Select the counterexample that shows that the conjecture is false.

Conjecture: The product of two positive numbers is always greater than either number ​

Answer:

there are 47 worms in the container

Step-by-step explanation:

empty container- 225 g.

full container- 751.4 g.

1 worm- 11.2 g.

equation

(751.4-225)/11.2

751.4-225= 526.4

526.4/11.2= 47 worms

The son mowed most of the lawn

7/20 of the lawn still needs to be mowed

Size of the lawn mowed by Miss Jones = 1/4

Size of the lawn mowed by her son = 2/5

To know who mowed the most lawn, find the LCM of the denominators

The LCM of 4and 5 = 20

Make the denominators of both fractions to be 20

Size of the lawn mowed by Miss Jones = 1/4 x 5/5 = 5/20

Size of the lawn mowed by her son = 2/5 x 4/4 = 8/20

Since 8/20 > 5/20, Miss Jone's son mowed more part of the lawn than Miss Jone

How much of the lawn still needs to be mowed:

Answer:

it is greater then -2

Step-by-step explanation:

heres how I was taught, if you have a number say like 8 then its greater the day 5 same for -8 and -5 the long it is away from 0 the greater it is

Answer:

See below

Step-by-step explanation:

Alternate exterior angles are equal if the lines crossed by the transversal are parallel

15x + 9 = 21x - 27

9 + 27  = 21x - 15 x

x = 6 °

ANSWER

3/7 (the correct option is not there)

EXPLANATION

There are 7 red balls and 3 white balls in the bag.

To find the probability of Doug being the first to draw the white ball, we have to assume that Andrew, Betsy and Cam all draw red balls.

There are a total of 10 balls there.

After Andrew Betsy and Doug pick their balls, there will be 7 balls left, that is:

4 red balls and 3 white balls.

Ther probaility of Doug picking the white ball will therefore be the number of white balls divided by the total number of balls.

That is:

P(Doug) = 3/7

That is the probability that Doug will win the $160.

An inequality which is represented by the number line above is: x < -7.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

In Mathematics, there are four (4) rules that are generally used to write an inequality and these include the following:

Next, we would apply the aforementioned rules to write the solution to the inequality shown in the number line above:

x < -7

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Answer:

48

Step-by-step explanaause tion:

because there are 12 ounces in orange juce  and 36 ounces of water  combime them together 48

Three patients had all the complaints.

In a finite set, the number of distinct elements is known as the cardinal number. It is written as n(A) and can be read as "the number of set elements."

Let's assume,

U is the set of patients who reported at the hospital on that day.

F is the set of patients who complained of fever.

S is the set of patients who had stomach troubles.

I is the set of injured patients.

The given data can be written as follows:

n(U) = n(F∪S∪I) = 100

n(F) = 70

n(S) = 50

n(I) = 30

n(F∩S) + n(S∩I) + n(I∩F) - 3×n(F∩S∩I) = 44

Using the cardinal number of the union of three sets formula, we get

n(F∪S∪I) = n(F) + n(S) + n(I) - n(F∩S) - n(S∩I) - n(I∩F) + n(F∩S∩I)

100 = 70 + 50 + 30 - (44 + 3×n(F∩S∩I)) + n(F∩S∩I)

100 = 150 - 44 - 2×n(F∩S∩I)

2×n(F∩S∩I) = 106 - 100 = 6

n(F∩S∩I) = 3

Therefore, 3 patients had all the complaints.

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The value of x is 8 cm.

The area of a rectangle is the space occupied by the rectangle inside its perimeter. A rectangle's area is calculated by multiplying its length by its width.

Given:

Length of rectangle = 20 cm

Width of rectangle= x cm

Area of rectangle = length × width

                             = 20x cm²

The dimensions of the smaller rectangle cut out of it are,

Length = 16cm

Width = x-3

Area of the smaller rectangle = length × width

                                                 = 16(x - 3) cm²

The area of the shaded portion will be equal to the difference between both areas which is given as 80 square centimeters.

20x - 16(x-3) = 80

Now, we need to solve this equation to obtain the value of x.

20x - 16x + 48 = 80

4x = 80 - 48

4x = 32

x = 32/4

x = 8

Therefore, the value of x is 8 cm.

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Using translation, the functions that could be the one graphed are given as follows:

A translation is when a function undergoes a change in it's definition, keeping the same shape and side length, just changing the position.

The possible translations are given as follows:

In the context of the graph of this problem, the parent function is the square root of x, defined as follows:

y = sqrt(x)

The domain of this function, as is the domain of the graph, is for non-negative values of x, hence:

x ≥ 0.

From the graph, the function was translated down a units, keeping the domain but changing the range, hence the translation has the following format:

y = sqrt(x) - a.

Hence the first two options can be correct, either with a = 1 or with a = 3.

The information to solve this problem is given by the image at the end of the answer.

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The solution of the equation 4 x - 1 = - 2 (x + 1) is x = [tex]\frac{-1}{6}[/tex]

4 x - 1 = - 2 (x + 1)                 (given)

4 x - 1 = - 2 x - 2                   (applying distributive law to RHS)

4 x - 1 + 2 x = - 2                  (transferring literal term from RHS to LHS)

6 x - 1 = - 2                           (simplifying literal terms of LHS)

6 x  = - 2 + 1                         (transferring constant term from LHS to RHS)

6 x = - 1                                (simplifying constant terms of RHS)

x = - 1 / 6                              (transferring literal coefficient from LHS to RHS)

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6 Coulombs are needed to produce the 96J of energy.

Physics defines energy as the quantity of work or capability that may be applied to a thing to make it functional. Additionally, it refers to the capacity to exert force on an object as well as energy that is neither generated nor destroyed.

96 J of energy and a 16 V potential difference

Using the following formula, the work or energy is:

Work completed equals Charge x Potential Difference.

Charge = thus work completed/potential difference

Charge equals 96/16, or 6 Coulombs.

Therefore, 6 Coulombs of charged are needed to produce 96J of energy.

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Complex numbers are numbers in the form

where i represents the imaginary number defined as the square root of minus one.

We call a as the real part of the complex number and b the imaginary part.

We want to rewrite the number

in terms of the imaginary constant.

Using the following property

We can rewrite the second term of our sum as

Then, our number can be rewritten as

Using the definition of the imaginary unit we can rewrite our number as

Then, we can rewrite the square roots as

The simplified version of our number is

It should be noted that the frequency distribution given appear to be normal as D. No, the frequencies increase, reach a maximum, then decrease.

It should be noted that the graph that's illustrated shows that there is a concentration of the data points in the middle.

It should be noted that this illustrates that isn't not normal and the bell shaped curve was illustrated.

Therefore, based on the information, the correct option is D.

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Answer:

3900*18%=702

Step-by-step explanation:

Answer:

[tex]y=x^2+6x-16[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

Given points on the curve:

The x-intercepts of a quadratic function are the points at which the line crosses the x-axis, so when y = 0.  

Therefore, the x-intercepts of the given function are -8 and 2.  

Substitute these into the intercept formula:

[tex]\implies y=a(x-(-8))(x-2)[/tex]

[tex]\implies y=a(x+8)(x-2)[/tex]

Substitute the other given point (-6, -16) into the equation and solve for a:

[tex]\begin{aligned} y&=a(x+8)(x-2)\\\textsf{When }(-6,-16)\implies -16&=a(-6+8)(-6-2)\\-16&=a(2)(-8)\\-16&=-16a\\\implies a&=1\end{aligned}[/tex]

Therefore, the equation of the function in intercept form is:

[tex]y=(x+8)(x-2)[/tex]

Expand to standard form:

[tex]\implies y=x(x-2)+8(x-2)[/tex]

[tex]\implies y=x^2-2x+8x-16[/tex]

[tex]\implies y=x^2+6x-16[/tex]

Therefore, the quadratic function in standard form is:

[tex]\boxed{ y=x^2+6x-16}[/tex]

The rate of plate motion in cm/year is equal to 3.3528 × 10⁻³ cm/year.

A conversion factor can be defined as a number that is typically used to convert (change) a number in one (1) set of units to another, either by dividing or multiplying.

Generally speaking, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion.

Conversion:

1 mile = 5280 feet

30 miles = X feet

Cross-multiplying, we have:

X = 30 × 5280

X = 158,400 feet.

Next, we would convert the value in feet to inch and then to cm as follows:

Distance = 158,400/12 = 13,200 inches.

In centimeters (cm), we have:

1 inch = 2.54 cm

13,200 inches = Y cm

Cross-multiplying, we have:

Distance, Y = 13,200 × 2.54

Distance, Y = 33,528 cm.

Now, we can determine the rate of plate motion in cm/year:

Rate = Distance/Time

Rate = 33,528/10,000,000

Rate = 3.3528 × 10⁻³ cm/year.

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Answer:

13$

Step-by-step explanation:

just divide 39 by three.

39 dive by 3=13

13 x 3=39

Answer:

3/10

Hope this helps!

Have a good day :)

Answer:

13 in

Step-by-step explanation:

Let the hypotenuse be x. Then, by the Pythagorean theorem,

[tex](x-8)^2 + 12^2=x^2 \\ \\ x^2-16x+64+144=x^2 \\ \\ 16x=64+144 \\ \\ x=4+9 \\ \\ x=13[/tex]

Answer:

  130 cars

Step-by-step explanation:

You want the value of x (the number of cars made) that minimizes the unit cost, given by C(x) = 0.4x² -104x +13586.

The minimum cost will be found at the vertex of this quadratic cost function. For quadratic ax²+bx+c, the vertex is found at x=-b/(2a).

The cost function has a=0.4 and b=-104, so the number of cars that must be made to minimize the unit cost is ...

  x = -b/(2a) = -(-104)/(2(0.4)) = 104/0.8

  x = 130

130 cars must be made to minimize the unit cost.

__

Additional comment

A graphing calculator can plot the cost function and show you the coordinates of the minimum cost. The attachment shows the minimum cost per car is $6826 when 130 cars are made.

THE ONLY WAY WE CAN PROVE THAT AB IS EQUAL CD IS BY CALCULATING THE DISTANCES AND THEN COMPARING THEM.

FOR AB

[tex] = \sqrt{( {x2 - x1})^{2} + ( {y2 - y1})^{2} } \\ = \sqrt{(( {6- 2})^{2} + ( ({4 - 2})^{2} } \\ = \sqrt{( {4})^{2} +( {2})^{2} } \\ = \sqrt{16 + 4} \\ = \sqrt{20} [/tex]

THE DISTANCEAB IS GIVEN ABOVE.

NOW LET US CALCULATE DISTANCE CD

[tex] = \sqrt{ ({8 - 4)}^{2} + ({6 - 4})^{2} } \\ = \sqrt{ {(4})^{2} + ({2})^{2} } \\ = \sqrt{16 + 4} \\ = \sqrt{20} [/tex]

WE CAN SEE THAT DISTANCE AB AND DISTAMCE CD ARE EQUAL THERE SE CAN NOW SAY

AB=CD

Answer:

No

do not share

Step-by-step explanation:

Two rays make up angle 7 and two DIFFERENT rays make up angle 8 (angle 6 is in between them) If they were a linear pair with a shared side, it would look like a loooong line with a ray sticking out that makes two angles. In the image, Angle1 and Angle2 are a linear pair. And Angle1 and Angle4 also.

They do not share at all.

We will have that he ate the following amount:

So, he ate the following:

He ate a total of 1/2 of the chocolate.

Answer:

kiss

i just thought of kiss I'm probably not correct to be honest

If the clas has 30 cups and fills individual bags with three-fourths cups then the number of bags that can be filled

= 30 / (3/4)

= 30 * 4/3

= 40

Hence 40 bags can be filled with popcorn

The derivative evaluated at t=1 minute will give us the rate of change (or the slope) of the line equation which approximate the function at that point. In other words, the rate of change is given by

Therefore, the answer is option 3 from top to bottom.