Which of the following is NOT a characteristic of a plane?

£40 is shared as £5, £15 and £20. 88p is shared as 16p, 32p and 40p. 180° is shared as 40°, 40° and 100°

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

a) Share £40 in the ratio 1:3:4

For the first ratio = (1/8) * £40 = £5

For the second ratio = (3/8) * £40 = £15

For the third ratio = (4/8) * £40 = £20

b) Share 88p in the ratio 2:4:5

For the first ratio = (2/11) * 88p = 16p

For the second ratio = (4/11) * 88p = £32

For the third ratio = (5/11) * 88p = 40p

c) Share 180° in the ratio 2:2:5

For the first ratio = (2/9) * 180° = 40°

For the second ratio = (2/9) * 180° = 40°

For the third ratio = (5/9) * 180° = 100°

The ratios are shown above

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Answer: The Number is 24.

Step-by-step explanation:
1) Set unknown number to a variable (I'm going to do x).
2) Set up equation: 5x = 120.

3) Simplify by dividing both sides by 5: 5x/5 = 120/5 = 24.

The perimeter of the plate is 60"

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

Length = 18"

Width = 12"

The perimeter of the rectangle piece can be calculated as

Perimeter = 2 * (Length + Width)

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

Perimeter = 2 * (18 + 12)

Evaluate

Perimeter = 60

Hence, the perimeyer is 60"

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The density of water is 1 g/mL, so for this problem, we would multiply 103.8 mL by 1 g/mL to get our answer of 103.8 grams.

The density of water is 1 gram per milliliter (1 g/mL). This means that for every milliliter of water, there is 1 gram. Therefore, to answer the question of how many grams of C12H24012 is needed to acquire the needed volume of water (103.8 mL), we need to multiply the volume of water by the density of water. To do this, we will use the equation: Mass (g) = Volume (mL) x Density (g/mL). For this problem, the equation would be: Mass (g) = 103.8 mL x 1 g/mL.Therefore, the answer to the question is 103.8 grams of C12H24012 is needed to acquire the needed volume of water.In conclusion, to figure out how many grams of C12H24012 is needed to acquire the needed volume of water, we need to multiply the volume of water (in mL) by the density of water (in g/mL). The density of water is 1 g/mL, so for this problem, we would multiply 103.8 mL by 1 g/mL to get our answer of 103.8 grams.

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The value of x is given as follows:

x = 155º.

For the triangle at the left, considering that the sum of the measures of the internal angles of a triangle is of 180º, the angle measures are given as follows:

For the triangle at the right, considering the ray formed at the top, the measures are given as follows:

An angle is supplementary with it's external angle, meaning that the sum of their measures is of 180º, hence the value of x is obtained as follows:

x = 180 - 25

x = 155º.

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Use identities:

Then apply to the left side of the given equation:

Proved

The value of angle PSQ is  136. 9 degrees

It is important to note the following;

Then, we have that;

30x + 6  + 11x - 5 = 180 degrees

Now, let's collect the like terms

30x + 11x + 6 - 5 = 180

add or subtract the like terms

41x = 180 - 1

41x = 179

Divide the values, we get;

x = 4. 36

Then,

PSQ = 30x + 6

PSQ = 136. 9 degrees

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There are quadratic equations as many as lead coefficients are. The functions that represent each parabola are:

Case A: y = (1 / 3) · (x + 4) · (x - 2)

Case B: y = (x + 4) · (x - 2)

Case C: y = 2 · (x + 4) · (x - 2)

Case D: y = - (1 / 3) · (x + 4) · (x - 2)

Case E: y = - 2 · (x + 4) · (x - 2)

In this problem we find five case of quadratic equations whose roots are x = - 4 and x = 2, but whose vertices are different. Quadratic equations can be described as a factor product of the form:

y = a · (x + 4) · (x - 2)

Where a is the lead coefficient.

The following parameters are for each parabola:

Case A: (x, y) = (- 1, - 3)

Case B: (x, y) = (- 1, - 9)

Case C: (x, y) = (- 1, - 18)

Case D: (x, y) = (- 1, 3)

Case E: (x, y) = (- 1, 18)

Now we determine the lead coefficient for each case:

Case A

- 3 = a · (- 1 + 4) · (- 1 - 2)

- 3 = - 9 · a

a = 1 / 3

Case B

- 9 = a · (- 1 + 4) · (- 1 - 2)

- 9 = - 9 · a

a = 1

Case C

- 18 = a · (- 1 + 4) · (- 1 - 2)

- 18 = - 9 · a

a = 2

Case D

3 = a · (- 1 + 4) · (- 1 - 2)

3 = - 9 · a

a = - 1 / 3

Case E

18 = a · (- 1 + 4) · (- 1 - 2)

18 = - 9 · a

a = - 2

All differences between all quadratic equations are due to different lead coefficients.

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The value of the areas are;

1. 24 cm²

2. 304cm²

3. 28. 36cm²

4. 5cm²

5. 189cm²

The formula for calculating the area of a triangle is expressed as;

Area = 1/2bh

Substitute the values

Area = 1/2 × 4 × 12

Multiply

Area = 24 cm²

For the area of a parallelogram

Area = ab, length of its sides

Substitute the values

Area = 304cm²

For the area of a rectangle

Area = lw, length and width

Area = 28. 36cm²

For the area of a pentagon

Area = 1/2 base × height

Area = 1/2 × 2.5 × 4

Area = 5cm²

For the area of a trapezium

Area = 1/2 (a + b)h

Area = 1/2 (18+24)9

Area = 189cm²

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Answer:

y <= 40

Step-by-step explanation:

Let's call the number of people traveling by van "x", and the number of people buying train tickets "y". We know that the total number of people in the group is 40, so we can write the equation:

x + y = 40

And we also know that the van can hold up to 12 people, so we can write the inequality:

0 <= x <= 12

Now, to find the number of train tickets, we just need to substitute

x = 40 - y into the second inequality:

0 <= 40 - y <= 12

Expanding and solving for y, we get:

0 <= 40 - y <= 12

-40 <= -y <= -28

y >= 28

y <= 40

So the number of train tickets needed (y) is equal to or greater than 28 and equal to or less than 40.

Answer:

Inequality:    12 + x ≤ 40

Solution:   x ≤ 28

Step-by-step explanation:

Let x be the number of train tickets that the group will need.

As the van holds 12 people and the rest will buy train tickets, an expression for the total number of people is:

If the group is up to 40 people then 12 + x will be less than or equal to 40:

Therefore, the inequality that can be used to find the number of train tickets that the group will need is:

To solve the inequality, subtract 12 from both sides:

⇒ 12 + x - 12 ≤ 40 - 12

⇒ x ≤ 28

Therefore the number of train tickets that the group will need is less than or equal to 28 tickets.

The toy rocket will hit the ground after approximately 3.86 seconds.

The rocket will hit the ground when its height is equal to zero, so we can use the equation h = -4.97t^2 + 38.5t + 5.6 to find the value of t that satisfies this condition. To do this, we set h equal to zero and solve for t:

0 = -4.97t^2 + 38.5t + 5.6

-5.6 = -4.97t^2 + 38.5t

4.97t^2 - 38.5t - 5.6 = 0

This is a quadratic equation and can be solved using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 4.97, b = -38.5, and c = -5.6.

Plugging in these values, we get:

t = (-(-38.5) ± √((-38.5)^2 - 4 * 4.97 * -5.6)) / (2 * 4.97)

t = (38.5 ± √(1466.25 + 113.92)) / 9.94

t = (38.5 ± √1580.17) / 9.94

The square root of 1580.17 is 39.67, so:

t = (38.5 ± 39.67) / 9.94

t = (38.5 + 39.67) / 9.94 or (38.5 - 39.67) / 9.94

The first solution gives us a time of approximately 3.86 seconds, while the second solution is negative and therefore represents an unrealistic result.

The toy rocket will hit the ground after approximately 3.86 seconds.

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In a case whereby Shana bought sodas and popcorn for the movies. Sodas cost $3 each and popcorn costs the system of equation involving the number of sodas, s, and the bags are:  (3s + 4p )= $26  and s+p = 7 .Then Shana bought 5 sodas and 2popcorn.

We know that :

Sodas cost =$3 each

popcorn costs= $4 per

total =$26

The system of equation can be written as :

(3s + 4p )= $26

We were also told that he bought things equal to the 7 things which can be expressed as:

s+p = 7

Then we can solve the equations as:

3s + 4p = 26 .............................................(1)

s+p = 7................................................................(2)

multiply equation by -3

-3s - 3p =-21  ..................................................................(3)

Then add (1) and 3

4p-3p = 26-21

p=5

Then substitute the value of p into equation 2 we have

s+5 = 7

s= 7-5

=2

s=2

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complete question:

Shana bought sodas and popcorn for the movies .Sodas cost $3 each and popcorn cost $4 per bag . Shana bought 7 things from the concession., all either sodas or bags of popcorn. Shana spent a total of $26 . Write a system of equations involving the number of sodas S ,and the bags of popcorn ,B .Solve the system to see how many of each shana bought

WE CAN USE THE GRAPH THAG CA HELP US IN THE PROBLEM

The numbers 2 2 2 2 can be arranged to make the equation true as follows

The numbers arranged by applying the rule which had acronym of PEMDAS

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

applying the sequence the problem is solved as follows

= (2 + 2/2)²

solving the parenthesis first we solve the problem inside the parenthesis. Inside the parenthesis we start with division

= (2 + 2/2)²

= (2 + 1)²

Then addition

= (3)²

having completed the parenthesis, we solve for the exponents

= 9

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The IR spectrum described could be an alkyl chloride with a carbonyl group, such as chloroform ([tex]CHCl_{3}[/tex]).

The IR spectrum described suggests the presence of several functional groups in the compound.

The strong, broad band in the 3600 to 3100 inverse centimeter range corresponds to the stretching vibration of the O-H bond in alcohols, while the strong, spiked peak in the 3000 to 2800 inverse centimeter range corresponds to the stretching vibration of the C-H bond in alkanes. The weak peak near 1850 inverse centimeters corresponds to the stretching vibration of the C=O bond in ketones, while the sharp peak near 1640 inverse centimeters corresponds to the stretching vibration of the C=C bond in alkenes.

The series of spiked bands in the 1500 to 1200 inverse centimeter range corresponds to the bending vibrations of the C-H bond in alkanes, while the two strong bands at 990 and 910 inverse centimeters correspond to the stretching vibration of the C-Cl bond in alkyl chlorides.

Based on this information, the compound that matches the IR spectrum described could be an alkyl chloride with a carbonyl group, such as chloroform ([tex]CHCl_{3}[/tex]).

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Answer: If a ball is chosen at random 80 times, with replacement, and there are an equal number of blue, green, pink, and red balls, then the probability of choosing a green ball each time is 1/4. Over many trials, the number of times a green ball is chosen would be roughly proportional to the probability of choosing a green ball, so we would expect the green ball to be chosen about 80 * (1/4) = 20 times.

However, since this is a random process, it is unlikely that the green ball will be chosen exactly 20 times. It is more likely that the actual number of green balls chosen will be slightly different, possibly higher or lower, than 20. So the answer is C: The color green would be chosen roughly 20 times, but probably not exactly 20 times.

Step-by-step explanation:

The inequality representing the situation is w >= 15, where w represents the weight of a can of tomatoes and the inequality states that it must be greater than or equal to 15 ounces.

The inequality that represents the situation is w >= 15, where w represents the weight of a can of tomatoes. This inequality states that the weight of a can of tomatoes is greater than or equal to 15 ounces, meaning that every can of tomatoes weighs at least 15 ounces.

This inequality represents a constraint or a condition on the weight of a can of tomatoes. In mathematical terms, the inequality w >= 15 says that the value of w, which represents the weight of a can of tomatoes, must be greater than or equal to 15 ounces. Any value that satisfies this inequality is considered a valid solution for the weight of a can of tomatoes. For example, 15 ounces, 16 ounces, 17 ounces, and so on are all valid weights for a can of tomatoes that meet the requirement of weighing at least 15 ounces.

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The complete question is:

At a supermarket, Each tomato can in a store weighs at least 15 ounces.

Let w stand in for the can of tomatoes' weight.

Which inequality best captures the circumstances?

[tex]w < 15 w < 15 W > 15 w > 15[/tex]

Answer:

c

Step-by-step explanation:

trust me

Answer:

Jennifer raised $25

Rebecca raised £50

Derek raised $37.50

Matthew raised $75

Step-by-step explanation:

J: 50% = dividing by 2, 50/2= 25

R: 50 is 100%, because that was the total

D: 75% = dividing by 4, timsing by three, so 50/4 is 12.5 x 3 is 37.5, put it into currency $37.50

M: We add another 25% onto 50 so 25+50=75.

(hope this works!!)

The value of sin a + cos a is √7/2.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

Based on the right-triangle theorem, which is known as Pythagoras theorem, there are three Pythagorean trigonometric identities in trigonometry as follows

Here we have

sin a × cos a = 3/8  

Multiply with 2 on both sides

=> 2(sin a × cos a) = 2(3/8)

=> 2 sin a cos a = 3/4  

Add sin²a + cos²a on both sides

=> sin²a + cos²a + 2 sin a cos a = 3/4 + sin²a + cos²a    

As we know (a + b)² = a²+ b² + 2ab  

=> (sin a + cos a)² = 3/4 + 1

=> (sin a + cos a)² = 7/4

=> sin a + cos a = √7/2

Therefore,

The value of sin a + cos a is √7/2.

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The predicted femur length for someone with a height of 218 cm is 68 cm.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

From the graph,

Coordinates = (30, 127), (35, 139), (40, 151).

Now,

The equation of the line of best fit.

y = mx + c

Where x is the femur length and y is the height.

Take two coordinates.

m = (139 - 127) / (35 - 30)

m = 12/5

m = 2.4

And,

(30, 127) = (x, y)

127 = 2.4 x 30 + c

127 - 72 = c

c = 55

So,

y = 2.4x + 55

Now,

For y = 218.

Solve for x.

218 = 2.4x + 55

218 - 55 = 2.4x

163 = 2.4x

x =163/2.4

x = 67.9

x = 68 cm

Thus,

The predicted femur length for someone with a height of 218 cm is 68 cm.

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Answer:

1. 11π/6

2. 43π/18

3. -π/4

4. - 43π/18

5. 23π/6

6. 25π/18

Step-by-step explanation:

A full circle has a measure of 360° in degrees and 2π radians in radians.

Since a full circle has a measure of 2π radians, then half a circle has a measure of π radians, and a quarter circle has a measure of π/2 radians.

1. 2π - π/6 = 11π/6

2. 61π/36 - π/2 = 61π/36 - 18π/36 = 43π/18

3. 5π/4 - π = π/4; -π/4

4. -36π/18 - 7π/18 = -43π/18

5. 2π + π + 5π/6 = 23π/6

6. 36π/18 - 11π/18 = 25π/18

The area of this compound figure is 85 cm².

The area of the compound figure given is calculated by subtracting the small area of the  figure from the big figure.

A (total) = 9 cm x 15 cm

A (total) = 135 cm²

The area of the small figure is calculated as follows;

A (small) = ( 9 cm - 4 cm ) x ( 15 cm - 5 cm )

A (small) = ( 5 cm ) x ( 10 cm )

A (small) = 50 cm²

The area of this compound figure = ( 135 cm² - 50 cm² ) = 85 cm²

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The price per can of a 12 pack of soda is 8.25.  the price per can of a 12 pack of soda is 0.6875.

To calculate this, we can use the following formula: Price per Can = Total Price of 12 Pack / 12 Price per Can = 8.25 / 12 Price per Can = 0.6875 Therefore, the price per can of a 12 pack of soda is 0.6875. To better understand the price per can of a 12 pack of soda, it is important to understand the concept of unit pricing. Unit pricing is the cost of a single item compared to a larger quantity. When shopping, it is beneficial to look at the unit pricing of items to ensure that you are getting the best deal. For example, if a 12 pack of soda is 8.25 and a 6 pack of soda is 4.00, then the unit price of the 12 pack is lower, which means it is a better deal. By understanding unit pricing, you can make the most cost-efficient decisions when shopping.

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Answer: Region Z

Step-by-step explanation: Region X is smaller than Region Y, while Region Y is smaller than Region Z.

For the given table -

The equation for line of best fit is Y = -1.000 · X + 11.25.

The correlation coefficient is -0.443533.

x and y have negative and strong correlation.

What is correlation coefficient?

A statistical concept known as the correlation coefficient aids in establishing a relationship between expected and actual values gained through statistical experimentation. The estimated correlation coefficient's value explains how well the expected and actual values match.

The table of data is given.

The formula for equation of the line of best fit is -

Y = b·X + a

On adding the values in a graphing calculator the equation is -

Y = -1.000 · X + 11.25

Here, the slope is -1 and y-intercept is 11.25.

The formula for correlation coefficient is -

r = [n(∑xy) - (∑x)(∑y)] / [n∑x² - (∑x²)][n∑y² - (∑y²)]

n = Number of values or elements

∑x = Sum of 1st values list

∑y = Sum of 2nd values list

∑xy = Sum of the product of 1st and 2nd values

∑x² = Sum of squares of 1st values

∑y² = Sum of squares of 2nd values

For the given table the values are -

n = 8, ∑x = 68, ∑y = 22, ∑xy = 145, ∑x² = 620, ∑y² = 274

Plug in all the values in the equation -

r = [8(145) - (68)(22)] / [8(620) - (620)][8(274) - (274)]

r = -0.443533

When the values of two variables grow while one variable's values fall. The correlation coefficient would be negative in that situation.

The weak and adverse association is indicated by the coefficient's negative value. And if "r" keeps moving in the direction of -1, the relationship is moving in the negative direction.

Therefore, the equation is Y = -1.000 · X + 11.25 and r value is -0.443533.

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A scatter plot would best display the relationship between the number of hours a student spent studying for several tests and the student's grade on each test.

A scatter plot is a graph that displays the relationship between two continuous variables. In this case, the number of hours a student spent studying is the independent variable, which would be plotted on the x-axis. The student's grade on each test is the dependent variable, which would be plotted on the y-axis. Each data point would represent a single test, with the x-coordinate indicating the number of hours studied for that test and the y-coordinate indicating the grade received.

By using a scatter plot, you can easily identify any patterns or relationships between the number of hours studied and the student's grades on each test. It can also help to identify any outliers or anomalies in the data.

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