To make yummy fruit punch,use 2 cups of grape juice for every 3 cups of apple juice. If you already have 12 cups of apple juice,how many cups of grape juice how many cups will you need to make fruit punch?

Final answer:

A decimal written in word form represents a mixed number if there's a whole number followed by 'and', then the fractional part, such as 'two and three tenths' for 2.3.

Explanation:

When a decimal is written in word form, the indication that the equivalent form is a mixed number rather than a fraction is the presence of a whole number followed by the word 'and', then the fractional part.

For example, 'two and three tenths' (2.3 in numeric form) is a mixed number, as it has a whole number 'two' and the fractional part 'three tenths'. In contrast, a number written solely as 'three tenths' would represent just a fraction (0.3 in numeric form).

The mean, median, and mode are measures of central tendency. The median value is based on the median , while the arithmetic average is based on the mean. The most frequently occurring value in a data set is based on the mode .

For example, if we have the following data set: {4, 18, 18, 19, 19, 19, 19, 19, 20, 20}, the mean is 17.5 (170/10), the median is 19, and the mode is 19.

Final answer:

By applying the Pythagorean theorem, it's determined that the set of line segments that could create a right triangle is option b. (15, 36, 39), as it's the only set that satisfies the equation a² + b² = c².

Explanation:

The question asks which set of line segments could create a right triangle. To solve this, we apply the Pythagorean theorem, which states for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a² + b² = c², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Therefore, the set of line segments that could create a right triangle is option b. (15, 36, 39).

Answer:

  b.  15, 36, 39

Step-by-step explanation:

You want the set of line segments that could form a right triangle.

A set of 3 integers is a Pythagorean triple if it satisfies the Pythagorean theorem:

  a² +b² = c²

The most common primitive triples are {3, 4, 5}, {5, 12, 13}. If two of three numbers match these, but the third does not, a right triangle cannot be formed.

We note that {3, 4, 5} has the smallest first number of any Pythagorean triple, and it is the only triple that is an arithmetic sequence.

We can reduce the given numbers to their lowest form to see if we can determine whether any is a Pythagorean triple:

  a. 15 : 30 : 35 = 3 : 6 : 7 . . . . . not a right triangle

  b. 15 : 36 : 39 = 5 : 12 : 13 . . . . forms a right triangle

  c. 15 : 20 : 29 = 3 : 4 : 5.8 . . . . . not a right triangle

  d. 5 : 15 : 30 = 1 : 3 : 6 . . . . not a triangle

__

Additional comment

The attachment shows the values of a² +b² -c² for the different answer choices. That expression will evaluate to 0 if the numbers form a right triangle. If the sum is negative, any triangle formed would be obtuse. As we noted above, choice D values do not even form a triangle.

Other Pythagorean triples commonly seen in algebra problems are ...

  {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, {20, 21, 29}

You may also notice that when the two largest numbers differ by 1, the smallest is the root of their sum: 3 = √(4+5), 5 = √(12+13), 7 = √(24+25), and so on. This is another way we can tell {3, 6, 7} is not a Pythagorean triple: 3 ≠ √(6+7).

There are 9 hours between 8:30 am to 5:30 pm

From the question, we have the following parameters that can be used in our computation:

Initial time  = 8:30 am

Final time = 5:30 pm

using the above as a guide, we have the following:

Number of hours = Final time - Initial time  

substitute the known values in the above equation, so, we have the following representation

Number of hours = 5:30 pm - 8:30 am

Evaluate

Number of hours = 9 hours

Hence, there are 9 hours between 8:30 am to 5:30 pm

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Answer: Angle addition postulate.

Explanation: If [tex]\angle TRV= 60^{\circ}[/tex] and [tex]\angle TRS=4x^{\circ}[/tex]

here, if we have to prove x=30

If there is a condition that TR is a line which meets with the line segment VS at point R then by the Angle addition postulate,  we can say that [tex]\angle TRV+\angle TRS=180^{\circ}[/tex]⇒[tex]x=30^{\circ}[/tex]

But,

In option (1) substitution property of equality

If there is condition that  [tex]\angle TRV=\angle TRS[/tex]

then we can use  substitution property of equality,

And, in this case [tex]4x^{\circ}=60^{\circ}[/tex]⇒[tex]x=15^{\circ}[/tex]

which is wrong. So, we can not use this property here.

In option (3) subtraction property of equality

There is no use of this property to find the value x.

In option (4) addition property of equality

There is no use of this property to find the value x.

The omitted reason in step 3 should be the angle addition postulate.

From the diagram attached ;

mTRV = 60 ; ∠TRS = 4x

According to the addition postulate :

mTRV + ∠TRS = 180° (sum of linear pair of angles).

Hence, the missing reason for the third step is the angle addition postulate.

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Final answer:

To factor the expression 10x + 40, we can factor out the greatest common factor (GCF) of 10 from both terms, resulting in 10(x + 4).

Explanation:

To factor the expression 10x + 40, we can first find the common factor for both terms, which is 10. Factoring out 10, we get 10(x + 4). This expression represents the original 10x + 40. In simpler terms, we've taken out the common factor of 10 from both terms, leaving us with 10 multiplied by the quantity (x + 4). This factored form is useful for simplifying expressions or solving equations. Essentially, factoring helps us break down a more complex expression into simpler parts, making it easier to work with and understand in various mathematical contexts.

Answer:

[tex]\frac{-\sqrt{2}-\sqrt{6}}{4}[/tex]

Step-by-step explanation:

PLATO

Answer: 74:111

Step-by-step explanation: To find 185 in ratio 2:3:

First, add the ratios: 2 + 3 = 5

Second, each ratio will be put over the total: [tex]\frac{2}{5}[/tex] and [tex]\frac{3}{5}[/tex]

Third, multiply the number by the fraction of each proportion:

185 . [tex]\frac{2}{5}[/tex] = 74

185 . [tex]\frac{3}{5}[/tex] = 111

So, 185 in ration 2:3 gives ratio 74:111.

Answer:

gross pay = $552.50

Step-by-step explanation:

Kenneth earns a commission on his total sales = [tex]4\frac{1}{2}[/tex] %

                                                                              = [tex]\frac{9}{2}[/tex] %

                                                                              = 4.5%

If his sales are 4500 this week.

His commission would be = 4.5% × 4500

                                           =  [tex]\frac{4.5}{100}\times 4500[/tex]

                                           = 0.045 × 4500

                                           = $202.50

His weekly salary is $350

Gross pay = 350 + 202.50 = $552.50

Kenneth's gross pay would be $552.50 this week.

An indifference curve is used in economics to show different combinations of goods that provide equal satisfaction to a consumer. Ambrose's indifference curve equation and marginal rate of substitution are given, representing his willingness to trade one good for another while holding utility constant.

An indifference curve is a graphical representation used in economics to show the different combinations of two goods that provide equal satisfaction or utility to a consumer. In this case, Ambrose has an indifference curve with the equation x2 = 20 - 4x1/21. To find his marginal rate of substitution (MRS), we need to calculate the slope of the indifference curve at the point (4, 16). The MRS is given as 25/4, which means that Ambrose is willing to give up 25/4 units of x1 in exchange for 1 unit of x2, while keeping his utility constant.

Answer:

They are both correct.

Step-by-step explanation:

SInce they both are saying the same amount of pages just in different ways, Kim is saying a thousand plus five hundred, that is 1500, and Kim says 15 hundred, which is basically 1500, so they are both rounding up the number to the nearest cent correctly just are expressing the number in different ways.

Final answer:

Dustin is currently 9 years old.

Explanation:

The question is asking us to solve for Dustin's current age given a relationship between his age and Elias's. To solve the problem, we need to set up an equation where Dustin's current age is represented by D and Elias's current age is represented by E.

We are told that Dustin is 11 years younger than Elias, which gives us the first equation:

E = D + 11

In two years, Dustin will be half as old as Elias. We can represent this future scenario with another equation:

D + 2 = (E + 2) / 2

To find Dustin's age, we will solve these two equations simultaneously. By substituting the expression for E from the first equation into the second equation, we get:

D + 2 = (D + 11 + 2) / 2

The equation simplifies to:

D + 2 = (D + 13) / 2

Now, we simplify and solve for D:

Therefore, Dustin is currently 9 years old.

To find the initial amount of water in the pail, set up a system of equations based on the total volume and the information provided after transferring some water. Solve the equations to obtain the initial quantity of 957 milliliters in the pail.

A student posed a problem: A tank and a pail contain a total of 5136 milliliters of water. Jacob pours 314 milliliters of water from the pail into the tank. The amount of water in the tank is now 7 times what is left in the pail. How much water was in the pail at first?

Let's denote the initial amount of water in the tank as T milliliters and in the pail as P milliliters. According to the given information, the combined quantity of water in both is 5136 milliliters:

After transferring 314 milliliters from the pail to the tank, the tank now has T + 314 milliliters, and the pail has P - 314 milliliters. It is also given that the water in the tank is now 7 times the water left in the pail:

Now, we have a system of two equations:
   

By solving these equations, we can find the initial amount of water in the pail, P. First, modify the second equation to isolate T:

Next, substitute the expression for T from the second equation into the first equation and solve for P:

Initially, there were 957 milliliters of water in the pail.