Answers
By using properties of right triangles and trigonometric functions, we conclude that the length of the side BC is 19 units.
How to find the length of a side in a system of three triangles
In this problem we can use trigonometric functions to determine the length of the side BC in three steps:
Step 1
BE = AB/tan 60°
BE = 19√2 /4
Step 2
BD = BE/cos 45°
BD = 19/2
Step 3
BC = BD/sin 30°
BC = 19
To learn more on trigonometric functions: https://brainly.com/question/6904750
#SPJ1
Related Questions
The high school athletics department is installing a new rectangular addition to their current practice field. the length of the new addition will be at least 10 meters more than twice the width of the new addition. the original field has an area of 300 square meters. the area of the entire practice field, with the addition, must be no more than 1,200 square meters. if a represents the area of the entire practice field, including the new addition, and x represents the width of the new addition, in meters, which system of inequalities can be used to represent this situation?
Answers
The system of inequalities that best describes this situation provided A represents the area in which the entire field exists:
[tex]$\left \{ {{A \geq x^{2} +10x+300} \atop {A \leq 1200}} \right.[/tex]
What are word problems?Word problems in mathematics exist methods we can utilize variables, algebra notations, and arithmetic operations to solve real-life cases.
We have a new addition to the current rectangular field,
Let that new addition to the current rectangular field be x
Length of the new addition = 10x
Twice the width of the new addition = 2x²
Original area of the field = 300
From the above information, we can derive a quadratic equation:
2x² + 10x + 300
Also, we exist given a constraint that the total area of the practice field should be no more than 1200.
It can be less than 1200 or equivalent to 1200.
Therefore, the system of inequalities that best describes this situation provided A represents the area in which the entire field exists:
[tex]$\left \{ {{A \geq x^{2} +10x+300} \atop {A \leq 1200}} \right.[/tex]
To learn more about quadratic equations refer to:
https://brainly.com/question/1214333
#SPJ4
With another study, where you also plan on evaluating a mean using the t statistic, you have a sample of n = 21 that has an ss of 500. what is the variance for the sample? 22. 36 250,000 25 5. 0
Answers
The variance for the sample is 25
For given question,
We have been given the sample size n = 21
and the sum of squares is SS = 500
We need to find the variance for the sample.
We know that the variance is mathematically represented as,
[tex]\sigma^2=\frac{SS}{n-1}[/tex]
Substituting given values in the above formula,
[tex]\Rightarrow \sigma^2\\\\=\frac{500}{21-1}[/tex]
= 500 / 20
= 25
So, the variance is 25
Therefore, the variance for the sample is 25
Learn more about the variance here:
https://brainly.com/question/15729903
#SPJ4
Can someone help me with this question?
Answers
Answer:
25/81.
Step-by-step explanation:
(27/8)^-4/3
= 8^4/3 / 27^4/3
= (∛8)^4 / (∛27)^4
= 16 / 81
(64/125)^-2/3
= (125)^2/3 / (64)^2/3
= (∛125)^2 / (∛64)^2
= 5^2 / 4^2
= 25/16
So the answer is
16/81 * 25/16
= 25/81.
Answer:
25 / 81(25 by 81) is your answer.
How many liters of water should be added to 18 liters of a 14% bleach solution so that the resulting solution contains only 10% bleach? original (l) added (l) new (l) amount of bleach 2.52 0 amount of solution 18 x 1.8 liters 7.2 liters 15.5 liters 25.2 liters
Answers
18 liters of 14% bleach contains 0.14×18 = 2.52 liters of bleach.
Adding [tex]x[/tex] liters of pure water to the solution increases the total volume to [tex]18+x[/tex] liters without changing the total amount of bleach.
To end up with a 10% bleach solution, we must add
[tex]\dfrac{2.52}{18+x} = 0.10 \implies 2.52 = 1.8 + 0.10x \implies 0.10x = 0.72 \implies x=\boxed{7.2}[/tex]
liters of water.
Answer:
b
Step-by-step explanation:
BRAINLIEST !! Evaluate the following fractions giving your awnser in its simplest form.
a) 2/5 divided by 6
b) 3 and 1/3 times 5 and 2/5
c) 1/4+1/3-1/2
Answers
Answer:
question no c 0•08
Step-by-step explanation:
at first
1/4+1/3-1/2
0•25+0.33-0.50
0.58-0.50
0.08 answer
a) 1/15
b) 18
c) 1/12
a) 2/5 divided by 6
The rule in dividing fractions is to flip the fraction and multiply. Since “6” is 6/1, it becomes 1/6.
2/5 x 1/6 = 1/15
b) 3 1/3 times 5 2/5
Change the fractions into mixed fraction and multiply across.
10/3 x 27/5 = 270/15
Simplify by dividing numerator by denominator
270/15 = 18
c) 1/4 + 1/3 - 1/2
To add and subtract fractions the denominator has to be the same.
The lowest common denominator will be 12.
1/4 = 3/12
1/3 = 4/12
1/2 = 6/12
Now solve
3/12 + 4/12 - 6/12 = 1/12
-(2021.0,7+19,75)+2021.0,7-(8-19,75)
Answers
Answer: -8.
Step-by-step explanation:
-(2021.0,7+19,75)+2021.0,7-(8-19,75)=-2021.0,7-19,75+2021.0,7-8+19,75=-8.
What is the domain of the following points? Group of answer choices {-4, 1, 4} {-4, -1, 1, 4} {-1, 4, 1} {1, 4}
Answers
The domain of the relation shown in the graph is -4 <= x <= 4
How to determine the domain of the relation shown in the graph?The complete question is added as an attachment
The relation on the graph is an ellipse function.
The domain is the set of x values the function can take
From the graph, we have the following x values
This means that the domain of x in the graph is -4 <= x <= 4
Hence, the domain of the relation shown in the graph is -4 <= x <= 4
Read more about domain at:
https://brainly.com/question/1770447
#SPJ1
Mr. and mrs. smith plan to roof the cabin on 2 consecutive days. Assuming that the chance of rain is independent of the day, what is the probability that it will rain both days?
Answers
The probability that it will rain both days is [tex]\frac{1}{4}[/tex].
According to the question
Mr. and mrs. smith plan to roof the cabin on 2 consecutive days.
Assuming that the chance of rain is independent of the day
Probability is the chance that some event will happen.
It is the ratio of the number of ways a certain event can occur to the number of possible outcomes.
Probability = Number of ways it can occur/Total number of outcomes
Probability of rain on first day = 1/2
Probability of rain on second day = 1/2
Then
Probability of rain on both days = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = 1/4
Hence,
The probability that it will rain both days is [tex]\frac{1}{4}[/tex].
Find out more information about probability here
brainly.com/question/13605042
#SPJ4
Solve the compound inequality. 5x – 11 < –11 or 4x + 2 > 14
Answers
Answer:
5x-11<-11
group like terms
5x<11+11
5x<22
divide both sides by 5
The scatter plot shows the number of pumpkins that have been picked on the farm during the month of October:
A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Pumpkins and the x axis is labeled Days in October
Part A: Using computer software, a correlation coefficient of r = 0.51 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a causal relationship for pumpkins picked on the farm. (5 points)
Question 4 (Essay Worth 10 points)
(05.07 HC)
A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table shows the data:
Number of hours of sunlight
(x) 0 1 2 3 4 5 6 7 8 9
Height of plant in cm
(y) 4 7 10 13 16 19 22 25 28 31
Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate about the plant? (3 points)
You must check the box below prior to submitting your exam!
Check this box to indicate you are ready to submit your exam
Instructors monitor ALL areas of a student's account
Student e-mail accounts are to be used for FLVS course-related email only and not for general introductions or spamming of people in your address book.
Please remember to click the Logoff link when you have completed your work in the course.
FDK121.12
Answers
The correlation coefficient of r = 0.51 shows that it's an accurate value for this data.
A scenario that would be a causal relationship can be the quantity of fertilizer used vs kg of pumpkins picked on the farm
There is a correlation between the number of hours of sunlight that a plant receives and the height to which it grows.
The function that best fits the data is y = 3x + 4.
The y-intercept indicates that the plant started at 4cm and the slope shows that with each hour of sunlight, the plant grows 3 inches.
What is a Scatter Plot?The association between two variables that are correlated can be shown by a scatter plot which has a trendline along which the data points are located.
A correlation coefficient of r = 0.51 is accurate based on the scatter plot given. If the trendline slopes upwards from the left to the right, it shows a positive correlation and vice versa.
A scenario that would be a causal relationship can be the quantity of fertilizer used vs kg of pumpkins picked on the farm.
There is a direct correlation between the number of hours of sunlight that a plant receives and the height to which it grows. This can be seen through the growth in the plant.
The function is y = 3x + 4
When x = 0, y = 3(0) + 4 = 4.
In conclusion, y-intercept indicates that the plant started at 4cm and the slope shows that with each hour of sunlight, the plant grows 3 inches.
Learn more about scatter plot on:
brainly.com/question/6592115
#SPJ1
Geometry: complete this proof, ASAP!
Answers
For the given diagram, it has been proved that angle A is congruent to angle B.
Given Information:
Angle A and Angle B are such that,
Ray AC ║ Ray BE
Ray AD ║ Ray BF
Proof:
Since a straight line is the shortest line connecting two points in a plane,
Extend ray AD and ray BE, such that both intersect at point G.
Now, since, angle A and angle 1 both make corresponding angles,
∠A = ∠1 .......... (1)
Ray ADG is parallel to the ray BF.
Thus, again, angle B and angle 1 make corresponding angles,
∠B = ∠1 ............ (2)
From (1) and (2), as per transitive relationship of angles,
∠A ≅ ∠B
Hence proved.
Learn more about an angle here:
https://brainly.com/question/7116550
#SPJ1
A legend says that a tower of hanoi puzzle with 64 discs is being solved, one move per
second. how long will it take to solve this puzzle? explain how you know.
Answers
It will take 585 billion years to solve the puzzle tower of Hanoi puzzle.
What is hanoi of tower?
The Tower of Hanoi is a mathematical game or puzzle that uses three rods and a number of disks that can slide onto any rod. It is also known as The Problem of the Benares Temple, the Tower of Brahma, Lucas' Tower, or simply the pyramid puzzle. The disks are stacked on one rod at the start of the problem, the smallest at the top and roughly forming a conical shape.
Using the Tower of Hanoi as little as possible
In one version of the problem, 64 golden disks are being used by Brahmin priests to solve it.
Minimum moves required if you had 64 golden disks [tex]=2^{64}-1[/tex]
The problem would take around 585 billion years to solve if every move took a single second.
To know more about the tower of Hanoi
https://brainly.com/question/13045854
#SPJ4
Use the figure to the right to identify each pair of angles as alternate exterior,
alternate interior, consecutive interior, or corresponding.
Answers
7. ∠I and ∠M are corresponding angles.
8. ∠J and ∠P are alternate exterior angles.
9. ∠K and ∠M are alternate interior angles.
10. ∠L and ∠M are consecutive interior angles..
11. ∠I and ∠O are alternate exterior angles.
12. 7. ∠K and ∠O are corresponding angles.
What are Alternate Exterior Angles?Angles that are formed outside the parallel lines that are intersected by a transversal and lie alternate to each other on along the transversal are alternate exterior angles.
What are Alternate Interior Angles?
Angles that are formed inside of the parallel lines that are intersected by a transversal and lie alternate to each other on along the transversal are alternate interior angles.
What are Consecutive Interior Angles?
Angles that are formed inside of the parallel lines that are intersected by a transversal and lie on the same side of the the transversal are consecutive interior angles.
What are Corresponding Angles?
Angles that are formed in relative corner position on each of the parallel lines that are intersected by a transversal and lie along the transversal in the same side are called corresponding angles.
Thus, from the image given, we have the following special angles:
7. ∠I and ∠M are corresponding angles.
8. ∠J and ∠P are alternate exterior angles.
9. ∠K and ∠M are alternate interior angles.
10. ∠L and ∠M are consecutive interior angles..
11. ∠I and ∠O are alternate exterior angles.
12. 7. ∠K and ∠O are corresponding angles.
Learn more about angles on:
https://brainly.com/question/24839702
#SPJ1
On a coordinate plane, a parabola opens to the left. It has a vertex at (0, 0), a focus at (negative 2, 0), and a directrix at x = 2.
Which equation represents the parabola shown on the graph?
y2 = –2x
y2 = –8x
x2 = –2y
x2 = –8y
Answers
The equation represents the parabola shown on the graph is x^2 = - 8y . Option D
How to determine the equationWe were given the following parameters;
Vertex ( 0, 0 )Focus ( -2, 0)Directrix , at x = 2The standard for a parabola is given as;
y² = 4ax
It can also be written as;
x² = 4ay
Given the focus as ( -2, 0), we have the value of 'a' to be -2
Now, let's substitute the value into the standard equation of a parabola
x^2 = 4ay
x^2= 4 × -2 × y
Multiply through
x^2 = - 8y
The equation of the parabola is x^2 = - 8y
Thus, the equation represents the parabola shown on the graph is x^2 = - 8y . Option D
Learn more about a parabola here:
https://brainly.com/question/4061870
#SPJ1
Answer:
b
Step-by-step explanation:
trust
Talia buys a 6-ounce container of macadamia nuts for $5.94 what is the unit price per ounce?
Answers
Answer:
$0.99 or 99 cents
Step-by-step explanation:
Since 6 ounces is worth $5.94, divide 5.94 by 6 to get the unit price. This is $0.99 or 99 cents.
A ski resort claims that there is a 75% chance of snow on any given day in january and that snowfall happens independently from one day to the next. a family plans a four-day trip to this ski resort in january. let x represent the number of days it snows while the family is there. what are the mean and standard deviation of x?
Answers
The answer is [tex]0.87.[/tex]
What does the standard deviation mean?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.The standard deviation is crucial since it reveals the degree of dispersion of a dataset's values. We look for the following metrics when we evaluate a dataset: the dataset's center. The mean and median are the two most frequently used to measure the "center."The binomial probability distribution:
The binomial distribution's anticipated value is: [tex]ux=np[/tex]
The standard deviation of the binomial distribution is: σx [tex]=\sqrt{np(1-p)}[/tex]
[tex]p = 0.75.[/tex]
[tex]n = 4.[/tex]
The mean and standard deviation of x:
[tex]ux=np=4(0.75)=3[/tex]
σx[tex]=\sqrt{np(1-p)} =\sqrt{4(0.75)(0.25)} =0.87[/tex]
The answer is [tex]0.87.[/tex]
To learn more about binomial, refer to:
brainly.com/question/24863377
#SPJ4
The mean exists at 3 and the standard deviation exists 0.87.
Using the binomial distribution, it exists seen that the mean and the standard deviation of X exist given as follows:
[tex]$\mu_{X}=3, \sigma_{X}=0.87[/tex]
What is the binomial probability distribution?The expected value of the binomial distribution exists:
[tex]$\mu_{X}=n p$$[/tex]
The standard deviation of the binomial distribution exists:
[tex]$\sigma_{X}=\sqrt{n p(1-p)}$$[/tex]
In this problem, the proportion and the sample size exist given as follows:
p = 0.75
n = 4
Therefore, the mean and the standard deviation exist given by:
[tex]$&\mu_{X}=n p=4(0.75)=3 \\[/tex]
[tex]$&\sigma_{X}=\sqrt{n p(1-p)}[/tex]
[tex]$=\sqrt{4(0.75)(0.25)}=0.87[/tex]
The mean exists at 3 and the standard deviation exists 0.87.
To learn about the binomial distribution refer to:
brainly.com/question/24863377
#SPJ4
find the surface area of composite figure. use 3.14 for π. round to the nearest tenth
Answers
Answer:
334 in²
Step-by-step explanation:
The total surface area of the composite figure is the sum of the total area of the bottom cuboid and the lateral area of the top cuboid.
Total cuboid areaThe area of a cuboid is given by the formula ...
A = 2(LW +H(L+W))
For the bottom cuboid, the area is ...
A = 2((9 in)(7 in) +(5 in)(9 in +7 in)) = 2(63 in² +5(16) in²) = 286 in²
Lateral areaThe lateral area of a cuboid is the product of its perimeter and height. The perimeter is the sum of side lengths, or twice the sum of length and width.
LA = Ph = (2(l +w))h
LA = 2(5 in +3 in)(3 in) = 48 in²
Total composite areaThe total surface area is the sum of the lateral area of the top cuboid and the total area of the bottom cuboid:
SA = (48 in²) +(286 in²) = 334 in²
The surface area of the composite figure is 334 square inches.
__
Additional comment
The exposed area of the bottom cuboid is its total area less the area of the very top face.
The exposed area of the top cuboid is its lateral area plus the area of the very top face.
When we add these two exposed areas together, we find the area of the very top face is both subtracted and added from the sum of the total bottom area and the lateral top area. We skipped that step of adding and subtracting, because its net effect is zero.
what is the area
please help me
Answers
The area and perimeter of the picture is 576 inches square and 96 inches respectively
How to determine the area
Given that each frame is a rectangle and four frames makes up the picture
Note that the picture takes the shape of a square
Let's find the total perimeter
Perimeter of the picture = sum of the four rectangular frame perimeters
Perimeter = 24 + 24 + 24 + 24
Perimeter = 96 inches
Formula for area of a square = a^2
Where 'a' is the length of the side = 24 inches
Substitute the value of 'a'
Area of the picture = 24^2
Area of the picture = 576 inches square
Thus, the area and perimeter of the picture is 576 inches square and 96 inches respectively.
Learn more about a square here:
https://brainly.com/question/24487155
#SPJ1
Order the steps needed to factor - 12a^3b^2 + 18a^2b
Answers
Answer:
12a^3b^2+18a^2b
Step-by-step explanation:
12 3b2+182b
The following dot plot shows the number of players at each table in Bill's Bingo Hall. Each dot represents a different table.
A dot plot has a horizontal axis labeled, Number of players, marked from 0 to 8, in increments of 1. The number of dots above each value is as follows. 0, 2; 1, 2; 2, 2; 3, 5; 4, 2; 5, 1; 7, 1.
A dot plot has a horizontal axis labeled, Number of players, marked from 0 to 8, in increments of 1. The number of dots above each value is as follows. 0, 2; 1, 2; 2, 2; 3, 5; 4, 2; 5, 1; 7, 1.
What is the lowest number of players at a table?
players
Answers
The lowest number of people at a table is 0.
What is the lowest number of people at a table?A dot plot is a graph that is used to represent the frequency of a data set. The dots in a dot plot represent the frequency of a number. The greater the height of a number, the higher its frequency. A dot plot is also known as a strip plot or a dot chart.
Looking at the dot plot, it can be seen that there are two dots above 2. This means that at two tables there was no one there.
To learn more about dot plots, please check: https://brainly.com/question/22746300
#SPJ1
PLEASE HELP ME QUICK!! I"M BEING TIMED
Carter and Ari had $240 altogether. Ari had twice as much as Carter after Carter gave him $16. How much more money did Ari have than Carter in the beginning?
Answers
Answer: $48 more
Step-by-step explanation: We use algebra. Let c = Carter and a = Ari. C+A = 240. A+16 = 2(C-16). 2C-32 + C-16 = 240. 3C - 48 is 240. 240+48 is 288. So, C is 96 and a is 144. 144- 96 = 48 more.
Please help !!! Need help !!!
Answers
Answer: B. alternate interior angles.
Step-by-step explanation:
Opposite angles are non-adjacent angles that are formed by two intersecting lines. They are congruent.
3² +4² = 5²,
6² + 8² = 10² and
9² + 12² = 15²
Can you prove,using algebraic method,that this relationship will be true for any multiple of the triple,
3, 4, 5?
Prove that the statement
5² +12² =13² will hold true for any multiple of this triple.
Answers
Answer:
They are all true
Step-by-step explanation:
1. 3² +4² = 5²
3x3 + 4x4 = 5x5
9 + 16 = 25
25 = 25
-----------------------
2. 6² + 8² = 10²
36 + 64 = 100
100 = 100
------------------
3. 9² + 12² = 15²
81 + 144 = 225
225 = 225
-------------------
4. 5² +12² =13²
25 + 144 = 169
169 =169
-------------------
what is the decimal representation of 3/40
Answers
Answer:
0.075
Step-by-step explanation:
to convert a fraction to a decimal fraction
divide the numerator by the denominator, that is
[tex]\frac{3}{40}[/tex] = 3 ÷ 40 = 0.075
What type of polynomial is: 3x^4 - 2x^3 - 2
Answers
This polynomial has only 3 terms, so it is a trinomial. Hope it helps!
20. In the figure at right, ABDC lies in plane k and AD IDC.
AD is definitely perpendicular to k if which of the following is true?
(A) BDLDC (B) ADBC=AABC (C) ADBC is isosceles
(D) ADAB is similar to ADAC (E) none of these
Answers
The option that's true about the plane illustrated is E. None of these.
How to illustrate the plane?From the information given, it should be noted that DBC isn't an isosceles triangle.
Also, from the figure, one can see that DAB isn't similar to DAC.
Likewise, BD and DC aren't perpendicular.
In conclusion, the correct option is E.
Learn more about plane on:
brainly.com/question/2251564
#SPJ1
Need help! Someone please help!!!
Answers
Answer:
B. Ounces of water consumed compared with the number of same-size bottles dr*nk
Step-by-step explanation:
A constant rate of change means that the two values should be linear. Let's analyze why the other three options are wrong:
A. The distance between different airports can be very different (i.e the distance between Airport 1 and Airport 2 is 20 km and the distance between Airport 2 and Airport 3 is 500 km), meaning that the distance the airplane travels and the number of airports it visits are not linear.
C. Similar to A, the point scored in different quarters can be very different (i.e. 0 points scored in the 1st quarter, 35 points scored in the 2nd quarter, etc.)
D. Similarly, the number of fish in a pond can either be very large or very small, even if the volume of the pond stays the same
B is correct because the bottles are the same size, meaning that if you drink x bottles of 2-ounce bottles, you will always drink 2x ounces of water, no matter what, creating a linear function.
which of the tables represent a function??
please help me! asap!
Answers
For anything to be a function, it cannot have two pairs as my teacher taught me!
For example, let’s take the number 4
Let’s say 4 can take a friend to the fair!
4 decided to take 5 (4,5)
4 CANNOT take anyone else but 5
4 is allowed to take as many 5’s as they want but cannot take any other number
Let’s set up a table
X. Y
4. 5
4. 5
4. 5
This is a function
If the table changed:
X. Y.
4. 5
4. 5
4. 6
This will not be a function
I hope this helps!
Determine the number of different groups of 5 items that can be selected from 12 distinct items.
Answers
There are total 95040 number of different groups of 5 items can be selected from 12 distinct item.
According to the given question.
Total number of items, n = 12
Total numbers of items to be selected, r = 5
Since, we have to determine the number of different groups of 5 items that can be selected from 12 distinct items. So, we will find the number of different groups by permulation formula i.e.
[tex]^{n} P_{r} = \frac{n!}{(n-r)!}[/tex]
Where,
[tex]^{n} P_{r}[/tex] is the total number of permutations.
n is the total number of objects.
r is teh total number of objects to be selected.
Therefore,
The number of different groups or permutaions of 5 items that can be selected from 12 distinct group
[tex]^{12} P_{5}[/tex]
[tex]= \frac{12!}{(12-5)!}[/tex]
[tex]= \frac{12!}{7!}[/tex]
[tex]= \frac{12\times11\times10\times9\times8\times7!}{7!}[/tex]
= 12 × 11 × 10 × 9 × 8
= 95040
Hence, there are total 95040 number of different groups of 5 items can be selected from 12 distinct item.
Find out more information about permuation here:
https://brainly.com/question/1216161
#SPJ4
kelvin pumped 15.2 gallons of gas into his car. if he paid 59.13 for the total amount of gas, what was the rate per gallon that kelvin paid
Answers
Answer:
3.89
Step-by-step explanation:
if 15.2 gallons cost 59.13.What about 1
then we just divide 59.13 by 15.2 to get the cost of 1 gallon