A family drank 4 gallons of juice over 5 weeks. During this time period,
at what rate did the family drink juice.

3. a. A solution or feasible region, is the triangular region in the graph of the inequality, with vertices (0.7, -3.35), (8, -7), (8, -25.25)

Please find attached the graph of the feasible region of the inequality, created with MS Excel

b. The feasible region in the graph of the inequality indicates that the inequality remains true for the coordinates of points within the feasible region

An inequality is an unequal comparison between values or expressions using inequality symbols such as <, >, ≤, and ≥.

3. The system of inequalities are presented as follows;

4·x + 8·y ≤ -24

-12·x - 4·y < 5

a. Making y the subject of the above inequalities, we get;

4·x + 8·y ≤ -24

y ≤ (-24 - 4·x) ÷ 8 = -3 - 0.5·x

y ≤ -3 - 0.5·x...(1)

-12·x - 4·y < 5

-4·y < 5 + 12·x

y > -1.25 - 3·x...(2)

The solution point is therefore;

-3 - 0.5·x = -1.25 - 3·x

2.5·x = 1.75

x = 1.75/2.5 = 0.7

The x-value of the solution point is therefore the point x = 0.7

y > -1.25 - 3 × 0.7 = -3.35

y > -3.35

The y-value of the solution point is the point y > -3.35

The solution point is therefore the point slightly to the right of the point (0.7, -3.35)

b. The solution space is the triangular region bounded by the points, (0.7, -3.35), (8, -7), and (8, -25.25)

A possible solution obtained from the graph is therefore, the point (6, -10), plugging in the values in the inequalities, we get;

When x = 6

y ≤ -3 - 0.5·x...(1)

y ≤ -3 - 0.5 × 6 = -6

The y-value at the point x = 6 is -10 ≤ -6, which satisfies the first inequality

The second inequality, indicates that we get;

y > -1.25 - 3·x

y > -1.25 - 3 × 6 = -19.25

The y-value at the selected point x = 6 is -10 > -19.25, which satisfies the second inequality

Therefore; The inequality is true at a specified point in the solution space as indicated from the graph

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The area of the ring formed by concentric circles is approximately 188.5 square units.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The ring is formed by two concentric circles.

The area of the ring can be found by subtracting the area of the smaller circle from the area of the larger circle.

The area of a circle with radius r is given by the formula A = πr².

So, the area of the larger circle with radius 16 is -

A1 = π(16)² = 256π

And the area of the smaller circle with radius 14 is -

A2 = π(14)² = 196π

Therefore, the area of the ring is -

A ring = A1 - A2

A ring = 256π - 196π

A ring = 60π

To round to the nearest tenth, we can approximate π as 3.14 -

A ring ≈ 60 × 3.14 = 188.4

Rounding to the nearest tenth, we get -

A ring ≈ 188.4 ≈ 188.5

Therefore, the area of the ring is 188.5 square units.

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Answer:

The mean of the sampling distribution of the sample proportions is the same as the population proportion, which is 0.67.

The standard deviation of the sampling distribution of the sample proportions can be calculated using the formula:

σp = sqrt [p * (1 - p) / n]

where p is the population proportion (0.67), n is the sample size (64), and σp is the standard deviation of the sampling distribution of the sample proportions.

Plugging in the values, we get:

σp = sqrt [0.67 * (1 - 0.67) / 64]

= sqrt [0.2211 / 64]

= 0.061

Therefore, the standard deviation of the sampling distribution of the sample proportions is 0.061.

Answer:

1. Pick an object in your house that is parabolic. As an example, I will use a banana.

2. Measure its height and width.

My banana's height is 3 in, and its width is 7 in.

(see the attached image)

3. Show the parabola made by the object on a Cartesian (rectangular) plane.

(see the attached graph)

4. The approximate quadratic for that graph is:

y = (1/4)x²

Supplementary angles have a measure of 180 degrees

The ramp rises 8.79 inches from the lowest point on the ground to the nearest hundredth.

A right angle triangle has a 90 degree angle as one of its angles. Trigonometric ratios can be used to determine the sides. The length of the fiberboard becomes the hypotenuse of the right triangle that is so constructed. As a result, the ramp rises 8.79 inches from the ground at its tallest point to the closest hundredth.

The opposite side of the right triangle is the height of the ramp that is created.

Hence,

sin 19° = opposite / hypotenuse

sin 19° = h / 27

cross multiply

h = 27 × sin 19°

h = 27 × 0.32556815445

h = 8.79034017034

h = 8.79 inches.

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The predicted prize money in year 10 of the contest is $11,790 for the given Scatter plot.

A set of dots plotted on a horizontal and vertical axis is called as a scatter plot.

We have to find the equation of linear regression using a calculator,

To find the equation, we need to put the entire set of points (x, y) given by the scatter plot in the calculator.

From the scatter plot, points are approximated as follows:

(1, 9.5), (2, 9), (3, 7), (4, 10), (5, 11), (6,10), and (7,10.5).

With the help of a calculator, the amount of prize money in year x of the contest is given by:

P(x) = 0.32143x + 8.28571

To find the predicted amount in year 10, we have to find the numeric value when x = 10,

Hence, P (10) = 0.32143 (10) + 8.28571 = $11,500.

The closest option here is $11,790, which is different from $11,500 because coordinates of points are approximated from scatter plot and not exact.

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The measurement for angle m ∠JMK is obtained as 47°.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

The measure of angle JML is given as = 80°.

The measure of angle KML is given as = 33°.

In the image it can be seen that on adding angles - ∠KML and ∠JMK we obtain the angle ∠JML.

This can be represented in the equation form as -

∠JML = ∠KML + ∠JMK

Substitute the values in the equation -

80° = 33° + ∠JMK

Simplify the equation given -

∠JMK = 80° - 33°

∠JMK = 47°

Therefore, the angle JMK measures 47°.

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Answer:

Amy will have £240 in her account.

Step-by-step explanation:

To calculate the amount of money Amy will have in her account after 2 years, we can use the formula:

A = P(1 + rt)

Where:

A = the total amount of money in the account after 2 years

P = the principal (the initial amount of money invested)

r = the interest rate (as a decimal)

t = the time in years

In this case, Amy invested £200 at an interest rate of 10% per year for 2 years. We can plug in these values into the formula and solve for A:

A = 200(1 + 0.1 × 2)

A = 200(1.2)

A = £240

Therefore, after 2 years, Amy will have £240 in her account.

This means that bone density scores below -1.88 are in the bottom 7% of scores, and scores above 1.88 are in the top 93% of scores.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

It is relates to bone density score distribution, where the bottom 7% of scores are separated from the top 93% of scores. This could be interpreted in a few different ways, but here's one way to approach it:

If we assume that the bone density scores are normally distributed (which is a common assumption in statistics), then we can use the properties of the normal distribution to estimate the cutoff values for the bottom 7% and top 93% of scores.

The standard normal distribution has a mean of 0 and a standard deviation of 1. Using this distribution, we can look up the cutoff values for the bottom 7% and top 93% of scores using a standard normal distribution table or calculator. These cutoff values represent the bone density scores below which 7% of scores fall and above which 93% of scores fall.

For example, using a standard normal distribution table, we can find that the cutoff value for the bottom 7% of scores is approximately -1.88, and the cutoff value for the top 93% of scores is approximately 1.88.

Therefore, This means that bone density scores below -1.88 are in the bottom 7% of scores, and scores above 1.88 are in the top 93% of scores.

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The normal distribution is  X ~ N(17, 0.8), the median is equal to mean which is 17 feet, the z-score is 2.5, the probability that a randomly selected giraffe will be shorter than 18 feet tall is 0.8944.

a. The distribution of X is normal, which we can write as X ~ N(17, 0.8).

b. Since the normal distribution is symmetric, the median is equal to the mean, which is 17 feet.

c. To find the z-score for a giraffe that is 19 feet tall, we use the formula:

z = (x - μ) / δ

where x is the height of the giraffe, mu is the mean height of the population (17 feet), and sigma is the standard deviation (0.8 feet). Plugging in the values, we get:

z = (19 - 17) / 0.8 = 2.5

So the z-score for a giraffe that is 19 feet tall is 2.5.

d. To find the probability that a randomly selected giraffe will be shorter than 18 feet tall, we need to find the area under the normal distribution curve to the left of x = 18. We can use a standard normal distribution table or a calculator to find this area, or we can standardize the value of x and use the standard normal distribution table or calculator. Using the latter method, we have:

z = (x - μ) / δ = (18 - 17) / 0.8 = 1.25

Looking up the area to the left of z = 1.25 in a standard normal distribution table or using a calculator, we find that the probability is approximately 0.8944. So the probability that a randomly selected giraffe will be shorter than 18 feet tall is 0.8944.

e. To find the probability that a randomly selected giraffe will be between 16.7 feet and 17.5 feet tall, we need to find the area under the normal distribution curve between x = 16.7 and x = 17.5. Again, we can standardize the values of x and use a standard normal distribution table or calculator. We have:

z1 = (16.7 - 17) / 0.8 = -0.38

z2 = (17.5 - 17) / 0.8 = 0.63

Looking up the area between z1 = -0.38 and z2 = 0.63 in a standard normal distribution table or using a calculator, we find that the probability is approximately 0.2981. So the probability that a randomly selected giraffe will be between 16.7 feet and 17.5 feet tall is 0.2981.

f. The 90th percentile for the height of the giraffe is the height x such that 90% of the giraffes have a height below x. In other words, we need to find the value of x such that the area under the normal distribution curve to the left of x is 0.9. Using a standard normal distribution table or calculator, we can find the z-score corresponding to the 90th percentile, which is approximately 1.28. We can then use the formula for z-score to find the corresponding height x:

z = (x - μ) / δ

1.28 = (x - 17) / 0.8

Solving for x, we get:

x = 17 + 1.28 * 0.8 = 18.024

So the 90th percentile for the height of the giraffe is 18.024 feet.

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Therefore, they need 25 pints of liquid A, 12.5 pints of liquid B, and 62.5 pints of liquid C to make the final mixture.

An equation is a mathematical statement that shows that two expressions are equal. It contains one or more variables, and the goal is to solve for the value(s) of the variable(s) that make the equation true.

Given by the question.

Let's denote the number of pints of liquid A, B, and C as A, B, and C, respectively. We know that:

A + B + C = 100 (since they are mixing 100 pints in total)

We also know that the concentration of acid in the final mixture is 45%, so:

0.1A + 0.4B + 0.6C = 0.45(100) = 45

Finally, we are told that there are twice as many pints of liquid A as liquid B, so:

A = 2B

We can use these three equations to solve for A, B, and C. First, substitute A = 2B into the equation A + B + C = 100:

2B + B + C = 100

3B + C = 100

Next, substitute A = 2B into the equation 0.1A + 0.4B + 0.6C = 45:

0.1(2B) + 0.4B + 0.6C = 45

0.2B + 0.4B + 0.6C = 45

0.6B + 0.6C = 45

Simplify this equation by dividing both sides by 0.6:

B + C = 75

We now have two equations with two variables:

3B + C = 100

B + C = 75

Subtracting the second equation from the first, we get:

2B = 25

B = 12.5

Substituting this value back into B + C = 75, we get:

12.5 + C = 75

C = 62.5

Finally, using A = 2B, we get:

A = 25

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Answer: If p varies inversely with q, it means that their product is a constant value, which we can represent as k. That is:

p*q = k

We can solve for k using the given values:

p = 2 when q = 1

2 * 1 = k

k = 2

Now we can substitute k into the equation to get the general equation that relates p and q:

p*q = 2

or

p = 2/q

Therefore, the equation that relates p and q is p = 2/q, where p and q are variables that vary inversely and 2 is the constant of proportionality.

Step-by-step explanation:

Answer:

D) 0.25 divided by 0.42.

Step-by-step explanation:

The answer can be found using the formula for conditional probability:

P(B|A) = P(A and B) / P(A)

Let A be the event of passing the first test and B be the event of passing the second test. We know that:

P(A and B) = 25%

P(A) = 42%

To find P(B|A), we need to divide P(A and B) by P(A):

P(B|A) = P(A and B) / P(A) = 0.25 / 0.42

So the answer is D) 0.25 divided by 0.42.

Answer:

(3 sqrt(2))/2

Step-by-step explanation:

Simplify the following:

6/sqrt(8)

Rationalize the denominator. 6/sqrt(8) = 6/sqrt(8)×(8^(1 - 1/2))/(8^(1 - 1/2)) = (6×8^(1 - 1/2))/8:

(6×8^(1 - 1/2))/8

The gcd of 6 and 8 is 2, so (6×8^(1 - 1/2))/8 = ((2×3) 2 sqrt(2))/(2×4) = 2/2×(3×2 sqrt(2))/4 = (3×2 sqrt(2))/4:

(3×2 sqrt(2))/4

2/4 = 2/(2×2) = 1/2:

Answer: (3 sqrt(2))/2

Given:-

To Do :-

Solution:-

We have ;

[tex]\implies \dfrac{6}{\sqrt8} \\[/tex]

We can write 8 as 2³ . So ,

[tex]\implies \dfrac{6}{\sqrt{2^3}} \\[/tex]

[tex]\implies \dfrac{6}{2\sqrt2} \\[/tex]

[tex]\implies \dfrac{3}{\sqrt2} \\[/tex]

Rationalize the denominator by multiplying numerator and denominator by √2 .

[tex]\implies \dfrac{3\sqrt2}{\sqrt2.\sqrt2} \\[/tex]

[tex]\implies\boxed{ \dfrac{3\sqrt2}{2}} \\[/tex]

This is given required answer.

and we are done!

Hence, in response to the provided question, we can say that Martina equation used 26 pounds of type A coffee in the mix as a result.

An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.

Assume Martina used x pounds of type A coffee in her blend. Then, based on the information provided, she used 4 pounds of type B coffee.

Type A coffee costs $4.30 per pound, so x pounds of type A coffee costs $4.30x dollars.

Because the entire cost of the blend is given as $689.00, we may formulate the following equation:

4.30x + 22.20x = 689.00

Mixing similar phrases yields:

26.50x = 689.00

When we divide both sides by 26.50, we get:

x = 26

Martina used 26 pounds of type A coffee in the mix as a result.

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The function f(x) = 223 - 6a? - 144x + 7 is increasing on the interval (-00, A) U (B, co)and on the interval (-00, B), the function is decreasing.

Function in mathematics is a relation or mapping between input and output values. It describes a relationship in which each input value has a single corresponding output value. Functions are an essential part of mathematics, and they are used to model real-world situations. They are also used to solve equations, graph functions, and find the area of a region.

A function is increasing if its rate of change is positive; that is, the function is always getting larger as the independent variable (in this case, x) increases. Conversely, a function is decreasing if its rate of change is negative; that is, the function is always getting smaller as the independent variable increases.

The function f(x) = 223 - 6a? - 144x + 7 is increasing on the interval (-00, A) U (B, co). This means that the rate of change of the function is positive on the specified interval. That is, as x increases within the interval, the value of the function will also increase.

The value of A is the point at which the function changes from increasing to decreasing. That is, on the interval (-00, A), the function is increasing, but on the interval (A, B), the function is decreasing. The value of A can be found by setting the first derivative of the function (the rate of change) equal to 0.

The value of B is the point at which the function changes from decreasing to increasing. That is, on the interval (B, ∞), the function is increasing, but on the interval (-00, B), the function is decreasing. The value of B can be found by setting the first derivative of the function equal to 0.

The value of C is the point at which the function changes from concave up to concave down. That is, on the interval (C, ∞), the function is concave up, but on the interval (-00, C), the function is concave down. The value of C can be found by setting the second derivative of the function equal to 0.

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1. The credit which Stacy's will receive is $255.670.97.

2. Stacy's outstanding balance will be $854.33.

A credit refers to the ability of a customer to obtain goods or services before payment based on trust that payment will be made in the future.

From July 28 - July 14, we have 14 days. We are using the 3% discount.

The Credit receivable =

= Partial payment / (1 - discount rate)

= $248 / (1-0.03)

= $248 / 0.97

= $255.670103

= $255.67

An outstanding balance refers to the amount you owe on any debt that charges interest, like a credit card.

Stacy’s outstanding balance:

= $1,110 - $255.67

= $854.33.

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The mean for the grouped frequency data-set given in this problem is as follows:

80.8.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The number of observations in the data-set is given as follows:

1 + 1 + 4 + 3 + 8 + 10 + 15 + 22 + 11 = 75.

We are given a frequency distribution, hence for each interval we take the midpoint, and thus the sum of the values is given as follows:

S = 1 x (52 + 57) + 4 x 62 + 3 x 67 + 8 x 72 + 10 x 77 + 15 x 82 + 22 x 87 + 11 x 92

S = 6060.

Hence the mean is given as follows:

6060/75 = 80.8.

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Answer:

there is (0,1.5) and (9,0)

Step-by-step explanation:

there is my prrof that this is the answer

By using a system οf equatiοns, the schοοl makes 180 chicken sandwiches, 180 turkey sandwiches, and 140 rοast beef sandwiches.

A system οf equatiοns is a set οf twο οr mοre equatiοns that need tο be sοlved tοgether tο find the values οf the variables that satisfy all οf the equatiοns.

Let's use a system οf equatiοns tο sοlve the prοblem.

Let c be the number οf chicken sandwiches sοld, t be the number οf turkey sandwiches sοld, and r be the number οf rοast beef sandwiches sοld.

Frοm the prοblem, we knοw that:

c + t + r = 500 (the tοtal number οf sandwiches sοld is 500)

3c + 3.5t + 4r = 1730 (the tοtal revenue frοm selling all sandwiches is $1730)

We alsο knοw that the cafeteria makes the same number οf chicken sandwiches as it dοes turkey sandwiches, sο: c = t

Nοw we can substitute c fοr t in the first twο equatiοns:

c + c + r = 500

3c + 3.5c + 4r = 1730

Simplifying these equatiοns, we get:

2c + r = 500

6.5c + 4r = 1730

We can sοlve fοr r in the first equatiοn:

r = 500 - 2c

Substituting this intο the secοnd equatiοn and sοlving fοr c, we get:

6.5c + 4(500 - 2c) = 1730

6.5c + 2000 - 8c = 1730

-1.5c = -270

c = 180

Sο the cafeteria sells 180 chicken sandwiches and 180 turkey sandwiches (since c = t). We can find the number οf rοast beef sandwiches by substituting c and t intο οne οf the οriginal equatiοns:

c + t + r = 500

180 + 180 + r = 500

r = 140

Therefοre, the schοοl makes 180 chicken sandwiches, 180 turkey sandwiches, and 140 rοast beef sandwiches.

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The corresponding values of x for the given figures are 1. 4√2 and 2. 6√3.

The ratio of a right-angled triangle's hypotenuse to its opposite side is known as the sine function in trigonometry. Use the sine function to get the unknown angle or sides of a right triangle. The sine of an angle in a right-angled triangle is the proportion between the hypotenuse and the side parallel to the angle.

The sine function defines the relationship between the opposing side and the hypotenuse.

For the first figure we can write:

sin (45) = opposite side / hypotenuse = x / 8

1/√2 = x/8

x = 8/√2 = 4√2.

For the second figure we have:

sin 60 = opposite side / hypotenuse

√3/2 = x/12

x = 12√3/2 = 6√3

Hence, the corresponding values of x for the given figures are 1. 4√2 and 2. 6√3.

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The answer you're probably wanting is "function," since it is a function.

Technically though, it's both.  A function is a relation, one where each x-value (or input) has exactly one y-value (or output).  So every function is a relation, but not every relation is a function.

Cost price of iPhone12 is $588.89

To determine Apple's cost for the iPhone 12, we need to work backwards from the retail price of $795 and account for the 35% mark-up.

If we assume that the retail price includes the mark-up and the wholesale price is the original cost price of the product, we can set up an equation to solve for the cost:

Cost + 35% of Cost = Retail Price

Let's simplify the equation by converting the percentage to a decimal:

Cost + 0.35Cost = $795

Combining like terms:

1.35Cost = $795

Dividing both sides by 1.35:

Cost = $588.89

Therefore, Apple's cost for the iPhone 12 is approximately $588.89. This means that Apple makes a profit of $206.11 per phone sold.

It's important to note that this calculation is based on the assumption that the retail price includes only the 35% mark-up and not additional costs such as marketing, shipping, and other expenses that Apple incurs. Additionally, the actual wholesale cost may vary depending on a number of factors such as production volume, component prices, and supplier negotiations.

While we can estimate Apple's cost for the iPhone 12 based on the mark-up and retail price, it's important to keep in mind that the actual cost and profit margins may be more complex and variable in reality.

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The sales of bottled water and carbonated soft drinks will be the same in the year 2028 (in 5.323 years).

To find the year when the sales of soda and water will be equal, we need to solve the equation:

Soda = Water

12.5 - 0.2475t = 8.2 + 0.56t

where

t = time

collecting like terms

12.5 - 8.2 = 0.2475t + 0.56t

4.3 = 0.8075t

Then we can solve for t by dividing both sides by 0.8075:

t ≈ 5.323

If t is in years, this tells us that the sales of soda and water will be equal in approximately 5.323 years.

To find the year when this will happen, we need to add 5.323 to the current year.

Assuming the current year is 2023, we get:

2023 + 5.323 ≈ 2028.323

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Answer:

2

Step-by-step explanation:

Answer:

SI=P*R*T/100

SI=270*2.25*2/100

SI=7.65

TOTAL AMOUNT=7.65+170=177.65

The value of x and y in the equation are 1 and -4 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . Example of Simultaneous equation is ;

3x + 2 = y equation 1

5x +3 = 2y equation 2

Simultaneous equations can be solved either by elimination or substitution methods.

y = -7x +3 ( equation 1)

y = -x-3 (equation 2)

subtract equation 1 from 2

-x -(-7) -3-3 = 0

-x+7 -6 = 0

x = 7-6

x = 1

substitute 1 for x in equation 1

y = -7(1) +3

y = -7+3

y = -4

therefore the value of x and y are 1 and -4 respectively

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