/tex] * (0.2)^7 * (0.8)^7]= 0.8962

Similarly, the probability that more than 7 bulbs from the sample are defective is:

P(x>7) = P(x=8) + P(x=9) + P(x=10) + P(x=11) + P(x=12) + P(x=13) + P(x=14)

Therefore, the probability that more than 7 bulbs from the sample are defective is

P(x>7) = [[tex]14 \choose8[/tex] * (0.2)^8 * (0.8)^6] + [[tex]14 \choose9[/tex] * (0.2)^9 * (0.8)^5] + [[tex]14 \choose10[/tex] * (0.2)^10 * (0.8)^4] + [[tex]14 \choose11[/tex] * (0.2)^11 * (0.8)^3] + [[tex]14 \choose12[/tex] * (0.2)^12 * (0.8)^2] + [[tex]14 \choose13[/tex] * (0.2)^13 * (0.8)^1] + [[tex]14 \choose14[/tex] * (0.2)^14 * (0.8)^0]= 0.0005

Therefore, the probability that less than 9 but more than 7 bulbs from the sample are defective is:

P(8≤x≤7) = P(x<9) - P(x≤7)

P(8≤x≤7) = P(x<9) - [P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4) + P(x=5) + P(x=6) + P(x=7)]= 0.8962 - 0.0018= 0.8944 (rounded to four decimal places)

Therefore, more than 7 out of the sample have a probability of failure, but less than 9 out of the sample probably have a failure.

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If f(x,y) gets close to L as we approach (0,0) along the x-axis (y = 0) and along the y-axis (x = 0), the limit of f(x,y) as (x,y) approaches (0,0) is L.

We can follow these steps:

Step 1: Approach (0,0) along the x-axis (y = 0)
Evaluate the limit of f(x,0) as x approaches 0. If the limit exists and is equal to L, proceed to step 2.

Step 2: Approach (0,0) along the y-axis (x = 0)
Evaluate the limit of f(0,y) as y approaches 0. If the limit exists and is equal to L, proceed to step 3.

Step 3: Conclude the limit
If both the limits in steps 1 and 2 exist and are equal to L, then the limit of f(x,y) as (x,y) approaches (0,0) is L. Otherwise, the limit does not exist.

So, if f(x,y) gets close to L as we approach (0,0) along the x-axis (y = 0) and along the y-axis (x = 0), the limit of f(x,y) as (x,y) approaches (0,0) is L.

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Answer:

2145

Step-by-step explanation:

Given: Sum of three consecutive odd integers = 39

Calculation:Let x, x + 2, x + 4 be the three consecutive odd integers.

Sum of three consecutive odd integers = 39

⇒ x + (x + 2) + (x + 4) = 39

⇒ 3x + 6 = 39

⇒ 3x = 33

⇒ x = 11

∴ The integers are 11, 13 and 15.

∴ Their product = 11 × 13 × 15 = 2145

You're welcome! :)

The sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 98% confidence level with an error of at most 0.03 is approximately 904

Since the commission wants a 98% confidence level, the z-score associated with that level is 2.33 (which can be found using a standard normal distribution table).

We also know that the commission wants an error of at most 0.03, so we can set up an equation:

0.03 = 2.33 x √(0.23 x 0.77) / √(n)

Solving for n, we get:

n = (2.33 x √(0.23 * 0.77) / 0.03)²

n = 903.78

So, the commission would need a sample size of at least 904 tenth grade students in order to estimate the fraction of students with reading skills at or below the eighth grade level at the 98% confidence level with an error of at most 0.03.

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Using a loan amortization calculator, we can generate a table that shows the borrower's monthly payments, the interest paid, the principal paid, and the remaining balance after each payment.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9."

Using a loan amortization calculator, we can generate a table that shows the borrower's monthly payments, the interest paid, the principal paid, and the remaining balance after each payment. Here is the loan amortization table for the $210,000, 15-year mortgage with an APR of 3.8%, assuming the borrower pays an extra $100 towards the principal each month:

Month Payment Interest Paid Principal Paid Extra Principal Paid Remaining Balance

1 $1,529 $662 $297 $100 $209,703

2 $1,529 $657 $301 $100 $209,402

3 $1,529 $652 $306 $100 $209,096

4 $1,529 $647 $311 $100 $208,783

5 $1,529 $642 $316 $100 $208,463

6 $1,529 $637 $321 $100 $208,137

7 $1,529 $632 $326 $100 $207,803

8 $1,529 $627 $331 $100 $207,463

9 $1,529 $622 $336 $100 $207,116

10 $1,529 $617 $341 $100 $206,762

11 $1,529 $611 $347 $100 $206,411

12 $1,529 $606 $352 $100 $206,052

13 $1,529 $601 $357 $100 $205,686

14 $1,529 $596 $362 $100 $205,322

15 $1,529 $590 $368 $100 $204,950

16 $1,529 $585 $373 $100 $204,570

17 $1,529 $580 $378 $100 $204,182

18 $1,529 $574 $384 $100 $203,787

19 $1,529 $569 $389 $100 $203,383

20 $1,529 $563 $395 $100 $202,972

21 $1,529 $558 $400 $100 $202,552

22 $1,529 $552 $406 $100 $202,125

23 $1,529 $547 $411  

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The percent increase when [tex]$x$[/tex] increases by one unit is approximately 15.8%.

What is exponential function?

An exponential function is a mathematical function of the form:

[tex]f(x) = a^x[/tex]

where a is a constant greater than zero and not equal to 1, and x is the variable that takes on real numbers.

To find the percent increase for the exponential function [tex]$A = 82\times 1.16^x$[/tex], we need to find the ratio of the final value to the initial value, subtract one, and then multiply by 100 to convert to a percentage.

Let's suppose we are interested in finding the percent increase when [tex]$x$[/tex] increases by one unit. We can start by calculating the initial value of [tex]$A$[/tex] when [tex]$x = 0$[/tex]:

[tex]$$A = 82 \times 1.16^0 = 82$$[/tex]

Then we can calculate the final value of [tex]$A$[/tex] when [tex]$x = 1$[/tex]:

[tex]$$A = 82 \times 1.16^1 \approx 95.12$$[/tex]

Now we can find the ratio of the final value to the initial value:

[tex]$\text{ratio} = \frac{\text{final value}}{\text{initial value}} = \frac{95.12}{82} \approx 1.158$$[/tex]

Next, we subtract one and multiply by 100 to get the percent increase:

[tex]$$\text{percent increase} = (\text{ratio} - 1) \times 100 \approx (1.158 - 1) \times 100 \approx 15.8%$$[/tex]

Therefore, the percent increase when [tex]$x$[/tex] increases by one unit is approximately 15.8%.

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The exact value of the cosine of angle A + B is equal to - 1239 / 1961.

In this problem we need to determine the exact value of a trigonometric function, this can be done by using definitions of trigonometric functions, Pythagorean theorem and trigonometric formulas:

Trigonometric function

sin θ = y / r

cos θ = x / r

tan θ = y / x

Pythagorean theorem

r² = x² + y²

Trigonometric formula

cos (A + B) = cos A · cos B - sin A · sin B

First, determine the exact values of sines and cosines:

Angle A

r = √(28² + 45²)

r = 53

sin A = 45 / 53

cos A = 28 / 53

Angle B

y = √(37² - 12²)

y = 35

sin B = 35 / 37

Second, calculate the exact value of the trigonometric function by trigonometric formula:

cos (A + B) = (28 / 53) · (12 / 37) - (45 / 53) · (35 / 37)

cos (A + B) = - 1239 / 1961

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Answer:

Hope you have understood this sum

Wendy's conclusion is invalid as she cannot generalize her findings as sample size is too small to represent the entire school population accurately.

Wendy's assessment is incorrect. This is due to the fact that she is unable to extrapolate from a sample of just 40 students who play football for the school. The sample size is insufficient to provide an accurate representation of the student body as a whole. Also, the football players might be more prone to injuries than those who don't participate in sports, which could further skew the results.

Moreover, Wendy did not choose the football team members using a random sample approach. Instead, she restricted her questions to those students who were already on the football team, thereby introducing sample bias. She might have unintentionally left out pupils who don't participate in athletics but may nonetheless have hurt themselves while doing other physical activities.

Wendy's assertion that 375 of the school's 1,000 kids have sustained sports-related injuries is therefore unfounded. Wendy would need to employ a more representative and random sampling technique that includes students from various sports teams as well as those who do not play sports in order to draw a reliable conclusion. She would also require a larger sample size to obtain a more accurate representative of the total student body.

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Complete Question: Wendy questioned the 40 members of the varsity football team about their experiences with sports-related injuries. "Sure," fifteen football players answered. Wendy came to the conclusion that 375 of the 1,000 pupils at her school had had sports-related injuries. Decide if Wendy's conclusion is true or not.

Answer:

14.65

Step-by-step explanation:

3.6 ft + 6.25+4.8=14.65

The equation of the line from the given graph is y = 3x + 1.

With the aid of the line's slope and a point on the line, the equation of a line may be created. For a better understanding of how a line's equation is created, let's learn more about the line's slope and the necessary point on the line. The slope of a line is the angle that the line makes with the positive x-axis and can be stated as a numerical integer, fraction, or as the tangent of that angle. The term "point" refers to a coordinate system point with the x and y coordinates.

From the given graph we observe the two coordinates of the line are (0, 1) and (3, 10).

The slope of the line is given as:

m = y2 - y1 / x2 - x1

m = (10 - 1) / (3 - 0)

m = 9/3 = 3

The point-slope intercept is given as:

y - y1 = m (x - x1)

Substituting the values:

y - 1 = 3 (x - 0)

y - 1 = 3x

y = 3x + 1

Hence, the equation of the line is y = 3x + 1.

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Answer:

[tex]4a^{2} + 4ab[/tex]

Step-by-step explanation:

as I can see in the image posted by you,

current length = a + b

current width = a

according to the condition, original paper length and width was twice of their current values,

original length = 2(a+b)

original width = 2a

therefore,

original area = 2(a+b) * 2a

original area = 4(a+b)a

original area = [tex]4a^{2} + 4ab[/tex]

Hopefully you found the answer helpful

Answer: Alexis is 1.4224 meters tall.

Step-by-step explanation:

If you want your answer rounded, it's 1.4 meters. I hope this helped you! Brainilist is highly appreciated and helpful! <3

The method that is most appropriate when calculating margin-of-error for population mean is (b) Student's t-distribution.

When calculating the margin of error for the population mean, the most appropriate method depends on the sample size.

If the sample size is large (n > 30) and the population standard deviation is known, then a normal z-distribution can be used to calculate the margin of error.

If the sample size is small (n < 30) or the population standard deviation is unknown, then Student’s t-distribution should be used to calculate the margin of error.

In this case, we are told that the information was obtained from 14 strands of this particular virus. Since n < 30, we should use Student’s t-distribution to calculate the margin of error.

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

Considering the following scenario, which method would be most appropriate when calculating the margin of error for the population mean?

A research scientist wants to know how many times per hour a certain strand of virus reproduces. she obtains information from 14 strands of this particular virus and finds the mean to be 7.4 . the population is assumed to be normally distributed.

(a) Normal z-distribution

(b) Student's t-distribution

(c) More advanced statistical techniques

1. sin ² x goes in the numerator. 2. sin x (sin x) is the numerator expanded. 3. Separate the two factors sin x / cos x and sin x / cos x. 4. Replace sin x / cos x with tan x. Use the trigonometric identity.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the connection between the angles and sides of a triangle. The three basic categories of trigonometric functions are sine, cosine, and tangent. In contrast to the fundamental trigonometric functions, the other three functions are essentially employed more frequently. For an explanation of these three main roles, use the diagram below as a guide. The sin-cos-tan triangle is the name for this illustration. Often, the right-angled triangle is used to define trigonometry.

The given trigonometric function is 1 / cos x csc² x.

Now, the csc²x can be written as:

sin²x / cos x. Thus, sin ² x goes in the numerator.

Now, sin x (sin x) is the numerator expanded.

Separate the two factors sin x / cos x and sin x / cos x

Replace sin x / cos x with tan x.

Use the trigonometric identity to complete the proof.

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To measure out exactly 1 gallon of water we need exactly six possible number of moves.

To measure out exactly 1 gallon of water using two jugs, one with a 3-gallon capacity and one with an 5-gallon capacity, you can follow some steps

Fill the 5-gallon jug with water completely. Pour the water from the 5-gallon jug into the 3-gallon jug, leaving 2 gallons of water in the 5-gallon jug.

Empty the 3-gallon jug completely. Pour the 2 gallons of water from the 5-gallon jug into the empty 3-gallon jug.

Fill the 5-gallon jug with water again. Pour water from the 5-gallon jug into the 3-gallon jug until it is full, which will leave exactly 1 gallon of water in the 5-gallon jug.

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Answer:

The coordinates of (-3,0) after a translation of 2 units up is the third one. (-3,2)

Answer:

20 : 50

Step-by-step explanation:

sum the parts of the ratio , 2 + 5 = 7 parts

divide 70 by 7 to find the value of one part of the ratio

70 ÷ 7 = 10 ← value of 1 part of the ratio , then

2 parts = 2 × 10 = 20

5 parts = 5 × 10 = 50

then

50 divided in the ratio 2 : 5 is 20 : 50

Answer:

Step-by-step explanation:

-145c is lower because it’s further left on a numberline

The length of the model car’s hood is 5√5 inches divided by 6, which is a simplified radical expression.

If the real car’s hood is 20√5 inches long and the model car uses a 1:24 scale, we can find the length of the model car’s hood by dividing the length of the real car’s hood by 24.

Length of model car’s hood = (Length of real car’s hood) / (Scale factor)

Substituting the given values, we get:

Length of model car’s hood = (20√5 inches) / 24

We can simplify this expression by dividing the numerator and denominator by the greatest common factor, which is 4:

Length of model car’s hood = (5√5 inches) / 6

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The final triangle has vertices at (3, -1), (3, -4), and (1, -4) on the graph.

In mathematics, a transformation refers to a function that maps points or shapes in one coordinate system to corresponding points or shapes in another coordinate system, while preserving certain properties such as size, shape, orientation, and distance.

Starting with the triangle on a graph with vertices at (-4, 4), (-4, 1), and (-2, 1), we can apply the given transformations as follows:

Go right 1 and down 5: This transformation corresponds to the function T(x, y) = (x + 1, y - 5). Applying this function to each vertex of the triangle, we get:

(-4, 4) -> (-3, -1)

(-4, 1) -> (-3, -4)

(-2, 1) -> (-1, -4)

Reflect on the y-axis: This transformation corresponds to the function R(x, y) = (-x, y). Applying this function to each vertex of the transformed triangle, we get:

(-3, -1) -> (3, -1)

(-3, -4) -> (3, -4)

(-1, -4) -> (1, -4)

Therefore, the final triangle has vertices at (3, -1), (3, -4), and (1, -4) on the graph.

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Answer:

2a + 3b - 6bc + c

Step-by-step explanation:

For our terms, we will use a, b, c, and bc terms.

Now, here is what I came up with.

[tex]2a+3b-6bc+c[/tex]

Step-by-step explanation:

"The difference of twice of a # and 10 is  = to 12

We're gonna do this like statement reason because I don't want to write a paragraph lol

2x-10=12             Given

2x=24                 Simplify (+10 to each side cancels on left, adds on the right)

x=12                    Simplify (divide by 2)

Yay!

Also if you have 2 chances maybe try -1? but I think 12 is right

Are angles C and D supplementary angles: B. No.

In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees. Mathematically, a supplementary angle can be calculated by using this mathematical equation:

C + D = 180

Where:

C and D are measure of the angles subtended.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of the given angles are not supplementary angles:

58 + 102 = 160° ≠ 180°

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Given that AB is a diameter. |BC| = |CD| and AÔD = 64°, The angles  of the quadrilateral ABCD is 90 degrees

Since |BC| = |CD|, we know that triangle BCD is an isosceles triangle.

Since triangle BCD is isosceles, angles BDC and CBD are equal. Let's call each of these angles x.

180 - 64

= 116 degrees

angle BCD = 180 - 116

= opposite angles in a cyclic quadrilateral are supplementary

116 + 64 + 2 OBC = 360

2 obc = 360 - 116 - 64

0bc = 180 / 2

= 90 degrees

Hence the angles  of the quadrilateral ABCD is 90 degrees

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Step-by-step explanation:

The third one is not      all of the others are

By answering the presented question, we may conclude that As a result, probability the chance of receiving heads and 4 is 1/12.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

Here is an example space diagram that depicts all of the possible outcomes when Leo flips a coin and rolls a dice:

Each row represents the outcome of rolling the dice, and each column indicates the outcome of flipping the coin. The table entries represent the combined outcome of rolling the dice and flipping the coin. For example, the occurrence of receiving heads on the coin flip and rolling a 1 on the dice is represented by the outcome in the top left corner (H1).

As a result, the chance of receiving heads and 4 is 1/12.

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Step-by-step explanation:

VOLUME of pyramid =   1/3  base area  * height

 Base area is a square = 3 x 3

                                   = 1/3 ( 3x3) * 16 = 48 in^3