Transformation that result in a change in the size of a figure are called ____.

Answers

Answer 1

Answer:

Transformation that result in a change in the size of a figure are called dilations.


Related Questions

Find the CIRCUMFERENCE of the circle.

Answers

Answer:

C=2πr

Step-by-step explanation:

Its on the wall of my math class

Mel uses one fourth of a yard of ribbon to make a hair bow how many hair bows can mel make with 1 yard of ribbon​

Answers

Answer:

4

Step-by-step explanation:

If its 1/4 then you can use it 4 times to equal a whole yard

Just need a quick reminder, I have a question asking write the expression using exponents. The expression is 12x12x12x12, what would I do here? I've forgotten

Answers

Answer:

the answer is \(12^{4}\)

Step-by-step explanation:

basically how many there are, you just put that in the top right

Answer:

20,736

Step-by-step explanation:

12x12x12x12

= 12^4

=20,736

Given the Characters A,B,C,H,I,T,U,V,1,2,3 and 4, how many seven-character passwords can be made? (no repeats are allowed.) How many if you have to us all four numbers as the first four characters in the password?

Answers

The total number of seven-character passwords that can be made with the given characters without repeats is 10,200.

This is calculated by finding the number of ways to choose the first character (11 options), then the second character (10 options), and so on until the seventh character (5 options), which gives 11x10x9x8x7x6x5 = 10,200.

If all four numbers have to be used as the first four characters in the password, then the number of possible passwords reduces to 2,400. This is calculated by finding the number of ways to choose the first four characters (4 options for each), then the remaining three characters (10 options for each), which gives 4x4x4x4x10x10x10 = 2,400.

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There are 4,387,810 possible seven-character passwords that can be made without repeats. If the first four characters must be the numbers 1, 2, 3, and 4, there are 6,720 possible passwords.

To calculate the total number of possible seven-character passwords without repeats, we use the formula for permutations: n! / (n-r)!, where n is the total number of characters and r is the number of characters in the password (in this case, 7). Using this formula, we get 10! / (10-7)! = 10 x 9 x 8 x 7 x 6 x 5 x 4 = 4,387,810.

If we must use the numbers 1, 2, 3, and 4 as the first four characters, we have 4! = 24 ways to arrange them. For the remaining three characters, we have 7 choices for each character (since we cannot repeat any of the previous four characters). Therefore, the total number of possible passwords is 24 x 7 x 7 x 7 = 6,720.

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Use the Squeeze Theorem to find lim f (1) given that 4 – -8

Answers

Using the Squeeze Theorem, we can find the limit of a function by comparing it with two other functions that have known limits. In this case, we are given that the limit of f(x) as x approaches 4 is -8. We can use the Squeeze Theorem to determine the limit of f(1) based on this information.

The Squeeze Theorem states that if we have three functions, f(x), g(x), and h(x), such that g(x) ≤ f(x) ≤ h(x) for all x in some interval containing a particular value a, and if the limits of g(x) and h(x) as x approaches a are both equal to L, then the limit of f(x) as x approaches a is also L.

In this case, we are given that the limit of f(x) as x approaches 4 is -8. Let's denote this as lim(x→4) f(x) = -8. We want to find lim(x→1) f(x), which represents the limit of f(x) as x approaches 1.

Since we are only given the limit of f(x) as x approaches 4, we need additional information or assumptions about the behavior of f(x) in order to use the Squeeze Theorem to find lim(x→1) f(x). Without more information about f(x) or the functions g(x) and h(x), we cannot determine the value of lim(x→1) f(x) using the Squeeze Theorem based solely on the given information.

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a parejas, resuelvan los siguientes problemas. En dos localidades hay habitantes que hablan una len- distinta al español: en El Cerrito son 3 de cada 4, mientras que en El Paseo son 5 de cada 7. gua a) ¿En cuál de las dos localidades hay un número ma- yor de hablantes de una lengua distinta al español? b) ¿De cuánto es la diferencia entre las dos localidades?​

Answers

The difference between the two localities is 1 speaker.

Let's solve the problems step by step:

a) To determine which of the two locations has a higher number of speakers of a language other than Spanish, we need to compare the ratios of speakers in El Cerrito and El Paseo.

In El Cerrito, 3 out of every 4 people speak a different language than Spanish. This can be written as a ratio: 3:4.

In El Paseo, 5 out of every 7 people speak a different language than Spanish. This can be written as a ratio: 5:7.

To compare the two ratios, we can find a common denominator. In this case, the least common multiple of 4 and 7 is 28.

In El Cerrito, the ratio becomes 21:28 (multiplying both sides by 7).

In El Paseo, the ratio becomes 20:28 (multiplying both sides by 4).

From the ratios, we can see that in El Cerrito, there are 21 out of 28 people who speak a different language than Spanish, while in El Paseo, there are 20 out of 28 people who speak a different language than Spanish.

Since 21 is greater than 20, El Cerrito has a higher number of speakers of a language other than Spanish.

b) The difference between the two localities can be calculated by subtracting the number of speakers in El Paseo from the number of speakers in El Cerrito.

In El Cerrito, there are 21 speakers of a different language than Spanish.

In El Paseo, there are 20 speakers of a different language than Spanish.

The difference is obtained by subtracting 20 from 21, resulting in a difference of 1 speaker.

Therefore, the difference between the two localities is 1 speaker.

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you are repeatedly flipping a fair coin. what is the expected number of flips until the first time that your previous 2012 flips are htht ...

Answers

The expected number of flips until the first time that your previous 2012 flips are HTHT is = 4096

According to the information given in the question,

A coin is flipped repeatedly until the first time that the previous flips are made in 2012 is HTHT.We have to find the expected number of flips made to get 2012 flips that are making HTHT.If we talk about a coin, a coin is having a 50 % probability to get either heads or tails.

Now to calculate the chances of getting HTHT for the first time will be,

E(x) = n × p

Where E(x) = the expected number of flips.

n = number of flips.

p = Probability of getting HTHT

Given,

n = 2012

p = ( \(\frac{1}{4096}\) )

E(x) = 4096

Therefore, the expected number of flips until the first time that your previous 2012 flips are HTHT is = 4096

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You are repeatedly flipping a fair coin. what is the expected number of flips until the first time that your previous 2012 flips are HTHT ...?you are repeatedly flipping a fair coin. what is the expected number of flips until the first time that your previous 2012 flips are HTHT ...?

In the Green Food System Strategy, the "vision to be achieved by 2050" (numerical targets) is presented. Select the number of the following targets that are correctly described.

-Chemical pesticide use (in terms of weight) will be reduced by 50% by 2050.

-With regard to chemical fertilizers, the use of chemical fertilizers produced in Japan from fossil fuels will be reduced by 30% by 2050.

-Regarding organic agriculture, expand the organic market and increase the ratio of organic farming to arable land to 30% (1 million hectares) by 2050.

-Regarding food loss, reduce household food loss by half from the FY2000 level by 2030.

a. 0 b. 1 c. 2 d. 3 or more

Answers

Option c. 2

Among the given targets, two targets are correctly described:

Regarding chemical pesticide use, the target is to reduce it by 50% by 2050. This aligns with the vision presented in the Green Food System Strategy.

In terms of chemical fertilizers, the target is to reduce the use of chemical fertilizers produced in Japan from fossil fuels by 30% by 2050. This target is also consistent with the strategy's vision.

The remaining two targets are not correctly described:

The target of expanding the organic market and increasing the ratio of organic farming to arable land to 30% (1 million hectares) by 2050 is not mentioned in the given options.

The target of reducing household food loss by half from the FY2000 level by 2030 is also not mentioned in the given options.

Therefore, the correct answer is option c. 2, as two of the targets are accurately described in the provided options.

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Help on math question precalculus math The graph has a vertical asymptote.Group of answer choices-True-False

Help on math question precalculus math The graph has a vertical asymptote.Group of answer choices-True-False

Answers

Recall that a vertical asymptote is a vertical line near which the function grows (or decreases) without bound.

Example:

From the given graph, we get that the graph does not have a vertical asymptote.

Answer: False.

Help on math question precalculus math The graph has a vertical asymptote.Group of answer choices-True-False

three ratios that are equivalent to 5:25:25, colon, 2.

Answers

Answer:

7 11 27

Step-by-step explanation:

i did the problem before

28. How do cyclic redundancy checks work?

Answers

Cyclic redundancy checks work by using a generator polynomial to calculate a unique value (CRC) based on the original data. This value is then appended to the data and verified by the receiver to ensure data integrity.

Cyclic Redundancy Checks (CRC) work as an error-detecting method used to ensure data integrity during transmission or storage. The process involves the following steps:

1. A predetermined polynomial (called the generator polynomial) is chosen for the CRC algorithm.

2. Before transmitting data, the sender divides the original data by the generator polynomial, using binary division.

3. The remainder obtained from the division is treated as the CRC value.

4. The sender appends the CRC value to the end of the original data, forming the transmitted message.

5. The receiver, upon receiving the message, performs the same binary division using the same generator polynomial.

6. If the remainder from the receiver's division matches the CRC value sent by the sender, it is assumed that the data is error-free.

7. If the remainder does not match, the receiver knows that an error occurred during transmission and can request the sender to retransmit the data.

In summary, cyclic redundancy checks work by using a generator polynomial to calculate a unique value (CRC) based on the original data. This value is then appended to the data and verified by the receiver to ensure data integrity.

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Formative REDO
1. Find the slope and y-intercept from the equation: y = -2x + 7
b=_
m=
2. Find the slope and y-intercept from the graph:
b=
m=

Answers

The equation in the problem is in slope intercept form. The slope-intercept form of a linear equation is: y = mx + b

What is meant by slope?

Slope is a numerical representation of how inclined a line is with respect to the horizontal. The slope of any line, ray, or line segment in analytical geometry is defined as the ratio of the vertical to the horizontal distance between any two points on the line, ray, or segment.A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change.The foundation of differential calculus is the idea of a slope. The rate of change for non-linear functions varies along the curve.Both the slope and the y intercept can have a positive or negative value. Slope is defined as the y-axis divided by the x-axis.

The slope-intercept form of a linear equation is: y = mx + b

Where m is the slope and b is the y-intercept value.

Therefore, for this equation y = -2x - 7

The Slope is: m = -2

The Y=Intercept is b = -7 (or)

slope and y-intercept from the graph: (0, -7)

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A boat travels 196 miles in 12 hours (with a constant speed). How much time will it take traveling 427 miles?

Answers

26 hours and 9 ish minutes. Just put 26 Hours

two angles that add up to 90 degrees are called ________ angles.

Answers

Answer: Right/complementary angles

Step-by-step explanation:

Two angles that add up to 90 degrees are called complementary angles.

Complementary angles are a pair of angles that, when added together, equal a right angle, which measures 90 degrees.

In other words, the sum of the measures of complementary angles is always 90 degrees.

Complementary angles often arise in geometry and trigonometry, and understanding their properties is important when working with angles and solving problems involving right triangles.

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a collection of nickels, dimes, and quarters consist of 70 coins with a total of $ 8.00 . if there are 2 times as many dimes as quarters, find the number of each type of coins.

Answers

The number of each type of coins are as follows:

q = 15 quarters.

d = 30 dimes.

n = 25 nickels.

How to determine the number of each type of coins?

In order to solve this word problem, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Let d represent the number of dimes.

Let q represent number of quarters.

Let n represent number of nickels.

Let T represent total number of coins.

Note: 1 quarter is equal to 0.25 dollar, 1 nickel is equal to 0.5 dollar, and 1 dime is equal to 0.1 dollar.

Translating the word problem into an algebraic equation, we have;

Dimes; d = 2q     .....equation 1.

Nickels; (70 - (q + 2q)) = (70 - 3q)     .....equation 2.

Total coins; T = n + d + q

0.5(70 - 3q) + 2q(0.1) + q(0.25) = 8.00

Multiplying all through by 100, we have:

5(70 - 3q) + 2q(10) + q(25) = 800

350 - 15q + 20q + 25q = 800

350 + 30q = 800

30q = 800 - 350

30q = 450

q = 450/30

q = 15 quarters.

For the number of dimes, we have:

Dimes, d = 2q

Dimes, d = 2(15)

Dimes, d = 30 dimes.

For the number of nickels, we have:

Nickels, n = (70 - 3q)

Nickels, n = (70 - 3(15))

Nickels, n = (70 - 45)

Nickels, n = 25 nickels.

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Consider the problem of finding a plane αTx=β (i.e. α1​x1​+α2​x2​+α3​x3​+α4​x4​=β with α=(0,0,0,0)) that separates the following two sets S1​ and S2​ of points (some points from S1​ and S2​ might lie on the plane αTx=β) : S1​={(1,2,1,−1),(3,1,−3,0),(2,−1,−2​,1),(7,−2,−2,−2)}, S2​={(1,−2,3,2​),(−2,π,2,0),(4,1,2,−π),(1,1,1,1)}. 1.1 Formulate the problem as a linear optimization problem (LO). 3p 1.2 Find a feasible solution (α,β) for (LO) if it exists, or show that no feasible solution exists. 2p

Answers

All the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

To formulate the problem as a linear optimization problem (LO), we can introduce slack variables to represent the signed distances of the points from the plane αTx = β. Let's denote the slack variables as y_i for points in S1 and z_i for points in S2.

1.1 Formulation:

The problem can be formulated as follows:

Minimize: 0 (since it is a feasibility problem)

Subject to:

α1x1 + α2x2 + α3x3 + α4x4 - β ≥ 1 for (x1, x2, x3, x4) in S1

α1x1 + α2x2 + α3x3 + α4x4 - β ≤ -1 for (x1, x2, x3, x4) in S2

α1, α2, α3, α4 are unrestricted

β is unrestricted

y_i ≥ 0 for all points in S1

z_i ≥ 0 for all points in S2

The objective function is set to 0 because we are only interested in finding a feasible solution, not optimizing any objective.

1.2 Finding a feasible solution:

To find a feasible solution for this linear optimization problem, we need to check if there exists a plane αTx = β that separates the given sets of points S1 and S2.

Let's set α = (1, 0, 0, 0) and β = 0. We choose α to have a non-zero value for the first component to satisfy α ≠ (0, 0, 0, 0) as required.

For S1:

(1, 2, 1, -1) - 0 = 3 ≥ 1, feasible

(3, 1, -3, 0) - 0 = 4 ≥ 1, feasible

(2, -1, -2, 1) - 0 = 0 ≥ 1, not feasible

(7, -2, -2, -2) - 0 = 3 ≥ 1, feasible

For S2:

(1, -2, 3, 2) - 0 = 4 ≥ 1, feasible

(-2, π, 2, 0) - 0 = -2 ≤ -1, feasible

(4, 1, 2, -π) - 0 = 5 ≥ 1, feasible

(1, 1, 1, 1) - 0 = 4 ≥ 1, feasible

Since all the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

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A random sample of 64 sat scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. the 95onfidence interval for the population mean sat score is: ________
a. 1.96. b. 1.998.
c. 1.645. d. 1.28.

Answers

The 95% confidence interval for the population mean SAT score is given as follows:

(1340, 1460).

How to calculate the confidence interval?

The confidence interval is calculated using the t-distribution, as the standard deviation for the population is not known, only for the sample.

The bounds are obtained according to the equation defined as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

In which the variables of the equation are presented as follows:

\(\overline{x}\) is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.

In the context of this problem, the values of these parameters are given as follows:

\(\overline{x} = 1400, n = 64, s = 240\)

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 64 - 1 = 63 df, is t = 1.998.

Then the lower bound of the interval is of:

1400 - 1.998 x 240/sqrt(64) = 1340.

The upper bound of the interval is of:

1400 + 1.998 x 240/sqrt(64) = 1460.

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Write an equation for a line with a slope of 3 and crosses the y-axis at the orgin.

Answers

y=3x is the equation

Find the value of r, if P(5, r) = 2P(6, r-1)

answer choices:

a. 3

b. 5

c. 8

d. 11

Answers

The value of r in permutation P(5, r) = 2P(6, r-1) is 11.  So, option d) is correct.

We know that the formula for the permutation of r objects taken from n distinct objects is P(n, r) = n! / (n-r)!. Using this formula, we can rewrite the given equation as:

5! / (5-r)! = 2 * 6! / (6-r+1)!

Simplifying this equation, we get:

5! / (5-r)! = 2 * 6! / (7-r)!

(5-r)! / 5! = (7-r)! / (2 * 6!)

(5-r)! / 5! = (7-r)! / 12

Since 5! = 120, we can simplify the left-hand side to:

(5-r)! / 120 = (7-r)! / 12

Multiplying both sides by 12, we get:

(5-r)! / 10 = (7-r)!

Multiplying both sides by 10, we get:

(5-r)! = 10 * (7-r)!

We can now manually try different values of r until we find one that satisfies the equation. Trying r = 3, we get:

(5-3)! = 10 * (7-3)!

2! = 10 * 4!

2 = 240

Since this is a contradiction, we can eliminate option (a) from the answer choices. Trying r = 5, we get:

(5-5)! = 10 * (7-5)!

1 = 20

Again, this is a contradiction, so we can eliminate option (b) from the answer choices. Trying r = 8, we get:

(5-8)! = 10 * (7-8)!

(-3)! = -10

Since the factorial of a negative number is undefined, this is not a valid solution, so we can eliminate option (c) from the answer choices. Therefore, the correct answer is (d) 11. Trying r = 11, we get:

(5-11)! = 10 * (7-11)!

(-6)! = 10 / 24

Simplifying the right-hand side, we get:

(-6)! = 5 / 12

Since the left-hand side is undefined for negative integers, we can eliminate this solution. Therefore, the only valid solution is r = 11, which we can confirm by checking that both sides of the equation are equal when r = 11. So, the correct answer is option (d).

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An isosceles triangle had two base angles equal to 13 degrees. What is the measure of the third angle?

Answers

The measure of the third angle of the isosceles triangle is θ = 154°

Given data ,

In an isosceles triangle, two sides are of equal length, and thus two base angles are also of equal measure.

Given that the two base angles of the isosceles triangle are both 13 degrees, we can denote one of the base angles as 13 degrees, and the other base angle as 13 degrees as well.

Let's denote the measure of the third angle as "x" degrees

The sum of angles in any triangle is always 180 degrees.

So , 13 + 13 + x = 180

Simplifying the equation:

26 + x = 180

Subtracting 26 from both sides of the equation:

x = 180 - 26

x = 154°

Hence , the measure of the third angle in the isosceles triangle is 154°

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I need this answer TODAY
A triangle has one side that measures x, and the other two sides each measure 4 Inches less than x. The perimeter is 19
Inches.
What is the measure of x?
5
3
9
2

Answers

Answer:3

Step-by-step explanation: the closest multiple of for is 16 then reminder 3

Answer:

9

Step-by-step explanation:

one side of a triangle =x

the other two sides measure = (x-4) each

perimeter = 19

therefore :

perimeter of a triangle = x + (x-4) + (x-4)

I.e = x+x+x-4-4=19

= 3x -8=19

= 3x = 19+8

3x=27

divide both sides by 3

x=9

Sindhu successfully solved the system of equations
3x + y = 9 and
- 2x - y = -7
Which of these statements could correctly descirbe what she did?

*optional but explain what makes it correct

Sindhu successfully solved the system of equations3x + y = 9 and - 2x - y = -7 Which of these statements

Answers

Step-by-step explanation:

when we add the 2 equations

3x + y = 9

-2x - y = -7

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

x + 0 = 2

we see, x = 2. as we solved for x.

then using this e.g. in the first equation

3×2 + y = 9

6 + y = 9

y = 3

so, the first answer is correct.

Find the quotient,
(24-31 - 612 + 11x + 8) + (1-2)
o 2% -12 + B7 -5 + 224 225
o 2% + 2 - 4x + 3 + 24 h
o 4 + 2x² - 2x + F + 24 h
O 4*? - 147+ + 167 – 10+

Answers

Answer:

124922593425

Step-by-step explanation:

if u do the probblem u get dis

Please help me in this question.I need it right now!!!

Please help me in this question.I need it right now!!!

Answers

Answer:

X=102 y=288 =390

Step-by-step explanation:

X=50+32=82=180-82=102

Y= 50+32=82=360-82=288

Total answer is =390

Liesa wants to put grass seeds on her rectangular shaped backyard. She measured her backyard as 80 feet long by 54 feet wide. How many square yards of grass seed will Liesa put down?

Answers

The area of the rectangular backyard  where Liesa will put down the grass seed is equal to 480 square yards.

Shape of the backyard is rectangular.

length of the rectangular backyard is equal to 80 feet

Width of the rectangular backyard is equal to 54 feet.

Area of Liesa's backyard in square feet is,

Area of the rectangular backyard = Length x Width

Substitute the values we have,

⇒Area of the rectangular backyard = 80 feet x 54 feet

⇒Area of the rectangular backyard = 4,320 square feet

Now, convert square feet to square yards,

Divide by the number of square feet in one square yard.

3 feet = one yard,

⇒ one square yard =  3 x 3

⇒ one square yard = 9 square feet.

Convert square feet to square yards, divide by 9.

Area in square yards = Area in square feet / 9

⇒Area in square yards = 4,320 square feet / 9

⇒Area in square yards = 480 square yards

Therefore, area where the Liesa will need to put down 480 square yards of grass seed in her backyard.

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what is the projection of (4 4) onto (3 1)

Answers

The projection of the point (4,4) onto the line passing through (3,1) is the point on the line that is closest to (4,4). To find this projection, we need to first find the direction vector of the line, which is (3-1, 1-0) = (2,1).

Next, we need to find the vector from the point (3,1) to the point (4,4), which is (4-3, 4-1) = (1,3).

Then, we can use the formula for projecting a vector onto another vector:

proj_v u = ((u · v) / (v · v)) v

where u is the vector we want to project, v is the vector we want to project onto, and · denotes the dot product.

Applying this formula, we get:

proj_v u = ((1,3) · (2,1)) / ((2,1) · (2,1)) (2,1)

= (5/5) (2,1)

= (2,1)

So the projection of (4,4) onto the line passing through (3,1) is the point (3,1) + (2,1) = (5,2).

To find the projection of vector (4, 4) onto vector (3, 1), you can follow these steps:

Step 1: Calculate the dot product of the two vectors.
Dot product = (4 * 3) + (4 * 1) = 12 + 4 = 16

Step 2: Calculate the magnitude squared of the vector you are projecting onto (3, 1).
Magnitude squared = (3 * 3) + (1 * 1) = 9 + 1 = 10

Step 3: Divide the dot product by the magnitude squared.
Scalar = 16 / 10 = 1.6

Step 4: Multiply the scalar by the vector you are projecting onto (3, 1) to find the projection.
Projection = 1.6 * (3, 1) = (4.8, 1.6)

So, the projection of (4, 4) onto (3, 1) is (4.8, 1.6).

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in a(n) choose... sequence, the difference between every pair of consecutive terms in the sequence is the same.

Answers

In an arithmetic sequence, the difference between every pair of consecutive terms in the sequence is the same.

How to solve an arithmetic sequence?

The general formula for the nth term of an arithmetic sequence is:

aₙ = a + (n - 1)d

where:

a is first term

n is position of term

d is common difference

Thus, we see that the difference between consecutive terms is always the same as common difference.

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Solve the absolute value equation, [x] – 2 = 5.​

Answers

Well to solve this you want to keep in mind that 2=-2 bc absolute value mean what oh yeah |-2| = 2 so you have to remember that and if you want this to work it would be 7-2=5

Answer:

x=7

Step-by-step explanation:

Ok so first off, the x variable being in absolute value form will not change the outcome of the problem at all since there are no other x variables in the equation.

x-2=5

(add 2 on both sides)

x=7

A public Interest group conducts a poll of 750 Randomly selected American households and finds that 67% of those surveyed have at least one dog.
a) construct and interpret a 90% confidence interval for the proportion of all American households who have at least one dog.
b) Explain what is meant by 90% confidence in this context

Answers

a. The 90% confidence interval for the proportion of all American households who have at least one dog is (0.636, 0.704). This means we can be 90% confident that the true proportion of all American households who have at least one dog lies within this range.

b. The 90% confidence means that if we were to repeat this poll many times with different samples of American households, we would expect 90% of the resulting confidence intervals to contain the true proportion of all American households who have at least one dog

a) To construct a 90% confidence interval for the proportion of all American households who have at least one dog, we can use the following formula:

CI = p ± zsqrt((p(1-p))/n)

where:

CI is the confidence interval

p is the sample proportion (67% or 0.67 in decimal form)

z is the z-score corresponding to the level of confidence (90% or 1.645 for a one-tailed test)

n is the sample size (750)

Plugging in the values, we get:

CI = 0.67 ± 1.645sqrt((0.67(1-0.67))/750)

CI = 0.67 ± 0.034

Therefore, the 90% confidence interval for the proportion of all American households who have at least one dog is (0.636, 0.704). This means we can be 90% confident that the true proportion of all American households who have at least one dog lies within this range.

b) In this context, 90% confidence means that if we were to repeat this poll many times with different samples of American households, we would expect 90% of the resulting confidence intervals to contain the true proportion of all American households who have at least one dog.

In other words, we can be reasonably sure that our sample proportion of 67% is a good estimate of the true proportion, with a margin of error of about 3.4 percentage points, based on the sample size and the level of confidence we have chosen.

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A cube has a volume of 197 meters cubed (197 m3) What is the approximate value of one edge of the cube? The approximate value of one edge of the cube is meters. Round your answer to the nearest hundredth. What is the approximate area of one face of the cube? The approximate area of one face of the cube is meters. Round your answer to the nearest hundredth.

Answers

The edge length and area of the face of the cube are 5. 82 meters and 203 square meters respectively

How to determine the value

The formuka for the volume of a cube is expressed as;

Volume = a^3

Where 'a' is the length of it's edge

From the information given, we have that the volume of the cube has a value of 197 cubic meters.

Now, substitute the value of the volume

We have;

197 = a^3

Take the cube root of both sides

a = 5. 82 meters

The formula for area of the face of a cube is given as;

Area = 6a ^2

Area = 6(5.82)^2

Area = 6(33. 85)

Area = 203 square meters

Thus, the edge length and area of the face of the cube are 5. 82 meters and 203 square meters respectively

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