A recipe for lemonade uses 5 scoops of mix for every 4 cups of water mai says:

"no matter how much lemonade you make, there is always one more scoop of mix than cups of water"

Is she correct?

Answer:

Assuming this is the full problem.

3x^2-8x+4

Step-by-step explanation:

Answer:

\(\displaystyle [6, -3]\)

Step-by-step explanation:

To begin this process, we will first select the second equation. Here is how the Substitution method wourks:

\(\displaystyle \left \{ {{3x + 5y = 3} \atop {x + 2y = 0}} \right. \\ \\ \\ \left \{ {{y = 2x + 3} \atop {x = -2y}} \right. \\ \\ 3[-2y] + 5y = 3 \hookrightarrow -6y + 5y = 3 \hookrightarrow -y = 3; -3 = y, 6 = x \\ \\ \\ \boxed{[6, -3]}\)

So, you substitute \(\displaystyle x\)for \(\displaystyle -2y\)and continue combining like-terms until you receive the y-value. You then plug this back into the system to get the x-value, which was what you saw.

I am joyous to assist you at any time.

Answer:

A.GFD=EFF

is not a pair of congruent angles in the diagram below

The solution set of the given homogeneous system in parametric vector form is x = t(-1, 1, 0), where t is a real number.

To find the solution set of the given homogeneous system, we can write the system in augmented matrix form and perform row operations to obtain the row-echelon form. The resulting row-echelon form will help us identify the parametric vector form of the solution set.

The given system can be written as:

4x1 + 4x2 + 8x3 = 0

-12x1 - 12x2 - 24x3 = 0

By performing row operations, we can simplify the system to its row-echelon form:

x1 + x2 + 2x3 = 0

0x1 + 0x2 + 0x3 = 0

From the row-echelon form, we can see that x3 is a free variable, while x1 and x2 are dependent on x3. We can express the dependent variables x1 and x2 in terms of x3, giving us the parametric vector form of the solution set:

x1 = -x2 - 2x3

x2 = x2 (free variable)

x3 = x3 (free variable)

Combining these equations, we have x = t(-1, 1, 0), where t is a real number. This represents the solution set of the given homogeneous system in parametric vector form.

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Answer:

the third one

Step-by-step explanation:

The graph of both functions are in the image at the end, and the vertex of g(x) are (0, 0).

Here we know that the function f(x) is:

f(x)= (x + 3)² - 2

And g(x) is a translation of 3 units to the right, 2 units up, and reflected over the x-axis, then we have:

g(x) = -[ f(x - 3) + 2]

Replacing f(x) we get:

g(x) = -[ (x + 3 - 3)²  -2 + 2]

g(x) = -x²

The graphs of both functions are the ones in the image at the end, there we can see that the vertex of g(x) is (0, 0).

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Answer:

5

Step-by-step explanation:

\(\sqrt{25*1}= \sqrt{25}\)

\(\sqrt{25}=5\)

Square root of 25 is 5, because 5x5=25.

789

Answer:

Step-by-step explanation:

The probability of less than 5 successes is approximately 0.065760577.

None of the given options (a. 9059, b. 9721, c. 0093, d. 0338, e. 1655) match this value exactly.

To find the probability of less than 5 successes in a binomial random variable with n = 15 and p = 0.6, we need to calculate the sum of the probabilities of getting 0, 1, 2, 3, and 4 successes.

Using the binomial probability formula, the probability mass function (PMF) for the binomial random variable is:

P(X = k) =\((nC_k) * p^k * (1 - p)^{(n - k)\)

Where n is the number of trials, p is the probability of success, X is the random variable, and k is the number of successes.

Let's calculate each individual probability:

P(X = 0) = \((15C_0) * (0.6^0) * (1 - 0.6)^{(15 - 0) }= 1 * 1 * 0.4^{15 }=0.000131072\)

P(X = 1) =\((15C_1) * (0.6^1) * (1 - 0.6)^{(15 - 1)} = 15 * 0.6 * 0.4^{14} = 0.000981535\)

P(X = 2) =\((15C_2) * (0.6^2) * (1 - 0.6)^{(15 - 2)} = 105 * 0.6^2 * 0.4^{13} = 0.00490657\)

P(X = 3) = \((15C_3) * (0.6^3) * (1 - 0.6)^{(15 - 3)} = 455 * 0.6^3 * 0.4^{12} = 0.0170688\)

P(X = 4) = \((15C_4) * (0.6^4) * (1 - 0.6)^{(15 - 4)} = 1365 * 0.6^4 * 0.4^{11 }= 0.0426726\)

Now, let's calculate the sum:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

=>0.000131072 + 0.000981535 + 0.00490657 + 0.0170688 + 0.0426726

=> 0.065760577

The probability of less than 5 successes is approximately 0.065760577.

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Answer:

13 team members are included in the​ histogram.

Step-by-step explanation:

Consider the provided information.

The required histogram is shown in the figure.

We need to find the team members included in the histogram.

For this, we will add the frequency or the height of each bar.

2+1+1+5+1+3=13

Hence, 13 team members are included in the​ histogram.

The graph of \(\(y = \sqrt{x+1}\)\) is a curve that starts at the point (-1, 0) on the y-axis and continues to rise as x increases, which is represented by the graph in option B.

The graph of \(\(y = \sqrt{x+1}\)\) is a curve that starts at the point (-1, 0) on the y-axis and continues to rise as x increases. It is a square root function, so the curve is smooth and continuous. The graph is always above or on the x-axis since the square root of a positive number is always non-negative.

As x approaches negative infinity, the graph becomes steeper and approaches the y-axis asymptotically. As x approaches positive infinity, the graph continues to rise but at a slower rate.

The shape of the graph resembles a half of a parabola that opens to the right. The vertex of the graph is located at the point (-1, 0).

Therefore option B represents the correct graph for \(\(y = \sqrt{x+1}\)\).

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Complete Question:

Which of the following is the graph of \(y=\sqrt {x-1}\)?

x times y plus x is equal to

xy + x

= x(y + 1)

Answer:

x (y + 1)

Step-by-step explanation:

x times y plus x

= x × y + x

= xy + x

= x (y + 1)

Hope it helps ⚜

The set that we must describe is composed of those which are at least 6.5. At least means that these values are either 6.5 or greater. Then if n is any element of this set it meets the following condition:

Then the answer is the first option.

To express the time of 58.329 seconds in word form, we can write it as "fifty-eight point three two nine seconds."

Word form is the written or spoken representation of a number using words. For example, the number 256 can be expressed in word form as "two hundred fifty-six".

To express the time of 58.329 seconds in word form, we can write it as "fifty-eight point three two nine seconds."

We can also express this as a mixed number by separating the whole number part and the fractional part:

58 + 0.329 = 58 and 329/1000

So, we can write it as "fifty-eight and three hundred twenty-nine thousandths seconds."

A mixed number can help us express the decimal in word form by separating it into two parts - the whole number part and the fractional part. This makes it easier to read and understand the value of the decimal in words.

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Answer:

Its  y=-2x+7/6

Step-by-step explanation:

The slope of the road and the change in elevation over a one-mile stretch of the road. The slope of the road and the change in elevation over a one-mile stretch of the road can be determined using the given inclination angle.

The inclination angle of the road, θ = 0.15 radian. The slope of the road is given as tangent of the inclination angle. Slope, S = tan θSlope, S = tan 0.15Slope, S = 0.26795The slope of the road is 0.26795 or 0.27 (approximate to two decimal places).The change in elevation, h can be determined using the relation between angle, slope and height as given below; h = L × sin θwhere L is the length of the road. For a one-mile stretch of the road, L = 1 mile = 1.609344 km. Substituting the values in the relation, we get; h = 1.609344 × sin 0.15h = 0.400138 km. The change in elevation is 0.400138 km.

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The mentioned function calculates and returns the interpolated values of a given function object over the specified x-axis limit and number of points. The interpolation style can be either 'linear' or 'nearest'.

Function interpolate_function (function, limit, points, int_style) is written below:

```def interpolate_function

(function, limit, points, int_style):    x = np.

linspace(0, limit, points)    if int_style =

= 'nearest':        return np.round(function(x))    elif int_style =

= 'linear':        return function(x)```

The `interpolate_function` function takes the following parameters:

function: This is the function object that will be used for interpolation.

limit: It is the x-axis limit in float value. points: It specifies the number of interpolated points in the output.

int_style: This is a string which specifies the interpolation style ('linear' or 'nearest').

Finally, we can summarize the function using the conclusion. This function calculates and returns the interpolated values of a given function object over the specified x-axis limit and number of points. The interpolation style can be either 'linear' or 'nearest'.

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Answer:

Step-by-step explanation:

Note:

Circumference of a circle = \(\pi d\)

Where d = diameter

We are given the diameter is 20cm, d = 20

Circumference of circle = \(\pi d\) = 20 \(\pi\)

Also, perimeter of a rectangle = 2 times length + 2 times width

We are told the length = 18 , width = x

Perimeter of rectangle = 2 times 18 + 2 times x

Perimeter of rectangle = 36 + 2x

The question also tells us that the circumference of the circle is EQUAL to the perimeter of the rectangle:

So this means:

Since Circumference of circle = 20\(\pi\)  ,

Perimeter of rectangle = 36 + 2x .

We can write:

Circumference of circle = perimeter of rectangle

20\(\pi\)   = 36 + 2x

Subtract 36 from both sides

20\(\pi\) - 36   = 2x

Divide both sides by 2 to solve for "x".

x = \(\frac{20\pi - 36 }{2} = ?\)

Plug it into your calculator and then just round it to 1 decimal place.

Take into account:

x = speed of the airplane

y = speed of the air

consider that the product in between time and speed is equal to the distance traveled in the time.

Then, if the airplane took 3 hours complete 600 miles, agaist the wind, you have that the distance traveled by the airplane is 3x without wind. The speed of the wind decelerates the airplane. The "distance traveled by the wind is 3y"

Then, when you subtract the previous terms you obtain:

3x - 3y = 600 factorize 3 left side

3(x - y) = 600

The formula for for Rn is given as Rn = Σ 18/n (1 - 12i/n + 36i²/n²).

We are given the function f(x) = 3x² on the interval [-1, 5] . This gives

Δx =6/n and xi= -1 + 6i/n.

Therefore,

Rn =  Σ f(xi) Δx

     = Σ 3 (-1 + 6i/n)² 6/n

     = Σ 18/n (1 - 12i/n + 36i²/n²)

The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input.

Informally, a function f gives each input x an output f(x). If f(x) approaches L as x approaches input p, we say that the function has a limit L at that location. More specifically, any input that is sufficiently close to p when f is applied forces the output value arbitrarily close to L.

The concept of limit is specifically used in the various definitions of continuity. Roughly speaking, a function is continuous if all of its limits agree with the values of the function. The term "limit" is also used in the definition of the mathematical term "derivative," which in one-variable calculus refers to the maximum value of the slope of secant lines on a function's graph.

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No 3.674 is not equal to 6.764

What is equality?

We say that two values, numbers , expression are equal if they have = sign in between them, Two value or number are said to be same if every digit from both the number is same and in same order. in other words if the difference between them is zero

We are given two numbers 3.674 and 6.764

We take the difference of them

We get

6.764- 3.674= 3.09

Which is not equal to zero

Hence the two numbers are not equal.

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The dimensions of the document using the given scales are:
1/4 scale: 5 inches by 8.5 inches
1/2 scale: 10 inches by 17 inches

The dimensions of the document using the given scales are:
1/4 scale: 5 inches by 8.5 inches
1/2 scale: 10 inches by 17 inches
3/4 scale: 15 inches by 25.5 inches
1 scale: 20 inches by 34 inches
1 and 1/2 scale: 30 inches by 51 inches.

To find the dimensions of the document using the given scales, we need to multiply the original dimensions by the scale factor.

For a scale of 1/4, we multiply the original dimensions (20 inches by 34 inches) by 1/4.
So, the dimensions would be (20 * 1/4) inches by (34 * 1/4) inches, which simplifies to 5 inches by 8.5 inches.

For a scale of 1/2, we multiply the original dimensions by 1/2.
So, the dimensions would be (20 * 1/2) inches by (34 * 1/2) inches, which simplifies to 10 inches by 17 inches.

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The equation that represents the exponential function passing through the points (-2, 1) and (2, 16) is: y = 4(2)^x

To write the exponential equation that passes through the points (-2, 1) and (2, 16), we can use the general form of an exponential function:

y = ab^x

Where y is the dependent variable, x is the independent variable, a is the initial value or y-intercept, and b is the base of the exponential function.

Step 1: Determine the value of a.

To find the value of a, substitute the coordinates of one of the given points into the equation. Let's use (-2, 1):

1 = ab^(-2)

Step 2: Determine the value of b.

To find the value of b, substitute the coordinates of the other given point into the equation. Let's use (2, 16):

16 = ab^2

Step 3: Solve the system of equations.

We now have a system of two equations with two unknowns (a and b):

1 = ab^(-2)

16 = ab^2

We can solve this system of equations to find the values of a and b. To do this, divide the second equation by the first equation:

16 / 1 = (ab^2) / (ab^(-2))

16 = b^4

Taking the fourth root of both sides, we get:

b = ±2

Step 4: Substitute the value of b back into one of the original equations to solve for a.

Let's substitute b = 2 into the first equation:

1 = a(2)^(-2)

1 = a / 4

a = 4

Alternatively, if we had chosen b = -2, we would have obtained a = -4, and the equation would be:

y = -4(-2)^x

Both equations represent exponential functions that pass through the given points.

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Answer & Step-by-step explanation:

In order to simplify a square root, you need to find a number that multiplied times itself equals the number in the radical. Now 7×7 is 49. Also, -7×-7 is 49 as well. But there is no number times itself that makes -49. No number times itself makes a negative number.

(You will, in time learn imaginary numbers in order to simplify this, but that can be for another day!)

The given statement: n(n+1)(2n+1) is divisible by 6 for all positive integers n.

Step-by-step explanation: We need to prove that n(n+1)(2n+1) is divisible by 6 for all positive integers n using mathematical induction.

Step 1: First, lets prove the statement for the smallest possible value of n. The smallest value of n is 1. So, let's check whether the given statement is true for n = 1 or not.

\(LHS = 1(1+1)(2*1+1) = 6\)

It is divisible by 6. Hence, the statement is true for n=1.

Step 2: Let's assume that the statement is true for n=k. So, we can say that n(n+1)(2n+1) is divisible by 6 for n=k. i.e., n(n+1)(2n+1) = 6a (for some integer a).

Step 3: We need to prove the statement is true for n=k+1.

So, we need to prove that (k+1){(k+1)+1}[2(k+1)+1] is divisible by 6

Using the assumption we made in step 2.

\(LHS = (k+1){(k+2)}[2k+3] = (k+1)(k+2)(2k+3)LHS = (2k+3)k(k+1)(k+2)LHS = 2[k(k+1)(k+2)] + 3[k(k+1)]\)

Now, k(k+1)(k+2) is divisible by 6 using the assumption made in step 2.

So, LHS = 2[k(k+1)(k+2)] + 3[k(k+1)] is also divisible by 6.

Hence, the statement is true for n=k+1.

Step 4: Using steps 1 to 3, we can say that the given statement is true for n=1 and if it is true for n=k, then it is also true for n=k+1.

Hence, by mathematical induction, we can say that the statement is true for all positive integers n.

Hence, it is proved that n(n+1)(2n+1) is divisible by 6 for all positive integers n.

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Answer:Write down the radius and volume.

Input them in the height of a cone formula for volume: h = 3 × V/(π × r²) where: V is the cone's volume; r is the radius; and. h is the resulting height.

It's as simple as that!

Step-by-step explanation: i took the test!

For practical answer; If we open a cone its a semi circle and the distance from center to a edge is radius so the height of the cone is the radius of that semi circle.

Answer:

(a + b)(m + n).  

Step-by-step explanation:

ma+na+nb+mb​

= ma + na + mb + nb

We factor this by grouping:

= a(m + n) + b(m + n)        m + n is common to both parts so we have:

(a + b)(m + n)