What is the difference between the 11th square number and the 2nd square number?​

Answer:

Substitute the value of the variable into the equation and simplify.

16

Step-by-step explanation:

Hope this helps! Have a great day!

Answer: 16

Step-by-step explanation:

\(- 3x -8=\\-3(-8)-8=\\24-8=\\16\)

X = 1 4 5 6

Y = 20 8 4 0

From the function: Y = 24 - 4X

If X = 1, then Y = 24 - 4(1) = 20

If X = 4, then Y = 24 - 4(4) = 8

If X = 5, then Y = 24 - 4(5) = 4

If X = 6, then Y = 24 - 4(6) = 0

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The probability of the complement of the event is 0.05.

The complement of an event is the probability of that event not occurring. The relationship between the probability of an event and its complement is that they always add up to 1.

Therefore, if the probability of an event occurring is p, then the probability of its complement not occurring is 1-p.

In the case where the probability of an event is 0.95, the probability of its complement not occurring would be 1-0.95 = 0.05. This means that the probability of the complement of the event is 0.05.

This concept is important in probability theory and is used to calculate the probabilities of events and their complements. It allows us to consider all possible outcomes of a given situation and calculate the likelihood of each of them.

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The smallest positive debt that can be paid off using sticker trading is $7$ dollars.

To find the smallest positive debt that can be paid off using sticker trading, we need to consider the values of the stickers (in dollars) and find the smallest positive amount that can be reached through a combination of these values.

Given that a Harry Potter sticker is worth $49 and a Twilight sticker is worth $35, we can approach this problem using the concept of the greatest common divisor (GCD) of these two values.

The GCD of $49$ and $35$ is $7$. This means that any multiple of the GCD can be represented using these sticker values.

In other words, any positive multiple of $7$ dollars can be paid off using sticker trading.

Therefore, the smallest positive debt that can be paid off using sticker trading is $7$ dollars.

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The linear function for the total cost C is:

A function is an expression, rule, or law that defines a relationship between one variable.

Example:

\(f(\text{x}) = 2\text{x} + 1\)

\(f(1) = 2 + 1 = 3\)

\(f(2) = 2 \times 2 + 1 = 4 + 1 = 5\)

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The total cost for x cubic yards.

\(\bold{C = 28 + 48x}\)

Thus, the function is C = 28 + 48x.

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9514 1404 393

Answer:

  x = 9/10

Step-by-step explanation:

Fractions can be eliminated by multiplying the equation by 12.

  6x +4x = 9

  x = 9/10 . . . . . . . divide by the coefficient of x

__

Check

  (9/10)/2 +(9/10)/3 = 3/4 . . . . put x into the original equation

  9/20 +3/10 = 3/4 . . . . . . . . . simplify a bit

  9/20 +6/20 = 15/20 = 3/4 . . . . . true

Answer:

x=11.34

Step-by-step explanation:

Answer:

\(5000( {1.03}^{t} ) = 20000\)

\( {1.03}^{t} = 4\)

\(t \times ln(1.03) = ln(4) \)

\(t = \frac{ ln(4) }{ ln(1.03) } = 46.9 \: years \)

Meetra will be 66.9 years (about 67 years) old when she has $20,000.

Answer: 22.4402

Step-by-step explanation:

Answer:

84.4% of 23 is 19.412.

Step-by-step explanation:

Let the unknown number be x.

Now, 84.4% of x = 19.412.

∴ (84.4 ÷ 100) × x = 19.412.

By simplifying the equation,

x = (19.412 × 100) ÷ 84.4

x = 1941.2 ÷ 84.4

∴ x = 23

Thus, 84.4% of 23 is 19.412.

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Answer:

\(x=-9\frac{1}{3}\)

Step-by-step explanation:

\(\frac{1}{2}(x+10)=\frac{1}{4}(x-8)\)

\(\frac{1}{2}x+5=\frac{1}{4}x-2\)

\(\frac{1}{2}x-\frac{1}{4}x=-5-2\)

\(\frac{3}{4}x=-7\)

\(x=-\frac{28}{3}=-9\frac{1}{3}\)

Answer:

1/16

Step-by-step explanation:

Answer:

\(x^2+2x-3\)

Step-by-step explanation:

Note that \(x^2-x-20=(x-5)(x+4)\), so, if the denominator is \((x-5)(x+4)(x+3)\), we need to multiply the numerator by \((x+3)\). And \((x-1)(x+3)=x^2+2x-3\).

Answer:

∠ 1 = 20°, ∠ 2 = 160°

Step-by-step explanation:

∠ 1 and ∠ 2 are adjacent angles and are supplementary, that is sum to 180°

x - 12 + 5x = 180 , that is

6x - 12 = 180 ( add 12 to both sides )

6x = 192 ( divide both sides by 6 )

x = 32

Thus

∠ 1 = x - 12 = 32 - 12 = 20°

∠ 2 = 5x = 5 × 32 = 160°

The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes

Calculating this expression will give us the answer in minutes.

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Answer:

Side length:11

Area: 121

Step-by-step explanation:

if its a square all sides should be equal so you can divide 44 by 4 which gives you 11 and then to find area you just multiply the two sides together which would be 11x11 and that equals 121

I'm pretty sure this is what it would be but it also seems over simplified and i might be missing something?

Answer:

The value is   \(p-value  =  0.22663\)

Step-by-step explanation:

From the question we are told that

    The proportion of bruised tomatoes p =  0.08

    The  null hypothesis is  \(H_o  :   p =  0.08\)

    The alternative hypothesis is  \(H_a  :  p >  0.08\)

    The sample size is  n  =  600

    The number of bruised tomatoes from the sample selected is  k  =  53

    The test statistics is  z =0.75

Generally the p-value is mathematically represented as

      \(p-value  =  P(Z > z)\)

=>    \(p-value  =  P(Z > 0.75)\)

From the z-table  

    \(P(Z > 0.75) =  0.22663\)

So  

    \(p-value  =  0.22663\)

Answer:

P-value ≈ 0.2266

Step-by-step explanation:

The volume of cone is 175 m³

Firstly,

Volume of Pyramid.

The volume (V) of a pyramid is  

V = ⅓Ah

Data:

V = 175m³

Calculation:

175 = ⅓× A× h

Ah = 175*3

Ah = 525m³

Secondly,

The volume (V) of a cone is

V = ⅓Ah

Data:

Ah = 525 m³

Calculation:

V = ⅓ A× h

V = 175 m³

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Answer:

7606.62

Step-by-step explanation:

Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.

\(p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\\)

Now just equate this to a time 0 payment at the same rate

\(10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62\)

As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.

Answer:

E(x) = 1.43 (Approx)

Step-by-step explanation:

Given:

Total number of camera = 7

Defective camera = 5

Sample selected = 2

Computation:

when x = 0

P(x=0) = 2/7 × 1/6 = 2/42

P(x=1) = [2/7 × 5/6] + [5/7 × 2/6] = 20/42

P(x=2) = 5/7 × 4/6 = 20/42

So,

E(x) = [0×2/42] + [1×20/42] + [2×20/42]

E(x) = 1.43 (Approx)

Answer:

-15

Step-by-step explanation:

When functions are "nested" like this (nested is not a math word; the mathy word is composed or composition) you need to start all the way on the inside.

f(g(-3))

means find g(-3) first, then put that answer into f.

g(x) = x - 7

g(-3) = -3 - 7

g(-3) = -10

We found g(-3) is -10, so now put -10 into f.

f(x) = 2x + 5

f(-10) = 2(-10) + 5

= -20 + 5

= -15

Answer:

Problem 9:  One solution

Problem 10:  Infinitely many solutions

Problem 11: One solution

Problem 12:  No solution

Step-by-step explanation:

Solving one-variable equations

When solving a one variable equation, there are two steps:

During Step 1 of that process, usually one will be combining like-terms to take two terms that contain x, and merging them into one term that contains x.  However, occasionally, the like terms contain x will completely cancel, leaving an equation with no variable left in it.

At that point, there are one of two possibilities:

If the remaining equation is true, it doesn't matter what the value of x is, the equation will be true.  This means there are infinitely many solutions (any value of x will make the equation true).

Similarly, if the remaining equation is false, it doesn't matter what the value of x is, the equation will be false.  This means there are no solutions (no values of x that will make the equation true).

Problem 9

\(3-x=x-3\)

Add "x" to both sides to move the x-term on the left side of the equation from the left, to the right side, and group like terms.

\(3=2x-3\)

We were able to combine like terms containing the x into a single term.  This equation will have one solution.

The remaining work is unnecessary to answer the question, but shows that there is one solution, the steps to find it, and what it is.

\(6=2x\)

\(3=x\)

Problem 10

\(4x-8=4(x-2)\)

Use the distributive property on the expression on right hand side of the equation ...

\(4x-8=4x-8\)

Observe that at this point, the entire left hand side of the equation EXACTLY matches that of the entire right hand side of the equation.

They are not just equal, they are exactly the same.

Attempting to move the term with x on the left hand side to the right hand side will require subtracting 4x from both sides, but combining like terms will cancel all terms with x on both sides....

\(-8=-8\)

Since negative eight is ALWAYS equal to negative eight, no matter what value you choose for x, the equation must be true because each side is the same exact expression.  This means there are infinitely many solutions.

Problem 11

\(5(1-x)=5+5x\)

Apply the distributive property on the expression on left hand side of the equation ...

\(5-5x=5+5x\)

Add 5x to both sides of the equation to move the terms with x on the left side to the right side of the equation, and combine like terms...

\(5=5+10x\)

Again, we were able to combine like terms containing the x into a single term.  This equation will have only one solution:

Subtract 5 from both sides...

\(0=10x\)

Divide both sides by 10...

\(0=x\)

Problem 12

\(x+2(x-7)=3x-7\)

Apply the distributive property on the expression on left hand side of the equation ...

\(x+2x-14=3x-7\)

Combine like terms on the left hand side of the equation...

\(3x-14=3x-7\)

To move the term with x from the left side to the right side, subtract 3x from both sides, and combine like terms...

\(-14=-7\)

Here, when combining like terms, the x all canceled out, and negative 14 is not equal to negative 7.  So, there is no solution so this equation.

Answer:

x=5

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

7+x=4(x−2)

7+x=(4)(x)+(4)(−2)(Distribute)

7+x=4x+−8

x+7=4x−8

Step 2: Subtract 4x from both sides.

x+7−4x=4x−8−4x

−3x+7=−8

Step 3: Subtract 7 from both sides.

−3x+7−7=−8−7

−3x=−15

Step 4: Divide both sides by -3.

−3x

−3

=

−15

−3

x=5

We can rewrite the expression in two possible ways as -

f{x} = {- x - 17}/{3}    and    f{x} = - {x + 17}/{3}

Given is the expression as -

f{x} = - {1/3}x - {17/3}

We can rewrite the expression in two possible ways as -

f{x} = {- x - 17}/{3}

and

f{x} = - {x + 17}/{3}

Therefore, we can rewrite the expression in two possible ways as -

f{x} = {- x - 17}/{3}    and    f{x} = - {x + 17}/{3}

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Quadratic function in vertex form:

Vertex: (h,k)

Given function:

y-intercept: find y when x is 0:

x-intercepts (solutions), equal the function to zero and solve x.

Domain of a funtion is the set of x-values for which the function is defined

Range of a function is the set of values the function takes

The solutionsrepresents the moment (time) the rocket is in the ground; as it starts at a height of 25 (y-intercept) the negative solution doesn't have sence in the situation;

Answer:

2x-10+x+x+10=180, or 4x=180

Step-by-step explanation:

So since the total is 180, you add them all up like an equation.

So,

2x-10+x+x+10

Combine like terms

4x=180

x=45

Then plug it back in to the equations.

x=45

(2x-10)=80

(x+10)=55

The answer is \(\frac{32x+105}{120}\).

The area of mathematics known as algebra is used to represent situations or problems using mathematical expressions. In algebra, we combine integers with variables like x, y, and z.

A fraction is a number that is a component of a whole. In algebra, fractions can be added, subtracted, multiplied, and divided just like in basic arithmetic.

The given equation is an algebraic fraction having variables in the numerator. This equation is written as,

\(\left(\frac{3}{5}x+\frac{3}{4}\right)-\left(\frac{1}{3}x-\frac{1}{8}\right)\)

First combine, x with the nearby fraction,

\(\begin{aligned}\left(\frac{3}{5}x+\frac{3}{4}\right)-\left(\frac{1}{3}x-\frac{1}{8}\right)&=\left(\frac{3x}{5}+\frac{3}{4}\right)-\left(\frac{x}{3}-\frac{1}{8}\right)\\&=\frac{3x}{5}+\frac{3}{4}-\frac{x}{3}+\frac{1}{8}\end{aligned}\)

Now, group the fraction with a common denominator,

\(\begin{aligned}\left(\frac{3}{5}x+\frac{3}{4}\right)-\left(\frac{1}{3}x-\frac{1}{8}\right)&=\left(\frac{3x}{5}-\frac{x}{3}\right)+\left(\frac{3}{4}+\frac{1}{8}\right)\\&=\left(\frac{3x\cdot3}{15}-\frac{x\cdot5}{15}\right)+\left(\frac{3\cdot2}{8}+\frac{1}{8}\right)\\&=\left(\frac{9x-5x}{15}\right)+\left(\frac{6+1}{8}\right)\\&=\frac{4x}{15}+\frac{7}{8}\\&=\frac{32x+105}{120}\end{aligned}\)

Therefore, the final answer is \(\frac{32x+105}{120}\).

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A 15-lb mixture, she should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts.

Based on the given information, we can set up the following system of equations:
Equation 1: x + y = 15 (since the total weight of the mixture is 15 pounds)
Equation 2: (5.90 * x) + (14.75 * y) = 9.44 * 15 (since the total cost of the mixture is the cost per pound multiplied by the weight of each component)
Now, let's convert this system of equations into matrix form:
| 1  1 |   | x |   | 15 |
| 5.90  14.75 |   | y | = | 9.44 * 15 |
To solve for x and y, we can use matrix algebra. We can multiply the inverse of the coefficient matrix by the right-hand side matrix to get the solution matrix:
| x |   | 1  1 |^-1   | 15 |
| y | = | 5.90  14.75 |      | 9.44 * 15 |
Using matrix calculations, we find that the inverse of the coefficient matrix is:
| 0.0877  -0.0576 |
| -0.0059   0.0678 |
Now, multiplying the inverse matrix by the right-hand side matrix gives us:
| x |   | 0.0877  -0.0576 |   | 15 |
| y | = | -0.0059   0.0678 | * | 9.44 * 15 |
Simplifying the multiplication gives us:
x = 1.256
y = 13.744
Therefore, the saleswoman should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts to get a 15-pound mixture.

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The slope of a line passing through two points (x1,y1) and (x2,y2) can be calculated using the formula:

slope = (y2-y1)/(x2-x1)

In this case, the two points are (8,-3) and (6,-7), so:

slope = (-7-(-3))/(6-8)

slope = (-7+3)/(-2)

slope = -4/(-2)

slope = 2

Therefore, the slope of the line passing through (8,-3) and (6,-7) is 2.

Answer:

2

Step-by-step explanation:

To find the slope from two points, we can use  the slope equation

m = ( y2-y1)/(x2-x1)

   = ( -7 - -3)/( 6 - 8)

   = (-7+3)/(6-8)

   = -4/-2

  = 2