twelve hours after being filled, all the balloons have decreased in size. predict which balloon will be the smallest. explain your reasoning.

Answer:

2x

Step-by-step explanation:

The size of the union according to the given data is 37.

The study of sets, which are collections of objects, is a topic covered by the mathematical field known as set theory. A set is a clearly defined group of unique items, sometimes referred to as its elements or members, in set theory.

Let's use the inclusion-exclusion principle to compute the number of elements in the union of four sets:

First, we add up the sizes of the individual sets:

4 x 15 = 60

Next, we subtract the sizes of the pair-wise intersections:

6 x 5 = 30

We have to multiply by 6 because there are 6 pairs of sets.

Now we need to add back the sizes of the three-way intersections:

4 x 2 = 8

We have to multiply by 4 because there are 4 triples of sets.

Finally, we need to subtract the size of the intersection of all four sets:

-1

Putting it all together, we have:

60 - 30 + 8 - 1 = 37

Therefore, the size of the union is 37.

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After solving the value of r = (-1 - t / 5).

Given equation:

6r + t = r - 1

6r - r + t = -1

5r + t = -1

5r = -1 - t

divide by 5 on both sides

5r/5 = -1 - t / 5

r = (-1 - t / 5)

Therefore r = (-1 - t / 5)

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the probability of the event that  a sample of 5 cans will have a meaningful amount of at least 12.13 oz is 0.0078

We are provided with the information that cans of coke are filled in the account of having normal distribution, with the provided means which is  12.00 oz and the standard deviation of 0.12 oz and the sample size is

n= 5.

let X be the sample mean, so the probability will be :

P(X[tex]\geq[/tex] 12.13) = 1- P(X<12.13)

               =1-  P(X-(μ/(σ/[tex]\sqrt{n}[/tex])) < (12.13 -12.00)/(0.12/[tex]\sqrt{5}[/tex]))

            = 1- P(z<2.42)

            = 1-0.9922

           =0.0078

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Cans of regular Coke are labeled as containing 12 oz. Statistics students weighted the content of 5 randomly chosen cans, and found the mean weight to be 12.13. Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.12 oz. Find the probability that a sample of 5 cans will have a mean amount of at least 12.13 oz.

50 boxes are needed to pack 600 granola bar when 12 granola bar in a single bar.

Given, a nack company that sells snacks may fit 12 granola bars in a box.

We must determine the number of boxes required to hold 600 granola bars.

By using the unitary technique, we can calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units. We typically utilize this technique for math calculations. This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

Now, the number of boxes= 600/12

=50

Therefore, to pack 600 granola bars they need 50 boxes.

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The slope of the line y = -3x is  -3.

The slope of a line is the measure of the steepness and the direction of the line. It is defined as the change in y coordinate with respect to the change in x coordinate of that line.

The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. Then the slope

m = Δy/Δx = dy/dx

Here the line is y = -3x

Differentiating the equation of line with respect to x, we get

   dy /dx = -3

⇒ dy /dx = m = -3.

Therefore, the slope of the line y = -3x was found to be -3.

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The area of rectangle ABCD is 23.5 cm² with vertices A(-1,11) B( 7,9) C(10,13) and D(2,7).

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies. The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

Given,

A(-1,11) B( 7,9) C(10,13) and D(2,7)

Calculate the length of the sides using the distance formula:

AB = √(7+1)² + (9 - 11)²

AB = √8² + 2²

AB = √16 + 4

AB = √20

AB = 4.47

BC = √(10-7)² + (13-9)²

BC = √3² + 4²

BC = √9 + 16

BC = √25

BC = 5

For area of rectangle:

Length × Width

5 × 4.47

23.5

The area of rectangle ABCD is 23.5 cm².

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The sidelength of the square is 6 units, with that we can find that the perimeter is 24 units.

For a square of side length S, the perimeter is give by the formula:

P = 4*S

In this case, the vertices of the square are given, and I and J are consecutive vertices, where:

I = (8, - 10)

J = (2, - 10)

Notice that the y-component is the same, then the side length of the square is:

S = 8 - 2= 6

Using the formula for the perimeter we get:

P = 4*S = 4*6 = 24

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The solution by Elimination Method of the given equations -x+9y=35 and 2x+2y=10 is given by, x=1,y=4.

Given the equations are,

-x+9y = 35 .............(i)

2x+2y = 10 ...........(ii)

From the equation (ii) we get,

2x+2y = 10

x+y = 5 ...............(iii)

Adding (i) and (iii) we get,

-x+9y+x+y = 35+5

10y = 40

y = 40/10

y = 4

Substituting the value of y in (i) we get,

-x+9*4 = 35

-x+36 = 35

-x = 35-36

-x = -1

x = 1

Hence the solution of the equations is, x=1,y=4.

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The number of fidget spinners that had not sold yet is; 9,455.

The quantities given in the problem are the total number of fidget spinners shipped each weeks and the number of them sold.

It follows from the task content that the total number of fidget spinners that had not sold yet be determined from the information given.

According to the task content;

1st week;

12,875 fidget spinners were shipped and 9,843 of them were sold.

The number of fidget spinners that had not sold yet is therefore; = 12875 - 9843 = 3,032.

2nd week;

19,175 fidget spinners were shipped and 12,752 of them were sold.

The number of fidget spinners that had not sold yet is therefore; = 19,175 - 12,752 = 6,423.

Ultimately, the total number of fidget spinners that had not sold yet is; 3,032 + 6,423 = 9,455.

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Answer:

14

Step-by-step explanation:

first add inside the parentheses 4+7=11

then add three 11+3=14

Answer: 3 + 11 = 14

Step-by-step explanation: Follow PEMDAS (Parentheses, exponent, multi, divi, add, subtract.)

If If the measure of an angle is not 180, then it is not a straight angle" relate to the conditional statement "If an angle is a straight angle, then its measure is 180." This is a A. counterexample.

Contraposition in logic and mathematics refers to the inference of going from a conditional statement to its logically equivalent contrapositive, as well as the associated proof method known as proof by contraposition. A statement's contrapositive has its antecedent and consequent inverted and flipped.

Any exception to a generalization is a counterexample. A counterexample disproves the generalization in logic, and it does so rigorously in mathematics and philosophy.

Find a case where P is true but Q is false to provide a counterexample to a conditional statement P Q. Here is the equivalent rule for negating a conditional: (P Q) (P Q) Once again, the "if-part" P must be true and the "then-part" Q must be false (that is, Q must be true).

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Answer:

(top to bottom)104.04...6800...272...3

Step-by-step explanation:

68 can go into 7075, 104 times.

68 goes into 275 4 times.

275-272=3

Answer:  [tex]h = \frac{3}{4}y[/tex] is the cone's height.

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

Work Shown:

Let's set up each volume equation.

[tex]\text{VL} = \text{volume of cylinder}\\\\\text{VL} = \pi*r^2*h\\\\\text{VL} = \pi*x^2*y\\\\[/tex]

[tex]\text{VC} = \text{volume of cone}\\\\\text{VC} = \frac{1}{3}*\pi*r^2*h\\\\\text{VC} = \frac{1}{3}*\pi*(2x)^2*h\\\\\text{VC} = \frac{4}{3}\pi x^2*h\\\\[/tex]

Then we're told that VL and VC are the same value. Let's equate the right hand sides and solve for h.

[tex]\text{VL} = \text{VC}\\\\\pi x^2y = \frac{4}{3}\pi x^2 h\\\\x^2y = \frac{4}{3}x^2 h\\\\3x^2y = 4x^2 h\\\\h = \frac{3x^2y}{4x^2}\\\\h = \frac{3y}{4}\\\\h = \frac{3}{4}y\\\\[/tex]

Answer:

3y

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $(r)$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]   [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $(r)$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

Given dimensions of the cylinder:

Therefore, the equation for the volume of the cylinder is:

[tex]\implies V_{\sf cylinder}=\pi x^2y[/tex]

Given dimensions of the cone:

Therefore, the equation for the volume of the cone is:

[tex]\implies V_{\sf cone}=\dfrac{1}{3} \pi x^2 h[/tex]

As the cylinder and the cone have the same volume, substitute the equation for the volume of the cylinder into the equation for the volume of the cone an solve for h:

[tex]\begin{aligned}V_{\sf cylinder}&=V_{\sf cone}\\\implies \pi x^2 y&=\dfrac{1}{3} \pi x^2 h\\y&=\dfrac{1}{3} h\\3y&=h\\h&=3y\end{aligned}[/tex]

Therefore, the height of the cone is 3y.

The required equation is y = 14.85x + 110.25.

The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.

Given that, Jake collects $311.95 after receiving 21 texts.

Therefore, he collected $311.95/21 per text.

$311.95/21 = $14.85

The collection balance was $422.20, therefore, Jake already has $422.20-$311.95 = $110.25.

Let Jake receives x texts, then he will get $14.85x, and Jake already has $110.25, therefore, the total collection after receiving x texts is:

y = 14.85x + 110.25

Hence, The required equation is y = 14.85x + 110.25.

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The average temperature last Sunday is 1.08T or (1 + 8/100)T.

Temperature simply means the hotness and coldness of a body.

In this case, last Sunday, the average temperature was 8 percent higher than the average temperature two Sundays ago.

This will be expressed as:

= T + (8% × T)

= T + (0.08 × T)

= T + 0.08T

= 1.08T

The temperature is 1.08T.

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Step-by-step explanation:

6+7=13,13+7=20,20+7=27,27+7=(34)!

Answer:

£5,900 in taxes

Step-by-step explanation:

How much Income Tax would be paid by someone earning £41,000 in a tax year when the basic rate of Income Tax is 20% and the annual tax-free personal allowance is £11,500?

41,000 - 11,500 = 29,500 taxable

20% = 0.2

29,500 * 0.2 = £5,900 in taxes

Answer:

512 ÷ 64 = 8 is the correct representation.

Test of significance is  the observed effect due to chance. Option (c) is correct .

What is a significance test?

What makes significance significant?

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Randomly selecting a white golf ball first and then a white golf ball second are independent events.

What do you mean by dependent events?

Events that are dependent upon prior events are called dependent events. The results of earlier events have an impact on these current ones. For example, two or more events that are interdependent are referred to as dependent events.

It is given that in the beginning we have 3 white balss and 2 yellow balls

Total number of balls = 3 + 2 = 5

Probability of first selecting a white ball = 3/5

Now remaining white balls = 3 - 2 = 1

Remaining total balls = 5 - 1 = 4

Probability of selecting second white ball = 2/4

Probability of selecting a white golf ball first and then a white golf ball second = 3/5 × 2/4 = 3/10

Both the events are dependent as if we select first white ball, then it will change the number of white balls for selecting second time.

Therefore,  randomly selecting a white golf ball first and then a white golf ball second are independent events.

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113 crates are needed for the company to mail an order of 8927 watermelon, if one crate can hold 79 watermelon.

A single or unique unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.

Given,

There are 8927 watermelon and each watermelon can hold 79. We have to divided the number  of watermelon by the number of watermelon each crate can hold, to get the how many crate is needed to mail the order.

8927/79

=113

Therefore, 113 crates will be needed by the company.

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The measure of angle B is 78°.

∠A = (2x - 9)°

∠B = (2x + 4)°

∠C = x°

In triangle ABC,

      ∠A + ∠B + ∠C = 180°

2x - 9 + 2x + 4 + x = 180

                   5x - 5 = 180

                        5x = 180 + 5

                        5x = 185

                          x = 185/5

                          x = 37

∠B = 2x + 4

     = 2*37 + 4

     = 74 + 4

     = 78

Hence, ∠B is 78°.

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Answer:

8 1/3

Step-by-step explanation:

We want to find a number, x, that when divided by 10/3 equals 2.5.  We can write that as:

  x/(10/3) = 2.5

x = (2.5)*(10/3)    [MULTIPLY BOTH SIDES BY (10/3)

x = 25/3

x = 8 1/3             [

Answer:

10x^2 + 26x - 56

Step-by-step explanation:

10 x^2 -14x + 40x - 56 =

= 10x^2 + 26x - 56

Answer: 5x -2x = 8 +7, 3x = 15 x = 15/3) X= 5

Answer: y = 4

Step-by-step explanation:

First, we have to look at the triangle and understand which sides match each other. The side measure of EF matches the side of KH. Since we know these are congruent sides, we can set them equal to each other in an equation. So,

7y - 11 = 17.00

Now we add 11 to both sides, isolating the variable.

7y = 28.00

Now, we divide by 7 on both sides.

7y/7 = 28/7

y = 4

Joe has $120 after all the trades, which is the entire amount.

Given that,

With $80, Joe opened a bank account. Then he took out $35, put in $115, and took out another $40.

To know how much balance left in his account after all the transactions in dollars;

Assume that,

Amount when account opened (x) = $80

Amount withdrawn (y) = $35

Amount deposited again (z) = $115

Amount withdrawn again (p) = $40

The total amount left after all the above transactions is;

A = x - y + z - p

  = 80 - 35 + 115 - 40

  = 195 - 75

A = $120

Therefore, the total amount left with Joe after all the transactions is $120.

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The given phrase written as an algebraic expression is  c / 25 .

The given phrase is : a number c divided by 25

So if we consider any number 'c' , then the number when divided by c can be written as c ÷ 25

The required expression to represent this is given by c / 25.

Expressions are phrases used to describe statements in mathematics that contain variables, numbers, sometimes both, and at least two terms joined by an operator. Mathematical operations include addition, multiplication, and division.

The two types of expressions used in mathematics are numerical expressions, which only contain numbers, and algebraic expressions, which also contain variables.

A symbol with an unknown value is referred to as a variable. A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided. A number that has been further multiplied by a variable is referred to as a coefficient in an equation.

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The slope of the line is B.

In mathematics, the slope of a line is the change in y-coordinate with respect to the change in x-coordinate.

The net change in the y coordinate is denoted by Δy and the net change in the x coordinate is denoted by Δx.

So the change in the y coordinate for a change in the x coordinate is:

The slope of a straight line can also be expressed as:

In general, the slope of a line is a measure of its steepness and direction. The slope of the line between two points (x1,y1) and (x2,y2) can be easily determined by finding the difference in the coordinates of the points.

If the x-coordinate of each point on a line is 5 more than half the y-coordinate, then x= y2+5.

To find the slope of the line, solve for y and put the equation in slope-intercept form (y = mx + b, where m is the slope).

To do so, first subtract 5 from both sides, then multiply the entire equation by 2 to get y = 2x − 10.

The slope is 2.

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