The length of the base of the plot is 12 feet, and the length of one side is 5 feet, as shown in the diagram. Tammy makes a scale drawing of
the plot using a scale of 1 inch to 2 feet. The area of the plot in the scale drawing is
square inches

Answer:

1.187991

Step-by-step explanation:

sin^2(225)−(cos(330))(cos(240))

=(−0.930095)2−(cos(330))(cos(240))

=0.865076−(cos(330))(cos(240))

=0.865076−−0.991199(cos(240))

=0.865076−(−0.991199)(0.325781)

=0.865076−(−0.322914)

=1.187991

Answer:

  2 hours, 150 miles

Step-by-step explanation:

The relation between time, speed, and distance can be used to solve this problem. It can work well to consider just the distance between the drivers, and the speed at which that is changing.

Jason got a head start of 20 miles, so that is the initial separation between the two drivers.

Jason is driving 10 mph faster than Britton, so is closing the initial separation gap at that rate.

The relevant relation is ...

  time = distance/speed

Then the time it takes to reduce the separation distance to zero is ...

  closure time = separation distance / closure speed = 20 mi / (10 mi/h)

  closure time = 2 h

Britton will catch up to Jason after 2 hours. In that time, Britton will have driven (2 h)(75 mi/h) = 150 miles.

__

Additional comment

The attached graph shows the distance driven as a function of time from when Britton started. The distances will be equal after 2 hours, meaning the drivers are in the same place, 150 miles from their starting spot.

Answer:

1/64

Step-by-step explanation:

10 = ½

20 = ¼

30 = ⅛

40 = 1/16

50 = 1/32

60 = 1/64

Answer:

0.015625 left.

Step-by-step explanation:

If we start with say 100g of the material, in 10 years there is 100 * 1/2 =

50g left   ( = 0.5 left).

In 20 years there is 100*(1/2)^2 = 25 g  left.

In n*10 years there is  100(1/2)^2 g

So in 60 years there is 100(1/2)^6 = 1.5625 g left

This is 1.5625 %

= 0.015625 of the origin material left.

Answer:

B

Step-by-step explanation:

5x - 625[tex]x^{4}[/tex] ← factor out 5x from each term

= 5x(1 - 125x³) ← this factor is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

1 - 125x³

= 1³ - (5x)³

= (1 - 5x) (1² + 5x(1) + (5x)² )

= (1 - 5x) (1 + 5x + 25x²)

Then

5x - 625[tex]x^{4}[/tex] = 5x(1 + 5x + 25x²)

Answer:

Let m be the number of muffins.

a) 4m <= 30

b) m <= 7.5, so the maximum number of muffins to buy is 7.

c) $4 × 7 = $28, so $2 will be left over.

The surface area of the pyramid is 34.8 in²

Since the figure is a square pyramid, its surface area, A = 4 × area of triangular face + area of square base.

Area of triangular face A' = 1/2bh where

So, A' = 1/2 × 4.3 in × 3 in

A' = 1/2 × 12.9 in²

A' = 6.45 in²

Area of square base A" = L² where L = length of base = 3 in

So, A" = (3 in)²

= 9 in²

Surface area of pyramid, A = 4A' + A"

= 4 × 6.45 in² + 9 in²

= 25.8 in² + 9 in²  

= 34.8 in²

So, the surface area of the pyramid is 34.8 in²

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Area of the sphere ≅ 339.62 in².

A sphere is a geometrical object in three-dimensional space that is the surface of a ball. Like a circle in a two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point in a three-dimensional space.

Area of sphere = 4[tex]\pi r^{2}[/tex]

diameter d = 2r

Given that,

diameter d = 10.4 , r =5.2 in

then, Area of sphere =  4[tex]\pi r^{2}[/tex]

                                   =   4×3.14×5.2×5.2                  

                                  ≅  339.62 in²

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Answer:

108.16 to the second power

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

thats what i got from the math i did

Using it's concept, the domain of the function is given as follows:

{x| –2 ≤ x <= 5}

The domain of a function is the set that contains all possible input values for the function.

The function described is defined for x between -2 and 5, hence the domain is given by the following interval:

{x| –2 ≤ x <= 5}

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Answer:

{x| –2 ≤ x < 5}

Step-by-step explanation:

The approximate year at which two revenues were equal is; 7.5 years

From the graph attached, we see that in the year 10, the revenue for printed ads was 2 million dollars & 3 million dollars for printed ads and online ads revenue respectively.

Thus, printed ad. Revenue line equation is;

(y - 2) = (3 - 2)(x - 10)/(0 - 10)

y - 2 = (x - 10)/-10

x - 10 = -10(y - 2)

x - 10 = -10y + 20

x - 10 = -10y + 20

x  + 10y = 30   -----(1)

At x = 12 years from the graph, we have;

12 + 10y = 30

10y = 18

y = 1.8

Thus, online ad. Revenue line equation is;

(y - 0) = ((3 - 0)/(10 - 0))(x - 0)

y = 3x/10

10y = 3x

10y - 3x = 0 -----(2)

At x = 12, we have;

10y = 3*12

10y = 36

y = 3.6

In year '12' the online ad revenue got doubled as that of printed ad revenue and afterward more than doubled.

B) The approximate year at which two revenues were equal is gotten by solving equation 1 and 2 simultaneously to get;

x = 7.5

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The exact value of cos 105° is equals to √2/4 - √6/4.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

In this case, 105 degrees, can be split into 45+60 (cos (45+60))

Use the sum formula for cosine to simplify the expression;

cos (A+B) = - (cos (A) cos (B) + sin (A) sin (B)).

The exact value of cos(60) is 1/2.

So, multiply 1/2 to cos (45) - sin (60) times sin (45).

The exact value of cos (45) is the square root of 2 over 2

(1/2) ⋅ (√2/2) - sin (60) ⋅ sin (45)

The Value of sin (60) is √3/2

(1/2) ⋅ (√2/2) - √3/2 ⋅ sin (45)

The exact value of sin (45) is √2/2

(1/2) ⋅ (√2/2) - √3/2 ⋅ √2/2

Therefore, The exact value of cos 105° is equals to √2/4 - √6/4.

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percentage of students say they have witnessed hazing and did not report it are  = 95%

No matter how voluntarily a person is to take part, hazing, initiation or deposition are all actions that are demanded of someone when they join or participate in a group and which humiliate, degrade, abuse, or imperil them.

involves humiliating a person or group. involves making fun of someone or something. involves or includes the deliberate destruction of or removal of private or public property for the purpose of affiliation with, initiation into, or as a requirement for continuing membership in an organization.

Paddling, beating, or other types of attack. Branding. consumption of disgusting substances or mixtures under duress or force.

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The athlete that has the shortest training ride is athlete A.

The athlete that has the shorter range is Athlete B.

The athlete that has the greater median is Athlete B.

The athlete that has the greater IQR is  athlete A.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers. The first whisker represents the minimum number and the second whisker represents the maximum number. The difference between the whiskers is known as range.

Range of Athlete A = 36 - 13 = 13

Range of Athlete B = 30 - 19 = 11

Training ride of  Athlete A = 16

Training ride of  Athlete B = 21

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

Median of  Athlete A = 20

Median of  Athlete B = 25

IQR of  Athlete A = 30 - 16 = 14

IQR of  Athlete B = 28 - 21 = 7

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The area that the dog can wander based on the information provided will be 931π.

From the information, we are told that the dog dog is attached to a 35-foot rope fastened to the outside corner of a fenced-in garden that measures 28 feet by 36 feet.

In this case, the dog is in an outside corner. The dog can trace 3/4 of a circle when it starts walking in a circle away form the wall.

The area that the dog can wander will be:

= 3/4(π35²) + 1/4(π(35 - 28)²)

= 3/4π(35)² + 1/4π(7)²

= (3/4 × 1225)π + (1/4 × 49)π

= 918.75π + 12.25π

= 931π

Therefore, the area that the dog can wander based on the information provided will be 931π.

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The lines are neither parallel nor perpendicular

The equations of the lines are given as

3 x minus y equals 5

3 y equals x minus 15

Rewrite the equations properly

3x - y = 5

3y = x - 15

Make y the subject in both equations

In 3x - y = 5, we have

y = 3x +  5

In 3y = x - 15, we have

y = 1/3x - 5

The slopes of the two lines are

m1 = 3

m2 = 1/3

The above values are not equal, and they are not opposite reciprocal

This means that the lines are neither parallel nor perpendicular

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The rate of change at 6 hours is -96

The function is given as:

P = 400 - 8t^2

Differentiate the function

P' = -16t

Set t = 6

P' = -16 * 6

Evaluate

P' = -96

Hence, the rate of change at 6 hours is -96

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: (h - g)(x) [/tex]

[tex]\qquad \sf  \dashrightarrow \: h(x) - g(x) [/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 2x - 6 - (2 {x}^{2} + 3x - 9)[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 2x - 6 - 2 {x}^{2} - 3x + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} - 2 {x}^{2} + 2x - 3x - 6 + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: - {x}^{2} - x + 3[/tex]

For, (h - g)(2.1), put x = 2.1

[tex]\qquad \sf  \dashrightarrow \: - {(2.1)}^{2} - (2.1) + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 4.41 - 2.1 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 6.51 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 3.51[/tex]

The figure 980 inches can be written as 980.0 inches. It contains two non-zero digits and a zero trailing before the decimal point. Hence, it has three significant figures.

Rules to Determine Number of Significant Figures:

There are three fundamental rules that one can use to determine the significant figures in any given number or value. These rules go as follows:

For the portion followed by a decimal point, zeroes at the end are not counted, but zero between two non-zero digits and zero in the initial portion of the floating point are counted while taking note of the significant figures in a decimal value.

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The volume of the given figure is 3617.3 km³

From the question, we are to calculate the volume of the given figure

The given figure is a cone.

The volume of a cone is given by the formula,

V = 1/3πr²h

Where V is the volume of cone

r is the base-radius of the cone

and h is the height is perpendicular height of the cone

From the given information,

r = 12 km

h = 24 km

Thus,

V = 1/3 × π × 12² × 24

(Take π = 3.14)

V = 1/3 × 3.14 × 12² × 24

V = 1/3 × 3.14 × 144 × 24

V = 1/3 × 10851.84

V = 3617.28 km³

V ≈ 3617.3 km³ (To the nearest tenth)

Hence, the volume of the given figure is 3617.3 km³

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Distance hour hand travel in 5 hours is 20.94 inches.

To find the distance hour hand travel in 5 hours:

Therefore, the distance hour hand travel in 5 hours is 20.94 inches.

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Answer:

C

Step-by-step explanation:

The inequalities y < 4 (x-1)² - 16 written in vertex form represents the graph region.

Option C is the correct answer.

It is a statement of an ordered relationship

- greater than,

- greater than or equal to,

- less than,

- less than or equal to between two numbers or algebraic expressions.

We have,

Inequalities where we need to find the coordinates and see which inequalities represent the graph.

y < 4 (x- 1)² - 11 ____(1)

y < -4 (x-1)² - 11 _____(2)

y < 4 (x-1)² - 16 ______(3)

From (1),

y =  4 (x- 1)² - 11

x = 0, y = 4 x 1 - 11 = 4 - 11 = -7

From (2),

y = -4 (x-1)² - 11

y = -4 x 1 - 11 = -4 - 11 = -15

From (3),

y = 4 (x-1)² - 16

x = 0, y = 4 x 1 - 16 = 4 - 16 = -12

We see that,

y < 4 (x-1)² - 16  gives us the coordinates (0, -12) on the graph.

Similarly,

x = 1, y = 4 x 0  - 16 = 0 -16 = -16

x = 1, y = 4 x 1 - 16 = 4 - 16 = -12

(1, -16) and (2, -12) coordinates are on the graph.

Thus,

The inequalities y < 4 (x-1)² - 16 written in vertex form represents the graph region.

Option C is the correct answer.

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3 /10 foot³ packing material is required to fill the box.

What is meant by volume of prism?

Volume =  base area × height

             = 9/10 × 1/3

             =  3 /10  foot³

Therefore, 3/10  foot³ packing material is required to fill the box.

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The complete question is-

An empty box is shaped like a rectangular prism. The box has a base area of 9/10 square foot and a height of 1/3 foot. How much packing material is required to fill the box?

Translating the triangle using the vector [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Translating the triangle using the vector [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.

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#43

So

200/2=100 pairs of 201

Sum

#44

400/2=200 pairs of 401

Sum

#45

800/2=400 pairs of 801

Sum

#46

2000/2=1000 pairs of 2001

Sum

Answer:

43.  20,100

44.  80,200

45.  320,400

46.  2,001,000

Step-by-step explanation:

Gauss's method

General formula for the sum of the first n integers:

[tex]1+2+3+ \dots +n=\dfrac{1}{2}n(n+1)[/tex]

Question 43

Given sum:  

Therefore, n = 200.

Substitute the value of n into the formula:

[tex]\implies \dfrac{1}{2}(200)(200+1)=100 \cdot 201=20100[/tex]

Question 44

Given sum:  

Therefore, n = 400.

Substitute the value of n into the formula:

[tex]\implies \dfrac{1}{2}(400)(400+1)=200 \cdot 401=80200[/tex]

Question 45

Given sum:  

Therefore, n = 800.

Substitute the value of n into the formula:

[tex]\implies \dfrac{1}{2}(800)(800+1)=400 \cdot 801 =320400[/tex]

Question 46

Given sum:  

Therefore, n = 2000.

Substitute the value of n into the formula:

[tex]\implies \dfrac{1}{2}(2000)(2000+1)=1000 \cdot 2001=2001000[/tex]

The points in a scatter plot cluster closely around the regression line, the correlation can be said to be the proportion of variance in Y that is determined or explained by X.

It is critical to understand that a correlation coefficient of zero indicates that there is no linear courting, but there can also nonetheless be a strong relationship among the 2 variables.

If one point of a scatter diagram is farther from the regression line than a few other factor, then the scatter diagram has as a minimum one outlier. If two or extra points are the identical farthest distance from the regression line not a commonplace prevalence), then every of those points is an outlier.

When the y variable has a tendency to increase because the x variable increases, we say there may be a high-quality correlation between the variables. when the y variable has a tendency to lower as the x variable increases, we are saying there's a bad correlation between the variables.

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The survey method was flawed since the sample was not random.

A survey is an investigation that is carried out on a sample of a population. However, for the sample to be representative of the population,  care must be taken to pick the participants in the survey at random. The principal ought to have carefully crafted a method in which the sample can be selected in a randomized manner.

For instance, the principal could have decided to take the fifth student in every row in all the classes in the school. In that way, the sample would be adequately randomized hence the result of the survey would be adjudged as representative of the situation in the entire population and thus it will be reliable as a tool that can be used to make scientific inferences.

Thus, the survey method was flawed since the sample was not random.

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Answer: C

Step-by-step explanation:

The survey method was flawed since the sample was not random.

Answer:

  9

Step-by-step explanation:

The 79-digit number of interest can be formulated as a sum of shorter numbers whose remainders can be computed.

The expanded form of the number can be written as ...

  a_44 = 01×10^78 +23×10^76 +45×10^74 +67×10^72 +89×10^70 +...

  +10×10^68 +11×10^66 +... +43×10^2 +44×10^0

Each number except the last is multiplied by a power of 10. Powers of 10 modulo 45 are ...

  10 mod 45 = 10

  100 mod 45 = 10

This lets us conclude that any positive power of 10 mod 45 is 10.

In short, all of the multiplication by powers of 10 can be collapsed to a single multiplication by 10. Hence, the mod 45 value of a_44 will be ...

  a_44 mod 45 = (((01 +23 +45 +67 +89) +10 +11 +12 +... +43)×10 +44) mod 45

  = (((01 +23 +45 +67 +89) mod 45 + sum(10 .. 43) mod 45)×10 +44) mod 45

  = (((225 mod 45) +(901 mod 45))×10 +44) mod 45

  = ((0 +1)×10 +44) mod 45

  a_44 mod 45 = 54 mod 45 = 9

__

Additional comment

The result can be confirmed by a suitable calculator.

__

The sum of the 34 numbers from 10 to 43 is the product of their average value (10+43)/2 = 26.5 and their number, 34. (26.5×34) = 901.

Answer: 9

Step-by-step explanation:

we can manually do this by dividing 1234567891011121314151617181920212223242526272829303132333435363738394041424344

on the calculator. I saw multiple hate comments on the answer above, and I wanted to test it manually - it still is 9.

The (B) arithmetic mean is the best estimate of next year's return.

Therefore, the (B) arithmetic mean is the best estimate of next year's return.

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The correct question is shown below:

The ______ mean is the best estimate of next year's return. multiple choice question.

(A) the average of the arithmetic and geometric mean

(B) arithmetic

(C) geometric