1. In Part A of this lab, you will measure the dimensions (length, width, diameter) of several geometric shapes. a. Using a ruler, you measure the length of a rectangle to be 12.75 cm and the width to be 3.64 cm. Calculate the area of this rectangle (show work), reporting your answer to the correct number of significant figures.

Answer:

y=x/3+5, y=x/3+3

Step-by-step explanation:

Line 1 : The gradient would be (7-3)/(6-(-6))=4/12=1/3, Therefore the answer is y=x/3+5

Line 2: The gradient would be (1-2)/((-6)-(-3))=(-1)/(-3)=1/3, Therefore the answer is y=x/3+3

Answer:

249

Step-by-step explanation:

We can see that the difference of every term in the given sequence is 9, because -12 + 9 = -3, -3 + 9 = 6 and 6 + 9 = 15. We may therefore assume that the sequence is arithmetic (a fancy word of saying that a sequence is increasing with a constant value every term).

Since the difference of every term is 9, we know that the explicit form of the sequence (where the value of every term is expressed in terms of the term number) is in the form \(9n+c\), where \(n\) is the term number and \(c\) is a constant we are going to figure out right now.

We know that the first term of the sequence is -12, so we see that\(9(1) + c = -12\) and hence \(c=-21\). Therefore, the 30th term of the sequence is \(9(30) - 21 = 249\).

The answers are:

\(m \angle1+ m\angle2 + m\angle3=180^o\)  is the sum of interior angles in a triangle.

\(m \angle1+ m\angle5 = m\angle AYX\) is Definition of parallel lines.

\(m \angle AYX+m\angle 4=180^o\) Definition of a straight angle

\(m\angle5=m\angle2\) is Substitution

\(m \angle1+ m\angle5 + m\angle4=m \angle AYX+m\angle 4\) Substitution

An angle in geometry is the measurement of the amount of rotation that occurs between two lines, rays, or line segments that have a shared endpoint, or vertex. Angles are expressed in terms of degrees, radians, or other angular measuring units.

A protractor, a tool with a semicircular or circular scale and degree markings, can be used to measure angles. Angles may also be labelled using symbols, such as ∠ABC or ∠PQR, in which the letter in the middle of the symbol designates the vertex of the angle.

An auxiliary line that is parallel to XZ given is the triangle formed by XYZ and AY.

\(m\angle 1+m\angle 2+m\angle3=180^o\) Definition of the sum of interior angles in a triangle

\(m\angle1=m\angle AYX\) Corresponding angles are congruent (alternate interior angles)

\(m \angle 2 = m \angle 4\) Corresponding angles are congruent (alternate interior angles)

\(m \angle AYX + m \angle 4 = 180^o\) Definition of a straight angle

\(m \angle 1 + m \angle 5 = m \angle AYX\) Definition of parallel lines

\(m \angle 5 = m \angle 2\) Substitution

\(m \angle 1 + m \angle 2 + m \angle 3 = m \angle 1 + m \angle 5 + m \angle 4\) Substitution

\(m \angle 1 + m \angle 5 + m \angle 4 = m \angle AYX + m \angle 4\) Substitution

\(m \angle 1 + m \angle 2 + m \angle 3 = m \angle AYX + m \angle 4\) Transitive property of equality

\(m \angle 1 + m \angle 2 + m \angle 3 = 180^o\) Substitution

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The set of input values (x-coordinates): (-7, -3, 0, 5) and the set of output values (y-coordinates): (1, 2, -2, -5) make up the domain and range of this set of ordered pairs.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input.

After we enter an x value, the function outputs this sequence of values.

So, we have the ordered pair:

{(-1, 2), (0, 5), (2, 7)}

Now, get the domain and range as follows:

The set of input values (x-coordinates): (-7, -3, 0, 5) ⇒ Domain

The set of output values (y-coordinates): (1, 2, -2, -5) ⇒ Range

Therefore, the set of input values (x-coordinates): (-7, -3, 0, 5) and the set of output values (y-coordinates): (1, 2, -2, -5) make up the domain and range of this set of ordered pairs.

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The value of n that will make the expression equal is 13

Equations are expressions separated by equal sign

Given the equation

11n = 143

Divide both sides by 11 to have;

11n/11 = 143/11

n = 13

Hence the value of n that will make the expression equal is 13

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More than once a week: 0.11

Once a week: 0.51

Every other week: 0.26

Every three weeks: 0.05

Less often than every three weeks: 0.07

To make a relative frequency distribution, follow these steps:

Count the number of occurrences of each category in the data. In this case, 11% of the 251 participants responded "more than once a week", so the number of occurrences for this category is 0.11 * 251 = 27.61 (rounded to 28). Similarly, 51% of the participants responded "once a week", so the number of occurrences for this category is 0.51 * 251 = 127.51 (rounded to 128). And so on for the other categories.

Divide the number of occurrences for each category by the total number of participants. In this case, the total number of participants is 251, so the relative frequency for "more than once a week" is 28 / 251 = 0.11. The relative frequency for "once a week" is 128 / 251 = 0.51. And so on for the other categories.

And that's it! These are the relative frequencies for each category in the data.

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Answer:

A

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (4, 1 ) and r = 2 , then

(x - 4)² + (y - 1)² = 2² , that is

(x - 4)² + (y - 1)² = 4 ← equation of circle

Answer:

d = 24

Step-by-step explanation:

1.25 = 3d/96 + 2d/96

1.25 = 3d + 2d / 96

1.25 = 5d/96

96 • 1.25 = 96 • 5d/96

96 • 1.25 = 5d

120 = 5d

120/5 = 5d/5

d = 24

Answer: 18

Step-by-step explanation:

\(\triangle HJK \cong \triangle HLK\) by HL. Therefore, \(JK=2\) by CPCTC.

Using the segment addition postulate, \(GK=9\).

Furthermore, \(\triangle HGK \cong \triangle HMK\) by HL. This means that \(MK=9\) by CPCTC.

Using the segment addition postulate again, \(GM=9+9=18\).

Given:

Here given values are area of parallelogram is 43

AB=7 cm

BC=9 cm and ABC<90

Required:

We need to find ABC

Explanation:

We know that the opposite sides of parallelogram are same so here AB=CD and BC=AD

AB=CD=7 cm and BC=AD=9 cm

Let me draw a figure

So here similarly opposite angles are also same

means A=C and B=D and angle on the same side means A , B and C , D are supplementary means addition is 180

here we have to find B so for B

we have formula for area

Area=AB*BC*sinB

Final Answer:

B=43.04 which is less then 90

Answer:

Step-by-step explanation: m=s-c/c

Answer:

20 for both

Step-by-step explanation:

hope this helps

f(x) is a linear function, so both the domain and the range are the set of real numbers.

The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.

To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.

Given the table:

X: 2 0 4

Y: -4 3 1

We can plot these points on a graph and see that they form a straight line.

Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.

Based on the given options, we can now evaluate each equation to see which one represents the line:

Y = 1/2x + 5

When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.

Y = -1/2x + 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.

Y = 2x - 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.

Y = -4x + 2

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.

In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.

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Answer:

x = 5

Step-by-step explanation:

4|0.5x - 2.5| = 0

|0.5x - 2.5|  = 0 / 4

0.5x - 2.5 = 0

0.5x = 2.5

x = 2.5 / 0.5

x = 5

There are a total of 3 forwards on the team.

A fraction represents a part of the whole or group of objects.In a fraction, numerator and denominator are separated by a horizontal bar known as the fractional bar

Given:

2/8 of the players are forwards.

Total number of players on the team = 12

We will determine the total number of forwards on the team by multiplying the total number of players by the fraction representing the forwards.

Fraction representing the forwards:

= 2/8

= 1/4

Total forwards on the team:

= 12 * (1/4)

= 3.

Translated question:

Of the 12 players on the team, 2/8 are forwards. What are the total forward in the team?

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Answer: We have f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

                        (f-g)(x)= 3x⁵-2x⁴-x²+x-21

Step-by-step explanation:

Here we have,

Given : f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

We know,

(f-g)(x)= f(x)-g(x)

= (3x⁵+6x²-5 ) - ( 2x⁴+7x²-x+16)

On subtracting g(x) from f(x) we get,

(f-g)(x)= (3x⁵+6x²-5  - 2x⁴-7x²+x-16)

On simplify,

 (f-g)(x) =3x⁵-2x⁴-x²+x-21

Hence,

(f-g)(x) = f(x) - g(x) = 3x⁵-2x⁴-x²+x-21

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Answer:

<6 and <4

Step-by-step explanation:

Complemetary angles are angles that their measure add up to 90 degrees

the angles meet this requirment in this image are angle <6 and angle <4

The number of people that like sausage or mushrooms as shown in the Vann diagram is 30.

Venn diagrams are diagrams used to visually depict sets, relationships between sets, and operations on sets

To determine the number of people that like sausage or mushrooms from the Vann diagram, we use the Formula below.

Formula:

n (S ∪ M) = n (S) + n (M) − n (S ∩ M) ................. Equation 1

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the people who like sausage or mushrooms is 30

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Answer:

Step-by-step explanation:

The angle of depression is the downward angle the air traffic controller

looks down from in the tower.  It also equals the angle of elevation which is the angle formed by the runway and the line of sight.

With this information you can find the remaining angle:

180 - (90 + 18)

180 - 108 = 72

Let Angle B = 72°

Angle A = 18°

Angle C =90°

We have one side - 140 feet - this is side a - it is across from angle A.

There is a right triangle formed by the runway (side b) the tower, side a, and the line of sight (side c)

Using the law of sines:

sin A/a = sinB/b

sin 18°/a = sin72°/b

.3090/140 = .9510/x

cross multiply and then divide

140 × .9510/.3090

133.14/.3090

430.873 ft

round to a tenth = 430.9 ft

Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160

Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units

Answer:

45 hihihihihihihihihihihihih

Step-by-step explanation:

Answer:

Your answer doesnt say how much the beetle wighs, probably the grasshopper though

Step-by-step explanation:

a ) Construction of stem and leaf display of the data is:

For n = 129 and with splint unit = 0.1, the stem and splint map of the given data on Shower- inflow rate( L/ min) is as follows

a stem-and-leaf display of the data.

   Stems                                                Leaves

       2                                                       28

       3                                                1344567789

       4                                                 01356889

       5                                          00001114455666789

       6                              0000122223344456667789999

       7                                     00012233455555668

       8                                                02233448

       9                                         012233335666788

      10                                             2344455688

      11                                                2335999

      12                                                     17

      13                                                      9

      14                                                     36

      15                                                  0035

      16                                                  None

      17                                                  None

      18                                                     3

b) From brume and splint map we note that minimal Shower inflow rate is2.2 whereas outside is18.3 L/ mim. farther typical or representative rate is7.0 L/min.

c) The display of data on steam and leaf chart shows that data is positively skewed means concentration of data on left side or lower value side is high as compared to other side.

d) Distribution is not symmetric rather very clear positive skew ness is observed through steam and leaf chart. Even distribution is Unimodal.

e) From steam and leaf chart is indicative to conclude that the highest observation 18.3 is outlier.

A stem and splint plot, also known as a stem and splint illustration, is a way to arrange data so that it's simple to see how constantly colorful feathers of values do. It's a graph that displays ordered numerical data. A stem and a splint are divided into each piece of data.

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Complete question:

The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses:

4.6 12.1 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.1

11.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.5

7.5 6.2 5.8 2.8 3.4 10.4 9.8 6.6 3.7 6.4

8.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.9 6.2

5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3

7.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.3 7.2

5.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.2

8.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.7

5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6

10.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.6

7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.3

9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2

8.3 3.1 4.9 5.0 6.0 8.2 6.3 3.8 6.0

(a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

Stems Leaves

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

(b) What is a typical, or representative, flow rate?

L/min

(c) Does the display appear to be highly concentrated or spread out?

highly concentrated, except for a few values on the positive sidehighly concentrated in the middle highly concentrated, except for a few values on the negative sidespread out

(d) Does the distribution of values appear to be reasonably symmetric? If not, how would you describe the departure from symmetry?

Yes, the distribution appears to be reasonably symmetric.No, the data are skewed to the right, or positively skewed. No, the data are skewed to the left, or negatively skewed.No, the distribution of the values appears to be bimodal.

(e) Would you describe any observation as being far from the rest of the data (an outlier)?

Yes, the value 2.2 appears to be an outlier.Yes, the value 15.5 appears to be an outlier. Yes, the value 18.3 appears to be an outlier.No, none of the observations appear to be an outlier.

Answer:

113 points per game

Step-by-step explanation:

8 basketball games

904 points in total

How many did they score per game?

______________________________

We know the Warriors scored 904 points at the end of the day, whilst having 8 basketball games said same day.

We need to split this equally to find our answer.

Divide the amount of points to the amount of games played :

904/8

113 points per game

Answer: y = -3x - 6

Step-by-step explanation:

One way to write a linear equation is with slope-intercept form.               Slope-intercept form is y = mx + b, where m is the slope, and b is the              y-intercept.

Thus, the equation is y = -3x - 6

Hope it helps :) and let me know if you are confused anywhere.

Answer:

y = -3x - 6

Step-by-step explanation:

Insert the information into the slope-intercept form equation:

y = mx + b

In this instance, the slope is -3 and the y-intercept value is -6. Therefore, the equation of the line is y = -3x - 6

The probability that all 4 computers with the critical file fail in this incident

P(x=4)=0.00085

This is further explained below.

Generally,  is  mathematically given as

\($H \rightarrow(n, m)$\)

p.d.F. of Hyper Geometric distribution

given, $N=39, n=4, M=8, x=4$

\(\begin{aligned}P(x=4) &=\frac{8}{4} \frac{39}{39} \\&=\frac{70 \times 1}{82251}\end{aligned}$$\)

\(\begin{aligned}&P(x=4)=8.5106 \times 10^{-4} \\&P(x=4)=0.00085\end{aligned}\)

In conclusion, P(x=4)=0.00085

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Answer:

Step-by-step explanation:

3) Mr. Bee

Homework papers : Exit tickets = 20 : 8

                                                    = 5 : 2

Mr. Carter

Homework papers : Exit tickets = 50 : 32

                                                     = 25 : 16

No, they are not equivalent ratios.

4) Cost of six pack of drinks =  $ 2.99

Unit rate = 2.99 ÷ 6

              = $ 0.50

No, her sister was wrong and the unit rate is $ 0.50

5) Cost of 3 lb = $ 1.89

Unit rate = 1.89 ÷ 3 = $ 0.63

Cost of  5 lb = $ 2.49

Cost of 1 lb = 2.49 ÷ 5  = $0.50

0.63 > 0.50

Best buy : 5 lb apples for $2.49

6) 6 bagels for $ 4.20

Unit rate = 4.20 ÷ 6  =$ 0.70

12 bagels  = $ 7.80

Unit rate = 7.80 ÷ 12 = $0.65

0.70 > 0.65

Best buy: 12 bagels for $ 7.80

Answer:

$50.00 is the discount price