How do you solve this preferably step by step 6(1+6×) = 14-×

The method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.

In order to enhance strong number sense in children, there are various methods that can be used.

In the given scenario, Mme Potatana asked the children to count as a whole class from 1 to 20 while Ntate Mafodi asked the children in his class to count seeds from the school's ground in a pile by touching each as they count.

Both methods have their own benefits, but the method of counting seeds by touching each can be more effective in enhancing strong number sense in children.

The method of counting seeds by touching each can be more effective in enhancing strong number sense in children because it allows them to experience each number physically.

This helps them in developing a strong sense of numbers. By touching each seed as they count, children can feel and see each number, which helps them in understanding numbers better. Additionally, it helps in developing the concept of one-to-one correspondence and counting by rote.

Here are some appropriate examples for enhancing strong number sense using the method of counting seeds by touching each:

1. Use counters: Provide children with counters such as small objects, blocks, or toys. Ask them to count the number of counters by touching each as they count.

2. Counting on fingers: Encourage children to count on their fingers. This helps them in developing a strong sense of numbers and helps them in understanding the concept of one-to-one correspondence.

3. Counting objects in a pile: Ask children to count objects in a pile by touching each as they count. This helps in developing the concept of counting by rote and helps in enhancing strong number sense.

Overall, the method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.

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Answer:

Center and above your top lip where it dips down....

The solution of the system of linear equations, is (1.167, 3.667).

Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,

y = -2x+6............(i)

y = 4x - 1.......(ii)

Equating the equations since the LHS is same,

-2x+6 = 4x-1

6x = 7

x = 1.167

Put x = 1.16 to find the value of y,

y = 4(1.16)-1

y = 4.66-1

y = 3.667

Therefore, the solution of the system of linear equations, is (1.167, 3.667).

You can also find the solution using the graphical method,

Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]

Hence, the solution of the system of linear equations, is (1.167, 3.667).

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Answer: The last option. X is greater than or equal to -3

Step-by-step explanation:

If you are searching for all of the values highlighted in red, then it must be every single value greater than x=-3 including the value itself (the dot located on the value is shaded, therefore you must include it within the domain).

Answer: 0.500001

Step-by-step explanation: Hope that helps!

Answer:

x=2

Step-by-step explanation:

10 - (x + 3) = 5

To solve for x, we can start by simplifying the left side of the equation:

10 - (x + 3) = 5

10 - x - 3 = 5

7 - x = 5

Next, we can isolate x on one side of the equation by subtracting 7 from both sides:

7 - x = 5

7 - x - 7 = 5 - 7

-x = -2

Finally, we can solve for x by dividing both sides of the equation by -1:

-x = -2

x = 2

Therefore, the solution to the equation is x = 2.

Answer:

0.75mg

Step-by-step explanation:

6 years is its half life, meaning that half of it will have iradiated by that point. 1.5 / 2 = 0.75

Answer:

Carbon-14 loses around 10% ( 0.1 in decimal form) of its mass, after one millennium.

Then if we start with a mass A of Carbon-14, after one millennium we will have a mass equal to:

A - A*0.1 = A*(0.9)

After another millennium, we will have a mass equal to:

A*(0.9) - A*(0.9)*0.1 = A*(0.9)^2

And so on, this is an exponential decay.

We already can see the pattern here, after x millenniums, the mass of carbon-14 will be:

M(x) = A*(0.9)^x

Now, in this problem we have 600 grams of carbon-14, then the equation for the mass will be:

y = M(x) = 600g*(0.9)^x

And the graph of this equation is shown below.

Answer:

S(t)=600(0.9)

Step-by-step explanation:

Losing mass at a rate of 10\%10%10, percent per millennium means the sample keeps 100\%-10\%=90\%100%−10%=90%100, percent, minus, 10, percent, equals, 90, percent of its mass each millennium.

So each millennium, the size is multiplied by 90\%90%90, percent, which is the same as a factor of 0.90.90, point, 9.

If we start with the initial mass, 600600600 grams, and keep multiplying by 0.90.90, point, 9, this function gives us the mass of the sample ttt millennia from now:

S(t)=600(0.9)^tS(t)=600(0.9)

t

The real dimensions of the object are 144 inches by 216 inches.

Given that, 6:1 scale with dimensions of 24 inches by 36 inches.

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

In a 6:1 scale, the real dimensions of an object would be 6 times the scaled dimensions. Therefore, the real dimensions of the object given in the question would be 24 inches x 6 = 144 inches by 36 inches x 6 = 216 inches. So, the real dimensions of the object are 144 inches by 216 inches.

Therefore, the real dimensions of the object are 144 inches by 216 inches.

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The cost of the carpentering of the floor at the rate 12 rupees per square meter is 60 rupees.

A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.

We have the room as a cuboid.

And its length is 6 meters and height is 3 meters.

The volume of the cuboid = length x height x width

90 = 6 x 3 x width

width = 90 / 18

width = 5 meter.

To find the cost of carpentering the floor, the rate of Rs. 12 per square meter.:

12 x width = 12 x 5 = 60 rupees.

Therefore, at the rate of 12 rupees per square meter, the cost of the carpentering of the floor is 60 rupees.

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The assumed line's and direction's parametric equation is x = 5 + t; y = -1; z = 3 -2t

How can the parametric equation be found?

The absence of points and lines renders the question insufficient.

I will therefore utilize the following presumptive parameters:

As the line traverses: (5, -1, 3)

The direction is  ~v = <1, 0, -2>

The parametric equation of the line is represented as:

r<x,y,z> = Line + t<direction>

This gives

r<x,y,z> = (5, -1, 3) + t<1, 0, -2>

Express the equation in terms of x, y and z

x = 5 + t * 1

y = -1 + 0 * t

z = 3 -2 * t

Solve the equations

x = 5 + t

y = -1

z = 3 -2t

Consequently, the assumed line's and direction's parametric equation is x = 5 + t; y = -1; z = 3 -2t

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Therefore , the solution of the given problem of probability comes out to be a complete probability model cannot be represented by this list.

The main objective of each considerations technique is to calculate the likelihood that a claim is true or that a particular incident will occur. Anything between 0 and 1, were 0 traditionally denotes a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.

Here,

The probabilities assigned to the outcomes do not add up to 1, hence the following list cannot be a complete probability model.

=> P(2) + P(3) + P(4)

=> 1/12 + 2/3 + 1/4

=>  (1 + 8 + 3) / 12

=> 12 / 12 = 1

In a complete probability model, the total of the probabilities should always be equal to 1, indicating that there is a probability of 1 that one of the events will occur.

In this instance, there is a missing probability since the sum of the probabilities assigned to the possible possibilities is less than 1.

Therefore, a complete probability model cannot be represented by this list.

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Using sampling concepts, it is found that the due to bias, the correct option is given by:

Rodell only polled fellow athletes; this sample does not represent nonathletes at the school.

The school is composed both by athletes and non-athletes, which should have different gaming apps, for example, athletes may be more likely to play sports games while non-athletes may favor RPG for example.

He surveys only athletes, hence, the correct option is:

Rodell only polled fellow athletes; this sample does not represent nonathletes at the school.

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Answer:

The correct answer is (A):

Rodell only polled fellow athletes; this sample does not represent nonathletes at the school.

Step-by-step explanation:

I did the quiz and got it right. Hope this helps you!!!!!

Answer:

  (b)  3 units

Step-by-step explanation:

You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.

The dilation factor multiplies every length.

If OB is 3/4, then OB' is 4(3/4) = 3.

The length of OB' is 3 units.

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Answer:

Step-by-step explanation:

2x- 45 + x = 180

3x - 45 = 180

x - 15 = 60

x  =  75

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

B) 352

Step-by-step explanation:

45% = 0.45

640 x 0.45= 288

288 is how many students walked to school

So to find how many took the bus to school

640- 288= 352

The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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Answer:

Step-by-step explanation:

Given

Factors of 1101:

Answer:

\( - 3(x + 4) {}^{2} - 4\)

Step-by-step explanation:

Vertex form is

\(a(x - h) {}^{2} + k = f(x)\)

We know that h and k are both -4. Let x be -2 and y be -16.

\(a( - 2 + 4) {}^{2} - 4 = - 16\)

\(a(2) {}^{2} - 4 = - 16\)

\(4a - 4 = - 16\)

\(4a = - 12\)

\(a = - 3\)

So the equation in vertex form is

\( - 3(x + 4) {}^{2} - 4\)

Answer:

  y = -x +3

Step-by-step explanation:

You want the slope-intercept equation of the line with the same intercept as -3y = -9 +3x, and the same slope as -2x -2y = -8.

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . where m is the slope, and b is the y-intercept

For the given equations, we can put them in this form to find the desired parameters.

  -3y = -9 +3x

  y = -x +3 . . . . . . . . . . divide both sides by -3

We observe that the y-intercept is +3, which we will need for our answer.

The slope-intercept form of the second equation is ...

  -2x -2y = -8

  x + y = 4 . . . . . . . . . . divide by -2

  y = -x +4 . . . . . . . . . . subtract x

We observe that the slope (coefficient of x) is -1, which we will need for our answer.

We want the equation of the line with slope -1 and y-intercept 3. It is ...

  y = -x +3 . . . . . . . . . . same as the equation of the first line

__

Additional comment

The slope-intercept equation (green) is plotted using dots, so that you can see it is coincident with the line described by the first equation (red). Parallel lines have the same slope, so our desired line must be parallel to the blue line. (It is.)

Answer:

A

Step-by-step explanation: if they both started with 10 points then peters score would be -2 and griffon would be 5

A! It is the only one that correctly compares them. F and D are true, but they don't say how the points compare. I hope this helps!

Answer:

15.8 cm²

Step-by-step explanation:

Please see attached photo for diagram.

We'll begin by calculating the angle A. This can be obtained as follow:

B = 56°

C = 78°

A =?

A + B + C = 180 (Sum of the angle in triangle)

A + 56 + 78 = 180

A + 134 = 180

Collect like terms

A = 180 – 134

A = 46°

Next, we shall determine the value of b by using the sine rule. This can be obtained:

Side opposite angle C (c) = 7.2 cm

Angle C = 78°

Angle B = 56°

Side opposite angle B (b) =?

b/Sine B = c/sine C

b/Sine 56 = 7.2/Sine 78

Cross multiply

b × Sine 78 = 7.2 × Sine 56

Divide both side by Sine 78

b = 7.2 × Sine 56 / Sine 78

b = 6.1 cm

Finally, we shall determine the area of the triangle. This can be obtained as follow:

Side opposite angle C (c) = 7.2 cm

Side opposite angle B (b) = 6.1 cm

Angle A = 46°

Area (A) =?

A = ½bcSineA

A = ½ × 6.1 × 7.2 × Sine 46

A = 15.8 cm²

Therefore, the area of the triangle is 15.8 cm²

Using linear approximation, the expression √125.2 can be approximated as approximately 10.02.

To find the equation of the tangent line to the function f(x) = √x at x = 125, determine the slope (m) and the y-intercept (b) of the tangent line.

First, find the slope (m) using the derivative of the function f(x) = √x:

f'(x) = 1 / (2√x)

Evaluate the derivative at x = 125:

f'(125) = 1 / (2√125) = 1 / (2 × 5) = 1/10

Now, find the y-coordinate of the point on the function f(x) at x = 125:

f(125) = √125 = 5

So, the tangent line at x = 125 passes through the point (125, 5) and has a slope of 1/10.

Using the point-slope form of a linear equation, the equation of the tangent line can be written as:

y - 5 = (1/10)(x - 125)

To simplify, multiply through by 10:

10y - 50 = x - 125

Rearranging the equation, express it in the form y = mx + b:

y = (1/10)x - 75/10 + 5

Simplifying further:

y = (1/10)x - 75/10 + 50/10

Combining the terms:

y = (1/10)x - 25/10

Therefore, the equation of the tangent line to f(x) = √x at x = 125 is y = (1/10)x - 25/10.

Now, use this tangent line to approximate the value of √125.2:

Substitute x = 125.2 into the equation:

y = (1/10)(125.2) - 25/10

y = 12.52 - 2.5

y ≈ 10.02

So, using linear approximation, approximate √125.2 as approximately 10.02.

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Answer:

23

Step-by-step explanation:

6 - (-2) - 3(-5).

PEMDAS says multiply first

6 +2 +15

Add

23

Answer:

Answer is 23

Step-by-step explanation:

First open brackets:

\( = 6 + 2 + 15\)

summ up:

\( = 23\)

Answer:

(5, 10) 1st quadrant

Step-by-step explanation:

It will be valued less than £1000 after x = -0.8260748 years.

Based on the given conditions, formulate:

6700 × (1 - 28%) = 1000

Calculate the sum or difference:

6700 ×0.72ˣ = 1000

Reduce the greatest common factor on both sides of the equation:

67 × 0.72ˣ = 10

Divide both sides of the equation by the coefficient of variable:

67 × 0.72ˣ / 67 = 10 / 67

Rewrite as fraction:

0.72ˣ = 10 / 67

Convert exponential to logarithm form:

x = log°.₇₂ 10 / 67

Convert decimal to fraction:

x = log°₍₇₂/₁₀₀₎  10 / 67

After simplifying -

get the result:

x = -0.8260748

Hence , After x = -0.8260748 years will it be worth less than £1000.

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Step-by-step explanation:

We can use the Pythagorean theorem to solve for side b:

\(c^2 = a^2 + b^2 \Rightarrow b^2 = c^2 - a^2\)

or

\(b = \sqrt{c^2 - a^2} = \sqrt{(6\:\text{m})^2 - (4\:\text{m})^2}\)

\(\:\:\:\:= 4.47\:\text{m}\)

Answer: 2√5 or 4.47213595

Step-by-step explanation:

Use the Pythagorean Theorem: a^2 + b^2 = c^2  

(a and b are the measures of the legs and c is the measure of the hypotenuse.)

Let's solve for a (the length of the other leg)  

*I hope that m is not a variable and just an abbreviation for meters.

b = 4 m  

c = 6 m

a^2 + 4^2 = 6^2

a^2 + 16 = 36

a^2 = √20

a = 2√5 = 4.47213595

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)