Using the slope-intercept form, the equation of the lines are
a. 2y = x + 9
b. 3y = x + 1
c. y = x - 6
d. y = x + 10
e. y = -1/2x + 1
What are the equation of line?In the given question, we have the coordinate of a point and the slope of the line.
To determine the equation of the straight line, we have to use the formula of slope-intercept which is given as; y = mx + c.
Plugging the values into the formula.
a. (3, 6) and slope = 1/2
equation of line = y = mx + c = 6 = 1/2(3) + c
6 = 3/2 + c
c = 9/2
The equation of line is y = 1/2x + 9/2 ; 2y = x + 9
b. The point is (2,1) and slope is 1/3
Equation of line is;
y = mx + c
1 = 1/3(2) + c
c = 1 - 2/3
c = 1/3
Equation of line is y = 1/3x + 1/3; 3y = x + 1
c. The point is (4, -2) and slope is 1
y = mx + c
-2 = 1(4) + c
c = -2 - 4 = -6
y = x - 6
d. The point is (-2, 8) and slope is 1
y = mx + c
8 = 1(-2) + c
c = 10
y = x + 10
e. The point is (-4, 3) and slope is -1/2
y = mx + c
3 = -1/2(-4) + c
3 = 2 + c
c = 1
y = -1/2x + 1
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Dakota is a quality control manager for a manufacturing plant that produces batteries for tablet computers. Based on prior history, Dakota knows that 0.6% of all tablet computer batteries produced are defective. He selects a random sample of n=1,200 tablet computer batteries from a recently produced lot and tests each battery to determine whether it is defective. What is the probability that Dakota finds 5 or fewer defective batteries? Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability.
Round your answer to four decimal places.
Using binomial probability, the probability is 0.8897
What is the probability that Dakota finds 5 or fewer defective batteries?Using binomial probability formula, we can determine the number of defective batteries
In this case, n = 1,200 (the sample size) and p = 0.006 (the probability of finding a defective battery).
We want to find the probability of finding 5 or fewer defective batteries, which is equivalent to finding the cumulative probability up to 5.
Let's calculate this probability:
P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
Using the binomial probability formula:
[tex]P(X = k) = C(n, k) * p^k * (1 - p)^(^n ^- ^k^)[/tex]
where C(n, k) represents the number of combinations of n items taken k at a time.
Plugging the values and solving;
P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) =
[tex]C(1200, 0) * 0.006^0 * (1 - 0.006)^(^1^2^0^0 ^- ^0^)\\+ C(1200, 1) * 0.006^1 * (1 - 0.006)^(^1^2^0^0 ^- ^1^)\\+ C(1200, 2) * 0.006^2 * (1 - 0.006)^(1^2^0^0 ^- ^2^)\\+ C(1200, 3) * 0.006^3 * (1 - 0.006)^(^1^2^0^0 ^- ^3)\\+ C(1200, 4) * 0.006^4 * (1 - 0.006)^(^1^2^0^0 ^- ^4)\\+ C(1200, 5) * 0.006^5 * (1 - 0.006)^(^1^2^0^0 ^- ^5^)[/tex]
To calculate these probabilities, we need to use a combination formula to determine the number of combinations. The combination formula is given by:
C(n, k) = n! / (k! * (n - k)!)
Now let's calculate the probability:
[tex]P(X \leq 5) = \\C(1200, 0) * 0.006^0 * (1 - 0.006)^(^1^2^0^0 ^- ^0^)\\+ C(1200, 1) * 0.006^1 * (1 - 0.006)^(^1^2^0^0 ^- ^1^)\\+ C(1200, 2) * 0.006^2 * (1 - 0.006)^(^1^2^0^0 ^- ^2^)\\+ C(1200, 3) * 0.006^3 * (1 - 0.006)^(^1^2^0^0 ^- ^3^)\\+ C(1200, 4) * 0.006^4 * (1 - 0.006)^(^1^2^0^0 ^- ^4^)\\+ C(1200, 5) * 0.006^5 * (1 - 0.006)^(^1^2^0^0 ^- ^5^)[/tex]
Using a calculator or statistical software to perform the calculations, we find that the probability is approximately 0.8897 when rounded to four decimal places
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the function g(x) is a transformation of the cube root parent function, f(x) = exponent 3 square root x, what function is g(x)?
The function g(x) in the context of this problem is given as follows:
A. [tex]g(x) = \sqrt[3]{x + 4} + 3[/tex]
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The parent function in this problem is given as follows:
[tex]f(x) = \sqrt[3]{x}[/tex]
The translated function was moved 4 units left and 3 units up, hence the function is defined as follows:
[tex]g(x) = \sqrt[3]{x + 4} + 3[/tex]
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how much time will it take to get to New Orleans by boat from Houston, Texas
Tom's estimated travel time is approximately 13.6 hours.
Based on the given scenario, Tom is traveling a distance of approximately 340 nautical miles from Houston to New Orleans by boat. He will be using a medium-sized recreational boat with an average speed of 25 miles per hour.
To estimate the time it will take for his journey, we can use the formula:
Time = Distance / Speed
Substituting the values, we have:
Time = 340 miles / 25 miles per hour
Calculating the division, we find that Tom's estimated travel time is approximately 13.6 hours.
However, it is important to note that this estimate assumes a continuous journey without considering other factors that may affect the travel time. Various elements can impact the actual duration, such as weather conditions, water currents, navigational challenges, refueling stops, and any necessary rest breaks.
Additionally, it is essential for Tom to adhere to all boating regulations and safety guidelines to ensure a smooth and secure voyage.
To obtain a more accurate estimate, Tom should consult local boating authorities, marinas, or experienced sailors familiar with the route.
They can provide valuable insights into the specific conditions and offer guidance on potential challenges that may affect the travel time. Planning for additional buffer time is also recommended to account for unforeseen circumstances and to prioritize safety during the journey.
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The complete question may be like:
Tom plans to travel by boat from Houston, Texas, to New Orleans, Louisiana. He wants to estimate the time it will take for his journey. The distance between the two cities by water is approximately 340 nautical miles. Tom will be traveling on a medium-sized recreational boat that has an average speed of 25 miles per hour. Considering normal weather conditions and assuming a continuous journey, how long will it take Tom to reach New Orleans?
Please provide an answer based on this scenario, taking into account the distance, average speed, and any other relevant factors.
NEED HELP ASAP WILL GIVE BRAINLIEST HELP!
Answer:
The correct answer is 2.
Question number 13 needs to answered
Final speed after slowing down by 15 miles per hour and reducing the speed by one third is 25 miles per hour.
Let's break down the steps to determine the final speed:
Step 1: Convert the speed from miles per minute to miles per hour.
Since you're driving one and a half miles per minute, we need to convert it to miles per hour. There are 60 minutes in an hour, so we multiply 1.5 by 60 to get 90 miles per hour.
Step 2: Slow down by 15 miles per hour.
Subtract 15 from the initial speed of 90 miles per hour, resulting in 75 miles per hour.
Step 3: Reduce the speed by one third.
To find one third of 75 miles per hour, we divide it by 3, which gives us 25 miles per hour.
Therefore, the final speed after slowing down by 15 miles per hour and reducing the speed by one third is 25 miles per hour.
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33 + 78 + 23 + 21 + 98 + 32 = ???
Answer:
The sum of 33, 78, 23, 21, 98, and 32 is 325.
Julle is selling candy bare to raise money for new band uniforms. Candy bar x sells for $2 and candy bar y sells for $3. The number of y candy bare Julla sells must be greater than or equal to three times the number of x candy bars she sells. She has at most 36 candy bars to sell. What is the maximum revenue she can make?
Answer:
n this question, you are asked how much the maximum revenue. Since candy Y sold for a higher price than candy X, that means you have to sell candy Y as much as possible.The number of candy Y must be >= 3 times candy X. Since this won't limit candy Y selling, then you can convert all 36 candy into candy Y and 0 candy X36 candy (Y) >= 0 candy(X) ----> the requirement is met.The revenue would be 36 candy Y * $3/candy Y= $108
Step-by-step explanation:
What is the value of x?
NO SPAM OR I WILL REPORT YOU AND BAN YOU IMMEDIATELY
Answer:
4.816
Step-by-step explanation:
5.66sin45 = 4.816
sin = opposite over hypotenuse
can someone answer the ones i got wrong please
When a student is selected at random, the solution for the various possible outcome would be given below as follows:
p(pass or did not study)=0.409
p(pass or did study)=0.312
p(fail and pass)= 0.201
p(pass or fail)= 1
How to calculate the possible outcome of the following given event?The formula that is used to calculate probability = possible outcome/sample space.
The total number of scores of the statistics students = 93
For p(pass or did not study):
possible outcome = 38
sample size = 93
probability = 38/93 = 0.409
For p(pass or did study):
possible outcome = 29
sample size = 93
probability = 29/93 = 0.312
For p(fail and pass):
p(fail) = 26/93
p(pass) = 67/93
probability = 26/93× 67/93
= 1742/8649
= 0.201
For p(pass or fail);
P(pass) = 67/93
P(fail) = 26/93
Probability of pass or fail = 67/93+26/93
= 93/93 = 1
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PLEASE HURRY!
The box plot shows the times for sprinters on a track team.
A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 42, 44, 50, 54, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.
Which of the following is the five-number summary for this data?
Min = 42, Q1 = 44, Median = 50, Q3 = 54, Max = 56
Min = 41, Q1 = 43, Median = 49.5, Q3 = 56, Max = 58
Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56
Min = 42, Q1 = 45, Median = 49, Q3 = 56, Max = 58
Seven numbers out of a set of nine numbers are 16, 17, 19, 19, 21, 21, and 25. If the mode of the eight numbers is 19 and the mean is 20, what are the other two numbers?
Show your work
To find the other two numbers in the set, we need to determine the missing numbers that satisfy the given conditions.
The mode of a set of numbers is the value(s) that appear(s) most frequently. In this case, the mode is given as 19, which means that 19 appears more times than any other number in the set.
The mean of a set of numbers is calculated by summing all the numbers and dividing by the total count. In this case, the mean is given as 20.
Given that the seven numbers provided are 16, 17, 19, 19, 21, 21, and 25, we can calculate the sum of these numbers:
16 + 17 + 19 + 19 + 21 + 21 + 25 = 138
To find the sum of all nine numbers in the set, we can use the mean formula:
Mean = (Sum of all numbers) / (Total count)
20 = (138 + x + y) / 9
Simplifying the equation, we have:
180 = 138 + x + y
x + y = 42
Now, since the mode is 19, we know that either x or y (or both) must be 19. Since the mode appears twice, we can assign 19 to both x and y:
x = 19
y = 19
Therefore, the other two numbers in the set are both 19.
12. Jaylee tiled his bathroom with 1.5 ft. by 1.5 ft. square tiles. Figure ABCD shows the 24 tiles he used.
A
B
1.5 ft
D15ft
What is the area of figure ABCD?
C
The area of the whole figure which is made up of 24 tiles would be = 54ft²
How to determine the total area of the tile used by Jaylee?To determine the total area of tiles used by Jaylee, the area for a single tile with a square shape should first be calculated with the formula given below as follows;
Area of a square = a²
a= side length = 1.5ft
area = 1.5×1.5
= 2.25ft²
The total number of tiles he used = 24 tiles.
Therefore, the total area of the rules he used = 2.25×24 = 54ft²
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April can buy a package of 10 folders for $1.20 or a package of 8 folders for $1.12. What is the unit price, per folder, in each package?
Each folder in the package of 10 costs $
Each folder in the package of 8 costs $
Answer:
Step-by-step explanation:
For the package of 10 folders: Unit price = $1.20 / 10 = $0.12 For the package of 8 folders: Unit price = $1.12 / 8 = $0.14
Given the geometric sequence where a1 = −9 and the common ratio is 5, what is the domain for n?
The domain for n in the given Geometric sequence is the set of positive integers: {1, 2, 3, 4, 5, ...}.
In a geometric sequence, each term is obtained by multiplying the previous term by a constant value called the common ratio (r).
In the given geometric sequence, the first term (a1) is -9 and the common ratio (r) is 5. Therefore, the sequence can be written as:
-9, -9 * 5, -9 * 5^2, -9 * 5^3, ...
To determine the domain for n, we need to determine the values of n for which the sequence is defined. In a geometric sequence, the term number n represents the position of a term in the sequence.
In this case, the first term corresponds to n = 1, the second term corresponds to n = 2, and so on. The domain for n consists of all the positive integers starting from 1, as the sequence extends indefinitely.
Therefore, the domain for n in the given geometric sequence is the set of positive integers: {1, 2, 3, 4, 5, ...}.
the domain does not include zero or negative values, as these positions in the sequence do not exist. The sequence only starts from the first term (n = 1) and continues indefinitely in the positive integer domain.
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subtract 8.263 from 13.48.
Answer:
13.48 - 8.263 = 5.217
Answer:5.217
Step-by-step explanation: caculate it
[tex]3^a = 9^b = 27^c[/tex] and a, b, and c don’t equal 0, what is [tex]\frac{a}{b} + \frac{b}{c} + \frac{c}{a}[/tex]
To solve the expression [tex]\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a}\\[/tex] given the conditions [tex]\large\sf\:3^a = 9^b = 27^c\\[/tex], we can use logarithmic properties and the fact that [tex]\large\sf\:3^2 = 9\\[/tex] and [tex]\large\sf\:3^3 = 27\\[/tex].
Let's start by finding the values of a, b, and c using logarithmic properties:
Taking the logarithm of both sides of [tex]\large\sf\:3^a = 9^b\\[/tex], we get:
[tex]\large\sf\:\log_3(3^a) = \log_3(9^b)\\[/tex]
Applying the power rule of logarithms, we can bring down the exponents:
[tex]\large\sf\:a\log_3(3) = b\log_3(9)\\[/tex]
Since [tex]\large\sf\:\log_3(3) = 1[/tex] and [tex]\large\log_3(9) = 2\\[/tex], we simplify to:
[tex]\large\sf\:a = 2b\\[/tex] ---- (1)
Similarly, taking the logarithm of both sides of [tex]\sf\:9^b = 27^c\\[/tex], we get:
[tex]\large\sf\:b\log_3(9) = c\log_3(27)\\[/tex]
Using the values of [tex]\sf\:\log_3(9)\\[/tex] and [tex]\sf\:\log_3(27)\\[/tex] as before, we have:
[tex]\large\sf\:b(2) = c(3)\\[/tex]
Simplifying, we get:
[tex]\large\sf\:2b = 3c\\[/tex] ---- (2)
Now, let's substitute the value of b from equation (1) into equation (2):
[tex]\large\sf\:2(2b) = 3c\\[/tex]
[tex]\large\sf\:4b = 3c\\[/tex]
Rearranging, we find:
[tex]\large\sf\:c = \frac{4b}{3}\\[/tex] ---- (3)
We now have expressions for a, b, and c in terms of b. Let's substitute these into the expression [tex]\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a}\\[/tex]:
[tex]\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a} = \frac{2b}{b} + \frac{b}{\frac{4b}{3}} + \frac{\frac{4b}{3}}{2b}\\[/tex]
Simplifying further, we get:
[tex]\large\sf\:\frac{2}{1} + \frac{3}{4} + \frac{2}{3}\\[/tex]
Finding the common denominator and combining the fractions, we have:
[tex]\large\sf\:\frac{24}{12} + \frac{9}{12} + \frac{8}{12}\\[/tex]
Adding the fractions together, we obtain:
[tex]\large\sf\:\frac{24 + 9 + 8}{12} = \frac{41}{12}\\[/tex]
Therefore, [tex]\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a} = \frac{41}{12}\\[/tex].
Results:
1. Machine A costs the most but offers the highest increase in coffee output. Operating the machine can be difficult, so employees will need training.
2. Machine B costs $100 less than machine A, produces acceptable coffee output, and is simple to use. No training is required.
3. Machine C costs the least, produces slightly less than the current machine, and is simple to use. No training is required.
11
Select the correct answer from each drop-down menu.
Complete the sentence to tell why the writer has created this proposal.
The writer has written the proposal to
A) determine which kind of coffee most people like
B) compare different coffee makers before making a purchase
C) analyze the budget for buying a new coffee maker
Answer:
Step-by-step explanation:
imagine copy and pasting your question.
The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company:
Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 6, 0. The vertex is at 3, 120.
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?
Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent?
Part C: Describe the constraints of the domain.
The Domain of the function would be the interval [0, 6].The increasing interval represents the point where the company is pricing the pens appropriately, resulting in increasing profit.Average rate of change = (f(5) - 120) / (5 - 3)
Part A:
The x-intercepts of the graph, located at the ordered pairs (0, 0) and (6, 0), represent the points where the profit function intersects the x-axis. In the context of the problem, these x-intercepts indicate the price values at which the company sells pens, resulting in zero profit. When the price is $0, the company does not make any profit, and when the price is $6, the company also does not make any profit. The x-intercepts represent the break-even points where the company covers its costs but does not generate any profit.
The maximum value of the graph, located at the vertex (3, 120), represents the peak profit achieved by the company. The vertex is the highest point on the graph and indicates the optimal price at which the company can maximize its profit. In this case, when the price of pens is $3, the company achieves a maximum profit of $120.
Regarding the intervals of increasing and decreasing profit, the function is decreasing to the left of the vertex (3, 120) and increasing to the right of the vertex. This means that for prices less than $3, the profit decreases, and for prices greater than $3, the profit increases. The decreasing interval represents the point where the company is pricing the pens too low, resulting in decreasing profit. The increasing interval represents the point where the company is pricing the pens appropriately, resulting in increasing profit.
Part B:
To find the approximate average rate of change of the graph from x = 3 to x = 5, we need to calculate the slope of the line segment connecting the two points. The average rate of change represents the average amount by which the profit changes per unit increase in price over the given interval.
Using the coordinates (3, 120) and (5, f(5)) on the graph, we can determine the change in profit and price:
Change in profit = f(5) - 120
Change in price = 5 - 3
Substituting the values of the points into the equation, we can calculate the approximate average rate of change:
Average rate of change = (f(5) - 120) / (5 - 3)
Part C:
The constraints of the domain refer to the limitations or restrictions on the values that x (the price of pens) can take. Based on the given information, the x-intercepts of the graph are at (0, 0) and (6, 0), indicating that the price cannot be negative or exceed $6. Therefore, the domain of the function would be the interval [0, 6]. The constraint is that the price of the pens must be within this range for the profit function to be applicable.
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Note the full question may be :
A bakery sells cupcakes for $2 each. The bakery's total revenue from selling cupcakes is given by the function R(x) = 2x, where x represents the number of cupcakes sold.
Part A: What does the x-intercept of the graph of R(x) represent? Explain its significance in the context of the bakery's revenue.
Part B: What is the slope of the graph of R(x)? Interpret the meaning of this slope in terms of the bakery's revenue and the price of cupcakes.
Part C: If the bakery wants to maximize its revenue, what should be the ideal number of cupcakes to sell? Explain your answer based on the graph of R(x).
In the figure below, S is the center of the circle. Suppose that JK = 16, MP= 8, LP = 2x + 4, and PS= 3.5. Find the
following.
The measure for NS is 3.5 cm and the value of x is 2.
We have,
JK = 16, MP= 8, LP = 2x + 4, and PS= 3.5.
Since PS is perpendicular to ML then
MP = LP
So, 8 = 2x+ 4
2x = 8-4
2x= 4
x= 4/2
x= 2
Now, ML = MP + PL = 16
and, JK = ML= 16
Then, NS = PS
NS = PS = 3.5 cm
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
The value of x in the given right triangle HJK include the following: C. 10.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):
Hypotenuse, x = 5 × 2
Hypotenuse, x = 10.
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Use the given proof to answer the question below:
Given ABCD is a parallelogram.
Prove: ADCB
D
A
1
2
3
4
S
6
Statements
ABCD is a parallelogram
ABI CD and AD IBC
and
AC = AC
ADCA ABAC
AD CB
Which of the options below complete the proof?
A. Statement 3: LBACZCAD and ZBCA LDCA
Reason 5: A.A.S. Postulate
B. Statement 3: LBACCAD and ZBCA = LDCA
Reason 5: A.S.A Postulate
C. Statement 3: LBAC LDCA and LBCA LDAC
Reason 5: A.A.S. Postulate
D. Statement 3: ZBAC LDCA and LBCA LDAC
Reason 5: A.S.A Postulate
Reasons
Given
Definition of parallelogram
Alternate interior angles theorem
Reflexive property
C.P.C.T.C.
The correct option is D.
Given that ABCD is a parallelogram, we need to prove AD ≅ CB.
So,
Properties of a parallelogram =
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Statement Reason
1. ABCD is a parallelogram Given
2. AB║CD and AD║BC Definition of parallelogram
3. ∠BAC ≅ ∠DCA and ∠BCA ≅ ∠DAC Alternate interior angles theorem
4. AC ≅ AC Reflexive property
5. ΔBAC ≅ ΔDCA A.S.A Postulate
6. AD ≅ CB CPCTC
Hence the correct option is D.
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23 POINTS PLS HELPPP!!!
Use the Law of Sines to find the length of side b in ABC. Round to the nearest tenth. Show your work.
Consider
ABC.
B
28°
112°
37
Angle C of the triangle measures 40°.
Side AC = 18.84
Side AB= 25.79
Given triangle,
∠A = 112°
∠B = 28°
BC = 37
Now,
Sum of all the interior angles of triangle is 180.
So,
∠A + ∠B +∠C = 180°
112° + 28° + ∠C = 180°
∠C = 40°
Now,
According to sine rule,
Ratio of side length to the sine of the opposite angle is equal.
Thus,
a/SinA = b/SinB = c/SinC
Let,
BC = a
AC = b
AB = c
So,
a/Sin112 = b/Sin28 = c/Sin40
37/0.921 = b/0.469 = C/0.642
Solving,
AB = c = 25.79
AC = b = 18.84
Thus with the properties of triangle side length and angles can be calculated.
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Which is the equation for the function shown? A parabola that opens upward graphed on a coordinate plane. The vertex is negative 1, negative 2, and the parabola passes through the points negative 3, 2, and 1, 2. A. f(x) = (x − 1)2 + 2 B. f(x) = (x + 1)2 − 2 C. f(x) = (x − 2)2 + 1 D. f(x) = (x + 2)2 − 1
The equation for the function shown is f(x) = (x + 1)² - 2. Option B
How to determine the equationFrom the information given, we have the deductions;
The vertex of the parabola is given as (-1, -2)
Using the form;
f(x) = a(x - h)^2 + k
Such that (h, k) represents the vertex coordinates.
Substitute the vertex coordinates into formula, we get;
f(x) = a(x - (-1))² + (-2)
= a(x + 1)² - 2
Now, substitute the value for a, we get;
2 = a(-3 + 1)² - 2
find the square and collect like terms
4 = a(4)
a = 1
Put value back into the equation
f(x) = 1(x + 1)² - 2
Multiply the value, we get;
f(x) = (x + 1)² - 2
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"Determine the length of the line segment shown."
The length of the segment shown in the graph is 10 units
The endpoints on the line segment are : (2, - 1) and (-4,7)
Length of line segmentThe Length of a line segment can obtained using the relation :
Length = √(x2 - x1)² + (y2 - y1)²
Here,
x2 = - 4, x1 = 2, y2 = 7, y1 = - 1
Length of segment = √((-4) - 2)² + (7 - (-1))²
Length of segment = √(-6)² + (8)²
Length of segment = √36 + 64
Length of segment = √100 = 10 units
Therefore, the length of the segment on the graph shown is 10 units.
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Find the area of each shape
The area of a triangle is 24 square feet and the area of a trapezium is 50 square feet.
From the given figure, the dimensions of trapezium are parallel sides a=7 ft, b= 13 ft and height = 5 ft.
Here, area of trapezium = 1/2 (Sum of parallel sides)×Height
= 1/2 ×(7+13)×5
= 1/2 ×20×5
= 50 square feet
Dimensions of triangle are base = 8 ft and height = 6 ft
Area of a triangle = 1/2 ×8×6
= 24 square feet
Therefore, the area of a triangle is 24 square feet and the area of a trapezium is 50 square feet.
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May I please get a little help with this question? Thank you so much.
The y-intercept of the function is (0, c)
The coefficients b determine the horizontal shift of the parabola compared to the parent function
If a is negative, the parabola opens downward
The y-intercept of the function is (0, c).
This means that when x = 0, the y-value is equal to c.
The constant term c represents the y-coordinate of the point where the parabola intersects the y-axis.
The coefficient b determines the horizontal shift of the parabola compared to the parent function.
The value of b affects the position of the vertex and determines if the parabola is shifted to the left or right.
A positive value of b shifts the parabola to the left, while a negative value of b shifts it to the right.
If a is negative, the parabola opens downward.
The coefficient a determines the shape of the parabola.
If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The sign of a determines the direction in which the parabola faces.
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A mail distribution center processes as
many as 175,000 pieces of mail each day.
The mail is sent via ground and air. Each
land carrier takes 1500 pieces per load
and each air carrier 1250 pieces per
load. The loading equipment is able to
handle as many as 200 loads per day.
Let x be the number of loads by land carriers
and y the number of loads by air carriers. Which
system of inequalities represents this situation?
Click on the correct answer.
1500x + 1250y≥ 175,000 x+y≥200
1250x + 1500y ≥ 175,000 x+y≤ 200
1500x + 1250y≤ 175,000 x+y≤ 200
1250x + 1500y≤ 175,000 x+y≤ 200
The correct system of inequalities is 1500x + 1250y ≥ 175,000 and x + y ≥ 200, option A is correct.
We have two carriers: land carriers and air carriers.
The land carriers can transport 1500 pieces of mail per load, and the air carriers can transport 1250 pieces of mail per load.
The loading equipment at the distribution center can handle up to 200 loads per day.
To represent this situation using a system of inequalities, we can define the variables x and y as the number of loads by land carriers and air carriers, respectively.
The first inequality, 1500x + 1250y ≥ 175,000, represents the total number of pieces of mail transported per day.
The second inequality, x + y ≥ 200, represents the total number of loads.
Hence, the correct system of inequalities is 1500x + 1250y ≥ 175,000 and x + y ≥ 200.
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In the incidence matrix for this figure, what would be the element in row 1 column 5?
In the incidence matrix, the element in row 1 column 5 is determined as 1.
What is the element in row 1 and column 5?The element in row 1 column 5 is calculated as follows;
In an incidence matrix, the rows represent the vertices of the graph, and the columns represent the edges.
Since vertex 1 and vertex 5 are adjacent to each other, the value of the element in row 1 column 5 will be 1, indicating that there is a connection between vertex 1 and vertex 5.
Had it been they are not adjacent, the element would have been 0. Since there will be no connection between them in the polygon.
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Write equivalent fractions for 2 2/3 and 2 1/4 using a common denominator please hurry
The equivalent fractions for the mixed numbers, with the same denominator, are given as follows:
32/12 and 27/12.
How to obtain the equivalent fractions?The mixed numbers in the context of this problem are given as follows:
2 and 2/3.2 and 1/4.The fractions that represent each number are given as follows:
2 + 2/3 = 6/3 + 2/3 = 8/3.2 + 1/4 = 8/4 + 1/4 = 9/4.The least common factor of 3 and 4 is given as follows:
3 x 4 = 12.
Hence the equivalent fractions are given as follows:
12/3 x 8 = 32/12.12/4 x 9 = 27/12.More can be learned about equivalent fractions at https://brainly.com/question/17220365
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Find probability between 240 and 300 apples.
Answer:
47.5% (rounds to 48%)
Step-by-step explanation:
You want the probability that a tree has between 240 and 300 apples, given the distribution of numbers of apples is normal with mean 300 and standard deviation 30.
CenterThe given diagram shows the center 95% of numbers of apples lies between 240 and 360. The number between 240 and 300 is half that symmetical distribution, so is ...
95%/2 = 47.5%
The probability a tree will have between 240 and 300 apples is about 47.5%.
__
Additional comment
The figure "95%" is an approximation. A closer value is 95.45%. Hence, a closer value to the probability is 47.7%.
No rounding requirement is shown. To the nearest whole percentage point, the probability would be 48%.
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