Which proportion could be used to solve forx?
Group of answer choices

The sequence follows a difference of 9.

The margin of error of a study showed that 387 out of 900 people eat fast food regularly. We want to construct a 90% confidence interval for the population proportion of people who east fast food is   0.0234.The correct answer is option b. 0.0234.

To find the margin of error for a 90% confidence interval, we can use the formula:

Margin of error = z*√(p*(1-p)/n)

Where z is the z-score for a 90% confidence level, p is the sample proportion, and n is the sample size.

In this case, the z-score for a 90% confidence level is 1.645, the sample proportion is 387/900 = 0.43, and the sample size is 900.

Plugging these values into the formula, we get:

Margin of error = 1.645*√(0.43*(1-0.43)/900)

Margin of error = 0.0234

Therefore, the margin of error for the 90% confidence interval is 0.0234. Answer is b. 0.0234

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The time taken to read 3 books is 8 weeks.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Christian read 1/4 book every 2/3 week.

Time taken to read 1 complete book is

1 × 2/3 ÷ 1/4

= 2/3 ÷ 1/4

= 2/3 × 4/1 (To divide two fractions, keep the first fraction same and change division to multiplication and inverse the second fraction)

= 8/3

Now, time taken to read 3 complete is

= 8/3 ×3

= 8

Therefore, time taken to read 3 books is 8 weeks.

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Answer:

Step-by-step explanation:

I'm guessing you meant to say Lewis had $30 starting.

Well since we have an inequality already, that saves time on me and I can show you how to solve!

[tex]30+11w\geq 89.99[/tex]

[tex]11w\geq59.99[/tex]

[tex]w\geq 5.4536[/tex]

If Lewis waited 5 weeks, he'd only have 85, so we need to round up to 6 weeks, where he'd have $96. Hope this helps!

The smallest number among the given options is 0.125.

To determine the smallest number, we can compare each of the given numbers.

0.625 > 0.25 > 0.375 > 0.5 > 0.125

As we can see, the smallest number is 0.125, which is option E.

Comparison symbols are those that tell us whether one number is greater than, less than, or equal to another. The symbols are:

To sort in descending order, you must first place the number with the largest denomination until you reach the number with the smallest denomination.

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Assuming the number of people who listen to the video increases by 45% each day, there would be approximately 24 new people who listen to the video on the 7th day after the initial 8 people.

According to the problem, the number of people listening to the video increases by 45% each day. Therefore, we can use the formula for compound interest to calculate the number of new people who listen to the video on the 7th day.

Let P be the initial number of people who listened to the video, which is 8.

Let r be the daily increase rate, which is 45% or 0.45 as a decimal.

Let n be the number of days, which is 7.

Then, the formula for compound interest is:

A = P(1 + r)^n

where A is the final number of people who listen to the video.

Plugging in the values, we get:

A = 8(1 + 0.45)^7

A ≈ 32

Therefore, the number of new people who listen to the video on the 7th day is approximately 32 - 8 = 24 people.

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According to the information, ball B is the one that reaches the highest height because after 1.5 seconds it has a height of 13m, while ball A has a height of 12m.

To identify the ball that reaches the highest we must solve the function shown. Additionally, to know what is the greatest height we must replace the value of x by 1.5 as shown below:

According to the above we can infer that this function gives a height less than the one shown in the table because the height of the ball is 12 and that of the table is 13. So 12 < 13.

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Answer:

Step-by-step explanation:

If the surface area of a cube is 160 in2, then which best describes the length of an edge of the cube?

The sum of two rational expressions with unlike denominators is 1/(x+1) + 1/(x+2).

To split the given rational expression into a sum of two rational expressions with unlike denominators, we will use the partial fraction decomposition method. Here are the steps:

1. Factor the denominator of the given rational expression: (x^(2)+3x+2) = (x+1)(x+2)
2. Set up the partial fraction decomposition: (2x+3)/(x+1)(x+2) = A/(x+1) + B/(x+2)
3. Multiply both sides of the equation by the common denominator to get rid of the denominators: 2x+3 = A(x+2) + B(x+1)
4. Set up a system of equations by equating the coefficients of the like terms: 2x+3 = (A+B)x + (2A+B)
5. Solve the system of equations to find the values of A and B: A=1, B=1
6. Substitute the values of A and B back into the partial fraction decomposition: (2x+3)/(x+1)(x+2) = 1/(x+1) + 1/(x+2)

Therefore, the sum of two rational expressions with unlike denominators is 1/(x+1) + 1/(x+2).

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The requried measure of the angle x in at the point of intersection of tangent and secant of the circle is 30°.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

Where h, k is the coordinate of the center of the circle on a coordinate plane and r is the radius of the circle.

Here,
From the figure the,
From a point, a tangent and a secant are drawn to the circle.
Since an equilateral triangle is formed with the help of a cord intersects the tangent and secant on the circumference of triangle.

Again from the figure, the sum of the angle in the triangle is equal to 180°.
90 - 60 + 180 - 60 + x = 180
30 + 120 + x = 180
x = 30°

Thus, the requried measure of the angle x at the point of intersection of tangent and secant of the circle is 30°.

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The angular speed of the pulley in rad/sec is 7.95 rad/sec, and the linear speed of the chain in cm/sec is 495.6 cm/sec.

First, we need to convert the pulley's rotational speed from RPM (revolutions per minute) to rad/s (radians per second). To do this, we can use the formula:

angular speed (in rad/s) = 2π × rotational speed (in RPM) / 60

Substituting the given values, we get:

angular speed (in rad/s) = 2π × 38 / 60 = 7.95 rad/s

Next, we can use the formula for linear speed of a point on the circumference of a circle:

linear speed = radius × angular speed

Substituting the values we have, we get:

linear speed = 26 cm × 7.95 rad/s = 206.7 cm/s

However, this is the linear speed of the pulley's circumference. Since the chain is attached to the pulley, its linear speed will be the same as the pulley's linear speed. Thus, the final answer for the linear speed of the chain is:

linear speed of chain = 206.7 cm/s × 2.4 = 495.6 cm/s

Here, 2.4 is the gear ratio of the chain to pulley.

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Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

First off, we need to remember that the arc measure is equal to the angle measure inside the circle. That means m(arc) MN is 70 degrees. Knowing this, we can find the measures of the other arcs:

m(arc)NP = 180 - 70 - 30 = 80

m(arc)QR = 70 based on vertical angles principle

m(arc)MR = 80+30 = 110 based on vertical angles and angle sum principles

Now we can list the answers using this:

1. 70

2. 70

3. 180

4. 210

5. 110

6. 110

Hope this helps!

Answer:D

Step-by-step explanation:

It’s D because 18 chocolate chip muffins and there are 9 blueberry muffins so for every blueberry muffin there is 2 chocolate chip muffins you could also do 18/9 and 2

Answer: ∠ABC = 29.745°

Step-by-step explanation:

I believe this is the answer , you should be golden.

Answer:

no se     y ademas me aparece en ingles :(

Step-by-step explanation:

S1, S2 ⊂ V are two sets of vectors which are each linearly independent, then S1 ∩ S2 is also linearly independent.

Let S1, S2 ⊂ V be two sets of vectors which are each linearly independent. To show that S1 ∩ S2 is linearly independent, we need to show that any linear combination of vectors in S1 ∩ S2 is equal to the zero vector only if all the coefficients are zero.

Let v1, v2, ..., vn be the vectors in S1 ∩ S2 and let a1, a2, ..., an be the coefficients in the linear combination a1v1 + a2v2 + ... + anvn = 0.

Since v1, v2, ..., vn are in S1 ∩ S2, they are also in S1 and S2. Therefore, the linear combination a1v1 + a2v2 + ... + anvn = 0 is also a linear combination of vectors in S1 and S2.

Since S1 and S2 are both linearly independent, this means that all the coefficients a1, a2, ..., an must be zero. Therefore, S1 ∩ S2 is also linearly independent.

In conclusion, if S1, S2 ⊂ V are two sets of vectors which are each linearly independent, then S1 ∩ S2 is also linearly independent.

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product of diagonal elements is 10 x -2 = -20.

To find the value of the determinant of the coefficient matrix, perform row operations to reduce it to an echelon form. First, multiply the first row by -3, the second row by 5, and the third row by 2. This yields the following matrix:

(-9)x + (0)y - 18z = -33

(25)x - 10y + 15z = 85

(4)x - (2)y - 14z = -6

Next, subtract the first row from the second row and the first row from the third row. This yields the following matrix:

(0)x + (10)y - (18)z = 52

(4)x - (2)y - (14)z = -6

Finally, subtract 4 times the second row from the third row. This yields the following matrix:

(0)x + (10)y - (18)z = 52

(0)x - (0)y - (2)z = -24

This matrix is in echelon form. The value of the determinant is simply the product of diagonal elements, which is 10 x -2 = -20.

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The coordinates of the other endpoint, Q, are (3,-8).

The midpoint formula is used to find the coordinates of the midpoint of a line segment. The formula is as follows:
M = ((x1+x2)/2, (y1+y2)/2)

In this case, the midpoint M=(1,-2) and one endpoint P=(-1,4) are given. We can plug these values into the formula to find the coordinates of the other endpoint, Q:
(1,-2) = ((-1+x2)/2, (4+y2)/2)

Solving for x2 and y2, we get:
x2 = 2(1) + 1 = 3
y2 = 2(-2) - 4 = -8

Therefore, the coordinates of the other endpoint, Q, are (3,-8).

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The correct option is For every 2 white marbles, Hal has 3 black marbles​.

The size, number, or amount of one thing or group as compared to the size, number, or amount of another, is called proportion.

A proportion is a mathematical comparison between two numbers. Often, these numbers can represent a comparison between things or people.

Proportion is an equation that defines that the two given ratios are equivalent to each other.

Proportions are actually equations with equal ratios.

A proportion or proportional situation occurs when two things are related in such a way that the ratios of corresponding parts are equal.

Given that, Hal compared the number of black marbles he had to the number of white marbles he had.

Number of black marble = 9

Number of white marble = 2

The proportion is 9 /2

= 3/2

Hence, the correct option is For every 2 white marbles, Hal has 3 black marbles​.

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The actual distance between City C and City D is 4,224,000 feet.

What is total distance?

Whole distance refers to the actual travel distance between the origin and destination locations of the item.

We can use the given scale to convert the distance between City A and City B to feet:

500 miles = 500 * 5280 feet = 2,640,000 feet

Since 1.6 feet represents this distance on the wall map, we have:

1.6 feet = 2,640,000 feet / x

where x is the actual distance represented by 1.6 feet on the map. Solving for x, we get:

x = 2,640,000 feet / 1.6 feet = 1,650,000 feet per foot

Therefore, the  total distance between City C and City D, which is 2.56 feet on the map, corresponds to:

2.56 feet * 1,650,000 feet per foot = 4,224,000 feet

So the actual distance between City C and City D is 4,224,000 feet.

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Y = 4114/5114

3 (a) To solve 2557⋅X=457 for X∈Z57 using Euclid's algorithm, take the GCD of 2557 and 457. That is, the GCD is:

GCD(2557, 457) = GCD(2557 - 457, 457)

                  = GCD(2157, 457)

                  = GCD(757, 457)

                  = GCD(357, 457)

                  = GCD(157, 457)

                  = 457


Therefore, the GCD of 2557 and 457 is 457, and thus the solution to the equation is X = 457/2557.

3 (b) To find all solutions to the equation 50114⋅Y=8114 for Y∈Z114, we need to rewrite the equation in terms of ordinary integers, since the inverse of 50114 does not exist. The equation can be rewritten as Y = 8114/50114 = 8114/(5114⋅2114) = 4114/5114. This equation is the same as the one in part (a), with 25 replaced by 5. Thus, the solution to this equation is Y = 4114/5114, which is the same solution found in part (a). Therefore, there is only one solution to this equation, and this solution is Y = 4114/5114.

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Two pairs of consecutive interior angles are ∠5 and ∠9; ∠6 and ∠7.

The correct option is C,

When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles.

The pair of non-adjacent internal angles that are located on the same side of the transversal are referred to as consecutive interior angles. On the internal side of a transversal, two consecutive interior angles are situated adjacent to one another. To recognize them, the characteristics of successive inner angles.

Thus, only one pair of the angle from the options is satisfying the third and fourth characteristics. So, the correct option is C) ∠5 and ∠9; ∠6 and ∠7.

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The graph of the inequality y ≥ (1/2)x - 1 and x - y > 1 is attached. Shannon's graph is correct.

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Inequalities are used for the non equal comparison of numbers and variables.

Given the inequalities:

y ≥ (1/2)x - 1     (1)

and

x - y > 1     (2)

The graph of the inequality is attached. Shannon's graph is correct.

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The projected number of people affected by Alzheimer's Disease at t=20 is 6.7336.

The projected number of people affected by Alzheimer's Disease can be found by plugging in the value of t into the given equation P(t)=-0.0002083(20)^(3)+0.0142(20)^(2)-0.099(20)+4.7.

Plug in the value of t=20 into the equation:
P(20)=-0.0002083(20)^(3)+0.0142(20)^(2)-0.099(20)+4.7

Simplify the equation by solving the exponents and multiplying the coefficients:
P(20)=-0.0002083(8000)+0.0142(400)-1.98+4.7

Simplify the equation further by performing the arithmetic operations:
P(20)=-1.6664+5.68+2.72

Simplify the equation to get the final answer:
P(20)=6.7336
Therefore, the projected number of people affected by Alzheimer's Disease at t=20 is 6.7336.

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p(t) = {

P35.00 if t ≤ 2

P35.00 + P15.00 × (t - 2) if 2 < t ≤ 12

P250.00 if t > 12

} is the required function to represent given information.

Expressions are commonly used in programming to perform calculations, manipulate data, and make decisions based on the results of evaluations.

To represent the parking fee using the function p(t), we need to consider the different rates depending on the number of hours parked. Here are the different cases we need to consider:

If t ≤ 2, the parking fee is P35.00

If 2 < t ≤ 12, the parking fee is P35.00 plus P15.00 for each hour (or fraction of it) after the first two hours. This can be represented by the equation:

p(t) = P35.00 + P15.00 × (t - 2)

If t > 12, the parking fee is a flat rate of P250.00.

We can combine these cases into a single function using a piecewise function. Here is the function p(t):

p(t) = {

P35.00 if t ≤ 2

P35.00 + P15.00 × (t - 2) if 2 < t ≤ 12

P250.00 if t > 12

}

This function represents the parking fee in terms of the number of hours parked (t). To use it, simply substitute the number of hours parked into the function and calculate the resulting fee. For example, if you parked for 4 hours, the fee would be:

p(4) = P35.00 + P15.00 × (4 - 2) = P65.00

Therefore, p(t) = {

P35.00 if t ≤ 2

P35.00 + P15.00 × (t - 2) if 2 < t ≤ 12

P250.00 if t > 12

} is the required function to represent given information.

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The value of perimeter of CAR is  12 + 6√2 + 6√3. (C)

The value of the perimeter of triangle CAR can be found by adding the lengths of all three sides of the triangle.

In this case, the perimeter would be the sum of side CA, side AR, and side CR.

To find the perimeter, we can use the formula P = CA + AR + CR.

If we plug in the given values for each side, we can solve for the perimeter:

P = 6 + 6√2 + 6√3

P = 12 + 6√2 + 6√3

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Both numbers are divisible by 2, 2 and 7.

What is Greatest Common Factor?

The greatest common factor (GCF) is the largest number that divides two or more numbers evenly. It is also known as the greatest common divisor (GCD) or highest common factor (HCF).

If 28 is the greatest common factor of two numbers, it means that both numbers have 28 as a factor. Thus, both numbers are divisible by 2, 2 and 7.

Additionally, the prime factorization of each number must contain all of the prime factors that are factors of 28, which are 2 and 7. However, there may be other prime factors as well. Without additional information, it is not possible to determine the complete prime factorization of each number.

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The Correct statement is

ST and KT intersect at 90 degree.

The basic qualities listed below make it simple to identify parallel lines.

Parallel lines are defined as straight lines that are always the same distance apart.

Parallel lines, no matter how far they are extended in either direction, never intersect.

Given:

We have given that ST || JK

First ST and JK have no perpendicular relation.

Now, ST and KT intersect at 90 degree.

Now, ST is not parallel to JT but it is given that ST || JK.

and, KT is act as transversal not JK.

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A valid inference is a conclusion that is true about the subject based on the evidence or premises provided.

Mathematically, we can represent a valid inference using logical notation. In the example above, we can use the following notation:

Premise 1: All humans are mortal.

Premise 2: Samantha is a human.

Conclusion: Samantha is mortal.

We can use the logical connective "if-then" to represent a valid inference. In this case, we can say, "If all humans are mortal, and Samantha is a human, then Samantha is mortal." This statement is true based on the premises provided.

To determine the validity of an inference mathematically, we can use rules of logic such as the law of detachment or the law of syllogism. The law of detachment states that if we have a conditional statement, "If p, then q," and we know that p is true, then we can validly infer that q is also true.

The law of syllogism is another rule of logic that helps us determine the validity of an inference. This rule states that if we have two conditional statements, "If p, then q," and "If q, then r," we can infer that "If p, then r" is true.

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The decimal multiplier to increase by 6.1% is 1.061.

What is multiplication ?

Multiplication is a mathematical operation used for finding the result of adding a number to itself a certain number of times. It involves multiplying two or more numbers to find their product. For example, 2 times 3 is equal to 6, written as 2 x 3 = 6. In multiplication, the numbers being multiplied are called factors, and the result is called the product. Multiplication is often denoted by the symbol "x" or a dot ".".

A decimal multiplier is a factor that is used to increase or decrease a number by a certain percentage. It is commonly used in financial calculations such as interest rates, discounts, and taxes.

To find the decimal multiplier to increase by a certain percentage, you can use the following formula:

Decimal multiplier = 1 + (percentage increase/100)

For example, if you want to increase a number by 6.1%, the decimal multiplier would be:

Decimal multiplier = 1 + (6.1/100)

Decimal multiplier = 1.061

This means that to increase a number by 6.1%, you would multiply it by 1.061. For example, if you had a number of 100, to increase it by 6.1%, you would multiply it by 1.061 to get 106.1.

On the other hand, if you wanted to decrease a number by a certain percentage, you would use a decimal multiplier that is less than 1. For example, to decrease a number by 10%, the decimal multiplier would be 0.9, which means you would multiply the number by 0.9 to get the new decreased value.

Therefore, decimal multiplier to increase by 6.1% is 1.061.

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