(a) The distribution of Y is P(Y = y) = (12^y * e^-12)/y!
(b) E(Y) = 12.
The random variable X is distributed as Bernoulli(p). Given X = x the random variable Y ~ Poisson(12) for 1> 0.
(a) The distribution of Y ~ Poisson(12) is given by:
P(Y = y) = (12^y * e^-12)/y!
(b) The expected value of a Poisson distribution is simply the mean, which in this case is 12. Therefore, E(Y) = 12.
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What is the constant of proportionality between
�
yy and
�
xx in the graph?
The response to the given question would be that The slope of the line is the constant of proportionality if the graph is a straight line through the origin.
what is proportionality?Partnerships that have the same ratio across time are said to be proportional. For instance, how many trees there are in an orchard and how many apples there are in a harvest of apples are determined by the average number of apples per tree. Proportional in mathematics refers to a linear connection between two numbers or variables. As the first quantity doubles, so does the other. When one of the variables drops to 1/100th of its previous value, the other also decreases. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two quantities stays the same at all levels. As an example, consider the diameter and circumference of a circle.
It is difficult to estimate the constant of proportionality between two variables, y and x, without first viewing the graph.
Nevertheless, the constant of proportionality may be calculated by dividing any y-value by its corresponding x-value if the two variables are directly proportional, which means that when x rises, y rises as well at a consistent pace.
If y = kx, where k is the proportionality constant, then mathematically, k = y/x at every point on the graph.
The slope of the line is the constant of proportionality if the graph is a straight line through the origin.
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If the velocity of an orbiting body were increased, its orbital path would change
into a parabola or hyperbola. If this were to happen, what would happen to the
object and its gravitational pull of the Sun?
The gravitational pull of the Sun on the object would decrease as the distance between them increased.
What is the gravitational pull?If the velocity of an orbiting body were increased, its orbital path would change from an elliptical orbit to a parabolic or hyperbolic orbit, depending on the extent of the increase in velocity.
The amount of gravitational pull on the object would decrease as the distance between the object and the Sun increased. This is because gravitational force decreases with distance according to the inverse-square law.
In summary, if the velocity of an orbiting body were increased to the point where its orbital path changed into a parabolic or hyperbolic orbit, the object would eventually escape the Sun's gravitational pull and move away from it in a straight line.
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a x=6 angle measure is 36
b x=9 angle measure is 36
c x=6 angle measure is 54
d x=9 angle measure is 54
Answer:
A
Step-by-step explanation:
6x° and 54° form the angle of 90° , that is
6x + 54 = 90 ( subtract 54 from both sides )
6x = 36 ( divide both sides by 6 )
x = 6
then
6x = 6 × 6 = 36°
An animal reserve is home to 8 meerkats. It costs the reserve $1.50 per day to feed each meerkat. Write an equation with two variables that can be used to determine the total cost of feeding the reserve's meerkats for any number of days.
Answer: Okay, so it's $8 per day to feed all of them. So one way you could answer it could be to say; "It costs $8 per day to feed all of the meerkats,..." then pick a number of days to multiply $8 by.
I hope this helps some!
3. Note this example is using weeks instead of years to calculate the interest. Mr. Lindsey is
going to start a fund for the student who completes the highest amount of classwork
assignments during the rest of the quarter. He puts in $50 at the beginning of week one and
that money will draw interest at a given rate each week for 5 weeks. At the beginning of week 3
his honey business is going so well that he puts another 25 dollars in to draw interest for the
remaining 3 weeks. He puts another 30 at the beginning of week 4.
a) Write an expression to model this situation 50/5)
b) If I paid 4% interest over that period, how much money would the winner get?
Answer: Your welcome!
Step-by-step explanation:
a) The expression to model this situation is (50/5) + (25/3) + (30/2). This expression represents the amount of money Mr. Lindsey has in the fund at each week, starting at $50 for the first 5 weeks, then adding $25 for the remaining 3 weeks, and then adding $30 for the last 2 weeks.
b) If 4% interest is paid over the period, the winner of the fund will get a total of $70.14. This is calculated by multiplying the expression from part a) by 1.04 (1.04 = 1 + 4%) to get the total amount of money in the fund at the end of the period. In this case, (50/5) + (25/3) + (30/2) * 1.04 = 70.14.
Question 10 of 10 6 st Answer here 5 E Given the two similar triangles above, what is the measure of side DE?
Answer:
DE = 3
Step-by-step explanation:
What is a scale factor?A scale factor consists of two or more shapes who look the same but have different scales or measures. A scale factor of [tex]\frac{1}{2}[/tex] means that the new shape is half the size of the original.
To solve for a missing length, we can use this expression:
[tex]a^{2} +b^{2} =c^{2}[/tex]Inserting our numbers into the expression:
[tex]8^{2}+ b^{2} =10^{2}[/tex][tex]64 + b^{2} = 100[/tex]Subtract 64 from each side:
[tex](64 - 64) + b^{2} =(100-64)[/tex][tex]b^{2} =36[/tex][tex]\sqrt{36} =6[/tex]Therefore, the missing side length is 6.
Looking at the side CB, it is 10 units long. If the new shape is 5 units long, that means that the scale factor from shape 1 to 2 is [tex]\frac{1}{2}[/tex], meaning it is half its size. If the new shape is half its size, we can use this expression to solve for the missing length:
6 × [tex]\frac{1}{2}[/tex] or 6 ÷ 2 = 3Therefore, the measure of DE is 3.
A route between Guilford and Bath has a distance of 180 kilometres.
Dave drives from Guilford to Bath. He takes 3 hours.
Olivia drives the same route. Her average speed is 15 kilometres per hour faster than Dave's.
(a) How long does it take Olivia to drive from Guilford to Bath?
Give your
answer in hours and minutes
Olivia will take time of 4 hour to drive from Guilford to Bath.
Explain the relation of speed and distance?Speed is the rate at which a distance changes over time. The speed is equivalent to s = D/T if D is the object's distance in time T. The units are the same as for velocity.Let the speed of Dave be 'x' km/h
Then,
Olivia's speed = ( x + 15 )km/h
Time = 3 hours.
Distance = 180 kilometres
Using relations:
Speed = distance /time
x + 15 = 180/3
x + 15 = 60
x = 60 - 15
x = 45 km/hr.
Time taken by Olivia to drive from Guilford to Bath.
45 = 180/t
t = 180 / 45
t = 4 hours.
Thus, it take Olivia 4 hour to drive from Guilford to Bath.
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Evaluate the expression when q = 8
11q
Answer: 88
Step-by-step explanation:
Plug 8 in for q
11 x (8) = 88
Bus #7 left River Street School partially filled with students and then stopped to pick up 15 more students at the Park School. it continued its route as follows:
At the next 4 stops it dropped off two students at each stop.
Three students got off at the following stop.
The next six stops let off one student at each stop.
Ten students then got off at the Centerville after-school-program, where five kindergarten students boarded the bus.
The bus then dropped off seven kids at its last stop, leaving only the driver aboard.
How many students were on the bus when it left the River Street School? Show your work and explain your reasoning.
14 students were on the bus when it left River Street School.
To find out how many students were on the bus when it left River Street School, we need to work backwards from the end of the route and account for all the students that were picked up and dropped off along the way.
At the last stop, seven students were dropped off, leaving only the driver aboard. This means that there were 7 students on the bus before the last stop.
Before that, five kindergarten students boarded the bus at the Centerville after-school-program, which means that there were 7 - 5 = 2 students on the bus before the kindergarten students boarded.
Before that, ten students got off at the Centerville after-school-program, which means that there were 2 + 10 = 12 students on the bus before they got off.
Before that, the bus made six stops and let off one student at each stop, which means that there were 12 + 6 = 18 students on the bus before those stops.
Before that, three students got off at one stop, which means that there were 18 + 3 = 21 students on the bus before that stop.
Before that, the bus made four stops and dropped off two students at each stop, which means that there were 21 + (4 x 2) = 29 students on the bus before those stops.
Finally, before that, the bus picked up 15 students at the Park School, which means that there were 29 - 15 = 14 students on the bus when it left River Street School.
14 students were on the bus when it left River Street School.
Starting from the end of the route and working backwards, we accounted for all the students that were picked up and dropped off along the way. By subtracting the number of students that were picked up from the number of students that were on the bus at each stop, we were able to find out how many students were on the bus when it left River Street School.
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Spring fever! Epidemiologists and teachers alike have noticed the cyclic occurrence of the dreaded spring fever. Students afflicted with this disease exhibit certain listlessness in class, and they seem to stare out the windows with remarkable tenacity. At Metro University, teachers have been monitoring the situation and diagnosing spring fever. Their observations began with week 0, the first week in April. The teachers’ data are shown in the following table:
Spring Fever Cases: Raw Data Week Newly Diagnosed with SF No SF Diagnosed
0 0 1,025
1 105 920
2 180 740
3 390 350
4 325 25
For weeks 1–4, fill out the table below. Calculate the incidence and prevalence, show your fractions and answers in the table, and round to the nearest thousandths decimal place. (0.000)
Therefore, teachers should anticipate the greatest increase in spring fever during the 4th week.
A) Spring Fever: Incidence and PrevalenceWeek New Cases Total Cases So Far Individual at Risk at Start of Week Weekly Incidence Prevalence
1 105 105 920 0.102 0.102
2 180 285 740 0.196 0.278
3 390 675 350 0.527 0.659
4 325 1000 25 0.929 0.976
B) Spring Fever: Incidence and Prevalence per 100
Week Weekly Incidence per 100 Prevalence per 100
1 10.2 per 100 10.2 per 100
2 19.6 per 100 27.8 per 100
3 52.7 per 100 65.9 per 100
4 92.9 per 100 97.6 per 100
C) The 4th-week incidence is much higher, indicating an increase from 0.527 in the 3rd week to 0.929 in the 4th week.
Therefore, teachers should anticipate the greatest increase in spring fever during the 4th week.
Incidence= Number of new cases at particular week/total number of cases in that week
Prevalence= Total number of cases diagnosed/total number of subjects
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Determine the range of the function \( y=\sec (\pi x-4 \pi)-3 \). The range of the function is (Type your answer in interval notation.)
Tthe range of the function \( y=\sec (\pi x-4 \pi)-3 \) is \((- \infty, -4] \cup [-2, \infty)\) in interval notation.
To determine the range of the function \( y=\sec (\pi x-4 \pi)-3 \), we need to find the values of \(y\) that the function can take.
First, let's consider the range of the function \(y=\sec(\theta)\). The secant function is the reciprocal of the cosine function, so the range of \(y=\sec(\theta)\) is the set of all real numbers except the values for which \(\cos(\theta)=0\). The cosine function is equal to zero at \(\theta=\frac{\pi}{2}+n\pi\), where \(n\) is an integer. Therefore, the range of \(y=\sec(\theta)\) is \((- \infty, -1] \cup [1, \infty)\).
Now, let's consider the transformation of the function. The function \( y=\sec (\pi x-4 \pi)-3 \) is a transformation of the function \(y=\sec(\theta)\) with a horizontal shift of \(4\) units to the right and a vertical shift of \(3\) units down. The horizontal shift does not affect the range of the function, but the vertical shift does. The range of the function \( y=\sec (\pi x-4 \pi)-3 \) is \((- \infty, -4] \cup [-2, \infty)\).
Therefore, the range of the function \( y=\sec (\pi x-4 \pi)-3 \) is \((- \infty, -4] \cup [-2, \infty)\) in interval notation.
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Angela used (1)/(5) of her beads to make some bracelets. She gave 78 beads to Santiago and had (1)/(2) of the beads left. How many beads did Angela have left?
If Angela used 1/5 of her beads and gave 78 to Santiago, she would have 130 beads left.
To find out how many beads Angela had left, we need to first find out how many beads she started with. We can do this by using the information given in the question and setting up an equation. Let's let x represent the number of beads Angela started with.
According to the question, Angela used (1)/(5) of her beads to make bracelets, so she had (4)/(5) of her beads left. She then gave 78 beads to Santiago, which left her with (1)/(2) of her original number of beads. We can write this as an equation:
(4)/(5)x - 78 = (1)/(2)x
To solve for x, we can first multiply both sides of the equation by 10 to get rid of the fractions:
8x - 780 = 5x
Next, we can subtract 5x from both sides of the equation to isolate the variable:
3x = 780
Finally, we can divide both sides of the equation by 3 to find the value of x:
x = 260
So Angela started with 260 beads. We proceed to find out how many you have left:
P = (1/2)(260)
P = 130
So Angela had 130 beads left after giving 78 beads to Santiago.
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When 508,000,000 is written in scientific notation, what will be the value of the exponent?
Step-by-step explanation:
When 508,000,000 is written in scientific notation, it will be represented as:
5.08 x 10^8
Therefore, the value of the exponent is 8.
How many milliliters of a 100:1000 solution would you need to obtain 40g of active ingredient? Select one: a. 0.4mL b. 4mL c. 400mL d. 40mL
To obtain 40g of active ingredient from a 100:1000 solution, you would need 400mL of the solution. The correct answer is option c. 400mL. A 100:1000 solution means that there are 100g of active ingredient in 1000mL of the solution. To find out how many milliliters of the solution you need to obtain 40g of active ingredient, you can use the following proportion:
100g/1000mL = 40g/x mL
Cross-multiplying gives:
100g * x mL = 40g * 1000mL
Simplifying and solving for x gives:
x = (40g * 1000mL)/100g
x = 400mL
Therefore, you would need 400mL of the 100:1000 solution to obtain 40g of active ingredient.
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Heather takes a 15 question exam. If she has an 87% chance to pick the correct answer, what is the probability of her getting exactly 12 out of 15 correct? Round your answer to two decimal places.
Provide your answer below:
The probability of Heather getting exactly 12 out of 15 correct can be found using the binomial probability formula:
P(X = 12) = (15 choose 12) * (0.87)^12 * (0.13)^3
= (15! / (12! * 3!)) * (0.87)^12 * (0.13)^3
= 455 * 0.087 * 0.0022
= 0.0828
Therefore, the probability of Heather getting exactly 12 out of 15 correct is 0.0828, or 8.28%.
To round this answer to two decimal places, we can use the following formula:
0.0828 * 100 = 8.28%
So the final answer is 8.28%.
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Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given.
Part A: Did either student verify the identity properly? Explain why or why not. (10 points)
Part B: Name two identities that were used in Student A's verification and the steps they appear in. (5 points)
The expression is proved by the following steps.
What is Trigonometric Functions?Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions.
The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
Part A:
student A verified the identity properly Reason student A applied the trigonometric identities
Part B:
The identities used in student A verification are
step 1: sec x = 1/cosx
cosecx= 1 /sin x
(sec x)(csc x) = cot x + tan x
Hence this above equation is proved.
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Gina Wilson unit7 homework 3
When two straight lines or rays intersect at a single endpoint then an angle is created. The vertex of an angle is that location where two points are come together.
What is the Supplementary angle?The sum of angles equal to 180° is called Supplementary Angle.
Complementary Angle, Sum of the angle is equal to 90°.
a. (10x + 7) + (4x + 5) = 180 ( Supplementary angle )
14x + 12 = 180
14x = 180 -12
x = 12
10x + 7 = 127°
4x + 5 = 53°
c. (5x -11) + (8x -3) = 90 ( Complementary Angle )
13x - 14 = 90
13x = 90 + 14
x = 8
5x - 11 = 29°
8x - 3 = 61°
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This is another math question, please help!!
Answer:
Blank 1: DE=59
Blank 2: EB=59
Blank 3: DB=118
Step-by-step explanation:
Set DE and EB equal to each other.
Solve for x.
9x-4=5x+24
-5x. -5x
4x-4=24
+4 +4
4x=28
x=7
Substitute 7 in for x.
DE: 9(7)-4=59
EB: 5(7)+24=59
DE+EB=59+59=118
1. Find the domain of the equation (
a) √(x + 2) - √2 = 2x b) sin^3 x = sin x + 1 c) tan x + cot x = sin x d) x+1 / x^2 -1 + cos x = csc x 2. Simplify each expression using the fundamental ident (a) (sin^2 θ) / (sec^2 θ -1)
(b) (1 / (1 + tan^2 x) + (1 / (1 + cot^2 x)
(c) 1 – (cos^2 x / 1 + sin x)
(d) sin θ / cos θ tan θ
1. Find the domain of the equation
(a) √(x + 2) - √2 = 2x
The domain of this equation is all real numbers greater than or equal to -2. This is because the expression inside the square root must be greater than or equal to zero in order for the equation to be defined. Therefore, x + 2 ≥ 0, which simplifies to x ≥ -2.
(b) sin^3 x = sin x + 1
The domain of this equation is all real numbers. This is because the sine function is defined for all real numbers.
(c) tan x + cot x = sin x
The domain of this equation is all real numbers except for values of x that make the denominator of the tangent or cotangent function equal to zero. These values are x = nπ, where n is any integer. Therefore, the domain is all real numbers except for multiples of π.
(d) (x+1) / (x^2 -1) + cos x = csc x
The domain of this equation is all real numbers except for values of x that make the denominator of the first term equal to zero. These values are x = 1 and x = -1. Therefore, the domain is all real numbers except for 1 and -1.
2. Simplify each expression using the fundamental identities
(a) (sin^2 θ) / (sec^2 θ -1)
Using the fundamental identity sec^2 θ = 1 + tan^2 θ, we can simplify the denominator to get:
(sin^2 θ) / (tan^2 θ)
Using the fundamental identity tan^2 θ = (sin^2 θ) / (cos^2 θ), we can simplify the expression further to get:
(cos^2 θ)
(b) (1 / (1 + tan^2 x) + (1 / (1 + cot^2 x)
Using the fundamental identities tan^2 x = (sin^2 x) / (cos^2 x) and cot^2 x = (cos^2 x) / (sin^2 x), we can simplify the expression to get:
(cos^2 x) + (sin^2 x)
Using the fundamental identity cos^2 x + sin^2 x = 1, we can simplify the expression further to get:
1
(c) 1 – (cos^2 x / 1 + sin x)
Using the fundamental identity cos^2 x = 1 - sin^2 x, we can simplify the expression to get:
1 - ((1 - sin^2 x) / (1 + sin x))
Distributing the negative sign and combining like terms gives us:
(sin^2 x) / (1 + sin x)
(d) sin θ / cos θ tan θ
Using the fundamental identity tan θ = (sin θ) / (cos θ), we can simplify the expression to get:
(sin θ) / ((cos θ) * ((sin θ) / (cos θ)))
Simplifying the denominator gives us:
(cos^2 θ) / (sin θ)
Using the fundamental identity cos^2 θ = 1 - sin^2 θ, we can simplify the expression further to get:
(1 - sin^2 θ) / (sin θ)
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Find all values of 1 for which det(A) = 0, using the method of this section. A=|λ-6 0 0| . |0 λ 4| . |0 5 λ-1| λ 1=_____ λ 2=_____ λ 3=_____ Fill the upper blank with the greater value of lif it exists. Fill the blank with the symbol "x" if there is no corresponding 1.
A = |λ-6 0 0| . |0 λ 4| . |0 5 λ-1| λ 1= 4.79 λ 2= 4.79 λ3 = 4.79, as the highest value of lif it exists is 4.79. therefore X=4.79
To find the values of λ for which det(A) = 0, we need to solve the equation det(A) = 0. The matrix determinant of a 3x3 matrix A is given by:
[tex]det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)[/tex]
In this case, the matrix A is:
A = |λ-6 0 0|
|0 λ 4|
|0 5 λ-1|
So, the determinant of A is:
[tex]det(A) = (λ-6)(λ(λ-1) - 4*5) - 0(0(λ-1) - 4*0) + 0(0*5 - λ*0)[/tex]
Simplifying the equation, we get:
[tex]det(A) = (λ-6)(λ^2 - λ - 20)[/tex]
Setting det(A) = 0, we can find the values of λ:
[tex](λ-6)(λ^2 - λ - 20) = 0[/tex]
This equation has three solutions:
[tex]λ 1 = 6λ 2 = (-1 + √81)/2 ≈ 4.79λ 3 = (-1 - √81)/2 ≈ -5.79[/tex]
So, the answer is:
λ 1 = 6
λ 2 = 4.79
λ 3 = -5.79
The greater value of λ is λ 2 = 4.79.
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Please help me with this math question!
Given that Line segment AB ║ LIne segment DC, and Line segment AD ║ Line segment BC,
∠ABC = 102°∠BCD = 78°∠CDA = 102°; and ∠DAB = 78°.What is the rationale for the above response?1) Note that ∠78° and ∠ABC are Supplementary Angles on the basis of angles on a straight line. Thus,
∠ABC = 180 - 78 = 102°
2) Note that ∠ABC and ∠BCD are Supplementary Angles on the basis of Adjacent Angles in a parallelogram.
Thus,
∠BCD = 180° - 102° = 78°
3) ∠CDA = 102° on the basis of Opposite angles of a parallelogram
4) ∠DAB = 78° on the basis of Opposite angles of a parallelogram
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When QuickSort splits the list exactly in half we saw that T(n) = 2T(n/2) + O(n) and then T(n) = (n lgn) by the Master Theorem. Here we're going to examine the case where QuickSort splits the list into one sublist of size an and another sublist of size (1 –a)n for some 0
The running time of QuickSort in this case is O(n log(n)), which is the same as the running time when QuickSort splits the list exactly in half.
When QuickSort splits the list into one sublist of size an and another sublist of size (1-a)n, the recurrence relation for the running time of QuickSort becomes T(n) = T(an) + T((1-a)n) + O(n). This is because the two sublists have different sizes and therefore take different amounts of time to sort.
To solve this recurrence relation, we can use the recursion tree method. The recursion tree for this recurrence relation looks like this:
```
T(n)
/ \
T(an) T((1-a)n)
/ \ / \
T(a^2n) T(a(1-a)n) T(a(1-a)n) T((1-a)^2n)
...
```
At each level of the recursion tree, the size of the subproblems decreases by a factor of a or (1-a), and the number of subproblems doubles. The work done at each level is O(n), since the partitioning step takes O(n) time.
The recursion tree has log_{1/a}(n) levels, since the size of the subproblems decreases by a factor of a at each level. Therefore, the total work done by QuickSort is O(n log_{1/a}(n)) = O(n log(n)), since log_{1/a}(n) = log(n)/log(1/a) = log(n)/(-log(a)) = -log(n)/log(a) = O(log(n)).
So the running time of QuickSort in this case is O(n log(n)), which is the same as the running time when QuickSort splits the list exactly in half.
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The table shows the dimensions of three cylinders.
Cylinders
Radius (inches)
Cylinder
W
X
Y
3
4
4.5
Height (inches)
9
2
6
Which two cylinders have the same lateral surface area in square
inches? Answer in capital letters and put them in alphabetical
order.
Cylinders X and Y have the same lateral surface area in square inches.
Which graph shows the solution to the inequality? x + 2 < -3 A) A B) B C) C D) D
Therefore , the solution of the given problem of inequality comes out to be the inequality x -5 is option B.
What does inequality imply in reality?Regardless of the equal symbol, a connection or group of numbers variables can be an inequality in mathematics. Equilibrium is always followed by equity. Inequality happens when ideals are still incompatible. Differences exist between inequality expression and fairness. We chose to utilize the most prevalent symbol because elements aren't always similar or comparable (). No mater how few or many variations there are, they can all be used to evaluate values.
Here,
Option B) B is the proper response.
We must isolate x on one side of the inequality in order to answer the inequality x + 2 -3. By taking 2 away from both edges, we arrive at:
=> x < -5
According to this inequality, x is any integer that is less than -5. Since x cannot equal -5,
we must create an open circle at this point on the number line and shade to the left of it to represent all the different values of x that could be used.
Looking at the available choices, we can see that the only graph that accurately depicts the inequality x -5 is option B) B.
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A customer is checking out at the grocery store and has filled a produce bag with 40 ounces of apples. If the store charges for apples by the pound, how many pounds of apples is the customer purchasing?
Step-by-step explanation:
such questions you can answer faster by either directly looking it up on the internet (1 pound = ... ounces), or by using the conversion or scale function on your calculator (e.g. the Windows basic calculator app has this function).
so, we find :
1 pound = 16 ounces
so, now it is easy to find how many pounds of apples were bought : every "group" of 16 ounces is 1 pound. so, we need to find how many such "groups" are in 40.
40/16 = 5/2 = 2.5 pounds.
18. Find m/BCA.
(9x + 1)
A
(5x + 12)
B
(10x-37)
C
Answer:
∠BCA 57 degrees
Step-by-step explanation:
∠ABC + (5x + 12) = 180
=> ∠ABC = 180 - (5x + 12)
∠BAC + (9x + 1) = 180
=> ∠BAC = 180 - (9x + 1)
∠BCA + (10x - 37) = 180
=> ∠BCA = 180 - (10x - 37)
∠ABC + ∠BAC + ∠BCA = 180
Substitute to find x
[180 - (5x + 12)] + [180 - (9x + 1)] + [180 - (10x - 37)] = 180
180 + 180 + 180 - 5x - 9x - 10x - 12 - 1 + 37 = 180
564 - 24x = 180
24x = 564 - 180
24x = 384
x = 384/24 = 16
Substitue x = 16
∠BCA = 180 - (10x - 37)
∠BCA = 180 - 10(16) + 37 = 57
Answer:
m∠BCA = 57°
Step-by-step explanation:
To find the measure of angle BCA we must first find the value of x.
The diagram gives expressions for the exterior angles of the triangle.
The exterior angles of a triangle sum to 360°. Therefore, to calculate the value of x, equate the sum of the exterior angles to 360° and solve for x.
⇒ (9x + 1)° + (5x + 12)° + (10x - 37)° = 360°
⇒ 9x + 1 + 5x + 12 + 10x - 37 = 360
⇒ 9x + 5x + 10x + 1 + 12 - 37 = 360
⇒ 24x - 24 = 360
⇒ 24x - 24 + 24 = 360 + 24
⇒ 24x = 384
⇒ 24x ÷ 24 = 384 ÷ 24
⇒ x = 16
Each interior and exterior angle of a triangle form a linear pair.
As the sum of angles of a linear pair is always equal to 180°, to find the measure of angle BCA, equate the sum of ∠BCA and its exterior angle to 180°:
⇒ (10x - 37)° + m∠BCA = 180°
Substitute the found value of x and solve for the angle:
⇒ (10(16) - 37)° + m∠BCA = 180°
⇒ (160 - 37)° + m∠BCA = 180°
⇒ 123° + m∠BCA = 180°
⇒ 123° + m∠BCA - 123° = 180° - 123°
⇒ m∠BCA = 57°
Therefore, the measure of angle BCA is 57°.
The library in Geotown has a large room with enough tables and chairs to seat 236 people. some of the tables are in the shape of a hexagon and seat six people each. The rest of the tables are octagonal and seat eight people each. if there are 35 tables in the room, how many are hexagons and how many are octagons?
The library in Georgetown has 35 tables, 5 of which are hexagons and 30 of which are octagons.
What are octagons?An octagon is a two-dimensional shape with eight sides and eight angles. It is a regular polygon, meaning that all of its sides and angles are equal. Octagons are often seen in everyday life, such as in stop signs, tiling, and in some types of architectural structures.
In order to answer this question, we must first solve a simple equation. We know that the total number of tables in the room is 35, and we know that each hexagonal table seats six people, while each octagonal table seats eight people. Therefore, we can set up an equation to represent the total number of people being seated at all of the tables: 6x + 8y = 236, where x is the number of hexagonal tables and y is the number of octagonal tables.
By solving this equation, we can determine that x = 5 and y = 30. This means that there are 5 hexagonal tables and 30 octagonal tables in the room. Therefore, the library in Georgetown has 35 tables, 5 of which are hexagons and 30 of which are octagons.
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Make x the subject of the formula x/a+y/b=1, hence, if a=4, b=1, y=2 evaluate x
When a = 4, b = 1, and y = 2, the value of x that satisfies the equation x/a + y/b = 1 is -4.
To make x the subject of the formula x/a+y/b=1, we can start by isolating x on one side of the equation. We can do this by subtracting y/b from both sides of the equation:
x/a = 1 - y/b
Next, we can multiply both sides of the equation by a to isolate x:
x = a(1 - y/b)
Now that we have a formula for x in terms of a, b, and y, we can evaluate x when a = 4, b = 1, and y = 2:
x = 4(1 - 2/1)
x = 4(1 - 2)
x = 4(-1)
x = -4
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NEED HELP DUE FRIDAY!!!!
Here is another triangle similar to DEF found in the lesson section labeled “Shrinking Triangles”.
• Label the triangle D”E”F”.
• What is the scale factor from triangle DEF to triangle D”E”F”?
• What are the coordinates of F”? Explain how you know.
• What are cos(D”), sin(D”), and tan(D”)?
The scale factor of dilation is 0.075 and the coordinates of F" are (0.9, 0.375)
Label the triangle D”E”F”.The label of the triangle is added as an attachment
The scale factor of the dilationFrom the complete question, we have
DE = 12 units
Then, we have
D"E" = 0.9 units
Using the above as a guide, we have the following:
Scale factor = D"E"/DE
Scale factor = 0.9/12
Scale factor = 0.075
So, the scale factor of dilation is 0.075
The coordinates of F"This is calculated as
F = Scale factor * F
So, we have
F = 0.075 * (12, 5)
F = (0.9, 0.375)
The trigonometry ratiosThe sine, cosine and tangent are calculated as
sin(D") = EF/DF
cos(D") = DE/DF
tan(D") = EF/DE
So, we have
sin(D") = 0.375/1 = 0.375
cos(D") = 0.9/1 = 0.9
tan(D") = 0.375/0.9 = 0.416
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Missing information in the question
Triangle DEF has coordinates D(0,0) E(12,0) F(12,5) and pictured is triangle D”E”F”.
DE = 0.9, EF = 0.375 and DF = 0.9
In one country, 7 out of 1,000 infants die before their first birthday. Convert this figure to a percentage. Is your answer greater than or less than 1%?
PLS NOW
Answer: 0.7% < 1%
Step-by-step explanation:
Percent is out of 100 so...
7/1000 = 0.7/100 = 0.7%
0.7% < 1% so the answer is less than 1%
Hope this helped!
