A recipe for homemade modeling clay includes cup of salt for every cup of water. If there are 6 cups of salt, how many gallons of water are needed?

Yes, Abbie will capture the moment when the candles are exactly the same height

Here we need to determine whether Abbie will capture the moment when the candles are exactly the same height in the 3 hours she has left to film, then we would need to know the rate at which the candles are burning.

According to this information would allow us to calculate how long it would take for the candles to burn down to the same height.

As we all know that the rate is a unique ratio where the two words are expressed in several units.

Here for the instance, let us consider that the price is 69 for 12 ounces if a 12-ounce can of maize costs 69.

It will clearly shows that this is not a proportion of two comparable units, like shirts.

Similarly, let us consider that the Cents and ounces are the two dissimilar units in this ratio.

Therefore, here let us assume that if we assume that the rate at which a candle burns is constant, then we can use the following formula to calculate the time it would take for the candles to burn down to the same height can be calculated as,

=> time = (height of taller candle - height of shorter candle) / (rate of taller candle - rate of shorter candle)

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Answer:

$325.02

Step-by-step explanation:

What is 2% administrative fee on $16,251?

2% = 0.02

We Take

16251 x 0.02 = $325.02

So, 2% administrative fee on $16251 is $325.02

The value of "n" is 6.

"n" is related to a circle with intersecting chords labeled 5, n+4, 7, and n+8 [1]. To find the value of "n", we can use the property that states that if two chords intersect inside a circle, the products of their segments are equal. Using this property, we can set up the following equation:

7(n+4) = 5(n+8)

Expanding the brackets, we get:

7n + 28 = 5n + 40

Simplifying, we get:

2n = 12

n=6

A circle is a two-dimensional geometric shape that is defined as a set of all points in a plane that are at a fixed distance (called the radius) from a given point (called the center). It is a closed shape, meaning that it has no beginning or end, and its boundary is a continuous curve.

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The least positive integer n such that \sigma(a^n) - 1 is divisible by 2021 for all positive integers a is \boxed{966}.

To find the least positive integer n such that \sigma(a^n) - 1 is divisible by 2021 for all positive integers a, we need to analyze the divisors of 2021. The prime factorization of 2021 is 43 \times 47.

Let's consider a prime p dividing 2021. For any positive integer a, \sigma(a^n) - 1 will be divisible by p if and only if a^n - 1 is divisible by p. This condition is satisfied if n is a multiple of the multiplicative order of a modulo p.

Since 43 and 47 are distinct primes, we can consider the multiplicative orders of a modulo 43 and modulo 47 separately. The smallest positive integers that satisfy the condition for each prime are 42 and 46, respectively.

To find the least common multiple (LCM) of 42 and 46, we factorize them into prime powers: 42 = 2 \times 3 \times 7 and 46 = 2 \times 23. The LCM is 2 \times 3 \times 7 \times 23 = 966.

Therefore, the least positive integer n such that \sigma(a^n) - 1 is divisible by 2021 for all positive integers a is \boxed{966}.

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Answer:

See below.

Step-by-step explanation:

A line can be named using a single small-case letter, or it can be named using any two points on the line in either order.

3.

You have 2 choices. Choose h or

\( \overleftrightarrow{CA} \)

4. You have five choices. Choose one of these.

\( \overleftrightarrow{HG}, \overleftrightarrow{GJ}, \overleftrightarrow{JG} \)

\( \overleftrightarrow{JH}, \overleftrightarrow{HJ} \)

Answer:

A line can be named using a single small-case letter, or it can be named using any two points on the line in either order.

3.

You have 2 choices. Choose h or

4. You have five choices. Choose one of these.

Step-by-step explanation:

Both Mathew and James are exerting the same amount of force, which is 400 newtons.

Force is a measure of the interaction between two objects and is expressed in newtons (N). In this case, both Mathew and James are exerting a force of 400 newtons. The weight of the sled and the tree stump, both weighing 200 lbs, does not affect the force exerted by Mathew and James.

The weight of an object is the force exerted on it due to gravity. In this context, the weight of the sled and the tree stump is the same, 200 lbs. However, when comparing forces, we consider the amount of force applied by an individual, which is independent of the weight of the object being pushed or lifted.

Therefore, Mathew and James are exerting the same amount of force, which is 400 newtons.

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The number of hours they can play the video games before the weekend, then the inequality that represents the situation will be:

8 - t ≤ 4

An inequality is a mathematical statement that compares two quantities or expressions that are not equal using the inequality signs such as:

We are give that:

Total hours Dominique is allowed to play is 8 hours, this means 8 hours is the maximum number of hours he can play in a week.

Number of hours to be played during for the weekend is given as, at least 4 hours. This means, the number of hours to play at weekend can be 4 hours or more.

If t represents the number of hours they can play the video games before the weekend, then the inequality that represents the situation will be:

8 - t ≤ 4

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The matrix cannot be inverted if any eigenvalue is 0, which also means that the determinant is zero. This suggests a linear dependence between the columns of A. As a result, A is not of full rank and is not invertible.

What does "linearly dependent" mean?

A set's ability to have at least one linear combination of its components equal to zero when the coefficients are taken from another provided set and at least one of those coefficients is not equal to zero.

                  This feature applies to matrices or vectors. adjective that depends on linearity.

What does it mean to be linearly dependent?

A group of non-zero vectors is said to be linearly dependent if at least one of them can be expressed as a linear combination of the others.

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Answer:

Step-by-step explanation:

hmmm... i would say that the days are uneven. that's all i got.

Answer:

140

Step-by-step explanation:

Let the number = x

Hence, the expression can be written has:

0.4 of x = 56

0.4x = 56

Divide both sides by 0.4

0.4x / 0.4 = 56 / 0.4

x = 140

Hence, 56 is 0.4 of 140

Answer:

Step-by-step explanation:

Given the population of yeast modelled by the function f(t)=a/1+be^-0.7t where t is measured in hours.

If at time t = 0 the population is 20 cells, then the equation becomes:

20 = a/1+be^-0.7t

20 = a/1+be^-0.7(0)

20 = a/1+be^-0

20 = a/1+b(1)

a/1+b = 20

a = 20(1+b) ........ equation 1

Also if the population is increasing at a rate of 12 cells/hour, then d(f(t)/dt = 12

Differentiate the expression with respect to time

f(t)=a(1+be^-0.7t)^-1

d(f(t)/dt =

a{-(1+be^-0.7t)^-2×(-0.7be^-0.7t)

a{-(1+be^-0.7t)^-2×(-0.7be^-0.7t) = 12

0.7abe^-0.7t/(1+be^-0.7t)² = 12 ..... equation 2

at t = 0, the equation becomes

0.7abe^-0/(1+be^-0)² = 12

0.7ab/(1+b)²= 12

0.7ab = 12(1+b)²

Substitute 1 into 2

0.7×20(1+b)b = 12(1+b)²

14(1+b)b = 12(1+b)²

Divide both sides by 1+b

14b = 12(1+b)

14b = 12+12b

14b-12b = 12

2b = 12

b = 6

Substitute b= 6 into the equation a = 20(1+b) to get a.

a = 20(1+6)

a = 20×7

a = 140

For us to be able to determine what happens to the yeast population in the long run. we will take the limit of f(t) as t approaches infinity.

Lim t -->/infty a/1+be^-0.7t

= a/1+be^-(infty)

= a/1+b(0)

= a

Since a = 140, hence the population of the yeast tends to 140 on the long run

Answer:

James deliver newspaper in 1 hour=130

Marks deliver newspaper in 1 hour= 210/3=70

so lf they work together to deliver 1000 newspaper they take 130+70=200. 1000/200=5.

so they take 5 hours to deliver 1000 newspaper.

It would take 5 hours for James and Mark to deliver 1000 newspapers.

Equation is an expression used to show the relationship between two or more variables and numbers.

James delivers 130 papers in one hour (130/1) and Mark delivers 210 papers in three hours(70 papers in 1 hours), hence:

For 1000 newspapers:

(130 + 70)t = 1000

t = 5 hours

It would take 5 hours for James and Mark to deliver 1000 newspapers.

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Answer:Okay, so the first thing to do here is show you that any number can be a fraction if you use a 1 as the denominator. Take a look:

1.80

1

What we really want to do though, is get rid of the decimal places completely so that the numerator in our fraction is a whole number. To do this, we have to count the numbers after the decimal point, which in this case is 80.

To get a whole fraction we need to multiply both the numerator and the denominator by 10 if there is one number after the decimal point, 100 if there are two numbers, 1,000 if it's three numbers and 10,000 if it's...well, you get the idea!

In our case 80 is 2 digits long so we need to multiply the numerator and denominator by 100.

Now we just need to do that multiplication to get our whole fraction:

1.80 x 100

1 x 100

=

180

100

The next step is to simplify this fraction and, to do that, we need to find the greatest common factor (GCF). This is sometimes also known as:

Greatest Common Divisor (GCD)

Highest Common Factor (HCF)

Greatest Common Denominator (GCD)

The GCF can be a bit complicated to work out by hand but you can use our handy GCF calculator to figure it out.

In the case of 180 and 100, the greatest common divisor is 20. This means that to simplify the fraction we can divide by the numerator and the denominator by 20 and we get:

180/20

100/20

=

9

5

And there you have it! In just a few short steps we have figured out what 1.80 is as a fraction. The complete answer for your enjoyment is below:

1 4/5

Note: because 180 is greater than 100 we have simplified this fraction even further to a mixed fraction.

Step-by-step explanation:

Answer:

254

Step-by-step explanation:

i think it is correct

Answer:

-76.5

Step-by-step explanation:

see image attached for sol

Recall that the discriminant of a quadratic equation:

is:

Also, if:

Now, notice that the discriminant of the given equation is:

Simplifying the above result we get:

Since 24>0, we get that the given equation has 2 different real roots.

Answer: The given equation has 2 different real roots.

Answer: answer is 12

Step-by-step explanation:

Answer:

LCM (k, n) = 10 and HCF(k, n) = 2

Step-by-step explanation:

The given parameters are;

The time after which Keshav takes  a break = k hours

The value of k = The first smallest prime natural number

Therefore, by mathematical definition, k = 2

The time after which Noel takes a break = n hours

The value of n = The fifth smallest composite natural number

The first five composite numbers are given as follows;

4, 6, 8, 9, and 10

Therefore, the fifth smallest composite natural number = 10 = n

The LCM (k, n) = LCM (2, 10) = Least common multiple of 2 and 10 is given as follows;

Dividing by 2, we get;

2/2 = 1,  10/2 = 5

Dividing the result by 5, we get;

5/5 = 1

Multiplying the devisors together gives;

5 × 2 = 10

Therefore, the LCM of 2 and 10 = 10

LCM(2, 10) = LCM (k, n) = 10

The HCF(k, n) = HCF of 2 and 10 = The highest common factor that divides both 2 and 10 is given as follows;

Dividing 2 and 10 by 2 gives;

2/2 = 1 and 10/2 = 5

Therefore, HCF(k, n) = The highest common factor of 2 and 10 = HCF(2, 10) = 2

Answer:

x = -6

Step-by-step explanation:

The correct statement is: the volume of the cylinder is 8 cubic inches more than that of the cone.

The volume of cone (V) = 1/3 * πr²h

Volume of cylinder (V) = πr²h

Where, r is the radius of their bases.

The base area formula for the cone = πr²

Calculate the area of the base of the cone that has a radius (r) of 2.5 in:

Area of the base of the cone = π(2.5)² ≈ 19.6

The volume of the cone (V) = 1/3 * πr²h = 1/3 * π * 2.5² * 6.5

≈ 42.5 cubic inches

Volume of cylinder (V) = πr²h = π * 2² * 4

≈ 50.3 cubic inches

The difference in volume = 50.3  - 42.5

= 7.8 ≈ 8 cubic inches

Therefore, the only statement that is true is: the volume of the cylinder is 8 cubic inches more than that of the cone.

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Answer:

1: No, this is not direct variation

2: Yes, this is direct variation with k= 2.34

Step-by-step explanation:

I’m Just Built Different

Answer:

144+49=x²

193. =x²

X =√193

x. =+-13.89

Answer:

2.5h=20

Step-by-step explanation:

:D

The greatest number of sides that can result from a cross section of a rectangular prism is 6.

To see why, consider a rectangular prism. The prism has 6 faces, which are all rectangles. If we take a cross section of the prism, the section will intersect some of the faces, resulting in a closed shape. The shape will have at most as many sides as the number of sides of the faces that the section intersects.

Since each face of the rectangular prism has 4 sides, the maximum number of sides that can result from a cross section is 4 x 6 = 24. However, this is only possible if the section intersects every face of the prism, which is unlikely to occur in general. In practice, a cross section of a rectangular prism is more likely to intersect just a few of the faces, resulting in a shape with fewer sides. Therefore, the greatest number of sides that can result from a cross section of a rectangular prism is 6, which occurs when the section intersects all 6 faces.

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There are six such possible numbers.

x =4, y =9 Number = 49

x = 5, y = 8 Number = 58

x = 6, y = 7 Number = 67

x = 7, y =6 Number = 76

x = 8, y =5 Number = 85

x = 9, y = 4 Number = 94

Let us say, the units digit of the number is y and the tens digit of the number is x.

So, we can represent the number as 10*x + y.

Now, let us reverse the digits of this number so that the units digit of the new number is x and tens digit of the new number is y.

So, we can represent this new number as 10*y + x.

The summation of both the numbers is 10*x + y + 10*y + x , which is equal to 11*x +11 *y.

For simplicity, 11*(x+y).

Now, we can clearly notice that 11 is not divisible by 13, so the number x+y must be divisible by 13.

Possible combinations:

  x =4, y =9. Number = 49

  x = 5, y = 8. Number = 58

  x = 6, y = 7. Number = 67

  x = 7, y =6. Number = 76

  x = 8, y =5. Number = 85

  x = 9, y = 4. Number = 94

Therefore, there are six such possible numbers.

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Answer:

The other endpoint would be (-7, -4)

Step-by-step explanation:

f(2x-3)=4x+5

Let, 2x-3=g

x=(g+3)/2

So,f(2{g+3}/2 -3)=4(g+3)/2 + 5

f(g)=2g+11

So,f(x)=2x+11

f(-2)=7 ##

Answer:

f(2x - 3) = 4x + 5

f(2x-3)=2(2x-3)+11

f(x)=2x+11

f(-2)=2×-2+11=-4+11=7

Answer:

2,090,000

Step-by-step explanation:

Area = Area of Chile + Area of Bosnia

Area of Chile = 2*1000000

Area of Bosnia = 9*10000

Area = 2,000,000 + 90,000

Area = 2,090,000

Answer:

Step-by-step explanation:

there total

= 2*\(10^{6}\) + 9*\(10^{4}\)

= 2*1,000,000 + 9*10,000

= 2,000,000 + 90,000

= 2,090,000

= 209*\(10^{4}\)

= 2,09*\(10^{6}\)

Answer:

The correct option is;

Reflection across the x-axis, vertical compression by a factor of 0.1, vertical translation 4 units down

Step-by-step explanation:

Answer:

reflection across the x-axis, vertical compression by a factor of 0.1, vertical translation 4 units down

Step-by-step explanation:

The answer above is correct.