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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:

2

Step-by-step explanation:

whose possible values are − 2 , 1 , 2 , 3 , and 6 .

Answer:

The price before tax at Barnes and Noble is $33, and the price before tax at Target is $33.25.

Step-by-step explanation:

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 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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Answer:

Step-by-step explanation:

x4 – 6x2 – 27 = 0

                        x=2.49,-2.49

3x4 = 2x

x=6

A statement which best describes one of these transformations is that: A. triangle 1 is rotated to result in triangle 2.

In Mathematics, there are four (4) main types of transformation and these include the following:

In Mathematics, a rotation simply refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Since triangle 2 has identical (similar) side lengths and angle measures, but is rotated and triangles 1 and 4 are identical, we can logically deduce that triangle 1 underwent a rotation to produce triangle 2.

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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:

Step-by-step explanation:

Given an ABCD inscribed quadrilateral, where the AB side is the diagonal of the circum-circle of the quadrilateral, we can calculate various properties by using basic trigonometry. Firstly, let us determine the length of BD. Since BCDZ = 120° and BC = 3cm ,we can use Sine rule to find out BD which will be equal to 4 cm. Secondly, we need to find AB and AD sides lengths as well as other angles in order for our calculations to be complete. To do this we will use Cosine rule since all three sides are known: BC=3cm; CD=5cm;BD=4 cm . This gives us a value for angle CBD which is approximately 39° and consequently angle BAD is also 39° since they add up together (BAD+CBD)to 180 degrees due their being opposite each other on a straight line..Finally ,using cosine again with these new values gives us both AB(6)and AD(2).

To summarise : Lengths -AB: 6 cm ; BD : 4 cm ;AD 2CM   Angles - BCDZ :120 ° ; CBD & BAD :39 °

In conclusion , given an ABCD inscribed quadrilateral whose one side was already identified as its circumference diameter it was possible through simple trigonometric equations such s Sines Rule or Cosines Rule determine its remaining lengths ans angles accurately .

If they purchased 7 bags of popcorn and 3 drinks, the price would be $44.25; p bags of popcorn and d beverages would cost 4.50p+4.25d.

What is a formula?

Equation is the name given to two or more expressions with the equal sign.

Due to that

$4.50 worth of popcorn

beverage for $4.25.

There are 3 drinks and 7 bags of popcorn.

So let's calculate the overall cost.

7(4.50)+3(4.25)

31.5+12.75

44.25

So if they purchased 7 bags of popcorn and 3 beverages, the price would be $44.25

The price for p bags of popcorn and d drinks must now be determined.

4.50p+4.25d

Therefore, the price would be $44.25 if they purchased 7 bags of popcorn and 3 drinks, and the cost would be 4.50p+4.25d for p bags of popcorn and d beverages.

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Answer:

a) The first term of the progression is 4.5.

b) The common difference of the progression is 4.

c) The sum of the first 10 terms of the progression is 225.

Step-by-step explanation:

To solve this problem, you can use the formula for the sum of an arithmetic series. An arithmetic series is a sequence of numbers in which each term is obtained by adding a fixed number, called the common difference, to the preceding term.

The sum of an arithmetic series with n terms and a common difference d is given by:

Sum = n/2 * (2a + (n-1)d)

Where a is the first term of the series and d is the common difference.

In this problem, you are given that the sum of the 4th and 6th terms is 42 and the sum of the 3rd and 9th terms is 52. You can use these two equations to solve for a and d.

First, let's find the sum of the 4th and 6th terms:

Sum = 4/2 * (2a + 3d) = 42

This simplifies to:

2a + 3d = 21

Next, let's find the sum of the 3rd and 9th terms:

Sum = 6/2 * (2a + 5d) = 52

This simplifies to:

2a + 5d = 26

Now that we have two equations, we can solve for a and d by using substitution or elimination.

To use substitution, we can solve the second equation for d:

d = (26 - 2a)/5

Then, we can substitute this expression for d into the first equation:

2a + 3((26 - 2a)/5) = 21

This simplifies to:

2a + 3(26 - 2a)/5 = 21

Which simplifies to:

2a + 3(26)/5 - 3(2a)/5 = 21

This simplifies to:

2a + 3(26)/5 - 6a/5 = 21

This simplifies to:

-4a + 3(26)/5 = 21

This simplifies to:

-4a + 39 = 21

This simplifies to:

-4a = -18

This simplifies to:

a = 4.5

Now that we know the value of a, we can substitute it back into one of the original equations to find the value of d:

2(4.5) + 3d = 21

This simplifies to:

9 + 3d = 21

This simplifies to:

3d = 12

This simplifies to:

d = 4

Now that we have found the values of a and d, we can use the formula for the sum of an arithmetic series to find the sum of the first 10 terms of the progression:

Sum = 10/2 * (2(4.5) + (10-1)(4))

= 10/2 * (9 + 36)

= 10/2 * 45

= 225

Therefore, the sum of the first 10 terms of the progression is 225.

Answer:

Hence,

Common difference is

First term is

Sum of first 10 terms is 47

Step-by-step explanation:

a4 + a6 =42 eq1

a3 + a9 =52 eq

a1=?

d=?

S10=?

From eq 1,

a4 + a6=42

a1+3d + a1+5d =42

2a1 + 8d= 42 eq 3

From eq 2,

a3 + a9 =52

a1+2d + a1+8d = 52

2a1 + 10d = 52 eq 4

Subtract eq 3 from eq

2a1 + 10d =52

-2a1 -8d = -42

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

2d = 10

d=5....

≈=======================

Putting value of d in eq

2a1 +10 d=52

2a1+ 50 =52

a1 =1

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

Now we find sum of first 10 terms,

S10 = 2a1 + 9d

S10 = 2+45

S10 = 47

===========

Answer:

The area is in contact with the ground if A box exerts 10,000 Pa of pressure on the ground. If the box weighs 1000 N is 10 m².

( which is D/10 m²).

Step-by-step explanation:

so what is pressure?

In the physical sciences, pressure is defined as the stress at a point within a confined fluid or the perpendicular force per unit area. A 42-pound box with a bottom area of 84 square inches will impose pressure on a surface equal to the force divided by the area it is applied to, or half a pound per square inch.

Answer: 10,000 pa

Step-by-step explanation:

Pressure = Force / Area

Force = 10,000

Area = 1 m^2

Pressure = 10,000 / 1

Pressure = 10,000 pa.

Answer:

What's the question? Ill try to answer in comments

Step-by-step explanation:

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

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

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

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

First number: "x";

Second number: "y";

Third number: "z".

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]

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

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]

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]

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]

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]

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.

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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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.

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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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

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 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: 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)

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)

Answer:

1/5

Step-by-step explanation:

(9-7)/10

2/10

(2:2) / (10:2)

1/5

Answer:

The answer is that the third example illustrates the associative property for addition. The associative property states that the order in which numbers are added does not affect the result. In other words, (a + b) + c = a + (b + c) for all numbers a, b, and c.

The third example follows this pattern:

(3 + 7) + 8 = 3 + (7 + 8) = (3 + 8) + 7

The other examples do not follow this pattern, so they do not illustrate the associative property for addition.

Step-by-step explanation:

The third example illustrates the associative property for addition. The associative property states that the order in which numbers are added does not affect the result. In other words, (a + b) + c = a + (b + c) for all numbers a, b, and c.

The third example follows this pattern:

(3 + 7) + 8 = 3 + (7 + 8) = (3 + 8) + 7

The other examples do not follow this pattern, so they do not illustrate the associative property for addition.

The first example illustrates the associative property for multiplication, which states that the order in which numbers are multiplied does not affect the result. In other words, (a x b) x c = a x (b x c) for all numbers a, b, and c.

The second example is not a valid mathematical expression, as it attempts to add a number and a product.

Answer:

(3 + 7) + 8 = 3 + (7 + 8) = (3 + 8) + 7

Step-by-step explanation:

The equations for associative property for addition are:

(a + b) + c = a + (b + c)

So, (3 + 7) + 8 = 3 + (7 + 8) = (3 + 8) + 7 is the answer!

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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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: 4.8

Step-by-step explanation:

Answer:  a is a rational number

Step-by-step explanation

Rational numbers are written in p/q form.

Answer:

Step-by-step explanation: As we know the number of elements in set A are 7 and the formula to calculate the number of proper subsets is 2^n – 1

Therefore substituting the values in formula .  n is number of elements of set A. Here n=7

so 2^7-1= 128-1=127

Ans:127

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:

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: