11(2x + 1) = 4x - 7
show work

Ashley sold 180 glasses of lemonade for a total cost of $180, 90 little cups for $1, and 90 large cups for $2.

let x = quantity of sold miniature cups

Let y = the quantity of big cups sold.

She sold 180 cups in total for $180, so:

x + y = 180

1x + 2y = 180

figuring out the equations in a system:

x = 90   y = 90

Small cups of lemonade cost $1, and large cups cost $2, at Ashley's summertime lemonade stand. 180 cups of lemonade in all were sold for $180 by her. We can work up a system of equations to determine how many cups of each variety she sold.

let x = quantity of sold miniature cups

Let y = the quantity of big cups sold.

She sold 180 cups in total for $180, so:

x + y = 180

1x + 2y = 180

We arrive at x = 90 and y = 90 after solving the system of equations. In other words, Ashley sold 180 cups of lemonade for $180 by selling 90 small cups at $1 each and 90 large cups at $2 each.

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If 800g:1kg is equal to 1:n then the value of n is 1/8.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

800g : 1kg = 1 : n

This can be written as,

800g/1kg = 1/n

Cross multiply.

n = 1kg/800g

[ 1 kg = 1000g ]

n = 1000g/8000g

n = 1/8

Thus,

The value of n is 1/8.

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Answer:i need more info

Step-by-step explanation:

Answer:

Answer 1

Because the alphabet can end,it is not unlimited

(a) The probability that both score more than 175 is 0.12 and (b) the probability that Thomas scores more than 175 and Sarah scores higher than Thomas is 0.04

If the occurrence of one event say A does not affect the occurrence of event B, then the two events are said to be independent such that;

P (A ∩ B) = P (A) × P (B)

a:

consider; event A represents Sarah scoring more than 175 and event B represents Thomas scoring more than 175

Thus, P(A) = Probability that Sarah scores more than 175 = 0.6

P(B) = The probability that Thomas scores more than 175 = 0.2

Since the scores are independent, therefore the probability that both Sarah and Thomas score more than 175 is,

P (A ∩ B) = (0.6) × (0.2)

P (A ∩ B) = 0.12

b:

If the occurrence of one event say A affects the occurrence of another event say B, then the two events are said to be dependent on each other such that;

P (A ∩ B) = P (B) × P (A|B)

As; P(B) = The Probability that Thomas scores more than 175 = 0.2

and P(A|B) = Sarah scores more than Thomas given that Thomas scores more than 175 = 0.2

Therefore;

P (A ∩ B) = (0.2) × (0.2) = 0.04

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Answer:

12709 balls

Step-by-step explanation:

Given

Dimension of Room = 15 ft by 20 ft by 10 ft

Diameter of Ball = 9.2 inches

Required

Determine the number of balls that can be occupied by the room

First, we need to calculate the volume of the room

This is done by multiplying the dimensions of the room

\(Volume = 15ft * 20ft * 10ft\)

\(Volume = 3000ft^3\)

Next, we calculate the volume of the ball.

The ball is a sphere.

So:

\(Volume = \frac{4}{3}\pi r^3\)

Where

\(r = \frac{1}{2} * Diameter\)

\(r = \frac{1}{2} * 9.2\)

\(r = 4.6\ in\)

So:

\(Volume = \frac{4}{3}\ * \frac{22}{7} * (4.6in)^3\)

\(Volume = 407.88419\ in^3\)

To calculate the number of balls, we then divide the volume of the room by volume of a ball

\(Balls = \frac{3000\ ft^3}{407.88419\ in^3}\)

Convert ft^3 to in^3

\(Balls = \frac{3000 * 1728in^3}{407.88419\ in^3}\)

\(Balls = \frac{3000 * 1728}{407.88419}\)

\(Balls = \frac{5184000}{407.88419}\)

\(Balls = 12709.4899167\)

\(Balls = 12709\) -- approximated

Hence, the room will contain 12709 balls

Angles themselves cannot be parallel or not parallel to each other. Parallel lines are the ones that never intersect and always maintain the same distance between each other. However, angles can be congruent or supplementary to each other.

If you are referring to two lines with angles formed by a transversal, you can determine if the angles are congruent by comparing their measurements.

Angles themselves cannot be parallel or not parallel to each other. Parallel lines are the ones that never intersect and always maintain the same distance between each other. However, angles can be congruent or supplementary to each other.

If you are referring to two lines with angles formed by a transversal, you can determine if the angles are congruent by comparing their measurements. Two angles are congruent if they have the same measure. This can be proven using various angle relationships and properties, such as vertical angles, corresponding angles, alternate interior angles, alternate exterior angles, etc. These relationships are based on the properties of parallel lines and transversals.

If you want to determine if two angles are supplementary (their measures add up to 180 degrees), you can add the measures of the angles and check if the sum is equal to 180 degrees.

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Answer: \(=16\sqrt{x}\)

Step-by-step explanation:

\(\sqrt{x}\frac{64}{4}=16\sqrt{x}\)

Answer:

The ladder is 35.71 feet up the building

Step-by-step explanation:

Here, we want to calculate how far up the building is the ladder placed

We should picture a right angled triangle with hypotenuse 50 and one of the other sides as 35

To find the height in this case, we proceed to use Pythagoras’ theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides

In this case, let the height be

50^2 = 35^2 + h^2

h^2 = 50^2-35^2

h^2 = (50+35)(50-35)

h^2 = (85)(15)

h^2 = 1275

h = square root of 1275

h = 35.71 ft

To make a table of values for a linear relationship;

Choose a group of x values before creating the table. Add each x value from the left side column to the equation. Evaluate the equation (middle column) to arrive at the y value

Given,

Linear relationship;

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.

Here,

We have to make a table of values for a linear relationship;

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Answer:

$34,104

Step-by-step explanation:

4,200 * $8.12 = $34,104

Answer:

The movie has earned 34,104 on the first day of the week

Step-by-step explanation:

4,200 x 8.12= 34104

Hope this helps!!!!!!

Explanation

To solve the question, we will be aware that

There are 3 hours between 6PM and 9PM ,

The main pump's emptying rate is 1/4 tanker per hour. It will be open

the entire 3 hours, so it will empty 3/4 of the tank.

this means that the auxiliary pump must empty the remaining 1/4

Thus

Thus, we will have

Therefore

The auxiliary pump should start by 6pm + 45 minutes = 6:45pm

Answer:

the answer is 8

Step-by-step explanation:

your welcome

Answer:

2.8 In is the answer to the question

Step-by-step explanation:

Nw+WD=ND

The phone's usage patterns, network coverage, and background apps can also affect its battery life, so it is important to keep these in mind as well.

Based on the information provided in part (d), we can see that the iPhone 12 Pro Max has a larger battery capacity than the iPhone SE (2020), which should theoretically give it a longer battery life. However, the battery life of a phone also depends on other factors such as the screen size, processor efficiency, and overall power consumption of the device.

Unfortunately, we do not have specific information about the battery life of these phones, so we cannot definitively say which one is better for someone looking for a phone with a battery life between 18 and 22 hours. It is possible that both phones could meet this requirement, but it ultimately depends on how the user utilizes their phone.

In general, it is recommended to check the battery life specifications and reviews of a phone before making a purchase decision, as this can help provide a better understanding of its battery performance. Additionally, factors such as the phone's usage patterns, network coverage, and background apps can also affect its battery life, so it is important to keep these in mind as well.

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The exact value of the area under the graph of f(x) over the interval [a,b] is False.

If f(x) is a constant function, meaning it has the same value for all x, then the graph of f(x) over the interval [a, b] will be a horizontal line.

The area under a constant function over any interval is simply the product of the constant value and the width of the interval.

However, the formula for the area of a rectangle is not applicable in this case because the graph of a constant function does not form a rectangle.

The area under a constant function is a rectangle only when the function is a constant height (y-value) over the entire interval, which is not the case for arbitrary constant functions.

To compute the exact value of the area under the graph of f(x) over the interval [a, b] when f(x) is a constant, you simply need to multiply the constant value by the width of the interval, which is (b - a).

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The area of the resulting surface of this infinite curve is π units.

In this question,

The infinite curve is y = e^−2x, x ≥ 0.

The curve is rotated about x-axis.

Since x ≥ 0, the limits will be 0 to ∞.

Then the area of the resulting surface is,

\(A= 2\pi \lim_{b\to \infty} (\int\limits^\infty_0{e^{-2x} } \, dx )\)

Now substitute,

u = -2x

⇒ du = -2dx

⇒ dx = \(-\frac{1}{2} du\)

Then,

\(\int\limits{-\frac{1}{2}e^{u} } \, du =-\frac{1}{2}\int\limits{e^{u} } \, du\)

Now substitute u and du, we get

⇒ \(-\frac{1}{2} \int\limits {e^{-2x} }(-2) \, dx\)

⇒ \(-\frac{-2}{2} \int\limits {e^{-2x} } \, dx\)

⇒ \((1) \int\limits {e^{-2x} } \, dx\)

⇒ \(\int\limits {e^{-2x} } \, dx\)

Thus the area of the resulting surface is

\(A= 2\pi \int\limits^\infty_0{e^{-2x} } \, dx\)

⇒ \(A= 2\pi [{e^{-2x}(\frac{1}{-2} ) } \,]\limits^\infty_0\)

⇒ \(A= \frac{2\pi}{-2} [{e^{-2(\infty)}-e^{-2(0)} } \,]\\\)

⇒ \(A= -\pi [0-1} \,]\\\)

⇒ \(A= \pi\)

Hence we can conclude that the area of the resulting surface is π units.

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The maximum size of the stack would be 3.

The maximum size of the stack when the function is called with the argument 4 is 3, since the function requires three recursive calls to compute the fourth Fibonacci number.

This can be seen more clearly when written out as the recursive definition of the nth Fibonacci number:

fib(n) = fib(n - 1) + fib(n - 2), where fib(0) =1 and fib(1) = 1.

For the example given of n = 4, you would need to make the following recursive calls:

fib(4) -> fib(3) + fib(2)

fib(3) -> fib(2) + fib(1)

fib(2) -> fib(1) + fib(0)

Therefore, the maximum size of the stack would be 3.

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To show that a series converges, we can use an upper bound on the terms. An upper bound is a value that is greater than or equal to all the terms in the series. In this case, we are looking for an upper bound on the largest probability in the multinomial(n;1/3,1/3,1/3) distribution.

The multinomial distribution is a probability distribution that describes the outcome of a random experiment where there are multiple possible outcomes and each outcome has a fixed probability. In this case, there are three possible outcomes, each with a probability of 1/3.

The largest probability in the multinomial(n;1/3,1/3,1/3) distribution is given by the maximum value of the multinomial coefficient:

$$\binom{n}{k_1,k_2,k_3}=\frac{n!}{k_1!k_2!k_3!}$$

where $k_1$, $k_2$, and $k_3$ are the number of times each outcome occurs in the experiment.

Since each outcome has a probability of 1/3, the largest probability occurs when $k_1=k_2=k_3=n/3$. Therefore, the largest probability is given by:

$$\binom{n}{n/3,n/3,n/3}=\frac{n!}{(n/3)!(n/3)!(n/3)!}$$

This value is an upper bound on the terms in the series and can be used to show that the series converges.

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Answer:

328 pies de largo

196.8 pies de ancho

Step-by-step explanation:

Ya que las medidas dadas estan en metros, podemos usar esas medidas para calcular la longitud y anchura en pies.

100 metros de largo.

60 metros de ancho.

Si sabemos que 1m es igual a 3,28 pies, simplemente tenemos que multiplicar las medidas en metros por 3.28 y nos va dar la medida del campo en pies.

100 * 3.28 = 328 pies de largo

60 * 3.28 = 196.8 pies de ancho

This problem is just try and error.

First we try number 2.5 since its the average of all the answers.

2.5^2=6.25

This is smaller than 7 so the answer is either 2.6 or 2.8

Now let's try 2.7

2.7^2=7.29

Which is bigger than 7 and that means the correct answer is 2.6 :)

The like terms in the expression are 3.2a - 4 1/3a and -a and + 7 - 1.

The simplified linear expression is 6 - 2.1a.

In mathematics, like terms are terms that have the same variables raised to the same power. Like terms can have difference coefficients.

The like terms in this expression are: 3.2a - 4 1/3a and -a

The second set of like terms are: + 7 - 1

In order to simplify the expression, add the like terms together

+ 7 - 1 = 6

To add 3.2a - 4 1/3a and -a, the numbers have to be in the same form. Thus, the mixed number would be changed to a decimal.

3.2a - 4.3a - a = -2.1a

The simplified expression becomes 6 - 2.1a

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Answer:

x = 4

x = -8

Step-by-step explanation:

hope this helped

The total number of laps Sarah should run today is given by the equation A = 16 laps

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of laps be represented as A

Now , the equation will be

The total distance ran by Sarah yesterday = 3,682 m

The distance of one lap = 263 m

So , the number of laps ran by Sarah yesterday = total distance ran by Sarah yesterday / distance of one lap

Substituting the values in the equation , we get

The number of laps ran by Sarah yesterday = 3682 / 263

The number of laps ran by Sarah yesterday = 14 laps

Now ,

The distance Sarah wants to run today = 4,222 m

So , the number of laps Sarah should run today A = distance Sarah wants to run today / distance of one lap

Substituting the values in the equation , we get

The number of laps Sarah should run today A = 4,222 / 263

The number of laps Sarah should run today A = 16.05 laps

The number of laps Sarah should run today A = 16 laps

Therefore , the value of A is 16 laps

Hence , the number of laps is 16 laps

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The required pounds of Bolivian coffee and Colombian coffee are 2500 and 1500 respectively.

A equation is supposed to be linear equation in two factors in the event that it is written as ax + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are direct conditions in two factors.

Let x be the pound of Bolivian coffee and y is that of Colombian coffee.

Bolivian coffee sells for $4.59 per pound, and Colombian coffee sells for $5.95 per pound and whole mixture sells for $5.10.

So,  4.59x + 5.95y = 5.10(4000)

4.59x + 5.95y = 20400--------------------(1)

and x + y = 4000-----------------------------(2)

On solving above two equation, we get

x = 2500 pounds and y = 1500 pounds

Thus, required pounds of two coffees are 2500 and 1500.

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To find Ted's current age, set up equations using Fred's age and solve for Fred's age. Use the information that Ted was twice as old as Fred seven years ago to find Fred's current age. Finally, use Fred's current age to find Ted's current age.

Ted's current age can be found by first using algebra to set up equations based on the information given in the problem. Let x be Fred's current age. Then, Ted's current age is x + 4. Seven years ago, Ted was x + 4 - 7 = x - 3 years old, and Fred was x - 7 years old. The problem states that Ted was twice as old as Fred seven years ago, so we can set up the equation 2(x - 7) = x - 3. Solving for x, we get x = 11, which means Fred is currently 11 years old. Therefore, Ted is currently 11 + 4 = 15 years old.

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The equation of the linear function having an x-intercept of -8 and a y-intercept of 4 is y = (1/2)x + 4.

What are lines and their slopes?

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, A linear function has an x-intercept of -8 and a y-intercept of 4.

So, The two points on the line are (- 8, 0) and (0, 4).

Now, slope(m) = (4 - 0)/(0 + 8).

slope(m) = 4/8.

slope(m) = 1/2.

As it has a y-intercept of 4 it is the value of b, In y = mx + b.

Therefore, The linear function is y = (1/2)x + 4.

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Answer:

\(y =-\frac{1}{2}(x +2)(x - 3)\)

Step-by-step explanation:

Given

\(x_1 = -2\)

\(x_2 = 3\)

\((x,y) = (-1,2)\) --- a point on the parabola

Required

The equation

First, calculate the equation from the zeros

\(y =k(x - x_1)(x - x_2)\)

Substitute \(x_1 = -2\) and \(x_2 = 3\)

\(y =k(x - -2)(x - 3)\)

\(y =k(x +2)(x - 3)\)

To solve for k, we substitute \((x,y) = (-1,2)\)

\(2 = k(-1+2)(-1-3)\)

\(2 = k(1)(-4)\)

\(2 = -4k\)

Divide by -4

\(k=\frac{2}{-4}\)

\(k=-\frac{1}{2}\)

So, the equation is:

\(y =k(x +2)(x - 3)\)

\(y =-\frac{1}{2}(x +2)(x - 3)\)

Answer: c

Step-by-step explanation: