Suppose you and your friend want to investigate how many of the moved-in students at Abu dhabia University are going home to their families over Christmas. You collect responses from a randomly selected sample of students. You are interested in estimating the population mean within ±0.4 with 95% certainty and your friend wants to estimate the population mean within ±0.2 with 95% confidence. Which of you needs to collect the most answers ie. requires largest sample?
(a) You.
(b) Your friend.
(c) You both need the same sample size.
Which is preferable: 95% or 99.99% confidence intervals? (
a) 95% because too high confidence levels generally lead to very wide and uninformative intervals.

If on a road trip, a family drives 200 miles the first day and 350 miles per day each remaining day. The family will need to travel for an additional 4 days to reach a distance of 1600 miles.

On the first day the family drives 200 miles.

For the remaining days they drive 350 miles per day.

Let's d represent the additional days.

Total distance covered on the remaining days:

350 miles/day × d days

= 350d miles

Total distance covered is:

200 miles + 350d miles

Set up the equation:

200 + 350d = 1600

350d = 1600 - 200

350d = 1400

Dividing both sides by 350:

d = 1400 / 350

d = 4

Therefore the family will need to travel for an additional 4 days to reach a distance of 1600 miles.

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The correct description that defines the prism square is option B: "Is another hand instrument that is also used to determine or set out right angles."

A prism square is a tool used in construction and woodworking to establish or verify right angles. It consists of a triangular-shaped body with a 90-degree angle and two perpendicular sides. The edges of the prism square are straight and typically have measurement markings. It is commonly used in carpentry, masonry, and other trades where precise right angles are essential for accurate and square construction. Option A describes a different tool involving mirrors set at an angle, which is not related to the prism square. Option C refers to a different instrument used for measuring slopes and is not directly related to the prism square.

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Answer:

If two of the angles are the same, the third angle is the same and the triangles are similar.

Step-by-step explanation:

If two of the angles are the same, the third angle is the same and the triangles are similar.

Answer:

32

Step-by-step explanation:

to form a linear pair means when the two angles are added, they equal 180 degrees

3x + 20 + x + 32 = 180

4x + 52 = 180

4x = 128

x = 32

Answer:

As the value of x increases, the value of y decreases

2/3y- 2/5 =5

add 2/5 on both sides:

2/3y = 5 + 2/5

Combine the fraction:

2/3y = 5 2/5

Write in improper Fraction:

2/3y = 27/5

Divide both sides by 2/3:

y = 27/5 ÷ 2/3

Change divide fraction to multiplication fraction:

y = 27/5 x 3/2

y = 81/10

Write in mixed number:

y = 8 1/10

Answer: y = 8 1/10

The two numbers that are multiplied to find out the amount she has after playing her rent is: 2/3 and 1800.

Total income of person: $1800 per month.

Rent amount = 1/3 * income

Remaining amount : 1 - 1/3 = 2/3 of income

So,

Remaining amount = 2/3*1800

Remaining amount = 1200

Thus, the two numbers that are multiplied to find out the amount she has after playing her rent is: 2/3 and 1800.

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The length of the shadow increasing at the rate of 400 ft/hr

What is angle of elevation ?

Angle of elevation is the angle formed between horizontal line and line of sight.

Let, x be the length of shadow then length of shadow changes at the rate of dx/dt.

we have

tanθ  = 400/ x

x = 400/tanθ

at θ = π/6

x = 400/ tanπ/6

x =692 feet

On differentiating the above equation with respective to

dx/dt = d/dt (400/tanθ)

by using trigonometric formula

dx/dt = d/dt (400cotθ)

by using constant multiple rule

dx/dt = 400 d/dt (cotθ) dθ/dt

by using trigonometric rule

dx/dt = 400(- \(cosec^{2}\)θ) dθ/dt

dx/dt = 400 d/dt(cotθ) dθ/dt

by using tirgonometric rule

dx/dt = 400(- \(cosec^{2}\)θ) dθ/dt

then , substitute the values of

θ = π/6 and dθ/dt

dx/dt = 400*(-4)*(-0.25)

dx/dt = 400 ft/hour

Hence , The length of the shadow increasing at the rate of 400 ft/hr

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Hello !

Answer:

\(\Large \boxed{\sf r=\frac{3}{2} }\)

Step-by-step explanation:

Let's remember :

We know that the volume of the sphere is equal to half its surface area.

\(\sf V_{sphere}=\frac{1}{2} A_{sphere}\\\\\sf \frac{4}{3}\pi r^3=\frac{1}{2} 4\pi r^2\\\\\sf \frac{4}{3}\pi r^3=2\pi r^2\)

Let's solve this equation for r.

First, substract \(\sf 2\pi r^2\)  from both sides :

\(\sf \frac{4}{3} \pi r^3-2\pi r^2=0\)

We can now factorize by taking out the highest common factor: 2r²

\(\sf 2r^2(\frac{2}{3} \pi r-\pi )=0\)

We can use the zero-product property.

There are two solutions :

The first solution is absurd : The radius of a sphere cannot be 0.

We conclude that we must keep the second solution.

Have a nice day ;)

When performing a significance-test for comparing dependent means, several assumptions are necessary to make a valid inference- Normality, Equal variances, Independence,Random-sampling.

Some of these assumptions are:

Normality: The distribution of differences between the paired observations must be approximately normal.

This can be assessed using a normal probability plot or by conducting a normality test.

Equal variances: The variances of the paired differences should be approximately equal.

This can be assessed using the Levene's test.

Independence: The paired differences should be independent of each other.

This means that each observation in one sample should not influence the corresponding observation in the other sample.

Random sampling: The observations should be selected randomly from the population of interest.

This ensures that the sample is representative of the population.

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A bijection between two sets is constructed below and also proved that it is both one-one and onto.

The phrase "one-to-one function" should not be mistaken with "one-to-one correspondence," which is used to describe bijective functions, in which each element in the codomain is a precise mirror image of a single element in the domain.

Any function that can work with the operations of two algebraic structures is said to be a homomorphism between them. An injective homomorphism is also referred to as a monomorphism for any commonly occurring algebraic structures, particularly vector spaces.

Let t∈T

Then,

t=2k+1, for some k∈Z

Let s=3k

Then,

s∈S and f(s)=2(s/3)+1

=2k+1

=t

Therefore, for every t∈T there exists s∈S such that f(s)=t

Thus, f is onto.

Hence,

f:S  ----> T is a bijective mapping

⇒|S|=|T|

Now, we have to define a mapping f:S ---?T

By f(x)=2(x/3)+1, ∀x∈S

Given,

S={3k|k∈Z} and T={2k+1:k∈Z}

We have to prove:

|S|=|T|

Let x, y∈ S with f(x)=f(y)

Then,

2(x/3)+1=2(y/3)+1

2(x/3)=2(y/3)

(x/3)=(y/3)

x=y

So, f is one-one

Now, we have proved that f is both one-one and onto.

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Answer:

-4

Step-by-step explanation:

Move variables to one side and numbers on the other.

12 - 3x = -6x

+ 3x +3x

12 = -3x

/-3 /-3

-4 = x

The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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The measure of the missing length of the trapezoid is equal to 3√39 units.

Trapezoids are quadrilaterals with only one pair of congruent sides and two pairs of congruent angles. The relationship between the longest and shortest legs (D, d) in a trapezoid is defined below:

D = d + 2 · c

Where c is the length of the horizontal leg of the right triangle in a trapezoid.

And the missing leg can be found by means of Pythagorean theorem:

x = √(r² - c²)

Where:

First, determine the length of shortest leg: (D = 40, d = 26)

40 = 26 + 2 · c

14 = 2 · c

c = 7

Second, find the longest leg by Pythagorean theorem:

x = √(20² - 7²)

x = 3√39

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The researcher should consider the following steps when creating the two groups: Random assignment, Pairing students with similar abilities, Controlling for potential confounding variables,

Collecting data and analyzing results.
Random assignment:

To minimize any potential bias, the researcher should randomly assign one student from each pair to receive extra homework problems while the other does not.
Pairing students with similar abilities:

In order to make a valid comparison, the researcher should pair students with similar algebra skills or previous performance in the subject.

This way, any observed differences in the test results are more likely to be due to the extra homework rather than differences in ability.
Controlling for potential confounding variables:

The researcher should control for any other factors that could influence students' algebra test results, such as attendance, study habits, and teacher quality.

After the two-week period, the researcher should collect the test scores of both groups and compare their performance.

This can be done using statistical methods, such as a paired t-test, to determine if there is a significant difference between the groups.

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Carl is correct the value of x by using the side splitter theorem is 6

\(\frac{6}{3} = \frac{12}{x}\)

Required

Is Carl correct?

The side splitter theorem is a theorem that states that when a line passes through the two sides of a triangle and is parallel to the third remaining side, the line divides the two sides proportionally.

Using the side splitter theorem, the proportion is:

\(\frac{AB}{BC} = \frac{AE}{ED}\\\)

This gives:

\(\frac{6}{3} = \frac{12}{x}\)

This proportion is equivalent to Carl's.

Hence, Carl is correct.

Solving further: Cross Multiply

6 * x = 12 * 3

6x = 36

Make x the subject

\(x=\frac{36}{6}\)

x =6

Carl is correct the value of x by using the side splitter theorem is 6

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The set of natural numbers {1,2,3,4,...} and the set of positive even numbers {2, 4, 6, 8, . . .} are different because natural numbers include all positive integers, while even numbers only include those that are divisible by 2 with no remainder.

Two important sets of numbers are natural numbers and even numbers. The set of natural numbers consists of numbers that are not negative, beginning with 1 and continuing indefinitely with 2, 3, 4, and so on.

The set of even numbers, on the other hand, consists of numbers that are divisible by 2, beginning with 2, 4, 6, and so on.

Positive integers refer to natural numbers. Any integer greater than zero is a positive integer.

Zero is not a positive integer. Hence, the set of natural numbers consists of {1,2,3,4,…}

On the other hand, the set of even numbers consists of {2, 4, 6, 8, . . .}.

Therefore, {1,2,3,4,…} and {2, 4, 6, 8, . . .} are two different sets of numbers where one set is composed of positive integers (natural numbers) and the other is composed of positive even numbers.

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Answer:a^2

Brailniest if this helped ;)

Also the ^ means an exponent just so you know

Answer:

95 points

Step-by-step explanation:

Let P = Big Town's points

5/2 = P/38

2P = 190

P = 95 points

Answer:

  45%

Step-by-step explanation:

The fraction of marbles that are blue is 36/80 = 9/20. To make that a percentage, multiply it by 100%.

  9/20 × 100% = 45%

45% of the 80 marbles are blue.

HELP ME PLES

PERIOD, FREQUENCY OR AMPLITUDE

1. Doesn't change period

2. More of this means more energy

3. Increases as a pendulum swings back and forth faster

4. Measured in cycles per second

5. Measured in meters or centimeters

6. This is decreases with smaller swing

7. If the frequency increases, this decreases

8. Measured in Hertz

9. Measured in seconds

10. if it swings back and forth slower, this decrease

11. As it dampens, this decreases

Answer:

B = 3

Step-by-step explanation:

The answer has to be 3 because this is a 3-4-5 triangle. We can also you the Pythagorean theorem to solve for B.

a²+b²=c²

(4)²+b²=(5)²

16+b²=25

b²=9

√b=√9

b=3

Answer:

Step-by-step explanation:

-8+x-4+9x = -8-4+x+9x

= -12+10x

PLEASE MARK BRAINLIEST.

please check the attachment for solutions

The complete table is

Sulfur atoms         6     9     12   27

Oxygen atoms     12    18    24   54    

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other.

A ratio can be compared by the division of two numbers. For example, the ratio of a and b can be represented as a: b and read as a is to b. Here a: b can be written as a/b

Here we have  

The ratio of oxygen atoms to sulfur atoms in sulfur dioxide is always the same. The table shows the number of atoms in different quantities of sulfur dioxide.  

The given table is

Sulfur atoms         6     9     12   ___

Oxygen atoms     12    __   ___   54      

Let x, y, and z be the missing values in the table

Given that ratio of oxygen atoms to sulfur atoms in sulfur dioxide is always the same.  

=> 12/6 = x/9 = y/12 = 54/z    

Now the x, y, and z values can be calculated as follows

Take 12/6 = x/9  

=> 2 = x/9    

=> x = 18  

Take 12/6 = y/12  

=> 2 = y/12

=> y = 24

Take 12/6 = 54/z  

=> 2 = 54/z

=> z = 54/2

=> z = 27    

Therefore,

The complete table is

Sulfur atoms         6     9     12   27

Oxygen atoms     12    18    24   54      

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The complete Question is given in the picture

The product of 56.2 and 9.2057 to the appropriate number of significant digits is 517.00.

The significant digits in a number are the digits that contribute to its precision. When multiplying numbers, the result should be rounded to the same number of significant digits as the factor with the least number of significant digits.

In this case, 56.2 has three significant digits, and 9.2057 has five significant digits. The factor with the least number of significant digits is 56.2. Therefore, the product should be rounded to three significant digits.

Multiplying 56.2 by 9.2057 gives 517.38134. Rounding this result to three significant digits gives us 517.00. The trailing zeros after the decimal point are significant in this case as they indicate the precision of the result. Hence, the correct answer is 517.00.

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The degree of the equation is 2. Then the number of solutions to the equation will be 2.

Given that:

Equation, 5x² + 3x + 8

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

The degree of the polynomial will be greater than or equal to the number of zeroes.

The degree of the equation is 2. Then the number of solutions to the equation will be 2.

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Answer:

The is no number that I can substitue in for x to make the statement true.

Step-by-step explanation:

s + 3 = x -6  Subtract x from both sides

3 = -6  We get a false statement.

Answer:

B, E, and D are correct

Step-by-step explanation:

Answer: We can start by using the proportion method to find the number of girls in the class.

If the ratio of girls to total students is 4:7, that means for every 4 girls, there are 7 students in total. We can set up a proportion:

4/x = 7/21

where x is the number of girls in the class.

To solve for x, we can cross-multiply and get:

4* 21 = 7* x

84 = 7x

Dividing both sides by 7 gives:

x = 12

So there are 12 girls in the class.

Step-by-step explanation: