a farmer measures the height of every tree in a large orchard in centimeters. the farmer wishes to present the data by grouping the results into groups of 25 cm. which graphical display would be most appropriate to display the results?

The greatest common factor ( GCF ) of 21 , 14 and 7 is given by A = 7

The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF

Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers

Product of HCF x LCM = product of two numbers

Given data ,

Let the GCF of the numbers be represented as A

Now , the equation will be

Let the first number be p = 21

Let the second number be q = 14

Let the third number be r = 7

Now , the factors of 21 = 1 , 2 , 3 , 7 and 21

The factors of 14 = 1 , 2 , 7 and 14

The factors of 7 = 1 and 7

So , the greatest common factors of 21 , 14 and 7 is 7

Hence , the GCF is 7

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Answer:

(-x+2)(2x+1) — first option

Step-by-step explanation:

The rectangles represent an x, red means negative and yellow is positive.

The squares represent a unit (the number 1).

The diagram attached below demonstrates how this works.

Basically the top row of this tile equation is (-x + 2)

And the column is (2x+1).

Expanding this makes -2x²+3x+2

In third-angle projection, the view of a component is drawn next to where the view was taken. In first-angle projection, the view is drawn on the other end of the component, at the opposite end from where the view was taken.

First angle Protuberance is a system of creating a 2D delineation of a 3D object. It's substantially used in Europe and Asia and has not been officially used in Australia for numerous times. In Australia, third angle protuberance is the favored system of orthographic protuberance. Note the symbol for first angle orthographic protuberance

Third Angle Projection the Object is placed in the Third Quadrant. This means that the Vertical Aeroplane is in front of the object and the Vertical Aeroplane is above the object. These changes in the position of the views are the only difference between protuberance styles.

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The area of the shaded region is 12.5 square inches.

First we can subtract the area of the smaller triangle from the area of the larger triangle.

The larger triangle has a base of 8 inches and a height of 5 inches, so its area is:

(1/2) * base * height = (1/2) * 8 in. * 5 in. = 20 in²

The smaller triangle has a base of 3 inches and a height of 5 inches, so its area is:

(1/2) * base * height = (1/2) * 3 in. * 5 in. = 7.5 in²

Subtracting the area of the smaller triangle from the area of the larger triangle, we get:

20 in² - 7.5 in² = 12.5 in²

Therefore, the area of the shaded region is 12.5 square inches.

Therefore the option is F. 15 in² (none of the given answer choices match the calculated area of 12.5 in²)

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The difference 6.96 - 0.04 is greater than 7.

Answer:

213 km

Step-by-step explanation:

Answer:

the length of the edge of the cube is 5 meters

Step-by-step explanation:

The surface area of a cube can be found using the formula:

Surface Area = 6 x (side length)^2.

Since the surface area of this cube is 150 square meters, we can set up an equation to solve for the side length:

150 = 6 x (side length)^2

Dividing both sides by 6, we get:

25 = (side length)^2

Taking the square root of both sides, we find the side length:

side length = sqrt(25) = 5 meters.

So the length of the edge of the cube is 5 meters.

Answer:

Step-by-step explanation:

60(12*5) as a square has 4 on the top same for the bottom and has 4 vertices. I hope this helps

Answer: Let's assume the exchange rate between ZAR and EUR is given by E1, and the exchange rate between ZAR and CAD is given by E2.

First, let's calculate the cost of the CD in ZAR:

5 EUR * E1 = 5 * E1 ZAR

Next, let's calculate how much money Teboho will have left after purchasing the CD:

250 ZAR - 5 * E1 ZAR = 245 ZAR - 5 * E1 ZAR

Now, let's calculate the cost of the CD in CAD:

7 CAD * E2 = 7 * E2 ZAR

We need to determine the value of E1 and E2 in order to compare the prices. However, without knowing the current exchange rates, we cannot determine the best option for Teboho. If the exchange rate between ZAR and EUR is favorable and the cost of the CD in ZAR is lower than the cost of the CD in CAD, Teboho should order the CD from Germany. On the other hand, if the exchange rate between ZAR and CAD is favorable and the cost of the CD in CAD is lower than the cost of the CD in EUR, Teboho should order the CD from Canada.

Step-by-step explanation:

Answer:

10 packages

Step-by-step explanation:

When Mr. Rankin opens the box and looks straight down on it, he could see two packages. The 12x9 paper package can fit two, side by side in the 18X12 box.

Then there also can fit a stack 5 packages tall. Each bundle is 2 inches tall and the box is 10 inches tall.

Two stacks, 5 deep is 10 packages. see image.

Using Cramers Rule, X = 10.34, Y = 0.85. See the computations below.

Cramer's rule is an explicit formula in linear algebra for solving a system of linear expressions with as many equations as unknowns, and it is true whenever the system has a unique solution.

Given:

10x - 4y = 100; ..................1) and

8x - 100y = -2; ...................2)

First things first, let's pick off the variables we will need for Cramer's equation:

Standard equation 1 = ax + by = c and Standard equation 2 = dx + ey = f. Therefore:

a = 10, b = -4, c = 100, d = 8, e = -100, f = -2

Step 1, calculate the denominator Delta (Δ):

Δ = a * e - b * d

Δ = (10 * -100) - (-4 * 8)

Δ = -1000 - -32

Δ = -968

Step 2, calculate the numerator for x

Numerator(x) = c * e - b * f

Numerator(x) = (100 * -100) - (-4 * -2)

Numerator(x) = -10000 - 8

Numerator(x) = -10008

X = Numerator (x) / Δ

x  = -10008/-968
x = 10.338842975207

x [tex]\approx[/tex] 10.34

y  =   Numerator(y)/Δ

y  =   -820/-968

y = 0.84710743801653

y [tex]\approx[/tex] 0.85

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The correct expression for 7c-3+2c=15 is c = -1

An expression is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division. The structure of an expression is: Expression = (Number, Math Operator, Number) For example, = 7 + 9 = 23 × 4 = 37 – 6 = 25 + 9 – 4 ÷ 2

Move all terms containing c to the left side of the equation.

Subtract 3c from both sides of the equation:

[tex]= > 7c+6-3c=2[/tex]

Subtract 3c from 7c:

[tex]= > 4c+6=2[/tex]

Move all terms not containing c to the right side of the equation.

Subtract 6 from both sides of the equation:

[tex]= > 4c=2-6[/tex]

Subtract 6 from 2:

[tex]4c=-4[/tex]

Divide each term in [tex]4c=-4[/tex] by [tex]4[/tex] and simplify.

Divide each term in [tex]4c=-4[/tex] by [tex]4[/tex]:

[tex]\frac{4c}{4} =\frac{-4}{4}[/tex]

Simplify the left side:

Cancel the common factor of [tex]4[/tex]:

[tex]c=\frac{-4}{4}[/tex]

Simplify the right side.

Divide [tex]-4[/tex] by [tex]4[/tex]:

[tex]c=-1[/tex]

Therefore, the correct expression for 7c-3+2c=15 is c = -1

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The question is:

How to solve this 7c-3+2c=15

Answer:

26 meters,

hope this helps!

Answer:

1- graphing

2- substitution

3- elimination.

Answer: (2,0)

Step-by-step explanation:

Midpoint formula( [tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])

P(-4, 6)

Q(8, -6)

Substitute into formula

-4+8/2

4/2

x = 2

6-6/2

0/2

y = 0

Answer (2,0)

The sector area of the sector defined by the minor arc CB is given as follows:

7.5 cm².

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr².

We have that the radius is half the diameter, hence it's measure is given as follows:

r = 3 cm.

The angle measure of arc CB is given as follows, considering that BD is half the circle = 180º.

CB + 84º = 180º.

CB = 96º.

An entire circle has an angle of 360º, hence the area of the sector is given as follows:

A = 96/360 x π x 3²

A = 7.5 cm².

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To prove that there exists a rational number between any two irrational numbers, we can use the fact that there exists a rational number between any two real numbers.

Let a and b be two irrational numbers with the property that a b. Then a and b are not rational by definition, which means they cannot be written in the form p/q, where p and q are integers and q is not equal to zero.

We can define a new number c = (a + b) / 2 because a b. This number is a rational number because it can be expressed as a fraction in lowest terms as (a + b) / 2.

As a result, we have demonstrated that a rational number c exists between any two irrational numbers a and b.

A similar argument can be used to demonstrate that there exists an irrational number between any two rational numbers.

Consider a and b to be two rational numbers such that a b. We can then define a new number c = (a + b) / 2.

If c is also rational, we're done because we can just use c as our desired number between a and b. However, if c is irrational, we have found our desired number between a and b, which is also irrational.

Assume that a and b are both even integers to see why c must be irrational in some cases. Then their average c is also even, implying that c can be written as p/q, where p and q are integers and q is not equal to zero, with both p and q being even. However, because p and q are both even, this contradicts the fact that they must have no common factors.

As a result, we have demonstrated that there exists an irrational number c between any two rational numbers a and b.

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Option d) [tex]y= 30.5(0.7)^x[/tex] is the function that best models the number of game systems sold in millions x years since 2015.

In mathematics, a function is a rule that associates each element in one set (called the domain) with a unique element in another set (called the range). The rule specifies how the input values (the elements of the domain) are transformed into output values (the elements of the range).

A function can be represented using various notations, such as f(x), where f is the name of the function and x is the input value, or y = f(x), where y is the output value and x is the input value. The function can be defined explicitly, as in[tex]f(x) = x^2,[/tex] or implicitly, as in the equation of a circle, [tex]x^2 + y^2 = r^2[/tex], where y is a function of x.

To determine which function best models the number of game systems sold, we need to observe the trend in the data.

We can see that the number of game systems sold is decreasing as time goes on, which means the function should be decreasing as well.

Option a) [tex]y=21.35(0.7)^x[/tex] is an exponential function with a base less than 1, which means it would also be decreasing. However, it starts with a higher initial value than the data suggests.

Option b) [tex]y= 30.5(21.35)^x[/tex] is an exponential function with a base greater than 1, which means it would be increasing. This function does not match the trend in the data.

Option c) [tex]y= 30.5(1.3)^x[/tex] is an exponential function with a base greater than 1, which means it would be increasing. This function also does not match the trend in the data.

Option d) [tex]y= 30.5(0.7)^x[/tex]is an exponential function with a base less than 1, which means it would be decreasing. Additionally, this function passes through all three data points, and it has a starting value that matches the first data point. Therefore, option d) is the function that best models the number of game systems sold in millions x years since 2015.

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If AB = 19 and AC = 17 then the value of x be 95/9 or 10.5555.

In geometry, a line that divides an angle into two equal angles is referred to as an angle bisector. By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.

The ray, line, or segment that divides an angle into two equal portions is known as the angle bisector in geometry. A 60-degree angle, for instance, will be split into two angles of 30 degrees each by an angle bisector. To put it another way, it separates one angle into two smaller congruent angles.

The segment AD bisects angle BAC.

Given: AB = 19 and AC = 17

AD is an angle bisector of BAC and divides the opposite side into segments that are proportional to the other two sides, that is

Let the equation be

[tex]$& \frac{B D}{C D}=\frac{A B}{A C}(\text { substitute values ) } \\[/tex]

[tex]$& \frac{x}{20-x}=\frac{19}{17}(\text { cross- multiply) } \\[/tex]

Simplifying the above equation, we get

[tex]$$x \cdot 17=380-19 x$$[/tex]

36x = 380

Divide both sides by 36, we get

[tex]$\frac{36 x}{36}=\frac{380}{36}$$[/tex]

x = 95/9 = 10.5555

Therefore, the value of x be 95/9 or 10.5555.

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The number of chips sold is 10

The number of candy bars sold is 23

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

The price of each candy bar = $1.50.

The price of each bag of chips = $1.25.

Number of chips = x

Number of candy bar = x + 13

Yesterday Melanie made $33.25.

So,

x + x + 13 = 33.25

Solve for x.

x + x + 13 = 33.25

2x + 13 = 33.25

2x = 33.25 - 13

2x = 20.25

x = 10.125

x = 10

Now,

Number of chips = 10

Number of candy bar = 10 + 13 = 23

Thus,

Number of chips sold = 10

Number of candy bar sold = 23

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Answer:

1.666... or 1 2/3

Step-by-step explanation:

The table needs to change number of Bags to Clementines.

And we know that they are only sold in pairs of 3 so we divide 5 by 3 to find the unit price

The value of P(-3) is -12, Quotient is (-2x² + x - 3) and Remainder is 6.

Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that a polynomial P(x) divided by a factor (x - a) is not really an element of the polynomial.

Given:

P(x) = -2x³-5x²-3.

Using the remainder theorem, the value of P(3) is given by:

P(-3)=  -2x³-5x²-3.

P(-3) =  -2(-3)³-5(-3)²-3

P(-3) = -2(-27) -5(-9) -3

P(-3) = -54 + 45 - 3

P(-3) = -12

As, the divisor of P(x) is (x+3).

so, the division is

                                  (x+3) | -2x³-5x²-3 | -2x² + x - 3

                                             -2x³-6x²

                                          __________

                                                        x² - 3

                                                        x² + 3x

                                                     ________

                                                               -3x - 3

                                                               -3x - 9

                                                              _______

                                                                      6

So, the Quotient is (-2x² + x - 3) and Remainder is 6.

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Answer: 123 students

32 % of 384 is 122.88. Since a percent of a person can't walk to school, we should round up. This means 123 students in the eighth grade walk to school each day.

I hope this helps and good luck <3!!

Answer:

1/24.

Step-by-step explanation:

There are 2 events here and they are independent, so the single probabilities are multiplied.

P(4 when die is rolled) = 1/6

P(A on the spinner) = 1/4

So, P(4 and A)

= 1/6 * 1/4

= 1/24.

Answer:

1. x = 0.75

2. p = 4

3. L = 11

4. t = 42

Step-by-step explanation:

1. The price of pen is x, then

=> 6x + 24 = 28.5

=> 6x = 4.5

x = 4.5/6 = 0.75

2. p is the number of lbs

=> 2p + 50 = 58

2p = 8

p = 4

3. Perimeter = 2(L + W)

2(L + 4) = 30

=> 2L + 8 = 30

2L = 22

L = 11

4. t is the number of tickets

3t + 24 = 150

3t = 126

t = 126/3 = 42

By making linear equation for given graph, slope of line will be 9.75 which is the amount she makes in an hour i.e. E.

What exactly is a linear equation?

The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.

Now,

As given she has a debt of $25 that will be y-intercept.

and as we can see from graph she earns $39 in 4 hours that means $9.75 in an hour which will be slope of line also, then the line will be represented as

y=9.75x-25  where x=hours worked and y=amount earned

hence,

         slope of line will be 9.75 which is the amount she makes in an hour.

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There are 8 different trips that can be made from City X to City Z, passing through City Y.

To find the number of different trips that can be made from City X to City Z, passing through City Y, we can use the multiplication principle of counting.

First, we need to choose one of the 2 major roads from City X to City Y. Then, for each of these roads, there are 4 major roads from City Y to City Z, and we need to choose one of these roads.

By the multiplication principle of counting, the total number of different trips from City X to City Z, passing through City Y, is the product of the number of choices at each stage. Thus, we get:

Number of different trips = Number of roads from City X to City Y x Number of roads from City Y to City Z

= 2 x 4

= 8

This calculation shows how the multiplication principle of counting can be used to find the total number of possible outcomes in a multi-stage process where the number of choices at each stage is known.

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Complete question is:

Automobile Trips. There Are 2 Major Roads From City X To City Y And 4 Major Roads From City Y To City Z. How Many Different trips can be made from City X to City Z, passing through City Y?

The weight of Franklin’s mountain bike in kilograms which  weighs 17,000 grams is equal to option A. 17 kilograms.

Weight of Franklin’s mountain bike  in grams is equal to 17,000 grams

Convert the grams into kilograms.

One kilograms is equal to one thousand grams

1 kilograms = 1000 grams

⇒ 1 grams = ( 1 / 1000 ) kilograms

⇒ 17,000 grams = ( 17,000 / 1000 ) kilograms

⇒ 17,000 grams = 17 kilograms

Therefore, after converting grams into kilograms the weight of Franklin’s mountain bike whose weight in grams is 17,000 grams  is equal to option A. 17 kilograms.

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Answer: (2, -1)

Step-by-step explanation:

For a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Over time, the rate of change quickens. As time goes on, the rate of increase accelerates. It is intended for the quick growth to be a "exponential increase".

The species of bacteria follow an exponential growth pattern.

The exponential growth is given as:

[tex]A(t) = A_0e^{kt}[/tex]

Where, A₀ is the initial population = 4000

k = constant

t = time = 30 minutes = 1/2 hour.

The bacteria doubles in 30 minutes, thus A(t) = 2(4000) = 8000.

Substituting the values in the equation:

[tex]8000 = 4000e^{k(\frac{1}{2} )}\\\\2 = e^{k(\frac{1}{2} )}[/tex]

Takin ln on both sides of the equation:

ln(2) = 1/2 k

2(ln(2)) = k

k = 1.38

The number of bacteria present after 3 hours:

[tex]A(t) = 4000e^{(1.38)(3)}\\\\[/tex]

A(t) = 256000

Hence, for a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.

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