Enter a number for y. Approximate to THREE decimal places (last digit should be 8). Thanks in advance!

Answer:

(3x + 2) (x + 2)

Step-by-step explanation:

general form = ax² + bx + c

3x² + 8x + 4

a = 3

b = 8

c = 4

6 × 2 = a . c = 4 × 3 = 12

6 + 2 = b = 8

3x² + 6x +2x + 4

3x (x + 2) + 2 (x + 2)

(3x + 2) (x + 2)

The price elasticity of demand measures the responsiveness of the quantity demanded to changes in the price of a product. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Using the given information, we can calculate the price elasticity of demand as follows:

Percentage change in price = 50%

Percentage change in quantity demanded = -25% (since it decreased)

Price elasticity of demand = (-25%) / (50%) = -0.5

Since the price elasticity of demand is negative, this means that pizza is a normal good (as the increase in price led to a decrease in quantity demanded). The magnitude of the elasticity (-0.5) indicates that the demand for pizza is relatively inelastic, meaning that a 50% increase in price led to only a 25% decrease in quantity demanded.

According to Amelia's results, 42% of students prefer coffee in the morning. If the margin of error is ±0.072, between 689 and 978 students at the school prefer coffee.

To calculate percentage;

total coffee takers/ total number of students surveyed x 100.

TCT= 63  TSS = 150 which then becomes 63/150x 100 = 42

To calculate margin of error;

TCT/TSS - ME  and TCT/TSS + ME, which becomes

63/150 + 0.072 = 0. 49

63/150 - 0.072 = 0.35

Next we calculate the the highest and lowest number by saying;

0.49 x total number of students in the school  1,981 =

0. 35 x total number of students in the school  1,981 =

The above answer is in response to the full question below;

There are a total of 1,981 students enrolled at Amelia's high school. Amella surveyed 150 of the students regarding their morning drink preference. Her results are recorded in the table.

Drinks                               number

Milk                                     45

Juice                                   18

Coffee                                 63

Smoothie                            11

Others                                 13

Complete the statement.

According to Amelia's results, [DROP DOWN 1] prefer coffee in the morning. If the margin of error is ±0.072, between [DROP DOWN 2] and [DROP DOWN 3) students at the school prefer coffee.

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A pound of sugar will cost $1.59 in 2022

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

Initial, a = 0.43

Rate, r = 3.6%

The equation of the function is represeted as

f(x) = a * (1 + r)^x

So, we have

f(x) = 0.43 * (1 + 3.6%)^x

2022 is 37 years from 1985

So, we have

f(x) = 0.43 * (1 + 3.6%)^37

Evaluate

f(x) = 1.59

HEnce, the cost is $1.59

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Answer:

216g³

Step-by-step explanation:

(6g)³

6³ = 216

g³ = g³

So, (6g)³ simplify will be 216g³

a. The anticipated level of profits for the expected sales volumes is $998,200.

b. The break-even volume using weighted-average contribution margin is 46,242 tacos.

c. The new break-even volume with the changed product mix is 51,690 tacos.

What is profit?

Profit is the financial gain that results when the revenue from a business or investment exceeds the costs, expenses, and taxes associated with it.

a. To calculate the anticipated level of profits, we need to first calculate the total revenue and the total variable costs. The total revenue is calculated by multiplying the selling price per taco by the expected sales volume for each flavor and adding them up:

Total revenue = (3.9 x 201,000) + (5.3 x 303,000) = $2,463,000

The total variable costs are calculated by multiplying the variable cost per taco by the expected sales volume for each flavor and adding them up:

Total variable costs = (1.95 x 201,000) + (2.65 x 303,000) = $1,357,800

The contribution margin is calculated as the difference between the total revenue and total variable costs:

Contribution margin = Total revenue - Total variable costs = $2,463,000 - $1,357,800 = $1,105,200

The anticipated level of profits is calculated as the contribution margin minus the fixed costs:

Anticipated profits = Contribution margin - Fixed costs = $1,105,200 - $107,000 = $998,200

Therefore, the anticipated level of profits for the expected sales volumes is $998,200.

b. The weighted-average contribution margin is calculated as follows:

Weighted-average contribution margin = [(Contribution margin per chicken taco x Percentage of chicken sales) + (Contribution margin per fish taco x Percentage of fish sales)]

Contribution margin per chicken taco = Selling price per chicken taco - Variable cost per chicken taco = $3.9 - $1.95 = $1.95

Contribution margin per fish taco = Selling price per fish taco - Variable cost per fish taco = $5.3 - $2.65 = $2.65

Using the given product mix of 42% chicken and 58% fish, we have:

Weighted-average contribution margin = [(1.95 x 0.42) + (2.65 x 0.58)] = $2.31

The break-even volume is calculated as follows:

Break-even volume = Fixed costs / Weighted-average contribution margin = $107,000 / $2.31 = 46,242 tacos

Therefore, the break-even volume using weighted-average contribution margin is 46,242 tacos.

c. If the product sales mix were to change to four chicken tacos for each fish taco, the new product mix would be 80% chicken and 20% fish. Using the same calculation as in part b, the new weighted-average contribution margin would be:

Weighted-average contribution margin = [(1.95 x 0.8) + (2.65 x 0.2)] = $2.07

The new break-even volume would be:

Break-even volume = Fixed costs / Weighted-average contribution margin = $107,000 / $2.07 = 51,690 tacos

Therefore, the new break-even volume with the changed product mix is 51,690 tacos.

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The probability of opening to a page that is either 8 or 12 is 2/13.

The probability of opening to a page that is either 8 or 12 can be found by adding the individual probabilities of opening to page 8 and page 12. Since there are 13 pages in total, each page has a 1/13 chance of being opened. Therefore, the probability of page number 8 is 1/13, and the probability of opening to page 12 is also 1/13.

The probability of opening to page 8 or page 12 is the sum of the individual probabilities:

P(opening to page 8 or page 12) = P(opening to page 8) + P(opening to page 12)

P(opening to page 8 or page 12) = 1/13 + 1/13

P(opening to page 8 or page 12) = 2/13

Therefore, the probability of opening to a page that is either 8 or 12 is 2/13 or about 0.1538

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Joseph's mom was driving at a rate of 93.75 km/h.

Let's start by using the formula;

distance = rate × time

Let's call the distance that Joseph and his mom traveled "D". Let's also call the time that Joseph and his mom traveled before Joseph's dad caught up "T". Since Joseph's dad traveled for one hour less than Joseph and his mom, his travel time was "T - 1".

We know that Joseph's dad drove for four hours at 75 km/h, so he covered a distance of;

75 km/h × (T - 1) h = 75T - 75 km

We also know that Joseph and his mom traveled for T hours at some rate, which we'll call "R", so they covered a distance of;

R × T = D km

Since they ended up at the same place, we can set these two distances equal to each other;

75T - 75 = D

Rearranging, we get;

D = R × T

Substituting the expression for D, we get;

75T - 75 = R × T

Simplifying;

75 = R - 75/T

We know that R is the rate at which Joseph's mom was driving, and we want to find that rate. We also know that T is the time that she was driving before Joseph's dad caught up. We can solve for R by substituting the values we know;

75 = R - 75/T

75 = R - 75/4

R = 75 + 75/4

R = 93.75 km/h

Therefore, Joseph's mom was driving at 93.75 km/h.

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Based on the information, the hedgehogs have made the better offer

The Turkeys are offering a yearly salary of S(t) = 90000t over the course of eight years. To calculate the present value of each payment, an equation is used:

PV = S(t) * e^(-rt)

The variable "r" denotes a continuous interest rate of 0.03. "t" equals the years from t=0 to the time of payment. By this method, the current value of the Turkeys' offer can be assessed as follows:

PV(Turkeys) = ∫[0,8] 90000t * e^(-0.03t) dt

= 736,918.63

Comparatively, the Hedgehogs propose a yearly salary of S(t) = 80000t for nine years. Utilizing the formula employed in the previous scenario, the following result is derived:

PV(Hedgehogs) = ∫[0,9] 80000t * e^(-0.03t) dt

= 753,472.49

Given these calculations and the presumption that Rogelio may earn a continuous interest rate of 3% on his funds, it would best serve him to accept the Hedgehogs’ item offer since they have offered him a more favorable contract based on the accumulated present value of both contracts.

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The expression in complete factored form is:

(q-7)(b-5)

Expressions can be evaluated by replacing the variables with specified values, and the resulting expression can then be made simpler using arithmetic operations.

In numerous branches of mathematics, such as algebra, calculus, and geometry, as well as in a number of scientific disciplines, including physics and engineering, they are employed.

The given expression is:

b(q-7)-5(q-7)

Notice that both terms have a common factor of (q-7). We can factor out this common factor to get:

(q-7)(b-5)

Therefore, the expression in complete factored form is:

(q-7)(b-5)

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Answer:

The answer is A. 4 < x < 12.

Step-by-step explanation:

By isolating the absolute value expression:

9|x – 8| < 36

|x – 8| < 4

Break this down into two separate inequalities, one without the absolute value:

x - 8 < 4 or x - 8 > -4

Simplifying each one:

x < 12 or x > 4

Now we can combine these two inequalities with an "and" statement, since the value of x must satisfy both inequalities:

4 < x < 12

Therefore, the solution to the inequality 9|x – 8| < 36 is 4 < x < 12.

Answer:   k=8

Step-by-step explanation:

Let's multiply all by common denominator (x-5)(x+2) to get rid of fractions

3(x+2) - k(x-5) = 46 - 5x

3x+6-kx+5k = 46-5x                    

3x - kx + 6 +5k  =46 -5x                In order to balance an equation you can set constants equal to each other and x terms equal to each other so:

3x-kx= -5x           or     6+5k=46

3-k=-5                               5k=40

-k=-8                                     k=8

k=8

The price markup when we bought products for $50.00 and sold for $67.00 is c. 34%.

Price markup is the amount by which the selling price of a product is increased from its cost price.

It is expressed as a percentage of the cost price.

We would use the below formula to find out the price markup:

Markup = (Selling price - Cost price) / Cost price * 100%

Here,

cost price = $50.00

selling price = $67.00.

Markup = (67.00 - 50.00) / 50.00 * 100%

Markup = 17 / 50 * 100%

Markup = 0.34 * 100%

Markup = 34%

Therefore, the price markup is 34%.

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Answer:

Eli speed is above the speed limit by 14.374km/h

Step-by-step explanation:

Eli speed=40mph

speed limit =50km/h

converting Eli speed to 40mph to km/h

E=64.374km/h

Eli speed- speed limit=64.374-50=14.374km/h

After considering the given data we conclude that the cubic feet of natural gas used by world  from 1990 to 2020 is 426,000 billion cubic feet.

It is known to us that the demand for natural gas was growing exponentially at the rate of 7% per year since 1990. Then, we can applu the formula for exponential growth:
[tex]A = P(1 + r)^t[/tex]

Here,
A = amount after time t,
P = initial amount (at time t=0),
r = annual growth rate expressed as a decimal,
t= time in years.
For the given case,
P = 70223 billion cubic feet,
r = 0.07 (7% growth rate),
t = 2020 - 1990 = 30 years.
Staging these values into the formula gives:
A = 70223(1 + 0.07)³⁰
A ≈ 426,000 billion cubic feet

Hence, if there is a higher requirement for natural gas and it  grows at a rate of 7% per year from 1990 to 2020, the world will have consumed approximately 426,000 billion cubic feet of natural gas by 2020.

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Stefanie bought 14 erasers.

Let's call the number of erasers Stefanie bought x.

We know that Stefanie paid $ 1.25 for the pencils, and she bought x erasers that each cost $ 0.50. So the total cost of the erasers is 0.5x.

Stefanie paid a total of $ 8.25, so we can write an equation:

1.25 + 0.5x = 8.25

1.25 + 0.5x - 1.25 = 8.25 - 1.25

Subtracting 1.25 from both sides, we get:

0.5x = 7

Dividing both sides by 0.5, we get:

x = 7 / 0.5

x = 7 × 2

x = 14

Therefore, Stefanie bought 14 erasers.

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Given question is incomplete, the complete question is below

Stefanie bought a package of pencils for $1.25 and some erasers that cost $0.50 each. She paid a total of $8.25 for these items, before tax. Exactly how many erasers did Stefanie buy?

Answer:

a. 2 (numbers less than 0 are negative)

b. 4  (numbers greater than and including 0 are 'not negative')                                                                                  

The expression of the inequality word problems for each question is: As expressed below

A) x is negative. This can be expressed as;

x < 0

B) y is non-negative. This can be expressed as;

y > 0

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We are given that a hose in the front yard can fill the pool in 30 minutes and a hose in the back yard can fill it in half the time (so 15 minutes). We are asked to find the time, we'll call "t," it takes for both hoses together to fill up the pool.

We can create a rational equation, [tex]\frac{1}{30}+\frac{1}{15}=\frac{1}{t}[/tex]. Solve to "t"

[tex]\frac{1}{30}+\frac{1}{15}=\frac{1}{t} \Longrightarrow \frac{1}{30}+\frac{1}{15}*\frac{2}{2} =\frac{1}{t} \Longrightarrow \frac{1}{30}+\frac{2}{30} =\frac{1}{t} \Longrightarrow \frac{3}{30} =\frac{1}{t}[/tex]

[tex]\Longrightarrow \frac{1}{t}=\frac{3}{30} \Longrightarrow \frac{1}{t}=\frac{1}{10} \Longrightarrow \boxed{t=10 \ min}[/tex]

Thus, b is the correct option.

The displacement over the interval is 0 and the distance over the interval is 27 meters

Given that

Velocity, v(t) = 3t² – 6t

Integrate to get the displacement function

So, we have

d(t) = t³ - 3t²

The interval is [0, 3]

So, we have

d(0) = 0³ - 3(0)² = 0

d(3) = 3³ - 3(3)² = 0

The displacement over the interval is 0

Recall that

v(t) = 3t² – 6t

So, we have

v(3) = 9

So, we have

distance = speed * time

This gives

distance = 9 * 3

Evaluate

distance = 27 meters

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The quotient of the rational expression is [tex]A = \frac{4(x+2)}{(x-2)}[/tex]

Given data ,

Let the first expression be represented as p

Let the second expression be represented as q

And , A = p / q

[tex]p= {\frac{(x^{2}-4) }{(x+3)}[/tex]

[tex]q= {\frac{x^{2}-4x+4 }{4x+12} }[/tex]

where , [tex]A = \frac{\frac{(x^{2}-4) }{(x+3)} }{\frac{x^{2}-4x+4 }{4x+12} }[/tex]

On simplifying , we get

[tex]A = \frac{4(x^{2} -4)}{(x-2)^{2} }[/tex]

Now , taking the common terms in the equation , we get

[tex]A = \frac{4(x-2)(x+2)}{(x-2)(x-2)}[/tex]

[tex]A = \frac{4(x+2)}{(x-2)}[/tex]

Hence , the equation is [tex]A = \frac{4(x+2)}{(x-2)}[/tex]

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The values that make the inequality "b/2 ≥ -2" True are {-2,-4,-1,-3,0}, and the equivalent inequality in terms of "b" is b ≥ -4.

In order to make the inequality b/2 ≥ -2 true, we need to find the values of "b" that satisfy the inequality.

We multiply both sides of the inequality by 2 to eliminate the fraction:

b/2 ≥ -2

2 × (b/2) ≥ 2 × (-2)

b ≥ -4

So, any value of "b" that is greater than or equal to -4 will make the inequality b/2 ≥ -2 true.

From the given numbers, the numbers which are greater than or equal to -4 are {-2,-4,-1,-3,0}

Also, the inequality in term of b is b ≥ -4.

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Step-by-step explanation:

Monte answered 9 questions each worth 4 points =  9x 4 = 36 points

 the rest of the 87 points were three-pointers  ( 87-36) = 51 points

      51 points / ( 3points /question)  = 17 three pointers

Answer: I think the answer is 29 I hope this is helping you

Step-by-step explanation: Since 87 divided by 3 gives an integer which is 29 and 29 times 3 is 87 I think this is the answer I'm not entirely sure but that's what I think

The number of each coin that Ken has is 17 nickels and 8 dimes.

In order to determine the values of the variables that satisfy each equation, a system of equations is a collection of two or more equations that must be solved concurrently. In contrast, there is just one unknown variable to be solved for in a single equation. A set of equations can be used to simulate more difficult issues with several variables and connections, such as those found in engineering or economics. Finding the values of the variables that satisfy all of the equations in a system of equations frequently entails employing algebraic techniques like substitution or elimination.

Let us suppose the number of nickels = x.

The number of dimes = y.

Thus, we have:

x + y = 25

x = 25 - y

The value of the nickel is 0.05 and that of dime is 0.10 thus:

0.05x + 0.10y = 1.65

Now for the two equations substitute the value of x from the first equation in the second equation:

0.05(25 - y) + 0.10y = 1.65

1.25 - 0.05y + 0.10y = 1.65

0.05y = 0.40

y = 8

Substituting the value of y to obtain x we have:

x + 8 = 25

x = 17

Hence, the number of each coin that Ken has is 17 nickels and 8 dimes.

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The correct answer is option 3 i.e. At the 0.05 level of significance, the data provides sufficient evidence to conclude that the difference between the averages is real.

What is a two-sample test?

A two-sample test, also known as a two-sample hypothesis test, is a statistical test used to compare the means of two different groups. The test determines whether there is a significant difference between the means of two populations or groups based on the samples drawn from each group. The test is typically used when the samples are independent and the data is continuous. The goal of the test is to determine whether the observed difference between the two sample means is statistically significant or whether it is simply due to chance variation.

To perform an independent two-sample test, we need to formulate our null and alternative hypotheses:

Null hypothesis: The mean hours of pay for freshman at public universities is equal to the mean hours of pay for freshman at private universities.

Alternative hypothesis: The mean hours of pay for freshman at public universities is not equal to the mean hours of pay for freshman at private universities.

We can use a two-sample t-test to compare the means of the two groups, assuming unequal variances since the sample sizes and standard deviations are different.

Using a statistical software or calculator, we can find the test statistic and p-value:

Test statistic: t = -9.767

p-value: < 0.001

Since the p-value is less than the level of significance (0.05), we reject the null hypothesis and conclude that the mean hours of pay for freshman at public universities is significantly different from the mean hours of pay for freshman at private universities.

Therefore, the answer is: At the 0.05 level of significance, the data provides sufficient evidence to conclude that the difference between the averages is real.

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The total number of signs require to sell is 21 to earn $882.

Let's start by using the information given to write an expression for Jim's weekly income, I, as a function of the price per sign, x.

The number of signs Jim sells per week is given by:

[tex]63 - x[/tex]

And since Jim charges x dollars for each sign, his weekly income is:

[tex]I(x) = x(63 - x)[/tex]

Now we can use this expression to solve the problem. We want to find the smallest number of signs Jim can sell to have an income of $882 in one week.

In other words, we want to find the value of x that makes I(x) equal to $882. So we can set up the equation:

[tex]x(63 - x) = 882[/tex]

Expanding the left-hand side:

[tex]63x - x^2 = 882[/tex]

Rearranging and putting in the standard quadratic form:

[tex]x^2 - 63x + 882 = 0[/tex]

Now we can use the quadratic formula to solve for x:

[tex]x = \frac{-b \pm \sqrt{(b^2 - 4ac})} { 2a}[/tex]

where a = 1, b = -63, and c = 882. Plugging in these values:

[tex]x = \frac{63 \pm \sqrt{(63^2 - 4*1*882})} { 2*1}[/tex]

[tex]x = \frac{63 \pm sqrt(441)} {2} \\x = \frac{63 \pm 21}2[/tex]

So the two possible values of x are:

[tex]x = 42 \\ x = 21[/tex]

Of these, the only value that makes sense for the problem is x = 42, since we can't sell a negative number of signs.

Therefore, the smallest number of signs Jim can sell to have an income of $882 in one week is:

63 - x = 63 - 42 = 21 signs.

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The rational function with the given characteristics is:

r(x) = (x+9)(x-4) / (x-3)(x+5), with a hole at x=-2 and a horizontal asymptote at y=4

Any function that can be represented as the ratio of two polynomial functions is said to be rational. Therefore, a rational function has the following form: f(x) = P/Q(x)

where Q(x) is not equal to zero and P(x) and Q(x) are polynomial functions. Any real number that does not cause the denominator Q(x) to equal zero is excluded from the domain of a rational function since division by zero is undefined.

Rational functions can display a wide range of distinct behaviours, including x- and y-axis intercepts, holes in the graph, and vertical and horizontal asymptotes. They are frequently employed to simulate a variety of processes, such as those in physics, chemistry, and economics.

A function approaches a horizontal line known as a horizontal asymptote as input (x) approaches positive or negative infinity.

In other words, it is a line that the function approaches steadily as x increases or decreases.

The existence of a horizontal asymptote and its location depend on the degree of the numerator and denominator for a rational function of the type f(x) = P(x) / Q(x), where P(x) and Q(x) are polynomial functions.

Three scenarios are possible:

The horizontal asymptote is the x-axis (y=0) if the degree of P(x) is smaller than the degree of Q(x).

According to the question,

We can start by utilising the following form to develop a rational function that satisfies the requirements: r(x) is equal to (x+9)(x-4)(x+2)/(x-3)(x+5).

This function contacts the x-axis at x=4 (where the numerator is zero but the denominator is not) and has a zero at x=-9 (where the numerator becomes zero). There are other vertical asymptotes where the denominator reaches zero but the numerator does not, for x=-5 and x=3.

We can remove the (x+2) element from both the numerator and the denominator to introduce a hole at x=-2, resulting in:

r(x) is equal to (x+9)(x-4)/(x-3)(x+5).

We can remove the (x+2) element from both the numerator and the denominator to introduce a hole at x=-2, resulting in:

r(x) is equal to (x+9)(x-4)/(x-3)(x+5).

The degree of the numerator must not be more than the degree of the denominator in order for the function to have a horizontal asymptote at y=4. There is a horizontal asymptote at y=4 because the numerator and denominator in this example have degrees of 2 and 2, respectively.

As a result, given the characteristics given, the rational function is:

With a hole at x=-2 and a horizontal asymptote at y=4, r(x) = (x+9)(x-4) / (x-3)(x+5).

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On solving the query we can say that Based on the provided sample data, we can conclude with a 98% confidence that the real population proportion is between 0.4392 and 0.7138.

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

We may use the following formula to create a confidence interval for the population proportion:

CI is equal to pz/2*(p(1-p)/n)

where:

p = sample percentage

Based on the ordinary normal distribution, z/2 is the z-score for the degree of confidence (with a 98% confidence level, z/2 = 2.33).

sample size, n

Given:

The population proportion's 98% confidence interval is as follows:

CI = (0.4392, 0.7138)

Based on the provided sample data, we can conclude with a 98% confidence that the real population proportion is between 0.4392 and 0.7138.

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On solving the query we can say that Based on the provided sample data, we can conclude with a 98% confidence that the real population proportion is between 0.4392 and 0.7138.

What is function?

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

We may use the following formula to create a confidence interval for the population proportion:

Cl is equal to pz/2"(p(1-p)/n)

where:

p = sample percentage

Based on the ordinary normal distribution, z/2 is the z-score for the degree of confidence (with a 98% confidence level, z/2 = 2.33).

sample size, n

Given:

The population proportion's 98% confidence

interval is as follows:

CI = (0.4392, 0.7138)

Based on the provided sample data, we can conclude with a 98% confidence that the real population proportion is between 0.4392 and 0.7138.

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Step-by-step explanation:

The domain of the new function remains the same as the domain of the original function because it only affects the coefficient of x, not the values of x itself.

However, the range of the new function changes because increasing the coefficient a shifts the entire graph of the function upwards. Specifically, the range of the new function becomes y ≥ 2 since the minimum value of the function is now 2, which occurs when x = 0.

Therefore, the correct answers are:

The domain stays the same.

The range becomes y ≥ 2.

The only value of k that allows us to write √50 + √k as a single term is

k = 25.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To be able to write the expression √50 + √k as a single term, we need to find a perfect square that is a factor of both 50 and k.

Prime factorizing 50, we get 50 = 2 * 5².

Since 50 contains a factor of 2, any perfect square factor of 50 must also contain a factor of 2. The only perfect square factor of 50 that contains a factor of 2 is 2*5² = 50 itself.

Now we need to find a perfect square that is a factor of k and contains a factor of 5. This can be done by prime factorizing k and seeing if any of the factors can be squared and still contain a factor of 5.

Let's try some values of k:

If k = 5, then √k = √5, which is not a perfect square, so it won't work.

If k = 25, then √k = 5, which is a perfect square that contains a factor of 5, so we can write √50 + √25 as 5√2 + 5 = 5(√2 + 1).

If k = 125, then √k = 5√5, which is not a perfect square, so it won't work.

Therefore, the only value of k that allows us to write √50 + √k as a single term is k = 25.

So, √50 + √25 can be written as 5(√2 + 1).

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