Select the correct answer. A number is selected at random from the set {2,4,6,8,10}. Which event, by definition, covers the entire sample space of this experiment?

In the given parallelogram ABCD the values for variables are - g = 6, y = 5 and x = 4.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

We know that in a parallelogram, opposite sides are congruent and parallel, and diagonals bisect each other.

Using this information, we can set up equations to solve for the variables.

From the given information, we have -

AE = CE = 2x - 5 = 5x - 17 (since diagonals bisect each other at point E)

BE = x + 2

DE = BE = (x + 2) = g (since diagonals bisect each other at point E)

We also know that opposite sides of a parallelogram are parallel.

Therefore, 10 is parallel to 2y, which means they have the same slope. We can write this as -

10/1 = 2y/1

10 = 2y

y = 5

Now we can use equation (1) to solve for x -

2x - 5 = 5x - 17

12 = 3x

x = 4

Finally, we can use x to solve for g -

(x + 2) = g

(4 + 2) = g

g = 6

Therefore, the values of x, y, and g are 4, 5, and 6, respectively.

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Answer:

M=a2-a1/b2-b1

Step-by-step explanation:

-3-a/-2-1

-4a/3

/-4/-4

a=3/-4

Answer:

therefore the answer would be B

The calculated volume of the square pyramid is 1437.33 cubic cm

From the question, we have the following parameters that can be used in our computation:

The figure

The volume of the square pyramid is calculated as

Volume = 1/3 * Base area * Height

using the above as a guide, we have the following:

Base area = 14 * 14

Base area = 196

Also, we have

Height = 22

Substitute the known values in the above equation, so, we have the following representation

Volume = 1/3 * 196 * 22

Evaluate

Volume = 1437.33

Hence, the volume of the pyramid is 1437.33 cubic cm

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The length of the rectangular garden given the area and width is 8/7 miles

A rectangle is a form of quadrilateral having opposing sides parallel and four right angles. The area of a rectangle can be calculated by multiplying the length by width.

Area of a rectangular garden = length × width

16 = x × 14

16 = 14x

x = 16 / 14

x = 8/7 miles

Therefore, the length of the rectangular garden given the area and width is 8/7 miles.

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Answer:

  x = 3

Step-by-step explanation:

Maybe you want the value of x such that ...

  4(6^x) = 864

Dividing by 4 gives ...

  6^x = 216

You may know that 216 = 6^3. Using that, we can equate exponents:

  6^x = 6^3

  x = 3

Alternatively, we can use logarithms to find x. Taking logs gives ...

  x·log(6) = log(216)

  x = log(216)/log(6) = 3

R = (ax - p)/(q + bx)

(ax - p) = R(q + bx)

ax - p = Rq + Rbx

ax - Rbx = Rq + p

x(a - Rb) = Rq + p

x = (Rq + p)/(a - Rb)

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

7 unique values can be created.

\(1,2,3,\dfrac{1}{2},\dfrac{1}{3},\dfrac{2}{3},\dfrac{3}{2}\)

Step-by-step explanation:

We need to find unique values that can be created by forming the fraction

\(\dfrac{x}{y}\)

where, \(x\) is either 4, 8, or 12 and \(y\) is either 4, 8, or 12.

Now, possible ordered pairs are (4,4), (4,8), (4,12), (8,4), (8,8), (8,12), (12,4), (12,8), (12,12).

For these ordered pairs the value of \(\dfrac{x}{y}\) are:

\(\dfrac{4}{4},\dfrac{4}{8},\dfrac{4}{12},\dfrac{8}{4},\dfrac{8}{8},\dfrac{8}{12},\dfrac{12}{4},\dfrac{12}{8},\dfrac{12}{12}\)

\(1,\dfrac{1}{2},\dfrac{1}{3},2,1,\dfrac{2}{3},3,\dfrac{3}{2},1\)

Here, 1 is repeated three times. So, unique values are

\(1,2,3,\dfrac{1}{2},\dfrac{1}{3},\dfrac{2}{3},\dfrac{3}{2}\)

Therefore, 7 unique values can be created.

Answer:

A

Step-by-step explanation:

The less than signs are not less than or equal to when there is open circles. In this situation, there is no open circles, so it is A.

Answer:

21

Step-by-step explanation:

5(7-4)*2/3+11

5*3*2/3+11

15*2/3+11

30/3+11

10+11

21

Answer:

21

Step-by-step explanation:

Subtract 4 from 7

5 ⋅ 3 ⋅ 2 ÷ 3 + 11

Multiply 5 by 3.

15 ⋅ 2 ÷ 3 + 11

Multiply 15 by 2.

30 ÷ 3 + 11

Divide 30 by 3.

10 + 11

Add 10 and 11.

21

Answer: 1

Step-by-step explanation:

Answer:

The perimeter of the scale floor is 34 inches.

Step-by-step explanation:

To solve, we can set up fractions:

\(\frac{21}{7}=\frac{30}{x}\)

Cross multiply and you get:

21x = 210

Divide each side by 21:

x = 10

Since you are trying to find the perimeter of the floor, you can use this equation:

2w + 2l = p

Substitute to solve:

2 ( width = 10 )

2 ( length = 7 )

2 ( 7 ) + 2 ( 10 ) = p

14 + 20 = p

34 = p

The population of the country will be 796 million approximately in the year 2022.

To find when the population of the country will be 796 million, we can set the equation equal to 796 and solve for t:

\(A = 433.4e^{(0.032t)}\\796 = 433.4e^{(0.032t)}\)

Divide both sides by 433.4:

\(e^{(0.032t)} = 1.836\)

Take the natural logarithm of both sides:

\(ln(e^{(0.032t)}) = ln(1.836)\)

0.032t = 0.605

Divide both sides by 0.032:

t = 18.91

Therefore, the population of the country will be 796 million approximately 19 years after 2003. To find the year, we add 19 to 2003:

2003 + 19 = 2022

Therefore, the population of the country will be 796 million approximately in the year 2022.

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Answer: 1) b = 2

2) c = 20

Explanation:

I hope this helped!

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Answer:

3) b = 2.24

4) c = 15.62

Step-by-step explanation:

Pythagorean formula:

a² + b² = c²

3)

a² + b² = c²

2² + b² = 3²

4 + b² = 9

b² = 5

b = 2.24

4)

a² + b² = c²

10² + 12² = c²

100 + 144 = c²

244 = c²

c = 15.62

We know that the area of a rectangle is given by the formula A = l × w, where A is the area, l is the length, and w is the width.

In this case, we are given that the width is 10 meters and the area is 150 square meters. So, we can plug in these values into the formula to find the length:

150 = l × 10

Dividing both sides by 10, we get:

15 = l

Therefore, the length of the rectangle is 15 meters.

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Answer:

7/8 = 87.5%

Step-by-step explanation:

You have only one of eight (1/8) evenly divided sections that is orange. The rest is not orange (1 - 1/8 = 7/8).

Therefore, spinning once will yield 7/8 odds of not landing on orange, or 0.875 or 87.5%.

The probability of not getting orange is 87.5%. The correct option is C.

Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favourable outcomes to all outcomes.

Probability = Number of favourable outcomes / Number of samples

Given that a spinner with repeated colours numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.

You only have one of eight (1/8) evenly divided orange sections.

The rest is not orange,

P = (1 - 1/8

P =  7/8

P = 87.5%

Therefore, spinning once will yield 7/8 odds of not landing on orange or 0.875 or 87.5%.

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Answer: 16

Step-by-step explanation:

there are 3 feet in one yard so divided 48 by 3 and you get 16

Answer:

16

Step-by-step explanation:

Answer: ( − 3 , − 64 )

Step-by-step explanation:

knowledge!

Answer:

672 sq cm

Step-by-step explanation:

Each triangular base is 1/2 (12 * 8) or 48, making them = 96.

One of the sides is 12 x 18 = 216

The other 2 sides are 10 x 18 = 180 x 2 = 360

Add them all together to get 672 sq cm

there exists an integer that is greater than 5 and whose square is smaller than 40, express as a mathematical quantifiers ∃x∈ℤ: x > 5 ∧ x² < 40

1.  Start by writing down the equation: x² < 40

2.  Take the square root of both sides of the equation to isolate the variable x: √x² < √40

3.  Simplify both sides of the equation: x < √40

4.  Check that the result makes sense: x < 6.3

5.  Take the integer part of the result: x < 6

6.  Since the requirement is that x is greater than 5, the answer is x = 6.

We start by writing the equation x² < 40 and then take the square root of both sides to get x < √40. We check that the result is reasonable and then take the integer part of the result to get x < 6. Since the requirement is that x is greater than 5, the answer is x = 6. To confirm, we can calculate that x² = 36 which is smaller than 40, and indeed, 6 is greater than 5. Therefore, the integer that is greater than 5 and whose square is smaller than 40 is 6. This can be expressed mathematically as ∃x∈ℤ: x > 5 ∧ x² < 40 which translates to: There exists an integer x such that x is greater than 5 and the square of x is smaller than 40.

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The plotted function and the function y = 3x - 6 represent a straight line and have have same slope and hence, both the lines are parallel to each other.

The general equation of a straight line is of the form -

y = mx + c

where -

[m] is slope of line

[c] is y - intercept

Given is a equation of a straight line and a graph of a straight line.

We have the following equation -

y = 3x - 6

For this equation, the slope of the straight line will be [m] = 3 and the y - intercept would be [c] = - 6. Refer to the graph attached with green color for all the possible set of solution.

Now, the equation of the line plotted on graph -

m = (4 - 0)/(0 + 1.3)

m = 3.07

m = 3 (approx.)

Its y - intercept [c] = 4

Therefore, the equation of the plotted line -

y = 3x + 4

Now, both the lines are plotted on the graph. It can be seen from the graph and from the equation that they have same slope and hence, both the lines are parallel to each other.

Therefore, the plotted function and the function y = 3x - 6 represent a straight line and have have same slope and hence, both the lines are parallel to each other.

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[The complete question needs the plotted graph. It is attached at the end  of the answer]

Answer:

The area of this triangle is (1/2)(9)(8) = 36.

Answer: 15 inches

Step-by-step explanation:if 6 units is 10 cm than half of that is 5 so add those together and BOOMM 15 ur welcome

The length of the sides of triangle ABC are: 6, 8, and 12.

One of the conditions that two triangles are similar is their Three pairs of corresponding sides are proportional.

In the given problem, the ratio of the sides of triangle ABC is 3 : 4 : 6

Another triangle, let's say triangle DEF, is made with its vertices at midpoints of the sides of triangle ABC.

Hence, all three pairs of corresponding sides have the same proportion.

AB/DE = BC/EF = AC/DF = 1/2

Due to similarity, the ratio of the sides of triangle DEF is also 3 : 4 : 6.

ratio f sides : perimeter = 3 : 4 : 6 : 13

Since its perimeter is 13, it means that the length of sides of triangle DEF are: 3, 4, and 6

Length of the sides of triangle ABC = 2 x length of the sides of Δ DEF

Length of the sides of triangle ABC are: 6, 8, and 12.

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Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

By doing a change of units, we know that he will need 40 pint jars to hold the whole volume of sauce.

We know that Joe makes tomato sauce to sell at a craft fair, and we know that he did make that sauce in 5-gallon batches.

We want to see how many jars do he need to hold these 5 gallons, so we need to perform a change of units.

Remember the relation:

1 gallon  = 8 pints.

So, for each gallon, he will need 8 pint jars, then for the 5 gallons, he will need:

5*8 pint jars = 40 pint jars.

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Answer:

C

Step-by-step explanation:

C 160/2 = 80

240/3 = 80

400 / 5 = 80

480 / 6 = 80

C is linear

In table C, there is a linear relationship between time and distance

The correct answer is Table C

A linear relation is a relationship between distance (d) and time (t) when a distance changes over time at a constant rate.

From table A

At t = 2 hour, d = 120 miles

\(\frac{Distance}{Time} =\frac{120}{2}=60 miles/hour\)

At t = 4 hour, d = 220 mile

\(\frac{Distance}{Time} =\frac{220}{4}=55 miles/hour\)

The relationship between distance and time is not linear.

From table B

At t = 1 hour, d = 70 miles

\(\frac{Distance}{Time} =\frac{70}{1}=70 miles/hour\)

At t = 2 hour, d = 150 miles

\(\frac{Distance}{Time} =\frac{150}{2}=75 miles/hour\)

The relationship between distance and time is not linear.

From table C

At t = 2 hour, d = 160 miles

\(\frac{Distance}{Time} =\frac{160}{2}=80 miles/hour\)

At t = 3 hour, d = 240 miles

\(\frac{Distance}{Time} =\frac{240}{3}=80 miles/hour\)

At t = 5 hour, d = 400 miles

\(\frac{Distance}{Time} =\frac{400}{5}=80 miles/hour\)

The relationship between distance and time is linear.

From table D

At t = 1 hour, d = 75 miles

\(\frac{Distance}{Time} =\frac{75}{1}=75 miles/hour\)

At t = 2 hour, d = 150 miles

\(\frac{Distance}{Time} =\frac{150}{2}=75 miles/hour\)

The relationship between distance and time is not linear.

Therefore, In Table C, there is a linear relationship between time and distance

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The daily fee is $34 and the mileage charge is $0.19 per mile.

Let's start by using variables to represent the daily fee and the mileage charge. Let's say the daily fee is "d" (in dollars per day) and the mileage charge is "m" (in dollars per mile).

From the information given, we can set up two equations:

For the first trip:

4d + 450m = 221.5 (equation 1)

For the second trip:

3d + 200m = 140 (equation 2)

We want to find the values of d and m that satisfy both equations.

Let's rearrange equation 1 to solve for d in terms of m:

4d = 221.5 - 450m

d = (221.5 - 450m)/4

Now we can substitute this expression for d into equation 2:

3[(221.5 - 450m)/4] + 200m = 140

Simplifying this equation gives:

166.125 - 337.5m + 200m = 140

-137.5m = -26.125

m = 0.19

So the mileage charge is $0.19 per mile.

To find the daily fee, we can substitute this value of m back into either equation 1 or 2 and solve for d. Let's use equation 1:

4d + 450(0.19) = 221.5

4d + 85.5 = 221.5

4d = 136

d = 34

So the daily fee is $34 per day.

Therefore, the daily fee is $34 and the mileage charge is $0.19 per mile.

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