What is Constant of Proportionality?
The ratio between two proportional quantities' constant values is known as the constant of proportionality.
The formula for calculating slope is expressed as:
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
Given: the coordinate points (5,225) and (3, 135). The constant of proportionality is expressed as:
m = [tex]\frac{135-225}{3-5}[/tex]
m = [tex]\frac{-90}{-2}[/tex]
m = 45
Hence, Constant of Proportionality is 45.
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his composite figure is made of two identical pyramids attached at their bases. Each pyramid has a height of 2 units. 2 identical pyramids with rectangular bases are connected at their base. The height of the pyramid is 2. The lengths of the sides of the rectangle are 5 and 0.25 units. Which expression represents the volume, in cubic units, of the composite figure? One-half (One-third (5) (0.25) (2) ) One-half (One-third (5) (0.25) (4) ) 2(One-third (5) (0.25) (2) ) 2(One-third (5) (0.25) (4) )
The expression that will represent the volume of the identical rectangular base pyramid is: 2[One-third (5) (0.25) (2)] cubic units.
How to evaluate the expression for the volume of the identical pyramidTo calculate for the volume of a rectangular base pyramid, we use the formula:
volume = 1/3 × area of base rectangle × height
volume of one identical pyramid = (1/3 × 5 × 0.5 × 2)cubic units
volume of the two identical pyramid = 2(1/3 × 5 × 0.5 × 2)cubic units.
Therefore, the expression that will represent the volume of the identical rectangular base pyramid is: 2[One-third (5) (0.25) (2)] cubic units.
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What is the probability that either event will occur?
Now, find the probability of event A and event B.
A
B
6
6
20
20
P(A and B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter
Answer:
0.12
Step-by-step explanation:
Given the frequencies of occurrence in the diagram, you want to know the probability of A and B.
ProbabilityThe probability of an event is the ratio of the number of times it occurs to the total number of trials.
The diagram shows the event (A and B) occurs 6 times out of a total of 6+6+20+20 = 52 trials.
P(A and B) = 6/52
P(A and B) ≈ 0.12
<95141404393>
Use ≈ 3.14 and round your answer
to the nearest hundredth.
10 ft
6 ft
square feet
The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.
We know that,
In geometry, a cylinder is one of the basic 3d shapes with two parallel circular bases at a distance. A curving surface connects the two circular bases at a predetermined distance from the centre. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases. One real-world example of a cylinder is an LPG gas-cylinder.
The surface area of this cylinder is defined as the product of the radius of the base and the height of the cylinder.
The surface area of this cylinder = (2π x r)h
We have given a radius of the base is 8 cm and the height of the cylinder is 10 cm.
The surface area of this cylinder = (2π x r)h
= (2π x 8)10
= (50.24)10
= 502.4
Thus, The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.
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The complete question is attached below:
(X-7)(x-7) multiply the binomials
The product of given two binomials which are (x-7)(x-7) is equal to x² - 14x + 49.
To multiply the binomials (x-7)(x-7), we use the distributive property of multiplication, which states that:
(a + b)(c + d) = ac + ad + bc + bd
Using this property, we can expand the expression as follows:
(x-7)(x-7) = x(x-7) - 7(x-7)
= x² - 7x - 7x + 49
= x² - 14x + 49
The distributive property of multiplication is a mathematical rule that states that when a number is multiplied by the sum of two or more numbers, it is equivalent to multiplying the number by each of the addends and then adding the products.
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A ferris wheel has a radius of 10 inches and is 2 inches off the ground. It makes a complete revolution every 10 seconds.
If a rider is directly horizontal to the center of the wheel and moving downward, find an equation that gives his height above the ground as a function of time .
Answer:
y = -10·sin(πt/5) +12
Step-by-step explanation:
You want the equation of the height of a rider of a Ferris wheel that has a radius of 10 and is 2 off the ground, with a period of 10 seconds, moving downward, starting from even with the center.
EquationThe general form of the equation will be ...
y = A·sin(2πt/T) + B
where A is a scale factor that is based on the radius and initial direction, and B is the height of the center of the wheel above the ground.
HeightWe assume that 2 [units] off the ground means the low point of the travel is at that height. Then the middle of the wheel is those 2 [units] plus the radius of the wheel:
B = 2 + 10 = 12
Scale factorThe scale factor A will be the radius of the wheel, made negative because the initial direction is downward from the initial height. That is, ...
A = 10
PeriodThe period (T) is given as 10 seconds.
Height functionPutting these parameters together gives ...
y = -10·sin(2πt/10) +12
y = -10·sin(πt/5) +12
__
Additional comment
We wonder if this wheel is really only 20 inches (20 in) in diameter, as that dimension seems suitable only for a model. We suspect it is probably 20 meters (20 m) in diameter.
Sometimes "m" is confused with "in" when it is written in Roman font and reproduced with poor resolution.
<95141404393>
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
KL = 7, so B is the correct answer.
What is the height, in meters, of a cylinder with surface area 104π m2 and radius 4 m?
PLEASE SOMONE HELP
The height h of the cylinder is 9 meters.
What is the height of the cylinder?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The surface area of a cylinder is expressed as;
Surface Area = 2πrh + 2πr²
Given that; the surface area is 104π m² and the radius as 4 m.
We need to solve for the height (h).
Plug the values into the above formula:
Surface Area = 2πrh + 2πr²
104π = 2πrh + 2πr²
104π = 2π( rh + r² )
Divide through by 2π
52 = rh + r²
52 = ( 4 × h) + ( 4² )
52 = 4h + 16
Subtract 16 from both sides
52 - 16 = 4h + 16 - 16
52 - 16 = 4h
36 = 4h
4h = 36
h = 36/4
h = 9 meters
Therefore, the height is 9 meters.
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find the center and radius by completing the square x2+6x+y2-4y=3
Answer:
Center: (-3, 2)
Radius: 4
Step-by-step explanation:
x2 + 6x + y2 - 4y = 3
x² + 6x + 9 + y² - 4y + 4 = 3 + 9 + 4
(x + 3)² + (y - 2)² = 16
(x + 3)² + (y - 2)² = 4²
Center: (-3, 2)
Radius: 4
-5-15x-10=-4x-8x
How do I do the is step by step?
Answer:
x = -5
Step-by-step explanation:
-5 - 15x - 10 = -4x - 8x
-5 - 10 = -4x - 8x + 15x
-15 = -12x + 15x
-15 = 3x
x = -5
#CMIIWelle can buy 2 quarts of milk for 3$ or 1 gallon of milk for 3$ which is the better deal
Answer:
Elle should buy 1 gallon of milk for $3.
Step-by-step explanation:
In one gallon of milk, there are four quarts. So we can multiply the number of gallons by four to convert it to quarts.
(1 gallon)x(4 quarts) = 4 quarts in one gallon
4 quarts is greater than 2 quarts so 1 gallon for $3 is a better deal than 2 quarts for $3.
hey i have a question about this assignment and want to check if my answers are right
The lengths of the sides and angles of the triangles, obtained using Pythagorean Theorem and trigonometric ratios are;
D. 19.2
C. 5.3
F. 2·√5
G. √3
H. 8·√3
K. 18.9
O. 15.5
N. 14.5
M. 41.4°
I. 74.1°
What is the Pythagorean Theorem?The Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the legs of the triangle.
D. x = √(15² + 12²) ≈ 19.2
C. x = √(10² - 8.5²) ≈ 5.3
F. x = 2·√(5) (Special triangles)
G. tan (60°) = 30/x = √3
x = 30/√3 = 10·√3
H. x/16 = (√3)/2
x = 16 × (√3)/2 = 8·√3
x = 8·√3
K. tan(34°) = x/28
x = 28 × tan(34°) ≈ 18.9
O. cos(55°) = x/27
x = 27 × cos(55) ≈ 15.5
N. sin(16°) = 4/x
x = 4/(sin(16°) ≈ 14.5
M. x = arccos(9/12) ≈ 41.4°
I. x = arcsin(25/26) ≈ 74.1°
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The rear window of Alex's van is shaped like a trapezoid with an upper base
measuring 36 inches, a lower base measuring 48 inches, and a height of 21 inches.
An 18-inch rear window wiper clears a 150° sector of a circle on the rear window, as
shown in the diagram below.
36 in.
21 in.
150 degrees
18 in.
48 in.
a. What is the area, in square inches, of the entire trapezoidal rear window? Show or explain how you got your answer.
b. What fractional part of a complete circle is cleared on the rear window by the 18-inch wiper? Show or explain how you got your answer.
c. What is the area, in square inches, of the part of the rear window that is cleared by the wiper? Show or explain how you got your answer.
d. What percent of the area of the entire rear window is cleared by the wiper? Show or explain how you got your answer.
a) The area of the entire trapezoidal rear window = 882 sq.in.
b) The fractional part of a complete circle is cleared on the rear window by the 18-inch wiper = 5/12
c) The area of the part of the rear window that is cleared by the wiper = 424.12 sq. in.
d) The percent of the area of the entire rear window is cleared by the wiper = 48.09%
We know that the formula for the area of trapezoid,
A = ((a + b) / 2) × h
Here, a = 36 in., b = 48 in. and height of the trapezoid h=21 in
Using above formula, the area of the entire trapezoidal rear window would be,
A = ((36 + 48) / 2) × 21
A = 882 sq.in.
Here, the 18-inch rear window wiper clears a 150° sector of a circle on the rear window.
We know that the measure of entire circle = 360°
So, the fractional part of a complete circle is cleared on the rear window by the 18-inch wiper would be,
150° / 360° = 5/12
Now we need to find the area of the part of the rear window that is cleared by the wiper.
We know that the formula for the area of sector of a circle is:
A = (θ/360) × πr²
Here, the central angle θ = 150° and radius r = 18 in.
A = (θ/360) × πr²
A = (150/360) × π × 18²
A = 424.12 sq. in.
Now we need to find the percent of the area of the entire rear window is cleared by the wiper.
P = [(area of the part of the rear window cleared by the wiper) / (area of the entire trapezoidal rear window)] × 100
P = (424.12 / 882) × 100
P = 48.09%
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I attached the question
Following a translation of (x, y) (x - 1, y + 2) and a dilation by a scale factor of 2 centred at the origin, the coordinates of T are T''(8, 8).
Following translation and dilation, we must take the following actions to determine the new coordinates of point T:
1) Translation: (x, y) = (x - 1, y + 2).
T' = (5 - 1, 2 + 2)
= (4, 4) applies the translation to the original coordinates of T.
2) Dilation: Scale factor of 2 centered at the origin
Multiply the translated coordinates by the scale factor of 2:
T'' = (2 × 4, 2 × 4)
= (8, 8)
Therefore, the coordinates of T after the translation (x, y) → (x - 1, y + 2) followed by a dilation by a scale factor of 2 centered at the origin are T''(8, 8).
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What is the measure in radians for the central angle of a circle whose radius is 8 cm and intercepted arc length is 5.6 cm? Enter your answer as a decimal in the box. radians
The measure in radians for the central angle is approximately 0.7 radians.
To find the measure in radians for the central angle of a circle, we can use the formula:
θ = s / r
where θ is the central angle in radians, s is the intercepted arc length, and r is the radius of the circle.
In this case, the radius is given as 8 cm and the intercepted arc length is 5.6 cm.
Plugging these values into the formula, we have:
θ = 5.6 cm / 8 cm
Simplifying the expression:
θ = 0.7
We may use the following formula to get the centre angle of a circle's measurement in radians:
= s / r
s is the length of the intercepted arc, r is the circle's radius and is the centre angle in radians.
The intercepted arc length in this instance is 5.6 cm, while the radius is specified as 8 cm.
When these values are plugged into the formula, we get:
θ = 5.6 cm / 8 cm
Condensing the phrase:
θ = 0.7
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2x+6 what would be its value if X=-3 *
Answer:0
Step-by-step explanation:
so if x = -3 that means u take -3 * 2 and u get -6 because a negative * A positive is negative so -6 + 6 is 0
Answer:
0
Step-by-step explanation:
Just substitute x=-3
2x+6 =
2(-3) + 6 =
-6 + 6 = 0
Given m ∥ n, find the value of x.
The value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3
What are angles formed by a pair of parallel lines cut by a transversal line?When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.
(2x - 13) + 123 = 180° {supplementary angles}
2x - 13 + 123 = 180°
2x + 110 = 180
2x = 180 - 110 {collect like terms}
2x = 70
x = 70/2 {divide through by 2}
x = 35
Therefore, the value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3
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PLS HELP! What is the domain and Rage of the given below?
And is it a Function or not?
X /-2/-2 /-1 /-1 /0
Y/ 5/-5/ 3/-3/-1
In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section we will practice determining domains and ranges for specific functions. Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above. We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0.
Diagram of how a function relates two relations.
We can visualize the domain as a “holding area” that contains “raw materials” for a “function machine” and the range as another “holding area” for the machine’s products.
We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded. For example, if a person has $100 to spend, he or she would need to express the interval that is more than 0 and less than or equal to 100 and write
(
0
,
100
]
. We will discuss interval notation in greater detail later.
Let’s turn our attention to finding the domain of a function whose equation is provided. Oftentimes, finding the domain of such functions involves remembering three different forms. First, if the function has no denominator or an even root, consider whether the domain could be all real numbers. Second, if there is a denominator in the function’s equation, exclude values in the domain that force the denominator to be zero. Third, if there is an even root, consider excluding values that would make the radicand negative.
Before we begin, let us review the conventions of interval notation:
The smallest term from the interval is written first.
The largest term in the interval is written second, following a comma.
Parentheses, ( or ), are used to signify that an endpoint is not included, called exclusive.
Brackets, [ or ], are used to indicate that an endpoint is included, called inclusive.
Ben records the time it took each person to complete a different event.
He is completing a table with information.
Note that in this case, the missing information which is the shortest time is 27 minutes. this is computed using the knowledge of the range.
What is range?The range of a collection of data in statistics is the difference between the highest and smallest values, calculated by subtracting the sample maximum and minimum. It's measured in the same units as the data.
Thus,
Range = Longest time - Shortest time
Since
Mean: 39 minutes
Range: 26 minutes
Longest time: 53 minutes
Shortest time = Longest time - Range
⇒ Shortest time = 53 - 26
= 27 minutes.
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Convert from radians to degrees.
1/4π
1/4π radians is approximately equal to 45 degrees.
To convert a value from radians to degrees, multiply the value by 180/π. For example, to convert π/4 radians to degrees, multiply π/4 by 180/π to get 45 degrees. This conversion is useful for converting angles between the two units of measurement.
Degrees = Radians × 180/π.
Therefore, to convert 1/4π radians to degrees, we have:
Degrees = (1/4π) × (180/π) ≈ 45°
Hence, 1/4π radians is approximately equal to 45 degrees.
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Please solve this question
The expression that represents a purely imaginary number is:
[tex]3i^5 + i (2 - 4i^3) - 2 (-3 + i)[/tex]
Option D is the correct answer.
We have,
A pure imaginary number is a number that does not have a real part and can be written in the form of bi, where b is a real number and i is the imaginary unit (√(-1)).
We have,
[tex]3i^5 + i (2 - 4i^3) - 2 (-3 + i)[/tex]
In this expression, we can simplify and rewrite it as:
[tex]3i^5 + i(2 - 4i^3) + 6 - 2i[/tex]
Now, let's evaluate the powers of i:
[tex]i^5 = i^{4 + 1} = i^4 \times i = 1 \times i = i\\i^3 = i^{2 + 1} = i^2 \times i = (-1) \times i = -i[/tex]
Substituting these values back into the expression:
[tex]3i^5 + i(2 - 4i^3) + 6 - 2i = 3i + i(2 - 4(-i)) + 6 - 2i[/tex]
= 3i + i(2 + 4i) + 6 - 2i
= 3i + 2i + 4i² + 6 - 2i
= 3i + 2i + 4(-1) + 6 - 2i
= 5i - 4 + 6 - 2i
= 5i - 2i - 4 + 6
= 3i + 2
The expression 3i + 2 represents a pure imaginary number, as it has no real part (the constant term is 2 and does not involve the imaginary unit i).
Thus,
The expression that represents a purely imaginary number is:
[tex]3i^5 + i (2 - 4i^3) - 2 (-3 + i)[/tex]
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A company packs its fruit salad in
containers that hold 1 5/8 pounds
How many containers does it
need to hold 585 pounds of fruit
salad?
Answer: 360 containers
Step-by-step explanation: 1 5/8 in decimal form is 1.625 pounds. Divide 585 by 1.625 pounds you get 360. It takes 360 containers to hold 585 pounds of fruit
Help with number 8 please
The simplification of the expression, ∛8x⁴y⁸ / 125 is [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex].
How to solve an exponential expression?The exponential expression can be solved as follows:
Therefore, let's simplify the expression.
To simplify the expression we have to deal with the exponential by applying it laws and also the cube root.
∛8x⁴y⁸ / 125
let's solve them individually,
125 = 5³ = 5 × 5 × 5
8 = 2³ = 2 × 2 × 2
Therefore,
∛8x⁴y⁸ / 125 = [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex]
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What is the product of 12 and 4 decreased by 15
The results of the product of 12 and 4 decreased by 15 is 33
How to solve product of numbers?Product refers to another term which means multiplication of numbers.
product of 12 and 4
= (12 × 4)
decreased by 15 means 15 is subtracted from the expression
= (12 × 4) - 15
Following the rules of PEMDAS
P = parenthesis
E = exponents
M = multiplication
D = Division
A = addition
S =subtraction
So,
(12 × 4) - 15
= 48 - 15
= 33
Hence, 33 is the product of 12 and 4 decreased by 15
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The value of the product of 12 and 4 decreased by 15 is 33
How to determine the product of 12 and 4 decreased by 15From the question, we have the following parameters that can be used in our computation:
The product of 12 and 4 decreased by 15
The product of 12 and 4 is expressed as
12 * 4
Evaluate
12 * 4 = 48
When decreased by 15, we subtract 15 from both sides of the equation
using the above as a guide, we have the following:
12 * 4 - 15 = 48 - 15
Evaluate
12 * 4 - 15 = 33
Hence, the product of 12 and 4 decreased by 15 is 33
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please helppppppppppppppppppppppp
Answer:
last option
Step-by-step explanation:
let g = 3,
9/5 + 7/2(3)
9/5 + 21/2
adjust to a common denominator of ten to get;
18/10 + 105/10
= 123/10 = 12 3/10
so the last option !
.....................................................................................
Answer:
(-6,0)
Step-by-step explanation:
An equation of a line can be modeled as y = mx + b where m is slope and b is y-intercept.
For the line r, we can model the equation as y = mx + 3 since the line intersects y-axis at (0,3) as seen in the attachment.
For the line t, we can model the equation as y = mx - 6 as the problem gives y-intercept for line t equal to -6. Hence, the line t intersects y-axis at (0,6)
Next, we have to find the slope of line t by finding the slope of line r in the attachment. Apply the rise over run by counting the steps, you can see in the attachment that I put to learn how to count rise and run of a line. Also note that the value in attachment here is a scalar quantity, meaning only magnitude, no direction.
So we will have the slope of -1 since a line graph is heading down so the output decreases as input increases. Therefore, we know that m = -1 for both lines. Therefore, for the line t, we can model the new equation to:
[tex]\displaystyle{y=-x-6}[/tex]
Then we find the x-intercept of the line by letting y = 0. Thus,
[tex]\displaystyle{0=-x-6}\\\\\displaystyle{x=-6}[/tex]
Therefore, the x-intercept of line t is at (-6,0).
Answer:
(-6,0)
Step-by-step explanation:
We need to determine the equation of line r first to find the x-intercept of line t.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
[tex]slope = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
For line r passing through (3, 0) and (0, 3), the slope is:
[tex]slope = \frac{3 - 0}{0 - 3} = -1[/tex]
Since line t has the same slope as line r, its slope is also -1.
The equation of a line in slope-intercept form (y = mx + b) is determined by its slope (m) and y-intercept (b).
We know that the slope (m) of line t is -1, and the y-intercept (b) is -6. Substituting these values into the slope-intercept form, we get:
y = -x - 6
To find the x-intercept, we set y = 0 and solve for x:
0 = -x - 6
Adding x to both sides:
x = -6
Therefore, the x-intercept of line t is (-6,0).
Can someone please answer and provide an explanation for these problems?
The distance between each pair of points include the following:
44. 2.8 units.
45. 5.8 units.
46. 12.0 units.
47. 16.6 units.
48. 7.1 units.
49. 4.5 units.
How to determine the distance between two end points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
Question 44.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(3 - 1)² + (2 - 4)²]
Distance = √[(2)² + (-2)²]
Distance = √8
Distance = 2.8 units.
Question 45.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-2 + 7)² + (0 - 3)²]
Distance = √[(5)² + (-3)²]
Distance = √34
Distance = 5.8 units.
Question 46.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-6 - 2)² + (-2 - 7)²]
Distance = √[(-8)² + (-9)²]
Distance = √145
Distance = 12.0 units.
Question 47.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(1 - 8)² + (-8 - 7)²]
Distance = √[(-7)² + (-15)²]
Distance = √274
Distance = 16.6 units.
Question 48.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-5 - 2)² + (-4 + 5)²]
Distance = √[(-7)² + (1)²]
Distance = √50
Distance = 7.1 units.
Question 49.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(5 - 3)² + (5 - 1)²]
Distance = √[(2)² + (4)²]
Distance = √20
Distance = 4.5 units.
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Rebecca takes out a loan that gathers compound interest. The bullet points below show the value of the loan over time.
Start = £2500.00
After 1 year = £2630.00
After 2 years = £2766.76
a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p.
b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p.
The rate is 5.2%
After 10 years, the money will amount to £4150.
What is compound interest?We know that the compound interest can be obtained from;
[tex]A = P(1 + r/n)^{nt}[/tex]
The rate is obtained from;
I = A - P
I = interest
A = amount
P = principal
r = rate
n = Number of times compounded
t = time in years
Then;
I = £2630.00 - £2500.00
I = £130
I = PRT/100
130 = 2500 * R * 1/100
R = 130 * 100/2500
R = 5.2%
After 10 years;
[tex]A = 2500 ( 1 + 0.052)^{10}[/tex]
A = £4150
Thus this is the amount after 10 years
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Show that the triangles are congruent for the given value in the variable.
5. GH= 3
HI= 3x-9 and x=4
HI= 3(4)-9=
= 12-9
= 3
so, GH = HI
Do the same for GJ and JI.
6. 36=2x
18=x
So, the angles are the same.
4x-11=61
4(18)-11=61
So, the sides are also the same meaning the triangles are congruent.
The graph shows the distribution of the amount of chicken (in ounces) that adults eat in one sitting. The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
A graph titled Chicken Consumption has amount (ounces) on the x-axis, going from 3.2 to 12.8 in increments of 1.2. The highest point of the curve is at 8.
What percentage of adults eat between 5.6 and 8 ounces of chicken in one sitting?
2.5%
34%
47.5%
95%
Using concepts of the normal and of the uniform distribution, it is found that the correct option is:
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
In an uniform distribution, all outcomes are equally as likely, thus they have the same height.
In the normal distribution,
The outcomes with the highest likelihood are those closest to the mean, thus they have the highest height.
This means that the mean of this distribution is 8.
The standard deviation cannot be a negative value,
So in this problem, it is 1.2,
Which means that the correct option is:
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
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HELP ASAP PHOTO INCLUDED
The volume of the shape for Jackson's ice cream is given as follows:
11.85 in³.
How to obtain the volume?The volume of a cone of radius r and height h is given by the equation presented as follows:
V = πr²h/3.
Hence the volume of the cone in this problem is given as follows:
V = 3.14 x 1.5² x 5/3
V = 11.78 in³.
The volume of an hemisphere of radius r is given as follows:
V = 2πr³/3.
Hence the volume of sphere is:
V = 2π x 1.5³/3
V = 7.07 in³.
Hence the total volume is given as follows:
11.78 + 7.07 = 11.85 in³.
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