Consider the following statement. ∀a ∈ Z, (a − 1) a is not an integer. (a) Select the correct negation for this statement. For every integer a, a − 1 a is an integer. There is an integer a such that a − 1 a is not an integer. For every integer a, a − 1 a is not an integer. There is an integer a such that a − 1 a is an integer. (b) Is the given statement true or false? If the statement is true, enter TRUE; if the statement is false, enter a value of a that could be used as part of a counterexample that justifies its falseness.

The required 80% confidence interval is (46.15, 49.85).

In frequentist statistics, a confidence interval is a range of estimates for an unknown quantity.

The most common confidence level is 95%, but when calculating confidence intervals, other levels, such as 90% or 99%, are also occasionally employed.

So, we know that:

n = 32

χ' = 48

s = 8

Create an 80% confidence interval using the equation below:

[tex]\left(\bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}}\right)[/tex]

To determine the critical value t for n-1 degrees of freedom and 1 -cl level of significance, use the formula below:

[tex]t_{0.2, d f=31}=\pm 1.309[/tex]

Create the confidence interval now:

[tex]\begin{aligned}& \left(48 \pm 1.309 \times \frac{8}{\sqrt{32}}\right) \\& (48 \pm 1.85) \\& (46.15,49.85)\end{aligned}[/tex]

Therefore, the required 80% confidence interval is (46.15, 49.85).

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Answer:

Step-by-step explanation:

x4 – 6x2 – 27 = 0

                        x=2.49,-2.49

3x4 = 2x

x=6

The equation of the line passes the origin. And the inclination of the line with the x-axis is 3/2. And the graph is given below.

An association between various factors brings about a straight model when a diagram is shown. The variable will have a level of one.

The straight condition is given as,

y = mx + c

Where m is the incline of the line and c is the y-block of the line.

The equation of the line is given below.

y = (3/2)x

The y-intercept is zero. Then the condition of the line passes the beginning. Furthermore, the tendency of the line with the x-pivot is 3/2.

The graph of the line is drawn below.

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Answer:

Area = 324ft²

Perimeter = 72ft

Step-by-step explanation:

Area of a square = length²

Area of a square = (18ft)² = 324ft²

Perimeter of a square = 4*length

Perimeter of a square = 4ft*18 = 72ft

With the help of algebra mathematical model equation for demand of company's product is given by the equation d = 1800 / p.

What is algebra?

The area of mathematics known as algebra deals with the representation of problems as mathematical expressions. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.

Let demand for company's product d vary inversely with its price p, which means

d ∝ ( 1/p ) or d = k * ( 1/ p) = k / p  ----- 1

As when p = 4.5, d = 400

Putting these in (1), we get 400 = k/ 4.5

Hence #k=400 x 4.5=1800 and our model equation is

d = 1800/p

Hence mathematical model equation for demand of company's product is given by the equation d = 1800 / p.

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Answer: 23 / 40 or 23:40

Step-by-step explanation:

Width = 69

Length = 120

so ratio of width is to length = 69 : 120

simplest form is 23 : 40 or 23 / 40 (fraction)

The multiplication of the linear expression - 5g(3g + 4) is given by -15g² - 20g.

The correct answer option is option D

Multiplication: This is the process of computing the sum of a number with itself a specified number of times, or any other analogous binary operation that combines other mathematical objects.

- 5g(3g + 4)

open parenthesis

= -5g × 3g - 5g × 4

= -15g² - 20g

In conclusion, the linear expression - 5g(3g + 4) when simplified equals -15g² - 20g

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Answer:

The intensity of the light is inversely proportional to the square of the distance from the source of light. Therefore, in this situation, where one light source has an intensity ten times that of the​ other, the distance from the stronger light source would be 0.7m before the total illumination​ is the least.

Step-by-step explanation:

Answer:

$ 2649.98

Step-by-step explanation:

1607 days = 1607/365 yrs

3000  =  (deposit) + deposit * i * 1607/365      where i = decimal interest 3000 =  deposit ( 1 + .03 * 1607/365)

   3000/(1 + .03 *  1607/365) = deposit = $ 2649.98  

To solve the problem, we will use the law of signs, to solve the problem

With the law of signs, we solve, but first we must know the following.

We know that the equations are those mathematical expressions that are called in members and separated, by their equal sign, which these carry their known data and unknown or unknown data, these are related through their mathematical operations.

So, the result of this equation is x = 0.12

¡Hope this helped!

Answer:

x = 0,  x = 12

Step-by-step explanation:

Given equation:

[tex](x+13)^2=(x+12)^2+(x-5)^2[/tex]

Expand:

[tex]\implies (x+13)(x+13)=(x+12)(x+12)+(x-5)(x-5)[/tex]

[tex]\implies x^2+26x+169=x^2+24x+144+x^2-10x+25[/tex]

Collect and combine like terms on the right side of the equation:

[tex]\implies x^2+26x+169=x^2+x^2+24x-10x+144+25[/tex]

[tex]\implies x^2+26x+169=2x^2+14x+169[/tex]

Subtract 169 from both sides:

[tex]\implies x^2+26x=2x^2+14x[/tex]

Subtract x² from both sides:

[tex]\implies 26x=x^2+14x[/tex]

Subtract 26x from both sides:

[tex]\implies 0=x^2-12x[/tex]

[tex]\implies x^2-12x=0[/tex]

Factor out the common term x:

[tex]\implies x(x-12)=0[/tex]

Apply the zero-product property:

[tex]\implies x=0[/tex]

[tex]\implies x-12=0 \implies x=12[/tex]

Solution:

Answer:

5/8

Step-by-step explanation:

1/4=2/8

7/8-2/8=5/8

5/8 cannot be simplified

Answer:

5/8

Step-by-step explanation:

(7-2)/8

5/8

Answer:  a is a rational number

Step-by-step explanation

Rational numbers are written in p/q form.

Answer:

1/5

Step-by-step explanation:

(9-7)/10

2/10

(2:2) / (10:2)

1/5

To find (f - g)(x), you can subtract g(x) from f(x):

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

= (2x2 + 2) - (6x2 + 6)

= -4x2 + (-4)

= -4(x2 - 1)

Therefore, the result of (f - g)(x) is -4(x2 - 1).

The measure of an angle X is 11° and 3X+2°=35° , 4X-9° =35° .

In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.

∠QPA = ∠UPA

3X+2 =4X- 9

4X-3X= 9 + 2

X= 11

The measure of X is 11

3X+2°=3(11)+2°

=35°

(4X-9)°=(4(11)-9)°

=35°

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Answer: $380

Step-by-step explanation:

    First, we will find the price per visit using addition.

$125 + $65 = $190

    Next, we notice it says "twice a month" in the question. We will multiply the value above by two to find the price per month.

$190 * 2 = $380

Answer:

twice a month of 125 + 65

2($125 + $65)

= 2($190)

= $380

Step-by-step explanation:

Answer:

A translation is a type of transformation that moves each point in a figure the same distance in the same direction

Step-by-step explanation:

Translations are often referred to as slides. You can describe a translation using words like "moved up 3 and over 5 to the left" or with notation.

Step-by-step explanation:

this is a college level question, and you need help with that ? elementary school students have to be able to answer this.

30 = 27 + 3

6 × 9 = 54

81 / 9 = 9

2 = 10 / 5

8 × 4 = 32

72 / 9 = 8

7 × 7 = 49

Answer:

a₄ = 15

Step-by-step explanation:

using the recursive relation [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 3 and a₁ = 6 , then

a₂ = a₁ + 3 = 6 + 3 = 9

a₃ = a₂ + 13= 9 + 3 = 12

a₄ = a₃ + 3 = 12 + 3 = 15

The Total volume of sand in cubic inches needed for the playground when the height of the sand in each sandbox is 4.5 in is; 2700 in³

We are told that the height of the sand, in inches (in.), is proportional to

the volume of sand.

Let the volume be denoted as V

Let the height be denoted as h

Thus;

V ∝ h

Then to equate this, we will have a constant of proportionality;

V = kh

where k is constant of proportionality

When the height of the sand is 1.25 in., the volume of the sand is 280 in³ and this gives;

280 = 1.25k

k = 250/1.25

k = 200

Now, ware told that the height of sand in a box is now 4.5 inches and so;

V = 200 * 4.5

V = 900 in³

Since the playground has 3 of such boxes, then we can say that;

Total volume of sand on the playground = 900 * 3 = 2700 in³

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The required weight of the two elephants together is 43369 pounds.

Addition  is an approach to consolidating things and considering them all together.Addition  in math is a course of consolidating at least two numbers. Addends are the numbers added, and the outcome or the last response we get after the interaction is known as the total.

We have,

One elephant weighs 23,453 pounds, and the other elephant weighs 19,916 pounds.

To find total weight of two elephant together,we have to add them.

23,453 pounds + 19,916 pounds

43369 pounds

Thus, required weight of two elephant is 43369 pounds.

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First, we can rewrite the given equation as:

where Ï is the non real cube root of unity.

We can then multiply both sides of the equation by Ï to get:

This simplifies to:

Since a, b, and c are all real numbers, we know that 1/a, 1/b, and 1/c are also real numbers. Therefore, the sum of these three real numbers must also be a real number. The only way that 1/a + 1/b + 1/c can equal 0 is if all three of these terms are equal to 0.

Thus, we can conclude that a = b = c = 0.

Since a, b, and c are all equal to 0, we know that abc + bcd + acd + abd must also equal 0. Therefore, the answer is 0.

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x = 5 will be the correct answer and Model is provided in attachment don't look at the beauty of my figure.

The solution of the equation 2x + 2 = 12 is x = 5. And the model and the graph are given.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Equation 2x + 2 = 12

The model for the equation is given in the attached image.

And the graph is also given in the attached image.

To solve for x:

2x + 2 = 12

Simplifying,

2x = 12 -2

2x = 10

Divide by 2,

2x / 2 = 10 / 2

x = 5.

Therefore, the solution of the equation is x = 5

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Answer:

reflection then rotation

Step-by-step explanation:

y = 1, and x = -1

if you need to show your work:

if you combine the two equations together (eliminating x), it goes like this

-3x - 4y = -1

3x - y = -4

-5y = -5

y = 1

this means:

-3x - 4 = -1

-3x = 3

x= -1

and

3x - 1 = -4

3x = -3

x = -1

To calculate the expected value of playing this game, we need to multiply the value of each possible outcome by its probability of occurring and then add these values together. In this case, there are 3 gold marbles, 7 silver marbles, and 28 black marbles in the bag, for a total of 38 marbles. So, the probability of selecting a gold marble is 3/38, the probability of selecting a silver marble is 7/38, and the probability of selecting a black marble is 28/38. The value of winning $3 if a gold marble is selected is $3 * (3/38) = $0.21. The value of winning $2 if a silver marble is selected is $2 * (7/38) = $0.37. And the value of losing $1 if a black marble is selected is -$1 * (28/38) = -$0.74. Adding these values together, we get $0.21 + $0.37 - $0.74 = -$0.16. Therefore, the expected value of playing this game is approximately -$0.16.

Answer:

16.5

Step-by-step explanation:

11/3 =3 and 1/3 so 55/3 and 1/3 = 16.5 or 16 and 1/2

Answer:

100.72

Step-by-step explanation:

[tex]Given,[/tex]

event requires each runner to jump 10 hurdles that are spaced 8.5 meters apart.

If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line,

Solution:

runner to jump 10 hurdles that are spaced 8.5 meters apart.

Distance between 10 hurdles

=(10-1)* 8.5

=9*8.5

=76.5

If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line,

Hence length of race = 13.72+76.5+10.5

=100.72

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Answer:

100.72 meters

Step-by-step explanation:

To find the total length of the race, we need to sum:

The distance from the starting line to the first hurdle is 13.72 meters.

The distance between each of the 10 hurdles is 8.5 meters.

There are 9 spaces between hurdles 1 and 10, so the distance between the hurdles is 9 × 8.5 = 76.5 meters.

The distance from the last hurdle to the finish line is 10.5 meters.

To find the total length of the race, add these distances together:

[tex]\begin{aligned}\textsf{Total length of the race} &=\sf 13.72\; meters + 76.5\; meters + 10.5 \;meters\\\\&=\sf 100.72\; meters\end{aligned}[/tex]

Therefore, the race is 100.72 meters long.

The outcomes listed must be independent is false about probability distributions.

In probability theory, statistics, and the theory of stochastic processes, independence is a key concept. Informally speaking, two occurrences are independent, statistically independent, or stochastically independent if their occurrence has no bearing on either their chances or probability of occurring. Similarly to this, two random variables are independent if the probability distribution of either one is unaffected by the realization of the other.

It is important to distinguish between two definitions of independence when working with collections of more than two occurrences. Informally, mutual independence of events refers to each event being independent of any combination of other events in the collection, whereas pairwise independence of events refers to any two events in the collection being independent of each other.

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Graph the line using the slope and y-intercept, or two points.

Slope:

1

y-intercept: (0,3)

x  y

0 3

1  4