2
The scores of seven people playing a card game are listed below.
56, 103, 114, 80, 141, 68, 150
What is the interquartile range of the scores?
OA. 35
OB. 73
O C. 102
OD. 94

Answers

Answer 1

Answer:

B. 73

Step-by-step explanation:

An explanation is in the picture if you need it.

2The Scores Of Seven People Playing A Card Game Are Listed Below.56, 103, 114, 80, 141, 68, 150What Is

Related Questions

Find the flux of F across S,
F. N dS
where N is the upward unit normal vector to S.
F(x, y, z) = xi + yj + zk
S: z = 1 − x^2 − y^2, z ≥ 0

Answers

The flux of F across S will be [tex]\frac{3\Pi}{2}[/tex]

A vector of magnitude 1 that is at some point perpendicular to a two-dimensional curve is referred to as the unit normal vector. Normally, you search for a function that returns not just one vector but all potential unit normal vectors of a given curve.

A vector that is perpendicular to a surface at a certain location is known as the normal vector, also referred to as the "normal" to a surface. The inward-pointing normal (pointing toward the interior of the surface) and outward-pointing normal are often distinguished when normals are taken into consideration on closed surfaces.

[tex]$Z_x=-2 x: \quad Z_y=-2 y$[/tex]

[tex]$N=\langle 2 x, 2 y, 1\rangle \quad: f=\langle x, y, z\rangle$[/tex]

[tex]f. $N=2 x^2+2 y^2+z=2 x^2+2 y^2+1-x^2-y^2$[/tex]

=1+x^2+y^2

[tex]x^2+y^2=1\\ \Rightarrow \quad x=r \cos \theta\\ \Rightarrow \quad y=r \sin \theta \\ \Rightarrow x^2+y^2=r^2 \\ 0 < r < 1: \quad 0 < \theta < 2 \pi[/tex]

[tex]$R \cdot v=\int_0^{2 \pi} \int_0^1\left(1+r^2\right)(r) dr d \theta$[/tex]

[tex]$=2 \pi \int_0^1 r+r^3 d r$[/tex]

[tex]$2 \pi\left[\frac{r^2}{2}+\frac{r^4}{4}\right]_0^1$[/tex]

[tex]$=(2 \pi)\left(\frac{1}{2}+\frac{1}{4}\right)$[/tex]

[tex]$=\frac{(2 \pi)(3)}{42}=\frac{3 \pi}{2}$[/tex]

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A water desalination plant can produce 2.8 * 10 to the power of 6 gallons of water in one day. How many gallons can it produce in 5 days?

Answers

Thus , multiplication factor answer is water desalination plant can produce 2.8 x 10⁶ gallons per day. Thus, it can produce 1.4 x 10⁷gallons in 5 days.

What is the difference between factors and multiplies?

A multiple is a number that can be divided by another number a certain number of times without a remainder. A factor is one of two or more numbers that divides a given number without a remainder. Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. To understand better, let us take a multiplication example of the ice creams. Each group has ice creams, and there are two such groups.

Here,

So if there was 5 days, it would produce 5 times the amount above.

So 5 × (2.8 × 10⁶) = 14 × 10⁶

We must rewrite in scientific notation, so:

14 x 10⁶ = 1.4 x 10⁷

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Thus , multiplication factor answer is water desalination plant can produce 2.8 x 10⁶ gallons per day. Thus, it can produce 1.4 x 10⁷gallons in 5 days.

What is the difference between factors and multiplies?

A multiple is a number that can be divided by another number a certain number of times without a remainder. A factor is one of two or more numbers that divides a given number without a remainder. Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. To understand better, let us take a multiplication example of the ice creams. Each group has ice creams, and there are two such groups.

Here,

So if there was 5 days, it would produce 5 times the amount above.

So 5 × (2.8 × 10⁶) = 14 × 10⁶

We must rewrite in scientific notation, so:

14 x 10⁶ = 1.4 x 10⁷

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4/9 down on a number line

Answers

Answer:

Step-by-step explanation:

                                                             !:}

-------------------------------------------------------------------------------------------------------------

0     1/9            2/9                   3/9     4/9        5/9   6/9   7/9   8/9  9/9

y = -5x + 50 and y= 5x + 10
( Pls find the x for the frist question) And the Y for the secound equation
Pls Answer for 100 brainlist

Answers

The values of x and y in the Simultaneous equation are 4 and 30 respectively

What are Simultaneous equations?

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 and 4x − 4y = 4.

y = -5x + 50 equation 1

y = 5x+ 10 equation 2

subtract equation 1 from 2

5x-(-5x) +10-50 = 0

10x -40 = 0

10x = 40

x = 40/10

x = 4

substitute 4 for x in equation 2

y = 5(4)+10

y = 20+10

y = 30

Therefore the value of x and y are 4 and 30 respectively

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Teresa wrote this expression to describe the total distance she was going to swim during two swim classes s+3 which situation could be described by this expression

Answers

The correct answer of expression 's+3' is (c) Teresa wasn't sure how far she would swim during the first class. She would swim 3 laps during the second class. She used the sign "+" instead of "x" or any other notation.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression is (Number/variable, Math Operator, Number/variable)

The answer here should be Option C, as she used the sign "+" instead of "x" or any other notation. She wanted to add something.

And as it is very clear that she wanted to write the information about two classes, so that makes the second term for second class and first term for first class.

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The complete Question is:

Teresa wrote this expression (s+3) to describe the total distance she was going to swim during two swim classes. Which situation could be described by this expression?

A. Teresa wasn't sure how far she would swim during the first class. She would swim 3 fewer laps during the second class.

B. Teresa wasn't sure how far she would swim during the first class. She would swim the same distance for 3 classes.

C. Teresa wasn't sure how far she would swim during the first class. She would swim 3 laps during the second class.

D. Teresa wasn't sure how far she would swim during the first class. She would swim 3 times farther during the second class.

12. Sarah uses long division to convert
a rational number 2 to a decimal.
P
Which of the following statements
cannot be true?
A. The decimal form of P
q
terminates with a zero in the
tenths place.
B. The decimal form of P
eventually repeats.
C. The decimal form of never
terminates or repeats.
D. The decimal form ofis 0.

Answers

Answer is D. If you’re converting fractions to decimals its always going to be a number, it cant just be zero. I hope this helps

Ramona used the regression equation y =. 444x – 21. 29, where x represents height and y represents shoe size, to predict the approximate height of a man who wears a size 8. 5 shoe. 1. Y =. 444 (8. 5) minus 21. 29. 2. Y = 3. 774 minus 21. 29. 3. Y = negative 17. 52. Ramona determined that her answer was incorrect because a man who is –17. 52 inches tall does not make any sense. What was Ramona’s mistake? She substituted the 8. 5 for the wrong variable. She should have added. 444 and 8. 5. The value for y should be positive. The solution of –17. 52 should be the shoe size

Answers

Ramona’s mistake was she just substituted the 8.5 for the wrong variable.

From given conditions:

Ramona used the regression equation y = 444x - 21.29,  

where x represents height and y represents shoe size,

According to Romana her answer is incorrect as a man who is -17.52 inches tall does not predict the approximate height of a man.

The 8.5 refer to shoes size, not height.

So substituting 8.5 for the x-variable is wrong, because x refers to height and y represents shoe size.

Therefore, Ramon just substituted the 8.5 for the wrong variable. She must replace 8.5 for y-variable, because that's the right one for shoe size.

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1.) What is the length of x?
2.) What is the area of the right triangle inside of the parallelogram?

Answers

Answer:

The area of x is 4

The area of the right triangle is 6

Step-by-step explanation:

The Pythagorean Theorem can be used when dealing with right triangles. So, if we use the equation a^2 + b^2 = c^2, we can find that 3^2 + x^2 = 5^2 or 9 + x^2 = 25. If we calculate, we can find that x is equal to 4. Now if we multiply by 3 and divide by 2, we can get the answer of 6 as the area of the right triangle.

Is 9x² 24x 16 a perfect square trinomial?

Answers

9x² + 24x + 16, which is the full quadratic trinomial expressed as (3x +4)².

What is a trinomial expression?

A trinomial expression is an algebraic expression containing three distinct terms, hence the name "trinomial expression". An algebraic expression called a trinomial expression contains three nonzero terms. A trinomial expression is formed when three monomials are added or subtracted from each other. A quadratic trinomial has the form: ax² + bx + c, where a, b, and c are nonzero real values.

Given that

9x² + 24x + 16

= (3x)² + 2(12x) + 16

= (3x)² + 2(3x)(4) + 4²

This is similar to a² + 2ab + b² = (a + b)².

So you can write:

= (3x + 4)²

= (3x +4) (3x + 4)

So this is a complete quadratic trinomial.

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Please I need the 3 of them

Answers

The following operations are used to transform the quadratic equation y = x² into parabolas in standard form:

Case 1

Horizontal translation, vertical translation. Horizontal stretch.

Case 2

Horizontal translation, vertical translation. Reflection in the x-axis, vertical stretch.

Case 3

Horizontal translation, vertical translation. Horizontal stretch.

How to determine the magnitude of horizontal and vertical translations for quadratic equations

In this question we find three cases of parabolas in standard form, that is, quadratic equations of the form:

y - k = a · (x - h)²

Where:

a - Vertex constant(h, k) - Coordinates of the vertex.

This parabola is translated both horizontally and vertically by using the following definitions:

Horizontal translation

x → x - a, where a > 0 for rightward translation.

Vertical translation

y → y - b, where b > 0 for upward translation.

Horizontal dilation

f(x) → f(k · x), where k is a non-negative real number.

Vertical dilation

f(x) → k · f(x), where k is a non-negative real number.

Reflection in the x-axis

f(x) → - f(x)

The procedure is summarize below:

Write the original function, that is, the equation of the parabola with vertex at origin.Apply dilation, translation and reflection definitions.

Finally, we summarize the procedure for each case:

Case 1

g(x) = x²

g(x) = [(1 / 2) · x²]

g(x) + 4 = [(1 / 2) · (x - 2)]²

Horizontal shift: 2 units right, vertical shift: 4 units down. Horizontal stretch.

Case 2

f(x) = x²

f(x) = - (1 / 2) · x²

f(x) - 2 = - (1 / 2) · (x - 4)²

Horizontal shift: 4 units right, vertical shift: 2 units down. Reflection in the x-axis, vertical stretch.

Case 3

h(x) = x²

h(x) = 2 · x²

h(x) - 5 = [2 · (x + 2)]²

Horizontal shift: 2 units left, vertical shift: 5 units up. Horizontal stretch.

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a 10-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 8feet from the base of the building. How high up does the ladder reach?

Answers

The ladder would reach a distance of 6 feet up the wall.

The Pythagorean theorem.

This is a theorem that can be used to determine the unknown side of a right angled triangle. It is given as:

/hyp/^2 = /opp/^2 + /adj/^2

In the given question, the ladder is placed a against a vertical wall of a building. Given that the bottom of the ladder is 8 feet to the base of the building. Therefore this is would form a right angled triangle, such that the Pythagorean theorem can be applied.

So that, let the height of the ladder on the wall be represented by t. Then;

10^2 = t^2 + 8^2

100 = t^2 + 64

t^2 = 100 -64

     = 36

t = (36)^1/2

t = 6 feet

Thus the ladder is placed 6 feet up the vertical wall.

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This is chemistry, but I asked two times when I picked chemistry as the subject, yet no one answered, so I am doing mathematics because this does include math.

Show ALL your WORK and make sure to LABLE all the numbers with the CORRECT UNITS; if you do, I will give you the brainliest:

A: A sample of sulfuric acid has a mass of 15.0 g. How many molecules are in this sample?

B: How many moles of sulfuric acid are present in 45 g of this sample?

C: How much would a .750 mole sample of Ammonium sulfate weigh?

D: What is the mass percent of hydrogen in this sample?

PS: Please do not spam or give the wrong answer; I will report the comment, the "answer', and your account if you do.

Answers

Answers
A = 21 molecules
B = 0.45 moles
C = 99.11475 grams
D = 2.055%

Explanations are below

1. Write the formula for sulfuric acid
H2SO4

2. Find how many g/mol sulfuric acid is
H = 2*1.008 = 2. 016
S = 1 * 32.07 = 32.07
O = 4 * 15.999 = 63.996

Add the products together
2.016 + 32.07 + 63.996 = 98.082 g/mol

2. Convert grams to mol
15.0 grams * 1 mol/98.082 = 0.152933259925369 ~ 0.15 mol

3. Convert mol to molecules
0.15 mol * 6.02*10^23 molecules/ 1 mol = 20.769 molecules ~ 21 molecules

B.
1. Convert grams to moles
45 grams * 1 mol/ 98.082 grams = 0.458799779776106 ~ 0.45 moles

C.
1. Write the formula for ammonium sulfate
(NH₄)₂SO₄

2. Find the weight of the formula above
N = 2 * 14.01 = 28.02
H = 8 * 1.008 = 8.064
S = 1 * 32.07 = 32.07
O = 4 * 15.999 = 63.996

Add the products together
28.02+8.064+32.07+63.99 = 132.153 g/mol

3. Convert mol to grams
0.750 mol * 132.153 g/ 1 mol = 99.11475 grams

D.
1. Find the molar mass of all elements and combined

H = 2*1.008 = 2. 016
S = 1 * 32.07 = 32.07
O = 4 * 15.999 = 63.996

Add the products together
2.016 + 32.07 + 63.996 = 98.082 g/mol

2. To find the mass percent, use the equation molar of element divided by molar mass of the products combined in parentheses times 100.
(2.016/98.082) * 100 —> 0.02055423013397 * 100 = 2.05542301339695 %
This can written as 2.055% since 2.016 has 4 significant figures

Which expression represents the length of the hypotenuse C of the triangle below

Answers

Answer:

[tex] \sqrt{a {}^{2} + b {}^{2} }[/tex]

Find the lengths of the diagonals of rectangle WXYZ.
WY = 14x + 10
XZ = 11x + 22
The length of each diagonal is
units.

Answers

The length of each diagonal is √(196x^2 + 816x + 324) units.

What is the formula for diagonal length?

The diagonal of a rectangle can be estimated using the hypotenuse formula, such as using the Pythagorean theorem calculator.

WX^2 = WY^2 + XZ^2

Given that WY = 14x + 10 and XZ = 11x + 22, we can substitute those values in the equation:

WX^2 = (14x + 10)^2 + (11x + 22)^2

WX^2 = 196x^2 + 816x + 324

WX = √(196x^2 + 816x + 324)

The same goes for the other diagonal, WZ.

WZ = √(196x^2 + 816x + 324)

So, the length of each diagonal is √(196x^2 + 816x + 324) units.

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how many times bigger is b than c

Answers

B is 10 times bigger than C

Find the measure of angle A.
110°
O 80°
O 105°
O 30°
O100°
14 + 6x
A
3x-3

Answers

Answer:

[tex]80^{\circ}[/tex]

Step-by-step explanation:

The interior angles of the triangle are [tex]70^{\circ}, (14+6x)^{\circ}[/tex], and [tex](3x-3)^{\circ}[/tex].

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]70+14+6x+3x-3=180 \\ \\ 81+9x=180 \\ \\ 9x=99 \\ \\ x=11[/tex]

So, [tex]m\angle A=14+6(11)=80^{\circ}[/tex].

latifa writes down a number. she says
if i find a cube root of that number and then quadruple the answer, i get 16
what number did latifa write down?

Answers

Answer:

8

Step-by-step explanation:

the cubed root of 8 equals 2

if you quadruple 2 (multiply it by 4), you will get 8

when processing an invoice what account is credited
a. accounts receivable
b. cash
c. accounts payable
d. the answer depends on the transaction

Answers

Answer:

accounts payable

Step-by-step explanation:

Because amount of money you owe

Can you help me with this

Answers

Answer: (-4, -6)(9, 2):

y=8/13x - 46/13 (Point slope form: y + 6 = 8/13 *(x+4)

(-4,-6) (9,2) is the correct answer

pls help with question image is linked

Answers

The kilogram of fruits sold each day are 135 kg, 110 kg and 70 kg

How to determine the amount sold each day

From the question, we have the following parameters that can be used in our computation:

Day 2 = Day 1 - 25

Day 3 = 2/7 * (Day 1 + Day 2)

Total weights = 315

Next, we use the following representations

x = Day 1, y = Day 2 and z = Day 3

So, we have the following equations

y = x - 25

z = 2/7(x + y)

x + y + z = 315

Substitute y = x - 25 in z = 2/7(x + y) and x + y + z = 315

z = 2/7(x + x - 25) = 2/7(2x - 25)

x + y + z = 315 ⇒ x + x - 25 + z = 315

So, we have

z = 2/7(2x - 25)

2x + z = 340

Substitute z = 2/7(2x - 25) in 2x + z = 340

2x + 2/7(2x - 25) = 340

So, we have

7x + 2x - 25 = 1190

Evaluate the like terms

9x = 1215

Divide by 9

x = 135

So, we have

y = x - 25 = 135 - 25 = 110

z = 2/7(x + y) = 2/7 *(135 + 110) = 70

Hence, the amounts are 135 kg, 110 kg and 70 kg

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What is the product of 3p and 4p² 5p 7?

Answers

The product of 3p, 4p² and 5p 7 is 120p⁹.

What is product?

Product is an item or thing that is created or produced by a business. It can refer to both physical and intangible items, such as machines, food, software, intellectual property, or services. The concept of a product is used in many different industries, including manufacturing, retail, technology, and finance. Products are typically sold in exchange for money, but can also be given away or traded. Products are an essential part of any business, as they are what generate income for a company.

This can be calculated by multiplying 3p (3 x p) with 4p² (4 x p²) and 5p 7 (5 x p x 7). The result of this multiplication is 120p⁹ (3 x 4 x 5 x p x p² x 7).

To understand this calculation better, we can break it down into its component parts.

The 3p component is 3 x p, which gives us 3p. The 4p² component is 4 x p², which gives us 4p². The 5p 7 component is 5 x p x 7, which gives us 5p 7. When these three components are multiplied together we get 3 x 4 x 5 x p x p² x 7,which is equivalent to 120p⁹.
In conclusion, the product of 3p, 4p² and 5p 7 is 120p⁹.

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Which polynomial is prime?
O x3 + 3x2 - 2x - 6
O x° - 2x- + 3x - 6
O 4x4 + 4x3 - 2x - 2
O 2x + x3-x+2

Answers

I think its C because i think its C

Select all the as that inequalities that have the same solution as -4x<20

A. -x<5
B. 4x>-20
C. 4x<20
D. X<-5
E. X>5
F. X>-5

Answers

Answer:

A, B, F

Step-by-step explanation:

Divide both sides of -4x<20 by 4, and we have A

Multiply both sides of -4x<20 by -1, since -1 is a negative number, we reverse the inequality, and we have B

Multiply both sides of -x<5 (A) by -1, since -1 is a negative number, we reverse the inequality, and we have F

A painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%. By what percent is the new frame bigger than the original frame if the width of the frame remains the same?
PLEASE HELP

Answers

The percent that the new frame is bigger than the original frame if the width of the frame remains the same is 9.1%.

How to illustrate the percentage?

From the information, the painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%.

Let the length be Illustrated as 10cm.

Width = 10% × 10cm

= 1cm

New Length = 10cm + (10% × 10cm)

= 11cm

The old perimeter will be:

= 2(1 + 10)

= 22cm

New perimeter will be:

= 2(1 + 11)

= 24cm

The percentage increase will be:

= (24 - 22) / 22 × 100

= 2/22 × 100

= 9.1%

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A)
Find the product of
f(x)=x²-x-4 and g(x)=x+4
With process

Answers

f(x)=[tex]x^{2}[/tex]-x-4 + g(x)=x+4 = the product is with process [tex]x^2+7 x+8$$[/tex] . It is the solution of f(x) and g (x) .

What do you meant by product ?

[tex]$$f(x)=x^2-x-4, g(x)=x+4: x^2+7 x+8$$$$\begin{aligned}& \text { Find } f \circ g \text { given } f(x)=x^2-x-4, g(x)=x+4 \\& f \circ g=f(g(x)) \\& g(x)=x+4 \\& =f(x+4)\end{aligned}$$$$\begin{aligned}& f(x+4): \quad x^2+7 x+8 \\& =x^2+7 x+8\end{aligned}$$[/tex]

When a number is multiplied by another number, its products can be found. Because 9 x 3 Equals 27, for instance, 27 is a product of 9 and 3. What you get when you multiply two numbers together is their product. As a result, the product of three and four is twelve, followed by five and four, and so on.

A number that is obtained by multiplying two or more other numbers together is referred to in mathematics as a product. For instance, the result of multiplying 2 by 5 is 10 when the two numbers are combined. Byproducts include things like straw from grain harvesting operations, salt from desalination plants, sawdust from sawmills, and manure from feedlot operations.

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The ratio of the measures of three sides of a triangle is 1/4:1/3:1/6. its perimeter is 31.5 inches

Answers

Answer:

10.5 inches, 14 inches, 7 inches

Step-by-step explanation:

Let's say x is the multiplier of the ratio value and the actual length of the sides:

1/4 * x = side 1

1/3 * x = side 2

1/6 * x = side 3

Since the perimeter is the sum of all sides, the perimeter is equal to:

31.5 = 1/4 * x + 1/3 * x + 1/6 * x  ==> 31.5 inches is the perimeter

(31.5 = x/4 + x/3 + x/6)*12  ==> multiply the equation by 12 since 12 is the

                                           LCM (Least Common Multiple) of 4, 3, and 6

12 * 31.5 = 12 * x/4 + 12 * x/3 + 12 * x/6  ==> multiply each term by 12

378 = 12x/4 + 12x/3 + 12x/6 ==> simplify

378 = 3x + 4x + 2x

378 = 9x

x = 378/9 ==> divide both sides by 9

x = 42

Now find each side length [Refer to the first three equations] :

Side length 1: 1/4 * 42 = 42/4 = 10.5 inches

Side length 2: 1/3 * 42 = 42/3 = 14 inches

Side length 3: 1/6 * 42 = 42/6 = 7 inches

Answer: 10.5 inches, 14 inches, 7 inches

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What is the value of S unit?

Answers

Triangle ABD is a right-angled triangle. The value of s which is the hypotenuse of the triangle ABD is 17 units.

What is triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.

Here,

Given information:

From the given figure, the following information can be extracted:

Triangle ABD is a right-angled triangle.

Base AB is 8 units, Height BD is 15 units.

s is the hypotenuse of the triangle ABD.

Use the Pythagoras theorem to solve for the value of s or AD,

AD²=AB²+BD²

s²=8²+15²

s²=289

s=17 units

Therefore, the value of s which is the hypotenuse of the triangle ABD is 17 units.

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16 quarts of soil are used to completely fill 5 flower pots. If each pot holds the same amount of soil, how many quarts will each pot hold?

How many quarts of soil are used to fill 3 flower pots?

Answers

9.6 quarts

First, find the unit rate, which is that when you divide 16 and 5 and you will get 3.2, then you multiply it with 3 for the 3 flower pots, and that's how you end up with the answer

The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.512.512, point, 5 years; the standard deviation is 2.42.42, point, 4 years.
Use the empirical rule (68 - 95 - 99.7\%)(68−95−99.7%)left parenthesis, 68, minus, 95, minus, 99, point, 7, percent, right parenthesis to estimate the probability of a lion living longer than 10.110.110, point, 1 years.

Answers

The probability of a lion living longer than 10.1 will be 0.1585.

What is a normal distribution?

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard deviation is 2.4 years.

The lifespan of a lion in a particular zoo is normally distributed with average lion lives:

Mean u = 12.5 years

Standard deviation s = 2.4 years

We are to use the empirical rule ( 68-95-99.7% ) to estimate the probability of a lion living between 5.3 and 10.1.

The empirical rule ( 68-95-99.7% ) states:

P ( u - s < X < u + s ) = 68%

P ( u - 2s < X < u + 2s ) = 95%

P ( u - 3s < X < u + 3s ) = 99.7%

The test has the following number of standard deviations (s):

u - s < X < u + s  = 12.5 - 2.4 < X < 12.5 + 2.4  = 10.1 < X < 14.9

u - 2s < X < u + 2s = 12.5 - 4.8 < X < 12.5 + 4.8  = 7.7 < X < 17.3

u - 3s < X < u + 3s = 12.5 - 7.2 < X < 12.5 + 7.2  = 5.3 < X < 19.7

Then the probability is calculated as,

P ( 10.1 < X < 14.9 ) = 0.68

P ( 7.7 < X < 17.3 ) = 0.95

P ( 5.3 < X < 19.7 ) = 0.997

We need P ( X < 10.1 ) and P ( X < 5.3 ):

P ( X < 10.1 ) = [ 1 - P ( 10.1 < X < 14.9 ) ] / 2

P ( X < 10.1 ) = [ 1 - 0.68 ] / 2

P ( X < 10.1 ) = 0.16

P ( X < 5.3 ) = [ 1 - P ( 5.3 < X < 19.7 ) ] / 2

P ( X < 5.3 ) = [ 1 - 0.997 ] / 2

P ( X < 5.3 ) = 0.0015

P ( 5.3 < X < 10.1 ) = P ( X < 10.1 ) - P ( X < 5.3 )

P ( 5.3 < X < 10.1 ) = 0.16 - 0.0015

P ( 5.3 < X < 10.1 ) = 0.1585

More about the normal distribution link is given below.

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What type of triangle do the points 3 2 (- 2 3 and 2/3 form a right triangle B equilateral triangle C isosceles triangle d none of these?

Answers

Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).

Let the given points be,

A = (3, 2), B = (-2, -3) and C = (2, 3)

The formula for the distance between two points:

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by [tex]D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$[/tex].

Therefore,

A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), B = [tex](x_{2} , y_{2} )[/tex] = (-2, -3)

[tex]& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}[/tex]  units

B = [tex](x_{1} , y_{1} )[/tex] = (-2, -3), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)

[tex]& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}[/tex]  units

A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)

[tex]& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}[/tex]  units

By using the Pythagorean theorem:

According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

Now, we can see that,

[tex]& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\[/tex]

[tex]& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2[/tex]

Therefore, the given triangle is a right angled triangle.

Therefore, option(A) s correct.

For more questions on Pythagoras's Theorem

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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.

A. right triangle

B. equilateral triangle

C. isosceles triangle

D. none of these

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