6. Use words and numbers to explain how the number 0.4 can mean 40/100 and 4/10 at the same time

Answer:

Below

Step-by-step explanation:

m = motorcylce speed

c = car speed = 2m-30

   difference in speeds =   2m-30 - m = m-30

      in two hours this speed accumulates 20 miles (rate * time = distance)

                    2 (m-30) = 20

                     2m - 60 = 20

                         m = 40     then c = 2m-30 = 50    mph

The population of the deer in year 2018 would be 11971.

Given,

In the question:

The model is used to estimate the deer population in a region, where x is the number of years after the year 2009. Using the model, estimate the deer population in the year 2018

Model is given as:

P = 2,3201 [tex](1.2)^x[/tex]

Now, According to the question:

The number of years from 2009 to 2018 = 9

Here, the equation that shows the deer population after x years since 2009,

P = 2,3201 [tex](1.2)^x[/tex]

Substitute x=9 in the above equation,

P = 2,3201[tex](1.2)^9[/tex]

P = 2320(5.15978)

P ≈ 11971

Hence,  the population of the deer in year 2018 would be 11971.

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Answer:

12. [tex]\frac{1}{z^{2} }[/tex]

13. x⁶

Step-by-step explanation:

*Note: When multiplying two of the same variables you add the exponents. When dividing two of the same variables you subtract the exponents. When a variable to a power is raised to another power you multiply the exponents.

The greatest width possible in line is 0.8.

What is line?

a line is an infinitely long to the object with no width, depth, or curvature. Thus, the  lines are the one of one-dimensional objects, though they may exist on it  two, three, or higher of the  dimension spaces. The word line may also refer to a line are the segment in everyday life, which has two points to denote its ends.

Sol-As per the given question The line r has slope 8 and coordinate (0.8).

The slope of the line r will not change.

And intercept is the addition of their ordinate will be.

Intercept = 5+3

Intercept = 8

So, the line r has slope 8 and coordinate (0.8).

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The series as represented in the task content is divergent and hence; diverges.

It follows from the task content that the series defined by the summation expression as represented above is to be identified as divergent or convergent.

It is noteworthy to know that;

If a sequence converges, it means that the limit of the sequence exists as n → ∞. Also, if the limit of the sequence as n → ∞ does not exist, Then, such series is said to diverges.

Therefore, by evaluation as the limit of the expression k sin²k / 1 + k³ as k → ∞ is; Undefined and hence does not exist.

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Answer:50%

Step-by-step explanation:

Answer:

The following question has been answered in the attached document. If there are any queries kindly let me know they will be resolved shortly.

PRO TIP:

don't forget to mention y=0 on x axis and x=0 on y axis whenever you are drawing a graph as it accounts for 1/2 mark in board exams.

The line cuts the y axis at (0, -4) Also (0,0) satisfies the inequality So the shaded region is towards (0, 0). Since there is a strict inequality, the line is a broken line

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, [tex]\geq[/tex], [tex]\leq[/tex]

A one degree inequation is known as linear inequation.

The given linear inequality is

2x - 3y < 12

For the point on x axis for the line 2x - 3y = 12

we put y = 0

[tex]2x - 3\times 0 = 12\\2x = 12\\x = \frac{12}{2}\\x = 6[/tex]

The line cuts the x axis at (6, 0)

For the point on y axis for the line 2x - 3y = 12

we put x = 0

[tex]2\times 0 - 3y = 12\\-3y = 12\\y = \frac{12}{-3}\\y = -4[/tex]

The line cuts the y axis at (0, -4)

Also (0,0) satisfies the inequality

So the shaded region is towards (0, 0)

Since there is a strict inequality, the line is a broken line

The graph has been shown in the figure attached

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Answer:

10

Step-by-step explanation:

I guess your question is

[tex] {(x - 3)}^{2} = 49[/tex]

[tex]x \: - 3 = \sqrt{49} \\ x - 3 = 7 \\ x = 7 + 3 \\ x = 10[/tex]

The equations that represent the circle having a diameter of 12 units and a center lying on y-axis are; x² + (y – 3)² = 36, and x² + (y + 8)² = 36.

The standard form of the equation of a circle is (x - h)² + (y - k)² + r², where (h, k) is the center of the circle, and r is its radius.

We have given that circle having a diameter of 12 units, will have a radius of 12/2 = 6 units. Thus, r = 6.

Since we know that circle having the center on the y-axis will have a center as (0, k) as all points on the y-axis have x-coordinate 0.

Thus, the equation of the circle, with a diameter of 12 units is;

x² + (y - k)² = 6², or,

x² + (y - k)² = 36.

From the given options, the equations x² + (y – 3)² = 36, and x² + (y + 8)² = 36, are correct.

Thus, the equations that represent the circle having a diameter of 12 units and a center lying on y-axis are; x² + (y – 3)² = 36, and x² + (y + 8)² = 36.

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Answer:

3.6  cups

Step-by-step explanation:

We have to make a proportion to solve this.

[tex]\frac{2cups}{5 gallons}[/tex] = [tex]\frac{x cups }{9 gallons}[/tex]

9 x 2 = 18

18 / 5 = 3.6.

The equation for the parabola with the given characteristics is:

y = (2/35)*(x + 7)*(x - 5)

We know that for a parabola that has the zeros x₁ and x₂, and a leading coefficient a, can be written as:

y = a*(x - x₁)*(x - x₂)

In this case, the roots (zeros) are at X =-7 and x = 5

Then we can write:

y = a*(x + 7)*(x - 5)

Now we also know that it passes through the point (0, -2), then we can write:

-2  =a*(0 + 7)*(0 - 5)

-2 = a*-35

2/35 = a

Then the equation for the parabola is:

y = (2/35)*(x + 7)*(x - 5)

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Answer:

at least put the possible answers

The number of notes of Rs. 100 is 1000, Rs. 50 is 1500, and Rs. 10 is 2500.

The ratio describes the number of times one number contains another. It helps to establish a relationship between two or three quantities.

The ratio between any two quantities is described as a:b. This can also be written as a to b or a/b.

The ratio of RS.100, RS.50, and RS.10 is 2:3:5.

From the given ratio, consider

The total amount is given as RS.200,000. This can be written as,

[tex]\begin{aligned}100\times2x+50\times 3x+10\times5x&=200,000\\200x+150x+50x&=200,000\\400x&=200,000\\x&=\frac{200,000}{400}\\x&=500\end{aligned}[/tex]

Therefore,

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If It is estimated that the sanctuary can sustain up to 600 deer. Absent constraints, the population would grow by 70% per year. After one year is 85 and after two years is 144.50.

Using this formula

A = P(1+r)t

Where:

A = Amount

P = Principal

r =Interest rate

t = time

Let plug in the formula

After one year:

A = 50(1+0.70)^1

A = 50(1.70)^1

A= 85 deer

After two years:

A = 50(1+.70)^2

A = 50(1.70)^2

A = 50(2.89)

A = 144.50 deer

Therefore the population growth is 85 deer and 144.5 deer.

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The complete question is:

A population of 50 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 600 deer. Absent constraints, the population would grow by 70% per year.

how many after one year

how many after two years

Answer:

9 : 4

Step-by-step explanation:

Ratio:

Find the quantity of yellow and red dye in the mixture.

 Yellow : Red = 9 : 2

 Total share = 9 + 2 = 11

    [tex]\sf \text{Quantiy of yellow} = \dfrac{9}{11}*44[/tex]

                                 = 9 * 4

                                = 36 litres

      [tex]\sf \text{Quantity of Red}= \dfrac{2}{11}*44[/tex]

                                  = 2 * 4

                                  = 8 litres.

Now, 8 litres of red dye is added.

New quantity of red dye = 8 + 8 = 16 liters.

New ratio of Yellow to red = 36 : 16

                                             = (36÷4) : (16÷4)

                                             = 9 : 4

The reflection of the graph in the x-axis gives the function

g(x) = -x² - 3x - 2

The given function is of the form f(x) = x² + 3x + 2 which represents a parabola.

The vertex of the function is at (-3/2 , -1/4)

The focus is at ( 3/2 , 0 )

The axis of symmetry is 2x+3 = 0 and the directrix is at 2x + 1 = 0

Now when the parabola is reflected along the x-axis we get

the focus at ( -3/2 , 0 )

the vertex is at  (-3/2 , 1/4)

Axis of symmetry remains the same

The directrix becomes 2y-1 =0

The red graph denotes the function f(x) while the blue graph denotes the function g(x) reflected on the x-axis.

Hence the reflection on the x-axis gives the function g(x) = -x² - 3x - 2

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The number represented in the statement is 7

The statements in the question can be highlighted as:

When represented as an equation, we have

5(3x - 10) = 55

Where x represents the number

Divide both sides by 5

3x - 10 = 11

Add 10 to both sides

3x = 21

Divide by 3

x = 7

Hence, the result is 7

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Answer:

I am definitely not one...Lol

Step-by-step explanation:

The equations that are true for x = –2 and x = 2 include the following:

x² – 4 = 0

4x² = 16

In order to determine which x-values are true solutions based on the given equations, we would have to test each of the x-values by substituting their values into the equations as follows;

When x = -2, we have:

x² – 4 = 0

(-2)² – 4 = 0

4 - 4 = 0 (True).

When x = 2, we have:

x² – 4 = 0

(2)² – 4 = 0

4 - 4 = 0 (True).

When x = -2, we have:

x² = -4

(-2)² = -4

4 = -4 (False).

When x = -2, we have:

3x² + 12 = 0

3(-2)² + 12 = 0

3(4) + 12 = 0

12 + 12 = 0

24 = 0 (False).

When x = -2, we have:

4x² = 16

4(-2)² = 16

4(4) = 16 (True).

When x = 2, we have:

4x² = 16

4(2)² = 16

4(4) = 16 (True).

When x = -2, we have:

2(x – 2)² = 0

2(-2 – 2)² = 0

2(-4)² = 0

2(16) = 0

32 = 0 (False).

When x = 2, we have:

2(x – 2)² = 0

2(2 – 2)² = 0

2(0) = 0 (True).

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Complete Question;

Which equations are true for x = –2 and x = 2? Select two options

x² – 4 = 0

x² = -4

3x² + 12 = 0

4x² = 16

2(x – 2)² = 0

The future value of an investment with such details must have a present value of $11120.58

Present value (PV) formula finds application in finance to calculate the present day value of an amount that is received at a future date. The present value formula (PV formula) is derived from the compound interest formula. The compound interest formula is,

FV = PV(1 + r/n)^nt

We can substitute the values into the formula

15000 = PV(1 + 0.06/12)^12*5

15000 = PV(1.005)^60

PV = 11120.58

The present value of an investment to give a future value of $15000 at 6% rate in 5 years is $11120.58

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The factored expression of (x - 3)^2 - 64y^4 is given as follows:

(x - 3)^2 - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).

The subtraction of perfect squares is a notable product that gives the simplification of an expression containing the subtraction of perfect squares as follows:

a² - b² = (a - b)(a + b).

In this problem, the expression is presented as follows:

(x - 3)^2 - 64y^4

This expression is a subtraction of perfect squares, as the terms are given as follows:

Then the expressions are given as follows:

Then the factored expression is presented as follows:

a² - b² = (a - b)(a + b).

(x - 3)² - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).

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Answer:

I am thinking the answere is -6 x 7 but I'm not completely

Answer:

60/15

Step-by-step explanation:

A fraction is simply a portion of a whole number, so 1/15 is the number 1 split into fifteen equal parts, therefore 15/15 = 1.

So 4 as a fraction with fifteen as the denominator would be 15/15 x 4, which equals 60/15.

Answer:

B and D are the correct answers.

Jai rate of reading in books per month is 1.5 books per month.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this case, Jai read 3 books in 2 month, his rate of reading in books per month will be:

= Number of books / Number of months

= 3 / 2

= 1.5 books per month

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Answer:

84unit square

Step-by-step explanation:

how many years do I need the 3

The answer is:  " 84 cm² " ;  or, write as:  " 84 square centimeters."
 ____

Step-by-step explanation:

Note the formula for the area; "A" ; of a parallelogram—as follows:
   A  =  b *  h  ;

  in which:

   A = the Area of this parallelogram given in the attached image;

for which we shall solve;  in units of:  cm²  ;  

             or, write as:  " square centimeters "
        →  {since all the measurements shown in the image are in units of:                

              "cm"  ["centimeters"].}
 ____
   b =  " base length " =  12 cm {as shown in the image};
 ____
   h =  " perpendicular height " = 7 cm {as shown in the image} .
 ____
To find the area;  A :
 We plug our given values into the equation/formula:
     →   A    =     b    *   h   ;
                 =  (12 cm) * (7 cm) ;
                 =   12 * 7 * cm * cm ;
          A    =    84  cm² .
_____________

Note of interest:  The following quadrilaterals are also parallelograms:
   squares, rectangles, and rhombuses [or, "rhombi"].
_____________
The answer is:  " 84 cm² " ;  or, write as:  " 84 square centimeters."

___

Hope this is helpful to you.
Wishing you well in your academic endeavors!

___

The number of people who do not like any of the three colour is 5, using the set theory.

What is Set theory?

A subfield of mathematics called set theory studies sets and their characteristics. Set theory's fundamental ideas are straightforward and seem to stand on their own. The set theory appears to be straightforward, but it is actually a very complex topic. Mathematicians have specifically demonstrated how almost all mathematical ideas and conclusions may be formalized within the theory of sets. This is regarded as one of the pinnacles of contemporary mathematics. Given this accomplishment, it is possible to assert that set theory serves as the foundation for mathematics.

In the given question, we have:

Total number of people in the survey = 25;

Number of people like red = 13;

The number of people who like blue = 8;

The number of people who like yellow = 13;

5 people like both Red & Blue,

4 people like both Blue & yellow,

7 people like both Red & Yellow

2 people like all three colors.

Let n be the number of people who do not like any of the three colour.

Using the concept of set theory, we can write it as:

3 + 4 + 1 + 5 + 2 + 3 + 2 + n = 25;

⇒20 + n = 25;

n = 25 - 20

n = 5;

Hence, The number of people  who do not like any of the three colour is 5;

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