Find the smallest Distinct positive numbers that provide a counter example to show the statement is false.The sum of any two different odd numbers is divisible by 4.

Part A.

To write the inequality we have to introduce variables that represent the things Laura needs to buy. For this reason let x be the number of sodas she buys and let y be the number of chips she buys.

Now, we know that each bag of chips cost $2.40 then tha ammount she spends in chips will be

Following the same reasoning, the ammount she spends in sodas will be

The total ammount she spends will be the sum of each ammount, that is:

Finally, we know that Laura has $48, so she can only spend less or equal this ammount.

Therefore the inequality representing this situation is

Part B.

To graph this inequality, first we have to graph the line given by

Doing this we obtained the following graph

Now we need to decide which semi plane represent the solution set of the inequality. Since we have a less or equal sign the right choice is the left one, then the graph of the inequality is

Therefore the graphs representing the number of chips and soda bottles Laura can buy is option B.

Part C.

To determine which combination of bottles of soda and chips Laura can buy we can graph the options we have. Remember that the x-axis represents the soda and the y-axis the chips. Hence the option we have will be equivalent to the points (4,24), (12,8), (16,8) and (28,4). Graphing this points we have

The only option allowed is the one that lies within the shaded region, therefore Laura can buy 12 bottles of soda and 8 bags of chips.

Answer:  Option (b) 21:18, option(c) 42:36, option(d) 63:54, option(e) 84:62 are equivalent ratios of 7:6

Step-by-step explanation: Hope this helped

Answer: -6 1/4, -6 9/10, -6 11/20

Step-by-step explanation: You find any number in decimals between them, then you covert into fractions if needed.

ANSWER

E. None of these

EXPLANATION

We want to find the converse of the statement.

A statement is made up of an hypothesis, then a conclusion.

So the converese is found by switching the hypothesis and the conclusion.

The statement given is:

If it is raining then we will go to the beach

The converse of this statement will therefore be:

If we will go to the beach then it is raining

The answer is Option E since the converse is not among the other options.

Answer:

Step-by-step explanation:

What is the determinant of H=[ matrix 2&4&9\\ 3&3&1\\ 4&5&3 matrix ]? 15 18 154 169Question

What is the determinant of H=[ matrix 2&4&9\\ 3&3&1\\ 4&5&3 matrix ]? 15 18 154 169

Answer:

Step-by-step explanation:

here are is answer and the steps it's in the pic below go check it out sorry if it's wrong have a nice day:)

For the functions f(x) and g(x), the two compositions are:

Here we have the next two functions:

f(x) = x² + 5

g(x) = 3x

The compositions are:

(f o g)(x) = f( g(x))

So we need to evaluate the function f(x) in g(x), this will give:

(f o g)(x) = f( g(x)) = g(x)² + 5

(f o g)(x) = (3x)² + 5

(f o g)(x) =  9x² + 5

The other composition is:

(g o f)(x) = g( f(x)) = 3*f(x)

(g o f)(x) = 3*(x² + 5)

(g o f)(x) = 3x² + 15

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Duck if the cost of 1 item and the catalog is $ 10 and onwards, the cost for every additional item is $ 4, then:

• The cost per item is $ 4

• The cost of the catalog is $ 6

I know you are able to select the correct choices.

Thanks for coming, Duck!

Answer:

Step-by-step explanation:

6$ cost of the catalog

The expression is given as

lnx=2.

To find the antilogarithm of the expression,

To compute the antilogarithm of a natural logarithm, take e to that power.

Hence the antilogarithm of lnx =2 to the nearest ten-thousandths is 7.3891.

Given in the question:

a.) The first costs $5 upfront and $4 per kilometer.

b.) The second costs $15 plus $3 per kilometer.

Let's generate the equation of each of the car service charges,

Let,

y = total cost of service

x = distance traveled

a.) The first costs $5 upfront and $4 per kilometer.

b.) The second costs $15 plus $3 per kilometer.

Let's determine the driving distance when the two companies charge the same.

We get,

Therefore, the two companies charge the same at a driving distance of 10 kilometers.

Summary:

1. The system of equations.

y = 5 + 4x

y = 15 + 3x

2. The solution.

x = 10

3. Graphing the system of equations.

Answer:

- The set-up fee is $50 ---- True

- The organizers were given a 10% discount on the catered meal. ---- True

Explanation:

Given that the expression that represent the total cost of a catered meal at a conference is;

The organizers of the conference were given a reduction in the cost of the catered meal due to the size of the event.

let a represent the percentage discount;

Sales tax was charged on the reduction price;

let b represent the sales tax;

The organizers were also charged a set-up fee.

Let c represent the set-up fee;

Comparing to the given equation;

So,

discount = 10%

sales tax = 4%

set up fee = $50.

Now let us determine which of the given options are true;

- The cost of the catered meal was less than the set-up fee -- Not enough information, Probably false.

- The sales tax rate was 10% -- false ( sales tax rate is 4%)

- The set-up fee is $50 ---- True

- The organizers were given a 10% discount on the catered meal. ---- True

A regular polygon is repeated to create a tessellation known as a normal tessellation. Recognize that the angles and sides of an ordinary polygon are the same. An equilateral triangle, a rectangular shape, or a hexagon can all be used to create regular tessellations.

Tessellations made from or larger than common polygons are known as semi-regular tessellations. Hexagons and equilateral triangles make up the semi-typical tessellation shown in the image. If we concentrate on the hexagons, we can see that the triangles are rotated around the hexagonal components to generate the pattern. It is a three.3.6 tessellation, as determined by our system for naming tessellations. The hexagon is represented by the six and the trees are the two triangles.

Regular polygons of the same size and shape make up regular tessellations. Multiple regular polygons combine to form semi-regular tessellations. There are only eight ways to arrange regular polygons to produce semi-regular tessellations.

Hence we derived the necessary information.

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To calculate the percentage error, the following formula would be applied;

ANSWER:

The percentage error, as shown in the calculations above is 3.5 % (to the nearest tenth of a percent)

True, 0.5 is the coefficient of v² in the expression v + 0.5v².

Given expression is v + 0.5v².

Follow the methods below to find the coefficient of a variable in a term:

Step 1: Encircle the variable and its power whose coefficient we're looking for.

So here we are looking for the coefficient of v²

Step 2: Forget about that variable and think about all the other numbers or variables that were written with it. That is the coefficient.

Hence, the required coefficient is 0.5.

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The short line on the sides of the triangle tells us that those sides are equal.

We can see that LN = NJ and

LO = KO

This means that triangle LNO is similar to triangle triangle LJK

LO/NO = (LO + OK)/JK

Given that NO = 16 and JK = 6x + 8, it means that

LO/16 = (LO + OK)/(6x + 8)

Since LO = OK, it means that

LO + OK = LO + LO = 2LO

Therefore

LO/16 = 2LO/(6x + 8)By cross multiplying, it becomes

LO(6x + 8) = 2LO * 16

LO(6x + 8) = 32LO

Dividing both sides of the equation by LO, it becomes

6x + 8 = 32

6x = 32 - 8

6x = 24

x = 24/6

x = 4

Given:

Principal, P = 6000

Rate, r = 4%

Time, t = 3 months

To find:

The simple interest

Explanation:

Using the simple interest formula,

Where t represents the number of months.

On substitution, we get

Final answer:

The simple interest is $60.

220000 pounds.

The final answer

Answer: 8

Step-by-step explanation:

σ =6.78

Count, N:6

Sum, Σx:372

Mean, μ:62

The standard deviation(σ) can be calculated using the formula below:

To calculate Mean( μ);

Mean( μ) = 62

Therefore, the standard deviation(σ) = 6.78

The shape consist of a cone and a cylinder

As such the volume of the shape is the sum of the volume of the two shapes.

The volume of a cone is given as

V = 1/3 Pi R^2H

and that of a cylinder is

V = Pi R^2H

where Pi is a constant 22/7, R is the radius and H is the height

Hence the volume of the figure

=1/3 * 22/7 * 6^2 * 10 + 22/7 * 6^2 * 12

= 22/7 (120 + 432)

= 22/7 * 552

= 1734.86 m^2

We have a point A=(7,-3) that is reflected over point C=(6,-5). This means that is refected in an axis that is perpendicular to the segment AC.

The image is point B, and we need to calculate its coordinates.

We can relocate the center of coordinates to point C, do the reflection and then relocate the original center of coordinates.

If now C became the center of coordinates A becomes:

Now, we can reflect it as normal:

Now, we convert this to the original coordinates as:

The point B is (5,-7).

Let's begin by listing out the information given to us:

We will observe that these two angles are complementary (they sum up to 90 degrees)

Hence, option A is the correct answer

Given:

The ages of people who attend a local church are normally distributed.

The mean age = μ = 39.5

And the standard deviation = σ = 18

The sketch of the normal curve will be as follows:

As shown the peak of the curve at the mean value = 39.5

and the distance between the consecutive numbers = 18

now, we will find the probability that a person chosen at random from this church is ages 21.5 or younger

So, we will find P( x < 21.5)

As shown, from the graph:

The answer will be = 0.1587

[tex] \frac{4 {x}^{2} - 36 }{x + 3} \\ = \frac{4( {x}^{2} - 9)}{x + 3} \\ = \frac{4(x + 3)(x - 3)}{x + 3} \\ = 4(x - 3) \\ = 4x - 12[/tex]

NOTE THE x+3 in the numerator cancels with the x+3 in the denominator.

Answer:

If you're solving for x and y, the answers are there!

Step-by-step explanation:

Hope this helps!

B. 3

1) Let's examine Juan's work

4+5 = 9 Multiplying the left side

(4+5)*3 =9

27 = 9 Divide only the right side by 3

9 = 3 False!

2) Then we can state that

B.

The only way Juan can maintain equality is by multiplying the right side by

3

27= 9

27 = 9 x 3

27 = 27 True!

3) The answer is B and 3.

Given:

Total no of pens is 8.

No of pens that works =4

No of pens that don't work = 4

The equation of the line passing through point (-4,-9) and has a slope -5/4 is 5x + 4y = 40

given data

A line passes through the point (-4,-9)

slope  = -5/4

Ax + By= C

slope = ( y - y1 ) / ( x - x1 )

-5/4 = ( y - 9 ) / ( x - -4 )

-5/4 ( x + 4 ) = ( y - 9 )

-5( x + 4 ) =  4( y - 9 )

-5x + 4 = 4y -36

4 + 36 = 4y + 5x

40 = 4y + 5x

rearranging to suit Ax + By = C

5x + 4y = 40

5x + 4y = 40  is the required equation of the line

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Answer:

Domain: A, [1, 7]

Range: [-4, 2]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

The equation to find the constant of proportionality or k is K=Y/X.

The value of the ratio between two proportional quantities, known as the constant of proportionality, is constant. When the product or ratio of two changing amounts gives a constant, that relationship is said to be proportionate. Depending on the kind of proportion between the two specified quantities—direct variation or inverse variation—the proportionality constant's value will vary.

When two variables are proportional to one another either directly or indirectly, their relationship can be expressed as y = kx or y = k/x, where k specifies how the two variables are related to one another. This k is referred to as the proportionality constant.

Hence the equation  to find the constant of proportionality or k is

K = Y/X

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The result when 4a² - 3a + 4 is subtracted from 3a² - 7a + 6 is
(-1)a² + (-4)a + 2.

What is subtraction?
The act of deleting items from a collection is represented by subtraction. The negative sign ("-") stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

Given, the minuend for the situation is= 3a² - 7a + 6
The subtrahend for the situation is= 4a² - 3a + 4
Therefore, the subtraction= Minuend - Subtrahend
= (3a² - 7a + 6) - (4a² - 3a + 4) = (-1)a² + (-4)a + 2
Thus, the result is (-1)a² + (-4)a + 2.

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