LEMON SQUASH
1 part concentrate
to 2 parts water

If you put 140ml of water in a glass, how much concentrate should be added?

Answers:

The total profit expression is a binomial.

The total profit expression is a polynomial.

The total profit expression has a constant term.

The total profit expression is a polynomial

The total profit expression is a binomial

The total profit expression has a constant term

The first step to determining which type of function it is, is to add the profits in both theatres together

(t³ - t² + 2t - 100) + (t² - 2t - 300) = t³ - 400

A polynomial function is a mathematical expression that is made up of different types of variables. They include non-zero coefficients, positive exponents, and constants.

Types of polynomials include :

1. Linear polynomial function : a linear function is a function that has a single variable raised to the power of 1.

An example is x + 2

The variable x is raised to the power of 1. 2 is the constant terms

2.  Quadratic polynomial function - A quadratic function is a function that usually has a single variable and it is raised to the power of 2.

An example is 2x² + 10x + 25

3. Cubic polynomial function : this is a function that usually has a single variable raised to the power of 3.

An example is 5y³ + y²

4. Binominal function: this  is a function that contains only two terms.

An example is   t³ - 400

t³ - 400

The above equation of the total profit has a constant term which is -400

The above equation is a polynomial. This is because it has different types of variables.

The above equation is a binomial equation because it has only two terms  t³ and 400

In order to determine the type of expression the total profit is, the first step is to add the two profit expressions provided in the question. Based on the expression derived, the type of expression it is can then be deduced.

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Answer:

45 words in 9 minutes

Step-by-step explanation:

90/18= 5 words per minutes

5*9= 45

Answer:

3x-45+100=?

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

If the price of the stock is now $2.40 then the original stock price was $10.

In order to determine the original stock price, we need to work backwards from the current price of $2.40 and the percentage drops of 40% and 60%.

Let's assume that the original stock price was "x".

Then, we know that the stock price fell by 40% when the company overestimated demand.

This means that the new stock price was 60% of the original price (100% - 40% = 60%).

So, after the first drop, the stock price was:0.6x

Next, the company was forced to recall the seats due to them deflating in heat.

This caused the stock price to drop by another 60%, but from the new lower price of 0.6x.

This means that the new stock price was 40% of the previous price (100% - 60% = 40%).

So, after the second drop, the stock price was:0.4(0.6x) = 0.24x

Finally, we are given that the current stock price is $2.40.

Setting this equal to the second drop price, we can solve for "x":0.24x = 2.40x = $10

Therefore, the original stock price was $10.

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The critical values for these cases are 1.833, 1.330, -3.162, and 2.797.

Case | n | α | Tail | Critical Value

1 | 10 | 0.05 | Right | 1.833

2 | 18 | 0.10 | Two-tailed | 1.330

3 | 28 | 0.01 | Left | -3.162

4 | 25 | 0.01 | Two-tailed | 2.797

The critical value is the value of the test statistic that separates the rejection region from the acceptance region. In a right-tailed test, the rejection region is the area to the right of the critical value. In a left-tailed test, the rejection region is the area to the left of the critical value. In a two-tailed test, the rejection region is the area in both tails of the distribution, with equal areas on either side of the critical value.

The critical value is determined by the significance level (α), the degrees of freedom (df), and the type of test (one-tailed or two-tailed). The significance level is the probability of rejecting the null hypothesis when it is true. The degrees of freedom are the number of data points minus the number of parameters estimated in the model. The type of test is determined by whether you are testing for a difference in means (one-tailed) or a difference in proportions (two-tailed).

To find the critical value, you can use a t-table. A t-table is a table that lists the critical values for the t distribution. The t distribution is a probability distribution that is used to test hypotheses about the mean of a population. The t distribution is similar to the normal distribution, but it has heavier tails, which means that it is more likely to produce extreme values.

To use a t-table, you need to know the degrees of freedom and the significance level. Then, you can look up the critical value in the table. The critical value is the value of the t statistic that separates the rejection region from the acceptance region.

In the cases you mentioned, the degrees of freedom are 10, 18, 28, and 25. The significance levels are 0.05, 0.10, 0.01, and 0.01. The type of tests are right-tailed, two-tailed, left-tailed, and two-tailed, respectively.

The critical values for these cases are 1.833, 1.330, -3.162, and 2.797.

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Answer:

C)

Step-by-step explanation:

one is zero and one is positive. The addition symbol indicates that you are adding a positive number

The bar representing her 7-day vacation will have a class width of 16 - 22 and a height of 1.

The frequency distribution of a collection of data reveals how frequently each unique value appears.

The most typical graph for displaying frequency distributions is a histogram. Although it closely resembles a bar chart, there are significant variances.

In the given histogram class width(horizontal width)  represents the number of days and frequency(vertical height) represents the number of vacations taken.

Therefore, The 7-day vacation yet she took this summer will be represented by a bar having a class width 16 - 22 and a height of 1.

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Answer:

11, subtraction, 23 - 12 = 11

Answer:

34.69 years for the first part.

Step-by-step explanation:

I got it right

The cost of the television before the 15% off incentive is applied is $600.

Let's denote the cost of the television before the incentive as x.

We know that after the 15% off incentive is applied, the cost of the television is $510. This means that the price after the discount is equal to 85% of the original price:

85% of x = $510

To find the original price (x), we can set up the equation and solve for x:

0.85x = $510

To solve for x, we divide both sides of the equation by 0.85:

x = $510 / 0.85 = $600

Therefore, the cost of the television before the incentive is $600.

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The effective Interest rate when interest is compounded daily .the correct answer is option d) 0.0463 percentage points

To find the effective interest rate when interest is compounded daily, we need to use the formula:

A = P(1 + r/n)^(nt)

where A is the ending balance, P is the principal, r is the stated annual interest rate, n is the number of times the interest is compounded in a year, and t is the time in years.

If interest is compounded monthly, n = 12, and if interest is compounded daily, n = 365.

Let's assume Anna borrows $1,000 for one year.

With monthly compounding, the effective interest rate can be found using the formula:

A = 1000(1 + 0.1022/12)^(12*1) = $1,102.52

Effective interest rate = (A - P)/P = ($1,102.52 - $1,000)/$1,000 = 10.25%

With daily compounding, the effective interest rate can be found using the formula:

A = 1000(1 + 0.1022/365)^(365*1) = $1,103.09

Effective interest rate = (A - P)/P = ($1,103.09 - $1,000)/$1,000 = 10.29%

The difference between the effective interest rates is:

10.29% - 10.25% = 0.04 or 0.04%

Therefore, the correct answer is option d) 0.0463 percentage points.

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The volume of the solid obtained by rotating the region bounded on the right by the graph of g(y) = 6/y and on the left by the y-axis for 3 ≤ y ≤ 11, about the x-axis using cylindrical shells is approximately V = 143.03 units^3.

To find the volume using cylindrical shells, we integrate the formula V = 2π∫[a, b] x * h(x) dx, where x is the radius of the shell and h(x) is the height of the shell.

In this case, the radius x is given by the distance from the y-axis to the graph of g(y), which is x = 1/y. The height of each shell is the difference in y-values, h(x) = 11 - 3 = 8.

Thus, the volume can be calculated as V = 2π∫[3, 11] (1/y) * 8 dx.

Simplifying, we have V = 16π∫[3, 11] (1/y) dx.

Integrating, we get V = 16π[ln|y|] from 3 to 11.

Evaluating the integral and rounding to the nearest hundredth, we find V ≈ 143.03 units^3.

Therefore, the volume of the solid obtained by rotating the given region about the x-axis using cylindrical shells is approximately 143.03 units^3.

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There are 10 possible selections of groups of 2 students.

We have,

Number of students in chess club= 5

and, 2 students selected at random.

So, the possible number of selection

= C(5, 2)

= 5! / 2! (5-2)!

= 5!/ 2! 3!

= 5 x 4 /2

= 10

Thus, there are 10 possible selection.

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Answer:

0.09

Step-by-step explanation:

Move the decimal 3 points over :)

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Answer:

The correct answer is C: Y = -1/2x - 4.The slope of the given line is -1/2, so any line that is parallel to it will have the same slope. In order to find the equation of a line with the same slope that passes through the point (2, -5), we can use the point-slope form of the equation of a line.The point-slope form of the equation of a line is:y - y1 = m(x - x1)where m is the slope of the line, and (x1, y1) is a point on the line.In this case, we can plug in the values m = -1/2, x1 = 2, and y1 = -5 to get:y + 5 = -1/2(x - 2)Solving for y, we get:y = -1/2x - 4Therefore, the equation of the line that is parallel to the given line and passes through the point (2, -5) is Y = -1/2x - 4.

Using the Secant Method with initial guesses x0 = 0 and x1 = 1, the approximations of the exact root α = 55​ of f(x) = x^5 - 5 are calculated as follows: x2 ≈ 0.2000, x3 ≈ 0.4647, x4 ≈ 0.5025, x5 ≈ 0.5019.

The Secant Method is an iterative numerical method used to approximate the root of a function. Starting with initial guesses x0 and x1, the algorithm is applied iteratively to find successive approximations of the root. In this case, we are approximating the root α = 55​ of f(x) = x^5 - 5.

Using the given initial guesses x0 = 0 and x1 = 1, we can calculate x2 using the Secant Method formula. Substituting the values into the formula, we have x2 ≈ 0 - f(0) - f(1) / (f(0) - f(1)) * (0 - 1). Evaluating f(0) and f(1) gives f(0) = -5 and f(1) = -4. Plugging in these values, we get x2 ≈ 0 - (-5) - (-4) / (-5 - (-4)) * (0 - 1) ≈ 0.2.

Using x2 as the new x1, we can continue applying the Secant Method formula to find x3, x4, and x5. Following the same steps as above, we get x3 ≈ 0.4647, x4 ≈ 0.5025, and x5 ≈ 0.5019. These values represent successive approximations of the exact root α = 55​ of the given function.

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Answer:

A.

Step-by-step explanation:

Count the arrows.  A has 1, B has 2, and C has 3.  D will have 4.  The pattern is also one vertical and one horizontal arrow being added alternately.

The following distributions has a mean that varies

II. The distribution of sample data

III. The sampling distribution of the sample mean

The correct answer is option v) II and III."

Here, we have,

In the context of statistical distributions:

I. The population distribution refers to the distribution of a specific variable within the entire population. The mean of the population distribution which is fixed and does not vary.

II. The distribution of sample data refers to the distribution of a variable within a specific sample. The mean of the sample data can vary from one sample to another.

III. The sampling distribution of the sample mean refers to the distribution of sample means taken from multiple samples of the same size from a population. The mean of the sampling distribution of the sample mean is equal to the population mean, but the individual sample means can vary from sample to sample.

Therefore, the mean varies in both the distribution of sample data (II) and the sampling distribution of the sample mean (III), but not in the population distribution (I).

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In Milgram's first study of obedience, the majority of teachers initially complied but refused to deliver more than slight levels of shock.

In Milgram's first study of obedience, participants were assigned the role of 'teacher' and were instructed to administer electric shocks to a 'learner' whenever they answered a question incorrectly. The shocks ranged from mild to severe, with the highest level labeled as 'XXX.' The learner was actually an actor, and no real shocks were administered.

The study found that the majority of teachers initially complied with the experimenter's orders and delivered shocks, but they refused to deliver more than slight levels of shock. This suggests that while they were willing to follow the instructions to some extent, they had moral reservations about causing significant harm to another person.

It is important to note that the study has been criticized for ethical concerns and the potential psychological harm it may have caused to participants. However, it remains a significant contribution to our understanding of obedience and the power of authority figures.

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We have as expression the matrix A*(B + C) = [[-5, 6, -8], [-3, 3, 4]]

To compute the indicated expression A*(B + C) for the given matrices, you first need to make sure that the matrices are compatible for multiplication. This means that the number of columns in the left-hand matrix (A) must match the number of rows in the right-hand matrix (B + C). Since A is a 2x2 matrix and (B + C) is a 2x3 matrix, they are compatible and the expression can be evaluated.

The expression can be evaluated by multiplying each row of A by each column of (B + C). To do this, start by adding the two matrices B and C together.

B + C = 0 2 3 + 3 1 5 = 3 3 8

Then, multiply each row of A by each column of (B + C):

A*(B + C) =
[-1 2] * [3 3 8] = [-5 6 -8]
[-1 2] * [3 3 8] = [-3 3 4]

The final answer is A*(B + C) =

[[-5, 6, -8], [-3, 3, 4]]

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The reflection across x = -2 will be x = 2.

The correct option from the given options is (a) a lower bound on how many donuts he can eat in one sitting.

A lower bound is a value which is equal to or greater than the minimum value of a set. In this given scenario, eight donuts are a lower bound on how many donuts a teenager can eat in one sitting. He might be able to eat more than eight donuts in one sitting but he cannot eat less than eight donuts in one sitting because it's a lower limit.

A lower limit or a lower bound is an absolute minimum. It is the minimum number of donuts that the teenager can consume in one sitting. In this scenario, there is a possibility that the teenager might eat more than eight donuts, but the lower limit is eight.

Therefore, the correct option is (a) a lower bound on how many donuts he can eat in one sitting.

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The equation to find the cost of each pair of shorts is 175 = 75 + 5x where each short cost $20

Cost of jackets= $75

Number of shorts= 5

Cost of each short = x

Total amount Jim spent= $175

Total amount Jim spent = Cost of jackets + (Number of shorts × Cost of each short)

175 = 75 + 5x

subtract 75 from both sides

175 - 75 = 5x

100 = 5x

divide both sides by 5

x = 100/5

x = $20

Ultimately, each pair of shorts cost $20

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Answer:

The forecasted 20% chance of rain represents the probability of rain on any given day. This does not mean that exactly 20% of the days will have rain, but rather each day independently has a 20% chance of rain.

To calculate the expected number of rainy days over the next 7 days, you can multiply the total number of days (7) by the probability of rain on any given day (0.20 or 20%).

So, the expected number of rainy days is 7 * 0.20 = 1.4 days.

This, of course, is a statistical average. In reality, you can't have 1.4 days of rain - you'll either have 1 day, 2 days, or some other whole number of days. But on average, over many sets of 7-day periods, you'd expect about 1.4 days to have rain.

To find the mass of the thin bars, we need to integrate the density function over the given interval. The density function is given as p(x) = 1 + sin x, for 0 ≤ x ≤ π.

We know that density is defined as mass per unit volume. In this case, the density function represents the mass per unit length. So, to find the mass of the thin bars, we need to integrate the density function over the given length.

The formula for mass is given as:

m = ∫ρ(x)dx

where m is the mass, ρ(x) is the density function, and dx is the infinitesimal length element.

So, in this case, we have:

m = ∫(1 + sin x)dx

Integrating this expression, we get:

m = x - cos x + C

where C is the constant of integration.

Now, we need to evaluate this expression for x = π and x = 0 and subtract the two to get the mass of the thin bars.

m = π - cos π - (0 - cos 0)

m = π + 1

Therefore, the mass of the thin bars with the given density function is π + 1.

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Using geometry or symmetry we get, the value of the double integral is 36π.

To evaluate the given double integral using geometry and symmetry, first observe that the region D is a semicircle with radius 6 centered at the origin (since y = sqrt(36 - x^2) is the equation of the upper half of the circle x^2 + y^2 = 36).

Now, let's set up the double integral in polar coordinates.

Let x = r * cos(θ) and y = r * sin(θ). Then, dA = r dr dθ, and the bounds for r and θ are 0 ≤ r ≤ 6 and 0 ≤ θ ≤ π, respectively. The double integral now becomes:

∬(7x+2) dA = ∬(7r*cos(θ) + 2)r dr dθ

Now, integrate with respect to r:

∫[0,π]∫[0,6] (7r^2*cos(θ) + 2r) dr dθ

= ∫[0,π] [(7/3)r^3*cos(θ) + r^2] (from r=0 to r=6) dθ

= ∫[0,π] (504*cos(θ) + 36) dθ

Now, integrate with respect to θ:

= [(504 * sin(θ) + 36θ) (from θ=0 to θ=π)]

= 504 * (sin(π) - sin(0)) + 36 * (π - 0)

= 36 * π

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The amount paid as a car loan is $19,500 at 6% compounded annually of the principal amount of $15,000.

The Amount is calculated by \(A=P(1+\frac{r}{n} )^{nt}\)

where A is the Amount

P is the Principal

r is the Interest rate (in decimals)

n is the frequency at which the interest is compounded per year

t is the Time duration

According to the question,

Principal = $15,000

interest rate = 6% compound annually

Since interest is compounded annually, n =1

Time duration = 6 years

Therefore,

\(A= 15,000*(1+\frac{0.06}{1})^{1*5}\\ = 15,000*(1+0.06)^{5}\\= 15,000*(1.06)^{5}\\= 15,000*1.3\\= 19,500\)

Hence, the amount paid is $19,500.

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Answer:

92%

Step-by-step explanation:

To convert a fraction to a percent, you can divide the numerator by the denominator to end up with a decimal, in this case 0.92. Then, to convert to a percent, move the decimal two places to the left. As a result, we have 92%.

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