Answer:
16 feet
Step-by-step explanation:
Area of triangle = 1/2(a x b)
A = 1/2(6.4 x 5)
A = 32/2
A = 16 feet
a ramp 27ft long rises to a platform. the bottom of the platform is 16ft from the foot of the ramp. find , the angle of elevation of the ramp. round your answer to the nearest tenth of a degree.
Angle of elevation of the ramp with a height of 27ft and a platform of 16ft is approximately 59.35°.
The ramp is 27ft long and rises to a platform, the bottom of the platform is 16ft from the foot of the ramp.
We need to find the angle of elevation of the ramp.
The angle of elevation of the ramp is the angle made by the ramp with the horizontal.
Let ABC be the ramp and D be the platform, as shown below: Let AB = 16ft and BC = 27ft.
We need to find the angle ABD.
Consider right-angled ΔABC In right-angled ΔABC,
we have:
tan⁻¹ (BC / AB)
θ = tan⁻¹ (27 / 16)
θ ≈ 59.35°
Hence, the angle of elevation of the ramp is approximately 59.35°.
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Question 7
Subtract-2x2 + 5xy + 4y2 from the sum
of x² - 2xy + y² and 3x² + 4xy - y²
Answer: 6x² - 3xy - 4y²
Step-by-step explanation:
The sum of x² - 2xy + y² and 3x² + 4xy - y² is:
(x² - 2xy + y²) + (3x² + 4xy - y²)
Simplifying and combining like terms, we get:
4x² + 2xy
Now, we need to subtract -2x² + 5xy + 4y² from this sum. To do this, we can change the sign of each term in -2x² + 5xy + 4y² and then add:
4x² + 2xy + (2x² - 5xy - 4y²)
Simplifying and combining like terms, we get:
6x² - 3xy - 4y²
Therefore, the answer is 6x² - 3xy - 4y².
8. Points P, Q, whose abscissae are 2 and 2+h, are taken on the curve y = 2x^2+1. Find the gradient of the chord PQ. To what value does this gradient approach as h decreases towards the value zero?
The gradient of the chord PQ is 2h + 8
What is the gradient of the chord?Let's first find the coordinates of points P and Q on the curve y = 2x^2+1.
Point P has an abscissa of 2, so its coordinates are (2, 2(2)^2+1) = (2, 9).
Point Q has an abscissa of 2+h, so its coordinates are (2+h, 2(2+h)^2+1) = (2+h, 2(4+4h+h^2)+1) = (2+h, 8+8h+2h^2+1) = (2+h, 2h^2+8h+9).
The gradient of the chord PQ is given by:
(m) = Δy /Δx
(m) = (2h^2+8h+9 - 9) / (2+h - 2)
(m) = (2h^2+8h) / (h)
(m) = 2h + 8
As h approaches zero, the gradient of the chord PQ approaches 8, because the term 2h becomes negligible compared to 8 when h is small. Therefore, the gradient of the tangent to the curve at point P is 8.
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A sample of 16 ten-year-old girls had a mean weight of 71.5 and a standard deviation of 12 pounds, respectively. Give the following information for a 95% confidence interval.
Sample mean =
Standard Deviation =
Sample size =
Do you use Z or t?
Z or t =
Standard Error (Rounded to nearest tenth)=
Margin of Error (Rounded to nearest tenth) =
Lower limit (Rounded to nearest tenth) =
Upper limit (Rounded to nearest tenth) =
For 95% confidence interval, Standard Error is 3, Margin of Error is 6.4, Lower limit is 65.1 and Upper limit is 77.9.
What is confidence interval?A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter with a certain degree of confidence based on a sample from that population. It is calculated from the sample data and provides a range of values within which the true population parameter is likely to fall.
According to question:1) standard error = s / √(n)
standard error = 12 / √(16)
standard error = 3
2) margin of error = t-value x standard error
margin of error = 2.131 x 3
margin of error = 6.393
3) lower limit = sample mean - margin of error
lower limit = 71.5 - 6.393
lower limit = 65.107
4) upper limit = sample mean + margin of error
upper limit = 71.5 + 6.393
upper limit = 77.893
Therefore, the information for a 95% confidence interval is:
Sample mean = 71.5 pounds
Standard Deviation = 12 pounds
Sample size = 16
Z or t = t
Standard Error = 3
Margin of Error = 6.4
Lower limit = 65.1
Upper limit = 77.9
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What is the next fraction in this sequence? Simplify your answer. 13/ 21 , 9/ 14 , 2/ 3 , 29 /42 ,
Answer:
5/7
Step-by-step explanation:
Make all the denominators 42.
26/42, 27/42, 28/42, 29/42
The pattern is the numerator increases by one each time.
30/42 = 5/7
Hope this helps!
Use the arc length formula to find the length of the curve y = 3x − 2, −3 ≤ x ≤ 1. Check your answer by noting that the curve is a line segment and calculating its length by the distance formula
As per the distance, the length of the curve y = 3x − 2 for −3 ≤ x ≤ 1 is 4√10.
To begin, let us recall that the arc length formula gives us a way to find the length of a curve in terms of the function that defines it. The formula is given by:
L = ∫aᵇ √[1 + (dy/dx)²] dx
where L is the length of the curve, a and b are the endpoints of the curve, and dy/dx is the derivative of the function that defines the curve with respect to x.
For the curve y = 3x − 2, we can find dy/dx by taking the derivative of the function with respect to x. This gives us:
dy/dx = 3
We can now substitute this into the arc length formula and integrate over the interval −3 ≤ x ≤ 1:
L = ∫−3¹ √[1 + (3)²] dx
L = ∫−3¹ √10 dx
L = √10 ∫−3¹ dx
L = √10 (1 - (-3))
L = √10 (4)
L = 4√10
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a sheet of 8-inch by 10-inch paper is placed on top of a sheet of $8 \frac{1}{2}$-inch by 11-inch paper, as shown. what is the area of the region of overlap in square inches?
The area of the region of overlap between the 8-inch by 10-inch paper and the 8(1/2)-inch by 11-inch paper measures 12 square inches.
The area of the region of overlap between an 8-inch by 10-inch paper and an 8(1/2)-inch by 11-inch paper can be found in the following steps:
Step 1: Calculate the area of each paper. The area of an 8-inch by 10-inch paper is:
[tex]$$\text{Area} = \text{length} \times \text{width} = 8 \text{ in.} \times 10 \text{ in.} = 80 \text{ sq. in.}$$[/tex]
The area of an 8 1/2-inch by 11-inch paper is:
[tex]$$\text{Area} = \text{length} \times \text{width} = \left( 8 \frac{1}{2} \right) \text{ in.} \times 11 \text{ in.} = 93.5 \text{ sq. in.}$$[/tex]
Step 2: Find the horizontal and vertical lengths of the region of overlap.
The horizontal length is the length that is common to both papers, which is 8 inches.
The vertical length is the amount by which the two papers overlap, which is 8(1/2) inches - 10 inches = -1(1/2) inches. However, since the region of overlap cannot have a negative length, we take the absolute value of this result, which is 1(1/2) inches.
Step 3: Calculate the area of the region of overlap.
The area of the region of overlap is the product of the horizontal and vertical lengths:
[tex]$$\text{Area of the region of overlap} = 8 \text{ in.} \times 1 \frac{1}{2} \text{ in.} = 12 \text{ sq. in.}$$[/tex]
Therefore, the area of the region of overlap in square inches is 12 square inches.
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3/7 of a number is 24. Find the number.
Determine the force in each member of the truss with the method of joints and state if the
members are in tension (T) or compression (C). Set d = 1 m and P = 10 kN. (Hint: Look for zero-
force members to simplify the calculations)
if the members are in tension or compression. Identify all zero force members: Likewise, we can find the reaction force at A by taking minutes about point A: RA x 8m - 5kN x 8m - 5kN x 8m = 0 RA = 5kN
To begin with, we really want to find the reaction forces at An and G.
We can do this by taking minutes about point G.
We realize that the amount of minutes at any point is zero when the framework is in equilibrium.
Consequently, we can compose: 5kN x 8m - RA x 10m = 0 RA = 4kN
Likewise, we can find the reaction force at A by taking minutes about point A: RA x 8m - 5kN x 8m - 5kN x 8m = 0 RA = 5kN
Since we have two distinct qualities for RA, we can presume that the framework isn't in equilibrium.
This really intends that there should be some outside force following up on the framework.
The two obscure forces are at first thought to be ductile (for example pulling away from the joint). In the event that this underlying supposition is mistaken, the registered upsides of the pivotal forces will be negative, meaning pressure.
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the complete question is:
Question l Find the forces in members HE; FH, FE; and FC of the truss as shown in Figure Q1. State if the members are in tension or compression. Identify all zero force members: (10 marks) 8 m 5 KN 8 m 8 m 5 KN 8 m 10 m Figure Q1.
what is the answer to 1/3(21y+39)= -36
A floor is shaped like a regular pentagon. Each side length is represented by (2×+ 4) inches and (4×-2) inches. Find the length of each side
The length of each side of the regular pentagon is 10 units
Let's use the fact that the floor is a regular pentagon to set up an equation involving the side lengths.
A regular pentagon has five sides of equal length, so we can set the two expressions for the side lengths equal to each other:
2× + 4 = 4 × - 2
Solving for x, we get:
2x = 6
x = 3
Now that we have the value of x, we can substitute it back into either expression for the side length to find the length of each side. Let's use the expression (2× + 4) inches:
2× + 4 = 2(3) + 4
= 6 + 4
= 10 units
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3. A triangle has an area of 6 square inches and a perimeter of 12 inches.
Suppose it is dilated by some scale factor, and the area and perimeter of
the image are calculated. Match each graph with the relationship it
represents.
A. Graph A
B. Graph B
C. Graph C
D. Graph D
1. Scale factor is the x-value; perimeter is the y-value
2. Scale factor is the x-value; area is the y-value
3. Perimeter is the x-value; scale factor is the y-value
4. Perimeter is the x-value; scale factor is the y-value
So, the correct graph should have the scale factor on the x-axis and the area on the y-axis. This is Graph B. The other graphs do not correctly represent the relationship between the scale factor, area, and perimeter.
What is graph?There are different types of graphs, including directed graphs (also called digraphs), where each edge has a direction, and undirected graphs, where each edge has no direction. Graphs can also be weighted, meaning that each edge has a value associated with it, or unweighted, where all edges have the same value.
Graphs can be represented visually, using diagrams that show the vertices as points and the edges as lines or arrows connecting them. Graphs are used in a variety of applications, including computer algorithms, data analysis, and optimization problems.
by the question.
The area of the original triangle is 6 square inches, and the perimeter is 12 inches. Let the lengths of the sides be a, b, and c. Then, we have:
[tex]a + b + c = 12[/tex] (perimeter)
[tex]s = (a + b + c)/2 = 6[/tex] (semi perimeter)
[tex]A =\sqrt(s(s-a)(s-b)(s-c)) = 6[/tex] (area)
Simplifying the equations, we get:
[tex]a + b + c = 12[/tex]
[tex]a + b + c - 2a - 2b - 2c = 0[/tex]
[tex]-a - b - c = -12[/tex]
[tex]-a - b - c + 2a + 2b + 2c = 0[/tex]
[tex]a + b + c = 0[/tex]
Therefore, the centroid of the original triangle is at the origin (0,0).
When the triangle is dilated by a scale factor of k, the new area and perimeter are given by:
[tex]A' = k^2A = 6k^2[/tex]
[tex]P' = kP = 12k[/tex]
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3) A lottery ticket says that the chances of winning are 1 in 8. Suppose you buy 10 of these lottery tickets. Find the probability that at least one of them will be a winner
The probability of at least one of your 10 lottery tickets being a winner is approximately 0.638 or 63.8%.
The probability of winning on a single lottery ticket is 1/8, which means that the probability of not winning is 7/8. If you buy 10 of these lottery tickets, the probability of not winning on any of them is:
(7/8)^10 = 0.362
This means that there is a 36.2% chance that none of your tickets will be a winner. To find the probability that at least one of your tickets will be a winner, we can use the complementary probability:
P(at least one winner) = 1 - P(no winners)
P(at least one winner) = 1 - 0.362
P(at least one winner) = 0.638
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For each value of y, determine whether it is a solution to y≤9.
y
8
4
9
12
Is it a solution?
Yes
O
No
O
O
O
X
S
The values of the provided statics are 8, 4, and 9, but not 12 are solutions to y 9. (For 8, 4, and 9): Answer: No (for 12).
Why do you use the term statics?Statics is the study of internal and external forces acting on a structure. Statics is the branch of mechanics that studies bodies in motion. Statics is the study of systems in which momentum does not change, whereas dynamics is the study of systems in which momentum changes.
The values of y that meet the inequality for y 9 are those that fall below or coincide with 9.
y = 8 satisfies y ≤ 9 because 8 is less than 9.
y = 4 satisfies y ≤ 9 because 4 is less than 9.
y = 9 satisfies y ≤ 9 because 9 is equal to 9.
y = 12 does not satisfy y ≤ 9 because 12 is greater than 9.
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10 decagrams = blank centigrams.
100
1,000
10,000
100,000
Answer:
10,000
Step-by-step explanation:
1 dekagram = 1000 centigrams
10 dekagrams = 10 x 1000 = 10,000 centigrams
So, the answer is 10,000
Sally did a survey amongst her friends to
see how many hours homework they
each did per month.
Tim
Mary
Keith
Sidra
KEY:
Equals 4 hours
00
a) How many hours homework
does Sidra do?
b) How many hours, in total, do
Sally's friends spend on
homework per month?
1. The number of hours which Sidra did on homework is 12 hours
2. The total number of hours which Sally's friends spend on homework per month is 64 hours.
How many hours homework does Sidra do?Sidra does 3 keys worth of homework, and since a key equals 4 hours, she does:
= 3 keys x 4 hours/key
= 12 hours of homework.
How many hours, in total, do Sally's friends spend on homework per month?To find the total number of hours that Sally's friends spend on homework per month, we need to add up the hours of homework done by each of her friends:
Tim: 5 keys x 4 hours/key = 20 hours
Mary: 2 1/2 keys x 4 hours/key = 10 hours
Keith: 5 1/2 keys x 4 hours/key = 22 hours
Sidra: 3 keys x 4 hours/key = 12 hours
Total hours of homework per month:
= 20 + 10 + 22 + 12
= 64 hours.
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The town council of Finleyville is meeting to discuss emergency evacuation plans. Finleyville is in a state where hurricanes occur. Some town councillors believe the town's emergency evacuation plan needs to be changed because there has been an increase in natural disasters in the area. Other town councilors believe the plan is fine as it is. The following chart was presented to the town council. Which statement best describes the information presented in the chart?
a graph showing the number of hurricanes of category 1 or higher that happened during a specific series of years. Between 1980?1989 there were 13; from 1990?1999 there were 14; from 2000?2009 there were 23; and from 2010?2017 there were 10.
The number of hurricanes has decreased steadily since 1980.
There have been fewer hurricanes because of a change in temperature.
The number of hurricanes was increasing but has decreased in recent years.
There are more tornadoes in Finleyville than there are hurricanes.
The statement that best describes the infοrmatiοn presented in the chart is: "The number οf hurricanes was increasing but has decreased in recent years."
What are hurricanes ?Hurricanes, knοwn generically as trοpical cyclοnes, are lοw-pressure systems with οrganized thunderstοrm activity that fοrm οver trοpical οr subtrοpical waters. They gain their energy frοm warm οcean waters.
The chart shοws the number οf hurricanes οf categοry 1 οr higher that οccurred during specific series οf years, and it indicates that the number οf hurricanes increased frοm 13 in 1980-1989 tο 23 in 2000-2009, and then decreased tο 10 in 2010-2017.
Therefοre, the chart suggests that the number οf hurricanes was increasing, but it has decreased in recent years. The chart dοes nοt prοvide any infοrmatiοn abοut tοrnadοes in Finleyville οr the relatiοnship between the number οf hurricanes and temperature.
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The statement that best describes the information in the graph is: "The number of hurricanes has increased but decreased in recent years." The graph shows that the number of Category 1 or greater hurricanes increased from 1980 to 2009, but decreased from 2010 to 2017.
Molly placed $115. 00 in a savings account. This savings account earns 1. 5% interest per year. She did not add or take out any money from this account. How much money did she earn in interest at the end of four years? *
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$115\\ r=rate\to 1.5\%\to \frac{1.5}{100}\dotfill &0.015\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (115)(0.015)(4) \implies I = 6.9[/tex]
3. When x = 6, which number is closest to the value of y on the line of best fit in the graph below?
09
01
07
10
0987
65
432
2
1
➤X
0 1 2 3 4 5 6 7 8 9 10
Answer:
9
Step-by-step explanation:
Can someone please help me with these, I wasn’t able to attend school cause I have Covid and I don’t know what’s going on. Please please help me
Answer: The answer for the first question goes as follows: Which one(s) have both pairs of opposite sides that are parallel? Rectangle, Rhombus, and square. Which one(s) have both pairs of opposite sides that are congruent? Rectangle, square, and rhombus. Which one(s) have all four sides congruent? Square and rhombus.
The answers to the second question are:
Circumference = pi * diameter. So, the distance around it is 100pi.Area of a circle = pi * r^2. So the area of the theater is 7854.0 ft^2.Step-by-step explanation:
Essentially, all of these parallelograms have different properties and properties that they share. For example, a property they share by the definition of a parallelogram is that all of them have two pairs of opposing sides that are parallel. Another property they share from the definition of a parallelogram is that opposite sides are congruent.
As such, rectangles, squares, and rhombuses have the properties that all parallelograms have because they are all parallelograms. However, they also have their own properties.
Rectangles: A rectangle has the properties of a parallelogram, as well as the property of having all of its angles be right angles. This also makes all of its angles congruent.Rhombuses: Rhombuses have the properties of a parallelogram, and they also have all four of their sides congruent. Squares: Squares are like rhombuses and rectangles put together. They have all of their angles as right angles and they have all four of their sides congruent.Second Question Explanation:
1. The question is describing a theater that has a circular base. Therefore, you can use the formula for the circumference of a circle, pi * diameter, to find the circumference (or distance around) the theater. The diameter is given to you: 100 ft. So just multiply that by pi.
2. The question is asking for the area of the theater. This means that you can use the formula for the area of a circle, A = pi * r^2. Note that it is asking you for the area, not the volume, so you would find the area of the circle, not the volume of the hemisphere. r represents the radius of the circle/theater. The diameter is given as 100 ft, and the radius is half of the diameter, so it is 50 ft. Now just plug the radius into the equation and you get the answer I showed.
Which equation is equivalent to pq=r?
Responses
A) p=logR q
B) p=logQ r
C) q=logR p
D) q=logP r
The equation is equivalent to pq=r is option (C) q=logR p
To determine which equation is equivalent to pq=r, we can use logarithmic properties. Taking the logarithm of both sides of the equation, we get
log(pq) = log(r)
Using the property that log(a×b) = log(a) + log(b), we can simplify the left side of the equation
log(p) + log(q) = log(r)
Now, we can compare this expression to each of the answer choices
A) p = logR q
Substituting this into the equation, we get
log(p) + logR(q) = log(r)
This is not equivalent to our expression, so A is not the correct answer.
B) p = logQ r
Substituting this into the equation, we get
log(logQ r) + log(q) = log(r)
This is also not equivalent to our expression, so B is not the correct answer.
C) q = logR p
Substituting this into the equation, we get
log(p) + logR(q) = log(r)
This matches our expression, so C is the correct answer.
D) q = logP r
Substituting this into the equation, we get
log(p) + log(q) = log(logP r)
This is not equivalent to our expression, so D is not the correct answer.
Therefore, the correct option is (C) q=logR p
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Isosceles Trapezoids: Only one pair of opposite sides are _______
Answer:
equal
Step-by-step explanation:
Use the following function to find d(0)
d(x)=-x+-3
d(0)=
Answer:
d(0) = -3
Step-by-step explanation:
d(x) = -x + -3 d(0)
d(0) = 0 - 3
d(0) = -3
So, the answer is d(0) = -3
What is the value of (sine 30 + cos 30 ) - (sin 60 + cos 60 )
The value of ( sin 30° + cos 30° ) - ( sin 60° + cos 60° ) is 0.
(sine 30 + cos 30 ) - (sin 60 + cos 60 )
= ([tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{3} }{2}[/tex]) - ([tex]\frac{\sqrt{3} }{2}[/tex] + [tex]\frac{1}{2}[/tex])
= [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{3} }{2}[/tex] - [tex]\frac{\sqrt{3} }{2}[/tex] - [tex]\frac{1}{2}[/tex]
= [tex]\frac{\sqrt{3} }{2}[/tex] - [tex]\frac{\sqrt{3} }{2}[/tex]
= 0
Trigonometry is a branch of mathematics that focuses on the relationships between angles and the sides of triangles. It involves the study of trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant, and their various properties and applications. These functions relate the angles of a right triangle to the lengths of its sides, and they can be used to solve a wide range of problems in fields such as engineering, physics, astronomy, and navigation.
Trigonometry also includes the study of trigonometric identities, which are mathematical expressions that are true for all values of the variables involved. These identities can be used to simplify complex trigonometric expressions and to prove other mathematical theorems.
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A straw that is 15cm long leans against the inside of a glass. The diameter of a glass is
5cm, and has a height of 8cm. How far past the edge of the glass would the straw extend?
Round your answer to the nearest tenth.
The straw would extend approximately 4.9 cm past the edge of the glass.
9) A survey asked 915 people how many times per week they dine out at a restaurant. Th results are presented in the following table. Number of Times Frequency 134 273 249 127 72 30 24 Total915 Consider the 915 people to be a population. Let X be the number of times per week a person dines out for a person sampled at random from this population. Compute the standard deviation A) 2.1 в) 1.5 C 1.9 D) 2.2 10) Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p 15, p 0.4, P(12) A) 0.0016 B) 0.0634 C 0 4000 D) 0.0000
The correct option is B) 0.0634.
1) Standard deviationThe table is shown as below:Number of Times Frequency 1 34 2 73 3 249 4 127 5 72 6 30 7 24 Total 915The given population contains 915 people. Let X be the number of times per week a person dines out for a person sampled at random from this population.The population standard deviation is given by the formula below:$$\sigma = \sqrt{\frac{\sum (X-\mu)^2}{N}}$$where N is the population size, X is the value of the individual element of the population, μ is the mean value of the population. $$\sigma = \sqrt{\frac{\sum (X-\mu)^2}{N}}$$$$= \sqrt{\frac{\sum X^2 - 2X\mu + \mu^2}{N}}$$We need to compute the variance first.$$\sigma^2 = \frac{\sum X^2 - 2X\mu + \mu^2}{N}$$$$= \frac{(1^2 \cdot 34 + 2^2 \cdot 73 + 3^2 \cdot 249 + 4^2 \cdot 127 + 5^2 \cdot 72 + 6^2 \cdot 30 + 7^2 \cdot 24) - 2\cdot 3.176 \cdot (34 + 2\cdot 73 + 3\cdot 249 + 4\cdot 127 + 5\cdot 72 + 6\cdot 30 + 7\cdot 24) + 3.176^2 \cdot 915}{915}$$$$= 3.5689$$Therefore, the population standard deviation is given by:$\sigma = \sqrt{3.5689} = 1.8911\approx 1.9$Hence, the correct option is C) 1.92) The probability of a binomial experiment can be calculated by the formula below:$${\rm P}(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$$where n is the number of trials, k is the number of successes, p is the probability of success for each trial, and $1-p$ is the probability of failure for each trial.Here, n = 15 and p = 0.4.We need to find the probability of getting 12 successes out of 15 trials. Hence, k = 12.Using the formula above, we get$${\rm P}(X=12) = \binom{15}{12}0.4^{12}0.6^{3}$$$$= \frac{15 \times 14 \times 13}{3 \times 2 \times 1} \cdot 0.4^{12} \cdot 0.6^{3}$$$$= 0.0633605376$$Hence, the correct option is B) 0.0634.
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use the equations 10,16,22,28
rule to determine the 10th term and the general term?
Answer:
Below in bold.
Step-by-step explanation:
10,16,22,28
16-10 = 6, 22-16 = 6 and 28-22 = 6
This is an arithmetic sequence with first term a1 = 10 and common difference d = 6
General (nth) term = a1 + d(n - 1)
10th term = 10 + 6(9 -1)
= 10 + 48
= 58.
Arrange the steps in the correct order to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm.
a = 55, m = 89
An inverse of a modulo m for a = 55, m = 89 using the Euclidean algorithm is 34.
In order to find an inverse of a modulo for each of the following pairs of relatively prime integers using the Euclidean algorithm can be found by:
Using the Euclidean algorithm to find the greatest common divisor (gcd) of a and m. In this case, we have:
89 = 1 x 55 + 34
The gcd of 55 and 89 is 1.
Using the extended Euclidean algorithm, work backwards up the chain of remainders to express 1 as a linear combination of a and m. In this case, we have: 34 x 55 - 21 x 89
The coefficient of a in the expression from step 3 is the inverse of a modulo m. In this case, the inverse of 55 modulo 89 is 34.
To verify that the inverse is correct, multiply a and its inverse modulo m. The product should be congruent to 1 modulo m. In this case, we have:
55 x 34 = 1870
11 = 1 x 11 + 0
Since the remainder is 0, we know that 55 x 34 is a multiple of 89, so it is congruent to 0 modulo 89. Therefore, we have:
55 x 34 ≡ 0 |89|
Adding 89 to the left-hand side repeatedly until we get a number that is congruent to 1 modulo 89, we find:
55 x 34 ≡ 0 + 89 x 7 ≡ 1 |89|
Therefore, the inverse of 55 modulo 89 is indeed 34.
To practice more questions about Euclidean algorithm:
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Every year, Shannon and her sister attend 'The Nutcracker' at the Arcadia Ballet. Last year, orchestra seating cost $50 per ticket. This year, each ticket was 14% more expensive. What was the cost of each ticket this year?
Answer:
$57
Step-by-step explanation:
14% of $50 is:
.14 × 50
= 7
This means the ticket was $7 more.
The price was $50 + $7
Each ticket cost $57.
Complete the following activity by identifying the location of the muscles, bones, and sensory organs.
Part One
1. Label each of the following body parts on the two pictures below: muscles, bones, and sensory
organs.
2. In the space provided, describe the function of each body part you labeled.
Name: Date:
Lesson 13.04: Building Muscles
Lesson Assessment: Building Muscles
Muscles:
Bones:
Sensory organs:
Muscles:
Part Two
In the space provided, describe how the bones, muscles, and sensory organs all work together.
I can give you with a general explanation of the functions of muscles, bones, and sensitive organs, as well as how they work together.
Muscles are responsible for movement and give the force needed to move bones. They're attached to bones via tendons and work in dyads or groups to produce coordinated movement. Muscles are also responsible for maintaining posture and generating heat.
Bones give a rigid frame for the body, cover internal organs, and serve as attachment points for muscles. They also store minerals similar as calcium and produce blood cells in the bone gist.
sensitive organs, similar as the eyes, cognizance, nose, and skin, descry and respond to stimulants in the terrain. They transmit information to the brain, which processes the information and generates an applicable response.
All three body corridor work together in the musculoskeletal system to produce movement, maintain posture, and respond to external stimulants. Muscles attach to bones and work together to produce coordinated movement. sensitive organs descry stimulants in the terrain and transmit information to the brain, which coordinates muscle movement and generates a response. Bones give the rigid frame and attachment points for muscles, as well as cover internal organs.