The algebraic description of the transformation of B(x, y) = B'(y + 0, 0 - x)
The algebraic description of the transformation of K(x, y) = K'(y + 0, 0 - x)
The endpoints of the new line segment are B'(4, -1) and K'(-3, -4).
As per the given data BK has endpoints B(1, 4) and K(4, -3).
Rotate BK clockwise 270 degrees about the origin.
Every point of a source image is transformed in a plane via a rotation that rotates it around a fixed point at a specific angle and direction. The fixed point is referred to as the rotational center.
The term "angle of rotation" refers to the rotation's amount and is expressed in degrees.
Rotating a figure 270 degrees clockwise is the same as rotating a figure 90 degrees anticlockwise.
Now, it would be (x, y) = (-y, x)
We have;
R (x, y) to R' (y, -x)
The algebraic description is simply written as;
R (x, y) = R'(y + 0, 0 - x)
B (x, y) = B'(y + 0, 0 - x)
K (x, y) = K'(y + 0, 0 - x)
To get the new endpoints, we simply write the transformation as shown;
B(1, 4) becomes B'(4, -1)
K(4, -3) becomes K'(-3, -4)
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2789\36 help me psss i have to take this test lie be so fl i like right nowww pls haelp me
Answer:
77.472222 etc
Step-by-step explanation:
5^3 x 7^5+9^8+0+0+0+0+0+0+(9^7x5^6)
Answer:
74,779,038,221
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given
[tex]5^3*7^5+9^8+0+0+0+0+0+0+9^7*5^6[/tex]
We can eliminate all the zeroes.
[tex]5^3*7^5+9^8+9^7*5^6[/tex]
Evaluate each term.
Raise 5 to the power of 3.
[tex]125*7^5+9^8+9^7*5^6[/tex]
Raise 7 to the power of 5.
[tex]125*16807+9^8+9^7*5^6[/tex]
Raise 9 to the power of 8.
[tex]125*16807+43046721+9^7*5^6[/tex]
Raise 9 to the power of 7.
[tex]125*16807+43046721+4782969*5^6[/tex]
Raise 5 to the power of 6.
[tex]125*16807+43046721+4782969*15625[/tex]
Multiply 125 by 16807.
[tex]2100875+43046721+4782969*15625[/tex]
Multiply 4782969 by 15625.
[tex]2100875+43046721+74733890625[/tex]
Add 2100875 and 43046721.
[tex]45147596+74733890625[/tex]
Add 45147596 and 74733890625.
[tex]74779038221[/tex]
A calculator would help but here you go.
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.
Write an expression to represent the area of the shaded region in simplest from
We know that the area of a square/rectangle is the multiplication of its length by its width. We also know that this specific area does not include the blank region, therefore we need to subtract it from the area of the shaded region!
We can come up with two expressions:
Shaded Area:
[tex](5x + 2)(3x - 1)\\= 15x^2-5x+6x-2\\=15x^2+x-2[/tex]
Blank area:
[tex](x)(x+7)\\x^2+7x[/tex]
Now all we have to do is subtract the blank area's expression from the shaded area's and simplify since the question asks for the simplest form.
[tex](15x^2+x-2)-(x^2+7x)\\15x^2-x^2+x-7x-2\\14x^2-6x-2[/tex]
Therefore, your final answer should be:
14x^2 - 6x - 2
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
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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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?
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
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
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 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?
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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Can you help me with this
Answer: (-4, -6)(9, 2):
y=8/13x - 46/13 (Point slope form: y + 6 = 8/13 *(x+4)
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
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.
when processing an invoice what account is credited
a. accounts receivable
b. cash
c. accounts payable
d. the answer depends on the transaction
Answer:
accounts payable
Step-by-step explanation:
Because amount of money you owe
What is the product of 3p and 4p² 5p 7?
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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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
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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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?
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
The ratio of the measures of three sides of a triangle is 1/4:1/3:1/6. its perimeter is 31.5 inches
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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Find the lengths of the diagonals of rectangle WXYZ.
WY = 14x + 10
XZ = 11x + 22
The length of each diagonal is
units.
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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4/9 down on a number line
Answer:
Step-by-step explanation:
!:}
-------------------------------------------------------------------------------------------------------------
0 1/9 2/9 3/9 4/9 5/9 6/9 7/9 8/9 9/9
Please I need the 3 of them
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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Find the measure of angle A.
110°
O 80°
O 105°
O 30°
O100°
14 + 6x
A
3x-3
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].
how many times bigger is b than c
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?
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.
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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
Which polynomial is prime?
O x3 + 3x2 - 2x - 6
O x° - 2x- + 3x - 6
O 4x4 + 4x3 - 2x - 2
O 2x + x3-x+2
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.
Is 9x² 24x 16 a perfect square trinomial?
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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Which expression represents the length of the hypotenuse C of the triangle below
Answer:
[tex] \sqrt{a {}^{2} + b {}^{2} }[/tex]
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?
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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pls help with question image is linked
The kilogram of fruits sold each day are 135 kg, 110 kg and 70 kg
How to determine the amount sold each dayFrom 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 value of S unit?
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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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.
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.
https://brainly.com/question/12421652
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1.) What is the length of x?
2.) What is the area of the right triangle inside of the parallelogram?
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.