Solve the equation, justify
each step with an algebraic
property.
7 = 16 + 3x

The measure of angle PZQ is equal to 70°.

In Mathematics, a circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis) with a measure of 360 degrees.

Generally speaking, the sum of all the angles around a point is equal to one full turn, which makes it equal to 360 degrees;

m∠PZR + m∠QZR + m∠PZQ = 360

120 + 170 + m∠PZQ = 360

290 + m∠PZQ = 360

m∠PZQ = 360 - 290

m∠PZQ = 70°.

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The cost of the car will be less than or equal to $4,450.

What is a equation?

An equation is a mathematical statement that indicates the equality of two expressions. It contains one or more variables and usually includes mathematical operations such as addition, subtraction, multiplication, division, or exponentiation.

Let the cost of the car be "d" (in dollars). Then, the total expenses, including taxes and fees, can be expressed as:

Total expenses = Cost of the car + Taxes + Fees

We can represent the cost of the car as "d", and the taxes and fees as a fixed amount "t". Therefore, the equation to model Samantha's total expenses can be written as:

Total expenses = d + t

From the problem, we know that Samantha paid a total of $4,450 for the car, taxes, and fees. Therefore, we can write:

d + t = 4450

To find the cost of the car, we need to isolate the variable "d" on one side of the equation. We can do this by subtracting "t" from both sides of the equation:

d + t - t = 4450 - t

Simplifying the equation, we get:

d = 4450 - t

To determine the cost of the car, we need to know the value of "t", which represents the total taxes and fees. Unfortunately, the problem does not provide this information, so we cannot determine the exact cost of the car. However, we do know that the cost of the car will be less than or equal to $4,450, since the total expenses cannot be negative.

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Answer:

10

Step-by-step explanation:

First, multiply everything in the parentheses.

Next, subtract 21x from both sides to get all the variables on one side.

Next, add 16 to both sides to get all the real numbers on one side

Finally, divide both sides by 30 so we can get the variable by it's self

Given thatPrecondition: `a>=2

`Postcondition: `d>=18

`Datatype and variable name: `int b,c,d`Codes: `a=a-8*3;`

`b=2*a+10;`

`c=2*b+5;` `

d=2*c;`

Solution To prove the given assignment segment with Hoare triple method, we use the following steps:

Step 1: Verify that the precondition `a >= 20` holds.Step 2: Proof for the first statement of the code, which is `a=a-8*3;`

i) The value of `a` is decreased by `8*3 = 24

`ii) The value of `a` is `a-24`iii) We need to prove the following triple:`{a >= 20}` `a = a-24` `{b = 2*a+10

; c = 2*b+5; d = 2*c; d >= 18}`

The precondition `a >= 20` holds.

Now we need to prove that the postcondition is true as well.

The right-hand side of the triple is `d >= 18`.Substituting `c` in the statement `d = 2*c`,

we get`d = 2*(2*b+5)

= 4*b+10`.

Substituting `b` in the above equation, we get `d = 4*(2*a+10)+10

= 8*a+50`.

Thus, `d >= 8*20 + 50 = 210`.

Hence, the given postcondition holds.

Therefore, `{a >= 20}` `

a = a-24`

`{b = 2*a+10; c = 2*b+5; d = 2*c; d >= 18}`

is the Hoare triple for the given assignment segment.

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Answer:

151 in^3

Step-by-step explanation:

The rocket consists of two shapes - a cone and a cylinder

the volume of the plastic = volume of cone + volume of cylinder

volume of a cylinder = nr^2h

Volume of a cone 1/3(nr^2h)

n = 22/7  

r = radius

the diameter is the straight line that passes through the center of a circle and touches the two edges of the circle.

A radius is half of the diameter

Radius = 5/2 = 2.5

Height of cone = 11 - 6 = 5

Volume of plastic = (22/7) x (2/5^2) x 6  + (1/3) x (22/7) x (2/5^2) x 5 = 117.9 + 32.7 = 150.6 in^3 = 151

Answer:

Mr Bean will get 1000 naira.

Step-by-step explanation:

They invested in the ratio of 5:3:2 , meaning that Mr Bean will get half the profit. 1/2 X 2000 = 1000

Answer:

r > 38

Step-by-step explanation:

Number of pages in the Quran = 532

Number of nights in a week = 7

Target is to read more than half by the end of the first week

In other to meet up,

Let number of pages to be read per night = r

Hence, the equality goes thus

Pages read per night × 7 > pages of the Quran / 2

7× r > 532 / 2

7r > 266

r > 266/7

r > 38

Hence, he must read more than 38 pages each night.

The length of the model car based on the information is 0.8 feet.

It should be noted that scale simply shows the relationship between a measurement on a model as well as the corresponding measurement on the actual object.

From the information, the model car is constructed with a scale of 1:15.

When the actual car is 12 feet long, the length of the model will be illustrated as x. This will be:

= 1/15 = x / 12

Cross multiply

15x = 1 × 12

15x = 12

Divide

x = 12 / 15

x = 0.8

The length is 0.8 feet.

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Answer: its 41 dude

The approximate solution for the equation \(x^3 - x - 1 = 0\) using the fixed-point iteration method with an initial guess

p0 = 1 is

p3 ≈ 1.4049.

To solve the equation x^3 - x - 1 = 0 using a fixed-point iteration method with three iterations and an initial guess p0 = 1, we can use the fixed-point iteration formula:

p_n+1 = g(p_n)

where g(x) is a function that transforms the equation into the form x = g(x).

First, let's rearrange the equation to isolate x:

x^3 - x - 1 = 0

x^3 = x + 1

x = (x + 1)^(1/3)

Now, we can define our fixed-point iteration function:

g(x) = (x + 1)^(1/3)

Let's perform the iterations:

Iteration 1:

p1 = g(p0)

= (p0 + 1)^(1/3)

= (1 + 1)^(1/3)

= 2^(1/3)

≈ 1.2599

Iteration 2:

p2 = g(p1)

= (p1 + 1)^(1/3)

= (1.2599 + 1)^(1/3)

≈ 1.5214

Iteration 3:

p3 = g(p2)

= (p2 + 1)^(1/3)

= (1.5214 + 1)^(1/3)

≈ 1.4049

After three iterations, the approximate solution for the equation \(x^3 - x - 1 = 0\) using the fixed-point iteration method with an initial guess

p0 = 1 is

p3 ≈ 1.4049.

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(a)The range of the given set of measurements is 4.

(b)The sample mean of the given set of measurements is approximately 5.625.

(c)The sample variance of the given set of measurements is approximately 2.337768, and the sample standard deviation is approximately 1.529.

(a) The range is the difference between the largest and smallest values in the set of measurements. In this case, the largest value is 8 and the smallest value is 4, so the range is 8 - 4 = 4.

To calculate the range, we subtract the smallest value from the largest value. In this case, the largest value is 8 and the smallest value is 4.

Range = Largest value - Smallest value

Range = 8 - 4

Range = 4

The range provides a simple measure of the spread or dispersion of the data. In this case, the range tells us that the values range from the smallest value of 4 to the largest value of 8, with a difference of 4 between them.

(b) The sample mean, denoted as x, is the sum of all the measurements divided by the total number of measurements.

To calculate the sample mean, we add up all the measurements and then divide by the total number of measurements. In this case, we have 8 measurements.

Sum of measurements = 4 + 4 + 7 + 6 + 4 + 6 + 6 + 8 = 45

Sample mean = Sum of measurements / Total number of measurements

Sample mean = 45 / 8

Sample mean ≈ 5.625

The sample mean represents the average value of the measurements and provides a measure of central tendency.

(c) The sample variance, denoted as s^2, measures the variability or dispersion of the data points around the sample mean. It is calculated as the average of the squared differences between each measurement and the sample mean.

To calculate the sample variance, we first calculate the squared difference between each measurement and the sample mean. Then, we average those squared differences.

Squared difference for each measurement:

(4 - 5.625)^2 = 2.890625

(4 - 5.625)^2 = 2.890625

(7 - 5.625)^2 = 1.890625

(6 - 5.625)^2 = 0.140625

(4 - 5.625)^2 = 2.890625

(6 - 5.625)^2 = 0.140625

(6 - 5.625)^2 = 0.140625

(8 - 5.625)^2 = 5.390625

Sum of squared differences = 2.890625 + 2.890625 + 1.890625 + 0.140625 + 2.890625 + 0.140625 + 0.140625 + 5.390625 = 16.364375

Sample variance = Sum of squared differences / (Total number of measurements - 1)

Sample variance = 16.364375 / (8 - 1)

Sample variance ≈ 2.337768

The standard deviation, denoted as s, is the square root of the sample variance.

Sample standard deviation = √(Sample variance)

Sample standard deviation = √(2.337768)

Sample standard deviation ≈ 1.529

These measures provide information about the dispersion or spread of the data points around the sample mean. A higher variance or standard deviation indicates greater variability in the measurements.

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Answer:

\(y=5x-18\)

Step-by-step explanation:

Given the following question:

Point A = (4, 2) = (x, y)
Slope = 5

To find the answer we are going to have to use the formula for slope intercept, substitute the values, then solve for the variable b to have our answer.

\(y=mx+b\)
\(y=2\)
\(m=5\)
\(x=4\)
\(2=5(4)+b\)
\(5\times4=20\)
\(2=20+b\)
\(20-20=0\)
\(2-20=-18\)
\(-18=b\)
\(b=-18\)
\(y=5x-18\)

Your answer is "y = 5x - 18."

Hope this helps.

Based on the information in the graph, it can be inferred that the percentage that you forgot to write down (Thursday percentage) corresponds to the number: 35%

To find the missing percentage we must carefully analyze all the information in the table. In this case, all the percentages are proportional, so we could infer that a rule of three would be the most effective way to find the missing percentage.

To perform the rule of three we must use two of the data already shown in the table. For example, the first data:

If 11 defective containers represent 27.5%, what percentage does 14 containers represent?

In accordance with the above, we can infer that 14 defective containers represent 35%. So the correct answer is C.

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The chi-square test of independence is typically used to analyze the relationship between two variables when both variables are nominal, the two variables have been measured on different individuals and the observations on each variable are within-subjects in nature. The answer is  D. all of the above

The chi-square test of independence is a statistical test that is used to determine if there is a significant association between two categorical variables. It is commonly used when both variables are nominal, meaning they consist of categories or groups rather than numerical values.

When conducting the chi-square test of independence, the data is typically collected by measuring the two variables on different individuals or units.

For example, researchers may collect data on the gender (nominal variable) and political affiliation (nominal variable) of different individuals and analyze whether there is a relationship between the two variables.

The test examines the observed frequencies of the different categories in a contingency table and compares them to the expected frequencies under the assumption of independence. If the observed and expected frequencies significantly differ, it suggests that there is an association between the two variables.

Therefore, the chi-square test of independence is applicable when both variables are nominal and the data is collected on different individuals. This allows researchers to investigate the relationship between the variables and determine if they are associated or independent.

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We must solve for x using the addition principle, the equation is as follows

In conclusion, the answer is x = -9

For the given isosceles triangle LMK, the distance between the points L and K is found as 5 units.

For the given question,

The coordinates of the points L and K taken from the graph are-

L = (-7, 4)

K = (-4, 8)

The distance between the points are found by the distance formula given as;

d = √(x₂ - x₁)² + (y₂ - y₁)²

Where x and y are the respective coordinates of two given points.

put the value;

LK = √(-4 + 7)² + (8 - 4)²

LK = √(3)² + (4)²

LK = √25

Taking square root both sides.

Lk = 5 units.

Thus, for the given isosceles triangle LMK, the distance between the points L and K is found as 5 units.

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The given equation, 16x² - y² + 16z² = 4, represents a quadric surface known as an elliptic paraboloid.

To determine the classification, we can examine the coefficients of the squared terms. In this case, the coefficients of x², y², and z² are positive, indicating that the surface is bowl-shaped. Additionally, the signs of the coefficients are the same for x² and z², indicating that the bowl opens upward along the x and z directions.

The negative coefficient of y², on the other hand, means that the surface opens downward along the y direction. This creates a cross-section in the shape of an elliptical parabola.

Considering these characteristics, the given equation represents an elliptic paraboloid.

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Answer:

The constant of proportionality in the inverse variation is -3000

Step-by-step explanation:

Given that the initial value of the car was X, after owning the car for 3 years the value is $15,000 and the value after 5 years was $9,000 we have;

At  year 3, value of car = $15,000

At year 5, value of car = $9,000

Rate of change of car value with time = Constant of proportionality

Rate of change of car value with time = (15000 - 9000)/(3 - 5) = -3000

The constant of proportionality = -3000

Therefore;

y - 15000 = -3000 × (x - 3)

y = -3000x + 9000 + 15000 = -3000·x + 24000  

The value of the car, y with time,x is, y = -3000·x + 24000

Answer:

48 and 32

Step-by-step explanation:

both numbers get rounded by 8 going up and down rounding it to 40

Answer:

¿Cómo andás? and ¿Dónde vivís?

Step-by-step explanation:

Hope this helps! <3

Answer:

cόmo andás and dόnde vivís

Step-by-step explanation:

The scale of the drawing is 0.25, which means that every 1 centimeter in the drawing represents 0.25 meters in real life.

To determine the scale of the drawing, we need to compare the measurements in the drawing to the measurements in real life. We know that the building at the college is 64 meters wide in real life, and 16 centimeters wide in the drawing. We can set up a proportion to solve for the scale:

16 cm / x = 64 m / 1

To solve for x (the scale), we can cross-multiply and simplify:

16 cm * 1 = 64 m * x

16 = 64x

x = 16/64

x = 0.25

Therefore, the scale of the drawing is 0.25, which means that every 1 centimeter in the drawing represents 0.25 meters in real life.

In order to determine the scale of Maria's drawing of the community college, we need to compare the actual width of the building (in meters) to its width in the drawing (in centimeters). To do this, we first need to convert one of these measurements to match the other.

Let's convert the actual width of the building from meters to centimeters. There are 100 centimeters in a meter, so we'll multiply the width of the building in meters (64) by 100:

64 meters × 100 = 6400 centimeters

Now that both measurements are in centimeters, we can compare them to find the scale. To do this, we'll divide the actual width (6400 centimeters) by the width in the drawing (16 centimeters):

6400 cm / 16 cm = 400

The result, 400, represents the scale of Maria's drawing. In other words, the scale of the drawing is 1:400. This means that 1 centimeter in the drawing represents 400 centimeters (or 4 meters) in real life.

So, Maria's scale drawing effectively reduces the size of the actual building by a factor of 400, making it easier to represent the entire community college on a smaller, more manageable scale.

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To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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125 x (5^4)7 as a single power of 5 is 28*5^4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

125 x (5^4)7

Now, 125 x (5^4)7

=125x140

=17500

=28*5^4

Therefore, by algebra the answer will be 28*5^4.

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Answer:

It would take her 10 track practices to get up to 40 miles.

Step-by-step explanation:

Answer:

y= Ix-3I    (that says absolute value btw)

Step-by-step explanation:

This is the result of starting with y = |x|, then shifting it three units to the right. Replacing x with x-3 moves the xy axis three units to the left, giving the illusion the V shaped curve moved 3 spots to the right.

We don't shift up or down since the vertex is on the x axis.

We also don't vertically compress or stretch the graph either.

Side note: the vertex for this graph is (3,0) which is the lowest point of the curve.

Answer:

1=4

5=8

2=5

Step-by-step explanation:

Answer:

1, 5, 2 is the x values.

Step-by-step explanation:

you just subtract 3 from the y's

The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

---------------------------------------------------------------------------

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

---------------------------------------------------------------------------

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

---------------------------------------------------------------------------

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

---------------------------------------------------------------------------

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

---------------------------------------------------------------------------

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

---------------------------------------------------------------------------

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

---------------------------------------------------------------------------

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

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To find the length of each piece that minimizes the area, we need to use calculus and optimization techniques. Let's denote the length of one of the pieces as x and the other as 40 - x.

For the piece bent into a square, its perimeter will be equal to x. Since a square has all sides equal, each side will have a length of x/4. The area of the square will then be (x/4)².

For the piece bent into a circle, its circumference will be equal to 40 - x. The radius of the circle will be (40 - x) / (2π). The area of the circle will then be π * ((40 - x) / (2π))².

To find the length of each piece that minimizes the total area, we need to find the critical points of the total area function. Taking the derivative of the total area function with respect to x and setting it equal to zero will help us find these critical points.

Now, to find the length of each piece that maximizes the area, we also need to use calculus and optimization techniques. In this case, we need to find the critical points of the total area function by taking the derivative of the total area function with respect to x and setting it equal to zero.

Once we have the critical points, we can evaluate the total area at those points and determine which length maximizes the area.

Please note that providing the actual numerical values for the lengths and areas would require further calculations based on the specific equations derived above.

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