A recipe uses cups of milk to make servings. If the same amount of milk is used for each serving, how many servings can be made using gallon of milk?

The value of p when x = 21 is p = 32/3 .

Given :

we know that ,

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form  p * x = k or p = k / x

we know that

For p = 14, x = 16

Find the value of k

k = p * x

substitute the values

k = 14 * 16

= 224

so

The equation is equal to

p = 224 / x

if x = 21

substitute the value of x in the equation

p = 224 / 21

Divide by 7 both numerator and denominator

p = 32 / 3

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Answer:

The next two terms in the Fibonacci sequence would be 23 and 37.

Step-by-step explanation:

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. So the next term in the sequence is found by adding the two previous terms, like this:

1 + 4 = 5

4 + 5 = 9

5 + 9 = 14

9 + 14 = 23

14 + 23 = 37

The base is the length of one of the triangle's sides, and the height is the distance from that side to the triangle's opposite corner.

A triangle is a polygon having three vertices and three edges. It is a fundamental geometric figure. Triangle ABC represents a triangle with three vertices: A, B, and C. Any three non-collinear points constitute a unique triangle and, by extension, a unique plane in Euclidean geometry. Triangles are polygons with three vertices that have three sides. The triangle's angles are constructed by joining the three sides end to end at a point. The triangle's three angles add up to 180 degrees.

Here,

The base of the triangle is the length of one of its sides, and the height is the distance from that side to the triangle's opposite corner.

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These values were found [tex]\lim_{x \to -\infty} f(x) = 0[/tex]  & [tex]\lim_{x \to \infty} f(x) = \infty[/tex] from the given equation.

What is the limit?

A limit in mathematics is the value that a function approaches as its input approaches some value. Limits are used to define continuity, derivatives, and integrals in calculus and mathematical analysis.

We have,

f(x) = 4xe³ˣ / 1

f(x) = 4xe³ˣ

[tex]\lim_{x \to \infty} f(x) = ?[/tex]l

[tex]\lim_{x \to -\infty} f(x) = ?[/tex]

[tex]\lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} 4xe^{3x}[/tex]

It is the form -∞ * 0 which is an undetermined form

Write it has a fraction then apply l'Hospital's Rule

[tex]\lim_{x \to -\infty} \frac{4x}{1 / e^{3x} } = \lim_{x \to -\infty} \frac{4}{ -3e^{3x} / e^{6x} }[/tex]

[tex]= \lim_{x \to -\infty} \frac{4}{-3/e^{3x}} } = \lim_{x \to -\infty} \frac{4e^{3x}}{ -3 }[/tex]

[tex]= \frac{4e^{-x}}{ -3 }[/tex]

[tex]= \frac{0}{ -3 } = 0[/tex]

[tex]\lim_{x \to \infty} f(x) = \lim_{x \to \infty} 4xe^{3x}[/tex]

Simply evaluate

[tex]\lim_{x \to \infty} 4xe^{3x} = \infty * \infty = \infty[/tex]

 (∞*∞ is not an undetermined form).

f(x) = 4xe³ˣ

[tex]\lim_{x \to -\infty} f(x) = 0[/tex]

[tex]\lim_{x \to \infty} f(x) = \infty[/tex]

Hence, these values were found [tex]\lim_{x \to -\infty} f(x) = 0[/tex]  & [tex]\lim_{x \to \infty} f(x) = \infty[/tex] from the given equation.

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Answer:

Direct Variation

y = 3x

y = (2/7)x

y = -0.5x

NOT Direct Variation:

x = -1

y = 4

y = 22x + 7

Step-by-step explanation:

Direct Variations are in the form

y = kx

This is very similar to:

y = mx + b except the b MUST be zero.

Also, direct variations always go through (0,0) that's why b must be 0.

So easy to pick out:

y = 3x

y = (2/7)x and

y = -0.5x are all in the form y = kx and have a y-intercept of zero.

y = 22x + 7 has that extra +7 tacked on to the end of the equation. It does not go through (0,0). It has a b that is 7. So it starts at (0,7). It is not a direct variation.

The other two, x = -1 and y=4 are both not direct variations. Neither starts at (0,0).

x=anumber is a vertical line and y=anumber is a horizontal line. These are not direct variations.

Answer:

[tex]c=2.50x[/tex]

Step-by-step explanation:

The cost per pound of chicken is [tex]50/20=\$2.50[/tex].

So, the equation is [tex]c=2.50x[/tex].

Answer:

C, D

Step-by-step explanation:

Compare each choice with

x² + 5x - 8 = 0

A.

x² + 7x - 9 = 2x + 1

x² + 5x - 10 = 0

No

B.

x² + 4x - 5 = x - 3

x² + 3x - 2 = 0
No

C.

x² + 10x - 2 = 5x + 6

x² + 5x - 8 = 0

Yes

D.

12x + 4 = 7x + 12 - x²

x² + 5x - 8 = 0

Yes

Answer: C, D

If the sum of two numbers is 36 and the larger number is 10 more than smaller number then the larger number is   .

the Sum of two numbers is given to be = 36 ;

also given that " larger number is 10 more than smaller number " ;

let the larger number be = "x" , and

the smaller number be = "y" .

So , according to the question ⇒ x + y = 36 ;

and x = y + 10 , putting x in above eqn.

we get , y + 10 + y = 36

2y + 10 = 36

2y = 36 - 10

2y = 26

y = 26/2 = 13

and x = 13 + 10 = 23 .

Therefore , the larger number is 23 .

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For a normal distribution, a negative value of z indicates D. the z is to the left of the mean.

A continuous probability distribution known as the "normal distribution" has values that are symmetrically distributed mostly around the mean.

The standard deviation determines the width of the curve in a normal distribution, which depicts a symmetrical plot of data around its mean value. It is represented graphically by the "bell curve.

Z is the number of standard deviations from the mean given by the formula:

z = ( X - μ ) ÷ ( σ )

where

x is the raw score,

μ is the population mean, and

σ is the population standard deviation

A negative value means that the number of standard deviations of an observation is to the left of the mean.

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3/2 is the quotient when 3/4 is divided by 1/2

When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal. Finding the reciprocal of the second fraction and this can be obtained by reversing its numerator and denominator—is and then dividing the  fractions. Multiply the two numerators after that. Multiply the two denominators after that, After that we need to simplify the fraction to its lowest form.

When we divide one number by another, the result obtained is also known as quotient.

so in order to find the quotient when both fraction is divied

quotient of the division = [tex]\frac{3}{4}[/tex] ÷[tex]\frac{1}{2}[/tex]

=> (3/4) / (1/2)

=> (3/4) * 2

=> 3/2

so quotient of the division = 3/2 or 1.5

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Answer:

144 seconds

Step-by-step explanation:

4.5 seconds = 5 pages

x second = 160 pages

cross multiply

you get: 5x= 160 ×4.5

which equals 720 divide it by 5 you get 144

If the four-digit personal identification number (PIN) cannot start with a 0 and must be an odd number, then 0 four-digit pins are conceivable.

There are 10 possible digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) that can be used in a four-digit PIN. However, we are told that the PIN cannot begin with a 0, so there are only 9 possible digits that can be used for the first digit.

For the second, third, and fourth digits, any of the 10 digits can be used. Therefore, there are 9 x 10 x 10 x 10 = 9,000 four-digit PINs that can be created using any of the 10 digits.

We are also told that the PIN must be an odd number. This means that the last digit of the PIN must be odd. There are 5 odd digits (1, 3, 5, 7, and 9), so there are 5 possible digits that can be used for the last digit.

For the first three digits, any of the 9 digits that can be used for the first digit can be used. Therefore, there are 9 x 10 x 10 = 900 four-digit PINs that can be created using only odd digits.

However, we have double-counted the PINs that begin with 0. Since these PINs are not allowed, we need to subtract them from the total number of possible PINs. There are 9 x 10 x 10 = 900 four-digit PINs that begin with 0, so we need to subtract these from the total number of possible PINs.

The final number of possible four-digit PINs that cannot begin with 0 and must be odd is 900 - 900 = 0. Therefore, there are 0 four-digit PINs that meet these criteria.

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The rate of flow for emptying the tank would be 0.15 liter/minute.

The rate at which the water level in the tank is changing is given by the equation:

ΔV/Δt = flow rate in - flow rate out

where ΔV is the change in the volume of water in the tank, Δt is the time interval over which the change occurs, and flow rate in and flow rate out are the rates at which water flows into and out of the tank, respectively.

In this case, the flow rate is 0.15 liter per minute, and the flow rate out is 0.27 liter per minute. The volume of water in the tank is 4.8 liters.

To determine how long it will take to empty the tank, we can set the volume of water in the tank to 0 and solve for the time interval:

0 = flow rate in - flow rate out

flow rate out = flow rate in

0.27 liter/minute = 0.15 liter/minute

Since the equation is not balanced, we cannot determine the time interval. In order to determine the time interval, we need to have information about both the flow rate in and the flow rate out. Without this information, it is not possible to determine how long it will take to empty the tank.

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We can determine the height of a triangle when we know the base and area of the triangle using the area formula of triangle in base and height, that is

A = 1/2 × b × h

A triangle is a three sided polygon. The height of the triangle is the perpendicular distance of the not-included vertex to the considered base.

The formula to determine area of a triangle of base b and height h is

A = 1/2 × b × h

Therefore to determine the height of a triangle when base and area is given, we substitute the given values in appropriate units in the formula.

h = 2×A/ b

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Yes, the number 16 is a square.

It is the square of the number 4, since 4 x 4 = 16.

A square root is a factor in mathematics that, when multiplied by itself, equals the initial number. For instance, 3 and -3 are both square roots of 9.

The square of a number's root is the value under the root. For instance, (3 + 2) = 3. Any even number's square unit will only include even numbers.

Each and every nonnegative real number x has a distinct nonnegative square root, known as the primary square root, which is represented by the symbol x, also known as the radical sign or radix. As an illustration, we write 9=3 to denote that 3 is the number 9's fundamental square root. The word (or integer) whose square root is being examined is known as the radicand. The word or number that appears beneath the radical symbol, in this case, 9, is referred to as the radicand. The principal square root can alternatively be expressed in exponent notation for nonnegative x as x1/2.

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The 3 consecutive odd numbers whose sum will be 45 are 13 , 15 and 19 .

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.

Now, the next odd number after (2k+1) will be (2k+3) because if we take (2k+2) then we can see that it is clearly divisible by 2.

Let the 3 numbers be x ,x+2 , x+4

The sum of numbers is 45

⟹x+x+2+x+4=45

3x+6=45

3x=39

x=13

Hence , the 3 consecutive odd numbers whose sum will be 45 are 13 , 15 and 19 .

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SSS means side side side, SAS means side angle side and AAA means angle angle angle.

There are some postulates which can be used to prove that the two given triangles are similar. If two triangles are similar then we can find as a result that their respective sides and angles are also equal.

If three sides are given then we will use the SSS postulate

If two sides and one angle is given then we will use the SAS postulate

If three angles are given then we will use the AAA postulate.

Therefore SSS, SAS, and AAA are postulated that are used to prove two triangles are similar.

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Since a rectangle is rolled along length then circumference of circle is equal to length of rectangle and breadth equals to height.

=) 2*pi*r = 42cm

=) 2*22/7 * r = 42cm

=) r = 42*7 / 2*22

=) r = 147/22 cm

Since Volume of cylinder = pi* r^2*h

= 22/7 * 147/22 * 147/22 * 16 cm^3

= 2245.09 cm^3.

The situation can be expressed in inequality as: 95x + 0.85y ≤ 500

On solving the maximum amount of miles that can be driven to stay under budget is 253

What is inequality?

If two real numbers or the algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality.

For example, x > 3 (x should be greater than 3)

According to the given question:

Total amount to spend is restricted to $500

Let the number of days be x and extra miles covered be y

The car rental company charges $95 per day to rent the car and charges $0.85 per mile.

Therefore the situation van be expressed as:

95x + 0.85y ≤ 500

If the car is rent for 3 days then the maximum amount of miles that can be driven to stay under budget are

95(3) + 0.85y ≤ 500

285 + 0.85y ≤ 500

0.85y ≤ 215

y ≤ 253

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Answer:

Step-by-step explanation:

42 is an even number so it is divisible by 2

42 divided by 2=21

42 has digits that add up to give 6

If the sum of a number adds up to give 3, 6 or 9 that number is divisible by 3

42 divided by 3=14

Factors of 42 are 21 and 2 and 14 and 3 and 42 and 1

Answer:

this it's no a math problem

g

=

p

2

−

m

Step-by-step explanation:

Total 1,512,000 "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

In the given question, we have to find how many "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

The given word is INQUISITIVE.

The total alphabets in the word INQUISITIVE is 11.

Let us first count the words without U and then insert U wherever applicable.

Now without U we have total 10 alphabets and the alphabet I is repeated by 4 times.

So permutations is 10!/4! = 151,200

Now we need to put U, we can see its 11 alphabets but U should not follow Q so it becomes 10 alphabets.

Hence, Total number of words = 151,200*10

Total number of words = 1,512,000

Hence, 1,512,000 "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

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The domain of the function [tex]f(x)=\frac{1}{x}[/tex]  is all real numbers except 0.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's domain is the collection of values it can take as input.

For example, let us take a function [tex]f(x)=\frac{1}{x}[/tex].

For this function, the domain is all the values x can take.

Here x cannot take 0 because 1/0 is not defined.

So, the domain of the function is all real values except 0 which can also be written as:

Domain= R-{0}

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How many pattern block trapezoids would create 2 hexagons?

First make the graph of the functions, then  if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.

Symmetric

A figure or shape that can be divided into two equal parts by a line is called symmetric figures.

Inverse Functions

The inverse function of a function f  is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.

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The equation Y=-2x is a linear equation, which can be plotted on a graph as a straight line.

The equation can be written in slope-intercept form as y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is m=-2 and the y-intercept is b=0. Therefore, the equation can be written as y=-2x+0.

The slope of the line is negative, meaning that as x increases, y decreases. The y-intercept is zero, which means that the line passes through the origin (0,0).

For example, if x = 2, then y = -2(2) + 0 = -4. Therefore, the point (2, -4) is on the line. Similarly, if x = 4, then y = -2(4) + 0 = -8, so the point (4, -8) is also on the line.

The graph of the equation y=-2x would thus be a line starting at the origin (0,0) with a negative slope. As x increases, y decreases, and the line never crosses the y-axis.

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The best way to find multiple missing numbers in a given integer array with duplicates in Java is to use a hash set and loop.

First, create a HashSet and add all elements from the array to it. Then, loop from 1 to the maximum element of the array and check if each number is present in the HashSet. If the number is not present, it is a missing number. To explain further, a hash set is an efficient data structure for storing unique elements of a collection, and using a loop to check for missing numbers ensures that all numbers from the array are accounted for.

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Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the inverse of a number a is [tex]\frac{1}{a}[/tex]

then

the inverse of 2 is [tex]\frac{1}{2}[/tex]