Alyssa’s lemonade recipe calls for 9 lemons for every 2.5 gallons of water. Brian’s recipe calls for 12 lemons for every 4 gallons of water. Whose lemonade will require more water if they each use 36 lemons? . can you help me

We need to buy 23.64 gallons of a 30% chlorine concentration to mix with 76.36 gallons of 85% chlorine concentration from the storage tank to clean the machine.

To calculate the required amount of a 30% chlorine concentration, we can use the following formula:

Amount of 85% chlorine mixture × % Chlorine in 85% mixture + Amount of 30% chlorine mixture × % Chlorine in 30% mixture = Amount of 64% chlorine mixture × % Chlorine in 64% mixture

We can plug in the given values:

Amount of 85% chlorine mixture = X Amount of 30% chlorine mixture = Y% Chlorine in 85% mixture = 85%% Chlorine in 30% mixture = 30%% Chlorine in 64% mixture = 64%

Using the above values, the formula can be rewritten as:

X × 85% + Y × 30% = 100 × 64%

Simplifying the above equation:

0.85X + 0.3Y = 64

Dividing by 0.3 on both sides, we get:

2.833X + Y = 213.33

Now, we can use the given information that the total amount of chlorine mixture required is 100 gallons.

Therefore: X + Y = 100 Solving the above system of equations, we get:

X = 23.64 gallons Y = 76.36 gallons

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If the mpc increases in value, the consumption function will become steeper.

What is MPC ?

MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. In economics, the marginal propensity to consume is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes.

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Given: The market price of a stock = $48.15, Dividend just paid = $5.79, Expected growth rate of dividend = 3.79%To find: Required rate of return for the stock Let's assume the required rate of return is "r" According to the constant growth model of dividends,

The present value of future dividends can be calculated as follows, PV of future dividends = D / (r-g)where D = dividend just paid = $5.79g = expected growth rate of dividend = 3.79%Now, let's substitute the given values, PV of future dividends = 5.79 / (r - 3.79%)As per the problem, the market price of the stock is $48.15. This means that the present value of all future dividends is equal to the current stock price. So we can set up the following equation, PV of future dividends = 48.15Substituting the value of the present value of future dividends in the above equation,5.79 / (r - 3.79%) = 48.15Solving for r, we get,r = 12.29%Hence, the required rate of return for the stock is 12.29%.

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Answer:

Step-by-step explanation:

If you mean:

3x+4-(x+8)^2, then

3x+4-(x^2+16x+64)

3x+4-x^2-16x-64

-x^2-13x-60

Answer:

-x^2-30x-60

Step-by-step explanation:

The magnitude of vector A is 16.04 and the angle θ in degrees between the calculated vector-and the +x-axis is 53.4° measured counterclockwise from the +x-axis.

Components of vector A, Aₓ = -9.35 and A_y = -13.4

Now we need to find the magnitude of this vector A

To find the magnitude of this vector A, use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

The magnitude of vector A is, A = √(Aₓ² + A_y²)

By substituting the given values, we have

A = √((-9.35)² + (-13.4)²) = 16.04

Therefore, the magnitude of vector A is 16.04.

The next part of the question is to determine the angle θ in degrees between the calculated vector-and the +x-axis, measured counterclockwise from the +x-axis.The angle θ is given by, θ = tan⁻¹(A_y / Aₓ)

By substituting the given values, we have

θ = tan⁻¹((-13.4) / (-9.35)) = tan⁻¹(1.43) = 53.4°

Therefore, the angle θ in degrees between the calculated vector-and the +x-axis is 53.4° measured counterclockwise from the +x-axis.

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To return true if both x and y are positive, you can use a simple if statement in Python that checks if both variables are greater than 0. If they are, the statement will return true.

Here is an example in Python:

```python
def check_positive(x, y):
 if x > 0 and y > 0:
   return True
 else:
   return False
```
In this example, the function `check_positive` takes in two variables, `x` and `y`, and checks if they are both greater than 0. If they are, the function returns `True`. If either `x` or `y` is less than or equal to 0, the function returns `False`.

You can also write this function more concisely using a single return statement:

```python
def check_positive(x, y):
 return x > 0 and y > 0
```
This function will return `True` if both `x` and `y` are greater than 0, and `False` otherwise.

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Answer:

126 people

Step-by-step explanation:

Given that, ratio of people who preferred tea to those who preferred coffee = 9:5

Let number of people who preferred coffee = x

Number of people who preferred tea = x + 36

Total number of people in survey = x + (x+36)

Ratio of people who preferred tea to those who preferred coffee = (x + 36)/x = 9/5

Cross multiply to solve for x

5(x + 36) = x(9)

5x + 180 = 9x

Subtract 5x from both sides

180 = 9x - 5x

180 = 4x

Divide both sides by 4

180/4 = x

45 = x

x = 45

Number of people who preferred coffee = x = 45

Number of people who preferred tea = x + 36 = 45 + 36 = 81

Total number of people in the survey = x + (x + 36) = 45 + 81 = 126 people

the area under the standard normal curve between z = -0.89 and z = 2.56 is approximately 0.8088 when rounded to four decimal places.

To find the area under the standard normal curve between z = -0.89 and z = 2.56, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we look up the values corresponding to z = -0.89 and z = 2.56.

The area to the left of z = -0.89 is given by the cumulative probability P(Z < -0.89). Looking up this value in the table, we find it to be approximately 0.1867.

The area to the left of z = 2.56 is given by the cumulative probability P(Z < 2.56). Looking up this value in the table, we find it to be approximately 0.9955.

To find the area between these two z-values, we subtract the cumulative probability of the lower bound from the cumulative probability of the upper bound:

Area = P(-0.89 < Z < 2.56) = P(Z < 2.56) - P(Z < -0.89)

= 0.9955 - 0.1867

= 0.8088

Therefore, the area under the standard normal curve between z = -0.89 and z = 2.56 is approximately 0.8088 when rounded to four decimal places.

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The value of the given power, 5^(-5), can be found by calculating the reciprocal of 5 raised to the power of 5.

To find the value of 5^(-5), we need to calculate the reciprocal of 5 raised to the power of 5, which is equivalent to raising 5 to the power of -5.

Using the rule for negative exponents, we know that a negative exponent indicates the reciprocal of the base raised to the positive exponent. In this case, 5^(-5) is equal to 1/(5^5).

To simplify further, we can calculate 5^5, which is equal to 3125. Therefore, the reciprocal of 3125 is 1/3125.

Hence, the value of the power 5^(-5) is 1/3125.

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The  trains are side by side after approximately 15 seconds.Option (b) is correct.

The position of the first train is given by the function:

\($$y_1 = 14t^2$$\)

The position of the second train is given by the function:

\($$y_2 = 130t + 1200$$\)

To find the time when the trains are side by side, we need to solve for the value of t that makes y1 = y2. Thus, we can set the two equations equal to each other:

\($$14t^2 = 130t + 1200$$\)

Rearranging the terms, we get:

\($$14t^2 - 130t - 1200 = 0$$\)

Dividing both sides by 2 to simplify the coefficients, we get:

\($7t^2 - 65t - 600 = 0$$\)

We can use the quadratic formula to solve for t:

\($t = \frac{-(-65) \pm \sqrt{(-65)^2 - 4(7)(-600)}}{2(7)} = \frac{65 \pm \sqrt{4225 + 16800}}{14}$$\)

Simplifying the expression under the square root, we get:

\($$\sqrt{21025} = 145$$\)

So the solutions are:

\($t_1 = \frac{65 + 145}{14}=15$$\)

\($t_2 = \frac{65 - 145}{14} \approx -5.71$$\)

Since time cannot be negative, we discard t2 as an extraneous solution. Thus, the viable time when the trains are side by side is:

\($t = t_1 =15$$\)

Therefore, the trains are side by side after approximately 15 seconds.

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We can conclude that it is extremely unlikely to obtain a sample mean greater than 904.8 minutes if the design engineer's claim about the population variance and mean is true.

We can use the Central Limit Theorem to approximate the distribution of the sample means.

Under the given assumptions, the mean of the sampling distribution of the sample means is equal to the population mean, which is 886886 minutes, and the standard deviation of the sampling distribution of the sample means is equal to the population standard deviation divided by the square root of the sample size, which is\(\sqrt{84648464/145145} = 41.77\) minutes.

Therefore, we can standardize the sample mean using the formula:

\(z = (\bar{x} - \mu) / (\sigma / \sqrt{n } )\)

where \(\bar{x}\)  is the sample mean, \(\mu\)  is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values we get:

z = (904.8 - 886886) / (41.77) = -21115.47

The probability of getting a sample mean greater than 904.8 minutes can be calculated as the area under the standard normal curve to the right of z = -21115.47.

This probability is essentially zero, since the standard normal distribution is symmetric and nearly all of its area is to the left of -6.

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The value of x for the given parallelogram is 4.8 cm.

According to the question,

We have the following information:

We have a parallelogram with base x cm, height 2.5 cm and area 12 square centimeters.

(More to know: in a parallelogram, the opposite sides are equal and parallel to each other. Opposite angles of parallelogram are equal and the sum of consecutive angles is 180°.)

We know that the following formula is used to find the area of the parallelogram:

Area of parallelogram = Base*height

x*2.5 = 12

x = 12/2.5

x = 4.8 cm

Hence, the value of x is 4.8 cm.

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There are 20,016 ways the yearbοοk can chοοse the winners οf mοst athletic, class clοwn, and best schοοl spirit frοm a class οf 28 students.

When the οrder οf the elements is unimpοrtant (unlike in permutatiοns), a cοmbinatiοn is a mathematical chοice made frοm a grοup οf different elements. There are three pοssible pairings οf the twο, fοr example, if three fruits are prοvided, such as an apple, a pear, and a range.

Fοrmally, a set S's k unique cοmpοnents make up a k-cοmbinatiοn, which is a subset οf S. Sο, if and οnly if twο cοmmunities have the same members, they are cοnsidered tο be identical. It dοesn't matter hοw each set οf individuals is arranged. the quantity οf K-cοmbinatiοns fοr an ensemble οf N cοmpοnents.

Tο determine the number οf ways the yearbοοk can chοοse the winners οf mοst athletic, class clοwn, and best schοοl spirit, we can use the permutatiοn fοrmula.

The number οf permutatiοns οf r οbjects taken frοm a set οf n distinct οbjects is given by:

nPr = n! / (n-r)!

where n! denοtes the factοrial οf n, which is the prοduct οf all pοsitive integers up tο n.

The οrder in which we chοοse the students matters because we are selecting winners fοr specific categοries. Therefοre, we can use the permutatiοn fοrmula tο calculate the number οf ways tο chοοse the winners as:

28P3 = 28! / (28-3)! = 28! / 25! = 28 x 27 x 26 = 20,016

Therefοre, there are 20,016 ways the yearbοοk can chοοse the winners οf mοst athletic, class clοwn, and best schοοl spirit frοm a class οf 28 students.

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The slant height of a cone that has a lateral area of 320π cm² and diameter of 20 cm is 32 cm.

The lateral area of a cone can be described as follows:

where

r = radius

l = slant height

Therefore,

r = 20 / 2 = 10 cm

l = ?

lateral area = 320π cm²

320π = π × 10 × l

320π = 10πl

divide both sides by 10π

l = 320π / 10π

l = 32 cm

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The correct value of the inequality as solves is x > 14 , and the error made by the student was that he directly divided the RHS by 7.

To simplify the equation we will multiply 7 on both the sides.

Then we will get the result as 7x > 98

Thus, we can say that the new inequality will be x > 14 ,

Hence , the mistake made by the student was that he didn't divided both the sides by 7 but only one side.

So a result, he obtained the incorrect result x>2.

Inequality is a concept in mathematics and uses symbols such as > , < , <= , >= etc.

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The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated by a normal distribution with a mean value of 125 seconds and a standard deviation of 20 seconds. The fastest 10% are to be given advanced training.

What task times qualify individuals for such training? (Round the answer to one decimal place.)The percentile score is used to solve this problem.
P = 10% = 0.10
z-score formula is:z = (X - μ) / σ
Plug in the values to get the z-score = z = (X - 125) / 20
Where X is the required time at which 10% of the employees must complete the task.
The inverse standard normal distribution function can be used to solve for X. Here's the formula for it:
X = μ + zσ = 125 + (-1.28)(20) = 99.6 seconds
The time required for the fastest 10% of workers to complete the task is 99.6 seconds. Therefore, individuals who complete the task within 99.6 seconds will be qualified for advanced training.

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a. The population of interest to the researchers were adults living in Tennessee. The sample of interest were the 575 study participants who were selected using a random-digit telephone dialing procedure.

b. The data collection method was a survey conducted through telephone interviews. The potential biases in the method used could include non-response bias, where individuals who do not have telephones or do not answer calls may be excluded from the study. Additionally, there may be social desirability bias, where individuals may not report their true insomnia status due to social pressures.

c. The variables measured in the study were years of education and insomnia status. Years of education is a quantitative variable, while insomnia status is a qualitative variable.

d. The researchers inferred that there is a relationship between education status and insomnia, where individuals with fewer years of education are more likely to have chronic insomnia. However, it should be noted that correlation does not imply causation and further research would be needed to establish causality.

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We need to  know about margin of error to solve the problem. The factors that influence margin of error are confidence level and sample size.

Margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result will reflect the result of a census of the entire population. Margin of error is influenced by three factors, confidence level, sample size and population standard deviation. In absence of population standard deviation, the margin of error is influenced by confidence level and sample size.

Therefore the margin of error is influenced by confidence level and sample size.

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Answer:

hjhjvv

Step-by-step explanation:

jg bb ;jhm b m

jjonmk

bj

'ol

B

Answer:

Units of Length

10 millimeters (mm) = 1 centimeter (cm)

10 decimeters = 1 meter (m)

10 decimeters = 1000 millimeters

10 meters = 1 dekameter (dam)

Answer:

\(m=\frac{11+19}{-20+2} \\m=\frac{30}{-18} \\m=\frac{-5}{3}\)

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Complete:  y2 - y1 over x2 - x1 with your given points.

11 - (-19)  =        30

______      ______  

-20 - (-2)  =     -18  

⁻³⁰⁄₁₈ =  ¹⁵⁄₃ = ⁵⁄₁        Simplify to lowest fraction            

Answer:

237 seats are empty

Step-by-step explanation:

Answer:

there are 237 seats that are empty

Step-by-step explanation:

Answer:

A. 2\(\frac{1}{2}\)

Step-by-step explanation:

You have to replace x with one of the values in the set. You have to find the one that works.

3\(\frac{1}{2}\)x = 8\(\frac{3}{4}\)

8\(\frac{3}{4}\) ÷ 3\(\frac{1}{2}\) = x

8\(\frac{3}{4}\) ÷ 3\(\frac{1}{2}\) = 2\(\frac{1}{2}\)

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The length of the line segments are 12 cm , 27 cm and 43 cm

A line segment is bounded by two distinct points on a line. Or we can say a line segment is part of the line that connects two points. A line has no endpoints and extends infinitely in both the direction but a line segment has two fixed or definite endpoints.

Given here total measure of the segments is 82 cm. Let the measure of the second segment be x then as per question we have

4x/9+ x + x+16=82

22x/9+16=82

22x/9=66

x        = 27 cm

Hence, the length of the segments are 12 cm , 27 cm and 43 cm

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Answer and Step-by-step explanation:

Samantha's recipe has:

3 parts cranapple juice

2 parts lemonade

In total, this recipe has:

t = 3 + 2

t = 5

ratio = \(\frac{2}{5}\)

Caden's recipe has

4 parts cranapple juice

3 parts lemonade

In total:

t = 4 + 3

t = 7

ratio = \(\frac{3}{7}\)

The punch with stronger lemon taste will be the one whose recipe have a bigger proportion of lemon.

For Samantha's recipe, the proportion is 2 ÷ 5 = 0.4

For Caden's, 3 ÷ 7 = 0.43

Caden's punch will have a slightly stronger taste of lemon, because its proportion is slightly higher than Samantha's.

Answer:

the answer is 4 hours

Step-by-step explanation:

42-10=32

for the gas money

32 divided by 8 =4 hours

Since

even degree function, it will have an even number of real zeros, and, since it has a degree of 4, there will be 4, 2 or 0 real zeroes