1. In a survey, it was found that the ratio of the people who liked modern songs and folk songs is 8:9, out of which 50 people like both songs, 40 liked folk songs only and 80 liked none of the songs.i) Represent the above information in a Venn - diagram. ii) How many people like folk song? iii) How many people like Modern song? iv) Find the number of people in the survey. ​

Therefore, the solution to the system of equations is (x, y) = (-3, 4).

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can be composed of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields such as physics, engineering, economics, and mathematics.

To solve the system of equations using elimination, we need to manipulate one or both equations so that one of the variables has the same coefficient with opposite signs. Here's how we can solve the system:

Multiply the first equation by -2 to get -4x - 10y = -28.

Add the second equation to the new equation to get -8y = -32.

Divide both sides by -8 to get y = 4.

Substitute y = 4 into either equation to solve for x.

Using the first equation:

[tex]2x + 5(4) = 14[/tex]

[tex]2x + 20 = 14[/tex]

[tex]2x = -6[/tex]

[tex]x = -3[/tex]

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We can use the formula for inverse variation, which states that the product of the time and the speed is constant:

time × speed = constant

Let's use t to represent the time needed to travel the distance at 54 miles per hour. We know that the time is 10 hours when the speed is 24 miles per hour. So we can set up the equation:

10 × 24 = t × 54

Simplifying, we get:

240 = 54t

Dividing both sides by 54, we get:

t = 240/54

Simplifying this fraction, we get:

t = 40/9

So it will take approximately 4.44 hours, or 4 hours and 26 minutes, to travel the same distance at 54 miles per hour.

The value of x in the Intersecting chords is 15

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

Intersecting chords

The value of x is then calculated as

x = 1/2(30 - 2x + 30)

So, we have

2x = 30 - 2x + 30

Evaluate the like terms

4x = 60

Divide

x = 15

Hence, the value of x is 15

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Determine the recommended range of water consumption17.7 ≤ x ≤ 37.6

A.54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the water usage should be between 17.7 and 37.6 HCF.

Scenario is that the water utility charges a fee of $29, plus an additional $1.41 per hundred cubic feet (HCF) of water, and the recommended monthly bill for a household is between $54 and $82.

Range of water usage in HCF (x) that fits this recommendation.
First, write the compound inequality to represent the scenario:
54 ≤ 1.41x + 29 ≤ 82
Now, to find the recommended range of water consumption, we need to isolate x in both inequalities.

Start with the left inequality:
54 ≤ 1.41x + 29
Subtract 29 from both sides:
25 ≤ 1.41x
Divide both sides by 1.41:
25 / 1.41 ≤ x
x ≥ 17.7 (rounded to one decimal place)
Next, consider the right inequality:
1.41x + 29 ≤ 82
Subtract 29 from both sides:
1.41x ≤ 53
Divide both sides by 1.41:
x ≤ 53 / 1.41
x ≤ 37.6 (rounded to one decimal place)
Combine both inequalities:

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The histogram shows that the majority of velvetleaf plants produced between 0 and 500 seeds. The highest count was 2,000 seeds, and the lowest count was 0 seeds. On average, velvetleaf plants produce around 500 seeds.

Answer:

5x+20

Step-by-step explanation:

you are given that y=2x-5 so you can substitue that for the y value.

-3x-4(2x-5) is your new equation. You can further simply it and you will get:

-3x+8x+20

5x+20

The main topic is the split-half reliability test used in psychological research to assess the internal consistency of a scale.

In psychological research, reliability is a crucial aspect of measuring constructs or attributes. One commonly used method for assessing the reliability of a scale is the split-half reliability test.

In this test, the scale questions are divided into two parts equally, and the resulting scores of both parts are correlated against one another.

For example, if a scale had 20 items, the items could be randomly split into two groups of 10 items each.

Scores are then calculated for each group, and the scores are correlated with each other to determine the degree of consistency between the two halves.

The correlation coefficient obtained from this analysis provides an estimate of the internal consistency of the scale.

A high correlation coefficient indicates a high level of internal consistency, indicating that the two halves of the scale are measuring the same construct or attribute.

Conversely, a low correlation coefficient suggests that the two halves of the scale are not measuring the same construct or attribute, and the scale may need to be revised or abandoned.

Overall, the split-half reliability test provides a quick and efficient method for evaluating the reliability of a scale.

However, it is important to note that this method does have some limitations, such as the possibility of unequal difficulty or discrimination of the items in each half of the scale.

Therefore, researchers often use other methods, such as Cronbach's alpha, in conjunction with the split-half reliability test to provide a more comprehensive assessment of the reliability of a scale

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The area of the intersection of the sphere and the plane in sq cm is 286.46 square centimeters.

The sphere is divided into two equal halves by the plane. The closest point on the plane is 3 cm away from the sphere's center. As a result, a right triangle is formed, with one leg equal to the sphere's radius and the other to the sphere's radius from the plane.

We may calculate the radius of the sphere using the Pythagorean theorem:

r^2 = (20/2)^2 - 3^2

r = sqrt(91) 9.54 cm and r2 = 91

A circle with a radius of 9.54 cm forms the point where the sphere and the plane cross. Its area is therefore: A = r2 A = (9.54)2 A 286.46 sq cm.

The sphere and plane's intersection therefore has a surface area of about 286.46 square centimeters.

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The probability that Kylee wins at most 2 prizes in 3 attempts is 0.95625.

To answer this question, we can use the binomial distribution formula:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

where X is the number of times Kylee wins a prize, and P(X = k) is the probability of winning k prizes in 3 attempts.

Using the binomial distribution formula, we can calculate these probabilities using the following formula:

[tex]P(X = k) = (n choose k) × p^k × (1-p)^(n-k)[/tex]

where n is the number of trials (in this case, 3), p is the probability of winning a prize (0.45), and k is the number of

successes we want to calculate the probability for.

Now, let's plug in the values for k = 0, 1, and 2:

[tex]P(X = 0) = (3 choose 0) × 0.45^0 × (1-0.45)^3 = 0.342

P(X = 1) = (3 choose 1) × 0.45^1 × (1-0.45)^2 = 0.4095

P(X = 2) = (3 choose 2) × 0.45^2 × (1-0.45)^1 = 0.20475[/tex]

Now, we can add up these probabilities to find the probability that Kylee wins at most 2 prizes:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.342 + 0.4095 + 0.20475 = 0.95625

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Based on the information given, the vertex of the parabola can be found using the coordinates of the turning point (also known as the vertex).

The vertex is located at (4,-4), which means that the value of x is 4 and the value of y is -4. Therefore, the coordinates of the vertex are (4,-4).

The fact that the curve is on the upper and lower quadrants of the right side of the cartesian coordinate system suggests that the parabola opens upwards.

Also, since the curve meets the x-axis at two points, this indicates that the parabola intersects the x-axis at those two points, which are (2,0) and (6,0).

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The functions 7 are inverse functions while the functions 8 are not inverse functions

To verify that f and g are inverse functions, we need to show that:

Let's apply these conditions to the given functions:

f(x) = 5x + 2; g(x) = (x−2)/5

f(g(x)) = f((x−2)/5) = 5((x−2)/5) + 2 = x − 2 + 2 = x

g(f(x)) = g(5x + 2) = ((5x + 2) − 2)/5 = 5x/5 = x

Since f(g(x)) = x and g(f(x)) = x, we can conclude that f and g are inverse functions.

f(x) = ½x − 7; g(x) = 2x + 14

f(g(x)) = f(2x + 14) = ½(2x + 14) − 7 = x

g(f(x)) = g(½x − 7) = 2(½x − 7) + 14 = x − 7 + 14 = x + 7

Since f(g(x)) = x and g(f(x)) ≠ x, we can conclude that f and g are not inverse functions.

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The best type of study to establish causality is a randomized controlled experiment.

In this type of study, participants are randomly assigned to different groups, and at least one group is given a specific treatment or intervention, while the other group(s) serve as a control group. By randomly assigning participants to groups, researchers can control for potential confounding variables that could impact the results.

For example, let's say we want to determine if a new medication reduces blood pressure. In a randomized controlled experiment, we could randomly assign some participants to receive the medication and others to receive a placebo. This would allow us to compare the effects of the medication on blood pressure to the effects of the placebo, while controlling for other variables that could impact blood pressure.

In contrast, observational studies, such as cohort studies or case-control studies, can only establish correlations between variables, not causation. This is because researchers do not have control over the variables being studied, and there may be other factors that are influencing the relationship between the variables.

Therefore, to establish causality, a randomized controlled experiment is the best type of study to conduct.

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the fraction that rounds to 5 is option B, 5 1/2.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

To round a fraction to 5, we need to find the fraction that is closest to 5. Therefore, we need to look at the fractional parts of each option and find which one is closest to 1/2.

A. 5 2/3 = 17/3, which is closer to 6 than to 5.

B. 5 1/2 = 11/2, which is exactly halfway between 5 and 6, so it rounds to 5.

C. 5 9/20 = 259/20, which is closer to 6 than to 5.

D. 4 9/20 = 209/50, which is closer to 4 than to 5.

Therefore, the fraction that rounds to 5 is option B, 5 1/2.

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Answer:

b

Step-by-step explanation:

in order to find the mean you have find the sum of the numbers and divide them by the amount of numbers.without 68 the sum is 310 divide it by 5 and tge answer is 62.however if you add 68 the sum is 378 divide it by 6 and the answer is 63.

therefore the answer increased by 1.

hope this helps :)

From this graph , it takes 0.75 seconds to reach the highest position.

A graph is a visual representation of the relationship between two sets of data or variables, typically via lines or curves. A diagram or pictorial representation of facts or values that is arranged might be referred to as a graph in mathematics. The relationship between two or more items is frequently represented by the points on the graph

The graph indicates that the peak is at (0.75, 9)

The x-axis displays the time in seconds, while the y-axis displays the height in feet.

Consequently, it takes 0.75 seconds to reach the highest position.

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The two null hypothesis that are correct answer are two-sample t-test and one-sample t-test.

Among the group of answer choices provided, the tests that require calculating degrees of freedom are the two-sample t-test and the one-sample t-test. Both of these tests belong to the t-test family and involve using degrees of freedom to determine the critical t-value.

In summary:
- Null hypothesis: The assumption that there is no significant difference between the sample and population or between two samples.
- T-test: A statistical test used to determine if there is a significant difference between the means of two groups or between a sample and population mean.
- Degrees of freedom: A value used in statistical tests that represents the number of independent values in a data set, which can affect the outcome of the test.

So answer is: two-sample t-test and one-sample t-test.

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The null hypothesis statistical tests that require calculating degrees of freedom are the two-sample t-test and the one-

sample t-test. The degrees of freedom are necessary to calculate the t-value for these tests. The chi-squared test also

requires degrees of freedom, but it is not a test for a null hypothesis.

The correct answer is: all of the above.

All these tests require calculating degrees of freedom:

1. Two-sample t-test:

Degrees of freedom are calculated using the formula (n1 + n2) - 2, where n1 and n2 are the sample sizes of the two

groups being compared.
2. Chi-squared test:

Degrees of freedom are calculated using the formula (rows - 1) * (columns - 1), where rows and columns represent the

number of categories in the data.
3. One-sample t-test:

Degrees of freedom are calculated using the formula n - 1, where n is the sample size.

The null hypothesis statistical tests that require calculating degrees of freedom are the two-sample t-test and the one-

sample t-test. The degrees of freedom are necessary to calculate the t-value for these tests. The chi-squared test also

requires degrees of freedom, but it is not a test for a null hypothesis.

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The Buckley family would pay $51 either way if they rented the truck for 4 additional days.

To solve the question :

Total cost for Kendall's Moving :

= $27 + $6x,

where

x = Number of additional days rented.

Total cost for Newton Rent-a-Truck :

= $7 + $11x

To find the number of additional days we will put both the equations i.e., $27 + $6x and $7 + $11x, equal to each other.

= $27 + $6x = $7 + $11x

Subtracting $7 from both sides :

= $20 + $6x = $11x

Subtracting $6x from both sides :

= $20 = $5x

Dividing both sides by $5 :

= x = 4

Hence, the number of additional days is 4.

So,

Kendall's Moving and Newton Rent-a-Truck would be the same if the truck is rented for 4 additional days by the Buckley family :

Putting the values of x in the equations :

Total cost for Kendall's Moving :

= $27 + $6x,

= $27 + $6(4)

= $51

Total cost for Newton Rent-a-Truck

$7 + $11x

= $7 + $11(4)

= $51

Hence, the Buckley family would pay $51 either way if they rented the truck for 4 additional days.

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Answer: The distance formula between two points (x1, y1) and (x2, y2) is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can find the distance between (7, -2) and (-1, -1):

d = sqrt((-1 - 7)^2 + (-1 - (-2))^2)

= sqrt((-8)^2 + (1)^2)

= sqrt(64 + 1)

= sqrt(65)

Therefore, the distance between (7, -2) and (-1, -1) is sqrt(65), or approximately 8.06 units.

Step-by-step explanation:

Positive divisors does n2 have are 5.

If an integer n has exactly three positive divisors, including 1 and n, it means that n is a perfect square of a prime number.

The reason for this is that a prime number has only two divisors: 1 and itself. Therefore, if n has exactly three positive divisors, n must be a perfect square of a prime number, since the only divisors of a perfect square are the divisors of its square root, and its square root must be a prime number.

Let's say that n is equal to p², where p is a prime number. The positive divisors of n are 1, p, and n (which is p²).

Now, to find the number of positive divisors of n², we can use the fact that any positive divisor of n² can be expressed in the form [tex]p^k[/tex], where 0 ≤ k ≤ 4 (since n² = p⁴).

Therefore, the positive divisors of n² are:

1, p, p², p³, and p⁴ (which is n²)

So, n² has 5 positive divisors: 1, p, p², p³, and n².

Hence, the answer is 5.

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The explanatory variable is whether or not a subject received tea before bedtime.

The theory behind this study is that drinking tea before bedtime may help with falling asleep faster.

Participants were randomly assigned to one group that received tea before bedtime and the other group that did not receive tea before bedtime.

The researcher then monitored the amount of time it took for each person to fall asleep.

The explanatory variable of this study is whether or not a subject received tea before bedtime, and the goal is to compare the amount of time it takes for each person to fall asleep depending on if they received tea before bedtime.

The results of this study will help determine if drinking tea before bedtime is an effective way to fall asleep faster.

The goal is to test whether or not this is true by comparing the amount of time it takes for each person to fall asleep depending on if they received tea before bedtime.

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Number of hours does it take for the temperature to change by -4. 4°C is 5.5 hours

To solve this problem, we can use the formula for finding the change in temperature

Change in temperature = rate of change × time

where the rate of change is -0.8°C per hour and the change in temperature we want to find is -4.4°C. So, we can plug in these values and solve for time

-4.4°C = (-0.8°C / hour) × time

Dividing both sides by -0.8°C / hour, we get

time = 5.5 hours

Therefore, it will take 5.5 hours for the temperature to change by -4.4°C.

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The combined amount in both accounts after 10 years is $16,869.58

To solve the problem, we need to use the following formulas:

Simple Interest = Principal x Rate x Time

Compound Interest = [tex]Principal * (1 + Rate/ n)^{n * Time}[/tex]

where:

Principal = the initial deposit

Rate = the interest rate (in decimal form)

Time = the number of years

n = the number of times interest is compounded per year

For Account 1:

Simple Interest = Principal x Rate x Time

= $6000 x 0.035 x 10

= $2100

The amount in Account 1 after 10 years will be the initial deposit plus the interest earned:

= $6000 + $2100

= $8100

For Account 2:

Since the interest is compounded annually, n = 1.

Compound Interest = [tex]Principal * (1 + Rate/ n)^{n * Time}[/tex]

= [tex]6000 *(1 + 0.035/1)^{1 * 10}\\= $6000 (1.035)^{10}\\= $8769.58[/tex]

After ten years, the amount in Account 2 will be $8769.58.

After ten years, the combined amount in both accounts will be:

$8100 minus $8769.58 equals $16869.58, resulting in a total of $16,869.58 in both accounts after ten years.

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Answer: Area = 144 π cm²

Step-by-step explanation:

We can use this formula to find the area of a circle:

➜ r is equal to the radius, also known as half the width of a circle.

      A = πr²

We will substitute our known values and solve for C by multiplying. Since the answer option includes π in our units, we do not multiply this into the 144.

      A = πr²

      A = π(12)²

      A = 144 π cm²

The domain of the function 8 - [tex](x-3)^{2}[/tex] is R which is all the real numbers.

What is domain of a function?

The set or grouping of all potential values that may be used in the function is known as the domain.

We are given a function as 8 - [tex](x-3)^{2}[/tex].

Now, in order to find the domain, we need to find the values where the function is not defined for a value of x.

But, there is no such value for x where the function is not defined.

This means that all values of x give an output.

So, the domain is the set of all the real numbers.

Hence, the domain of the given function is R.

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The two triangles are congruent based on the ASA Congruence Postulate.

The ASA Congruence Postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

The image shown above shows two triangles that has three pairs of congruent triangles and a pair of corresponding congruent sides.

Therefore, both triangles are congruent by the ASA Congruence Postulate.

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The total length of all 10 ribbons is 35 inches when they are placed end to end.

Inches are a unit of length in the imperial system of measurement, which is primarily used in the United States, the United Kingdom, and some other countries. One inch is equal to 1/12 of a foot or 2.54 centimeters.

The inch is commonly used to measure the length or distance of small objects, such as the size of a computer screen, the length of a pencil, or the height of a person. Inches are also used to measure the dimensions of larger objects, such as the width of a door or the size of a piece of furniture.

If John has 10 ribbons, each measuring 3 ½ inches long, we can find the total length of all the ribbons by multiplying the length of one ribbon by the number of ribbons:

Total length = 10 × 3 ½ inches

To multiply a whole number and a mixed number, we can first convert the mixed number to an improper fraction, then multiply:

Total length = 10 × (7/2) inches

Total length = 35 inches

Therefore, the 10 ribbons, placed end to end, would be 35 inches long.

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Answer: 1/3

Step-by-step explanation:

1/3x1/3x1/3=1/27

The inverse of (x-A)^c = B, where A = 2x + 1, is x = -(B^(1/c) + 1).

To find the inverse of the expression in (x - A)^c = B, where A = 2x + 1, we can use the following steps:

First, solve for x in terms of A

x = (A - 1) / 2

Substitute the expression for A into the original equation

(x - (2x + 1))^c = B

Simplify

(-x - 1)^c = B

Take the c-th root of both sides

-x - 1 = B^(1/c)

Solve for x

x = -(B^(1/c) + 1)

Therefore, the inverse of the expression in (x - A)^c = B, where A = 2x + 1, is given by

x = -(B^(1/c) + 1)

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--The given question is incomplete, the complete question is given

" Inverse of this in (x-A)^c = (B)

—-

where A = 2X+1 "--

The volume of the basketball is 4.19x³

The volume of the box is 8x³

The volume of air is 3.81x³

We know that the basketball is a sphere of radius x, and the volume of a sphere of radius R is:

V = (4/3)*pi*R³

Where pi = 3.14

In this case the radius is x, so the volume is:

V = (4/3)*3.14*x³

V = 4.19x³

b) The cube has a side length of 2x, then the volume (the cube of that) is:

V = (2x)³

V = 8x³

c) The volume of air is the difference between the volume of the cube and the volume of the ball:

volume of air = 8x³ -  4.19x³ = 3.81x³

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