Learning Task 2: Give the place value of the underlined digits. Write
your answers in your notebook
1. 2. 284
2. 2. 6853
3. 3. 1763
4. 19. 0365
5. 0. 0128
6. 0. 827
7. 4. 7659
8. 86. 047
9. 0. 8273
10. 21. 843​

The height of the line in a frequency polygon and the height of the bars in a histogram both represent the frequency or count of the data in a particular category or range of values.

What is Polygon?

In two dimensions, a polygon is a closed object made up of segments of straight lines that join at least three points. A polygon in mathematics can be convex or concave and have any number of sides.

The height of the line in a frequency polygon is proportional to the frequency of the data. The frequency value is marked at the highest point of the line, which is drawn between the midpoints of each category or range of values.

The height of the bar in a histogram, which is proportional to the number of data points in that category or range of values, denotes the frequency of the data. To depict the frequency distribution of the data, bars are drawn next to one another with no space in between.

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The height of the line in a frequency polygon and the height of the bars in a histogram both represent the frequency or count of the data in a particular category or range of values.

What is Polygon?

In two dimensions, a polygon is a closed object made up of segments of straight lines that join at least three points. A polygon in mathematics can be convex or concave and have any number of sides.

The height of the line in a frequency polygon is proportional to the frequency of the data. The frequency value is marked at the highest point of the line, which is drawn between the midpoints of each category or range of values.

The height of the bar in a histogram, which is proportional to the number of data points in that category or range of values, denotes the frequency of the data. To depict the frequency distribution of the data, bars are drawn next to one another with no space in between.

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The value of x is 2.045 by simple algebra.

Use the time formula, t = d/s, which states that time is equal to distance divided by speed, to solve for time. Time is a function of both speed and distance.

Until it reaches its destination 200 miles distant, a car is driving on a little highway at either 55 or 35 miles per hour, depending on the posted speed restrictions.

x is the duration, in hours, that the vehicle is travelling at 55 mph.

Y is the duration, in hours, that the vehicle is travelling at 35 mph.

55x + 35y = 200 is the equation defining the relationship.

We must locate:

If the trip takes the car 2.5 hours at 35 miles per hour, how long does it take to travel at 55 miles per hour?

∵ 55x + 35y = 200

The drive takes the car 2.5 hours at a speed of 35 mph.

Y shows the duration of time for an automobile travelling at 35 mph.

∴ y = 2.5

- To obtain the value of x, substitute the value of y into the equation.

∴ 55x + 35(2.5) = 200

∴ 55x + 87.5 = 200

- Take 87.5 off of both sides.

∴ 55x = 112.5

- Subtract 55 from both sides.

x equals 2.045 hours.

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The proof of the area of the circle equation is shown below

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

Area of radius 1 = π

The area of a circle is proportional to the square of its radius.

When the radius is multiplied by a scale factor of "r," the area is multiplied by the square of that factor: r^2.

So, the area of a circle of radius "r" is given by π * r^2 square units.

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In this exponential growth function, after 5 hours it contains 1944mg and after 6 hours it contains 5832mg.

What is exponential function?

An exponential function is defined by the formula f(x) = aˣ, where the  x is any real number , acts as an exponent. The exponential curve depends on the exponential function  which  depends on the value of the x.

Where a>0 and a is not equal to 1.

If many functions, “x” is a variable and “a” is a constant, which is the base of the function.

Given that, every hour, the mass of bacteria in a sample multiplies by 3.

Then the exponential function can be taken as f(x)= 3ⁿ x where f(x)= mass of bacteria, n=time(hours), x= original mass.

Here x= 8 mg

a) if n=5 hours then the exponential function will be

f(x)= 3⁵ × x

putting x=8 we get,

f(8)= 3⁵ × 8

 = 1944

b) if n=6 hours then the exponential function will be

f(x)= 3⁶ × x

putting x=8 we get,

f(8)= 3⁶ × 8

 = 5832

Hence, after 5 hours it contains 1944mg and after 6 hours it contains 5832mg.

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There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, cosecant, tangent and cotangent.

By using a right-angled triangle as a reference, the trigonometric functions and identities are derived:

sin Î= Opposite Side/Hypotenuse

cos Î= Adjacent Side/Hypotenuse

tan Î= Opposite Side/Adjacent Side

sec Î= Hypotenuse/Adjacent Side

cosec Î= Hypotenuse/Opposite Side

cot Î= Adjacent Side/Opposite Side

All these are taken from a right-angled triangle.

When the height and base side of the right triangle are known, we can find out the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas.

The reciprocal trigonometric identities are also derived by using the trigonometric functions.

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The probability of all three balls being brown is 0.092 or about 9.2%.

To calculate the probability that all three balls are brown, we need to consider the total number of possible outcomes when selecting three balls from the urn one at a time. The urn contains 30 balls in total, of which 8 are purple, 10 are orange and 12 are brown. To find the probability that all three balls selected are brown we need to use the formula for conditional probability:

Probability of all three balls being brown = (Probability of selecting first brown ball) × (Probability of selecting second brown ball given that the first ball was brown) × (Probability of selecting third brown ball given that the first two balls were brown).The probability of selecting a brown ball on the first draw is 12/30, the probability of selecting a brown ball on the second draw given that the first ball was brown is 11/29 and the probability of selecting a brown ball on the third draw given that the first two balls were brown is 10/28

Therefore, the probability of all three balls being brown is (12/30) * (11/29) * (10/28) = 0.092 or about 9.2%.

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Answer:-2, 4

Step-by-step explanation:

The graph that matches the inequality equation represented as 3x − 2y ≥  4 is

A. The graph shows a solid line, which crosses the y-axis at negative 2 and the x-axis at 4 thirds, with shading above the line.

There are some points that help in interpreting inequality graphs.

The first part is to arrange the equation in the form so that y is the subject of the formula and to the left.

3x − 2y ≥  4

-2y ≥ 4 - 3x

y ≤ 3/2 x - 2

Then watch out for dashed lines or solid lines

dashed lines means there is no equality sign in the inequality > OR <

solid line means there is equality in the inequality  ≤ OR ≥

Another part is the shaded portion

shading above the line defines greater than

shading below the line defines less than

comparing with y = mx + b shows that the intercept which is b is -2

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To graph the system of inequalities:

y ≤ −5x + 2

y < 3x − 1.5

We can start by graphing the boundary lines for each inequality:

For y ≤ −5x + 2, the boundary line is y = -5x + 2, which has a slope of -5 and a y-intercept of 2. Since the inequality includes "less than or equal to," we will use a solid line to represent the boundary.

For y < 3x − 1.5, the boundary line is y = 3x - 1.5, which has a slope of 3 and a y-intercept of -1.5. Since the inequality is "less than" and not "less than or equal to," we will use a dashed line to represent the boundary.

Next, we need to determine the shading for each inequality:

For y ≤ −5x + 2, we shade below the solid line because y is less than or equal to the other side of the inequality.

For y < 3x − 1.5, we shade below the dashed line because y is less than the other side of the inequality.

Based on the given options, the correct answer is:

The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.

The solution of the algebraic expression is n ≥ - 64

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

We an algebraic expression 3/4(n) + 12 ≥ -36. In order to solve this inequality, you need to find the value of n. That is:

3/4(n) + 12 ≥ -36

3/4(n)  ≥ -36 - 12

3/4(n)  ≥ -48

3n  ≥ -48 × 4

3n ≥ - -192

n ≥ -192/3

n ≥ - 64

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The area of the new figure will be 3/2 times the area of the original figure. Option C is correct.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
Tyrell dilated a figure by a scale factor of 3/2.
It implies that the new figure will be larger than the original size.
And makes the area of the new figure will be 3/2 times the area of the original figure.

Thus, the area of the new figure will be 3/2 times the area of the original figure. Option C is correct.

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Step-by-step explanation:

a. The profit function, P(x), can be found by subtracting the cost function from the revenue function.

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

P(x) = (-0.04x² + 320x) - (85x + 120,000)

P(x) = -0.04x² + 235x - 120,000

b. To find the profit if 1000 bicycles are produced and sold, substitute x=1000 into the profit function:

P(1000) = -0.04(1000)² + 235(1000) - 120,000

P(1000) = -40,000 + 235,000 - 120,000

P(1000) = 75,000

So, the profit would be $75,000 if 1000 bicycles are produced and sold.

c. To find the break-even point, we set the profit function equal to zero and solve for x:

P(x) = 0

-0.04x² + 235x - 120,000 = 0

Using the quadratic formula or factoring, we can find that the break-even point occurs when:

x = (235 +/- sqrt(235^2 - 4(-0.04)(-120,000)))/(2(-0.04))

x = (235 +/- sqrt(55,089,000))/(-0.08)

x = (235 +/- 7,500)/(-0.08)

x = (235 - 7,500)/(-0.08) or (235 + 7,500)/(-0.08)

x = -31,250/ -0.08 or 5,375/-0.08

x = 3906.25 or -64,375

Since negative values of x do not make sense in this context, the break-even point occurs when 3906.25 bicycles are produced and sold.

The required center of the given circle is (-1, -4) and the radius is 1.

The equation of a circle with center (h,k) and radius r is :

r² = (x−h)² + (y−k)²

To put the equation x² + y² + 2x + 8y = 8 into this form, we need to complete the square for both x and y.

First, we'll complete the square for x:

x² + 2x = x² + 2x + 1 - 1

Next, we'll complete the square for y:

y² + 8y = y² + 8y + 16 - 16

Now we can add the two completed squares together and add the constant from the original equation:

(x² + 2x + 1) + (y² + 8y + 16) = 8 + 1 + 16

x² + 2x + 1 + y² + 8y + 16 = 25

Finally, we can divide both sides by 25 to get the equation in the standard form of a circle:

(x² + 2x + 1)/25 + (y² + 8y + 16)/25 = 1

(x + 1)² + (y + 4)² = 1

Thus, the center of the circle is (-1, -4) and the radius is 1.

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The probability that a 68-year-old will live to be 78 years old is approximately 60%. However, this number can vary depending on the individual's health, lifestyle, and family history.

The probability that a 68-year-old will live to be 78 years old is determined by their life expectancy. Life expectancy is the average number of years that a person is expected to live based on their age, gender, and other factors. According to the United States Census Bureau, the average life expectancy for a 68-year-old is 18.6 more years. This means that the probability of a 68-year-old living to be 78 is approximately 60%.

The probability that a 68-year-old will live to be 78 years old is approximately 60%. However, this number can vary depending on the individual's health, lifestyle, and family history.

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The parent graph of the parabola is illustrated below.

The term parabola is defined as the quadratic function is a U-shaped curve is called a parabola.

Here we need to define the parent graph of the parabola.

As we all know that the parent graph is the graph of a relatively simple function and it is known as the process before the transforming the function in various ways such as the graph can be translated, reflected, or otherwise changed.

For example here we have take the simplest parabola is y = x² whose graph is shown below and while we looking into the graph we have identified that it passes through the origin (0,0) and is contained in Quadrants I and II.

As this graph is known as the "Parent Function" for parabolas also known as quadratic functions.

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The function value is 5/2 when x is 0 and value of function is 4 when x =-3.

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=|1-x|/2 + 2

We need to find the value of function when x is 0 and when x is -3.

Plug in value x =0

f(0)=|1-0|/2+2

=1/2+2

f(0)=5/2

Now we have to find the function when x is -3

f(-3)=|1+3|/2+2

=4

Hence, the function value is 5/2 when x is 0 and value of function is 4 when x =-3.

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Answer: The linear function is represented by f(x) = (4x/3) + 12

Step-by-step explanation: Taking a linear function's equation pattern to be the graph of y = ax + b, plot the sollutions for such:

(8) = (-3)a + b, and similarly: (-4) = 6a + b, solving for that will lead to a = (4/3) and b = (12), thus: f(x) = (4x/3) + 12.

Answer:

definatly fan, i do not know about the water heater if it blows air then i think its true  last 2 i would select

Step-by-step explanation:

Answer:

it's a fan cause a turbine is currently a fan

A system of equations that has no solution can be represented by two lines in a coordinate plane that are parallel.

A system of equations is said to have no solution if there is no set of values that can simultaneously satisfy both equations. This can occur when the equations are inconsistent, meaning that they cannot be true at the same time, or when the equations are dependent, meaning that one equation is a multiple of the other.

Parallel lines have the same slope but different y-intercept, this means that there's no point that belongs to both lines, that's why the system has no solution.

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So, the probability that a customer buys either pet supplies or baby supplies is 0.77.

The probability that a customer buys either pet supplies or baby supplies is represented by P(A U B).

Using the formula for the probability of the union of two events: P(A U B) = P(A) + P(B) - P(A ∩ B),

We can substitute in the given probabilities: P(A U B) = 0.64 + 0.25 - 0.12

Therefore, the equation that represents the probability that a customer buys either pet supplies or baby supplies is:

P(A U B) = 0.64 + 0.25 - 0.12 = 0.77

This means that the probability that a customer buys either pet supplies or baby supplies is 0.77.

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All the mathematical expression are,

1) 15 + x = 3

2) 16y = 48

3) 3x - 12 = 33

4) 5 (x - 18) = 50

5) 10 + x/4 = 14

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We can translate the expressions as;

1. The sum of fifteen and a number is three.

Let a number = x

Hence, We get;

⇒ 15 + x = 3

2. The product of sixteen and a certain number is forty-eight.

Let a number = x

So, We get;

⇒ 16y = 48

3. Twelve less than thrice a certain number is thirty-three.

Let a number = x

Hence, We get;

⇒ 3x - 12 = 33

4. Five times the difference between a number and eighteen is fifty.

Let a number = x

Hence, We get;

⇒ 5 (x - 18) = 50

5. Ten more than the quotient of a number and four is fourteen.

Let a number = x

Hence, We get;

⇒ 10 + x/4 = 14

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Karen solved the equation by expanding it to 5x + x - 7 = 36. She then subtracted x from both sides to get 5x - 7 = 36. Next, she added 7 to both sides to get 5x = 43. Finally, she divided both sides by 5 to get x = 6.

Karen solved the equation

x - 7 + 5x = 36

by expanding it to

5x + x - 7 = 36.

This expands the equation to two terms, 5x and -7, which can then be manipulated to solve for the variable x. To do this, she subtracted x from both sides of the equation, leaving

5x - 7 = 36.

She then added 7 to both sides of the equation, leaving

5x = 43.

Finally, she divided both sides of the equation by 5 to get x = 6, which is the solution to the equation. This method works because, by subtracting x from both sides and adding 7 to both sides, she was able to isolate the variable and solve for it.

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Answer:

y = 163°

Step-by-step explanation:

Vertically opposite angles are equal. So, y = 163°

Also, the points u give for the question is halved for the person who writes the answer. So, I will get 10 points, not 20. Anyways, Cheers!

The cost of each sixty minute tape is $1.083 and the cost of each ninety minute tape is $7.331.

Algebraic equation

This question can be solved using the algebraic equation:

Let x be the cost of each sixty minute tape and y be the cost of each ninety minute tape.

We can set up the following equations:

5x + 9y = 71.40

8x + 7y = 74.65

We can subtract the first equation from the second equation to solve for x:

8x + 7y = 74.65

-5x - 9y = -71.40

3x - 2y = 3.25

Divide both sides by 3 to solve for x:

3x - 2y = 3.25

3 3

x -  2 2

y =  1.083

Now substitute x = 1.083 into the first equation:

5(1.083) + 9y = 71.40

5.415 + 9y = 71.40

Subtract 5.415 from both sides to solve for y:

5.415 + 9y = 71.40

-5.415 -5.415

9y = 65.985

Divide both sides by 9 to solve for y:

9y = 65.985

9 9

y =  7.331

Therefore, the cost of each sixty minute tape is $1.083 and the cost of each ninety minute tape is $7.331.

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The inequality that can be used to find the price that Jerome should charge for each cookie if he wants to have a profit of more than $25 is x > 0.9.

An inequality is a mathematical statement that compares the value of two expressions using one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), ≠ (not equal to). Inequalities are used to express relationships between numbers and can be used to describe constraints or limitations in real-world problems.

Let x be the price Jerome charges for each cookie.

We can write the inequality as:

x(50) > 20 + 25

To solve for x, we divide both sides by 50:

x > (20 + 25)/50

x > 0.9

So Jerome should charge more than $0.9 for each cookie if he wants to have a profit of more than $25.

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Answer:

6 1/2

Step-by-step explanation:

1 1/6+ 2 1/6+ 3 1/6=6 3/6

Then you would simplify and get 6 1/2

The value of x for the similar triangles is equal to 11.

The triangles are similar, this implies that the length 5 cm of the smaller triangle is similar to the length (3x + 7 + 5) cm of the larger triangle

and the length cm of the smaller triangle is similar to the length (48 + 6) cm of the larger triangle

so;

5/(3x + 12) = 6/54

6(3x + 12) = 5(54) {cross multiplication}

18x + 72 = 270

18x = 279 - 72 {subtract 72 from both sides}

18x = 198

x = 198/18 {divide through by 18}

x = 11

Therefore, the value of x is equal to 11 for the similar triangles.

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The maturity value after 100 days as calculated from the data given in the question is found to be as $1032.87.

The formula to calculate the interest rate is ,

Interest = ( Principal x  rate x time )/100

Interest = 1000 x 12 x 100/365 x 100

Interest = 12000/365

Interest = 32.87

Therefore, the maturity value will be ,

= Principal + Interest

= 1000 + 32.87

= $1032.87.

Therefore , the maturity value thus becomes  $1032.87.

The rate of interest is referred to as the amount which the borrower will give to the lender once their contract period for a loan is over.

A lot of business is based upon rate of interest only, they lend money and earn their profit by this interest only after the given time period. Principal is the amount primary amount.

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For the three red lights, we have a "9 sockets choose 3" option. In those 9C3 methods. The solution is 1260 (9C3) (6C4)(2C2).

For the three red lights, we have a "9 sockets choose 3" option. In those 9C3 methods.

There are now just 6 open sockets after the 3 red bulbs have been installed.

Put three red bulbs in the first three sockets.

None = 9C3

There are 4 yellow bulbs in 4 sockets.

Way count is 6C4

Two sockets hold two blue bulbs.

Number of ways = 2C2

For the four yellow lights, we have a choice of "6 sockets, choose 4" 6C4 in that manner.

There are just 2 open sockets left once the 4 red lights are screwed in.

The blue lights are available in "2 sockets pick 2." Consequently, (2C2) = 1 way.

Once those two bulbs were screwed in, a bulb was present in each socket.

Total number of methods is 84 * 15 * 1 or 9C3 * 6C4 * 2C2.

1260 different ways in total.

So, there are 1260 total ways.

The solution is 1260 (9C3) (6C4)(2C2).

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Answer:

150 because when you get 180-30=150