An experiment consists of tossing a coin and casting a die then observing the outcomes. Describe an appropriate sample space for this experiment.

The vertical difference in height between

i. A and B = 1.55

ii. B and C = 1.27

iii. A and C. = 2.82

the angle of elevation from A to C

The vertical difference in height is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The directions describes a right angle triangle o

A and B

sin 15 = vertical difference / 6

vertical difference = 6 sin 15

vertical difference = 1.55

B and C

sin 25 = vertical difference / 3

vertical difference = 3 sin 25

vertical difference = 1.27

A and C

A to B + B to C

= 1.55 + 1.27

= 2.82

angle of elevation from A to C

sin x = 2.82 / 5

x = arc sin (2.82/5)

x = 34.33 degrees

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Answer:

Step-by-step explanation:

How many pattern block trapezoids would create for hexagons?

2 trapezoids compose a hexagon using equal-size shapes: 2 trapezoids, 6 triangles, or 3 blue rhombuses. compose hexagons using different shapes. So 2 trapezoids create 1 hexagon. This means 6 trapezoids make 3 hexagons.

The exact number of trapezoids needed to create three hexagons depends on the size and shape of the hexagons.

However, in general, you would need at least 18 trapezoids.

An hexagon is a six-sided polygon. It is made up of six equilateral triangles and six trapezoids.

If you are looking to create larger hexagons you will need more trapezoids.

Depending on the size and shape, you could need as many as 24 or more trapezoids.

An hexagon is a six-sided polygon. It is made up of six equilateral triangles and six trapezoids.

Hence, To create an hexagon using pattern blocks, you need 10 equilateral triangles and 20 trapezoids.

Therefore, to create 5 hexagons.

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Answer:

13 square units

Step-by-step explanation:

The composite figure can be decomposed into

2 semicircles each of diameter 3

1 rectangle of height 1 and length 5

1 square of side 1

Radius of each semicircle = 3/2 = 1.5 units
Area of a semicircle of radius r = 1/2 area of circle of radius r = 1/2 x π x r²
Two semicircles make a circle

So area of the two semicircles = 2 x (1/2 x π x r²) = πr² = π x 1.5²
= 2.25π = 7.07

= 7 square units rounded to nearest whole number

Area of the rectangle = width x length = 1 x 5 = 5 square units

Area of square of side 1 = 1 x 1 = 1 square unit

Total area of shaded area = 7 + 5 + 1 = 13 square units

Answer:

Your score as a percent is **92%**. Here is how I calculated it:

To convert a fraction to a percent, you need to divide the numerator by the denominator, multiply the result by 100, and add a "%" sign

In your case, the fraction is 23/25, so you need to divide 23 by 25, multiply by 100, and add a "%".

23 ÷ 25 = 0.92

0.92 × 100 = 92

92 + "%" = 92%

Therefore, your score as a percent is 92%.

Step-by-step explanation:

For the given width length ratio and perimeter of rectangle, the length of rectangle is 80 cm.

The perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.

Let the width of the rectangle be 3x, and the length be 4x (since the ratio of the width to the length is 3:4).

The perimeter of a rectangle is the sum of the lengths of all four sides, so we have:

Perimeter = 2(length + width)

Substituting the expressions for the length and width, we get:

280cm = 2(4x + 3x)

Simplifying the right-hand side, we get:

280cm = 14x

Dividing both sides by 14, we get:

x = 20

Therefore, the length of the rectangle is 4x = 4(20) = 80 cm

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1. 121 degree. 2. 15 degree. The side of the dilated triangle increases by scale factor. Here, 1.5, thus: 3. LM = (20)(1.5) = 30 4. MN = 26(1.5) = 39 5. RT = 57/1.5 = 38. 6. Triangle RST is congruent to triangle LMN.

Transformations involve the reflection, refraction, or translation of forms on a coordinate plane. Felix Klein put forth a novel perspective on geometry in the 19th century called transfinite geometry. The majority of geometric principles depend on the transmissions of objects.

Transfrmatiions enable the modification of any image in a coordinate plane. You can better understand the graphics in video games by using the mathematical laws of transmission.

As a result, the red triangle is a dilation of the blue triangle.

When triangle is dilated the angles remain the same. Thus,

1. 121 degree.

2. 15 degree.

The side of the dilated triangle increases by scale factor. Here, 1.5, thus:

3. LM = (20)(1.5) = 30

4. MN = 26(1.5) = 39

5. RT = 57/1.5 = 38

6. Triangle RST is congruent to triangle LMN.

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Answer:

To convert 6 feet into meters, first create a conversion factor to convert from feet to meters. Make sure the original unit is in the denominator, then cancel feet. Next, multiply the original measure by the conversion factor to get 1.8288 meters, or 1.83 meters if you simplified it.

Step-by-step explanation:

The percentage of the shipping crate when compared to the total weight of the shipment would be = 16%

The weight of two granite specimen = 22 pounds

The weight of the crate = 20 pounds

The weight of shipping crate = 8 pounds

The total weight of the whole shipment = 22+20+8 = 50 pounds.

Therefore the percentage of shipping crate as compared to the total weight;

= 8/50 × 100/1

= 800/50

= 16%

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The answers are a) standard deviation ≈  0.02 b) probability ≈ 0.95 c) standard deviation ≈  0.031 d) probability ≈ 0.8098 e) decrease in P = 0.1402

Given: p = 75% or 0.75

n = 450

a) The sampling distribution of the sample proportion is approximately normal with mean = 0.75 and standard deviation is [tex]\sqrt \frac{p(1-p)}{n}[/tex]

= [tex]\sqrt{\frac{0.75(1-0.75)}{450} }[/tex] = 0.02

b) [tex]\^{p} - p[/tex] = 0.04

[tex]z = \frac{\^{p} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

z = ±1.96(approx.)

p(-0.04 <  [tex]\^{p} - p[/tex] < 0.04)

=P(-1.96 < z < 1.96) = 1 - 2P(z < -1.96)

= 1 - 2(0.0250) = 0.95

c) The sampling distribution of the sample proportion is approximately normal with mean = 0.75 and standard deviation [tex]\sqrt \frac{p(1-p)}{n}[/tex]

= [tex]\sqrt{\frac{0.75(1-0.75)}{200} }[/tex] = 0.031

d) [tex]\^{p} - p[/tex] = 0.04

[tex]z = \frac{\^{p} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

z = ±1.31(approx.)

p(-0.04 <  [tex]\^{p} - p[/tex] < 0.04)

=P(-1.31 < z < 1.31) = 1 - 2P(z < -1.31)

= 1 - 2(0.0951) = 0.8098

e) Determine the difference in probabilities (of part b) and part d))

The loss in precision by decreasing the sample size 0.9500 - 0.8098 = 0.1402

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Complete question is:

In 2008 the Better Business Bureau settled 75% of complaints they received. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.75, the same as the overall proportion of complaints settled in 2008. a) Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of [tex]\overline{p}[/tex].b) Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion? c) Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of [tex]\overline{p}[/tex] . d) Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion? e) As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (b)?

Check the picture below.

By expression, x - y = x' - y' , Distance of 3rd and 4th obstacle is equal to distance of 7th and 9th obstacle.

Distance is a numerical measurement of how far apart objects or points are, it is the length along a line or line segment between two points on the line or line segment.

Given,

The distance between obstacle three and obstacle seven is the same as the distance between obstacle four and obstacle nine.

Distance of 7th obstacle = x

Let,

Distance of 9th obstacle = y

Distance of 3rd obstacle = x'

Distance of 4th obstacle = y'

Distance between obstacle 3 and 7 = x - x'

Distance between obstacle 4 and 9 = y - y'

Distance between obstacle three and obstacle four = x' - y'

Distance between obstacle seven and obstacle nine.= x - y

According to the question

x-x' = y-y'

⇒ x - y = x' - y'

Hence, Distance between third and fourth obstacle is same as distance between 7th and 9th obstacle.

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If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent by the ASA congruence condition. Hence, option a. is the right answer.

According to the definition, we know that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent by the ASA congruence condition.

Let us consider two triangles △ABC and △QRP as shown below -

So, in △ABC and △QRP, we have,

∠B=∠R

∠C=∠P

BC=RP

∴ By ASA congruence test for triangles, we get △ABC ≅ △QRP

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The complete question is -

If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent by _____ congruence condition.

a. ASA

b. AAA

c. SAS

d. RHS

Answer:

Step-by-step explanation:  (10)(A) Add and subtract polynomials of degree one and degree two. (10)(B) Multiply polynomials of degree one and degree two. (10)(C) Determine the quotient

Hope it helps =}

Answer:

b

Step-by-step explanation:

Answer:

y – 7 = 3(x – 5)

Step-by-step explanation:

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 3}(x-\stackrel{x_1}{5}) \\\\\\ y-7=3x-15\implies {\Large \begin{array}{llll} y=3x-8 \end{array}}[/tex]

The image of (2, 3) under a dilation with center at the origin and a scale factor of −3 will be (-6, -9).

What is Image of a point ?

Dilation is the process of resizing or altering an object. With the aid of the specified scale factor, it is a transformation that reduces or enlarges the objects. The initial figure is referred to as the pre-image, while the new figure acquired after dilatation is known as the image.

Given point : (2,3)

the scale factor is -3 which means the point should be enlarged by -3 times to get the desired image.

So, we can write as : (a, b) where,

     a = 2 × -3 =  -6

and, b = 3 × -3 = -9

Hence, the coordinates of the image will be (-6, -9).

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As per the ratio, the number of men on the sight-seeing tour is 4.

In the given sight-seeing tour, we are told that there were 14 people in total. We are also given the ratio of women to children, which is 5 to 2. This means that for every 5 women on the tour, there were 2 children.

To find the number of men on the tour, we need to first find the number of women and children. We can do this by dividing the total number of people by the ratio of women to children.

Let's use a variable to represent the number of sets of 5 women and 2 children. We'll call this variable "x".

So, the number of women on the tour is 5x and the number of children is 2x.

Now, we can set up an equation to find the value of x:

5x + 2x = 14

This equation represents the total number of women and children on the tour, which is equal to 14.

Simplifying the equation, we get:

7x = 14

Dividing both sides by 7, we get:

x = 2

This means that there were 2 sets of 5 women and 2 children on the tour. So, the number of women is:

5x = 5(2) = 10

The number of children is:

2x = 2(2) = 4

Now, we can find the number of men by subtracting the number of women and children from the total number of people:

14 - 10 = 4

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For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.

What is meant by temperature?

Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.

The given equation is:

[tex]C = \frac{5}{9} (F- 32)[/tex]

where C = temperature in Celsius

          F = temperature in Fahrenheit

The above equation can be rewritten as:

C = 5/9F - 160/9

Now, this is an equation of a straight line with a formula,

y = mx + c

Comparing,

m = 5/9 which is the slope of the equation.

This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.

So the option I is true.

Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.

So option II is true.

Option III is not true as is discussed above.

Therefore for the given equation of temperature, the correct option is Option D.

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Answer:

D

Step-by-step explanation:

I have nothing else to say- lol

Mr. Titus travels a total of 7476 miles annually between Charlotte, North Carolina, and New York City.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that twelve times a year, Mr. Titus makes the trip from Charlotte to New York City and back. Each round trip covers a total distance of 623 miles.

The total distance will be calculated as:-

Distance = 12 x 623

Distance = 7476 miles

Therefore, Mr. Titus' annual mileage between Charlotte, North Carolina, and New York City is 7476 miles.

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The soap used by the machine last year is 5399.76 gallons.

The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage." This percent symbol can always be changed to a fraction or decimal equivalent by using "divided by 100."

Let the soap used last year = x.

Then, according to the given condition:

4,508.8 = x (1 - 16.5%)

4,508.8 = x (83.5/100)

x = 4,508.8(100) / 83.5

x = 5399.76

Hence, the soap used by the machine last year is 5399.76 gallons.

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Answer:

Domain is x-value and range is y-values

Step-by-step explanation:

x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary, if k = 1

x = -1, y = 6, z = 1 is the solution.

Ax = [tex]\left[\begin{array}{ccc}1&1&1\\1&2&3\\1&4&7\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]

and b = [tex]\left[\begin{array}{ccc}6\\14\\30\end{array}\right][/tex]

the augmented matrix is [A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\1&2&3:14\\1&4&7:30\end{array}\right][/tex]

we need to reduce the augmented matrix [A:B] to row echelon form by applying elementary row transformations only.

operating R₂→R₂-R₁ , R₃→R₃-R₁

[A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&3&6:24\end{array}\right][/tex]

operating, R₃→R₃-3R₃

~  [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&0&0:0\end{array}\right][/tex]

which is the row echelon, form of the matrix [A:B]

we have rank of [A:B] = the number of the non zero rows in echelon form = 2

also by the same elementary transformation we get,

A ~ [tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex]

∴ rank of A = 2

since rank A = rank  [A:B] = 2 < number of unknowns

therefore, the given equation are consistent and will have an infinite number of solutions.

We see that the given system of equations is equivalent to the matrix equation

[tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]  =  [tex]\left[\begin{array}{ccc}6\\8\\0\end{array}\right][/tex]

which gives the equations x + y + z = 6 ........(1)

and y + 2z = 8 .......(2)

from (2), y = 8 - 2z, putting the value of y in (1) we get,

x = 6 - y - z = 6 (8 - 2z) z = z - 2

taking z = k, we get x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary,

if k = 1

x = -1, y = 6, z = 1 is the solution.

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The number of wires that cut from of 200 meters is 66 meters 66 centimeters.

What are the nearest two places?

The second place to the right of the decimal point, or the hundredth place, is used to round a decimal number to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.

Given the length of the wire is 200 meters.

Assume that he cuts n pieces of length 3 meters.

The length of n pieces is 3n.

Therefore the equation is

3n = 200

n = 200/3

n= 66.66

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At 9:00 a.m., the rate of people entering the amusement park is 533 people per hour, while the rate of people leaving the amusement park is 67 people per hour.

(1) At 9:00 a.m., the rate of people entering the amusement park is given by the derivative of the entering function, which is:

f'(t) = 400 + 200cos(πt/12).

At t = 9, this rate is 400 + 200cos(π*9/12) = 400 + 200cos(3π/4) ≈ 533 people per hour.

(2) At 9:00 a.m., the rate of people leaving the amusement park is given by the derivative of the leaving function, which is:

g'(t) = 200 - 200cos(πt/12).

At t = 9, this rate is 200 - 200cos(π*9/12) = 200 - 200cos(3π/4) ≈ 67 people per hour.

the complete question is :

both are measured in people per hour and the time t is measured in hours after midnight. these functions are valid for , the hours during which the park is open. at time , there are no people in the park. (1) how fast are people entering the amusement park at 9:00 a.m.? (2) how fast are people leaving the amusement park at 9:00 a.m.?

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[tex]m=15-0.75g[/tex] is the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. While the definition of an equation in English is any well-formed formula consisting of two expressions related by an equals sign, the definition of an equation and its cognates in other languages may have subtly different meanings. For instance, an équation is defined as having one or more variables in French.

According to the question,

Total money = $15

The games at the arcade cost $0. 75.

Let total amount of money be 'm' and arcade games played by him be 'g'.

Now,

Equation to represent the remaining money,

[tex]m=15-0.75g[/tex]

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Answer:

6 students must play both piano and guitar

A statement which best describes the graph of y ≥ -x² + 8x - 2 include the following: B. The vertex is at (4, 14). The parabola is a solid line that opens down. Shading is above the parabola.

Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, we can logically deduce that the graph is a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).

By critically observing the graph of the given quadratic function, we can logically deduce that the solutions (roots) and vertex are as follows;

x = 0.258, y = 0.

x = 7.742, y = 0.

Vertex = (4, 14).

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The probability of the intersection of two events occurring can never be more than the probability of the union of two events occurring.

False.

It should be stated that the likelihood of the intersection of two events occurring is always less than the likelihood of the events occurring together.

It is always less likely than or equal to the likelihood of either event occurring alone for an intersection of two events, which is the chance that both occurrences take place.

In other words, the probability of the intersection and the probability of the union are subsets of one another.

The chance of the intersection of two events occurring can never be greater than the likelihood of the union of two events occurring, hence that is the right statement.

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Answer: I agree with Moriah. If two equations represent the same proportional relationship, then they should have the same constant of proportionality. In this case, the constant of proportionality in p = 1.5 and 2/3p = q is different, so the two equations cannot represent the same proportional relationship.

It's possible that the two equations represent two different proportional relationships, but without more information it's impossible to determine if that is the case.

Step-by-step explanation:

Answer:

1m/sec

Step-by-step explanation:

Mr. Hall spent 3 seconds to increase his speed to 3m/sec increasing 1m/sec, don't over think it.

Answer:

The length of the unknown side of the triangle is

[tex]5 \sqrt{5} [/tex]