A mum of 5 children has truncated her children’s heights in metres to 2 decimal places, and written them down in the table.

a) Write down the intervals within which each child’s actual height lies.

b) Write down the minimum and maximum height difference between the tallest and shortest child.

The domain is all values of x that makes the expression defined.

Set-Builder Notation: {x| x ≤ 3 }

Interval Notation: (-∞,3]

Given the function in the question;

y = 5√(6−2x)​

To find the domain, set the radicand greater than or equal zero and solve for x.

6 - 2x ≥ 0

Subtract 6 from both sides

6 - 6- 2x ≥ 0 - 6

-2x ≥ -6

Divide both sides by -2

-2x/-2 ≤ -6/-2

x ≤ -6/-2

x ≤ 3

Therefore, the domain is;

Set-Builder Notation: {x| x ≤ 3 }

Interval Notation: (-∞,3]

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The correct answer is option A. For P= -1/2 0 1/2 1/2 0 -1/2 0 0 1 D= 0 4 0 0 0 4 -1 0 0. The matrix can be diagonalized using the eigenvectors.

To diagonalize the matrix, the eigenvectors must be found first. The eigenvectors can be found by solving the characteristic equation and finding the eigenvalues. The eigenvalues of the matrix are 2 and -1. The eigenvectors associated with each eigenvalue are determined by solving the eigenvalue equation.

The eigenvectors for the matrix are [1, -2], [1, 2], [1, 0], and [0, 1]. After the eigenvectors are found, the matrix can be diagonalized by constructing the transformation matrix P. The transformation matrix P is composed of the normalized eigenvectors. The transformation matrix P is: P=[-1/2, 0, 1/2, 1/2, 0, -1/2, 0, 0, 1], and the diagonal matrix D is composed of the eigenvalues.

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Answer:

Step-by-step explanation: We will determine if ratios are proportional using cross multiplication.

first, we will check option (a)

12/15 =5/4

12*4 = 15*5

48 is not equal to 75. So, these are not proportional.

now, we will check option (b)

15/12 = 5/4

15*4 = 12*5

60 = 60.

as the left-hand side is equal to the right-hand side.

So, option (b) is correct.

Answer:

[tex]\textsf{B)} \quad \dfrac{15}{12}\; \textsf{and}\;\dfrac{5}{4}[/tex]

Step-by-step explanation:

If two fractions are equal, they form a proportion.

Therefore, to determine if two ratios form a proportion, rewrite the fractions so that their denominators are the same, then compare.

[tex]\textsf{A)}\quad \dfrac{12}{15}\; \textsf{and}\;\dfrac{5}{4} \implies \dfrac{12 \times 4}{15\times 4}\; \textsf{and}\;\dfrac{5\times 15}{4\times 15}\implies \dfrac{48}{60}\; \textsf{and}\;\dfrac{75}{60}[/tex]

As the two fractions are not equal, they do not form a proportion.

[tex]\textsf{B)} \quad \dfrac{15}{12}\; \textsf{and}\;\dfrac{5}{4}\implies \dfrac{15}{12}\; \textsf{and}\;\dfrac{5 \times 3}{4 \times 3}\implies \dfrac{15}{12}\; \textsf{and}\;\dfrac{15}{12}[/tex]

As the two fractions are equal, they form a proportion.

[tex]\textsf{C)} \quad \dfrac{6}{5}\; \textsf{and}\;\dfrac{4}{5}[/tex]

The denominators of these two fractions are already the same.

Therefore, as the two fractions are not equal, they do not form a proportion.

[tex]\textsf{D)} \quad \dfrac{5}{6} \; \textsf{and}\;\dfrac{4}{5}\implies \dfrac{5\times 5}{6\times 5} \; \textsf{and}\; \dfrac{4\times 6}{5\times 6}\implies \dfrac{25}{30}\; \textsf{and}\;\dfrac{24}{30}[/tex]

As the two fractions are not equal, they do not form a proportion.

The difference between the population means - 3.4 and -1.84 when calculated is found to be -2.62 years.

The 95% confidence interval for the difference in true mean ages of cars owned by students and faculty is between -3.4 and -1.84 years.

We know that the sample of 138 cars which belongs to the students have an average age of 5.13 years. The standard deviation = 3.45 years.

Then again,

A sample of 111 cars which belongs to the faculty have an average age of 7.75 years.  The standard deviation= 2.08 years.

So the difference between them will be , s - f

= 3.45 - 2.08 = 1. 37

and the mean will be , mean of students - mean of faculty =

-2.62.

This is the point of difference between their means.

The SD is found to be as 0.3961.

and MOE is 0.78

with these details now we will calculate the required intervals,

The lower end is found to be as  -2.62 - 0.78 = -3.4

The upper end is found to be as  -2.62 + 0.78 = -1.84

Therefore, the mean difference between the cars is - 3.4 and -1.84.

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Answer:

Step-by-step explanation:

3(23-2b) + 3b = 48

1. Use the distributive property and distribute the 3 before the parenthesis

             3(23-2b)   (make sure you read the (-) as part of the 2b so it's -2b

              69 - 6b

2. 69 - 6b +3b = 48   (combine like terms...the bs: -6b + 3b)

    69 -3b=48

3. 69 - 3b = 48         (subtract 69 from both sides)

   -69           -69

4. -3b = -21      (divide both sides by negative three...we want the b to be +

   /-3    /-3

Answer: b = 7

So, C is your answer

Answer:

Option b.  -2x + 3y - 6 = 0

Step-by-step explanation:

Let's look for a linear equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

Calculate the slope first.  Slope is the Rise/Run of any two points on a straight line.   Using the given points, (0,2) and (3,4) we find:

  Rise = 4 - 2 = 2

  Run = 3 - 0 = 3

Slope, m, Rise/Run = (2/3)

The equation becomes y = (2/3)x + b

To find b, enter either of the two given points.  

y = (2/3)x + b

2 = (2/3)(0) + b  :  for point (0,2)

b = 2

The equation becomes:  y = (2/3)x + 2

Reformat this to match the format of the answer options.  

y = (2/3)x + 2    

3y = 2x + 6      [Multiplied by 3]

3y - 2x - 6 = 0

-2x + 3y - 6 = 0     [rearrange]

This matches option b.

The processing capability for the size of the Santa rounded to three decimal places is 1.07.

CP (Process Capability) is a statistical measure that compares the performance of a process to the specifications of that process. It can be calculated using the formula:

CP = (USL - LSL) / (6 * standard deviation)

Where:

USL = Upper Specification Limit (3.5 + 0.9) = 4.4 cm

LSL = Lower Specification Limit (3.5 - 0.9) = 2.6 cm

Standard deviation = 0.28 cm

Substituting these values into the formula:

CP = (4.4 - 2.6) / (6 * 0.28) = 1.8 / 1.68 = 1.07

So, CP rounded to three decimal places is 1.07

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The correct statement regarding the probabilities from the table is given as follows:

C The golf ball is 2 times as likely to be orange as it is to be pink.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of balls for this problem is given as follows:

4 + 11 + 8 + 18 = 41.

Hence the probability of selecting each ball is obtained as follows:

Hence statement C is correct, as:

2 x 4/41 = 8/41.

(which is the probability of orange, obtained multiplying the probability of pink by two).

The number of pink balls is of 4.

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The surface area that can be painted with one complete rotation of the roller is 226.19 inches².

Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.

A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.

SA = 2πrh

where SA = surface area

r = radius of the base = 3 inches

h = height of the cylinder = width = 12 inches

Plug in the values and solve for the surface area.

SA = 2πrh

SA = 2π(3 inches)(12 inches)

SA = 226.19 inches²

Hence, the surface area that can be painted with one complete rotation of the roller is 226.19 inches².

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The 5 ways to solve problems are identifying the problem, generating different solutions, choosing one solution, implementing the chosen solution and evaluating the result.

A problem is any type of disruption from normality that is impeding progress. A problem can be time-consuming and requires too much energy to solve it.

There are 5 different steps to solving a problem

Step 1. Identify the Problem

Step 2. Generate potential solutions

Step 3. Choose one solution

Step 4. Implement the solution you’ve chosen

Step 5. Evaluate results

Sometimes it is required to start the process entirely over. To make the problem-solving process easier, it’s best to facilitate the solution as much as possible. Try to concentrate on the solution instead of the problem. Finally, be in the correct psyche to want to change. This contains having the right mindset language, both are positive and open-minded. With sufficient practice, any problem can be solved.

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The mean number of rooms = 6

We know that the formula for the mean.

mean = sum of all observations / total number of observations

First we find thr total number of rooms, from given frequency table.

Number of Rooms        Frequency          Total number of rooms

           4                             4                              16

           5                             7                              35

           6                             10                            60

           7                             12                             84

           8                             5                              40

           9                             2                               18

So, the total number of rooms of 40 houses in a town would be,

16 + 35 + 60 + 84 + 40 + 18 = 253

And the total number of houses = 40

Using above formula of mean,  the mean number of rooms would be,

x = 253/40

x = 6.325

Therefore, on an average there are 6 rooms in each house.

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Answer:

30 degrees

Step-by-step explanation:

2(l+w) + 4a and 2l+2w + 2(2a) are two equivalent expressions which represent the total fencing material required to surround the playground and flower beds.

Mathematical expressions are a way of representing mathematical ideas, concepts, and operations using symbols and notation. They can take many forms, including numbers, variables, and operators. They can also be combined to create more complex expressions, equations, and formulas.

Explain:

The total fencing material required to surround the playground and flower beds would be the sum of the fencing material for the playground and the fencing material for the flower beds.

So, one possible expression for the total fencing material required to surround the playground and flower beds would be: 2(l+w) + 4a

Another possible expression for the total fencing material required to surround the playground and flower beds would be: 2l+2w + 2(2a)

Please note that these expressions are based on the information provided, and the actual total fencing material required will depend on the specific dimensions of the park and playground, and may differ from these expressions.

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The complete problem equation will be c = k*m + b

The cost equation for renting a car from the ABC Car Rental Company in terms of the number of miles driven, m, and the cost, c, would likely take the form of:

c = k*m + b where k is the rate of cost per mile and b is the fixed cost for renting the car independent of the miles driven.

It is important to note that this is a general equation and the specific cost equation of the ABC Car Rental Company is not provided. Also, this equation assumes that the cost of renting a car is linear to the miles driven, which may not be the case in practice. Other factors such as the type of car and duration of the rental period could also be included in the cost equation.

Therefore, the problem equation will be c = k*m + b

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Answer: 6.2

Step-by-step explanation:

Answer:

3, 2

Step-by-step explanation:

In order for the equation to be equal to zero, the following must be true:

x-3 = 0   or,

x-2 = 0

Therefore the 2 solutions are x=3, x=2

The distance in miles represented by a length on the map of 7 inches is 0.28

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

Given;

The scale of a map says that 2 inches represents 50 miles.

2 inches = 50 miles

1 Mile = 2/50 inches

Hence, 7 Mile = 7 * 2/50 inches

7 Mile = 14/50 inches

7 Mile = 0.28 inches

Therefore, the scale factor of 7miles in the map will be 0.28inches

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Answer:

15 lessons

Step-by-step explanation:

The number of boxes to complete the partial quotient model is found to be as 19 cars .

On dividing 95 from 5 we will get 19 as the quotient.

95 / 5 = 19

The quotient is the number that is produced when two integers are divided. It is the outcome of the division process , when we divide a number from another the result is known as quotient.

In arithmetic division, four primary terms are used which are  divisor, dividend, quotient, and remainder. In this post, each phrase will be defined and shown using examples.

Dividend = Divisor + Quotient + Remainder

If the divisor is not able to completely divide the dividend then it leaves a remainder.

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Answer:

x = -2/4 = -1/2

Step-by-step explanation:

The sum of 4 times a number and 5 is 3.

Let sum = +

times = *

is means =

a number = x

So, 4x + 5 = 3.  Then we solve it !

Subtract 5 to both sides to get 4x = - 2.

Next, we divide 4 to both sides to get x = -2/4 = -1/2

Answer:

The number is -8

Step-by-step explanation:

You can set up the question as (x/4)+5 = 3

x/4 = -2

x = -8

Answer:

√259 or 16.09

Step-by-step explanation:

Hello!

I'll be labeling the vertices so that it is easier to understand the sides.

These are both right triangles, and we can find the measures of right triangles (given two other sides) by using the Pythagorean theorem:

[tex]a^2 + b^2 = c^2[/tex]

In Triangle BCD, we have the measures of the hypotenuse and a leg. We can use that to find the missing side: CB

Since DB is the hypotenuse, it would be side c, and we can say that CD can be side a.

CB in simplest radical form is 5√21.

We can now solve for x, because now in triangle ABC, we have the measures of two sides: hypotenuse AC and leg CB.

AB in simplest radical form is √259, which is approximately 16.09.

The solution for x is √259 or 16.09.

In the coordinate geometry the translation represents one type of transformation to change the location without changing the shape, size.

As given in the question,

In the coordinate geometry,

Therefore, in the coordinate geometry the translation represents one type of transformation to change the location of the geometrical figure.

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Answer:

Step-by-step explanation:

6

2/3

15

13

Hit

Miss

2/5

3

5

215

2

Not score

Score

Find the probability that Ryan misses the target and does not score a goal,

(2 marks)

Lia gave away 3/5 of the trail mix, which is equal to 2 2/5 pounds.

Lia bought 4 3/5 pounds of trail mix. She gave 3/5 of it to her iter.Since Lia bought 4 3/5 pounds of trail mix, we can express this as 4 + 3/5 pounds, or 9/5 pounds.

To find out how much trail mix Lia gave away, we can multiply 9/5 by 3/5.

3. 3/5 multiplied by 9/5 is equal to 27/25.

To simplify this fraction, we can divide both the numerator and denominator by 3.

27/25 can be simplified to 9/5 or 2 2/5 pounds.

Therefore, Lia gave away 2 2/5 pounds of the trail mix.

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The parent function of a line (usually of the form y = ax + b) is y = x.

The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.

For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.

Linear functions have x as the term with the highest degree and a general form of y = a + bx. All linear functions have a straight line as a graph. The parent function of linear functions is y = x, and it passes through the origin. The domain and range of all linear functions are all real numbers.

These functions represent relationships between two objects that are linearly proportional to each other.

Therefore, the parent function of a line (usually of the form y = ax + b) is y = x.

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The equation 2x + 3y = 5 has one real solution.

To find it, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable.

For example, you can solve for y to get y = (5 - 2x)/3, and then substitute this into the equation to get 2x + 3((5 - 2x)/3) = 5, which you can then solve for x. Doing this will give you x = 5/4, which means that the solution is (5/4, 5/3).

Linear equations are equations that involve two variables and can be expressed in the form ax + by = c, where a and b are constants and x and y are the variables. These equations have one real solution, which can be found by solving for one of the variables and then substituting the result into the equation to find the other variable. Once both variables are known, the solution to the equation is the point (x,y) that satisfies both equations.

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multiple 5x 3 3/4 then change to an improper fraction

The odds against exactly 5 cars passing over the bridge in that time are given as follows:

5.25:1.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

An odd, conversely, is calculated as the division of the number of desired outcomes by the number of non-desired outcomes.

The probability(in favor) that 5 cars will pass over a small bridge in a 4-minute period is 0.16, hence the odds are given as follows:

0.16 : (1 - 0.16) = 0.16 : 0.84.

To obtain the odds against, we must exchange the desired and the non-desired outcomes, meaning that the odds against is then given as follows:

0:84 : 0.16.

As the quotient of 84 by 16 is of 5.25, the simplified odd is given as follows:

5.25 : 1.

Meaning that it is 5.25 times more likely that exactly 5 cars do not pass over the bridge over that time rather that they do pass.

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