Answers
a) The measure of side PN of the triangle is PN = 18 cm
b) The measure of ∠CDA = 45°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the first triangle be represented as ΔOMP
Let the second triangle be represented as ΔOPN
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Now , the measure of OP = √ ( OM² - MP² )
Substituting the values in the equation , we get
The measure of OP = √ ( 25 )² - ( 7 )²
The measure of OP = √ ( 625 - 49 ) = √ ( 576 )
The measure of OP = 24 cm
And , the triangle OPN is a right triangle ,
So , the measure of PN = √ ( ON )² - ( OP )²
Substituting the values in the equation , we get
The measure of PN = √ ( 30 )² - ( 24 )²
The measure of PN = √ ( 900 - 576 ) = √ ( 324 )
The measure of PN = 18 cm
Therefore , the measure of PN of the triangle is 18 cm
b)
The two parallel lines are l₁ and l₂ where line t is the transversal
The measure of ∠FAE = 55°
The measure of ∠GAF = 80°
Now , the measures of angles in a straight line is 180°
So , the measure of ∠GAB = 180° - ( 55° + 80° )
The measure of ∠GAB = 45°
And , measure of ∠GAB = measure of ∠DAE ( alternate angles are equal )
So , the measure of ∠DAE = 45°
And , the measure of ∠DAE = the measure of ∠CDA ( alternate interior angles of a transversal line are equal )
Therefore , the measure of ∠CDA = 45°
Hence , the side PN of triangle is 18 cm and angle ∠CDA = 45°
To learn more about triangles click :
https://brainly.com/question/16739377
#SPJ1
Related Questions
The number of chirps that crickets make is closely related to the temperature in after environment. When the temperatures between 12 and 38°C ,we can tell the temperature by counting the number of chirps.
Answers
Answer:
a) 32° Celsius
b) C = m/3 + 4
c) 30 chirps
d) m = 3C - 12
This would be the equation needed to find the number of chirps as a function of temperature
Step-by-step explanation:
Part a.
Since there are 84 chirps in 25 seconds
we get temperature, C = 84/3 + 4 = 28 + 4 = 32° Celsius
part b.
Equation is
C = m/3 + 4
Part c.
We have C = 14
Therefore
14 = m/3 + 4
Multiply throughout by 3
==> 3 x 14 = 3 x m/3 + 3 x 4
==> 42 = m + 12
Subtract 12:
42 - 12 = m30 = m
or m = 30 chirps
part d.
Inverse of the function C = m/3 + 4 is m expresses as a function of C
C = m/3 + 4
Multiply by 3 both sides:
3C = m + 12
3C - 12 = m
or m = 3C - 12
This would be the equation needed to find the number of chirps as a function of temperature
The sum of two three-digit number b67 and aa5 is a four-digit number 1a12. What is the value of (a + b)?
Answers
Answer: 13
Step-by-step explanation: The two numbers are 967 and 445 making a=4 and b=9. We know a+b= 9+4 which is 13. For starters, you add the last digits of b67 and aa5 so 7+5=12 which is why the four digit number ends in two. When adding, the one from 12 would carry so the second to last digit on the four digit number would have to be 11. To get eleven you would add 7 and 4. The seven comes from the second digit in the b67 number including the one that came from 7+5=12. Now we know a=4. Knowing this now aa5= 445 and 1a12= 1412. We can now substract 445 from 1412 to get 967. b67= 967. To check 967+445=1412.
In one hour, John can produce 20 loaves of bread or 18 cakes. In one hour, Phyllis can produce 30 loaves of bread or 15 cakes. Which of the following statements is true?
a. John has a comparative advantage in producing cakes.
b. Phyllis has an absolute advantage in both goods.
c. Phyllis has a comparative advantage in producing cakes.
d. John has an absolute advantage in both goods.
Answers
Correct Answer is c. Phyllis has a comparative advantage in producing cakes.
What is comparative advantage?
Comparative advantage is an economic concept that refers to the ability of an individual, firm, or country to produce a particular good or service more efficiently compared to others.
The opportunity cost of producing one cake for John is (20 loaves of bread) / (18 cakes) = 1.11 loaves of bread per cake.
The opportunity cost of producing one cake for Phyllis is (30 loaves of bread) / (15 cakes) = 2 loaves of bread per cake.
Since Phyllis has a lower opportunity cost of producing cakes (2 loaves of bread per cake) compared to John (1.11 loaves of bread per cake), Hence, Phyllis has a comparative advantage in producing cakes.
To learn more about comparative advantage, Visit
https://brainly.com/question/2827889
#SPJ4
using the priority list t2, t7, t6, t4, t10, t8, t9, t3, t1, t5, schedule the project below with two processors.
Answers
The average T2, T7, T6, T4, and T10 in Processor 1
T8, T9, T3, T1, and T5 on Processor 2.
Work on tasks t2, t7, t6, t4, and t10 will be done by processor 1. The first task to be finished is task t2, followed by tasks t7, t6, t4, and lastly t10. Work on tasks t8, t9, t3, t1, and t5 will be done by processor 2. The first work to be finished is task t8, followed by t9, t3, t1, and ultimately t5. In order to finish the job quickly, both processors will cooperate, with Processor 1 concentrating on the early tasks and Processor 2 concentrating on the later duties. This guarantees that the project is finished on schedule and that all the tasks are carried out in the proper order.
Learn more about average here
https://brainly.com/question/24057012
#SPJ4
5. Use the slope formula to calculate the slope of the path you selected in question 4. Round your answer to the nearest hundredth. Show your work. Use the coordinates from question 1 and the pair in question 3 that matches the path you chose. Then use the Compass Tool to confirm your answer by dragging the point on the line that goes through the boat. (5 points: 3 points for a correctly written equation and work, 2 points for the slope)
Answers
The equation for the given scenario is y=50/57x-3.16.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).
From the given figure, the coordinate points are (129, 110) and (300, 260).
Substitute (x₁, y₁)=(129, 110) and (x₂, y₂=(300, 260) is slope formula, we get
Slope (m) =(260-110)/(300-129)
= 150/171
= 50/57
Substitute, m=50/57 and (x, y)=(129, 110) in y=mx+c, we get
110=50/57 (129)+c
110=113.16+c
c= -3.16
Substitute, m=50/57 and c= -3.16 in y=mx+c, we get
y=50/57x-3.16
Therefore, the equation for the given scenario is y=50/57x-3.16.
To learn more about the slope of a line visit:
https://brainly.com/question/14511992.
#SPJ1
Jenny uses half of a garden space to
plant roses. She uses 1/4 of that space
to plant pink roses. What fraction of
the entire space does Jenny use for
pink roses?
Answers
The fraction of the entire space jenny use for pink roses is 1/8 of the whole garden
What is word problem?A word problem in math is a math question written as one sentence or more that requires children to apply their math knowledge to a 'real-life' scenario.
These word problem are translated into mathematical equations.
Represent the total garden by x
Jenny uses 1/2 of the garden to plant roses
= 1/2×x = x/2
She uses 1/4 of the space to plant pink roses
= 1/4 × ×/2
= x/8
Therefore she uses 1/8 of the whole garden to plant pink roses.
learn more about word problem from
https://brainly.com/question/21405634
#SPJ1
triangle abc is an equilateral triangle with side length 6. arcs are drawn centered at the vertices connecting midpoints of consecutive sides. find the area of the shaded region
Answers
The area of the shaded region is [ (36 * √3)/4 - 3 * (9 * √3)/4 ] square units = (36 * √3)/4 - 27 * √3/4 square units = 9 * √3/4 square units.
What is the area of triangle?The area of a triangle can be found using the following formula:
Area = (base * height) / 2
The area of the shaded region can be found by subtracting the sum of the areas of three small equilateral triangles from the area of the original equilateral triangle.
Each of the small equilateral triangles has side length 3, since it is half the length of the original triangle's sides. The area of each small triangle is (3^2 * √3)/4 = (9 * √3)/4 square units.
The area of the original equilateral triangle is (6^2 * √3)/4 = (36 * √3)/4 square units.
Hence, the area of the shaded region is [ (36 * √3)/4 - 3 * (9 * √3)/4 ] square units = (36 * √3)/4 - 27 * √3/4 square units = 9 * √3/4 square units.
To learn more about area of triangle, visit
https://brainly.com/question/17335144
#SPJ4
On Monday it took 5 people 3 and half hours to build a wall. An identical wall needs to be built on Tuesday but only 2 people are available. Each person is paid £9.30 for each hour or part of an hour they work. Work out how much each builder will be paid for the work completed on Tuesday.
Answers
Each builder will be paid £32.55 for work on tuesday.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that on Monday it took 5 people, three and half hours to build a wall. An identical wall needs to be built on Tuesday but only 2 people are available. Each person is paid £9.30 for each hour or part of an hour they work.
5 people take 3.5 hours to build a wall.
1 person will take (3.5/5) hours to build a wall.
2 persons will take (3.5/5 x 2) hours to build a wall.
1 person is paid £9.30 for each hour. So 2 persons will get -
£{9.30 x 3.5/5 x 2}
£32.55
Therefore, each builder will be paid £32.55 for work on tuesday.
To solve more questions on functions, visit the link below-
brainly.com/question/17613163
#SPJ1
The equation
V
=
23900
(
0.91
)
t
V
=
23900
(
0.91
)
t
represents the value (in dollars) of a car
t
t
years after its purchase. Use this equation to complete the statements below.
The value of this car is at a rate of
The purchase price of the car was .
Answers
Answer: The equation represents the value (in dollars) of a car t years after its purchase, so the purchase price of the car would have been the value of the car when t = 0. Plugging in t = 0 into the equation, we get:
V = 23900 * (0.91)^0
V = 23900
So the purchase price of the car was $23,900.
Regarding the rate of decrease in the value of the car, we can observe that the value decreases at a rate proportional to (0.91)^t, so the rate of decrease is proportional to 0.91.
Step-by-step explanation:
What is the area of the parallelogram?
(-6.6)
(-9,-3)*
(-5-3)
(-2,6)
Answers
Answer:
36 square units
Step-by-step explanation:
You want the area of the parallelogram with vertex coordinates (-6, 6), (-9, -3), (-5, -3), (-2, 6).
AreaThe area of a parallelogram is the product of the base length and the height perpendicular to that base.
Here, the base is a horizontal line, so its length is the difference of the x-coordinates of the end points:
-5 -(-9) = 4 . . . . base
The height is the difference of y-coordinates between the top edge and the bottom edge:
6 -(-3) = 9 . . . . height
Then the area is ...
A = bh = 4·9 = 36 . . . . square units
please help answer this:
Answers
The monomial is 6² completes it and makes it (6p - 7q)².
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
We know a monomial is a polynomial that consists of a single term.
Given, __ - 42pq + 49q².
= ___ - 42pq + 7²q².
Now, 6×7 = 42,
Therefore, ___ - 42pq + 7²q²,
= 6²p² - 42pq + 7²q².
= (6p)² - 42pq + (7q)².
= (6p - 7q)².
learn more about polynomials here :
https://brainly.com/question/11536910
#SPJ1
which of the follwoing is not one of the three privacy rights created by the supreme courtt through its interpretation of vasious constitutional amendments
Answers
The Supreme Court's interpretation of numerous constitutional amendments did not result in the creation of the right to privacy or any of the other three privacy rights. The average freedom against arbitrary searches and seizures, the right to due process, and the right to free speech are the three privacy rights.
The Supreme Court's interpretation of numerous constitutional amendments did not result in the creation of the right to privacy or any of the other three privacy rights. The freedom against arbitrary searches and seizures, the right to due process, and the right to free speech are the three privacy rights. The Fourth, Fifth, and First Amendments of the Constitution, respectively, gave rise to these rights. The right to privacy has been developed and is safeguarded by the Supreme Court through its interpretation of the various amendments, despite the fact that it is not expressly stated in the Constitution. Individuals are protected by the right to privacy from having their private information or activities revealed without their permission. Additionally, it gives people the freedom to decide how they want to live their life, including the right to marry, the right to access contraception, and the right to help getting an abortion. Despite not being one of the three privacy rights established by the Supreme Court, the right to privacy is still a crucial kind of protection for people. It guarantees that people have control over the information they share, the choices they make, and the respect for their privacy.
Learn more about average here
https://brainly.com/question/24057012
#SPJ4
The complete question is
which of the following is not one of the three privacy rights created by the supreme court through its interpretation of various constitutional amendments right to privacy or any of the other three privacy rights.
Which binomial below is a factor of the polynomial 3a^2+6a-2a-4 A. (a – 2) B. (a + 4) C. (3a – 2) D. (3a + 2)
Answers
The solution is Option C.
The value of the quadratic equation is A = 3a² + 4a - 4 , where the factor of a is given by a = 2/3
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
A = 3a² + 6a - 2a - 4 be equation (1)
On simplifying the equation , we get
A = 3a² + 4a - 4
Now , when the factor of the equation is ( 3a - 2 ) = 0
Adding 2 on both sides of the equation , we get
3a = 2
Divide by 3 on both sides , we get
a = 2/3
Substitute the value of a in the equation , we get
A = 3 ( 2/3 )² + 4 ( 2/3 ) - 4
On simplifying the equation , we get
A = 3 ( 4/9 ) + 8/3 - 4
A = ( 4/3 + 8/3 ) - 4
A = ( 12/3 ) - 4
A = 4 - 4
A = 0
Hence , the binomial ( 3a - 2 ) is a factor of the equation
To learn more about quadratic equations click :
https://brainly.com/question/25652857
#SPJ1
Graph the numbers that are the solution to both x + 1 < 9 and 4x ≤ 8.
Answers
The solution of the inequality are shown in figure.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequalities are,
⇒ x + 1 < 9
⇒ 4x ≤ 8
Now, We can simplify as;
⇒ x + 1 < 9
Subtract 1 both side;
⇒ x < 9 - 1
⇒ x < 8
⇒ 4x ≤ 8
Divide by 4;
⇒ x ≤ 4
Thus, The solution of the inequality are shown in figure.
Learn more about the inequality visit:
https://brainly.com/question/25944814
#SPJ1
What is the volume of a block of wood with a height of 3 inches, a length of 5 inches and a width of 10 inches?
30 inches cubed
15 inches
150 inches
150 inches cubed
help pls
Answers
= 150
Therefore your answer is 150 inches cubed
Answer:
150 in cubed
Step-by-step explanation:
What is the discriminant of the quadratic equation 9x^2-2x-9=09x
2
−2x−9=0?
Answers
[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{9}x^2\stackrel{\stackrel{b}{\downarrow }}{-2}x\stackrel{\stackrel{c}{\downarrow }}{-9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-2)^2-4(9)(-9)\implies \text{\LARGE 328}[/tex]
The doctor has ordered baby Nathaniel to receive Gentamicin IM 1.3 mg/kg q 8 hours. Nathaniel weighs 8.1 pounds. How much gentamicin would you give baby Nathaniel? **Rounding rule: This is a dosage not a portion of ml, so round to the 100th place.
______ mg
Answers
We would give 4.78 mg of Gentamicin to baby Nathaniel.
What is unit conversion?Unit conversion means the conversion between different units and measurements of the same quantity done by the process of multiplication or division.
Given,
Dosage of Gentamicin per kg = 1.3 mg/kg
Weight of the baby = 8.1pounds
1 pound = 0.4536 kg
8.1 pounds = 3.674 kg
Weight of the baby in kilograms = 3.674 kg
Then dosage to the baby = 3.674 × 1.3
= 4.7762 ≈ 4.78mg
Hence, 4.78 mg of Gentamicin, baby Nathaniel would receive.
Learn more about unit conversion here:
https://brainly.com/question/19420601
#SPJ1
5. Six differently colored balls (red, blue, green, orange, purple, and white) are placed in a basket. Without looking, three balls are removed. What is the total number of combinations that include a red ball?
a. 3
b. 10
c. 20
d. 60
e. 80
Answers
A sine function has the following key features:
Period = 4
Amplitude = 4
Midline: y = 1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
What will the graph look like?
Answers
The Sine Function is y = 4 sin(π /2 x ) + 1
What is Sine function?In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle.
Given:
Period = 4
Amplitude = 4
Midline: y = 1
y-intercept: (0, 1)
We know that
y = Asin (Bx + C) + D
A = the amplitude = 4
So, B = 2pi / period
= 2π / 4
= π /2
and, C = phase shift
C = 0
Also, D = midline = 1
So, the sine Function is
y = 4 sin(π /2 x ) + 1
Learn more about sine function here:
https://brainly.com/question/12015707
#SPJ1
Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 78.7 Mbps. The complete list of 50 data speeds has a mean of x=16.44 Mbps and a standard deviation of s=39.37Mbps.
a. What is the difference between carrier's highest data speed and the mean of all 50 data speeds?
b. How many standard deviations is that [the difference found in part (a)]?
c. Convert the carrier's highest data speed to a z score.
d. If we consider data speeds that convert to z scores between - 2
and 2 to be neither significantly low nor significantly high, is the carrier's highest data speed significant?
Answers
(a). There is a 57.16 Mbps difference. (b). There is a 2.74 standard deviation difference. (c). 2.74 is the z-score (d). The maximum data rate offered by the carrier is more than 2.
What is an appropriate response?When something is careful and purposeful, you use the word measured to describe it. The men's voices were measured and quiet. Voters will be attracted to her more considered reaction. These are a couple of those illustrations. using a thermometer to measure body temperature using a measuring cylinder to determine the weight of produce in a store. Measuring the stature of an infant to retain his/her growth record.
(a). (74.5 - 17.34) = 57.16
(b). 57.16/20.79
= 2.74
(c). z = (X - μ)/sd
= (74.5 - 17.34)/20.79
= 2.74
(d). Because it is higher than 2, the carrier's greatest data speed is noteworthy.
To know more about Measured visit:
https://brainly.com/question/4725561
#SPJ1
in pavlov's experiments he paired the presentation of food with a buzzer and measured salivation to each. in this experiment the buzzer was the
Answers
In Pavlov's experiments, he paired the presentation of food with a buzzer and measured salivation to each. In this (b) conditioned stimulus (CS)
Like many great scientific advances, Pavlovian conditioning (aka classical conditioning) was discovered accidentally. Ivan Petrovich Pavlov (1849–1936) was a physiologist, not a psychologist.
During the 1890s, Russian physiologist, Ivan Pavlov was researching salivation in dogs in response to being fed. He inserted a small test tube into the cheek of each dog to measure saliva when the dogs were fed (with a powder made from meat).
Pavlov predicted the dogs would salivate in response to the food placed in front of them, but he noticed that his dogs would begin to salivate whenever they heard the footsteps of his assistant who was bringing them the food.
The complete question is-
In Pavlov's experiments, he paired the presentation of food with a buzzer and measured salivation to each. In this
experiment the buzzer was the ___.
A. unconditioned stimulus (US)
B. conditioned stimulus (CS)
C. unconditioned response (UR)
D. conditioned response (CR)
learn more about Pavlov's experiments,
https://brainly.com/question/29750150
#SPJ4
Use the associative law of
the expression 22 x (12 x 9).
O 12 × 9 × 22
O (12 x 9) x 22
O
O
(22 × 12) × 9
multiplication to rewrite
(22 x 9) x 12
Answers
(22 x 12) x 9 or 22 x 12 x 9. In both cases, the product is obtained by multiplying 22 by 12, and then multiplying that result by 9, which gives us 3024.
How the associative law words?The associative law of multiplication states that the way in which the numbers are grouped within an expression does not change the product. In other words, you can change the grouping of the factors and still obtain the same result. For example, the expression 22 x (12 x 9) can be rewritten as (22 x 12) x 9 or 22 x 12 x 9, and the product will be the same in all cases.
According to question:In the expression 22 x (12 x 9),
the associative law can be used to rearrange the factors into
(22 x 12) x 9 or
22 x 12 x 9.
In both cases, the product is obtained by multiplying 22 by 12, and then multiplying that result by 9, which gives us 3024.
To know more about Multiplication visit:
brainly.com/question/5992872
#SPJ1
State the coordinate of the image of the given point B (4,9) under a dilation with center
at the origin with the given scale factor of 2.
Answers
As a result, the coordinate of the picture of point B (4, 9) under dilation with the origin as the center and a scale factor of 2 is (8, 18).
What is coordinate?Coordinates are a pair of integers that are used to locate a point or object in a two-dimensional plane. A point's location on a 2D plane is defined by two integers called the x-coordinate and the y-coordinate. The distance between two points is known as the x-coordinate, or abscissa, while the distance between two points is known as the y-coordinate, or ordinate. Point (3, 2), for example, is three units distant from the positive y-axis and two units away from the positive x-axis.
Here,
A dilation with center at the origin and scale factor of 2 will stretch or shrink the distances from the origin by a factor of 2. If the given point B is (4,9), its image under the dilation will be:
(2 * 4, 2 * 9) = (8, 18)
So the coordinate of the image of point B (4, 9) under the dilation with center at the origin and scale factor of 2 is (8, 18).
To know more about coordinate,
https://brainly.com/question/16634867
#SPJ1
I honestly don’t know what I’m doing please help
Answers
Answer:
6.5
Step-by-step explanation:
C = 2πr
40.841/2π = r
6.5 = r
Answer:
○ [tex]\displaystyle 6,5\:ft.[/tex]
Step-by-step explanation:
[tex]\displaystyle {\pi}d = C \\ 13,000094062…{\pi} = 40,841 \\ \\ \boxed{6,5000470308…} = \frac{13,000094062…}{2} \\ \\ \\ \boxed{\boxed{6,5 \approx r}}[/tex]
I am joyous to assist you at any time.
Mary buys a pack of sugar paste to cover her cakes. the pack is in the shape of a cuboid measuring 5cm by 8cm by 9cm a) she rolls out her sugar paste into rectangular sheet of pasty of uniform thickness measuring 30cm by 60cm. Work out the thickness of this rectangular sheet. B) Mary cuts out two circular pieces of pastry, each of diameter 25cm from her rectangular sheet of pastry. What volume of pastry remains when she removes these two circular pieces of pastry?
Answers
A. The thickness of the rectangular sheet of sugar paste is 1/5 cm.
B. The volume of the remaining pastry can be expressed as approximately 45.84 cm³.
What is the volume of the cuboid?The volume of a cuboid is equal to the product of the length, width, and height of a cuboid.
The volume of a cuboid is length × breadth× height
A) The volume of the cuboid pack of sugar paste is 5 cm x 8 cm x 9 cm = 360 cm³.
To find the thickness of the rolled-out rectangular sheet, we need to divide the volume of the pack by the area of the rectangular sheet:
thickness = volume/area
thickness = 360 cm³ / (30 cm x 60 cm)
thickness = 360 cm³ / 1800 cm²
thickness = 1/5 cm
So the thickness of the rectangular sheet of sugar paste is 1/5 cm.
B) The two circular pieces of pastry each have a diameter of 25 cm and thus a radius of 25/2 = 12.5 cm.
The volume of each circular piece of pastry can be calculated as:
V = π × (radius)² × thickness
V = π × (12.5 cm)² × 1/5 cm
V = π × 156.25 × 1/5 cm³
V = 50 × π cm³
Since Mary cuts out two circular pieces, the total volume of pastry that she removes is 2 x 50 x π cm³. The remaining volume of pastry is the original volume of the pack minus the volume of the two circular pieces:
Volume remaining = 360 cm³ - 2 × 50 × π cm³ = 45.84 cm³
The volume of the remaining pastry can be expressed as approximately 45.84 cm³.
Learn more about the volume of cuboids here:
brainly.com/question/23118276
#SPJ1
9. The radius a of a circle inscribed by an isosceles triangle whose sides are A, B and C is given by. a[(S-A)(S-B)(S-C)/S]¹/2 Where S is an abbreviation for (A + B + C)/2. Check this equation for dimensional consistency.
Answers
It should be noted that r = [(s - a)(s - b) (s - c)/s]1/2, dimensionally consistent.
How to convey the informationThe radius a of a circle inscribed by an isosceles triangle whose sides are A, B and C is given.
r = [(s - a)(s - b) (s - c)/s]1/2, where s = (a + b + c)/2.
a, b , c actual lengths of the sides,
s = average length of the sides
So that we can write
L = [(L - L)(L - L) (L - L)/L]^1/2
= [(L)(L) (L)/L]^1/2
= [L^2]^1/2
= L
Therefore r = [(s - a)(s - b) (s - c)/s]1/2, dimensionally consistent.
Learn more about equations on:
https://brainly.com/question/2972832
#SPJ1
Adding improper fractions 5/12 + 1/4
Answers
By adding improper fractions 5/12 + 1/4, we get 8/12 or 2/3.
What is the least common multiple?
The LCM is multiple which is useful if fractions need to be expressed in the same name, and the further discussion can be defined as follows: When the other number is multiple, LCM will have the larger number: Example: So, the 2 and 4 LCM.
1/4 and 5/12 do not have a common denominator, so we first take LCM of the denominators.
LCM = 12
Therefore, we make 1/4 with denominator 12,
i.e, 1x3/4x3 = 3/12
Now, we can add the two fractions which have a common denominator.
3+5/12 = 8/12 which can be simplified to 2/3 (after cutting the numerator and denominator with 4.)
Hence, by adding improper fractions 5/12 + 1/4, we get 8/12 or 2/3.
To learn more about the least common multiple visit,
https://brainly.com/question/16054958
#SPJ1
if z is directly proportional to the product of x and y and if z is 15 when x is 5 and y is 6, then x, y, and z are related by the equation
Answers
Since z is directly proportional to the product of x and y, then x, y, and z are related by this equation: z = xy/2.
How to determine the equation?Mathematically, a proportional relationship or direct variation can be represented by the following equation:
y = kx
Where:
k is the constant of proportionality. x, y, and z represents the variables of a proportional relationship.Based on the information provided, we have the following:
z ∝ xy
z = kxy
In order to have a proportional relationship and equivalent ratios, the variables z, x, and y must have the same constant of proportionality:
Constant of proportionality (k) = z/xy
Constant of proportionality (k) = 15/(5 × 6)
Constant of proportionality (k) = 15/30
Constant of proportionality (k) = 1/2.
For the equation, we have:
z = kxy
z = 1/2 × xy
z = xy/2
Read more on proportionality here: brainly.com/question/12866878
#SPJ1
find the expansion of (x y)5 a) using combinatorial reasoning
b) using the binomial theorem.
Answers
Using combinatorial reasoning, the expression of[tex](x y)5 is x^5y^5 + 5x^4y^6 + 10x^3y^7 + 10x^2y^8 + 5xy^9 + y^10[/tex]. Using the binomial theorem, it is[tex]1x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5[/tex].
a) Combinatorial reasoning involves breaking the expression down into different combinations of x and y, and then multiplying each combination. In this case, (x y)5 can be broken down into
[tex]x^5y^0 + x^4y^1 + x^3y^2 + x^2y^3 + x^1y^4 + x^0y^5[/tex],
and the coefficient of each term is the number of ways that combination can be derived from the expression. For example, there are 5 ways to arrange the combination [tex]x^4y^1[/tex], so its coefficient is 5. When the coefficients are multiplied with the combinations, they become
[tex]5x^4y^1 + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5[/tex],
which is the expansion of (x y)5.
b) The binomial theorem states that for any expression of the form [tex](x + y)^n[/tex], the expansion can be found by multiplying the term[tex]x^n[/tex]with the coefficient of each term in Pascal’s triangle. For example, for[tex](x + y)^5[/tex], the coefficient of[tex]x^5[/tex] is 1, the coefficient of[tex]x^4y[/tex]is 5, the coefficient of[tex]x^3y^2[/tex]is 10, the coefficient of [tex]x^2y^3[/tex]is 10, the coefficient of[tex]x^1y^4 is 5[/tex], and the coefficient of[tex]y^5[/tex]is 1. Thus, the expansion of [tex](x + y)^5 is 1x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5.[/tex]
Learn more about expression here
https://brainly.com/question/14083225
#SPJ4
If I took 480 minutes a day in school (that would be 8 hours a day in school), and there is 4 weeks in a month, and all together we spend time in 10 months in school, if 1 hours is 60 minutes, then how much time and days to we spend in school.
Answers
You spend 480 minutes per day at school. We will assume that you go to school for 5 days per week.
480 minutes × 5 days = 2,400 minutes per week
There are 4 weeks in a month, so we will multiply the minutes per week by 4 weeks to get the monthly time spent in school.
2,400 minutes per week × 4 weeks = 9,600 minutes per month
You are in school for 10 months, so we will multiply the minutes per month by 10.
9,600 minutes per month × 10 months = 96,000 minutes in school
Now, we will divide the time in school by the number of minutes in school per day.
96,000 minutes in school ÷ 480 minutes per day = 200 days in school
Answer: 96,000 hours or 200 days