z
Note: Figure is not drawn to scale,
If x = 4 units, y = 17 units, and z = 3 units, then what is the surface area of the rectangular prism shown above?
OA.
131 units
OB. 330 units
C.
204 units
D
262 units2

The mean for a given set of observations is 10.

The mean is the average of a set of variables in mathematics and statistics. The mean may be calculated in a variety of methods, including the simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean. A data set's mean (average) is calculated by summing all of the numbers in the set and then dividing by the number of values in the set. When a data collection is arranged from least to largest, the median is the midway value. The mode is the number that appears the most frequently in a data collection.

Here,

given set of observation,

=2,4,6,8,10,30

=(2+4+6+8+10+30)/6

=10

The mean for given set of observation is 10.

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Answer:

222222222222222222222%

Answer: A = 67%

Step-by-step explanation:

Three commonly used types of graphs are bar graphs, Pie Chart, and line graphs. Every sort of graph is appropriate for displaying a one-of-a-kind kind of records.

Graph:

The term graph is a pictorial illustration of facts in an organized way. Charts are normally fashioned from different data factors that represent the link among two or more matters.

Bar Graph:

A bar graph is a chart that displays complete data in rectangular bars, with the height of the bars proportional to the values ​​they represent. Chart bars can be displayed vertically or horizontally. A bar chart, also called a bar chart, is a graphical representation of grouped data. It is a method of data processing. Bar Graph are great for displaying data independent of each other and do not need to be in any particular order when displayed. Bars provide a visual indicator for comparing amounts in different categories. A bar chart has two lines, the horizontal and vertical axes (also called x-axis and y-axis), a title, labels, and a scale range.

Pie Chart:

Pie Chart is a chart type that visually represents data in a pie chart. It is one of the most commonly used charts for representing data with attributes of circle, sphere, and angle data to represent real-world information. The shape of the pie chart is circular, the circle represents all the data and the slices of the pie represent portions of the data and are plotted separately.

For Example: A full circle represents a value of 100. Divided into 10 slices or sectors. Different colors represent the ingredients used to prepare the cake. What is the exact amount of each component represented by a particular color in the pie chart below?

Solution: As you can see, the pie he is divided into 10 segments or sectors. To calculate the exact amount of ingredients added to the cake, divide the value across sectors.

H. 100 in sectors. So 100 ÷ 10 = 10.

Line graph:

A line chart is a graphical representation of changes that occur over a period of time. A line chart has a horizontal axis called the x-axis and a vertical axis called the y-axis. The x-axis usually has a period of time that measures the quantity of a particular thing or item on the y-axis. Line charts are useful for analyzing trends, whether the quantity on the y-axis is increasing or decreasing over time. A line chart clearly shows an uptrend or a downtrend.

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Answer:

[tex]y=\frac{1}{2}x+4[/tex]

Step-by-step explanation:

[tex]y-3=\frac{1}{2}(x+2) \\ \\ y-3=\frac{1}{2}x+1 \\ \\ y=\frac{1}{2}x+4[/tex]

Answer: y = 1/2 x + 4

Step-by-step explanation:

1) They gave you the slope so: y= 1/2x + b

2) Goes through point (-2,3) so: 3 = 1/2(-2) + b

3) 3 = -1 + b

4) b = 4

5) answer: y = 1/2x + 4

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The square root of 4 is 2 (2 x 2 = 4). This implies 4 is perfect square of 2.

Hence square root of 4 is not an irrational number.

What is an irrational number?

An irrational number is one that cannot be represented by whole numbers and/or fractions (also called ratios)  is an irrational number because those decimals just go on and on and there is no pattern to be represented by a fraction. Many square roots are also irrational numbers.

According to the given question:

The square root of 4 is 2 (2 x 2 = 4). This implies 4 is perfect square of 2. Squaring of 2 gives 4 and square root of 4 gives 2. 2 is a rational number i.e. it can be represented in p/q form.

Hence square root of 4 is not an irrational number.

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1. Always (by definition)

2. Always (triangle inequality)

3. Always (Pythagorean theorem)

4. Sometimes (take x=y=1 and x=4, y=3)

5. Never (by definition)

6. Sometimes (Only if area = circumference)

7. Sometimes (Consider when scale factor = 1)

8. Never (Lines extend infinitely)

9. Sometimes (Only if both angles are right angles)

10. Always (Angle-angle similarity)

By applying concepts of Quadratic Inequality and applying on graphs option C is correct.

A quadratic inequality of the form

y>ax^2+bx+c

(or substitute <,≥ or ≤ for > ) denotes a section of the plane enclosed by a parabola.

Graphing the parabola is the first step in graphing a quadratic inequality. Then, depending on the inequality, fill in the area either above or below it.

If the inequality symbol is ≤ or ≥ , then the region includes the parabola, so it should be graphed with a solid line.

Otherwise, a dotted line should be drawn around the parabola to show that the region excludes the border if the inequality symbol is either <or >.

If it is > then the region above the dotted line is taken and if it is < the region below it is taken.

In the given question

y>(x-3)^2-1;

So the region above the dotted line should be taken which is option C.

By applying concepts of Quadratic Inequality and applying on graphs option C is correct.

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The coefficient of variation is 200%.

The coefficient of variation is the ratio of the standard deviation to the mean. One form of measure of dispersion is the coefficient of variation. A number called a measure of dispersion is used to assess the degree of data variability. As a result, the coefficient of variation is used to assess how much data deviate from the mean or average value. The acronym CV stands for coefficient of variation.

Given that,

Arithmetic mean = 10
Standard deviation = 20

Therefore of coefficient of variation is SD/AM*100 = 20/10*100 = 200%

Hence, the coefficient of variation is 200%.

Correct question: If the arithmetic mean is 10 and the standard deviation is 20 then what is the coefficient of variation?

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The complete table is solved and shown below.

Given is to complete the output table as given.

Now, we can write -

for [x] = - 4,   y = - 3

for [x] = - 3, y = - 1 =  {- 3 + 2}

for [x] = 1, y = 1 + 2 = 3

for [x] = 2, y = 2 + 2 = 4

for [x] = 5, y = 5 + 2 = 7

Therefore, the complete table is shown and solved above.

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The number of siblings is 41.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

we have given,

The graph represents the number of siblings each student in a class.

the graph which represents the frequency of the number of students on the y-axis and the number of siblings on the x-axis.

Number of siblings = (0 * 6) + (1 * 7) + (2 * 4) + (3 * 2) + (4 * 5)

= 41

Hence, the number of siblings is 41.

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Answer:

[tex]x=5[/tex]

Step-by-step explanation:

[tex]x+3=8\\x=8-3\\x=5[/tex]

[tex]{\huge{G = \frac{P-2M}{2} }}[/tex]

Since, The given line is the line which is parallel to the y-axis that is a vertical line, It makes 90 degree with the positive x-axis, The slope is undefined that is tan(90).

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

x=-4

This is a vertical line parallel to y-axis.

It makes 90 degree with positive x-axis in anti-clockwise direction.

slope = tan(90) = undefined.

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The total cost before the sales tax was 19.828 pounds.

For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.

We have to determine the total cost before sales tax.

As per the question, we have prices as:

cost of turkey = 3.95 per pound

cost of egg cheese = 1.3 per pound

cost of egg salad = 0.89 per pound

The total cost of turkey = 3.8 × 3.95  = 15.01 pounds

The total cost of cheese = 2.2 × 1.3 = 2.86 pounds

The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds

The total cost before sales tax = 15.01 + 1.958 +2.86

Apply the addition operation, and we get

The total cost before sales tax = 19.828 pounds

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The question seems to be incomplete the correct question would be:

Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?

No, two equilateral triangles need not to be always congruent with one another .

Justification of answer:

The reason is that although an equilateral triangle's angles are all 60 degrees, their corresponding sides are not necessarily the same .

1. All 3 side of an equilateral triangles have same length .

2. All 3 angles of an equilateral triangles have same measure.

3. Each angles of an equilateral triangles is 60 degree .

4. Area of equilateral triangles = [tex]\frac{\sqrt{3} }{4} *a^2[/tex]

5 . Perimeter of an equilateral triangles = 3*a

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Answer:

To get from Trisha's house to Brandon's house, Trisha should first walk 2 blocks west and 4 blocks north to get to school. From there, she should walk 4 blocks east and 2 blocks south to get to Brandon's house. This means that Trisha should follow the following directions to get from her house to Brandon's house:

Walk 2 blocks west

Walk 4 blocks north

Walk 4 blocks east

Walk 2 blocks south

These directions will take Trisha from her house to Brandon's house.

Step-by-step explanation:

Answer:

2 and 6 (A)

Step-by-step explanation:

The true equations among the given expression are

True equation has same value at the left hand side and the right hand side of the equations after simplifying

The true equation is shown below

48 ÷ 8 + 2³ = 5 + 3²

applying PEMDAS

Exponents

48 ÷ 8 + 8 = 5 + 9

Division

6 + 8 = 5 + 9

Addition

14 = 14

(8 * 7) / 2 − 12 = 22 − 2 * 3

Parenthesis

56/2 - 12 = 22 - 2 * 3

Division

28 - 12 = 22 - 2 * 3

Multiplication

28 - 12 = 22 - 6

Subtraction

16 = 16

since the values in LHS = RHS the both equation are true

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Linear equations are easy to solve .They are a type of mathematical equation that involve one or more variables, in which all terms are of the first degree.

The general form of a linear equation is Ax + B = C, where A, B and C are numerical coefficients and x is a variable. Linear equations can be solved by first rewriting the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Then, the y-intercept can be determined by substituting in a value for x and solving for y. To find the slope, two points on the line must be chosen, and the formula            m = (y2 - y1)/(x2 - x1) is used to calculate the slope. Once the slope and y-intercept are known, the equation can be written in its slope-intercept form and solved for x.

Linear equations can also be solved using the substitution method, where one of the variables is substituted with a numerical value. This method can be used when the equation is already written in its standard form, Ax + B = C. By solving for x, the value of x can be found and substituted back into the equation to find the value of C.

Finally, linear equations can also be solved using the elimination method, which is used when there are two linear equations with two unknowns. The two equations are added together, and the coefficients of one of the variables are eliminated. This method is useful for solving systems of linear equations.

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Volume of the rectangle is estimated as;

Volume =  length x width x height

A three-dimensional object's volume is a measurement of the amount of space it occupies. We'll look at the procedure for calculate a box's volume on this page.

The size of a box:

View the box illustration below:

As you can see, there are three dimensions to take into account when dealing with a box or other three-dimensional object: length, width, and height.

Thus, the volume is calculated using the formula length x width x height:

V = l x w x h

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An example of discontinuous change is an adolescent experiencing puberty.

The term "discontinuity" is used in the literature on behaviour in a number of distinct contexts. It should specifically relate to a rapid change in a system's properties.

A discontinuity is stated to have happened when a two-month-old human infant's attention, vocalisation, and sniffing scores do not predict their scores on the same test at four months. "Discontinuity" is also used to describe the rearrangement of rank on a specific measure.

The first twenty years of a person's life are when discontinuous change is most noticeable, such as during birth and puberty. These gaps in continuity are not puzzling. Many biological and physical systems have the capacity to change abruptly and discontinuously.

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When a human infant's attention, vocalization, and sniffing scores at two months do not predict their results on the same test at four months, a discontinuity is said to have occurred. Rearranging rank on a certain measure is referred to as "discontinuity."

Discontinuous change is most apparent throughout a person's first twenty years of life, such as during puberty and childbirth. These discontinuities are not mysterious. Many biological and physical systems are capable of rapid, discontinuous change.

A unit rate's component is always 1. To find the unit rate, divide the fraction by the fraction such that the denominator is equal to one.

The meaning of math units:

Of mathematics, a unit can be thought of as the right side point in a number or the number one. In this instance, the unit number in the number 6713 is 3. A unit is also a term that may be used to describe the common measurement units.

The dimensions of a unit:

The area of a unit as depicted on the subdivision or annexation map that created the unit is referred to as its size. The lot, tract, or parcel size divided by the number of dwellings is the unit size for two-family and multiple-family homes on a single unit.

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The best graph to present the data is Multiple bar diagram

The term graph in math refers easiest ways to represent data is using graphs. And it is also used to compare different values, understand how different parts impact the whole, or analyze trends.

By using the graph you can easily understand the data.

Basically, the types of graph that are suitable for specific data depends on the nature and the given conditions of the data.

Here we have some mostly used types of diagrams used to represent data are line diagrams, bar diagrams, semi-logarithmic charts, multiple bar diagrams, subdivided bar diagrams, pie diagrams, stem and leaf plots, box plots, and ogives.

Here the best graph to display the data is a Multiple bar diagram (MBD).

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the probability that the two cards dealt to Satara (without replacement) will both be hearts is 7%

Total Number of cards left in the deck = 10

Number of hearts left in the deck = 3

Probability = (required outcome / Total possible outcomes)

Required outcome = hearts card in the deck

Without replacement, deal Satara two cards as follows:

The chance that the first card is a heart:

P(first card being hearts) = necessary result / all possible results

P(first card is a heart) equals 3/10.

The probability that the second card is a heart:

It cannot be replaced because:

Required result = (3 - 1). = 2

The total number of outcomes is (10 - 1) = 9 P(the second card is a heart) = 2 /9

The likelihood that the two cards are hearts is (3/10 x 2/9) = 6/90 = 0.0666 x 100% = 6.66%

= 7% (nearest whole number)

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Answer:D

Step-by-step explanation:

The extent of the variations that could occur or the dividing lines between them several styles and prices across the steel spectrum. the scale or extent of a procedure, move, or activity.

The statistical range for a certain data collection is the range of values between the highest and lowest values. Comparing the top and lowest observational values also allows one to visualize the range. By deducting the greatest value from the lowest, the sample interval is determined. The sample range is a critical indicator of variability for variables with continuous variation.

here ,

There is a range of values between the lowest and highest. The lowest and greatest values in the example are 2 and 9, respectively.

Therefore, the range is 9 x 2 = 8.

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The total balance he will have in the accounts at the end of 2 years will be $870.88. The correct option is D.

In most cases, simple interest paid or received over a specific time period is a fixed percentage of the principal amount borrowed or lent. Borrowers must pay interest on interest as well as principal because compound interest accrues and is added to the accumulated interest from previous periods.

Given that Thomas deposited $450 into an account that pays 4.5% simple interest and deposited $350 into an account that pays 4.25% compounded annually.

The simple interest is calculated as,

SI = ( 450 x 4.5 x 2 )

SI = $40.5

Amount = 450 + 40.5

Amount = $490.5

The compound interest will be calculated as,

A = 350 ( 1 + 0.0425 )²

A = $380.38

The total balance in the account after 2 years will be,

Total balance = $490.5 + $ 380.38

Total balance = $870.88

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The system of equations has "no solution" because they are parallel lines.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

In general, any equation of the form y = k, where k is a constant, represents a horizontal line that extends indefinitely in both directions.

The system of equations y = 0 and y = -5 describes two lines in the coordinate plane.

The first equation, y=0, is the x-axis.

The second equation, y=-5, is a horizontal line 5 units below the x-axis.

As we know, y = 0 and y = -5 are two parallel lines.

Therefore, no solution exists.

Hence, the system of equations has no solution.

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Answer:

3

Step-by-step explanation:

"Real zeros" are x-intercepts. So this graph crosses the x-axis three times. There are three real zeros.

Generally, you can (sloppy interpretation) interchange the words: zeros, solutions, roots and x-intercepts.

For any questions that ask for these, change y or f(x) to zero and solve it.

Simplifying 3 to the 3rd power gives 27.

Raising a base number to an exponent is referred to as "power" in mathematics. It indicates that "base number" and "exponent" are the two fundamental components of powers. The exponent shows how many times the base number has been multiplied, whereas the base number is defined as a number that is multiplied by itself. In a nutshell, power is a number that has exponents used to express it. It means that the same element has been multiplied repeatedly. In the context of powers, the following specific terminology may be used:

Whenever a number:

Squared – power is 2

cubed – Power is 3

“to the power of” – used for powers more than 3

3 to power 3= [tex]3*3*3=27[/tex]

Simplifying 3 to the 3rd power gives 27.

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