Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. HELP ASAP!!
Answers
Answer:
KM = 10.68; angle K= 55; angle M=35
Step-by-step explanation:
Using Law of Cosine, you can find KM. Then using Law of Sines, you can find the angle of M. Find the sum of angle M and 90. Then subtract the total of that to 180 to fine angle K. (sidenote: your angle K should be bigger then angle M since the side measurement of K is larger than M.)
A correct option is option (b).
Given,
[tex]KL=6.2\\LM=8.7\\KM=x(let)[/tex]
Trigonometric ratios:
The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
The given triangle is right angle triangle then
[tex]KM^2=LM^2+KL^2\\KM=\sqrt{(8.7)^2+(6.2)^2}\\KM=\sqrt{114.13}\\ KM=10.68[/tex]
Now, calculate the angles.
[tex]\angle m=sinm\\=\frac{P}{H}\\ =\frac{6.2}{10.6}\\ m=35[/tex]
Again,
[tex]\angle k=sink\\=\frac{P}{H}\\ =\frac{8.7}{10.6}\\ k=55[/tex]
Learn more about trigonometric ratios:
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Related Questions
Please help! Brainliest if correct!
Answers
Answer:
x:(x +15)
Step-by-step explanation:
The corresponding sides that are in proportion are apparently ...
PS:PQ = PT:PR
PT = x
PR = x+15
so the proportion of interest is ...
28:40 = x:(x+15)
Identify the three similar triangles in the figure we should to name the verticals in the correct order
Answers
Answer: ΔABC ~ ΔBDC ~ ΔADB
Step-by-step explanation:
Match the degrees of each angle:
In ΔABC: ∠A = 60° , ∠B = 90° , ∠C = 30°
In ΔBDC: ∠B = 60° , ∠D = 90° , ∠C = 30°
In ΔADB: ∠A = 60° , ∠D = 90° , ∠B = 30°
Answer:
See below.
Step-by-step explanation:
Triangle ABC is similar to triangle ADB is similar to triangle BDC.
Select the correct answer.
What is the sum of
Answers
The sum of the mixed fraction numbers - 6 ⁴/₅ and 6 ⁴/₅ will be 0. Then the correct option is C.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
- 6 ⁴/₅ and 6 ⁴/₅
Convert the mixed fraction number into a fraction number. Then we have
- 6 ⁴/₅ = -34/5
6 ⁴/₅ = 34/5
Then the sum of the expressions will be given as,
⇒ - 34/5 + 34/5
⇒ 0
The sum of the mixed fraction numbers - 6 ⁴/₅ and 6 ⁴/₅ will be 0. Then the correct option is C.
More about the Algebra link is given below.
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Half of the students in a freshman class are 14 years old one third are 15 and the rest are 13 . Is the mean age greater than or less than the median age
Answers
Answer:
the mean age is greater
Step-by-step explanation:
The mean age is ...
(1/2)14 + (1/3)15 + (1/6)13 = 14 1/6
The median age is 14. (half the students are 14 or younger)
The mean age is greater.
_____
1 -1/2 -1/3 = 6/6 -3/6 -2/6 = 1/6 . . . . . 1/6 of the students are 13.
Answer:
Step-by-step explanation:
Given that half of the students in a freshman class are 14 years old one third are 15 and the rest are 13
If no of students are n, then we have
n/2 have ages as 14, n/3 as 15 and remaining n/6 as 13.
Average would be total/n
= [tex]\frac{\frac{14n}{2}+\frac{15n}{3} +\frac{13n}{6} }{n} \\=7+5+\frac{13}{6} =14.67[/tex]
Median would be middle entry when arranged in ascending order hence = 14
Mean > median
A bag contains 12 red marbles, 5 yellow marbles, and 15 green marbles. How many additional red marbles must be added to the 32 marbles already in the bag so that the probability of randomly drawing a red marble is ?
Answers
Answer:
18 red marbles.
Step-by-step explanation:
The complete question asks the probability of randomly drawing a red marble is 3/5?
Let x be the number of red marbles that must be added.
To find x we will do the following:
[tex]\frac{x+12}{x+32} =\frac{3}{5}[/tex]
=>[tex]5(x+12)=3(x+32)[/tex]
=> [tex]5x+60=3x+96[/tex]
=> [tex]2x=36[/tex]
This gives x = 18
Hence, 18 red marbles will be added to the bag.
Geometry: write a two column proof
Answers
Step-by-step explanation:
[tex]\angle1\ and\ \angle 2\ \text{are complementary}\to m\angle1+m\angle2=90^o\\\\m\angle ACX=m\angle1+m\angle2=90^o\to XA^{\to}\perp XC^{\to}[/tex]
What is the equation of the line with m = 2.5 and b = 7? A. y = −2.5x − 7 B. y = 2.5x −7 C. y = −2.5x + 7 D. y = 2.5x + 7
Answers
Answer:
y=2.5x+7
Step-by-step explanation:
You are basically being asked to use slope-intercept form for linear equations. It says y=mx+b where m is the slope and b is the y-intercept.
Plug in 2.5 for m and 7 for b giving you y=2.5x+7.
The equation is: y = mx + b
y = 2.5x + 7
so it's option D.
I really need this answer
Answers
Answer:
D
Step-by-step explanation:
If the lines are parallel, the slope of both of them are going to be the same. So if one line is 3, the other one will be too.
The answer is:
If the red line has a slope of 3, the slope of the red line will also be 3.
So, the correct option is, D. 3
Why?We need to remember that if two or more lines are parallel, they will share the same slope, no matter where are located their x-intercepts and y-intercepts, the only condition needed for them to be parallel, is to have the same slope.
So, if two lines are parallel, and one of them (the red line) has a slope of 3, the slope of the other line (the green line) will also be 3.
Have a nice day!
Find the GCF of the following numbers:
n and (n-1), where n is a natural number, greater than 1.
13 POINTS! NEED ANSWER QUICK! THANKS!!
Answers
Answer:
1
Step-by-step explanation:
The numbers are mutually prime, so the GCF is 1.
Answer:
1
Step-by-step explanation:
n-1 and n are consecutive integers.
Examples of consecutive pairs:
(7,8)
(10,11)
(100,101)
and so on...
The remainder will always be 1 when doing n divided by n-1.
n=(n-1)(1)+1.
All this is here to try to convince you that n and n-1 will only have common factor of 1.
To find the standard equation for a circle centered at the origin, we use the distance formula, since the radius measures? A. The distance from any point in the circle to the origin.B. The circumference c. The distance from any point inside the circle to the origin.D. The distance from the x-coordinate to the origin.
Answers
Answer:
A. The distance from any point in the circle to the origin
Step-by-step explanation:
The distance formula tells you that the distance (d) is related to the coordinates of two points (x1, y1) and (x2, y2) by ...
d² = (x2 -x1)² +(y2 -y1)²
For points (x, y) on the circle and (0, 0) at the origin, this becomes ...
d² = (x -0)² +(y -0)²
If we want the distance to the point (x, y) to be equal to the radius of the circle, this becomes ...
x² +y² = r² . . . . . . the standard equation of a circle centered at the origin
Answer: The distance from any point in the circle to the origin
Step-by-step explanation:
answer key
Stone Pine Corporation, a calendar year taxpayer, has ending inventory of $150,000 on December 31, 20X2. During the year 20X2, the corporation purchased additional inventory of $375,000. If cost of goods sold for 20X2 is $470,000, what was the beginning inventory at January 1, 20X2?
Answers
Answer:
beginning inventory is $245000
Step-by-step explanation:
Given data
ending inventory = $150,000
purchased additional inventory = $375,000
goods sold = $470,000
to find out
beginning inventory
solution
according to question beginning inventory is calculated by this formula i.e.
beginning inventory = ( cost of goods sold + ending inventory ) - amount of inventory purchase .....................1
now put all value cost of goods sold, ending inventory and amount of inventory purchase in equation 1 and we get beginning inventory
beginning inventory = ( cost of goods sold + ending inventory ) - amount of inventory purchase
beginning inventory = ( 470000 + 150000 ) - 375000
beginning inventory = 245000
so beginning inventory is $245000
In formulating hypotheses for a statistical test of significance, the null hypothesis is often
A) A statement of “no effect” or “no difference.
B) The probability of observing the data you actually obtained.
C) A statement that the data are all
D) 0. 0.05.
Answers
Answer:
A) A statement of “no effect” or “no difference.
A widget company produces 25 widgets a day,5 of which are defective.Find the probability of selecting 5 widgets from the 25 produced where none are defective
Answers
Answer:
1/5
Step-by-step explanation:
The probability of selecting 5 widgets from the 25 produced where none are defective is 0.2914.
To calculate the probability of selecting 5 non-defective widgets from the 25 produced.
The number of ways to choose 5 non-defective widgets:
[tex]\[ \binom{20}{5} = \frac{20!}{5!(20-5)!} \][/tex]
[tex]\[ = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{1860480}{120} \][/tex]
= 15504
The total number of ways to choose 5 widgets from the 25 produced:
[tex]\[ \binom{25}{5} = \frac{25!}{5!(25-5)!} \][/tex]
[tex]\[ = \frac{25 \times 24 \times 23 \times 22 \times 21}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{7893600}{120} \][/tex]
= 53130
The probability:
Probability = (Number of ways to choose 5 non-defective widgets)/(Total number of ways to choose 5 widgets)
[tex]\[ = \frac{15504}{53130} \][/tex]
[tex]\[ = 0.2914 \][/tex]
Complete question:
A widget company produces 25 widgets a day, 5 of which are defective. Find the probability of selecting 5 widgets from the 25 produced where none are defective.
Please help with #12
Answers
Answer:
a. 1 1/8 b. 8/9
Step-by-step explanation:
You can set this up as a proportion to solve. For part a. we know that 2/3 of the road is 3/4 mile long. 2/3 + 1/3 = the whole road, so we need how many miles of the road is 1/3 its length. Set up the proportion like this:
[tex]\frac{\frac{2}{3} }{\frac{3}{4} } =\frac{\frac{1}{3} }{x}[/tex]
Cross multiplying gives you:
[tex]\frac{2}{3}x=\frac{1}{3}*\frac{3}{4}[/tex]
The 3's on the right cancel out nicely, leaving you with
[tex]\frac{2}{3}x=\frac{1}{4}[/tex]
To solve for x, multiply both sides by 3/2:
[tex]\frac{3}{2}*\frac{2}{3}x=\frac{1}{4}*\frac{3}{2}[/tex] gives you
[tex]x=\frac{3}{8}[/tex]
That means that the road is still missing 3/8 of a mile til it's finished. The length of the road is found by adding the 3/4 to the 3/8:
[tex]\frac{3}{4}+\frac{3}{8}=\frac{6}{8}+\frac{3}{8}=\frac{9}{8}[/tex]
So the road is a total of 1 1/8 miles long.
For b. we need to find out how much of 1 1/8 is 1 mile:
1 mile = x * 9/8 and
x = 8/9. When 1 mile of the road is completed, that is 8/9 of the total length of the road completed.
This question might be confusing to me because it talks about Unknown angle problems with Algebra and I may need help on this, please.
Answers
Answer:
40 = x
Step-by-step explanation:
They reflect each other like a mirror, so set 120 equal to 3x, then simply divide by 3 to get your answer.
Each cone of the hourglass has a height of 15 millimeters. The total height of the sand within the top portion of the hourglass is 45 millimeters. The radius of both cylinder and cone is 6 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass?
Answers
Answer:
The answer is 126 seconds.
Step-by-step explanation:
Volume of the cone is given as:
[tex]\frac{1}{3} \pi r^{2} h[/tex]
Volume of cylinder is given as:
[tex]\pi r^{2} h[/tex]
We can find the total volume of the sand by adding volume of cone and volume of cylinder.
Height for cylinder is 30 mm (as we will subtract the cone height from 45mm that is 45-15=30)
Total volume of sand = [tex]\pi /3*(6^{2})*(15)[/tex] + [tex]\pi *(6)^{2}*(30)[/tex] = 1260π mm³
Given is - Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second.
So, for all the sand to drip down, it will take [tex]\frac{1260\pi }{10\pi }[/tex]= 126 seconds.
Use division of numbers in scientific notation to answer the question.
(8.64 × 104)
(2.4 × 102)
What is the quotient in scientific notation?
3.6 × 102
6.24 × 102
1.104 × 107
2.0736 × 109
Answers
Answer:
[tex]3.6*10^{2}[/tex]
Step-by-step explanation:
we have
[tex]\frac{8.64*10^{4}}{2.4*10^{2}}=\frac{8.64}{2.4}*10^{4-2}\\ \\=3.6*10^{2}[/tex]
Answer:
A) 3.6 × 10^2
Step-by-step explanation:
Got it right in the instruction on Edge 2021 ;D
The problem is in the pictures, please show step by step how to do it. Thanks! :)
Answers
Answer:
-4,-5/2
Step-by-step explanation:
2x^2+3x-20 =0
2x^2+8x-5x-20 =0
2x(x+4)-5(x+4) =0
(x+4)(2x-5) =0
Either,
x+4=0
x=-4
Or,
2x-5=0
2x=5
x=5/2
[tex]2x^2+3x-20=0\\2x^2+8x-5x-20=0\\2x(x+4)-5(x+4)=0\\(2x-5)(x+4)=0\\x=\dfrac{5}{2} \vee x=-4[/tex]
Mustafa, Heloise, and Gia have written more than a combined total of 222222 articles for the school newspaper. Heloise has written \dfrac{1}{4}
4
1
start fraction, 1, divided by, 4, end fraction as many articles as Mustafa has. Gia has written \dfrac{3}{2}
2
3
start fraction, 3, divided by, 2, end fraction as many articles as Mustafa has.
Write an inequality to determine the number of articles, mmm, Mustafa could have written for the school newspaper.
What is the solution set of the inequality?
Answers
Answer:
m + m/4 + 3m/2 > 22m > 8 . . . . m restricted to multiples of 4, perhapsStep-by-step explanation:
Let m represent the number of articles Mustafa has written. Then the total number of articles written must satisfy the inequality ...
m +m/4 +3m/2 > 22
This has solution ...
(11/4)m > 22
m > (4/11)22
m > 8 . . . . . . . . the solution to the inequality
If all the numbers are integers, and the ratios are exact, then we must have m be a multiple of 4 (that is, 4 times the number of articles Heloise wrote).
The solution set will be ...
m ∈ {12, 16, 20, 24, ...} (multiples of 4 greater than 8)
Answer:
inequality - m+ 1/4m + 3/2m > 22
solution set - m>8
Step-by-step explanation:
i promise
Please help *image attached*
Answers
Answer:x=25
Step-by-step explanation:
One line is 180 , AB equals 180 ,angle AD is 110,180-110=70
So corner O on line DC is 70 and angle CE is 60. 60+70=130
180-130=50, 2x=50,50/2=25
A country has 50 million people, 30 million of whom are adults. Of the adults, 5 million are not interested in working, another 5 million are interested in working but have given up looking for work, and 5 million are still looking for work. Of those who do have jobs, 5 million are working part time but would like to work full time, and the remaining 10 million are working full time. What is this country's labor force participation rate?
Answers
Answer:
66.7% is the answer.
Step-by-step explanation:
A country has 50 million people, 30 million of whom are adults.
Of the adults, 5 million are not interested in working.
5 million are interested in working but have given up looking for work.
5 million are still looking for work.
Of those who do have jobs, 5 million are working part time but would like to work full time, and the remaining 10 million are working full time.
Total labor force = Employed people + Unemployed people
=> 15 million+ 5 million = 20 million
The labor force participation rate is [tex]\frac{20million}{30million} \times100[/tex]
= 66.66% ≈ 66.7%.
The labor force participation rate of the country is 66.7%, calculated by dividing the number of employed and actively seeking employment individuals (20 million) by the total adult population (30 million) and multiplying by 100.
To calculate the labor force participation rate, we include only those adults who are either employed or actively seeking employment. In the given scenario, the country has 30 million adults. Out of these, 5 million are not interested in working, 5 million have given up looking for work, and there are 15 million employed (10 million full-time and 5 million part-time). Therefore, the labor force includes those employed full-time, employed part-time, and those actively looking for work, adding up to 20 million.
The labor force participation rate is calculated by dividing the number of people in the labor force (20 million) by the total adult population (30 million) and multiplying the result by 100 to convert it into a percentage:
Labor Force Participation Rate = (Number in labor force ÷ Total adult population) x 100
Labor Force Participation Rate = (20 million ÷ 30 million) x 100
Labor Force Participation Rate = (2÷3) x 100
Labor Force Participation Rate = 66.7%
Could someone check that I did this correctly? It's about complex numbers. Thank you!
Answers
Answer:
All your steps are correct. Well done!
The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? Use the portion of the standard normal table below to help answer the question.
16%
32%
34%
84%
Answers
Answer:
The answer is 16%
Step-by-step explanation:
Given a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes
so a time less than or equal to 3 hours and 20 minutes is a time 1 standard deviation OUTSIDE from the mean
Use the probability table:
The probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes
= Probability of z being outside 1 SD from mean
= 1 - Probability of z within 1 SD from mean
= 1 - 0.84
= 0.16 or 16%....
Three fourths of a gasoline storage tank is emptied by filling each of five trucks with the same amount of fuel what part of the total capacity of the storage tank did each vehicle receive
Answers
Answer:
Each vehicle received [tex]\frac{3}{20}[/tex] of the total capacity of the storage tank
Step-by-step explanation:
we know that
To find out what part of the total capacity of the storage tank that each vehicle received, divide three fourths by five
so
[tex]\frac{(3/4)}{5}=\frac{3}{20}[/tex]
therefore
Each vehicle received [tex]\frac{3}{20}[/tex] of the total capacity of the storage tank
NEED HELP WITH A MATH QUESTION
Answers
Answer:
33π square units
Step-by-step explanation:
The area of a sector is given by this formula. The larger sector angle is 2π-π/6 = 11π/6 radians.
A = (1/2)r²θ = (1/2)6²(11π/6) = 33π . . . . square units
Answer:
Area of larger sector = 33π units²
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where 'r' is the radius of circle
To find the area of circle
Here r = 6 units
Area = πr²
= π * 6²
= 36π units²
To find area of large sector
The central angle of larger sector = 360 - 30 = 330
Area of larger circle = (330/360) * area of circle
= (330/360) * 36π
= 33π units²
Use the following net to find the surface area of the solid figure it represents.
Answers
For this case we have that by definition, the surface area of a cylinder is given by:[tex]SA = LA + 2B[/tex]
Where:
LA: It is the lateral area of the cylinder
B: It is the area of the base
We have as data that:
[tex]LA = 75.36 \ cm ^ 2\\B = 28.26 \ cm ^ 2[/tex]
Substituting:
[tex]SA = 75.36 + 2 (28.26)\\SA = 75.36 + 56.52\\SA = 131.88[/tex]
Finally, the surface area is:
[tex]131.88 \ cm ^ 2[/tex]
Answer:
Option D
Answer:
The solid formed is a cylinder
The total surface area is [tex]131.88cm^2[/tex]
Step-by-step explanation:
The given net is made up of a rectangle and two circles.
The total surface area is the area of the rectangle plus the area of the two circles.
This implies that:
[tex]S.A=75.36+2(28.26)[/tex]
[tex]\implies S.A=75.36+56.52[/tex]
[tex]\implies S.A=131.88cm^2[/tex]
The rectangular surface can be folded into the curved surface of a cylinder with the two circles becoming the lid.
YO PLZ HELP ASAP!!! MARKIN BRAINIEST!!!
Answers
Answer:
My estimate would be D, if you view 0, -23 as the vertex and compare the other values, the values on D show the most similarities.
Definitely not B since it's exponential.
I SEE YALL LOOKING BUT NOT HELPING PLEASE SOMEONE
Answers
Answer:
the pitcure isnt clear.
Question about Radicals.
Answers
Answer:
Conjugate
Step-by-step explanation:
Those are conjugates. In factoring polynomials, if you have one with a + sign separating the a and the square root of b, you will ALWAYS have one with a - sign. They will always come in pairs. Same with imaginary numbers.
draw a diagram for this statement
eight percent of the 320 students like sports
use your diagram to determine the number of students who do not like sports
Answers
80% of 320 is 256
Therefore 20% is 64
Approximately 26 out of 320 students like sports. Therefore, about 294 students do not like sports.
Explanation:To draw a diagram for the given statement, we begin with understanding that the total of 320 students represents 100%. Therefore, if 8% of the students like sports, we would multiply 320 by 0.08 (or 8%).
The calculation would be:
320 * 0.08 = 25.6
However, because we cannot have a fractional student, we round this figure to 26. This implies that about 26 students like sports.
To calculate the number of students who do not like sports, subtract the number that do from the total, which is 320. That calculation would be:
320 - 26 = 294
Therefore, approximately 294 students do not like sports.
Learn more about Percentages here:https://brainly.com/question/30697911
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