Given below is the stem-and-leaf display representing the amount of syrup used in fountain soda machines in a day by 25 McDonald's restaurants in Northern Virginia. 911, 4, 7 100, 2, 2, 3, 8 11/1, 3,

Answer:

Aiden should use the Standard unit of Mass

Kilogram.

Step-by-step explanation:

He can use other unit also like gram, pound, ounce, tone etc

The missing values in the equation are

a) a = 4 and c = 2

b) b = 3, c = 2 and d = -3

To factorize 8x² + 22x + 5, we need to find two numbers that multiply to 8 * 5 = 40 and add up to 22. These numbers are 2 and 20.

We can use these numbers to split the middle term:

8x² + 2x + 20x + 5

Now we can factor by grouping:

(8x² + 2x) + (20x + 5)

2x(4x + 1) + 5(4x + 1)

(2x + 5)(4x + 1)

rearranging

(4x + 1)(2x + 5)

Therefore, a = 4 and c = 2

To factorize 10x² - 9x - 9, Using factorization by grouping method:

10x² - 9x - 9

10x² - 15x + 6x - 9

10x² - 15x + 6x - 9

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

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

Therefore b = 3, c = 2 and d = -3

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Answer:

Savannah's age = 6 years

Step-by-step explanation:

Let

Savannah's age = x

Dylan's age = 15

Dylan is 15, which is 3 years older than twice his sister Savannah’s age

Dylan = 2x + 3

Find Savannah's age

2x + 3 = 15

Subtract 3 from both sides

2x + 3 - 3 = 15 - 3

2x = 12

Divide both sides by 2

2x / 2 = 12 / 2

x = 6

Therefore,

Savannah's age = x

= 6 years

Dylan's age = 2x +3

= 2*6 + 3

= 12 + 3

= 15 years

Answer:

Y= -1/2x -1

Step-by-step explanation:

Answer:

y = f(x + 2)

Step-by-step explanation:

Most of the kinetic energy of the water is transferred into the water, then the thermal energy will increase. Hence, option C is correct.

Kinetic energy is the term used in physics to describe the force that a moving item has. It is described as the amount of effort necessary to accelerate anybody with a particular mass from rest to a given velocity. Except variations in speed, the body retains the kinetic energy it gains during acceleration.

The body uses exactly the same amount of energy when slowing down from its current rate to a state of rest. Formally, kinetic energy refers to any term in a system's Lagrangian that has a derivative with respect to time.

As per the given information in the question,

When the kinetic energy of the diver is transferred into the water, the thermal energy will increase.

The entity's thermal energy grows as the average kinetic energies of its particles rise. As a result, an object's thermal energy rises as its temperature does.

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Answer:

75,582

Step-by-step explanation:

There are 21,168 ways to form a subcommittee of 3 men and 5 women from the given committee.To form a subcommittee of 3 men and 5 women from a committee consisting of 9 men and 10 women, you can use the combination formula.

A combination is a selection of items from a larger set, where the order of items does not matter. The formula for combinations is:

C(n, r) = n! / (r!(n-r)!)

where n is the total number of items in the set, r is the number of items to be chosen, and ! represents the factorial function (e.g., 5! = 5 x 4 x 3 x 2 x 1).

For this problem, you will first find the number of ways to choose 3 men from the 9 men, and then the number of ways to choose 5 women from the 10 women.

For men:
C(9, 3) = 9! / (3!(9-3)!)
C(9, 3) = 9! / (3!6!)
C(9, 3) = 84

For women:
C(10, 5) = 10! / (5!(10-5)!)
C(10, 5) = 10! / (5!5!)
C(10, 5) = 252

To find the total number of ways to choose the subcommittee, you will multiply the number of ways to choose the men by the number of ways to choose the women:

Total ways = 84 (ways to choose men) x 252 (ways to choose women)
Total ways = 21,168

So, there are 21,168 ways to form a subcommittee of 3 men and 5 women from the given committee.

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As per the details given, the area of the triangle with sides a = 12, b = 15, and c = 13 is approximately 74.83 square units.

To calculate the area of a triangle with given sides a = 12, b = 15, and c = 13, one can use Heron's formula.

Heron's formula implies that the area (A) of a triangle with sides a, b, and c can be found using the semi-perimeter (s) and the lengths of the sides:

s = (a + b + c) / 2

A = sqrt(s * (s - a) * (s - b) * (s - c))

After putting the values:

a = 12

b = 15

c = 13

First, the semi-perimeter wil be:

s = (a + b + c) / 2

s = (12 + 15 + 13) / 2

s = 40 / 2

s = 20

Now, use Heron's formula to find the area:

A = sqrt(s * (s - a) * (s - b) * (s - c))

A = sqrt(20 * (20 - 12) * (20 - 15) * (20 - 13))

A = sqrt(20 * 8 * 5 * 7)

A = sqrt(5600)

A ≈ 74.83

Thus, the area of the triangle with sides a = 12, b = 15, and c = 13 is approximately 74.83 square units.

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Answer:

8

Step-by-step explanation:

updated in party settings on a daily morning in party mode with me in my room with a

The 7 is not a variable because variables are letters. The number seven is a coefficient because they are numbers used to multiply a variable. Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient. Example: In ax2 + bx + c, "x" is a variable, and "a" and "b" are coefficients

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The probability that a standard normal random variable z is between -2.4 and 0.4 is approximately 0.6472.

To find the probability that a standard normal random variable z is between -2.4 and 0.4, we can follow these steps:

Step 1: Look up the cumulative probability corresponding to -2.4 in the standard normal distribution table. The cumulative probability at -2.4 is approximately 0.0082.

Step 2: Look up the cumulative probability corresponding to 0.4 in the standard normal distribution table. The cumulative probability at 0.4 is approximately 0.6554.

Step 3: Subtract the cumulative probability at -2.4 from the cumulative probability at 0.4 to find the probability between the two values:

P(-2.4 < z < 0.4) = 0.6554 - 0.0082

= 0.6472.

Therefore, The probability that z is between -2.4 and 0.4, when z is a standard normal random variable, is approximately 0.6472. This means that there is a 64.72% chance that a randomly selected value from a standard normal distribution falls within the range of -2.4 to 0.4.

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Answer: 102

Step-by-step explanation:

Let the number of adults tickets be represented by x

Let the number of children tickets be represented by y.

We can then form an equation which will be:

x + y = 259 ....... i

6x + 5y = 1397 ...... ii

From equation i, y = 259 - x ...... iii

Put equation iii into ii

6x + 5y = 1397

6x + 5(259 - x) = 1397

6x + 1295 - 5x = 1397

Collect like terms

6x - 5x = 1397 - 1295

x = 102

The number of adult tickets that the theater sold last night is 102.

Answer:

simplify -1-18

Step-by-step explanation:

Subtract  18  from −1

− 19

Answer:

2/3 + 1/5 = 13/15

Step-by-step explanation:

If you agree to be a part of your friend's partnership business, you will receive $5,000 at the end of each of the next 6 years.

To calculate the equivalent amount needed in one large payment at the end of year 6, we need to consider the time value of money. The discount rate represents the rate of return required for an investment to be considered worthwhile. In this case, the partnership generates a 3% annual return.

Using the concept of present value, we can calculate the equivalent amount needed. We need to find the present value of receiving $5,000 at the end of each year for 6 years, discounted at a rate of 3% per year.

The formula to calculate the present value of an annuity is:

PV = PMT * \([(1 - (1 + r)^(-n)) / r]\)

Where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods.

Substituting the given values, we have:

PV = $5,000 *\([(1 - (1 + 0.03)^(-6)) / 0.03]\)

Solving this equation will give us the equivalent amount needed in one large payment at the end of year 6.

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Answer:

hope it help

Step-by-step explanation:

step by step naYn

Answer:

b, the second option

Step-by-step explanation:

The angle of 6 and 70 degrees is 64 degrees.

When we say "the angle of 6 and 70 degrees", we are referring to the angle between a line that goes through 6 degrees on the unit circle and the line that goes through 70 degrees on the unit circle.

To find the angle between two points on the unit circle, we first need to visualize the points and draw the lines that pass through them.

The angle between these two lines is the angle we are looking for. We can use the formula for the difference of two angles to find the angle:

Angle = |6 - 70| = |-64| = 64 degrees

The absolute value of the difference between 6 and 70 degrees is 64 degrees. Therefore, the angle of 6 and 70 degrees is 64 degrees.

We can verify our answer by drawing the unit circle and the lines passing through 6 and 70 degrees. The angle between these lines should be approximately 64 degrees.

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It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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Answer:

Step-by-step explanation:

Answer:

30 + 0.89m

Step-by-step explanation:

I think this is the correct answer.

Cintia bought 17 orders of chicken nuggets and 7 orders of French fries for her friends.

Let's solve the problem step by step:

Let's assume the number of orders of French fries as 'x'.

According to the given information:

The chicken nugget order was 4 fewer than three times the amount of French fries. This can be expressed as:

Number of chicken nugget orders = 3x - 4

She bought a total of 24 chicken nuggets and French fries. So we can set up the equation:

Number of chicken nugget orders + Number of French fry orders = 24

Substituting the expressions we derived earlier:

(3x - 4) + x = 24

Simplifying the equation:

4x - 4 = 24

4x = 28

x = 7

Now that we have found the value of 'x' as 7, we can substitute it back into the expressions to find the number of chicken nugget orders and French fry orders:

Number of chicken nugget orders = 3x - 4 = 3(7) - 4 = 21 - 4 = 17

Number of French fry orders = x = 7

Therefore, Cintia bought 17 orders of chicken nuggets and 7 orders of French fries for her friends.

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The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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Domain of the radical function of the form f(x) = √(ax + b) + c is given by the solution of the inequality ax + b ≥ 0 and the range is the all possible values obtained by substituting the domain values in the function.

We know that the general form of a radical function is,

f(x) = √(ax + b) + c

The domain is the possible values of x for which the function f(x) is defined.

And in the other hand the range of the function is all possible values of the functions.

Here for radical function the function is defined in real field if and only if the polynomial under radical component is positive or equal to 0. Because if this is less than 0 then the radical component of the function gives a complex quantity.

ax + b ≥ 0

x ≥ - b/a

So the domain of the function is all possible real numbers which are greater than -b/a.

And range is the values which we can obtain by putting the domain values.

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Answer:

yeah

Step-by-step explanation:

Answer:

A={x| x>7} = 8,9

B= {5,6}

1,

2,{5,6,8,9}

3,{}

4{}

Answer:

x≥-2

y<3

y≥x+3

Step-by-step explanation:

For x≥-2 the line is passing through -2 on the X axis

For y<3 the dotted line is passing through 3 on the y axis and as it is dotted it is just less than

For y≥x+3 the line is passing through -3 on the x axis and 3 on the y axis so it must be y=x+3. Then you apply the inequality so it becomes y≥x+3

Hope it helps :)

The inequalities to describe the shaded area on the grid​ are

\(\rm \bold {x\geq -2}\\\bold{y<3}\\\\bold{y \geq\ x+3}\)

The shaded area of the grid is surrounded by three lines the equations of all three lines are given as below in form of inequalities.

For a solid line the " equality"  is included but for a dashed line " equality" is not included.

x ≥ -2

y < 3

The equation of third line can be found out by writing standard form of straight line

\(\rm y = mx +c \\m = Slope \;of\; the\; line\\c = y\; axis \; intercept \; value\)

As we can observe from the figure that the line passes through (0,3) and (-3,0) and hence we write the equation of line as

\(\rm y = (3-0) /(0-(-3)) ( x+3) \\y = 1\times x + 3\\y = x+3 \\So \; the\; inequality\; can \; be\; written\; as\\y\geq x+3\)

Since the area above the line y = x+3 is of our concern hence greater than equal to sign is used.

So the inequality for third line is

\(\rm\bold{ {y\geq x+3}}\)

The inequalities to describe the shaded area on the grid​

\(\rm \bold {x\geq -2}\\\bold{y<3}\\\\bold{y \geq\ x+3}\)

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he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Answer:

2/10 + ___ = 1/2              

Step-by-step explanation:

2/10 + 3/10 = 1/2

The constant of proportionality, or unit rate, is a crucial concept in understanding proportional relationships and making calculations based on them.

The constant of proportionality, also known as the unit rate, in a proportional relationship is the value that relates two quantities in a way that they always have the same ratio. In a verbal description of a proportional relationship, the constant of proportionality is the number that tells you how much one quantity changes when the other quantity changes by one unit.

For example, if a recipe for chocolate chip cookies calls for 2 cups of flour and makes 24 cookies, and you want to make 36 cookies, you can use the constant of proportionality to determine how much flour you need. The relationship between the amount of flour and the number of cookies is proportional, and the constant of proportionality is the unit rate of flour per cookie. In this case, the constant of proportionality is:

2 cups of flour ÷ 24 cookies = 1/12 cups of flour per cookie

To make 36 cookies, you would need:

36 cookies x 1/12 cups of flour per cookie = 3 cups of flour

So, the constant of proportionality, or unit rate, is a crucial concept in understanding proportional relationships and making calculations based on them.

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