Given:
The ratio of the measures of the angles of a triangle is 1:2:3.
To find:
The measures of each angle.
Solution:
Let the measure of angles be x, 2x and 3x respectively.
We know that, sum of all the interior angles of a triangle is 180 degrees by the angle sum property.
Using angle sum property, we get
[tex]x+2x+3x=180^\circ[/tex]
[tex]6x=180^\circ[/tex]
Divide both sides by 6.
[tex]x=\dfrac{180^\circ}{6}[/tex]
[tex]x=30^\circ[/tex]
Now,
First angle: [tex]30^\circ[/tex]
Second angle: [tex]2(30^\circ)=60^\circ[/tex]
Third angle: [tex]3(30^\circ)=90^\circ[/tex]
Therefore, the measure of all the angles are 30°, 60° and 90° respectively.
Find the value of an investment of $15,000 for 13 years at an annual interest rate of 4.55% compounded continuously.
Answer:
A = $27100.5
Step-by-step explanation:
We are given;
Principal: P = $15,000
Interest rate: r = 4.55% = 0.0455
Time in years: t = 13 years
The formula for the value of the investment after t years of continuous compounding is;
A = P(e^(rt))
A = 15000(e^(0.0455 × 13))
A = 15000 × 1.8067
A = $27100.5
At time T equals zero, water begins to drip out of the pipe into an empty bucket. After 42 minutes, there are 6 inches of water in the bucket. Right Ellen air function rule to model how many inches of water W are in the bucket after any number of minutes T.
the values of 'm' and 'b' are 0.5 and 0 respectively.
Step-by-step explanation:
What is this? Please answer if u know what u are doing oh and thank you for reading this
Compare -4 ____ -12 9 ___ -35
when you multiply 2/3 by a fraction less than one,how does the product compare to the factors?
Answer:
The product is less than either of the factors. Multiplying a number < 1 with 2/3 another number < 1, will give a fraction of a fraction, and part of a fraction is an even smaller fraction. Another way of looking at it: Fractions less than one have numerators smaller than their denominators. When multiplying fractions, you multiply across, so multiplying two fractions that are both less than one will always give a numerator much smaller than the denominator, and a larger denominator makes for a smaller number. I hope this helps, but if you have questions, ask.
Simplify 7(2+5) using Distributive Property
Answer:
[tex]\huge\boxed{\boxed{49}}[/tex]
Step-by-step explanation:
Hello.
In order to simplify this expression, we need to add
2+5, which is equal to 7
Multiply that times 7:
49
And we're done!
I hope it helps & have an outstanding day!
~ST2710 :)
Select the point on the graph that matches the value of
20/9
Answer:
The dot just past 2.
Step-by-step explanation:
It's the dot right next to 2,
2.2
Please help UwU
also hope your day is going GREAT
if correct i will give BRAINIEST
Answer:
b bro and u get a good day too
Answer:
Pretty sure its C >:]
Explanation:
It's the third option because if you put a piece of paper in the corner its a lil more than 90 degrees, so it wouldn't be B (there's a little more white space left). And it obviously wouldn't be A because that's self explanatory, lol.
And you can't make a perfect square in the inside of the angle so that's another way to tell.
Extra:
I hope you have an amazing day too,, you seem very nice ^-^ good luck on your schoolwork today :]
Hello! :)
Please help me answer this question ! And explain how you answers it. I will give brainslt :)
Answer:
1. False
2. False
3. True
Step-by-step explanation:
1. It fails the 'Vertical Line Test.' Draw a line through the center of the relation and see if the line passes through the graph more than once. It does, therefore it fails the test. Meaning it is not a function.
2. Domain (x) is all the x-values in the equation, the relation only contains the x-values x>0 and x<7 (0 - 7). Meaning it does not contain all real numbers.
3. The range (y) contains negative numbers because the relation is partially in the 4th quadrant, meaning it MUST contain a negative y-value.
The harbormaster decides how many trips the ferry needs to
make for 37 cars. The ferry can carry 8 cars at a time. How many trips does the ferry need to make so that all cars can cross the harbor?
Answer:
The ferry needs to make 5 trips.
Step-by-step explanation:
All we need to do is divide the numbe of trips by how many cars at a time.
37 ÷ 8 = 4.62500
4.62500 ≈ 5
Jayden budgets $400 of his $3,200 monthly income towards donations. What percent of his income does he donate each month?
Answer:
12.5%
Step-by-step explanation:
400 divided by 3200= .125
.125 x 100= 12.5
12.5%
If the empire state building stands at around 1,454 feet and something is born every 0.00000000000000000000005 second how long is the average toenail length for a standard bridge troll? (I'm asking for a friend of mine..)
Answer:
Length = 0
Step-by-step explanation:
The bridge troll is tearing his toe nails up climbing the Empire State Building.
Solve this mattistep equation
SHOW YOUR WORK
f. (t + 3) = 40
Answer:
t=37
Step-by-step explanation:
t+3=40
Step 1: Subtract 3 from both sides.
t+3−3=40−3
t=37
10.) Which equation below represents the model? A. m - 11 = 43 B. 11m = 43 C. m + 11 = 43 D. m + 43 = 11.) What is the value of m? A. m = 32 B. m = 54 C. m = 4 D. m = 29 Use the model below to answer questions 12 and 13. С -8 -14
Answer:
A
Step-by-step explanation:
m - 11 = 43
Please hurry I need this fast
Answer:
C
Step-by-step explanation:
Answer:a
Step-by-step explanation: a
Jesse is traveling up and down a stream in a kayak. He can paddle the kayak at an average rate of 5 miles/hour, and the round-trip is a total distance of 16 miles. When cis
the speed of the current, this expression can be used to find the difference of the time it takes Jesse to travel upstream (against the current) and downstream (with the
current).
8/5-c - 8/5+c
Find the difference in simplest form.
Answer:
16c
Step-by-step explanation:
The simplest form is: [tex]\frac{16c}{25-c^2}[/tex].
Total distance = 16 miles.
So each distance = 16/2=8 miles.
Given: He can paddle the kayak at an average rate of 5 miles/hour.
And the speed of the current is = c
So the speed while going up = (5-c)
The speed while going down=(5+c).
So the time while going up = [tex]\frac{8}{5-c}[/tex]
The time while going down=[tex]\frac{8}{5+c}[/tex].
So the difference is:
[tex]\frac{8}{5-c}-\frac{8}{5+c}\\=\frac{8(5+c)}{(5-c)(5+c)}- \frac{8(5-c)}{(5-c)(5+c)}\\=\frac{8(5+c)-8(5-c)}{(5-c)(5+c)}\\=\frac{40+8c-40+8c}{(5-c)(5+c)}\\=\frac{16c}{(5-c)(5+c)}\\=\frac{16c}{25-c^2}[/tex]
Learn more: https://brainly.com/question/6237128
an ancient atifact is 4 time older then an anitque book
Find the average rate of change for the given function
from x = -1 to x = 5. (4 points)
NEED EXPLAINING THX
Answer:
- 1
Step-by-step explanation:
All you need to do is find the slope. How you do that is y2-y1/x2-x1
Yours would look like this:
[tex]\frac{1-7}{5-(-1)}=\frac{-6}{6}[/tex]
Then you simplify to get -1
Please help me solve this question will give you braisnlt !
Answer:
C
Step-by-step explanation:
In slope intercept form y=mx+b
m is your rate of change/ slope
since the slope is +5
This means that your rate of change, in this case elevation, is 5 feet per minute.
As for b which is your y intercept, the -30 can be represented by the point (0,-30) on a graph it would be -30ft below the x axis. Meaning that if the diver lets say is the point he is 30 feet below sea level and acsending at a rate of 5 feet per minute.
Find (x + 3) (x^2 – 2x – 8).
Answer:
(x−4)(x+2)(x+3
i think
Answer:
x^3 +x^2 -14x -24
Step-by-step explanation:
Use distributive property:
x(x^2)+x(-2x)+x(-8)+3(x^2)+3(-2x)+3(-8)
x^3 -2x^2 -8x +3x^2 -6x -24
x^3 +x^2 -14x -24
Answer the questions
1.find the value of x
2.find m
3.finds
Answer:
x = 13°
Step-by-step explanation:
m<EGF + m< FGH = m<EGH
or, 3x+6+5x-7 = 103°
or, 8x-1 = 103°
or, 8x = 103°+1°
or, x = 104°/8
or, x = 13°
Now,
m<EGF = 3x+6
= 3×13+6
= 39+6
= 45
m<FGH = 5x-7
= 5×13-7
= 65-7
= 58
Lin is shopping for a couch with her dad and hears him ask the salesperson, “How much is your commission?” The salesperson says that her commission is 5.5% of the selling price.
How much commission will the salesperson earn by selling a couch for $495? (round to the nearest 100th)
Answer:
27.23
Step-by-step explanation:
495*0.055=27.225 --> 27.23
Answer: 27.23
Step-by-step explanation:495*0.055=27.225 --> 27.23
multiply .035 times a power of ten so that the product is greater than 1 but less than 100
Answer:
0.035 x 10^3
Step-by-step explanation:
yes
Write an integer for:
13° below zero
Defects in computer hard-drives will usually render the entire computer worthless. For a particular model, the percent defective in the past has been 1%. If a sample size of 400 is taken, what would the 95.5% lower control chart limit be?
Answer:
0.00005
Step-by-step explanation:
We have the average fraction defective as p = 1%
= 0.01
N = 100
Then 95.5% deviation = 2σ
From there we have,
σ = √p*(1-p)/n
When we input these values, into the formula, we will have
σ = √0.01(1-0.01)/100
= √0.01(0.99)/100
= √0.000099
= 0.00995
The LCL = p - 2σ
= 0.01 - 0.00995
= 0.00005
lower control chart limit be is 0.00005
The 95.5% lower control chart limit be is 0.0005.
Given,
The average fraction percent in the past defective as p = 1% = 0.01
Sample size N = 400
Then ,
According to the question ,
95.5% deviation = 2x
We have,
x = [tex]\frac{\sqrt{p (1-p)} }{n}[/tex]
We put these values, into the formula,
x = [tex]\frac{\sqrt{0.01 ( 1 - 0.01) } }{400}[/tex]
= [tex]= \frac{\sqrt{(0.01) (0.99)} }{400}[/tex]
= [tex]\frac{0.99}{400}[/tex]
= 0.0000245
The LCL = p - 2x
= 0.01 - 0.0000245
= 0.00005
The Lower control chart limit be is 0.00005
For the more information about Standard deviation click the link given below.
https://brainly.com/question/23907081
At a game show, there are three doors marked 1, 2, and 3. A contestant is allowed to select one of three keys labeled A, B, and C and then use it to open one of the doors. The sample space showing the ways in which a contestant can select a key and a door is represented in the table.
Door
1 2 3
Key A A-1
A-3
B B-1 B-2 B-3
C C-1 C-2
C-3
What is the missing term in the table? If there were two doors instead of three doors, what would the sample size be?
A.
The missing term is A-2. The sample size would be 6.
B.
The missing term is C-2. The sample size would be 8.
C.
The missing term is C-2. The sample size would be 9.
D.
The missing term is B-2. The sample size would be 12.
Answer:
It is A
Step-by-step explanation:
The answer is A. The missing term is A-2. The sample size would be 6.
a. To answer the question, we need to know what sample space is.
What is a sample space?A sample space is the total number of possible outcomes of an event.
Now, since there are Doors 1, 2 and 3 and Keys A, B and C. The sample space is
Key A: A-1, A-2, A-3
Key B: B-1, B-2, B-3
Key C: C-1, C-2, C-3
So, the missing item is A-2.
b.
The sample size would be 6.
To answer the question, we need to know what sample size is.
What is sample size?The sample size is the size of the sample space.
If there were two doors instead of 3, the sample size would be since we have 2 doors and 3 keys. The sample size is 2 × 3 = 6.
So, the sample size would be 6.
So, the answer is A. The missing term is A-2. The sample size would be 6.
Learn more about sample space here:
https://brainly.com/question/2117233
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Solve the proportion34.5x=5672 , rounding your answer to the nearest tenth
Answer:
164.4
Step-by-step explanation:
34.5x=5672
34.5 34.5
x=164.4
You are a personnel director and are interested in predicting the Number of Shares of Company Stock (Y) using the Number of Years Employed with the Company (X). You randomly selected 8 employees and found that the average number of shares is 525 and the average number of years employed is 22.5. If the slope (b1) is 20.0, what is the least squares estimate of the intercept (b0)?
a. 25.0
b. 75.0
c. 40.0
d. 80.5
e. None of these are correct
Answer:
b. 75.0
Step-by-step explanation:
Calculation for the least squares estimate of the intercept (b0)
Using this formula
Intercept (b0) least squares estimate=[Shares average number-(Slope (b1)*Average number of years employed)]
Let plug in the formula
Intercept (b0) least squares estimate=[525-(20.0*22.5)]
Intercept (b0) least squares estimate=525-450
Intercept (b0) least squares estimate=75.0
Therefore the least squares estimate of the intercept (b0) will be 75.0
i need help again again again again again
Answer:
D. 340.511
Step-by-step explanation:
when rounding 4 and lower rounds to 340 but 5 and up rounds to 341
What is the width of the vegetable garden?
Answer:
The width of the vegetable garden is 3 feet.
Step-by-step explanation:
12 ÷ 4 = 3