Help me please sjsjdjs it’s due in a few minutes

Help Me Please Sjsjdjs Its Due In A Few Minutes

Answers

Answer 1

Answer:

The answer is the 3rd dot.

Step-by-step explanation:

hope this helps

Answer 2

Answer:

The one right below 8

Step-by-step explanation:


Related Questions

1. Mr. C has a square soccer field. The length of the soccer field is 18 feet.
What is the area of the soccer field:,
What is the perimeter of the soccer field

Answers

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

If a₁ = 6 and an
an-1 + 3 then find the value of a4.

Answers

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

Fill in the blanks 30 = 27 __ ___x 9 = 54 81 / ___ = 9 2 = ___ / 5 8 x ___ = 32 72 / ___ = 8 7* __ = 49

Answers

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

3 miles is the same as how many kilometers?
Hint: 1 mi≈ 1.6 km
Round your answer to the nearest tenth.

Answers

Answer: 4.8

Step-by-step explanation:

The intensity of illumination at any point from a light source is proportional to the square of the reciprocal of the distance between the point and the light source. Two​ lights, one having an intensity ten times that of the​ other, are 7 m apart. On the line between the two light​ sources, how far from the stronger light is the total illumination​ least?

Answers

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:

7. Sketch a model to represent the equation
2x + 2 = 12. Then, solve the equation.

Answers

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.

What is an equation?

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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Emily loves to go the spa she and her friends go twice a month each visit she gets a 90 minute massage for $125 and a deluxe manicure and pedicure for $65. How much does she spent at the spa each month?

Answers

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:

heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ  -{ elyna s }-

in a survey, 32 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $48 and standard deviation of $7. construct a confidence interval at a 80% confidence level. give your answers to one decimal place.

Answers

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

What is a confidence interval?

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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work out and simplify where possible 7/8 - 1/4

Answers

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

A bag contains 3 gold marbles, 7 silver marbles, and
28 black marbles. Someone offers to play this game:
You randomly select one marble from the bag. If it
is gold, you win $3. If it is silver, you win $2. If it is
black, you lose $1.
What is your expected value if you play this game?

Answers

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.

Please help please and thank you.

Answers

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)

what is the measure of X

Answers

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

What is meant by an angle?

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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-3x-4y=-1, 3x-y=-4 solve by elimination

Answers

Answer: x=-1 and y=1



Hope it’s correct

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

What is the value of p?
p=?°

Answers

Answer:

p = 82°

Step-by-step explanation:

Since Triangle HIJ is an isosceles triangle, the base angles of the triangle are equal.

Angle IHJ = 180 - 131

= 49° (sum of angles on a straight line)

Angle IJH = Angle IHJ = 49°

p = 180 - 49 - 49

= 82° (sum of angles in a triangle)

A company has found that the demand for its product varies inversely as the price of the product. When the price x is 4.75 dollars, the
demand y is 500 units.
Find a mathematical model that gives the demand y in terms of the price x in dollars.

Answers

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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Select all of the following equation(s) that are quadratic in form.
x4 – 6x2 – 27 = 0
3x4 = 2x
2(x + 5)4 + 2x2 + 5 = 0
6(2x + 4)2 = (2x + 4) + 2
6x4 = -x2 + 5
8x4 + 2x2 – 4x = 0

Answers

Answer:

Step-by-step explanation:

x4 – 6x2 – 27 = 0

                        x=2.49,-2.49

3x4 = 2x

x=6

what is the translation rule

Answers

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.

100 POINTS!!!!
a) The next 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, how long is the race? Show your work. (3 points)
PLEASE QUICK

Answers

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,

To Find: how long is the race

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

Mark me Brainliest pls

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.The distances between the hurdles.The distance from the last hurdle to the finish line.

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.

(Multiplying Linear Expressions MC)

Simplify −5g(3g + 4).
A: −15g + 4
B: −15g − 20g
C: −15g2 + 4
D: −15g2 − 20g

Answers

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

The correct answer option is option D

How to multiply linear expression?

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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7. When the height of the sand in a particular rectangular sandbox is
leveled out then the height of the sand, in inches (in.), is proportional to
the volume of sand, in cubic inches (in.3), in the sandbox. When the
height of the sand is 1.25 in. the volume of the sand is 280 in.3. A
playground has 3 of these sandboxes.
What is the total volume of the sand, in cubic inches (in.3), that is
needed for the playground when the height of the sand in each sandbox
is 4.5 in.?
Show your work in the provided space.

Answers

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

How to solve mathematical proportions?

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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Let a,b,c,d be real numbers such that 1/a+Ï + 1/b+Ï + 1/c+Ï = 2/Ï
where Ï is non real cube root of unity choose the correct answer. abc+bcd+acd+abd is equal to

Answers

First, we can rewrite the given equation as:

1/a+Ï + 1/b+Ï + 1/c+Ï = (1/Ï)(1/a + 1/b + 1/c)

where Ï is the non real cube root of unity.

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

1/a + 1/b + 1/c = 2(1/a + 1/b + 1/c)

This simplifies to:

1/a + 1/b + 1/c = 0

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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(×+13)²=(×+12)²+(×-5)²
Give it to me please :(​​

Answers

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

Law of signs:- × - = +- × + = -+ × - = -+ × + = +

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

¿What are the equations?

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.

Solving problem: x² + 26x + 169 = x² + 24x + 144 + x² - 10x + 25x² + 26x + 169 = 2x² + 14x + 169x² + 26x - 2x² - 14x = 0-x² + 12x = 012x - x² = 0x (12 - x) = 0x = 0.12

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:

x = 0,  x = 12

The sum of three numbers is 24. The third is 11 less than 3 times the second. 8 times the first is 4 less than 10 times the second. Find the numbers

Answers

Answer:

F + S + T = 24 F= 1st number, S = 2nd, T = 3rd

Step-by-step explanation:

T = 2S - 11

9F = 7 + 2S

divide by 9

F + (7+2S)/9

substitute for F and T

(7+2S)/9 + S + 2S -11 = 24

7+2S + 9S + 18S - 99 = 216

29S = 216 + 99 - 7 = 308

S = 308/29 = the 2nd number

T = 2S -11 = 616/29 -11 = 616/29 - 319/29 = 297/29 = 3rd number

F = (7+2S)/9 = (7 +616/29)/9 = 819/261 = 1st number

the 3 numbers are 819/261, 308/29 and 297/29

they sum to 819/261 + 308/29 + 297/29 = about 3.14 + 10.62 +10.24 = 24

F =( 7+2(10.62))/9 = (7+ 21.24)/9 = 28.24/9 = 314

S = 308/29 = 10.62

T = 2S-11 = 2(10.62) - 11 = 21.24-11 = 10.24

although odds are the problem may have been mis-copied or has a slight typo, with more integer type solutions in the corrected version.  If the problem had an 8 instead of  9,  (8F = 7+ 2S)    then F=3.5, S=10.5, T = 10 as exact answers, not rounded off.    3.5+10.5+ 10 = 24

Answer:

First number: [tex]\frac{167}{21}[/tex];

Second number: [tex]\frac{142}{21}[/tex];

Third number: [tex]\frac{130}{14}[/tex].

Step-by-step explanation:

1. Assign variables to each number.

First number: "x";

Second number: "y";

Third number: "z".

2. Form equations based on the problem's statement.

Equation 1. "The sum of three numbers is 24", hence:

[tex](1)x+y+z=24[/tex]

Equation 2. "The third is 11 less than 3 times the second.", hence:

[tex](2)z=3y-11\\ \\(2)-3y+z=-11[/tex]

Equation 3. "8 times the first is 4 less than 10 times the second.", hence:

[tex](3)8x=10y-4\\\\(3)8x-10y=-4[/tex]

3. Group the 3 equations.

[tex](1)x+y+z=24\\\\(2)-3y+z=-11\\\\(3)8x-10y=-4[/tex]

4. Expand the equations.

As you may see, the 3 variables don't always appear on all 3 equations. Therefore, we'll have to introduce them even though they don't appear. For this, we write the variable with a coefficient of 0 next to it

[tex](1)x+y+z=24\\\\(2)0x-3y+z=-11\\\\(3)8x-10y+0z=-4[/tex]

5. Rewrite the equations as a 3x4 matrix.

Using the coefficient of each variable in each equation, rewrite the system of equation into a matrix like this:

[tex]\left[\begin{array}{cccc}1&1&1&24\\0&-3&1&-11\\8&-10&0&-4\end{array}\right][/tex]

6. Convert this matrix into the row-echelon form.

Check the attached image to see the steps to making this convertion.

a) Getting the 1 on column 1.

Since there's already a 1 there, we skip this step.

b) Getting the 0 on column 1.

Since there's already a 0 there, we skip this step.

c) Getting the 0 on column 1.

Multiply row 1 values by "-8" and add them to row 3. The result of these operations should be:

[tex]\left[\begin{array}{cccc}1&1&1&24\\0&-3&1&-11\\0&-18&-8&-196\end{array}\right][/tex]

d) Getting the 1 on column 2.

Since we are working with column 2 and row 2, you may use the pivot value "-3" (the one that corresponds to the intersection of column 2 and row 2) and divide row 2 by itself to obtain a 1. Result is the following:

[tex]\left[\begin{array}{cccc}1&1&1&24\\0&1&-\frac{1}{3} &\frac{-11}{-3} \\0&-18&-8&-196\end{array}\right][/tex]

e) Getting the 0 on column 2.

Multiply row 2 by "18" and add it to row 3. Resulting table is:

[tex]\left[\begin{array}{cccc}1&1&1&24\\0&1&-\frac{1}{3} &\frac{-11}{-3} \\0&0&-14&-130\end{array}\right][/tex]

f) Getting the 1 on column 3.

We are working with column 3 and row 3, the intersection value is "-14" and we may use it as a pivot value. Hence, we may divide row 3 by "-14" in order to obtain the number 1 in column 3. Final table is:

[tex]\left[\begin{array}{cccc}1&1&1&24\\0&1&-\frac{1}{3} &\frac{-11}{-3} \\0&0&1&\frac{-130}{-14}\end{array}\right][/tex]

7. Calculate the values.

Starting from the bottom up, take the expression of the resulting matrix and calculate the values of each variable.

a) From row 3 we have:

[tex]0x+0y+z=\frac{-130}{-14} \\ \\z=\frac{130}{14}\\ \\[/tex]

b) From row 2 we have:

[tex]0x+y-\frac{1}{3} z=\frac{-11}{-3} \\ \\y-\frac{1}{3} z=\frac{11}{3}\\ \\y-\frac{1}{3} (\frac{130}{14} )=\frac{11}{3}\\ \\y-\frac{130}{42} =\frac{11}{3} \\ \\y=\frac{11}{3}+\frac{130}{42}\\\\y=\frac{11*14}{3*14}+\frac{130}{42}\\ \\y=\frac{154}{42}+\frac{130}{42}\\ \\y=\frac{284}{42} \\\\y=\frac{142}{21}[/tex]

c) From row 1 we have:

[tex]x+y+z=24\\ \\x+\frac{142}{21}+\frac{130}{14} =24\\ \\x=24-\frac{142}{21}-\frac{130}{14}\\ \\x=\frac{1008}{42} -\frac{284}{42} -\frac{390}{42} \\ \\x=\frac{167}{21}[/tex]

8. Verify that the numbers work correctly in each of the equations.

Equation 1: [tex]\frac{167}{21} +\frac{142}{21} +\frac{130}{14} =24[/tex] Correct.

Equation 2: [tex]-3(\frac{142}{21} )+\frac{130}{14} =-11[/tex] Correct.

Equation 3: [tex]8(\frac{167}{21} )-10(\frac{142}{21} )=-4[/tex] Correct.

9. Conclude.

First number: [tex]\frac{167}{21}[/tex];

Second number: [tex]\frac{142}{21}[/tex];

Third number: [tex]\frac{130}{14}[/tex].

Important: Check the attached Excel sheet to see the changes made in the matrix.

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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!

Answers

The answer would be A.

Answer:  a is a rational number

Step-by-step explanation

Rational numbers are written in p/q form.

11/3 of x is 55 find x

Answers

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

11/3 x = 55

11 x = 55x3

11 x = 165

x=165/11

X=15

work out and simplify where possible 9/10 - 7/10

Answers

Answer:

1/5

Step-by-step explanation:

(9-7)/10

2/10

(2:2) / (10:2)

1/5

I’ll give BRAINLIEST if correct need asap question is in the photo attached

Answers

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

Slope:

1

y-intercept: (0,3)

x  y

0 3

1  4

How much would you need to deposit in an account now in order to have $3,000.00 in the account in 1607 days?

Assume the account earns 3% simple interest.

You would need to deposit_____ in your account now.

Answers

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  

Two elephants are being delivered to the zoo. One elephant weighs 23,453 pounds, and the other elephant weighs 19,916 pounds. How many pounds do the elephants weigh together?

Answers

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

How to add two similar quantity?

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.

According to question:

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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which of the following is false about probability distributions? O point the probabilities must total O. each probability should be greater than or equal to O. each probability should be positive, less than or equal to O. the outcomes listed must be independent.

Answers

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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