A two-digit number is formed using the digits 1, 2 and 3. Repetition of digits is allowed. (a) List the sample space. (b) Find the probability that the two-digit number formed is (i) divisible by 3, (ii) a perfect square, (iii) a prime number, (iv) a composite number.​

Answer:

1. 200

2.(1,4)

3.  5

4. (3,1)

5. NO SOLUTION

Step-by-step explanation:

Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ A=900\\ b=2a\\ h=40 \end{cases}\implies 900=\cfrac{40(a+2a)}{2} \\\\\\ 1800=40(3a)\implies 1800=120a\implies \cfrac{1800}{120}=a\implies \boxed{15=a}~\hfill \boxed{b=30}[/tex]

If the Time taken by object is 2 hour then the height will be 80.4 feet.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

We have Given the function as

h(t) = 50t - 4.9t²

If time = 2 hours then put the value of t=2 in the above Equation we get

h(t) = 50t - 4.9t²

h(t) = 50(2) - 4.9(2)²

h(t) = 100 - 4.9 x 4

h(2) = 100 - 19.6

h(2)= 80.4

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Answer:

23 to 42

23:42

[tex]\frac{23}{42}[/tex]

The solution is, c. Sarah rounded the area of the floor to 100 square feet., is statement BEST explains why Sarah’s prediction is incorrect.

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

rectangular dining room floor, which has a length of 12 feet and a width of 9 feet.

The cost to install the carpet is $5 per square foot.

so, area of the floor = A= l. w

                                     = 108 ft^2

so, total cost = 108* 5

                     =$ 540

i.e. Sarah rounded the area of the floor to 100 square feet.

because, 100*5 = $500

Hence, The solution is, c. Sarah rounded the area of the floor to 100 square feet., is statement BEST explains why Sarah’s prediction is incorrect.

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The amount of solar radiation available is 415.4 W/m² and the albedo was higher during the last glacial maximum than it is today because there was more ice and snow on the planet.

Radiation refers to the emission and transmission of energy through space or a material medium in the form of electromagnetic waves or energetic particles. Radiation can take many forms, including light, X-rays, and radio waves, and can be either ionizing (having enough energy to remove electrons from atoms and molecules) or non-ionizing (having insufficient energy to cause ionization). Radiation is a fundamental aspect of physics and plays a crucial role in many natural processes, such as nuclear reactions and the warming of the Earth by the sun.

a) The amount of solar radiation available to warm the average square meter on Earth during the last glacial maximum can be found by multiplying the solar constant by the average albedo:

En = 1363 W/m² * 0.305 = 415.4 W/m²

b) The albedo was higher during the last glacial maximum than it is today because there was more ice and snow on the planet. Ice and snow are very reflective and therefore have a high albedo, which means that they reflect more of the incoming solar radiation back into space, making the planet cooler. During the last glacial maximum, there was more ice and snow, which led to a higher average albedo and a cooler planet.

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From the data that teacher described, the following information could be determined:

1. The distribution of midterm and final exam scores for the students. This would allow you to see the range of scores and the overall performance of the students.

2. The average midterm and final exam scores for the students. This would give you an idea of the average performance of the students on each exam.

3. The correlation between final exam and midterm scores. This would indicate if there were a relationship between performance on the midterm and final exams.

4. The distribution of total points calculated for each student. This would allow you to see the range of total scores and the overall performance of the students.

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Answer:

B

Step-by-step explanation:

The entry "cash 700000" is listed as a credit in the T account because it represents an increase in the cash balance of the account. In accounting, credits are used to record increases in asset accounts, such as cash. When cash is received, it is recorded as a credit to the cash account, which increases the balance of the account. Therefore, in this case, the entry "cash 700000" is a credit entry because it represents an increase in the cash balance.

The interest rate of the account that Steve invested in after the given number of years would be = 16%

The total amount of money invested (p) = $2,807

The time of investment= 13 years

The interest generated at the end of the given years = 9,044.13-2807 = $6,237.13

Therefore the rate = ?

The formula for simple interest:

= P×T×R/100

6,237.13= 2,807× 14 ×r/100

Make r the subject of formula;

r= 6,237.14×100/2807×14

r = 623714/39298

r= 15.87139294

r= 16%

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Answer:

To find out how many packs of cardinal flower seeds you bought, you need to divide the total amount you spent ($36) by the cost per pack ($4).

$36 ÷ $4 = 9

Therefore, you bought 9 packs of cardinal flower seeds.

A pack of cardinal flower seeds costs $4. You spend $36 on seeds. The correct answer is 9.

Cardinals love sunflower seeds, particularly black oil sunflower seeds. Their thin shells are quite easy for cardinals to break. These songbirds can also eat hulled and heavier-shelled striped sunflower seeds due to their sturdy beaks.

So, if we spend $36 on seeds. we are going to use 36 and 4 to find are answer:

→ 36/4

→ = 9

Therefore, A pack of cardinal flower seeds costs $4. You spend $36 on seeds. The correct answer is 9.

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The answer is 10.67 ft. The distance, x, from Player 1 to wall is 10.67 ft.

Given, Two different triangles for player 1 and player 2.

Both triangles have right angle and same angle where they are connected. So other angle is also same. All angles are same so they are similar triangles. smaller triangle is similar to larger triangle.

The distance x in the figure is required.

The required distance is x = 10.65 ft

The given triangles ABC and CDE are similar by Angle.

∠B = ∠D = 90°

∠ACB =∠ECD

The ratio of the sides is:

[tex]\frac{BC}{CD} = \frac{12}{9} = \frac{4}{3}[/tex]

So,

[tex]\frac{AB}{ED} =\frac{4}{3}[/tex]

x/8 = 4/3

x = 4/3 * 8

x = 10.65 ft

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Answer:

0.65*10=6.5

10*0.35=3.5

10-3.5=6.5

So, it is decreasing by 35%

Step-by-step explanation:

A. The displacement is the change in position, which is given by the change in the height, so:

i. [1,2] = -5.46 m/s

ii. [1,1.1) = -1.39 m/s

iii. [1,1.01) = -0.138 m/s

iv. [1,1.001) = -0.0138 m/s

(a) To find the average velocity over a time interval, we need to calculate the displacement during that time interval and divide it by the length of the interval. The displacement is the change in position, which is given by the change in the height, so:

i. [1,2]: Δs = y(2) - y(1) = [20(2) - 1.87(2)²] - [20(1) - 1.87(1)²] ≈ -5.46

Average velocity = Δs / Δt = -5.46 / (2 - 1) = -5.46 m/s

ii. [1,1.1): Δs = y(1.1) - y(1) = [20(1.1) - 1.87(1.1)²] - [20(1) - 1.87(1)²] ≈ -1.39

Average velocity = Δs / Δt = -1.39 / (1.1 - 1) = -1.39 m/s

iii. [1,1.01): Δs = y(1.01) - y(1) = [20(1.01) - 1.87(1.01)²] - [20(1) - 1.87(1)²] ≈ -0.138

Average velocity = Δs / Δt = -0.138 / (1.01 - 1) = -0.138 m/s

iv. [1,1.001): Δs = y(1.001) - y(1) = [20(1.001) - 1.87(1.001)²] - [20(1) - 1.87(1)²] ≈ -0.0138

Average velocity = Δs / Δt = -0.0138 / (1.001 - 1) = -0.0138 m/s

(b) The instantaneous velocity at t=1 is given by the derivative of the height function with respect to time, which is:

dy/dt = 20 - 3.74t

So the instantaneous velocity at t=1 is:

dy/dt(1) = 20 - 3.74(1) = 16.26 m/s (approximately)

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Answer:

2

Step-by-step explanation:

the degree of polynomial is 2

Kerys should substitute the values of k from 0 to 4 (inclusive) in the binomial theorem expression to expand the binomial (2x + y)⁴.

The binomial theorem states the principle for expanding the algebraic expression (x + y)ⁿ and describes it as the total of the phrases involving the unique exponents of the x and y variables. Each word in a binomial expansion has a coefficient, which is a numerical value.

here, we have,

The binomial theorem states that the expansion of the binomial (x+y)^n is given by the formula:

(x+y)n = ∑nk=0nCk xn-kyk = ∑nk=0nCk xkyn-k

The variable n represents the power to which the binomial is raised, in this case n = 4.

The variable k is the exponent of the second term in the binomial (b), in this case y.

So, with k = 0, the term will be aⁿ = (2x)⁴, with k = 1, the term will be

a^(n-1) *b = (2x)³y , and so on.

Therefore, he should substitute the values of k from 0 to 4 (inclusive) in the binomial theorem expression to expand the binomial (2x + y)⁴.

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Answer:

A: No solution

B: Unique Solution: (0, 0)

Step-by-step explanation:

In System A, you may notice that in both equations the two equations have variables with the same coefficient, and this is ideal for the elimination method of solving the equation. We want to add the equations in a way that cancels out variables. So let's multiply the top equation by negative one: [tex]-1(2x+3y)=-(9)\implies -2x-3y=-9[/tex]

Now from here we want to add the two equations:

[tex]\ \ -2x-3y=9\\+2x+3y=4\\0+0=13[/tex]

And the statement provided is clearly not true, 0 is never equal to 13, meaning the systems of equation has no solution, which occurs when you have two parallel lines.

In this case, we can easily solve this using substitution, since y is equal to 7x that means we can substitute in 7x for y in the second equation:

[tex]y=x\implies 7x=x[/tex]

And from here we subtract x from both sides, and divide by 6 giving us:

[tex]x=0[/tex]

And now we can take this value and plug it into either equation to solve for our y value, and it's most convenient to plug it into the y = x equation... since there's nothing to solve, we just get:

y = 0

So x = 0, and y = 0, meaning there is a unique solution of (0, 0)

The first mechanic worked for 5 hours and the second mechanic worked for 15 hours.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Two mechanics worked on a car.

The first mechanic charged $55 per hour,

and the second mechanic charged $65 per hour.

The mechanics worked for a combined total of 20 hours,

and together they charged a total of $1250.

Let x be the number of working hours of the First mechanic and y be the

number of working hours of the second mechanic.

So

x + y = 20  {equation 1}

55x + 65y = 1250 {equation 2}

Substituting the value of y from the equation 1 to the equation 2,

55x + 65(20 - x) = 1250

55x + 1300 - 65x = 1250

-10x = -50

x = 5

And y = 15

Therefore, x = 5 and y = 15.

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Answer:

10 degrees

Step-by-step explanation:

In a triangle, the interior angles of a triangle (the angles in the inside) will always add up to 180 degrees.

We're given that the triangle is a right triangle which immediately gives us one angle, of 90 degrees, since that's a right angle. We're also given another angle of 80, and adding up these two angles plus the last angle, should give us 180.

Let's represent the unknown angle as "A", giving us the equation: [tex]90 + 80+ A= 180[/tex]

Now from here we can combine the 90 and 80 to get:

[tex]170+A=180[/tex]

Now from here we subtract 170 from both sides (to maintain equality and get rid of the 170):

[tex]170-170+A=180-170[/tex]

We simplify 170-170 to 0, which we don't need to put in the equation as 0 + A is just A. We also simplify 180 - 170 to 10:

[tex]A=10[/tex]

So the other acute angle is 10 degrees.

The triangle's missing angle, according to the provided assertion, is (a) 62° (b) 57° (c) 59° (d) sin0

Trigonometry is typically included in math courses for sophomores or juniors. Trigonometry is frequently included as a unit or term emphasis in other math classes in adding to being given as a separate course.

(a) sin(28°) = cos(90° - 28°) = cos(62°)

      62° is right answer.

(b) cos (33°) = sin (90° – 33°) = sin (57°)

      57° is correct answer.

(c) cos (31°) = sin(90° - 31°) = sin (59°)

      59° is correct answer

(d) cos(90° - 0) = sin0

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135 and 59 are the values of fog(5) and gof(5) respectively.

Composite functions are also known as function of a function. Given the functions below;

f(x) = x^2 + 6x

g(x) = x + 4

For fog(5)

fog(5) = f(g(5))

f(g(x)) = f(x +4)

f(g(x)) = (x+4)^2 + 6(x+4)

f(g(5)) = (9)^2 + 6(9)

f(g(5)) = 81. + 54 = 135

For gof(5))

g(f(x)) = g(x^2 + 6x)

g(f(x)) = x^2 + 6x + 4

g(f(5)) = 5^2 + 6(5) + 4

g(f(5)) = 59

Hence the value of the composite values fog(5) and gof(5) area 135 and 59

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The equation of the line is y=-2x/5 -10

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: A line that passes through (5,-12) and m=-2/5

Thus using the slope intercept form constructing it we get

y=mx+c

Putting (5,-12) and m=-2/5

-12=-2/5×5+c

c=-12+2

c=-10

The equation of the line is y=-2x/5 -10

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Answer:

see below

Step-by-step explanation:

g(t) = 5t² - 3t+ 6

g(2) = 5*4 - 3*2 + 6  =20

g(-1) = 5*1 -3* (-1) +6 =5+3+6 = 14

g(t+2) = 5(t+2)² - 3(t+2) + 6

= 5*(t²+4t+4) - 3t -6+6

= 5t²+20t+20-3t

= 5t²+17t+20

The equation of line is y = -2x + 9

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 1 , 7 )

The slope of the line is m = -2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 7 = -2 ( x - 1 )

y - 7 = -2x + 2

Adding 7 on both sides of the equation , we get

y = -2x + 9

Hence , the equation of line is y = -2x + 9

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Answer:

Step-by-step explanation:

This graph goes up to 2 and down to -2, which tells us that the amplitude of the waves is 2. In the equation for the parent graph, y = sinx, we will throw the 2 out front which is where the amplitude goes in sin and cos curves:

y = 2sinx

The value of (13 - 7) is 6 and it can be determined by using the method of making a group of 10 in which arithmetic operations and rearrangement of the given expression is performed.

The term arithmetic stems from the Greek noun arithmos, which means "number," with pauses in Latin, Anglo-French, and Middle English along the route. Even the most elementary math contains a large vocabulary. The study of numbers and their operations, which are relevant to all other fields of mathematics, are part of the discipline of arithmetic operations. Addition, subtraction, multiplication, and division are the basic operations that make up this system.

Given that, expression: 13 - 7

The steps to determine the value of (13 - 7) by making a group of 10 are as follows:

Step 1 - Breakup 13 into the tens and the ones:

= (10 + 3) - 7

Step 2 - Breakup 7 into the tens and the ones:

= (10 + 3) - (10 - 3)

Step 3 - Rewrite the above expression:

= (10 - 10) + (3 + 3)

Step 4 - Subtraction of 10 by 10:

= (3 + 3)

Step 5 - Addition of 3 by 3:

= 6

So, the value of (13 - 7) is 6 and it can be determined by using the method of making a group of 10.

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The complete question is as follows:

My monthly take-home pay would be $2461.16.

My yearly take-home pay would be $29533.92.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

If my take-home pay every Monday is $615.29 then my monthly take-home pay would be,

= (4×615.29).

= $2461.16  (as we have 4 Mondays in a month).

Now, My take-home pay for a year would be,

= (4×12×615.29).         (as we have 4 Mondays in a month and 12 months in a

                                                                                                                      year)                                                 = $29533.92

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A linear equation indicating the number of grades students will receive in Mr. Perez's class is as follows;

Slope: 2.

Y-Intercept: 7.

Equation: y = 2x + 7.

In Mathematics, the slope-intercept form of a line can be calculated by using this mathematical expression:

y = mx + b

Where:

From the information provided above, we have the following slope and y-intercept on the line:

Y-intercept = 7

Slope, m = 2

Therefore, the required equation of line is given by:

y = mx + c

y = 2x + 7

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However, we can't determine the exact number of participants with this information alone.

an individual who engages in or becomes engaged in a specific action. Examples. Over three thousand people will be competing in the games, a worldwide athletic event. She has contributed significantly to the conversation.

Let's use logic to determine the possible rankings of the participants:

A placed seventh, so at least 6 people ranked higher than A.

B placed sixth, so at least 5 people ranked higher than B.

C ranked above A and B, so C must have ranked at least fifth. This means there are at least four people who ranked higher than C.

D does worse than E and ranks penultimate, which means D ranked second to last. Therefore, there must be at least two people who ranked worse than D. Also, E must have ranked higher than D, so there is at least one person who ranked higher than D.

Putting this information together, we know that there are at least 6 + 5 + 4 + 2 + 1 = 18 people who participated in the contest.

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The sentence regarding how many books must be sold to make a profit is given as follows:

Anna must sell at least 2 books to make a profit.

The profit function is given by the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

The revenue function and the cost function for this problem are given as follows:

Hence the profit function is given as follows:

P(x) = 6.56x - 1.09x - 10.063.

P(x) = 5.47x - 10.063.

A profit is made when:

P(x) > 0.

Hence:

5.47x - 10.063 > 0

5.47x > 10.063

x > 10.063/5.47

x > 1.84.

As the number of books is a countable amount, we have that:

Anna must sell at least 2 books to make a profit.

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