How can I write this differently, 270 students don’t like carrots

Answers

Answer 1

Answer:

270 students dislike carrots.

Step-by-step explanation:


Related Questions

r=19m how to find the circumference

Answers

Answer: 119.38

Step-by-step explanation:

C = 2πr = 2·π·19 ≈ 119.38052

find the nth term of this quadratic sequence 4, 7, 12, 19, 28, . ..​

Answers

Answer:

an = a1 + (n-1)d

Untuk barisan ini, kita dapat menentukan a1 = 4 dan d = 3, karena selisih antar suku bertambah 3. Jadi, rumusnya menjadi:

an = 4 + (n-1)3

a5 = 4 + (5-1)3

a5 = 4 + 12

a5 = 16

Jadi, suku ke-5 dari barisan ini adalah 16.

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The probability of event A occurring is 0. 65. The probability of events A and B occurring together is 0. 33. Events A and B are independent. What

is the probability of event B?

Enter a number to the nearest hundredth in the box.

Answers

The probability of event A occurring is 0. 65. The probability of events A and B occurring together is 0. 33. Events A and B are independent. The probability of event B is 0.68.

Probability:

The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probabilities of two complementary events A and B - either A occurring or B occurring - add up to 1.

Given that:

P(A) =0.65

P(A∩B) = 0.33

And event A and B are independent.

Using the probability formula:

  P(B) = 1 - P(A) + P(A∩B)

⇒ P(B) = 1 - 0.65 + 0.33

⇒ P(B) = 0.68

Therefore , the probability of event B is 0.68.

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The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A. (true or false)

Answers

The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A.

The above statement is True.

Eigenvalue:

An eigenvalue is a special set of scalar values ​​associated with the most probable system of linear equations in a matrix equation. Eigenvectors are also called eigenvalues. It is a non-zero vector which can be modified by at most its scalar factor after applying a linear transformation.

According to the Question:

If the geometric multiple of the eigenvalues ​​is greater than or equal to 2, the linearly independent set of eigenvectors is no longer unique to the multiple as before. For example, for the diagonal matrix A=[3003], one could also choose the eigenvectors [11] and [1−1], or any pair of two linearly independent vectors.

Sometimes vectors are simply expanded to vector times matrix. If this happens, this vector is called the eigenvector of the matrix and the "stretch factor" is called the eigenvalue. Example: Given a square matrix A, λ is the eigenvalue of A, and the corresponding eigenvector x is

Ax = λx.

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Here is a sketch of a curve.
The equation of the curve is y = x² + ax + b
where a and b are integers.
The points (0, -7) and (7, 0) lie on the curve.
Find the coordinates of the turning point of the curve.
Finish your answer by writing, Turning point at (..., ...)
YA
O
+

Answers

[tex]{\Large \begin{array}{llll} y=x^2+ax+b \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y=-7 \end{cases}\implies -7=0^2+a(0)+b\implies \boxed{-7=b} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=7\\ y=0 \end{cases}\implies 0=7^2+a7+\stackrel{b}{(-7)}\implies 0=49+7a-7 \\\\\\ 0=42+7a\implies -42=7a\implies \cfrac{-42}{7}=a\implies \boxed{-6=a} \\\\\\ ~\hfill {\Large \begin{array}{llll} y=x^2-6x-7 \end{array}}~\hfill[/tex]

now, let's get the "vertex" using the coefficients.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -6}{2(1)}~~~~ ,~~~~ -7-\cfrac{ (-6)^2}{4(1)}\right) \implies \left( - \cfrac{ -6 }{ 2 }~~,~~-7 - \cfrac{ 36 }{ 4 } \right) \\\\\\ \left( 3 ~~~~ ,~~~~ -7 -9 \right)\implies {\Large \begin{array}{llll} (3~~,~-16) \end{array}}[/tex]

For what values of c does the quadratic equatrion x^2-2x+c=0 have two roots of the same sign

Answers

The roots have positive or same signs when c>0.

Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.

[tex]b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2[/tex]

Roots of quadrant equation have Samsame sign if product of roots >0.

[tex]\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0[/tex]

Roots of quadratic equation have positive sign if product of roots<0.

c>0.

Combining results, we get:-

roots have positive signs when:-

c>0.

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6th graders has 5 hours of homework per week.
7th graders has 7 hours of homework per week.
9th graders has 12 hours of homework per week.
10th graders has 15 hours of homework per week.
What is the 5th graders expected hours of homework per week?
What is the 8th graders expected hours of homework per week?
Describe the correlation between hours of homework per week and grade level.

Answers

Answer:

The given data suggests that there is a positive correlation - as grade level increases, so does the expected hours of homework.

Step-by-step explanation:

It is difficult to accurately predict the expected hours of homework for 5th and 8th graders based on the given data. However, we can try to make an estimate by assuming a linear correlation between grade level and hours of homework.

Using the given data, we can plot a scatter plot with grade level on the x-axis and hours of homework on the y-axis. We can then draw a line of best fit through the data points to estimate the correlation.

Assuming a linear correlation, we can use the slope-intercept form of a line to calculate the expected hours of homework for 5th and 8th graders. The equation of the line of best fit is:

y = 2.5x - 6.5

where y is the expected hours of homework per week and x is the grade level. Using this equation, we can estimate that the expected hours of homework per week for 5th graders would be:

y = 2.5(5) - 6.5 = 6 hours

And the expected hours of homework per week for 8th graders would be:

y = 2.5(8) - 6.5 = 16 hours

It is important to note that this is just an estimate based on the given data, and actual hours of homework may vary depending on the school and curriculum.

As for the correlation between grade level and hours of homework per week, the given data suggests that there is a positive correlation - as grade level increases, so does the expected hours of homework. This is likely due to the increasing complexity and workload of the curriculum as students progress through school. However, it is important for schools to ensure that the amount of homework assigned is reasonable and does not cause undue stress or negatively impact students' well-being.

22) i) A cuboid has dimensions 60cm x 24cm x 30cm. How many small cubes with side 5cm can be placed in the given cuboid?

Answers

Answer:

345.6

Or 345 full cubes

Step-by-step explanation:

To answer this question we first need to find the volume of the cuboid!

To find volume we use the equation...

area of cross-section × heightor l × w × h

For the cuboid we are given the dimensions 60, 24 and 30 so we just need to multiply them...

60 × 24 × 30 = 43200

We now need to the the volume of the cube which we can just do by cubing the value given

5³ = 125

We now need to divide the two results together to find out how many cubes would fit...

43200 ÷ 125 = 345.6Or 345 full cubes

Hope this helps, have a lovely day!

a bin can hold 28 pounds. each toy car weighs 7 ounces. how many toy cars can the bin hold? (2 points) 64 toy cars 72 toy cars 88 toy cars 92 toy cars

Answers

A bin can hold 28 pounds. each toy car weighs 7 ounces., so the bin can hold 64 toy cars.

How to determine the number of toy cars

To determine the number of toy cars the bin can hold, we must first convert the weight limit of the bin and the weight of the toy cars to a uniform unit of measure.

We'll then divide the weight limit of the bin by the weight of one toy car. After that, we'll multiply the resulting value by the number of ounces in one pound (16).

Here's how to solve the problem:

1 pound = 16 ounces

Therefore, a bin that can hold 28 pounds can hold:28 × 16 = 448 Ounces

The weight of one toy car is 7 ounces.

Divide the weight limit of the bin (448 ounces) by the weight of one toy car (7 ounces):

448 ÷ 7 = 64

Therefore, the bin can hold 64 toy cars.

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please help me
9-9÷9÷9-9÷9​

Answers

Answer:

0

Step-by-step explanation:

0

Thank me...........

Hi I need help on this question It's teacher conferences week and I want to get this done before this week

Answers

Answer:

y = -3/8x + 3

Step-by-step explanation:

The slope intercept form is y = mx + b

Our equation is 3x + 8y = 24

3x + 8y = 24

8y = -3x + 24

y = -3/8x + 3

So, the answer is y = -3/8x + 3

given the following limit lim(x;y)!(0;0) xy x y , show that the function f (x; y) does not have a limit as (x; y) ! (0; 0).

Answers

To show that a function does not have a limit as (x, y) approaches (0, 0), we need to examine the limit along different paths .

How can we show that a function does not have a limit as (x, y) approaches (0, 0)?

To show that the function f(x, y) does not have a limit as (x; y) ! (0; 0), we need to examine the limit lim

(x;y)!(0;0) xy x y .

Convert the given limit into a more recognizable form. The given limit is

lim(x, y) -> (0, 0) (xy / (x + y)).

Analyze the limit along different paths. Let's examine the limit along two distinct paths - the

x-axis (y = 0)

and

the y-axis (x = 0).

For the x-axis (y = 0), the limit becomes

lim(x, 0) -> (0, 0) (x * 0 / (x + 0))

= lim(x, 0) -> (0, 0) (0) = 0.

For the y-axis (x = 0), the limit becomes

lim(0, y) -> (0, 0) (0 * y / (0 + y))

= lim(0, y) -> (0, 0) (0) = 0.

Compare the results of the two paths. Both limits along the x-axis and y-axis are equal to 0. However, this is not enough to conclude that the function f(x, y) has a limit as (x; y) ! (0; 0).

Examine another path, such as the line y = x. In this case, the limit becomes

lim(x, x) -> (0, 0) (x * x / (x + x))

= lim(x, x) -> (0, 0) (x^2 / 2x)

= lim(x, x) -> (0, 0) (x / 2)

= 0 / 2 = 0.

Consider another path, like

y = -x.

For this path, the limit becomes

lim(x, -x) -> (0, 0) (x * -x / (x - x))

which is undefined, since the denominator is zero.
Since we have found a path

(y = -x)

where the limit is undefined, we can conclude that the function f(x, y) does not have a limit as (x; y) ! (0; 0).

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Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree. (number 7)

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From the use of the angle of elevation, the length of ladder is 47 feet.

What is the angle of elevation?

The angle between the horizontal and a line of sight or an object above the horizontal, which is commonly stated in degrees or radians, is known as the angle of elevation. Determining an object's position in relation to an observer or a reference point is a common use of trigonometry and geometry.

We know that we have to use the idea of the angle of elevation in this case. We know that;

Cos 65 = 20/x

x is the length of the ladder

x =20/Cos 65

x = 20/0.4225

x = 47 feet

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The product of two consecutive positive even integers is 120. Find the value of the
lesser integer.

Answers

Answer:

10. Other number is 12.

Explanation:

The prime factors of 120 are 2*2*2*3*5

To end up with even numbers, the odd numbers must be multiplied by even numbers. The only even numbers are 2s, while there are two odd numbers, 3 and 5.

So we MUST be talking about 2*3 and 2*5 with a 2 left over. That’s 6 and 10, which are by no stretch of the imagination consecutive. But we can either double the 10 (giving us 6 and 20, even less “consecutive”) or the 6.

Double 6 and we have 12. 10 and 12 are consecutive even numbers, because you can add two to get the next one.

QUESTION 2
What portion of a whole does three fifths of two thirds represent?

Answers

Answer:

2/5

Step-by-step explanation:

3/5 * 2/3 is your equation

Multiply the numerators: 3*2=6

Multiply the denominators: 5*3=15

You get: 6/15

Simplify by dividing both the numerator and denominator by 3.

6/15=2/5

How to graph it on a coordinate plan to the right 5x-3y=18

Answers

Tο shift the graph tο the right, we can simply add a pοsitive cοnstant tο the x values οf each pοint befοre plοtting them. Fοr example, if we want tο shift the graph tο the right by 2 units.

What is cοοrdinate plan?

The intersectiοn οf twο number lines creates a twο-dimensiοnal plane knοwn as a cοοrdinate plane. The x-axis, a hοrizοntal number line, and the y-axis, a vertical number line, are twο examples οf these number lines.

Tο graph the equatiοn 5x - 3y = 18 οn a cοοrdinate plane, we can fοllοw these steps:

1. Sοlve fοr y in terms οf x:

5x - 3y = 18

-3y = -5x + 18

y = (5/3)x - 6

2. Chοοse sοme values fοr x and use the equatiοn tο find the cοrrespοnding y values. Fοr example, we can chοοse x = 0, 3, and 6:

When x = 0: y = (5/3)(0) - 6 = -6

When x = 3: y = (5/3)(3) - 6 = -3

When x = 6: y = (5/3)(6) - 6 = 2

3. Plοt the pοints (0, -6), (3, -3), and (6, 2) οn the cοοrdinate plane.

4. Draw a straight line passing thrοugh these three pοints. This line represents the graph οf the equatiοn 5x - 3y = 18.

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pls help find y. 4x+5y-y+3x​

Answers

Answer:

7x+4y

Step-by-step explanation:

combine like terms

Answer:

4?

Step-by-step explanation:

find the radius of circle Q

Answers

The radius of the given circle is x = 3 and x = 3/11.

How are quadratic equations solved, and what are they?

A polynomial equation of degree two is a quadratic equation, indicating that the variable's maximum exponent is 2. There are various ways to solve a quadratic equation, including factoring, completing the square, and applying the quadratic formula. Finding two quadratic expression factors that multiply to produce the constant term c and add to produce the linear term b's coefficient is known as factoring. The quadratic expression is completed by adding and removing a constant component to create a perfect square trinomial that can be factored or solved by calculating the square root.

In the given figure connect the points QF and QG using a line segment, thus forming two right angled triangle.

The perpendicular segment QA divides the base into two equal parts. Thus, the base of the triangle is 8.

Using the Pythagorean theorem we have:

(QF)² = (8)² + (4x + 3)²

QG² = 8² + (7x - 6)²

In the figure QF = QG = r thus:

(8)² + (4x + 3)² = 8² + (7x - 6)²

Expanding using the algebraic identity:

16x² + 24x + 9 = 49x² - 84x + 36

33x² - 108x + 27 = 0

3(11x² - 36x + 9) = 0

Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Substitute the values a = 11, b = -36, and c = 9:

x = (-(-36) ± √((-36)² - 4(11)(9))) / 2(11)

x = (36 ± √(1296 - 396)) / 22

x = (36 ± √900) / 22

x = (36 ± 30) / 22

x = (36 + 30) / 22 = 3

x = (36 - 30) / 22 = 3/11

x = 3 and x = 3/11.

Thus, the radius of the given circle is x = 3 and x = 3/11.

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A company is buying new computers. The company needs no more than 220 desktops and at least 50 laptops. A total of at least 200 computers must be bought. Write a system of linear inequalities to represent the constraints of this situation. Let x represent the number of desktops, and let y represent the number of laptops.

Answers

x + y ≥ 200 (at least 200 computers must be bought)
x ≤ 220 (no more than 220 desktops)
y ≥ 50 (at least 50 laptops must be bought)

Let f be a differentiable function defined by f(x) = 3x + 2e −3x , and let g be a differentiable function with derivative given by g′(x) = 1 x + 4. It is known that lim g(x) = [infinity].


x→[infinity]


The value of lim f(x) g(X) is:______


x→[infinity]

Answers

The value of lim f(x)g(x) as x approaches infinity is 0.

L'Hopital's rule is a mathematical tool used to evaluate limits of functions that are in an indeterminate form.

To find the limit of f(x)g(x) as x approaches infinity, we can use L'Hopital's rule since it is an indeterminate form of infinity times zero. We have:

lim x→[infinity] f(x)g(x) = lim x→[infinity] [(3x + 2e^(-3x))(1/x + 4)]

= lim x→[infinity] [(3 + 2e^(-3x)/x)/(1/x + 4)^(-1)]

Applying L'Hopital's rule to the fraction in the numerator, we get:

lim x→[infinity] [(2e^(-3x)(-3)/x^2)/(1/x + 4)^(-1)]

= lim x→[infinity] [(6e^(-3x)/x^2)/(1/x + 4)]

= lim x→[infinity] [(6e^(-3x)/(x + 4x^2))]

= 0

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Weight of a badminton racket is 0. 950 kg find the weight of 12 such rackets

Answers

The weight of 12 badminton rackets, each weighing 0.950 kg, is 11.4 kg.

The weight of an object refers to the force exerted by gravity on that object. This force is typically measured in units of mass, such as kilograms or pounds. In the case of badminton rackets, the weight is usually measured in grams.

Now, let's consider the weight of a single badminton racket. You've been given the information that the weight of one racket is 0.950 kg. This means that the force exerted by gravity on that racket is 0.950 kg.

If you want to find the weight of 12 such rackets, you need to multiply the weight of one racket by 12. This gives you:

0.950 kg x 12 = 11.4 kg

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6. If g(x) = 7x-4, find g(8)-g (-5)


PLEASE HELP I BEG

Answers

This is the answer, here is the working solution

-1/2 (6- 8x to the power of 2)

(The 8x is to the power of 2)

Answers

Answer:

-3+[tex]4x^{2}[/tex]

Step-by-step explanation:

Answer needed ASAP!!
:)

Answers

The answer of the given question based on the finding the m∠QTS from a circle with the measure of minor arc the answer is the measure of angle ∠QTS is 60° degrees.

What is Arc?

In geometry, arc is  portion of a curve or  circle. It is defined as the part of the curve that is contained between two points, called endpoints, on curve. The length of  arc is  fraction of the circumference of  circle, determined by the measure of  central angle that subtends it.

An arc is typically denoted by  two endpoints, with  small arc or arc symbol above the two letters. For example, an arc with endpoints A and B would be denoted as "⌒AB" or "AB".Arcs can be classified based on their measure or  position of their endpoints.

An arc with measure less than 180 degrees is called  minor arc, while an arc with measure greater than 180 degrees is called  major arc. An arc with measure equal to 180 degrees is called semicircle.

Since arc QS is a minor arc, we know that angle ∠QTS is half the measure of arc QS. Therefore, we have:

m∠QTS = (1/2) m arc QS

m∠QTS = (1/2) (120°) [Substituting the given value of m arc QS]

m∠QTS = 60°

Therefore, the measure of angle ∠QTS is 60° degrees.

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Find the lengths of the diagonals of rectangle QRST when QS = 20x - 5 and RT = 14x + 7.



A) 70


B) 99. 7


C) 17. 5


D) 35

Answers

The correct option is D i.e.35. A line segment connecting the rectangle's two opposed vertices is known as the diagonal.

The rectangle is split into two identical right triangles by its diagonal. The two-dimensional shape of a rectangle has four sides, four vertices, and four angles. A rectangle's two diagonals are the same length.

Two diagonals divide a rectangle into two right-angled triangles, with the diagonal serving as the hypotenuse on each diagonal. The diagonals cut each other in half, creating an acute angle and an obtuse angle respectively. The diagonal of the rectangle form two congruent triangles.

Since the diagonals of a rectangle are equal

∴ QS = RT

20x - 5 = 14x + 7

6x = 12

x = 2

QS = RT = 35

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What is the slope of the line described by the equation below?
y = -6x +3
O A. -6
() в. -з
O C. 6
OD. 3
SUBMIT

Answers

This line is in slope intercept form, which is represented by the equation y=Mx+B.

In this form, M represents the slope of a line, and B represents the line’s y-intercept.

In your equation, y=-6x+3, M is -6 and B is 3. So, your y-intercept is 3 and your slope is -6.

list one advantage and one disadvantage of the secant method compared with the bisection method for finding a simple zero of a nonlinear equation g

Answers

There are often other methods that can converge faster than bisection method.

Advantages and disadvantages of the secant method and bisection method are:Advantages of the secant method:The secant method is faster than the bisection method since it converges faster to the root.It needs less iterations to get the root.Disadvantages of the secant method:The secant method may not converge to a root.In comparison to bisection method, it is more complex and therefore requires more computational time and effort.Advantages of the bisection method:It is more straightforward and simple to implement.In the case of continuous functions, it will always converge to a root.Disadvantages of the bisection method:It is much slower and requires more iterations to converge to a root than the secant method.There are often other methods that can converge faster than bisection method.

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20. You conduct a simulation regarding how many registered voters voted in the last election. Your null hypothesis is that the percentage of people who voted is less than-
is that the percentage of people who voted is greater than 65%.
You determine that the results of your simulation have a p-value of 0.08. What does this mean?
Under the tested hypothesis, the outcome of the simulation has a probability of 8%. With a significance level of 1%, you should reject the null hypothesis.
O
Under the tested hypothesis, the outcome of the simulation has a probability of 8%. With a significance level of 1%, you should fail to reject the null hypothesis.
O
Under the tested hypothesis, the outcome of the simulation has a probability of 0.8%. With a significance level of 1%, you should fail to reject the null hypothesis.
O
Under the tested hypothesis, the outcome of the simulation has a probability of 0.8%. With a significance level of 1%, you should reject the null hypothesis.
O
M
PREVIO

Answers

Under the tested hypothesis, the outcome of the simulation has a probability of 8%. With a significance level of 1%, you should fail to reject the null hypothesis.

Describe p-value?

In statistics, the p-value is a measure of the strength of evidence against a null hypothesis. It is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true.

In hypothesis testing, the null hypothesis is a statement about a population parameter that is being tested. The alternative hypothesis is another statement about the population parameter that is being tested as an alternative to the null hypothesis. The p-value is used to determine whether the observed data provides strong evidence against the null hypothesis in favor of the alternative hypothesis.

Under the tested hypothesis, the outcome of the simulation has a probability of 8%. With a significance level of 1%, you should fail to reject the null hypothesis.

The p-value is the probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true. In this case, the null hypothesis is that the percentage of people who voted is less than or equal to 65%. Since the p-value (0.08) is greater than the significance level of 1%, we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the percentage of people who voted is greater than 65%.

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The result of the simulation has an 8% probability under the tested hypothesis. You should be unable to deny the null hypothesis at a significance level of 1%.

Describe p-value?

The p-value in statistics is a gauge of the weight of proof opposing a null hypothesis. In the event that the null hypothesis is correct, it is the likelihood of getting a test statistic that is equally extreme or more extreme than the observed value.

The null hypothesis in hypothesis testing is a claim made about the demographic parameter under investigation. In place of the null hypothesis, a different claim is made about the demographic parameter in the alternative hypothesis. The p-value is used to assess whether the recorded data strongly support the alternative hypothesis over the null hypothesis.

The p-value, under the assumption that the null hypothesis is correct, is the likelihood of getting a result that is equally extreme or more extreme than the observed result. In this instance, the null hypothesis is that less than or equivalent to 65% of eligible voters cast ballots.

We are unable to reject the null hypothesis because the p-value (0.08), which is higher than the 1% threshold of significance, is not zero. This implies that we lack sufficient evidence to draw the conclusion that more than 65% of eligible voters cast ballots.

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which type of number property is 28​

Answers

Answer:

28 is an integer, which is a type of rational number. It has various number properties, including:

Even number: 28 is an even number because it is divisible by 2.

Composite number: 28 is a composite number because it has factors other than 1 and itself. The factors of 28 are 1, 2, 4, 7, 14, and 28.

Abundant number: 28 is an abundant number because the sum of its proper divisors (the divisors other than itself) is greater than 28. The sum of the proper divisors of 28 is 1 + 2 + 4 + 7 + 14 = 28.

Perfect number: 28 is not a perfect number because the sum of its proper divisors is not equal to 28.

Harshad number: 28 is a Harshad number because it is divisible by the sum of its digits. The sum of the digits of 28 is 2 + 8 = 10, and 28 is divisible by 10.

Automorphic number: 28 is not an automorphic number because its square (784) does not end with the digits 28.

It is a composite number, its proper divisors being 1, 2, 4, 7, and 14.

Rewrite each expression as the product of two fractions, one of which is equal to 1. Then, write it as an
equivalent, but simpler, expression.
(a)
105
10²
(b)
(c)
18

Answers

For (a), 105 can be written as the product of two fractions, one of which is equal to 1. The expression would be:

105 = (105/1) × (1/1)

This expression can be simplified to:

105 = 105

For (b), the expression can be written as the product of two fractions, one of which is equal to 1. The expression would be:

5/2 = (5/2) × (1/1)

This expression can be simplified to:

5/2

For (c), the expression can be written as the product of two fractions, one of which is equal to 1. The expression would be:

18 = (18/1) × (1/1)

This expression can be simplified to:

18 = 18

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