A new car is purchased for $30,000 and over time its value depreciates by one halfevery 5 years. What is the value of the car 11 years after it was purchased, to thenearest hundred dollars?

Step-by-step explanation:

Matrix budgeting is a model developed to evaluate where your additional money goes or should go, and it helps to manage personal finances. Also called as a budget matrix, it's a plan or a blueprint in chart or table form designed to allocate financial resources in the ranking order of your goals and priorities.

Answer:

13

Step-by-step explanation:

a2+b2=c2

12^2+5^2=c^2

144+25=169

square root of 169

13

Answer:

2 units

Step-by-step explanation:

vertical distance will be the magnitude of the difference in the 'y' coordinates

| -.8 - 1.2| = 2 units

The equation required is 9/ 4 (or 2 1/4).

An equation is a mathematical expression which require the application of some mathematical principles so as to simplify it, or determine the value of the unknown.

In the given equation, it can be simplified as;

1/2 + 5/8 + 9/8

find the LCM of the equation,

1/2 + 5/8 + 9/8 = (4 + 5 + 9)/ 8

                        = 18/ 8

divide the numerator and denominator by 2, to have

18/ 8 = 9/ 4

        = 2 1/4

The equation expected is 9/ 4 (2 1/4).

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The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.

Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).

We know that the area of the smaller rectangle is 676 square centimeters:

L * W = 676    ----(1)

We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.

The area of the larger rectangle is 3457 square centimeters:

41 * H = 3457    ----(2)

Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.

In order to find H, we can use equation (2):

H = 3457 / 41

H ≈ 84.22

Now we can substitute this value of H into equation (1):

L * W = 676

We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.

Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676

By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:

L = 13

W = 52

Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.

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Answer: Obtuse Angle

Step-by-step explanation: A 90 degree angle is a right angle anything larger then a right angle is a obtuse angle.

Answer:

It would be called an obtuse angle

Step-by-step explanation: so you see if it was exactly 90 degrees it would be called a right angle. Anything above 90 (b91 92 93 etc...) degrees would be an obtuse angle and anything below 90 ( 89 88 87 etc..) would be an acute angle except an 180 degree angle would be a straight angle. Hope that helps!

have a wonderful Sunday!

Answer:

Step-by-step explanation:

You want the number of text messages sent by each of Yolanda, Ryan, and Henry if they sent a total of 127, and Ryan sent 7 more than Yolanda, while Henry sent 4 times as many as Yolanda.

The relationships expressed in the problem statement can be written as equations:

Using the last two equations to substitute into the first, we have ...

  y +(y +7) +(4y) = 127

  6y = 120 . . . . . . . . . . . . subtract 7

  y = 20 . . . . . . . . . . . divide by 6

  r = 20 +7 = 27

  h = 4·20 = 80

Yolanda sent 20 text messages, Ryan sent 27, and Henry sent 80.

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Answer:

Step-by-step explanation:

r = 8/3 units

h = 13 units

Volume of cone = (1/3) πr²h

                           \(= \frac{1}{3}* 3.14 * \frac{8}{3}* \frac{8}{3}*13\\\\= 96.76 cubic units\)

If the radius of the base of the cone, r, is \( \frac{8}{3} \) units and the height, h, is 13 units, what is the volume of the cone ?

\( \bullet \) Radius of the base of the cone (r) is \( \frac{8}{3} \) units.

\( \bullet \) Height (h) of the cone is 13 units.

Volume of the cone.

We know,

Formula of volume of cone is \( \frac{1}{3} \) πr²h

So, volume of the cone = \( \frac{1}{3} \) × \( \frac{22}{7} \) × \( (\frac{8}{3})² \) × 13

= \( \frac{1}{3} \) × \( \frac{22}{7} \) × \( \frac{8}{3} \) × \( \frac{8}{3} \) × 13

= \( \frac{22 \: × \: 8 \: × \: 8 \: × \: 13}{3 \: × \: 7 \: × \: 3 \: × \: 3} \)

= \( \frac{18304}{189} \)

= 96.85 cubic units.

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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The situation which can be represented with the equation y = 7x among the answer choices is; Jordin climbs x stairs that each have a height of 7 inches. What is the total number of inches, y,

Jordin climbs?

It follows from the task content that the proportional relationship is a representative of the situation where;

Hence, y is the total height Jordin climbs while x is the number of stairs Jordin climbs.

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According to the given  expression There will be 910 women among the 1,560 runners.

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself.

Using mathematical operations like addition, subtraction, multiplication, and division, a combination of numbers and integers can be expressed numerically in mathematics.

I'm looking for 7/12 of 1560. I really do mean, "Divide 1560 among 12 groups and count how many there are in each category overall."

1560 divided into 12 groups.

1560/12

=130.

There are 130 people in each group. We multiply to determine how many there are in the seven groupings.

130/7

=910

Among the 1,560 runners, 910 of them will be female.

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The following phrases are used in place of supply chain:

Supply network ; Demand chain ; Extended enterprise ; Supply web.

The supply chain is a networked system of businesses, people, information, and assets created to locate, produce, and transport items from their point of origin to their final destination, which is often from the a supplier to a customer.

Modern supply chains sometimes span several nations and involve numerous processes, making them exceedingly complicated.

The fundamental steps in such a supply chain are as follows:

Thus, the following phrases are used in place of supply chain:

Supply network ; Demand chain ; Extended enterprise ; Supply web.

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Answer: \((f \cdot g)(x) = x^4-11x^2+30.\)

Step-by-step explanation:

We want to find the value of \(f(g(x)).\) To do this, we plug in \(g(x)\) into the expression for \(f(x).\) This gives us:

\(f(g(x)) = (x^2-9)^2+7(x^2-9)+12 = x^4-18x^2+81+7x^2-63+12 = \boxed{x^4-11x^2+30}.\)

A: Mai answered 5  open-ended questions correctly,

B: Priya answered 15 multiple-choice questions correctly,

C: expression for the condition is y = 10 + 4a + 6b.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given points on each multiple choice question = 4

points on each open-ended question = 6

extra credit for winners = 10 points

A. If Mai answered 13 multiple-choice questions correctly and earned a total score of 92,

the total score of multiple choice questions = 13*4

the total score of multiple choice questions = 52

score left  = 92 - 52 - 10 (reducing 10 for extra points)

score left  = 30

open-ended questions she answers correctly = 30/6

open-ended questions she answers correctly = 5

B:  If Priya answered 4 open-ended questions correctly and earned a total score of 94,

the total score of open-ended questions = 4*6

the total score of open-ended questions = 24

the score left  = 94 - 24 - 10 (reducing 10 for extra points)

score left  = 60

multiple choice questions she answers correctly = 60/4

multiple choice questions she answers correctly = 15

C:  an expression that will represent a student's score in first period,

let y be the total score,

a be the number of multiple choice questions answered,

the total score of multiple choice questions = 4a

and b be the number of  open-ended questions answered,

the total score of open-ended questions = 6b

expression is,

y = 10 + 4a + 6b  (adding 10 for extra points)

Hence Mai answered 5  open-ended questions correctly,

Priya answered 15 multiple-choice questions correctly,

and expression is y = 10 + 4a + 6b.

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Answer:

Step-by-step explanation:

f(x) = |2x−1|+3, reflected over the y-axis becomes

g(x) = |-2x−1|+3

We needed the point (0.5, 3) to go to the other side of the y-axis to get the point (-0.5, 3).

Answer:

Scale factor of 3

Matrices are a type of data structure that can be used to represent and manipulate data in a variety of ways.

One way to use matrices to represent data is to store the data in the form of a matrix. For example, a matrix could be used to represent a table of values, where each row represents a different data point and each column represents a different attribute or feature of the data.

Matrices can also be used to manipulate data by performing mathematical operations on the matrix elements. For example, matrices can be added, subtracted, and multiplied to perform operations such as matrix addition, matrix subtraction, and matrix multiplication. These operations can be used to perform various types of data manipulation, such as combining data from different sources, transforming data, or calculating statistics.

In addition to performing mathematical operations, matrices can also be used to store and manipulate data in other ways. For example, matrices can be used to represent and manipulate images and other types of data that have a two-dimensional structure. Matrices can also be used to represent and manipulate data in higher dimensions, such as data with a three-dimensional structure.

Overall, matrices are a powerful tool for representing and manipulating data in a variety of contexts, and they are widely used in a range of fields including mathematics, computer science, engineering, and data analysis.

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Matrices are a type of data structure that can be used in a variety of ways to represent and manipulate data.

One method for utilizing grids to address information is to store the information as a framework. A table of values, for instance, could be represented by a matrix, with each row representing a distinct data point and each column representing a distinct attribute or feature of the data.

The plural form of a matrix, a rectangular array or table in which numbers or elements are arranged in rows and columns, is referred to as a matrices. They can have as many columns and rows as you want. Matrix operations include addition, scalar multiplication, multiplication, transposition, and others.

When performing these matrix operations, certain rules must be followed. For example, they can only be multiplied if the first and second columns are exactly the same, and they can only be added or subtracted if they have the same number of rows and columns.

Matrices can also be used to manipulate data by performing mathematical operations on the matrix elements. For example, matrices can be added, subtracted, and multiplied to perform operations such as matrix addition, matrix subtraction, and matrix multiplication. These operations can be used to perform various types of data manipulation, such as combining data from different sources, transforming data, or calculating statistics.

In addition to performing mathematical operations, matrices can also be used to store and manipulate data in other ways. For example, matrices can be used to represent and manipulate images and other types of data that have a two-dimensional structure. Matrices can also be used to represent and manipulate data in higher dimensions, such as data with a three-dimensional structure.

In general, matrices are extensively utilized in a variety of fields, including mathematics, computer science, engineering, and data analysis. They are a powerful tool for representing and manipulating data in a variety of contexts.

Hence the matrices be used to represent and manipulate data.

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Answer: (x > -3).

Step-by-step explanation:

To solve the inequality 4(1 - x) < 16, we will simplify and solve for x:

4(1 - x) < 16

Distribute the 4:

4 - 4x < 16

Subtract 4 from both sides:

-4x < 12

Divide both sides by -4. Note that when dividing by a negative number, the inequality sign flips:

x > -3

The solution to the inequality is x > -3. This means that x must be greater than -3 for the inequality to hold true.

To graph the solution on a number line, we mark a shaded region to the right of -3, indicating that all values greater than -3 satisfy the inequality:

The open circle at -3 indicates that -3 is not included in the solution since the inequality is strict (x > -3).

here's the graph for 4(1-x)<16

The inequalities which satisfy the number line shown is x>2 and x>=2.

We are given that;

The number line showing inequality

Now,

x>2 satisfies the equation by the given number line

x>=2 satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

Therefore, by the number line the answer will be x>2 and x>=2 .

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Answer:

\(14 + 4 + 5.5 + 3 + 5.5 {?}^{2} \)

Answer:

Step-by-step explanation:

We have 2 congruent large prisms and one small one.

Volume of a large one= 2*2*14 = 56 cm^3.

Volume of smaller one = 4*3*2 = 24 cm^3.

So volume of the whole prism

= 2*56 + 24

= 136 cm^3.

Surface area of a large one = 3*2*14 + 2*2*5.5 + 2*2*2 = 114

Surface Area  of smaller one = 4*3*2 + 2*2*4 =  40

So surface area of the whole prism

= 2 * 114 + 40

= 268 cm^2.

The solution is, the percent of error, rounded to the nearest percent is 25%.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

While viewing a herd of cattle on a ranch, Herbert estimated that there were 750 cattle in the herd.

The actual number of cattle in the herd was 600.

now, we have to find the percent of error, rounded to the nearest percent.

so, we get,

Herbert estimated that there were 750 cattle in the herd.

The actual number of cattle in the herd was 600.

so, error = 750 - 600

              = 150

so, we get,

the percent of error = 150 * 100 / 600

                                 = 25%

Hence, The solution is, the percent of error, rounded to the nearest percent is 25%.

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The probability of of the order spelling MATH is 1/24.

Probability is the chance of happening something or the occurrence of something . We can also define the probability as the chance of occurring or the chance of selecting something from the total set of value. It is always ranges from 0 to 1 where 0 is minimum value and 1 is maximum value of probability.

Formula for probability is :

\(prabability(event) = \frac{Favourable \ outcomes}{Total \ outcomes}\)

where, the total outcomes is the sample space of our given data or we can say the total number of values in the sample space.

In the question given,

The sample space is the different ways of arranging the letter which is equals to 4 factorial.

=> Sample space = 4! = 24

and the Favorable outcome is the word "MATH".

Thus, The probability is 1/24,  because out of 24 of them only one can spell math.

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Answer:

0.0314 = 3.14% probability to get a sample average of 35 or more customers if the manager had not offered the discount

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

A small hair salon in Denver, Colorado, averages about 30 customers on weekdays with a standard deviation of 6.

This means that \(\mu = 30, \sigma = 6\)

5 consecutive weekdays.

This means that \(n = 5, s = \frac{6}{\sqrt{5}} = 2.6832\)

What is the probability to get a sample average of 35 or more customers if the manager had not offered the discount?

This is 1 subtracted by the pvalue of Z when X = 35.

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{35 - 30}{2.6832}\)

\(Z = 1.86\)

\(Z = 1.86\) has a pvalue of 0.9686

1 - 0.9686 = 0.0314

0.0314 = 3.14% probability to get a sample average of 35 or more customers if the manager had not offered the discount

Answer:

$1.76

Step-by-step explanation:

$1.10+$1.10 = $2.2

$3.96 - $2.2 = $1.76

The function g( x ) is translated to the left by 9 units and down by 5 units.

Given data ,

Let the first function be represented as f ( x )

where the value of f ( x ) = | x |

Let the translated function be g ( x )

where the value of g ( x ) = | x + 9 | - 5

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

On translating to the left , f ( x + a )

So , the function f ( x ) is translated 9 units to the left by f ( x + 9 ) = | x + 9 |

Now , when the function is translated 5 units down , f ( x ) - 5

So , the translated function is g ( x ) = | x + 9 | - 5

Hence , the function is translated to the left by 9 and up by 5 units.

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The values that used to create the box and whisker plot

[using these values]

Minimum value: Lower whisker: 12

Q1: 23.5

Q2 (median): 36

Q3: 46

Maximum value: Upper whisker: 56

Here, we have,

Step 1: Order the data set from smallest to largest:

12, 19, 28, 32, 34, 38, 45, 47, 50, 56

Step 2: Calculate the lower quartile (Q1), median (Q2), and upper quartile (Q3):

Q1 (25th percentile): The value that separates the lowest 25% of the data from the rest. Since we have 10 data points, the first quartile will be the average of the 2.5th and 3.5th data points. In our case, it's the average of the 2nd and 3rd data points:

Q1 = (19 + 28) / 2 = 23.5

Q2 (50th percentile or median): The value that separates the lowest 50% of the data from the rest. Since we have an even number of data points, the median will be the average of the 5th and 6th data points:

Q2 = (34 + 38) / 2 = 36

Q3 (75th percentile): The value that separates the lowest 75% of the data from the rest. Since we have 10 data points, the third quartile will be the average of the 7.5th and 8.5th data points. In our case, it's the average of the 7th and 8th data points:

Q3 = (45 + 47) / 2 = 46

Step 3: Calculate the interquartile range (IQR):

IQR = Q3 - Q1 = 46 - 23.5 = 22.5

Step 4: Determine the whiskers:

Lower whisker: The smallest value that is not smaller than Q1 - 1.5 * IQR

Upper whisker: The largest value that is not larger than Q3 + 1.5 * IQR

Lower whisker limit: 23.5 - 1.5 * 22.5 = -10

Upper whisker limit: 46 + 1.5 * 22.5 = 79.5

Our data points are all within these limits, so the lower whisker is at the smallest value, 12, and the upper whisker is at the largest value, 56.

Now, you can plot the box and whisker plot using these values:

Minimum value : Lower whisker: 12

Q1: 23.5

Q2 (median): 36

Q3: 46

Maximum value: Upper whisker: 56

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create a box and whisker plot for the following set of data

12, 19, 28, 32, 34, 38, 45, 47, 50, 56

Answer:

y = 0.45x

Step-by-step explanation:

proportional relationships must pass through the point 0,0

both the x and y intercepts must equal 0