For Matthew's lemonade recipe, 4 lemons are required to make 6 cups of lemonade. At what rate are lemons being used in cups of lemonade per lemon

Answer:

Step-by-step explanation:

11-2.5= 8.5

8.5-2.5=6

your answer is 2.5

Answer:

y=x^2

Step-by-step explanation:

The probability that they are not all the same color is approximately 0.875. This can be calculated by taking the total number of possible combinations of three cards from a standard 52-card deck (52 x 51 x 50) and dividing it by the total number of possible outcomes (52 x 51 x 50 x 48 x 47 x 46).

1. Calculate total possible combinations of three cards from a standard 52-card deck:

52 x 51 x 50

= 13,200

2. Calculate total possible outcomes:

52 x 51 x 50 x 48 x 47 x 46

= 1,415,072

3. Divide total combinations by total outcomes:

13,200/1,415,072

= 0.0093 or 0.875 (rounded to the nearest thousandth)

The probability of not all three cards being the same color is 0.875. This can be calculated by dividing the total number of combinations of three cards from a standard 52-card deck by the total number of possible outcomes. This ratio is then rounded to the nearest thousandth for the final result.

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Answer:

235 miles per hour and 2,115 miles in 9 hours

Step-by-step explanation:

First determine how many miles the jet files in one hour:

470/2 =235 miles/hour

We want to know how many hours the jet could fly in 9 hours, so we multiply this value by 9.

235 x 9 = 2115 miles

Therefore, the jet could fly 2115 miles in 9 hours.

Wages earned: $94,891

Interest received: $1,799

Contribution to tax-deferred saving plan: $3,510

Donation to charity: $4,447

Based on the given information, Tina, a single woman, earned wages of $94,891, received $1,799 in interest from a savings account, contributed $3,510 to a tax-deferred saving plan, and donated $4,447 to charity.

To summarize:

Wages earned: $94,891

Interest received: $1,799

Contribution to tax-deferred saving plan: $3,510

Donation to charity: $4,447

These figures represent Tina's financial activities and reflect her income, savings, and charitable contributions.

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Given:

Line P Q has points (-5, 3) and (5, 1).

Line R S has points (-4, -2) and (0, -4).

To find:

The relationship between lines PQ and RS.

Solution:

If a line passing through two points, then the slope of line is

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

Line P Q has points (-5, 3) and (5, 1). So, slope of line PQ is

\(m_1=\dfrac{1-3}{5-(-5)}\)

\(m_1=\dfrac{-2}{5+5}\)

\(m_1=\dfrac{-2}{10}\)

\(m_1=\dfrac{-1}{5}\)

Line R S has points (-4, -2) and (0, -4). So, slope of line RS is

\(m_2=\dfrac{-4-(-2)}{0-(-4)}\)

\(m_2=\dfrac{-4+2}{0+4}\)

\(m_2=\dfrac{-2}{4}\)

\(m_2=\dfrac{-1}{2}\)

Slopes of two parallel lines are equal.

\(m_1\neq m_2\)

They are not parallel because their slopes are not equal.

Therefore, the correct option is C.

Answer:

the correct answer is c

Step-by-step explanation:

Edu2020

The cost of 7 tickets will be $242.20.

In order to determine the cost of 7 tickets, the mathematical operation that would be used is multiplication. Multiplication is the process of determining the product of two or more numbers.

Multiplication is the process used to determine the result when a number is taken times. The sign used to represent multiplication is x. Other mathematical operations are addition, division and subtraction.

In order to determine the cost of 7 tickets, the cost of one ticket would be multiplied by 7.

Cost of 7 tickets = cost of one ticket x 7

$34.60 x 7 = $242.20

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Answer:

3/7

Step-by-step explanation:

12/28=3*4/4*7=3/7

Answer:

the answer is m=5/3, hope this really helps.

Answer:

slope: \(\frac{5}{3}\)

slope-intercept form: y=\(\frac{5}{3}\)x+\(\frac{10}{3}\)

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The inequality that represents the graph in the given diagram is: y ≥ 4x - 6.

The inequality sign to use depends on the boundary line, whether it is dashed or solid line. And also, it depends on where the shaded area of the graph lies, above or below the boundary line.

The boundary line in the graph is a solid line, and the shaded area is above the boundary line, therefore, the inequality sign we would use is, "≥".

Find the slope (m) of the boundary line.

Slope (m) = rise/run = 4 units / 1 unit

Slope (m) = 4

The y-intercept (b) is -6 [this is where the value of x = 0, and also the point where the y-axis is intercepted].

Substitute m = 4 and b = -6 into y ≥ mx + b

y ≥ (4)x + (-6)

y ≥ 4x - 6

Thus, the inequality that represents the graph in the given diagram is: y ≥ 4x - 6.

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The probability that a randomly chosen person has diabetes is approximately 10.45%.

The probability that a randomly chosen person has diabetes can be calculated by dividing the number of people with diabetes by the total population. Using the given data, we have:

Total population = 100%Probability of having diabetes = 10.5%Number of people with diabetes = 34.2 million

To find the probability of a randomly chosen person having diabetes, we divide the number of people with diabetes by the total population as follows:

Probability of having diabetes = (Number of people with diabetes / Total population) x 100%

= (34.2 million / 327 million) x 100%

= 0.1045 or 10.45%

Therefore, the probability that a randomly chosen person has diabetes is approximately 10.45%.

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Answer:

\(Total\ Rent = 49 + 5m\)

Step-by-step explanation:

Given

Rent per day = $49

Addition = 5 cents per mile

Required

Determine the rent for a day and m miles

First, we need to generate a formula from the given parameters;

Let d represent number of days and m represent additional miles;

\(Total\ Rent = 49 * d + 5 * m\)

\(Total\ Rent = 49 d + 5 m\)

Solving for the rent for a day and m miles

We have that: d = 1 and m = m

Substitute these in the formula above

\(Total\ Rent = 49 * 1 + 5 * m\)

\(Total\ Rent = 49 + 5m\)

Hence, the total rent is

\(Total\ Rent = 49 + 5m\)

The ordered pair given in the first row of the table can be written as (8, f(8)).

f(3) is equal to 7.

f(x) = -5 when x is -6 or -2.

The table represents a function where the input values (x) correspond to the output values (f(x)). Let's analyze the given information to complete the statements:

The ordered pair given in the first row of the table can be written using function notation as (x, f(x)) = (8, f(8)). This means that when x is equal to 8, the corresponding function value is f(8).

To find f(3), we look for the row in the table where x is equal to 3. From the given table, we can see that when x is 3, the corresponding function value f(x) is 7. Therefore, f(3) is equal to 7.

Similarly, to find when f(x) is equal to -5, we look for the rows in the table where the function value is -5. From the table, we can see that when x is equal to -6 and -2, the function value f(x) is -5. Therefore, we can say that f(x) = -5 when x is -6 or -2.

In summary:

The ordered pair given in the first row of the table can be written as (8, f(8)).

f(3) is equal to 7.

f(x) = -5 when x is -6 or -2.

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The confidence interval can be expressed as (27.4%, 38.0%).

This confidence interval can be calculated using the formula (X ± z*σ/√n), where X is the sample mean, z is the z-score that corresponds to the desired confidence level (in this case, 95%), σ is the population standard deviation, and n is the sample size.

This is calculated using the formula:

lower bound = point estimate - margin of error and

upper bound = point estimate + margin of error.

In this case, the point estimate is 33.2% and the margin of error is 5.8%.

Therefore, lower bound = 33.2% - 5.8% = 27.4% and

upper bound = 33.2% + 5.8% = 38.0%.

This means that we are 95% confidence interval that the true population proportion lies between 27.4% and 38.0%.

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Answer:

it would be .1111111111

Hope this helps

Answer:

.1 repeating

Step-by-step explanation:

.1 repeating= .11111111111

Hope this helps.

Answer:

5,674,200,000,000

Step-by-step explanation:

Answer:

m < 1 = 23°

m < 2 = 90°

m < 3 = 67°

m < 4 = 113°

Step-by-step explanation:

m < 2 is a right angle. Therefore, m < 2 = 90°.

Since m < 2 is 90°, then m < 1 + m < 67° = 90°

To solve for m < 1: subtract m < 67° from m < 2:

90° - m < 67° = 23°.  Thereforem m < 1 = 23° (acute angle).

m < 67° + m < 4 = 180° (supplementary angles).

To solve for m < 4: subtract m < 67° from 180°  

180° - m < 67° = 113° .

Therefore, m < 4 = 113° (obtuse angle).

The sum of m < 4 and m < 3 = 180° (supplementary angles).

180° - m < 4 = m < 3

180° - 113° = 67°

Therefore, m < 3 = 67° (acute angle).

The selling price of the 6 dining chairs is $3690

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

6 dining chairs together cost $1845.00. The chairs were sold to get a profit of 100%. Let x represent the selling price

The formula needed is:

Profit = [(selling price - cost price)/cost price] * 100%

Hence, substituting:

100% = [(x - 1845]/1845] * 100%

(x - 1845]/1845 = 1

x - 1845 = 1845

x = 3690

The selling price is $3690

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The value of Expected value, variance, and standard deviation of y of given probability distribution is 6.4, 9.76 and 3.12 respectively.

To compute the expected value of y, denoted E(y), we use the formula:

E(y) = Σ [y × f(y)]

Using the given probability distribution, we have:

E(y) = (2 × 0.20) + (4 × 0.30) + (7 × 0.40) + (8 × 0.10) = 1.6 + 1.2 + 2.8 + 0.8 = 6.4

Therefore, the expected value of y is 6.4, rounded to 1 decimal place.

To compute the variance of y, denoted Var(y), we use the formula:

Var(y) = E(y^2) - [E(y)]^2

where E(y) is the expected value of y, and E(y^2) is the expected value of y squared. To find E(y^2), we use the formula:

E(y^2) = Σ [y^2 × f(y)]

Using the given probability distribution:

E(y^2) = (2^2 × 0.20) + (4^2 × 0.30) + (7^2 × 0.40) + (8^2 × 0.10) = 1.6 + 3.6 + 19.6 + 6.4 = 31.2

Substituting this and the previously calculated E(y) into the formula for Var(y), we get:

Var(y) = E(y^2) - [E(y)]^2 = 31.2 - 6.4^2 = 31.2 - 40.96 = 9.76

Therefore, the variance of y is 9.76, rounded to 2 decimal places.

we take the square root of the variance to find the standard deviation:

σ = √Var(y) = √9.76 = 3.12

Therefore, the standard deviation of y is 3.12, rounded to 2 decimal places.

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____The given question is incomplete, the complete question is given below:

The following table provides a probability distribution for the random variable y 2 4 7 f(u) 0.20 0.30 0.40 0.10 8 a. Compute E(y) (to 1 decimal). 5.2 b. Compute Var(y) and ơ (to 2 decimals). Var(y)

The probability that a flight between New York City and Chicago is less than 64 minutes is 0.28, or 28%.

Since the time to fly between New York City and Chicago is uniformly distributed between 50 and 100 minutes, we can use the formula for the uniform probability density function (PDF) to find the probability that a flight is less than 64 minutes:

f(x) = 1 / (b - a), for a ≤ x ≤ b

where a = 50 and b = 100 are the minimum and maximum times, respectively.

To find the probability that a flight is less than 64 minutes, we need to integrate the PDF from a to 64:

P(X < 64) = \(\int\limits^{64}_{50}\) f(x) dx = \(\int\limits^{64}_{50}\\\)(1 / 50) dx = (1 / 50) * [x]|₅₀ ⁶⁴

= (1 / 50) * (64 - 50) = 0.28

This means that approximately 28% of flights will arrive in less than 64 minutes.

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the area inside the ellipse is π * a * b, and the volume of the solid obtained by revolving the upper half of the ellipse about the x-axis can be calculated using the integral described.

(a) The area inside the ellipse given by the equation x² / a² + y² / b² = 1 can be calculated using the formula for the area of an ellipse, which is A = π * a * b. Therefore, the area inside the ellipse is π * a * b.(b) To calculate the volume of the solid obtained by revolving the upper half of the ellipse from part (a) about the x-axis, we can use the method of cylindrical shells. The volume can be obtained by integrating the cross-sectional area of each cylindrical shell as it rotates around the x-axis.

The cross-sectional area of each cylindrical shell is given by 2πy * dx, where y represents the y-coordinate of the ellipse at a given x-value and dx represents the thickness of each shell. We can express y in terms of x using the equation of the ellipse: y = b * √(1 - x² / a²).Integrating from -a to a (the x-values that span the ellipse) and multiplying by 2 to account for the upper and lower halves of the ellipse, we have:

Volume = 2 * ∫[from -a to a] (2π * b * √(1 - x² / a²)) dx

Evaluating this integral will give us the volume of the solid.

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Given : A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week . and graph

To Find :  Maximum profit , breakeven point , profit interval

Solution:

The maximum profit the florist will earn from selling celebration bouquets is $ 675

peak of y from Graph

The florist will break-even after  Selling 20     one-dollar decreases.

at breakeven

Break even is the point where the profit p(x) becomes 0

The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0 ,20).

after 20 , P(x) is - ve

Answer: EDMENTUM AND PLATO

First Blank: $625

Second Blank: 20

Third Blanks: ( 0, 20 )

Step-by-step explanation:

The equation represents the area of the dark grey part of the square is option d 4/5 x 1/2 = 4/10

Given,

The area of square = 1 sq.units

The square is divided into 10 rectangles

We have to find the area of the dark grey shaded part of the square;

Here,

Area of square = 1 sq.units

Square is divided into 10 rectangles.

Then area of one rectangle = 1/10

Now,

The dark grey shaded area consists of 4 rectangles.

Then the area of the shaded region = 1/10 × 4 = 4/10

That is

The equation represents the area of the dark grey part of the square is option d 4/5 x 1/2 = 4/10

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Answer:16

Step-by-step explanation:

Answer:

71th term is 141

Step-by-step explanation:

\(a_{1}=1\\\\common \ difference = d = second \ term - first \ term\\\\ = 3 - 1 = 2\\\\a_{n} = 141\\\\a + (n -1)*d = a_{n}\)

1 + (n - 1)*2 = 141         {Use distributive property}

1 + 2n - 2 = 141    

2n - 1 = 141

2n = 141 + 1

2n = 142

n = 142/2

n = 71

Answer:

71st term

Step-by-step explanation:

First, find the nth term: 2n - 1 (the difference is 2, and the 0th term or the number before the 1 is -1). Next, set the nth term equal to 141 and solve for n. 2n - 1 = 141. We would add one to both sides → 2n = 142, then divide both sides by 2. n = 71.

Hope this helps!

If you have a binomial experiment with p = 0.1 and a sample size of 900, then the variance of the distribution is option (b) 81

The variance of a binomial distribution measures the spread or variability of the distribution. It tells us how far the observations are from the mean. In this case, the binomial experiment has a probability of success of 0.1 and a sample size of 900.

The formula for the variance of a binomial distribution is Var(X) = np(1-p), where n is the sample size and p is the probability of success in each trial. Substituting the given values, we get:

Var(X) = 900 × 0.1 × (1 - 0.1) = 81

So the variance of the distribution is option (b) 81.

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