suppose that m varies directly as z, and m 120 when z 15. write an equation that expresses this variation.

Through the given information in the question, the value of x could be 12.

The perimeter of a rectangle is the total distance around the outside of the rectangle. It is calculated by adding together the length of all four sides of the rectangle. If the length of the rectangle is denoted by 'l' and the width is denoted by 'w', then the formula for the perimeter (P) of the rectangle is:

P = 2l + 2w

Alternatively, the formula can also be written as:

P = 2(l + w)

The perimeter of a rectangle is given by the sum of the lengths of all four sides. Therefore, we can write:

AB + BC + CD + DA = 22

We know that AB = CD = 9 since they are opposite sides of the rectangle. We also know that DA = BC = x - 5, since they are the other two sides of the rectangle.

Substituting these values into the perimeter equation, we get:

9 + x - 5 + 9 + x - 5 = 22

Simplifying the equation, we get:

2x - 2 = 22

2x = 24

x = 12

Therefore, the value of x could be 12.

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Answer:

1) \(1.276 \times 10^{7}\,m\), 2) \(5.101 \times 10^{8}\,km^{2}\), 3) \(5.974 \times 10^{24}\,kg\), 4) \(7.723\times 10^{9}\), 5) \(1.350 \times 10^{18}\), 6) \(3.618\times 10^{8}\,km^{2}\)

Step-by-step explanation:

(This exercise is written in Portuguese and for that reason explanation will be held in Spanish, which has strong similarities with that language)

La notación científica presenta el siguiente formato:

\(x.y \times 10^{n}\)

Donde:

\(x\) - Un dígito entero.

\(y\) - Dígitos decimales consecutivos.

\(n\) - Grado de potencia.

Para cálculos cotidianos se recomienda el uso de tres decimales consecutivos. A continuación, se presentan los números convertidos a la forma de notación científica:

1) \(12.756.000\,m\)

El grado de la potencia es siete (7).

\(1.276 \times 10^{7}\,m\)

2) \(510.072.000\,km^{2}\)

El grado de la potencia es ocho (8).

\(5.101 \times 10^{8}\,km^{2}\)

3) \(5.973.600.000.000.000.000.000.000\,kg\)

El grado de la potencia es veinticuatro (24).

\(5.974 \times 10^{24}\,kg\)

4) \(7.722.522.000\)

El grado de la potencia es nueve (9).

\(7.723\times 10^{9}\)

5) \(1.350.000.000.000.000.000\)

El grado de la potencia es dieciocho (18).

\(1.350 \times 10^{18}\)

6) \(361.800.000\,km^{2}\)

El grado de la potencia es ocho (8).

\(3.618\times 10^{8}\,km^{2}\)

A new car valued at 28000 and depreciate at 9% per year from original price. Find the value of the car 3 year after the purchase is ;$25480

A new car, valued at $28,000, depreciates at 9% per year

Value of the car one year after purchase

Initial Value  P = $ 28000

Rate of depreciation = 9 %

Time = 1 year

Amount = A

Amount after n year =  P(1 - r/100)ⁿ

Amount after 1 year  = 28000(1 -9/100)¹

= 280 * 91

=  25480

value of the car one year after purchase  = $25480

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Yes, the forester was justified in using a Normal model to analyze the woods, because the histogram is unimodal and symmetric. So option A is correct.

A histogram is a type of graph that uses vertical bars to show the distribution of a set of data. This particular histogram is unimodal, meaning that it has one peak which is an indication that the data is distributed normally. Additionally, the histogram is symmetric, which is another indication that the data is normally distributed.
Using a Normal model to analyze the woods is a valid approach because it allows the forester to identify the average diameter of the trees, as well as the spread of the data. It also allows him to check for any outliers, or points that fall outside the normal range. With this information, the forester can determine if the woods is suitable for sale, or if the buyer should be aware of any unexpected features.
Overall, the histogram is an effective way for the forester to analyze the data and determine if a Normal model is appropriate. By noting the unimodal and symmetric nature of the histogram, the forester can be sure that a Normal model will accurately represent the data, allowing him to make an informed decision about the woods.

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An inequality is a mathematical statement that uses symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to) to compare two quantities. In real life, we can use inequalities to describe a wide range of situations. For example, let's say you are buying groceries and you have a budget of $50. You could use the inequality  total cost of groceries < $50 to describe your situation. This inequality states that the total cost of the groceries must be less than $50, or you will exceed your budget.

In another real life situation, let's say you are training for a race and you want to run a certain distance in a specific amount of time. You could use the inequality distance > speed × time to describe your goal. This inequality states that the distance you run must be greater than the product of your speed and the time it takes you to complete the race. Inequality statements can also be used in social science and economics. For example, we can use an inequality to describe the income distribution in a society. We could say that the top 10% of earners have an income greater than the bottom 90% of earners, using the inequality top 10% income > bottom 90% income.

In summary, inequalities can be used to describe real life situations by comparing two quantities using symbols such as <, >, ≤, or ≥. We can use inequalities to describe a wide range of situations, from grocery shopping to income distribution.

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The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

A vector equation of a surface in three-dimensional space is a function that maps a pair of parameters, say u and v, to a three-dimensional point in space (x, y, z) represented as a vector. The vector equation can be written in the form of r(u, v) = <x(u, v), y(u, v), z(u, v)>.

In general, there are different ways to represent the same surface using vector equations. For example, the surface of a sphere of radius r centered at the origin can be represented by the vector equation r(u, v) = <r sin(u) cos(v), r sin(u) sin(v), r cos(u)>, where u is the polar angle (measured from the positive z-axis) and v is the azimuthal angle (measured from the positive x-axis).

Vector equations can be useful in studying the geometry and properties of surfaces, such as determining their tangent planes, normal vectors, curvature, and surface area. They can also be used to parametrize surfaces for numerical calculations and simulations.

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

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Answer:

3h−3k

Step-by-step explanation:

Answer:

container A

Step-by-step explanation:

In Container A, we can plot the points (0,60) adn (2, 35)

The slope is :

\(m_A = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{35-60}{2-0} \\\\= \frac{-25}{2}\\ \\m_A = -12.5\\\)

For container B, the slope is:

\(m_B = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{32-54}{3-1} \\\\= \frac{-22}{2}\\ \\m_B = -11\\\)

The negative sign of the slope indicates the direction of the slope

\(|m_A| = 12.5\\\\|m_B| = 11\)

12.5 > 11

The slope of container A is steeper than container B

Therefore, the water is draining out of container A at a faster rate than container B

Answer:

(x-7)(x^2-5)

Step-by-step explanation:

Answer:

the winner got 1480 votes

the loser got 1320 votes

Step-by-step explanation:

2800/2=1400

1400-80     80 is half 160

=1320

the winner got 1480 votes

the loser got 1320 votes

1480 is 160 more than 1320

A set with 18 elements has\($2^{18}$\) subsets. Each element can either be a part of a subset or not, meaning that there are 2 possibilities for each of the 18 elements in a subset.

Thus, the total number of possible subsets is\($2^{18}$\).Since we are looking for the number of subsets with an odd number of elements, we can first find the number of subsets with an even number of elements and subtract that from the total number of subsets.

We know that half of the subsets will have an even number of elements, so the number of subsets with an even number of elements is $2^{17}$.Therefore, the number of subsets with an odd number of elements is $2^{18} - 2^{17}$. To simplify this, we can factor out a \($2^{17}$\) to get \($2^{17} (2-1)$ which simplifies to $2^{17}$.\) Thus, a set with 18 elements has $2^{17}$ subsets with an odd number of elements.

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Answer:

Volume = 500 cm³

Step-by-step explanation:

Given the following data;

Side length of the base = 10cm

Height = 15 cm

To find the volume of pyramid with a square base;

Mathematically, the volume of a pyramid with a square base is given by the formula;

Volume of square-based pyramid = A(h/3)

Where;

A is the area of the square base.

h is the height of the pyramid.

First of all, we would find the area of the square base;

Area of square, A = L²

A = 10²

A = 100 ft²

Next, we find the volume of the square-based pyramid;

Volume = 100(15/3)

Volume = 100 * 5

Volume = 500 cm³

Answer:

it isn't the equation so it can't be any roots...

Step-by-step explanation:

\((2+1)^2+2=10-6\\4+4+1+2=10-6\\11\neq 4\)

x = -24

Step-by-step explanation:

i hope this helps :)

Answer:A

Step-by-step explanation:

Possible options:

uppercase letter: 26

lowercase letter: 26

number: 10

upper or lowercase letter: 50

Note: I'm interpreting the "no upper or lower case letters can be repeated in the sequence" to mean you could have Aa0b, where A is used as the uppercase and a is used as the lower case letter, but then you can't use A or a for the last character.

26 · 26 · 10 · 50 = 338,000 combinations

Now is using "A" and "a" isn't allowed, then you have:

Possible options:

uppercase letter: 26

lowercase letter: 25

number: 10

upper or lowercase letter: 48

26 · 25 · 10 · 48 = 312,000 combinations

The nullity of the matrix is 3, and the the column space of A is a subspace of R6 with dimension 5. Option (c) and (d) are correct.

Suppose we have a 6 x 8 matrix A with five pivot columns. The nullity of A is defined as the dimension of the null space of A, which is the set of all solutions to the homogeneous equation Ax = 0. Since the number of pivot columns in A is 5, we can use the rank-nullity theorem to determine the nullity of A. The rank-nullity theorem states that the sum of the rank and nullity of a matrix equals its number of columns.

Therefore, if A has five pivot columns, its rank is also 5. Thus, the nullity of A can be calculated as:

nullity A = number of columns - rank of A

= 8 - 5

= 3

Hence, the nullity of A is 3.

On the other hand, the rank of A is 5, which means that the columns of A are linearly independent and span a subspace of dimension 5. Thus, option C is correct. Alternatively, we can also say that the column space of A is the subspace of R6 spanned by its columns, which has dimension 5. Therefore, option D is also correct.

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Answer:

r = 11

Step-by-step explanation:

Hi there!

This scenario represents a linear relation, given the equation \(m=rp+k\).

Linear equations are typically written in the form \(y=mx+b\), where m is the slope and b is the y-intercept. As you can see, \(y=mx+b\) and the given equation \(m=rp+k\) share the same form.

This makes r the slope. This is also stated in the question, as r is the amount of money ($) paid per page.

The ordered pairs in the table represents points on a graph, if we were to graph this. For example, (9, 308) and (12, 341) both fall on the graph of this relation.

To solve for r, we must solve for the slope using the slope equation:

\(r=\displaystyle \frac{y_2-y_1}{x_2-x_1}\) where two points are \((x_1,y_1)\) and \((x_2,y_2)\).

We can use any two points from the table in this equation. For example, (9, 308) and (12, 341):

\(r=\displaystyle \frac{341-308}{12-9}\\\\r=\displaystyle \frac{33}{3}\\\\r=11\)

Therefore, the value of r is 11.

I hope this helps!

The required solutions of the situation of the function are  x = 3/4  or x = -1/4.

A unique connection where each input only produces one output. A common notation for it is "f(x)," where x denotes the input value. as in f(x) = x/2 ("f of x equals x divided by 2") Since there is only one output ("x/2") for each input ("x"), it is a function: • f(2) = 1.

We have,

f(x)=2x-1

g(x)=3/8x

To find the value of x for f(x) = g(x).

f(x) = g(x)

2x-1 = 3/8x

16x² - 8x = 3

16x² - 8x - 3 = 0

16x² - 12x + 4x - 3 = 0

4x(4x - 3) + (4x - 3) = 0

(4x - 3)(4x + 1) = 0

x = 3/4  or x = -1/4

Thus, required solution are  x = 3/4  or x = -1/4.

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The main difference between a binomial and multinomial experiment lies in the number of possible outcomes for each trial.

In a binomial experiment, there are two possible outcomes (success or failure), denoted by k = 2. On the other hand, a multinomial experiment involves multiple possible outcomes, with k representing the number of distinct outcomes.

In a binomial experiment, each trial has two possible outcomes, typically labeled as success (S) and failure (F). The number of successful outcomes is of interest, and the probability of success remains constant for each trial. The binomial distribution is characterized by parameters such as the number of trials, the probability of success, and the number of successful outcomes.

In contrast, a multinomial experiment involves multiple possible outcomes, with each outcome occurring with a certain probability. The number of possible outcomes is denoted by k, and each outcome can be categorized or labeled differently. The multinomial distribution considers the probabilities associated with each outcome and their respective frequencies.

In summary, the difference between a binomial and multinomial experiment lies in the number of possible outcomes for each trial. A binomial experiment has two outcomes (success or failure), while a multinomial experiment involves multiple distinct outcomes, with the number of possible outcomes denoted by k.

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The value of the function when x = 2 is 9

The given parameters are

f(x) = 2x^2 - 3x + 7

When x = 2, we have;

f(2) = 2(2)^2 - 3(2) + 7

Evaluate

f(2) = 9

Hence, the value of the function when x = 2 is 9

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Answer:

The total surface area of the 20 pieces exceeds the surface area of the original cube by 1368 square centimeters.

Step-by-step explanation:

The formula of surface area for the entire cube (\(A_{s,c}\)), measured in square centimeters, is:

\(A_{s,c} = 6\cdot l^{2}\) (Eq. 1)

Where \(l\) is the side length, measured in centimeters.

If this cube is sliced into 20 pieces, the surface area of each slice (\(A_{s,s}\)), measured in square centimeters, is equal to:

\(A_{s,s} = 4\cdot \left(\frac{1}{20}\right)\cdot l^{2}+2\cdot l^{2}\)

\(A_{s,s} = \frac{1}{5}\cdot l^{2}+2\cdot l^{2}\)

\(A_{s,s} = \frac{11}{5}\cdot l^{2}\) (Eq. 2)

And the surface area of all slices (\(A_{s,as}\)), measured in square centimeters, is:

\(A_{s,as} = 44\cdot l^{2}\) (Eq. 3)

Then, we calculate the excess of surface area (\(\Delta A\)), measured in square centimeters, by applying the following formula:

\(\Delta A = A_{s,as}-A_{s,c}\)

\(\Delta A = 44\cdot l^{2}-6\cdot l^{2}\)

\(\Delta A = 38\cdot l^{2}\) (Eq. 4)

If \(l = 6\,cm\), then the excess of surface area is:

\(\Delta A = 38\cdot (6\,cm)^{2}\)

\(\Delta A = 1368\,cm^{2}\)

The total surface area of the 20 pieces exceeds the surface area of the original cube by 1368 square centimeters.

Answer:

Increases

Step-by-step explanation:

It increases because, the greater the value of x the smaller the fraction is. If x was 25 the fraction would be 5/25 this makes the value of the equation 5.2. Now if x was a smaller positive number like 5. Then the fraction would be 5/5 which would cause the equation to be equal to 6.

To locate the stations and draw cirradius cles on the map of California, follow these steps:

1. Identify the city stations on the map: Find the city stations indicated on the map, such as San Francisco, Los Angeles, and San Diego.

2. Use a compass: Set your compass to the scale provided on the map.

For example, if the scale says 1 inch = 100 km, adjust your compass accordingly.

3. Determine the distance from the epicenter: Based on the information provided, determine the distance from each city station to the epicenter. If it is not provided, refer to additional resources or data.

4. Draw the circles: Place the compass point on each city station and draw a circle with a corresponding to the distance determined in

step 3. Ensure the radius is in scale with the map.

5. Identify the epicenter: The point where all the circles intersect is the approximate location of the epicenter.

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Answer:

The answer is actually 2.

C= 2cm.

Answer:

she would need 7 ounces

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

The greatest common factor of polynomial  64xyz−36xy + 24x  is 4x

The greatest common factor of a polynomial is a monomial that divides all terms of the polynomial.

The given polynomial is:

64xyz−36xy + 24x

Notice that there are 3 terms:

64xyz

−36xy

24x

To find the greatest common factor, notice that each terms contain x.

Next, find the gcf of 64, 36, 24.

Using prime factorization:

64 = 2⁶

36 = 2² × 3²

24 = 2³ × 3

Hence the gcf (64, 36, 24) = 2² = 4

Therefore the gcf of  64xyz−36xy + 24x  is 4x

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Note that m<4+m<1+m<5=180 can be used to show that m<2+m<1+m<3=180 because both set of angles are related to parallel lines b and a. [See attached image]

Note that parallel lines do not bend or curve. They demonstrate equal tangentiality across every on the same line being equal to equidistant to each other.

Thus, we can state that m∠4+m<∠1+m∠5=180° because the are all angles on a straight line. Recall that angles on a straight line all sum up to 180°.

Also, note that m∠2+m∠1+m∠3=180° because angles n a triangle sum to 180°.

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To meet the​ recommendation, the ramp needs to have a horizontal distance of at least 16 feet. The ramp has a horizontal distance of 17.9 feet.

If the ramp has a horizontal distance of 17.9 feet, it meets the recommended minimum distance of 16 feet for a ramp with a maximum slope of 1:12, as per the ADA Accessibility Guidelines.

It's important to note that the slope of the ramp should also be taken into consideration to ensure that it is safe and easy to use for individuals with disabilities. If the ramp's slope is too steep or too shallow, it may not meet accessibility standards and could pose a hazard to users.

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