hard ratio question.
Joseph makes fizzy orange in the ratio 3:5.
orange juice is bought in bottles of 2 litres costing £1.20 each.
Lemonade comes in bottles that are 3 litres costing £1.50 each.
He wants to sell 250 ml bottles and make a profit of 60% on each one.
How much should he sell each one for?
the answer is 22p but i'm confused how to get to that answer- i'd really appreciate any help!

11. There are 259,200 minutes in 180.0 days.

12. A person weighing 125 pounds 8 ounces weighs approximately 56,699,168 milligrams.

13. The distance from Santa Maria to Los Alamos is approximately 2,610,830 centimeters.

14. Santa Maria's elevation of 6.30 × 10^5 millimeters is approximately 0.63 kilometers.

15. The projectile will travel approximately 54,000 feet in 18 minutes.

16. The herd will consume approximately 364 bales of hay in a year.

17. 0.8 yards is approximately 73.152 centimeters.

18. The swimmer will swim approximately 78.00696 meters in 70.0 seconds.

19. You can purchase approximately 1.15896 grams of saffron for $15.00.

20. 1.80 × 10^-4 tons is approximately 16.32853 grams.

11. To convert days to minutes, we'll use the conversion factor 1 day = 24 hours and 1 hour = 60 minutes.

180.0 days * 24 hours/day * 60 minutes/hour = 259,200 minutes

Therefore, there are 259,200 minutes in 180.0 days.

12. To convert pounds and ounces to milligrams, we'll use the conversion factors:

1 pound = 453.592 grams

1 ounce = 28.3495 grams

1 gram = 1000 milligrams

125 pounds * 453.592 grams/pound * 1000 milligrams/gram + 8 ounces * 28.3495 grams/ounce * 1000 milligrams/gram = 56,699,168 milligrams

Therefore, a person weighing 125 pounds 8 ounces weighs approximately 56,699,168 milligrams.

13. To convert miles to centimeters, we'll use the conversion factor 1 mile = 1609.34 meters and 1 meter

= 100 centimeters.

16.25 miles * 1609.34 meters/mile * 100 centimeters/meter = 2,610,830 centimeters

Therefore, the distance from Santa Maria to Los Alamos is approximately 2,610,830 centimeters.

14. To convert millimeters to kilometers, we'll use the conversion factor 1 kilometer = 1,000,000 millimeters.

6.30 × 10^5 millimeters * 1 kilometer/1,000,000 millimeters = 0.63 kilometers

Therefore, Santa Maria's elevation of 6.30 × 10^5 millimeters is approximately 0.63 kilometers.

15. To convert feet to minutes, we'll use the conversion factor 1 minute = 60 seconds.

3.00 × 10^3 feet * 1 minute/60 seconds = 50 feet/second

To convert 18 minutes to seconds:

18 minutes * 60 seconds/minute = 1080 seconds

50 feet/second * 1080 seconds = 54,000 feet

Therefore, the projectile will travel approximately 54,000 feet in 18 minutes.

16. To find the number of bales of hay consumed in a year, we'll use the conversion factor that there are 52 weeks in a year.

14 bales * (52 weeks/2 weeks) = 364 bales

Therefore, the herd will consume approximately 364 bales of hay in a year.

17. To convert yards to centimeters, we'll use the conversion factor 1 yard = 91.44 centimeters.

0.8 yards * 91.44 centimeters/yard = 73.152 centimeters

Therefore, 0.8 yards is approximately 73.152 centimeters.

18. To convert yards to meters, we'll use the conversion factor 1 yard = 0.9144 meters.

85.4 yards * 0.9144 meters/yard = 78.00696 meters

Therefore, the swimmer will swim approximately 78.00696 meters in 70.0 seconds.

19. To convert ounces to grams, we'll use the conversion factor 1 ounce

= 28.3495 grams.

$15.00 * (28.3495 grams/$368.00) = 1.15896 grams

Therefore, you can purchase approximately 1.15896 grams of saffron for $15.00.

20. To convert tons to grams, we'll use the conversion factor 1 ton

= 907,184.74 grams.

1.80 × 10^-4 tons * 907,184.74 grams/ton = 16.32853 grams

Therefore, 1.80 × 10^-4 tons is approximately 16.32853 grams.

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An equation of the line with the given gradient and points is \(y=\frac{2x}{3} -\frac{7}{3}\)

Given the following data:

To find an equation of the line with the given gradient and points:

Mathematically, the equation of a line is given by this formula:

\(y-y_1 =m(x-x_1)\)

Where:

Substituting the given parameters into the formula, we have;

\(y-(-3) =\frac{2}{3} (x-[-1])\\\\y+3=\frac{2}{3} (x+1)\\\\3y+9=2x+2\\\\3y=2x+2-9\\\\3y=2x-7\\\\y=\frac{2x}{3} -\frac{7}{3}\)

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The name for a data value that is far above or below the rest is called an outlier.

An outlier is an observation that deviates significantly from other observations in a dataset. It is an extreme value that lies outside the typical range of values and may have a disproportionate impact on statistical analyses and calculations. Outliers can occur due to various reasons, including measurement errors, data entry mistakes, or genuine rare events. Identifying and handling outliers appropriately is important in data analysis to ensure accurate and reliable results.

When dealing with outliers, it is important to assess whether they are the result of errors or genuine extreme values. Statistical techniques, such as box plots, scatter plots, or z-scores, can be used to detect outliers. Once identified, the appropriate action depends on the nature and cause of the outliers. In some cases, outliers may need to be corrected or removed from the dataset, while in other cases, they may provide valuable insights or require further investigation.

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Answer:

P(-2 ≤ x ≤ 2) = .6

Step-by-step explanation:

Given

The data in the above table

Required

Find P(-2 ≤ x ≤ 2)

To solve for P(-2 ≤ x ≤ 2); we have to consider the boundary covered by the interval

The interval -2 ≤ x ≤ 2 according to the table is -2 , 0 and 2

Solving further;

P(-2 ≤ x ≤ 2) = P(-2) + P(0) + P(2) ----- (1)

From the table;

P(-2) = .33

P(0) = .16

P(2) = .11

Substitute these values in (1) above

P(-2 ≤ x ≤ 2) = P(-2) + P(0) + P(2) becomes

P(-2 ≤ x ≤ 2) = .33 + .16 + .11

P(-2 ≤ x ≤ 2) = .6

The two figures shown are made of unit squares. The positive difference of the perimeters, in units, is 8.

Perimeter is the total distance around the boundary of the shape. Since each square has a side length of 1 unit, the perimeter is equal to the number of sides.

1. Figure A: Counting the number of unit squares on the boundary of the shape, the perimeter of the first shape is:   8+4+4+4+4=24 units.

2. Figure B:Counting the number of unit squares on the boundary of the shape, the perimeter of the second shape is: 10+2+10+2=24 units.

The positive difference of the perimeters in units = |24 - 24| = 0 units. Therefore, the positive difference of the perimeters, in units is 0.

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The probability is 1, or 100%, that a randomly selected person from this sample believed either the true headline or the false headline.

Probability is a measure of the likelihood or chance that a specific event will occur. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.

The probability that a randomly selected person from this sample believed the true headline or believed the false headline can be calculated by adding the number of people who believed the true headline to the number of people who believed the false headline and dividing by the total sample size.

In this case, the number of people who believed the true headline is 120, and the number of people who believed the false headline is 80. Therefore, the total number of people who believed either headline is 120 + 80 = 200.

The total sample size is also 200, so the probability that a randomly selected person from this sample believed the true headline or believed the false headline is:

(120 + 80) / 200 = 200 / 200 = 1

Therefore, the probability is 1, or 100%, that a randomly selected person from this sample believed either the true headline or the false headline.

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Complete Question:

In a sample of 200 people, 120 believed a true headline and 80 believed a false headline. What is the probability that a randomly selected person from this sample believed the true headline or believed the false headline?

Answer:

a = 80

b = 3/4

the general equation is;

y = 80•(3/4)^x

Step-by-step explanation:

Here, we want to get the values of a and b

We are going to use the two points given

(0,80) and (1,60)

So we have this as;

for the first point;

80 = a•b^0

anything raised to power of 0 is 1

Thus;

80 = a * 1

a = 80

for the second point;

60 = 80 * b^1

60 = 80b

b = 60/80

b = 3/4

So we have the general equation as;

y = 80•(3/4)^x

Hello!

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15% = 15/100

The fraction can be reduced:

3/20

Hope it helps you!

~SparklingFlower :)

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Answer:

\(\frac{3}{20}\)

Step-by-step explanation:

15%

= \(\frac{15}{100}\) ( divide numerator/ denominator by 5 )

= \(\frac{3}{20}\)

Answer:

statistical experiments performed on a well defined sample space

Step-by-step explanation:

experiments can be performed either by probability, or other repetitive actions on sample space for possible outcomes.

The provided questions cover various aspects of a 2-period production economy, including the household's problem, firm's problem, market clearing conditions, Social Planner's Problem, competitive equilibrium, and welfare theorems.

(a) The Household's problem is to maximize its utility over two periods subject to its budget constraint. The household's problem can be formulated as follows:

Max U(Co, C1) = log(Co) + ß log(C1)

subject to the budget constraint:

Co + (1+r)C1 ≤ (1+r)Ko + W0 + W1,

where Co and C1 are consumption in period 0 and 1 respectively, ß is the discount factor, r is the interest rate, Ko is the initial capital endowment, W0 and W1 are the wages in periods 0 and 1 respectively.

(b) The Firm's problem is to maximize its profit by choosing the optimal combination of capital and labor. The firm's problem can be formulated as follows:

Maximize F(K, L) - RK - WL,

where F(K, L) is the production function, K is capital, L is labor, R is the rental rate of capital, and W is the wage rate.

(c) The market clearing conditions are:

Capital market clearing: K1 = (1 - δ)K0 + S - C0, where δ is the depreciation rate, S is savings, and C0 is consumption in period 0.

Labor market clearing: L = L0 + L1, where L0 and L1 are labor supplies in periods 0 and 1 respectively.

(d) The Social Planner's Problem is to maximize social welfare, which is the sum of the household's utility and the firm's profit. The Social Planner's Problem can be formulated as follows:

Maximize U(C0, C1) + F(K, L) - RK - WL,

subject to the production function F(K, L) and the market clearing conditions.

(e) A Competitive Equilibrium is a situation where all markets clear and agents (household and firm) make optimal decisions based on prices and market conditions. It is characterized by the following conditions:

Household's problem is solved optimally.

Firm's problem is solved optimally.

Market clearing conditions hold.

(f) To solve the Social Planner's Problem, we need to set up the Lagrangian and solve for the optimal values of consumption, capital, and labor. The Lagrangian can be written as:

L = U(C0, C1) + F(K, L) - RK - WL + λ1[(1+r)K0 + W0 + W1 - Co - (1+r)C1] + λ2[K1 - (1 - δ)K0 + S - C0] + λ3[L - L0 - L1],

where λ1, λ2, and λ3 are the Lagrange multipliers.

(g) To solve the Competitive Equilibrium, we need to determine the prices of capital (R) and labor (W) that clear the markets. This can be done by equating the demand and supply of capital and labor, and solving the resulting equations.

(h) The First Welfare Theorem states that under certain conditions, a competitive equilibrium is Pareto efficient. It implies that a competitive equilibrium is a socially optimal allocation of resources. To verify the theorem, we need to demonstrate that the competitive equilibrium allocation is Pareto efficient.

(i) The Second Welfare Theorem states that any Pareto efficient allocation can be achieved as a competitive equilibrium with appropriate redistribution of initial endowments.

To verify the theorem, we need to show that given an initial Pareto efficient allocation, we can find prices and redistribution of endowments that lead to a competitive equilibrium that achieves the same allocation.

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Complementary and supplementary angles can be adjacent or non-adjacent; their relationship is based on the sum of their measures, not their spatial arrangement.

No, complementary and supplementary angles do not have to be adjacent angles.

Complementary angles are two angles that add up to 90 degrees. For example, if angle A measures 30 degrees, then its complementary angle B would measure 60 degrees. Complementary angles can be adjacent (when they share a common vertex and side) or non-adjacent (when they are not next to each other).

Supplementary angles, on the other hand, are two angles that add up to 180 degrees. For example, if angle C measures 120 degrees, then its supplementary angle D would measure 60 degrees. Like complementary angles, supplementary angles can be adjacent or non-adjacent.

In summary, the terms complementary and supplementary refer to the relationship between the measures of angles, rather than their spatial arrangement. Adjacency is a separate concept that refers to angles that share a common vertex and side. Complementary and supplementary angles can be adjacent or non-adjacent depending on their spatial configuration.

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Note the binomial expansion,

(a + 1/a)³ = a ³ + 3a + 3/a + 1/a ³

so

a ³ + 1/a ³ = (a + 1/a)³ - 3 (a + 1/a)

Similarly,

(a + 1/a)² = a ² + 2 + 1/a ²

We're given a ² + 1/a ² = 79, so

(a + 1/a)² - 2 = 79

(a + 1/a)² = 81

a + 1/a = ±9

but a > 0, so we ignore the negative solution.

Then

a ³ + 1/a ³ = 9³ - 3×9 = 702

Answer:

Addition Identity Property

Step-by-step explanation:

Addition Identity Property because a number + 0 = that number is Addition Identity Property.

Answer:

Probability of an event must be from 0 to 1.

Here,6/5 is more than 1 i.e. 1.2.

Hence,the answer is incorrect.

First find the center, then graph all the points that are at a distance of R units from that center.

A circle of radius R is the set of all points that are at a distance R from a given point (the center of the circle).

So to graph it, we need to know these two things, radius and center.

Once we do, first we graph the center on the coordinate plane.

Once we find the center, we can find all the poiints that are at a distance of R units from our center, so we need to graph these. Once we do, we will have the graph of our circle on the coordinate plane.

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Answer:

y=1/2x+2

Step-by-step explanation:

hope it helps ^^

Answer is the following:

B

Answer:

$15 per hour and he worked 5 hours yesterday.

Step-by-step explanation:

Since we know that the number of hours he works and know how much he got paid we need to look for how much he makes each hour.

Set up the equation like this.

7x=105

Divide by 7 to isolate the x

x=15

That means he makes 15 dollars per hour. For the 2nd part, we are looking for how many hours he worked. We know that he gets 15 dollars per hour so we can set up the equation like this.

15x=75

Divide by 15 to isolate the x

x=5

That means he worked 5 hours yesterday.

P.S. give me crown

Answer:

 He worked approximately 4-5 hours because when he worked 7 hours a day he earned 105 dollars that means he made 15 dollars an hour so he only worked 4-5  hours that day and he made 75 dollars.  

Step-by-step explanation:

This is a short answer so u dont have to write that much.

Answer: 9/2

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so:

\(\frac{x}{6}=\frac{3}{4}\\\\x=\frac{18}{4}=\boxed{\frac{9}{2}}\)

Answer:

y = -3x-8

Step-by-step explanation:

(x - 3)² + y² = 100/9  is the equation of a circle with a radius of 10/3 and a xy-plane with a center at (3, 0) and an endpoint at (1, 83).

The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric about the center for all angles. A circle is a plane figure that is bounded by a single curved line and in which all straight lines drawn from any point inside the circle to the boundary are equal. Its center is the point, and its perimeter is the bounding line.

given

Circle Formula: (x - h)² + (y - k)² = r²  ; (h, k) is the center & r is the radius

Use the distance formula for (3, 0) and (1, 1/8 )

\(r = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }\\ r = \sqrt{( 3 - 1)^{2} + ( 0 - 8/3 )^{2} }\)

\(\sqrt{\frac{100}{9} }\\ r = \frac{10}{3}\)

Center (h, k) = (3, 0)   Radius (r) =  10 / 3

(x - h)² + (y - k)² = r²

(x - 3)² + (y - 0)² = (10/3)²

(x - 3)² + y² = 100/9

So (x - 3)² + y² = 100/9  is the equation of a circle with a radius of 10/3 and a xy-plane with a center at (3, 0) and an endpoint at (1, 83).

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Chad drank 6.4 liters of water altogether. He drank 2.3 liters of water before going jogging on Monday and 3.8 liters of water after jogging.

Water is an essential substance that plays an important role in the human body. It is crucial to drink enough water to maintain the body's normal function. In this problem, we need to determine the total amount of water Chad drank on Monday. According to the problem, Chad drank 2.3 liters of water before going jogging. After the jog, he drank 3.8 liters of water.

To find the total amount of water Chad drank, we need to add the amount of water he drank before and after the jog. Therefore, the total amount of water Chad drank on Monday is 2.3 liters + 3.8 liters = 6.1 liters.

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if we flip a coin, we would expect the probability of its landing heads to be the same as its landing tails is referred to as the law of large numbers.

The law of large numbers is a probability and statistics, which defines that as a sample size grows, its mean gets closer to the average of the whole population.

This is due to the sample being more representative of the population as the sample becomes larger.

This is the theorem that describes the result of performing the same experiment a large number of times because the average of the results obtained from a large number of trials is close enough to the expected value.

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The answer choice which represents the solutions of the given absolute value equation as given is; Choice A. x =4 and x = -7.

Since it follows from the task content that the given absolute value equation is;

| 2x + 3 | = 11.

Hence, the equation can be solved as follows;

2x + 3 = 11. OR 2x + 3 = -11

2x = 11 - 3. OR. 2x = -11 - 3

2x = 8. OR 2x = -14

x = 4. OR. x = -7.

It therefore follows that the values of x which hold true for the given equation are: x = 4 and x = -7.

Ultimately, the correct answer choice is; Choice A. x =4 and x = -7.

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Answer:

The answer is 0

Step-by-step explanation:

Answer:

10\(x^{5}\)

Step-by-step explanation:

The list is: 30\(x^{7}\), 60\(x^{5}\), 110\(x^{8}\)

Find the GCF

We see

30, 60, and 110 have the greatest common factor is 10.

\(x^{7}\), \(x^{5}\), \(x^{8}\) have the greatest common factor is \(x^{5}\)

So, the greatest common factor for the list of terms is 10 \(x^{5}\)

Answer: x = 0

Step-by-step explanation:

1 - 3x = 3x + 1

then add 3x on both sides

1 = 6x + 1

then subtract 1 on both sides

0 = 6x

then divide by 6 on both sides

0 = x

so x = 0

Answer:

x would be unknown bc there wouldnt be an answer since

1-3x=3x+1

if we take away 1 forom both sides were left with -3x=3x and it would be 6x if we combined them which can be possible bc it would be nothing = 6x if that makes sense

Step-by-step explanation:

There are 7 degrees of freedom.

In performing the pooled-variance t test, the degrees of freedom can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)

Substituting the given values:
df = (4 - 1) + (5 - 1)
df = 3 + 4
df = 7

Therefore, there are 7 degrees of  freedom.

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There are 7 degrees of freedom for the pooled-variance t-test.

To perform a pooled-variance t-test, we need to calculate the degrees of freedom. The formula for degrees of freedom in a pooled-variance t-test is:

\(\[\text{{df}} = n_1 + n_2 - 2\]\)

where \(\(n_1\)\) and \(\(n_2\)\) are the sample sizes of the two independent samples.

In this case, \(\(n_1 = 4\)\) and \(\(n_2 = 5\)\). Substituting these values into the formula, we get:

\(\[\text{{df}} = 4 + 5 - 2 = 7\]\)

In a pooled-variance t-test, we combine the sample variances from two independent samples to estimate the population variance. The degrees of freedom for this test are calculated using the formula \(df = n1 + n2 - 2\), where \(n_1\)and \(n_2\) are the sample sizes of the two independent samples.

To understand why the formula is \(df = n1 + n2 - 2\), we need to consider the concept of degrees of freedom. Degrees of freedom represent the number of independent pieces of information available to estimate a parameter. In the case of a pooled-variance t-test, we subtract 2 from the total sample sizes because we use two sample means to estimate the population means, thereby reducing the degrees of freedom by 2.

In this specific case, the sample sizes are \(n1 = 4\) and \(n2 = 5\). Plugging these values into the formula gives us \(df = 4 + 5 - 2 = 7\). Hence, there are 7 degrees of freedom for the pooled-variance t-test.

Therefore, there are 7 degrees of freedom for the pooled-variance t-test.

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The shaded area of the figure is equal to 297 square centimeters.

In this question we find a shaded figure, whose area can be found as a subtraction of the areas of two triangles from the area of a rectangle. The area formulas are defined below:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

Now we proceed to compute the shaded area:

A = (18 cm) · (22 cm) - 0.5 · (9 cm) · (13.2 cm) - 0.5 · (9 cm) · (8.8 cm)

A = 297 cm²

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The formula to find the resolution of an image, also known as its pixel density, is Pixels per Inch (PPI) or Pixels per Centimeter (PPCM). This formula is used to determine the number of pixels in a given area of an image.

The higher the PPI or PPCM, the greater the resolution of the image.

To calculate PPI, you need to know the total number of pixels in the image (width x height) and the physical size of the image (width x height in inches or cm). Once you have this information, you can use the following formula: PPI = (pixels / physical size) x (inches/cm).

For example, if an image has a resolution of 1920 x 1080 pixels and is printed at a size of 8 x 6 inches, the PPI would be (1920 x 1080) / (8 x 6) = 240 PPI.

In conclusion, PPI or PPCM is the formula used to find the resolution of an image, also known as its pixel density. It is calculated by dividing the total number of pixels in the image by its physical size and multiplying it by inches/cm.

The higher the PPI or PPCM, the greater the resolution of the image. It is important to consider the PPI or PPCM when choosing an image to print or display in order to ensure that it will be of high quality and have a high resolution.

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