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The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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Answer:

answer is D

Step-by-step explanation:

(2^3)^-2= 2^(3)*(-2)
             = 2^-6
             = 1/2^6
             = 1/64

     

The expressions (a), (d), (e) and (f) have values less 1.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Solving each expression :-

1) 4¹¹ / 4¹⁴        

= 4¹¹ × 4⁻¹⁴

= (4)¹¹⁻¹⁴

= 4⁻³

= 1 / 4³

2) (3⁵)² / 3⁸

= 3¹⁰ / 3⁸

= 3¹⁰⁻⁸

= 3²

= 9

3) 4⁻¹ × 4⁵

= 4⁻¹⁺5

= 4⁴

= 64

4) (2³)⁻²

= 2⁻⁶

= 1 / 2⁶

5) (5⁴)² x 5⁻¹¹

= 5⁸ x 5⁻¹¹

= 5⁻³

= 1 / 5³

6) (6⁻⁴ x 6⁶) / 6³

= 6² / 6³

= 1 / 6

Hence, the expressions (a), (d), (e) and (f) have values less 1.

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The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24

Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.

Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9

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This statement essentially establishes a relationship between the sets X, Y, and z, stating that there exists a subset Y for each element x in X such that the elements in Y are present in some subset z of X.

The given statement is a symbolic representation of a logical proposition involving quantifiers and logical connectives. Let's break down its meaning:

∀ X ∃ Y ∀u(u ∈ Y ↔ ∃z(z ∈ X ∧ u ∈ z))

The symbol ∀ (universal quantifier) indicates that the statement applies to all elements in the set X.

The symbol ∃ (existential quantifier) indicates that there exists at least one element in the set Y.

The statement can be interpreted as follows:

"For all elements x in the set X, there exists a set Y such that for every element u in Y, u is an element of Y if and only if there exists a set z in X such that u is an element of z."

In simpler terms, the statement asserts that for every element x in the set X, there is a set Y that contains elements u if and only if there exists a set z in X that also contains u.

It is important to note that the precise meaning and implications of this statement may depend on the context and interpretation of the sets X, Y, and their elements.

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If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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The value of u is 2 in the given right-angled triangle.

The given figure is a right-angled triangle with hypotenuse 'u' and the other two sides as \(\sqrt{2}\) and v.

We have to find the value of 'u' using Pythagoras theorem or trigonometric identities.

It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In a right-angled triangle ABC, if

BC = hypotenuse

AC and AB are the other two sides then,

\(BC^2 = AC^2 + AB^2\).

For this problem, we can find the value of u by using trigonometric identities.

From the figure, we have an angle of 45°.

Consider Cos 45°.

Cos Ф = base / hypotenuse

Cos 45° = \(\sqrt{2}\) / u ...........(1)

From trigonometric identities of cosine.

We have,

Cos 45° = 1 / \(\sqrt{2}\)............(2)

From (1) and (2)

We get,

1 / \(\sqrt{2}\) = \(\sqrt{2}\) / u

u = 2.

Thus the value of u is 2 in the given right-angled triangle.

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Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

Answer:

its the second from the top

Answer:

I believe it's B

Step-by-step explanation:

hope it works

From the resulting solution, the correct linear inequality graph is Graph C.

Given the inequality equation below:

2(2x-1)+7< 13 or -2x+5 ≤ -10.​

Simplify the expression

2(2x-1)+7< 13

Expand

4x - 2 + 7 < 13

4x + 5 < 13

4x < 13 - 5

4x < 8

x < 2

For the inequality -2x+5 ≤ -10.

-2x+5 ≤ -10

-2x  ≤ -15

x  ≥ 7.5

Hence the solution to the given system of inequalities are x < 2 and x  ≥ 7.5

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The graph of the y+2x=6 is given in the attachment.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The standard equation of a line is expressed as y = mx + b, m is the slope

and b is the y-intercept.

Given the equation y = 2x - 2

If x = -2

y = 2(-2) - 2

y = -4-2

y = -6

If x  = 4

y = 2(4) - 2

y = 8-2

y = 6

The point (-2, -6) and (4, 6 )must be on the line graph.

Hence, the graph of the y+2x=6 is given in the attachment.

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Answer:

ther is 33 shepp in the zooo

Step-by-step explanation:

25 +8 =33

Answer:

5,4,6,7

Step-by-step explanation:

The digits 4​, 5​, 6​, 7​, and 8 are randomly arranged to form a​ five-digit number. Complete parts​ (a) and​ (b) below.

​(a) Find the probability that the number is odd.

The probability that the number is odd

​(Type an integer or a simplified​ fraction.)

​(b) Find the probability that the first and last digits of the number both are odd.

The probability that the first and last digits of the number both are odd is  

.

​(Type an integer or a simplified​ fraction.)

The value of measure of side q is,

⇒ q = 17.5

We have to given that;

In triangle QRS,

QS = r

SR = q

QR = 11

Hence, We can formulate;

sin 39° = QR / SR

0.63 = 11 / q

q = 11 / 0.63

q = 17.5

Thus, The value of measure of side q is,

⇒ q = 17.5

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Answer:

8) x + 20

9) 20x

10) 20/x

11) x-20

Step-by-step explanation:

8) x + 20

9) 20x

10) 20/x

11) x-20

Answer:

6in

Step-by-step explanation:

angle C = 55 <-- 180-70-55=55
meaning the triangle is an isosceles so two sides would be the same.

Relative interest refers to the comparison of interest rates between different financial instruments or investment opportunities. It allows individuals or investors to assess and evaluate the attractiveness of various options based on their potential returns.

1. Understand the basic concept: Interest is the cost of borrowing money or the return earned on invested funds. Relative interest involves comparing the interest rates of different financial instruments or investments to determine which one offers a more favorable return.

2. Identify the investment options: Start by identifying the different investment opportunities or financial instruments available. These can include savings accounts, certificates of deposit (CDs), bonds, stocks, or other investment vehicles.

3. Research interest rates: Research and gather information about the current interest rates offered by each investment option. This information can usually be found on financial websites, through financial institutions, or by consulting with a financial advisor.

4. Compare interest rates: Once you have the interest rates for each investment option, compare them side by side. Look for the differences in rates and identify which options offer higher or lower returns.

5. Assess risk and return: Consider the level of risk associated with each investment option. Higher returns often come with higher risk, so it's essential to evaluate the risk-reward tradeoff.

6. Make an informed decision: Based on the comparison of interest rates and the risk-reward assessment, make an informed decision on which investment option aligns with your financial goals and risk tolerance.

Always remember to consider your financial goals, risk tolerance, and consult with a financial advisor if needed.

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Answer:

For 4 years she is charged $20. She has to pay back $420

Step-by-step explanation:

Answer:

Step-by-step explanation:

Start with h(t) = -16t^2 + initial height, which here is h(t) = -16t^2 + 1296.  Set this = to zero, which corresponds to the object hitting the ground (h = 0):

0 = -16t^2 + 1296.  Dividing all terms by -16, we get t^2 = 81, whose positive square root is 9.  It takes 9 seconds for the object to hit the ground.

There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Null hypothesis (H₀): There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Alternative hypothesis (H₁): There is a significant difference between the mean scores of Education and Nursing students in mathematics.

We will use significance level (α) of 0.01.

Given:

Sample mean for Education students (x₁) = 88.50

Sample mean for Nursing students (x₂) = 90.25

Standard deviation for the Education student sample (s₁) = 7.5

Standard deviation for the Nursing student sample (s₂) = 8.2

Sample size for Education students (n₁) = 25

Sample size for Nursing students (n₂) = 29

The t-test statistic for two independent samples is:

t = (x1₁ - x2) / sqrt((s₁² / n₁) + (s₂² / n₂))

t = (88.50 - 90.25) / sqrt((7.5² / 25) + (8.2² / 29))

t ≈ -0.8187

In this case, df = 24.

The critical value for α = 0.01 and df = 24 is approximately ±2.797.

Since |-0.8187| < 2.797, the absolute value of the t-test statistic is smaller than the critical value.

Therefore, we fail to reject the null hypothesis.

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Answer:15

Step-by-step explanation:

4+(2/3)+x=29

4+2/3x+3/3x=29

4+5/3x=29

5/3x=29-4=25

5/3x=25

(5/3x) divided by (5/3)=25 divided by (5/3)

x=15

The total savings of Shelly is $15 and the total savings of Jack is $14.and this can be determined by forming the linear equation in two variables.

Given :

Let the total saving of Jack be 'x' and the total saving of Shelly be 'y'. The linear equation that represents the total savings of Jack and Shelly is given by:

x + y = 29

x = 29 - y      ---- (1)

The linear equation that represents that "Jack has saved 4 dollars more than 2/3 as much as Shelly" is given by:

\(x = 4+\dfrac{2}{3}y\)    --- (2)

Now, substitute the value of 'x' in the above equation (2).

\(29-y=\dfrac{2}{3}y + 4\)

Simplify the above equation in order to determine the value of 'y'.

\(29-4=\dfrac{2}{3}y+y\)

25 \(\times\) 3 = 5y

y = $15

Now, substitute the value of y in the equation (1).

x = 29 - 15

x = $14

So, the total savings of Shelly is $15 and the total savings of Jack is $14.

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The speed limit for the highway in rounded to the nearest whole is 33 mi/h.

The speed is the ratio of the distance in a given time interval. The distance is represented by a unit of length and the time is represented by a unit of time.

There are different units for the length or distance. In the International System Units (SI), the standard unit of distance is the meter (m) and the standard unit of time is the second (s). Nonetheless, there are others units, for example: inches (in), miles (mi) and  yards (yd).

For solving this exercise, you need to know the relation between the given units for distance and time.

The question gives - 100 km/h. The kilometer (km) is a multiple of the  standard unit of distance -  the meter (m) and the hour is a submultiple of the  standard unit of time  - the second (s)

For solving this question, it is necessary that you know the relation between km/h and mi/h. See  below.

\(\text{1 km/h}= 0.6213712 \ \text{mi/h}\)

Now you can solve the question from a math tool - Rule of three. Thus,

\(\text{1 km/h}= 0.6213712 \ \text{mi/h}\)

\(100 \ \text{km/h}= \text{x mi/h}\)

\(\text{x}= 100 \times 0.6\)

\(\text{x}=33 \ \text{mi/h}\)

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Answer:

3550

Step-by-step explanation:

I hope this helps!

Answer:

3550

Step-by-step explanation:

Round each number: 709 ⇒ 700, 645 ⇒ 650, 798 ⇒ 800, 704 ⇒ 700, 658 ⇒ 700

Add the rounded numbers: 700 + 650 + 800 + 700 + 700

Start slow: 700 + 650 = 1350

1350 + 800 = 2150

2150 + 700 = 2850

2850 + 700 = 3550

Answer:

5:2

Step-by-step explanation:

A ratio is basically a fraction but horizontally for eg. this: 5:8! This question is asking us to find the ratio of the emails that Jamie received to the emails that she answered.

According to the question, Jamie got 20 emails and responds to 8 of them. The ratio would look like this: 20:8 (because a ratio is just a fraction but horizontal, doesn't mean that there will be mixed numbers!) but not this 8:20. Ratios have a specific order that they have to be in and that will vary depending on the question. If the question says to find the ratio of emails that Jamie responded to to the emails that she received, then in this case 8:20 would be correct.

For now, the answer is 20:8. However, we still need to simplify it by finding its lowest common factor (unless the question asks you to not simplify it, it's better to simplify the answer like a fraction). The lowest common factor would be 4 for 20 and 8. 4 goes in 20 5 times sand 4 goes into 8 2 times.

Your final answer should be: 5:2

If you have any further questions please ask!

Answer:

10x + 15y

Step-by-step explanation:

5(2x + 3y)

Use the distributive property

5*2x + 5*3y

10x + 15y

Answer:

(0,1)

(-2,0)

(2,2)

Step-by-step explanation:

Answer: A) B.

B) D.

C) D.

Step-by-step explanation: It’s easy, next time show the people the image of the question, because how do you expect us to answer it?

The correct match for each linear system with one of the phase plane direction fields will be:

1:B

2:C

3:D

4:A

What is plane?

In geometry, a plane is a surface made up of all the straight lines connecting any two locations on it. It is, in other words, a level or flat surface. A plane is uniquely defined in a Euclidean space of any number of dimensions by one of the following: three non-collinear points are used. Other names for it include a two-dimensional surface. A plane has an unlimited width, an endless length, zero thickness, and no curvature. The flat surfaces of a cube or cuboid, as well as the flat surface of paper, are all true instances of geometric planes, despite the fact that it is difficult to envision a plane in real life.

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Answer:

Theres 3, 8 8 8

or 111, 111*8=888.

Two correct answers

Step-by-step explanation: