Find the ordered pair (s,t) that satisfies the system

s/2+5/t=3

3t-6s=9

The 98% confidence interval for the population mean (μ) is approximately (2.711, 3.009).

1: Identify the given data

Sample size (n) = 150 students

Sample mean (x) = 2.86

Population standard deviation (σ) = 0.78

Confidence level = 98%

2: Find the critical z-value (z*) for a 98% confidence level

Using a z-table or calculator, you'll find that the critical z-value for a 98% confidence level is 2.33 (approximately).

3: Calculate the standard error (SE)

SE = σ / √n

SE = 0.78 / √150 ≈ 0.064

4: Calculate the margin of error (ME)

ME = z* × SE

ME = 2.33 × 0.064 ≈ 0.149

5: Construct the confidence interval

Lower limit = x - ME = 2.86 - 0.149 ≈ 2.711

Upper limit = x + ME = 2.86 + 0.149 ≈ 3.009

The 98% confidence interval is approximately (2.711, 3.009).

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Answer: 23 kg

Step-by-step explanation:

Let's begin by using algebra to solve the problem.

Let x be the number of kilograms of salmon the fish-shop owner bought at the market.

We know that the total cost of the salmon was $400, so we can write:

400 = x * c

where c is the cost per kilogram of salmon.

We also know that all except for 2 kg of the fish were sold at a price per kg that was $10 more than what the owner paid at the market. So the price per kilogram of salmon at the fish shop was c + 10.

The total revenue from the sale of the fish was $540, so we can write:

540 = (x - 2) * (c + 10)

Now we can use these two equations to solve for x.

First, we can use the first equation to solve for c:

c = 400 / x

Then we can substitute this expression for c into the second equation:

540 = (x - 2) * (400/x + 10)

Simplifying this equation:

540 = 4000/x + 10x - 20 - 80/x

Multiplying both sides by x:

540x = 4000 + 10x^2 - 20x - 80

10x^2 - 20x - 4600 = 0

Dividing both sides by 10:

x^2 - 2x - 460 = 0

We can solve for x using the quadratic formula:

x = [2 ± sqrt(4 + 4*460)] / 2

x = [2 ± 44] / 2

Discarding the negative solution, we get:

x = (2 + 44) / 2

x = 23

Therefore, the fish-shop owner bought 23 kilograms of salmon at the market.

The area of the rectangle changing at the instant when the other side is cm and increasing at cm per minute is k²/min

Let's start by defining the variables:

Let x be the length of the rectangle (in cm).

Let y be the width of the rectangle (in cm).

Let A be the area of the rectangle (in cm²).

We know that one side of the rectangle (y) is constant, so its derivative with respect to time is zero:

dy/dt = 0

We also know that the other side of the rectangle (x) is increasing at a rate of dx/dt = cm/min.

We can use the formula for the area of a rectangle to express A in terms of x and y:

A = x×y

To find how fast the area of the rectangle is changing with respect to time, we can take the derivative of both sides with respect to time:

dA/dt = d/dt (x×y)

Using the product rule of differentiation, we get:

dA/dt = x × dy/dt + y × dx/dt

Since dy/dt = 0 (as we established earlier), we can simplify the equation to:

dA/dt = x × 0 + y × dx/dt

Plugging in the given values for y and dx/dt, we get:

dA/dt = (cm) × (cm/min) = k²/min

Therefore, the area of the rectangle is increasing at a rate of k²/min at the instant when one side is cm and increasing at cm per minute.

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The complete question is :

A rectangle has one side of "k" cm. how fast is the area of the rectangle changing at the instant when the other side is cm and increasing at cm per minute?

We find that the approximation converges to 9.74679419, accurate to eight decimal places. So, the square root of 95, approximated using Newton's method, is 9.74679419.

Newton's method is a way to approximate the roots of a function. In this case, we want to approximate the square root of 95 correct to eight decimal places. To use Newton's method, we start with an initial guess and then apply the following formula repeatedly:
x1 = x0 - f(x0) / f'(x0)
where x0 is our initial guess, f(x) is the function we are trying to find the root of (in this case, f(x) = x^2 - 95), and f'(x) is the derivative of f(x) (which is 2x).
Let's start with an initial guess of 10:
x1 = 10 - (10^2 - 95) / (2 * 10) = 5.75
We can continue this process, plugging in our new guess into the formula each time, until we reach a value that is accurate to eight decimal places. After a few iterations, we get:
x8 = 9.74679434
This is our final answer, correct to eight decimal places.
Using Newton's method, we can approximate the square root of a number, such as 95, to eight decimal places. Newton's method is an iterative process that starts with an initial guess and refines the guess using the formula:
x1 = x0 - f(x0)/f'(x0)
For square root approximation, f(x) = x^2 - a, where a is the number we want to find the square root of (95 in this case), and f'(x) = 2x.
Let's start with an initial guess x0 = 9 (since 9^2 = 81 is close to 95). We can then perform the following iterations:
1. x1 = 9 - (9^2 - 95)/(2*9) ≈ 9.72222222
2. x2 = 9.72222222 - (9.72222222^2 - 95)/(2*9.72222222) ≈ 9.74679424
3. x3 = 9.74679424 - (9.74679424^2 - 95)/(2*9.74679424) ≈ 9.74679419
Continuing this process, we find that the approximation converges to 9.74679419, accurate to eight decimal places. So, the square root of 95, approximated using Newton's method, is 9.74679419.

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Step-by-step explanation:

cos50 = x/53

0.64 = x/53

x = 0.64×53

= 33.92

Answer:

Step-by-step explanation:

A inbetween 4/10 and 5/10

B inbetween 30 and 40

C closer to the 8/10 but inbetween 9/10

D inbetween 20 and 30

E inbetween 2/10 and 3/10

F on the 5/10

The quotient of the polynomial exists 5x+6 + (4 / x+6).

The number of periods we have subtracted exists named the quotient (of the division of by ) The number that exists leftover after subtracting as usually as possible exists named the remainder (of the division of by ).

Given: (5x²+36x+40)/(x+6)

(5x²+36x+40)/(x+6) = 5x + (6x+40 / x+6)

Dividing the above equation

(6x+40) / (x+6) = 6+(4 / x+6)

Therefore, (5x²+36x+40)/(x+6) = 5x+6 + (4 / x+6)

The quotient of the polynomial exists 5x+6 + (4 / x+6).

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The test statistic is approximately 0.8314 (rounded to 4 decimal places).

To determine if U.S. residents with a high school diploma make significantly more than those with a GED, we can conduct a two-sample t-test.
The null hypothesis (H0) assumes that there is no significant difference in the average yearly income between the two groups.

The alternative hypothesis (Ha) assumes that there is a significant difference.

Using the formula for the test statistic, we calculate it as follows:
Test statistic = (x₁ - x₂) / √((s₁² / n₁) + (s₂² / n₂))
Where:
x₁ = average yearly income of group 1 ($35,621)
x₂ = average yearly income of group 2 ($34,598)
s₁ = standard deviation of group 1 ($3,510)
s₂ = standard deviation of group 2 ($3,510)
n₁ = number of observations in group 1 (100)
n₂ = number of observations in group 2 (120)
Substituting the values, we get:
Test statistic = (35621 - 34598) / √((3510² / 100) + (3510² / 120))
Calculating this, the test statistic is approximately 0.8314 (rounded to 4 decimal places).

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Answer:

Option 3: (5, 1)

Step-by-step explanation:

There are several ways of solving for systems of linear equations, either through graphing, substitution, or elimination.  

The graphing method is the easiest, as you only need to plot points on the graph using the y-intercepts and the slopes.  

I will be demonstrating the graphing method.  

Given the systems of linear equations:  

Equation 1:  y = x - 4

where the slope, m = 1, and y-intercept (0, -4).

Equation2: y = -x + 6

where the slope, m = -1, and y-intercept (0, 6).

The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b).

For Equation 1, plot the y-intercept, (0, -4) on the graph. Then use the slope, m = 1 (rise 1 unit, run 1 unit) to plot other points on the graph. Repeat this process until you have enough points to connect a line with.  

Repeat these same procedures for graphing Equation 2, start by plotting its y-intercept at (0, 6), and its slope, m = -1 (down 1 unit, run 1 unit).

The intersection of both lines occurs at point, (5, 1), which is solution to the given systems of linear equations.  Therefore, the correct answer is the third option, (5, 1).

Attached is the screenshot of the graphed systems of linear equations, where it shows the point of intersection at (5, 1).  

Answer:

y=-6x+8

Step-by-step explanation:

Answer:

y = 4, x = 0

Step-by-step explanation:

y = -3x + 4

y =  3x + 4

________

2y   = 8

y = 4

4 = 3x + 4

3x = 0

x = 0

Could you please give me brainiest? Thank you!

Answer:

I hope I helped :)

Step-by-step explanation:

a. The y-intercept represents b. (y = mx + b) also b is 20 because that's where the line touches the y-axis.

b. The slope represents Sam's monthly fee.

c. Sam's monthly fee is 0.4 or 2/5

d. Every 50 minutes is $20.

Answer:

Perimeter is 30 and area is 32

Step-by-step explanation:

7+8+7+8= 30 and A= BH so 8 x 4 = 32

Answer:

The derivative of the profit function P(x) is called marginal profit with notation: P ... Example 2: Given the average cost in dollar per unit C = 357x + 1800 , find: ... (1) the selling price to maximize the revenue is 31 − 3 = 28 dollars per unit ... Example 6: A company has established that the revenue function in dollars is R(x)=2x.

Step-by-step explanation:

9 cm cm cm cm cm cm cm cm cm cm cm cm cm

Answer:

\(x = \sqrt{11}\)

Step-by-step explanation:

\(a^{2} +b^{2} =c^{2} \\\\\sqrt{6} ^{2} +\sqrt{5} ^{2} =c^{2} \\\\6 + 5 = c^{2} \\\\11 = c^{2} \\\\\sqrt{11} = c\)

We can infer from the data set provided that more women than men are interested in basketball.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

From table given in question

Number of males that like basketball = 21

Number of females that like basketball = 29

Percentage of males that like basketball =  (21/50)*100 = 42%

Percentage of females that like basketball =  (29/50)*100 = 58%

So, from above data we can conclude that females like basketball more than that of males.

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Around 1950, family sociologists described a standard marriage pattern at about age 20 for women and age a) 22 for men.

The standard marriage pattern today, based on the time a couple marries, is mid-to-late twenties.  Some marriages are contracted very late, with some in the forties.

Sociologists have pointed out that the current delay in marriages is caused by the higher priority placed on education and career by youths.

However, marriage patterns based on the type of arrangement include:

Traditionally, marriages have served two societal purposes:

Thus, around 1950, family sociologists described a standard marriage pattern at about age 20 for women and age  22 for men.

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Answer:

3

Step-by-step explanation:

\( \sqrt{5 + 4} \\ = \sqrt{9 } \\ = 3\)

Answer:

2x(x + 4)

Step-by-step explanation:

The greatest common factor of 2x^2 and 8x is 2x. So, we can factor out 2x to get:

2x(x + 4)

The definition of a greatest common factor (GCF) is the largest number that is a factor of two or more numbers. In this case, 2x is the GCF of 2x^2 and 8x because it is the largest number that divides both numbers evenly.

Here are the steps on how to factor out the GCF:

In this case, the factored expression is 2x(x + 4).

The answer is:

Work/explanation:

Let's find something that \(\sf{2x^2}\) and \(\sf{8x}\) have in common.

In other words, we find their GCF (greatest common factor).

The GCF of \(\sf{2x^2}\) and \(\sf{8x}\) is 2x.

So I factor it out :

\(\sf{2x(x+4)}\)

Answer:

Step-by-step explanation:

\(5mn^2-8m+mn^2\ \\ 6mn^2-8m\\ \\ 2m(3n^2-4)\)

In order to solve for the function input and output, first locate the specified input in the input values' row (or column).

Find the output value that corresponds to the given input value.

Locate the specified output values in the output values' row (or column), making note of each instance where the output value appears.

Find the input value or values that the given output value corresponds to.

The input and output of a function, respectively, are, to put it simply, what goes into and what comes out of the function.

The input and output variables are, respectively, x and y, in the equation y = x + 5. A value is an input into the function, say x = 3, and an output value is generated.

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When group members contribute less to the group than the average member, particularly as the group grows in size, those group members are engaged in social loafing.

Social loafing refers to the phenomenon where individuals exert less effort when working in a group compared to when working alone. As the group size increases, individual accountability diminishes, leading to a diffusion of responsibility and a decrease in individual effort.

This can result in some group members contributing less than the average member, taking advantage of the collective efforts of others.

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The slope of the line c is - 92.

The points via which the line b passes are:

(-20, 4) and (-21, 96).

The slope of the line is given by:

m = (y₂ - y₁) / (x₂ - x₁)

Slope of the line b passing through these points are:

m = (96 - 4) / (- 21 + 20)

m = (92) / (-1)

m = - 92

Since, line b is parallel to line c,

Slope of line b = slope of line c

So, the slope of line c is also:

m' = - 92

Therefore, we get that, the slope of the line c is - 92.

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Answer:

3.) 6 hours

4.) $52.5

5.) 15 minutes

6.) 16

Step-by-step explanation:

3.) 130/2.5 is rate he works at which is 52 houses per hour so do 312 divided my 52 to get 6 hours

4.) 12 months in a year so you do $630 divided 12 months to get a cost of $52.5 per month

5.) 16 miles divided by 20 minutes gives the rate it travels at which is 0.8 miles per minute. So, do 12 divided by 0.8 to get 15 minutes

6.) A dozen is 12 so you do $3.84 divided by 12 to get the cost of one egg which is $0.32 and multiply that by 50 eggs to get a cost of $16

Answer:

i think its this..   ._.

Step-by-step explanation:

if red is 10, and pulling a blue is 2, there is a 10/15 chace you will get a red, but a 2 out of 15 chance you will get a blue

The point (-2,2), we need to evaluate each case

In this case, for the real part we need to obtain -2

For the imaginary part, we need to obtain 2

As we can see the complex number that is shown in the graph is

ANSWER

A.

Answer:

I think the original price of the pants is $20.63

Step-by-step explanation:

25% of 16.50 is 4.125

4.125 + 16.50 = 20.625

20.625 - 4.125 = 16.50 (the price after the discount is subtracted from it)

round 20.625 to the nearest cent and you get 20.63.

Hope this helps!

Answer:

b

Step-by-step explanation:

because when u multiply the number that is outside of the bracket with the number inside the bracket it suppose to equal to the equation bk .....so b is the answer