Mrs B invested $30,000, part at 5%, part at 8%. The total interest on the investment was $2100, how much did she invest at each rate?

(Please show working)

Rewriting all numbers in base 5

1000 = 13000

1001 = 13001

1002 = 13002

2000 = 31000

The base 5 number whose digits have least sum are 13000 and 31000

The decimal notation of the numbers are 1000 and 2000

Define unit number.

The rightmost point in a number or the number one are both acceptable definitions of the word "unit" in mathematics. A unit can also be an item or a person that is seen as distinct and whole but is actually a component of a whole or group. An identification number for a unit in a declaration is referred to as a unit number.

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All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Birdseed that costs ​$0.67 a pound and sunflower seeds that cost ​$0.97 a pound. Angela​ Leinenbachs' pet store wishes to make a 30 pound mixture of birdseed and sunflower seeds that sells for ​$0.79 per pound.

Assume that she used [x] pound and [y] pound of each type. We can write -

0.67x + 0.97y = 0.79 x 30

0.67x + 0.97y = 23.7

Plot the graph of this function. All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

Therefore, all the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

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Answer:

1st: One solution

2nd: Infinite many solutions

3rd: No solution

4th: No Solution

5th: One Solution

Step-by-step explanation:

1st:

The solution is (6,9)

x = 6 if a vertical line going though (6,0)

y = 9 is a horizontal line going through (0,9)

The two lines with intersect at (6,9)

2nd:

3y = 15x + 6  If you divide all the way through by 3, you get

y = 5x + 2

This is identical to the first equation given.  Since it is the same line, the answer is infinite many solutions.

3rd:

3y = x + 2  Divide all the way through by 3

y = 1/3 x + 2/3

9y = 3x + 7  Divide all the way through by 9

y = 1/3 x + 7/9

Since the slopes are the same in both equations (1/3), these line are parallel and will never intersect.

4th:

Since the slopes are both the same (2), the lines are parallel and they will never intersect, so the answer is no solution.

5th:

2y = 3x  Divide both sides by 2

y = 3/2

-5y = -10  Divide both sides by -5

y = 2x

These equations are proportional so they go through the origin.  They both have a y intercept of zero, so they intersect at (0,0).  The answer is one solution.

A good point estimator for the population variance is: s².

A two-tailed test can be defined as a type of hypothesis test in which a rejection of the null hypothesis occurs for values of the point estimator in either tail of the sampling distribution.

In Statistics, the basis of an inference about the population is usually used to determine statistical inference based on all of the statistics that are calculated from samples.

This ultimately implies that, the sample mean should be close to the population mean, the sample proportion should be close to the population proportion, and the sample standard deviation should be close to the population standard deviation.  

In this context, we can logically deduce that standard deviation (s²) is considered as a good point estimator for the population variance.

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A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as:

Area = πr²

The total sector of a circle is 360°

The area of the sector of 270° is 37.68 square meters.

A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as:

Area = πr²

We have,

The radius of the circle = 4 m

The total sector of a circle is 360°

The area of the sector with 270°.

= (270°/360°) x πr²

= 0.75 x πr²

= 0.75 x 3.14 x 4²

= 37.68

= 37.7 square meters

Thus,

The area of the sector of 270° is 37.68 square meters.

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Answer:

Real, Irrational

Step-by-step explanation:

5sqrt2 is NOT:

Natural (1,2,3...)

Whole (0,1,2,3...)

Integer (...-3,-2,-1,0,1,2,3...)

Rational (can be written like a ratio)

Imaginary (have the number i in it.)

It IS Irrational, will have neverending decimal with no repeating pattern.

5sqrt2 = 7.0710678119...

It IS REAL and IRRATIONAL.

The relationship between the variables is that an increase in the degree of slope cause an increase in the loss of soil

The possible graph that completes the question is added as an attachment

From the attached graph, we have the variables represented to be

Next, we determine the relationship

To start with:

The relationship between the variables on a graph is simply  the end bahavior of the graph

In this case, we can see that:

As the degree of the slope increases, the loss of soil also increase

However, the increase in the slope does not cause a constant increase in the loss of soil

The loss of soi starts by increasing slowly as the degree of slope increases, then the loss of soil increases sharply as the degree increases further

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Answer:

the last one= It takes longer to fall because it experiences greater air resistance.

also the reason is the air resistance provides an upthrust to the parachute which takes longer time to fall

Answer: It takes longer to fall because it experiences greater air resistance.

Answer:

33.8ohms

Step-by-step explanation:

10A : 13ohm

26A : 33.8ohm

Answer:

[tex] = \frac{8(x + 3) {}^{2} }{2(x + 3)} = 4(x + 3) = 4x + 12[/tex]

Hopefully this will help u

Answer:

y2−5y=750 

750 -y(y-5)=0750−y(y−5)=0  and (y+25)(y-30)=0

The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.

Capacity refers to the product of the length, width, and height of a three-dimensional object or space.

The capacity of an object means the same as its volume.

Olympic-size swimming pools have the following standard dimensions:

Length = 50 m

Width = 25 m

Height = 2 m

Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)

= 660,000 gallons (2,500 x 1,000 ÷ 3.785)

An interval estimate shows the lower and upper limits.

6 x 105 gallons = 630 gallons

Thus, the capacity of the swimming pool is Option B.

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A. 100 gallons to 500 gallons

B. 500 gallons to 1,000 gallons

C. 1,000 gallons to 1,500 gallons

D. 1,500 gallons to 2,000 gallons

Answer:

==============

Since both points have same x-coordinate, the distance between them is the difference of y-coordinates:

Correct choice is D

Answer:

32 units

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

Define the two given points:

Substitute the two points into the distance formula and solve for d:

[tex]\implies d=\sqrt{(-7-(-7))^2+(8-(-24))^2}[/tex]

[tex]\implies d=\sqrt{(-7+7)^2+(8+24)^2}[/tex]

[tex]\implies d=\sqrt{(0)^2+(32)^2}[/tex]

[tex]\implies d=\sqrt{32^2}[/tex]

[tex]\implies d=32[/tex]

Note: As the two given points have the same x-coordinate, the line segment (between the points) is a vertical line. Therefore, to find the distance between the two given points, simply calculate the difference between the y-coordinates:  

[tex]\implies 8 - (-24) = 8+23=32[/tex]

The order of reasons that best justifies each step of the equation's solution is as follows;

It follows from the task content that the reasons which best justify each step of the solution be identified.

Therefore; Given the equation; -2(x - 5) = 4x; we have;

Ultimately, the reasons which best justifies each of the steps as required are as provided above.

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Answer:  Justification for each step is provided below.

Step-by-step explanation:

Original Equation: -2(x - 5) = 4x

-2x + 10 = 4x  -->  Distributive property - simplify the left side

-2x + 10 + 2x = 4x + 2x  -->  Addition property of Equality - add 2x to both sides

10 = 6x  -->  Simplifying

10/6 = 6x/6   -->   Division Property of Equality - divide each side by 6

5/3 = x   -->  Simplifying

The instantaneous rate of change of monthly output with respect to the number of workers is equal to 184.

The instantaneous rate of change can be defined as a type of function that describes the average rate at which a quantity increases or decreases with respect to another quantity at a particular instant.

In Mathematics, the instantaneous rate of change can be calculated by taking the derivate of the function with respect to an independent variable. This ultimately implies that, the instantaneous rate of change is equivalent to the change in the derivative value at a particular instant.

Taking the derivate of the given function, we have:

Q(x) = 15,000 + 2x²

Q'(x) = d/dx(15,000) + d/dx(2x²)

Q'(x) = 0 + 2x(2)

Q'(x) = 4x.

At x = 46, we have:

Q'(x) = 4(46)

Q'(x) = 184.

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Complete Question:

The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x² units, (40 ≤ x ≤ 60), where x is the number of workers employed at the mill. If there are currently 46 workers, find the instantaneous rate of change of monthly output with respect to the number of workers. That is, find Q'(46).

Q'(46) =

Answer:

23/5 > (sqrt(18)

Step-by-step explanation:

there are many ways you could go about this,

I subtracted (sqrt(18)) from (23/5) and because the answer i got was greater than 0, 23/5 must be bigger than sqrt18

0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.

In mathematics, the decimal representation of numbers allows for the use of trailing zeros after the decimal point. When a decimal number has trailing zeros, such as in the case of 0.8 and 0.80, they are considered equivalent because they represent the same value.

The trailing zeros after the decimal point do not change the numerical value of the number. The number 0.8 represents eight tenths, and adding a trailing zero to make it 0.80 does not change its value; it still represents eight tenths. The zero after the decimal point in 0.80 is simply a placeholder, indicating that there are no hundredths or smaller fractional parts.

It is common to use trailing zeros in decimal representations to indicate the precision or accuracy of a measurement. For example, if a measurement is known to be accurate to two decimal places, it is common to represent it as 0.80 rather than 0.8 to indicate the level of precision.

Therefore, mathematically speaking, 0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.

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An integral graph with graph spectrum is the utility graph.The utility graph's adjacency, incidence, and graph distance matrices are displayed in the aforementioned graphs.

These technologies enable users to mathematically represent their ideas, dynamically link several representations, form hypotheses, and finally create totally new concepts.

Use a graphing utility

See attached file

 The value  of X in the interval  [0, 2π) are

X1=0

X2=π/2-----1.5708

X3=π------- 3.1416

Values of X  (0,1.5708,3.1416)

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Step-by-step explanation:

Percentage means to be out of 100 . So, 20% is equivalent of being 20100 . That evaluates out to 0.20 . Removing the unnecessary 0 at the end gives us the decimal 0.2 , which is the correct answer.

The area to the right of x in the normal distribution is 0.807

The normal distribution is the probability distribution that helps to find the probability for continuous variables.

For a probability x, for a normal distribution, we have that

P(X ≤ x) + P(X ≥ x) = 1

Since the area to the left of x in a normal distribution is 0.193, we require the area to the right of x.

Since P(X ≤ x) + P(X ≥ x) = 1 where

Making P(X ≥ x) subject of the formula, we have that

P(X ≥ x) = 1 - P(X ≤ x)

Given that P(X ≤ x) = 0.193

Substituting this into the equation, we have  

P(X ≥ x) = 1 - P(X ≤ x)

P(X ≥ x) = 1 - 0.193

P(X ≥ x) = 0.807

So, the area to the right of x is 0.807

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Line l was translated down 8 units, is true for the transformation that took place.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

Given that, parallel lines l, m, and n are shown. If line l is mapped to line m and line m is mapped to line n,

We can see line is the original line is l which is first mapped into line m then into line n, so, we can say line is mapped to n.

Hence, Line l was translated down 8 units, is true for the transformation that took place.

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Solution :

[tex]\qquad \sf  \dashrightarrow \: log(x) + 5 \: log(y) - 4 \: log(z) [/tex]

[tex]\qquad \sf  \dashrightarrow \: log(x) + \: log(y {}^{5} ) - \: log(z {}^{4} ) [/tex]

( a log(x) = log(x^a) )

[tex]\qquad \sf  \dashrightarrow \: log( x {y}^{5} ) - log(z {}^{4} )[/tex]

( log (a) + log (b) = log (ab) )

[tex]\qquad \sf  \dashrightarrow \: log( \frac{ x {y}^{5} }{z {}^{4} }) [/tex]

( log (a) - log (b) = log (a/b) )

David share is £8

Vicky share is £28

From the question, we have

David and Vicky share £36 in the ratio 2:7.

David share = £36 *2/9 = £8

Vicky share = £36 *7/9 = £28

Multiplication:

The product of the numbers is what is obtained in mathematics when two or more numbers are multiplied. We frequently perform it since it is one of the fundamental mathematical operations. Using multiplication tables is the most straightforward use. In mathematics, adding a number repeatedly in relation to another is represented by multiplying two integers. These figures can be natural figures, whole figures, fractional figures, integer figures, or other figures. When m is multiplied by n, m is either added to itself n times or multiplied by n.

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As per the concept of transformation, the image of the polygon after a reflection in the line y = - x is has vertices at A(0,-2), B(-4,-3), C(-4,-6), D(0,-5) as shown in the diagram attached below.

Transformation:

Transformation refers the movement of a point from the initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.

Given,

Here we have the vertices A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the equation for line y = -x.

Now we have to plot the graph  with the given vertices and its image after a reflection in the line y = -x .

Here reflection refers flipping of a figure.

Therefore, if a point A(x, y) is reflected about the line y = - x, the new point would be at A'(-y, -x)

For the given the polygon with vertices at A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the image of the polygon after a reflection in the line y = -x has vertices at:

A(0,-2), B(-4,-3), C(-4,-6), D(0,-5)

The image of the polygon is attached below.

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The evaluated expression of (6x+3y) - z² divide by 2x when x = -3, y = 4 and z = -6 is 5.3

An algebraic expression consists of unknown variables, numbers and arithmetic operators.

Therefore, let's evaluate the expression, (6x+3y) - z² divide by 2x when x = -3, y = 4 and z = -6.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

In other words, to evaluate the expression, we have to substitute the given value of the variable and simplify the expression.

Therefore,

(6x+3y) - z² = (6(-3)+3(4)) - (-6)² = (-18 + 12) - 36 = -32

2x = 2(-3) = -6

Hence,

- 32 / -6 = 5.3

Therefore,

(6x+3y) - z² / 2x when  x = -3, y = 4 and z = -6 is 5.3

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The point slope equation and slope of some lines are given below

1) For y - 6 = 3(x - 5), slope = 3

2) For  y - 4 = -9(x + 8), slope = -9

3) y - 2 = 5x, slope = 5

4) Point slope equation of line whose slope = -10 and passing through   (1, 4)

   y - 4 = -10(x - 1)

5) Point slope equation of line whose slope = 2 and passing through    (5, -3)

      y  + 3 = 2(x - 5)

6) Point slope equation of line whose slope = [tex]\frac{1}{2}[/tex] and passing through    (-7, -7)

   [tex]y +7 = \frac{1}{2}(x +7)\\[/tex]

What is equation of line in point slope form?

The most general form of equation of line in point slope form is given by [tex]y - y_1 = m(x - x_1)[/tex] , [tex](x_1, y_1)[/tex] is a point on the line

Where m is the slope of the line

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

1) y - 6 = 3(x - 5)

  y - 6 = 3x - 15

  y = 3x - 15 + 6

  y = 3x - 9

  Slope = 3

  If x = 0,

  [tex]y = 3 \times 0 -9\\y = -9[/tex]

  (0, -9) is a point on the line

2) y - 4 = -9(x + 8)

   y - 4 = -9x - 72

   y = -9x - 72 + 4

   y = -9x - 68

   Slope  = -9

   If x = 0

   [tex]y = -9 \times 0 -68\\y = -68[/tex]

   (0, -68) is a point on the line

3) y - 2 = 5x

   y = 5x + 2

  Slope = 5

    Putting x = 0

    [tex]y = 5 \times 0 + 2\\y = 2[/tex]

    (0, 2) is a point on the line

4) Slope = - 10

    The line passes through (1, 4)

    Point slope equation

      y - 4 = -10(x - 1)

5) Slope = 2

    The line passes through (5, -3)

     Point slope equation

      y - (-3) = 2(x - 5)

      y + 3 = 2(x - 5)

6) Slope = [tex]\frac{1}{2}[/tex]

      The line passes through (5, -3)

     Point slope equation

       [tex]y - (-7) = \frac{1}{2}(x - (-7))\\y +7 = \frac{1}{2}(x +7)\\[/tex]

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The function operation (f - g)(x) of the functions f(x) = -3x² + 2x - 3 and g(x) = 2x² - 3x + 4 is -5x² + 5x - 7.

A function is simply a relationship that maps one input to one output.

Given the functions in the question;

To determine the function operation (f - g)(x), replace the function designators with the real functions and simplify.

(f - g)(x) = f(x) - g(x)

(f - g)(x) = ( -3x² + 2x - 3 ) - ( 2x² - 3x + 4 )

Apply distributive property to eliminate the parenthesis.

(f - g)(x) = ( -3x² + 2x - 3 ) - ( 2x² - 3x + 4 )

(f - g)(x) = -3x² + 2x - 3 - 2x² + 3x - 4

Collect and add like terms

(f - g)(x) = -3x² - 2x² + 2x + 3x - 3 - 4

(f - g)(x) = -5x² + 5x - 7

Therefore, the function operation (f - g)(x) is -5x² + 5x - 7.

Option A is the correct answer.

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