Let us find the length of rope Jules will need using the pythagoras theorem .
Width of the moat ( let the moat be the base of this triangle ) = 14 foot
Distance from Roma's window to the boat ( let this be the side of the triangle where the right angle is present ) =20 feet
Then the length of rope needed ( hypotenuse ) =
= Let us name the triangle that is formed as △ ABC . Then ;
In △ ABC :
AB = the width of moat ( leg of triangle ) = 14 foot
BC = The distance from the window to the moat ( base ) = 20 feet
AC = Length of rope needed ( hypotenuse ) =
= AB ² + BC² = AC² ( according to the pythagoras theorem the square on the hypotenuse will be equal to the sum of the squares on the other two legs )
= 14² + 20² = AC²
= 196 + 400 = AC²
= 596 = AC²
= 24 × 24 = AC × AC
= 24 foot = AC = length of rope needed by jules .
Therefore , Jules will need a 24 foot rope so that his girlfriend can slide down and escape from her apartment .
G
Which fraction is equivalent to 6?
12 / 2
3
2 2+1 3
7, because
6 6+17
mo
2 1 1 3
because 6 - 3 and
39
2 /
3
12
2 1
because =
6 3 and
2
nd 3 -
3
12
2 1
8.
because 6 2
2+1 3
6+28
Answer:
what is the question
Step-by-step explanation:
i don't understand what you're trying to say
Question 1
In this unit, you learned about common logarithms. Since most calculators can be used to find the values of common logarithms only, it’s desirable to be able to convert logarithms with bases other than 10 to common logarithms. This conversion can be done using the change of base formula.
Part A
Rewrite the logarithmic equation y = logbm in exponential form.
Part B
Using a log with base c , take the log of both sides of your answer from part A. Then use the power property and solve for y .
Part C
The original equation was y=logbm . Use substitution and your answer from part B to write the change of base formula.
Part D
Watch this video for two examples of how to use the change of base formula to simplify and evaluate logarithmic expressions. Then simplify (or evaluate, if possible) this expression: log3z x logz27
Part E
Use the change of base formula and a calculator to evaluate log7 300. Round your ans
Answer and Step-by-step explanation:
Part A: Exponential equation is the "opposite" of logarithmic equation, so:
[tex]y=log_{b}m[/tex]
[tex]b^{y}=m[/tex]
Part B: Using log with base c:
[tex]log_{c}b^{y}=log_{c}m[/tex]
Power property of logarithm states that if the anti-logarithm is elevated at a power, the elevated number can be pulled in front of the logarithm:
[tex]ylog_{c}b=log_{c}m[/tex]
Solving for y:
[tex]y=\frac{log_{c}m}{log_{c}b}[/tex]
Part C: To facilitate the use of calculators, which only have values for the base-10 log and natural log, we use change of base formula, i.e., transform
[tex]y=log_{b}m[/tex]
into
[tex]y=\frac{log_{c}m}{log_{c}b}[/tex]
Part D: [tex](log_{3}z)(log_{z}27)[/tex]
Change of base will be:
[tex]log_{3}z=\frac{log_{10}z}{log_{10}3}[/tex]
[tex]log_{z}27=\frac{log_{10}27}{log_{10}z}[/tex]
Solving:
[tex](log_{3}z)(log_{z}27)[/tex] = [tex](\frac{log_{10}z}{log_{10}3})(\frac{log_{10}27}{log_{10}z} )[/tex]
[tex](log_{3}z)(log_{z}27)[/tex] = [tex]\frac{log_{10}27}{log_{10}3}[/tex]
[tex](log_{3}z)(log_{z}27)[/tex] = [tex]\frac{log_{10}3^{3}}{log_{10}3}[/tex]
[tex](log_{3}z)(log_{z}27)[/tex] = [tex]\frac{3log_{10}3}{log_{10}3}[/tex]
[tex](log_{3}z)(log_{z}27)[/tex] = 3
Part E: [tex]log_{7}300[/tex]
Using change of base:
[tex]log_{7}300=\frac{log300}{log7}[/tex]
[tex]log_{7}300=\frac{2.48}{0.85}[/tex]
[tex]log_{7}300[/tex] ≈ 3
I need help please
Range is y so we set -5x = whatever number you pick from the range values listed, so
-5x = -5 making x=1
-5x = 0 making x=0
-5x = 10 making x=-2
-5x = 15 making x=-3
The domain is {1,0,-2,-3}
Started at 20° and dropped 4° each minute
Answer:
hey mate I couldn't understand ur question.......plz recheck....
Answer:
What's the rest of the question?
Step-by-step explanation:
The table below shows the results of a survey of 1000 American college students and their age breakdown. Use the table to answer questions
Answer:
c
Step-by-step explanation:
Question 16 (1 point)
Solve for X using Special Rights
X
13
y
1412
7
С
14
772
Answer:
d
Step-by-step explanation:
Can you have say from us the aks place
A die is rolled. The set of equally likely outcomes is (1, 2, 3, 4, 5, 6). Find the probability of getting a 3.
Answer:
Step-by-step explanation:
1/6
The probability of getting 3 is 1/6.
What is the probability?Probability is defined as the possibility of an event to be happened which is the ratio of no. of favorable outcomes and total no. of outcomes.
Probability of an event = P(E) = No. of favorable outcomes/Total No. of outcomes
Here given that the dice are fair and six-sided is rolled.
Total no. of outcomes by rolling the dice = 6 i.e. {1,2,3,4,5,6}
The event is to get the number 3 by rolling the dice.
The favorable outcome is = {3}
Number of favourable outcomes= 1 i.e. {3}
As the dice is the set of equally likely outcomes.
Probability of getting 3 = P(getting 3)= No. of favorable outcomes/Total No. of outcomes= 1/6
Therefore the probability of getting 3 is 1/6.
Learn more about probability
here: https://brainly.com/question/14192140
#SPJ2
How do you solve this question
/
Answer:
5/18
Step-by-step explanation:
Parentheses next to each other mean to multiply. So, this problem means you need to multiply -4/9 and -5/8. To multiply fractions, you just have to multiply across. To make it easier to understand what I mean...
-4 x -5 = 20 (when you multiply two negatives, it makes a positive)
9 x 8 = 72
20/72 simplifies to 5/18.
Hope this helps!! Have a wonderful day C:
Select all the expressions that are rational numbers.
a. 3.14159…
b. –9.1234567123…
c. –9.293847210103938…
d. 227
e. –26
Answer:
d,e
Step-by-step explanation:
rational numbers are positive and negative whole numbers.
Answer:
d,e
Step-by-step explanation:
Here is a set of signed numbers: 7, -3, 1/2, -0.8, 0.8, -1/10, -2
Order the numbers from least to greatest.
first gets brainllest
Answer:
7, 0.8, 1/2, -0.8, -1/10, -2, -3,
Step-by-step explanation:
accidently put greatest to least just flip it i still want brainliest tho
Define the opposite and the absolute value of -8.]
Answer:
8 because this is a negitive and the oppisite is postivie so it is 8
Step-by-step explanation:
-8 is negitive on the oppisite side of the number line is positive 8 the answer is 8.
Answer:
The opposite of -8 is 8. The absolute value of -8 is 8.
Step-by-step explanation:
Which refers to the standards used to make a judgment or decision when designing a product?
prototypes
criteria
designs
investigations
Answer:
criteria
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
5 1/3 minus -2 2/3 someone please answer
Answer:
8
Step-by-step explanation:
Answer:
2.7
Step-by-step explanation:
Find the quotient. 0.16/-0.2
- 0.8
Simple division. Shouldn’t be that hard
If the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have?
Оооо
20
24
Answer:
24
Step-by-step explanation:
. I'm very bad in math help would mean alot to me
Answer:
(6,1)
Step-by-step explanation:
In order to find the third point, you first need to identify the side length of XZ. X is (1, 1) and Z is (1, 5). In order to find the length of this segment, you just need to subtract 1 from 5 since that is the difference in the y-values and the x-values are the same.
Now, you know that XZ = 4. The problem says that the area of the triangle is 10, and the area of a triangle is a = [tex]\frac{1}{2}[/tex]bh, so you can just insert the values into the equation to solve for the base:
a = [tex]\frac{1}{2}[/tex]bh
= 10 = (1/2) * b * 4
= 10 = 2b
= 5 = b
Because the base is 5 units long, you can just add 5 to the x-value of the point Z, since Y is 5 units to the right of it
Y is (1 + 5, 1)
Y is (6,1)
−3.5=x4 please help me
Classify the following triangle. Check all that apply.
A. Right
B. Isosceles
C. Obtuse
D. Acute
E. Equilateral
F. Scalene
Answer:
is there a chart to this question?
because I can't tell the answer just by looking at it
Step-by-step explanation:
it's a b c d and f are all the correct answers
(__-3)(__+7)=2x^2+x-21
Answer:
(x - 3)(2x + 7) = 2x^2 + x - 21
Step-by-step explanation:
2x^2 + x - 21 = (__ - 3)(__ + 7)
The first term of the trinomial is 2x^2 which can be factored into 2x * 2.
You need to place 2x in one blank and x in the other blank.
Try it both ways. Then multiply the factors out to see which one gives you the correct middle term.
Try 2x - 3.
(2x - 3)(x + 7) = 2x^2 + 14x - 3x - 21 = 2x^2 + 11x - 21
This gives the middle term 11x, but we need the middle term to be x, so now we try x - 3.
(x - 3)(2x + 7) = 2x^2 + 7x - 6x - 21 = 2x^2 + x - 21
This gives the correct middle term, x, so this is the correct factorization.
Answer:
(x - 3)(2x + 7) = 2x^2 + x - 21
13
In the figure shown below, if line mis parallel to line n, then find the value of x. (This is a 2 part question.)
m
(2x-10)
(65 - x)
Part A
Write the equation to find the value of x. (DO NOT find x, just write the equation.)
(2x - 10) (65 - x)
Part B
What is the value of x?
Y
Answer:
2x-10 = 65-xStep-by-step explanation:
just add up both alternate internal angles as they are both equal
so, the equation is: 2x-10 = 65-x
Answer:
The right equation will be 2x - 10 = 65 - x (you were wrong lol)
Step-by-step explanation:
We have: 2x - 10 = 65 - x
=> 2x - 10 + x = 65
=> 3x = 65 + 10 = 75
=> x = 75/3 = 25
P/S: After some little chats with the others, this might be wrong :(
Approximately how many litres is 70 fluid ounces?
Use the conversion 20 fluid ounces = 1 pint and 134
pints = 1 litre
Anyone willing to answer this?
Answer:
1. perpendicular; the opposite?
2. Parallel; the slopes are the same?
Step-by-step explanation:
Just use Math
way
Plz answer I will mark u brainiest!!!!
Answer:
65
Step-by-step explanation:
Please help
Find the length of the unknown side. Round your answer to the nearest whole number. (4 points)
Image of a right triangle with legs labeled 12 meters and 8 meters. Hypotenuse is unknown.
13 meters
14 meters
200 meters
208 meters
Answer: 14 meters
Step-by-step explanation:
Pythagorean Theorem formula = a^2 + b^2 = c^2
8^2 + 12^2 = c^
64 + 144 = 208
Now find the square root of 208 = 14.422
Answer:
You answer is 24! hope yhis helps
Step-by-step explanation:
How long does it take for the baseball to reach its maximum height? (2)
b. What was the initial height of the ball? (2)
form A : h(t)= -16t^2 + 96t +7
form b: -16(t-3)^2 +151
help please
Answer: ha no way have the same question
Step-by-step explanation:
Which of the following must be negative?
I. The product of 2 negative numbers.
II. The product of 2 positive numbers.
III. The product of 3 negative numbers.
The ratio of a number x and four added to two
Answer:
hope it helps...
Step-by-step explanation:
The ratio of a number x and four added to two:
= 4x + 2 = 0
= 4x = -2
= 4x/4 = -2/4
= x = -2/4
= x = -1/2
UCF is a major Metropolitan University located in Orlando Florida. UCF is advertising their bachelor in Economics with the statistic that the starting salary of a graduate with a bachelor in economics is $ 48,500 according to Payscale (2013-13). The Director of Institutional Research at UCF is interested in testing this information. She decides to conduct a survey of 50 randomly selected recent graduate economic students. The sample mean is $43,350 and the sample standard deviation is 15,000. Alpha = 0.01
Answer:
The claim is rejected
Step-by-step explanation:
Claim: UCF is advertising their bachelor in Economics with the statistic that the starting salary of a graduate with a bachelor in economics is $ 48,500 according to Payscale (2013-13).
Null hypothesis: [tex]H_0: \mu = 48500[/tex]
Alternate hypothesis :[tex]H_a : \mu \neq 48500[/tex]
n = 50
Since n is more than 30 .
So we will use Z test
x=43350
Standard deviation = 15000
[tex]Z=\frac{x-\mu}{\frac{s}{\sqrt{n}}}\\Z=\frac{43350-48500}{\frac{15000}{\sqrt{50}}}\\Z=-2.42[/tex]
Refer the z table
p value = 0.00776
[tex]\alpha = 0.01[/tex]
p value < [tex]\alpha[/tex]
So, We are failed to accept null hypothesis
Hence The claim is rejected
On Friday a local hamburger shop sold a combined total of 336 hamburgers and cheeseburgers the number of cheeseburgers sold was two times the number of hamburgers sold how many hamburgers were sold on Friday
Answer:
112
Step-by-step explanation:
H + 2H = 336
3 = 336/H
112=H