-
18 The diagram shows triangle PQR.
Diagram NOT
accurately drawn
P
17.8 cm
360
R
26.3 cm
Calculate the length of PR.
Give your answer correct to 3 significant figures.
Answers
Answer:
The length of PR is 15.8 cm
Step-by-step explanation:
We will solve the question using the cosine rule
In ΔPQR
∵ (PR)² = (PQ)² + (RQ)² - 2(PQ)(RQ)(cos∠Q)
∵ PQ = 17.8 cm
∵ RQ = 26.3 cm
∵ m∠Q = 36°
→ Substitute them in the rule above
∵ (PR)² = (17.8)² + (26.3)² - 2(17.8)(26.3)(cos36)
∴ (PR)² = 316.84 + 691.69 - 936.28(cos36)
∴ (PR)² = 251.0635685
→ Take √ for both sides
∴ PR = 15.8449856
→ Correct it to 3 significant figures
∴ PR = 15.8 cm
∴ The length of PR is 15.8 cm
Related Questions
Which expression is equivalent to 3m+1-m?
A-2+m-1+m
B-1+m
C-3m-1
D-3m
Answers
Answer:
A
Step-by-step explanation:
Answer:
option (a) is correct.
2 + m - 1 + m is an equivalent expression to the given expression 3m+1-m
Step-by-step explanation:
Given expression 3m+1-m
We have to choose an equivalent expression from given options.
Equivalent expression are those expression that looks different but are same.
Like 4+2 = 6 and 3+ 3 = 6
Both have same value but looks differently.
Like terms are term having same variable with same degree.
Consider the given expression 3m+1-m
Simplify by adding like terms,
3m + 1 - m = (3-1) m + 1
Thus, (3-1) m + 1 = 2m + 1
Also 2m + 1 can be written as m + m + 2 - 1
Thus, option (a) is correct.
Which ordered pair is a solution of the equation? y=-2x-5y=−2x−5
Answers
Answer:
x=3y
Step-by-step explanation:
Step 1: flip the equation.
2x−5y=y
Step 2: Add 5y to both sides.
2x−5y+5y=y+5y
2x=6y
Step 3: Divide both sides by 2.
2x
2
=
6y
2
x=3y
Answer:
if this is for khan academy and is a multiple choice choose the answer (neither) if not its 5
Step-by-step explanation:
y - 2x - 5y = 2x - 5
4x+ 4y = 5
Every year, the value of a property in singapore appreciates by 15% of its value in the previous year. If the value of the property was $899300 in 2012, find ite value in 2010.
Answers
Answer:
629 510$
Step-by-step explanation:
$899300 - (30% of $899300)
cuz its two years away from 2010 so it will have gone up 30 % so to rewind time, just go back 30%
Answer:
649744.25
Step-by-step explanation:
899300-15%-15%=649744.25
What is the probability that a random sample of 400 U.S. youth will provide a sample proportion (p¯) that is within 0.03 of the population proportion (p)?
Answers
Complete Question
The proportion of adult women in the United States is 51% (p=0.51).What is the probability that a random sample of 400 U.S. youth will provide a sample proportion (p¯) that is within 0.03 of the population proportion (p)?
Answer:
The probability is [tex]P( 0.48 < p < 0.54 ) = 0.77[/tex] or [tex]P( 0.48 < p < 0.54 ) = 77\%[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 400
The population proportion is p = 0.51
Generally the standard deviation of this sampling distribution is mathematically represented as
[tex]\sigma = \sqrt{\frac{p(1-p)}{n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{0.51(1-0.51)}{400} }[/tex]
=> [tex]\sigma = 0.02499[/tex]
Generally the lower limit for the range of the population proportion within 0.03 is
[tex]a = p - 0.03[/tex]
=>[tex]a = 0.51 - 0.03[/tex]
=>[tex]a = 0.48[/tex]
Generally the upper limit for the range of the population proportion within 0.03 is
[tex]b = p + 0.03[/tex]
=>[tex]a = 0.51 + 0.03[/tex]
=>[tex]a = 0.54[/tex]
Generally the probability that a random sample of 400 U.S. youth will provide a sample proportion (p¯) that is within 0.03 of the population proportion (p) is mathematically represented as
[tex]P( a < p < b) = P( \frac{a - p }{\sigma } < \frac{\^ p - p }{\sigma} < \frac{b - p}{\sigma } )[/tex]
=> [tex]P( 0.48 < p < 0.54 ) = P( \frac{0.48 - 0.51 }{0.02499 } < \frac{\^ p - p }{\sigma} < \frac{0.54 - 0.51}{0.02499 } )[/tex]
[tex]\frac{\^ p -p }{\sigma } = Z (The \ standardized \ value\ of \ \^ p )[/tex]
=> [tex]P( 0.48 < p < 0.54 ) = P( -1.2 < Z < 1.2 )[/tex]
=> [tex]P( 0.48 < p < 0.54 ) = P( Z < 1.2) - P(Z < -1.2 )[/tex]
From the z table the area under the normal curve to the left corresponding to 1.2 and -1.2 is
[tex]P( Z < 1.2) =0.88493[/tex]
and
[tex]P( Z < -1.2) =0.11507[/tex]
So
[tex]P( 0.48 < p < 0.54 ) = 0.88493 - 0.11507[/tex]
=> [tex]P( 0.48 < p < 0.54 ) = 0.77[/tex]
what is special about the y coordinate that goes with the x coordinate of 1 on a proportional graph
Answers
Answer and Step-by-step explanation:
There is a two-dimensional numbers line in a coordinate plane, which has a horizontal line x-axis, and the vertical line is known as the y-axis. These lines intersect each other at zero points, and they are perpendicular. Zero points are known as the origin. The axes divide the plane into quadrants.
A point in the coordinate plane is of the form of (x, y). This point is named as ordered pair; the first number is from the x coordinate, and the second number from the y coordinate.
To make a graph, we draw a dot, starting from the origin, at the coordinate that communicates to the ordered pair. The y coordinates describe how many steps to move up or down ( positive or negative), and x coordinates tell us to move right or left ( positive or negative).
The completeness property for points describes:
Exactly one point in the plane given the number of ordered pair
And
Exactly one ordered pair of numbers at a given point in the plane.
A relation is ordered pairs; the x coordinates are known as domain, and the y coordinate is known as the range.
The domain contains the value that corresponds to the independent variable and the range equal to the dependent variable.
A parent volunteer group is raising money by making custom hats to sell at
school activities. They plan to sell the hats for $12. Each hat costs $6 to
make. They spent $50 for advertising.
Use n to represent the number of hats they sell. Multiply this by the money
they make for each hat, then subtract the advertising cost.
Which expression represents the money that the group raises?
A. 12n - 6 - 50
O B. 50 - (12 – 6) n
O C. (12 - 6)n - 50
O D. 12 - 6n - 50
Answers
Answer:
B
Step-by-step explanation:
The answer is B because you minus 50 from 12 and 6.
A bakery bakes 68 batches of 56 cupcakes each week. How many individual cupcakes do they make each week?
Answers
Answer:
3808
Step-by-step explanation:
Sam's new room is square, and each side measures 15 feet. What is the
area of the room?
Answers
Answer:
225 feet
Step-by-step explanation:
Square sides are always the same size so just multiply 15x15.
Area = 225 feet
Using a Table of Values to Find a Solution to a System
a) Complete the table below to solve the equation 2.5x-10.5=64(0.5)x.
x f(x)=2.5x-10.5 g(x)=64(0.5)x
2
3
4
5
6
b) Give the solution for the equation:
Answers
Answer:
This problem wants you to substitute the answers from the table into the equation to find the solution, which is when the input gives the same output basically.
f(x) = 2.5x -10.5 g(x) = 64(0.5)^x
when x= 2... when x= 2...
f(2) = 2.5(2) - 10.5 g(2) = 64(0.5)^2
f(2) = 5 - 10.5 = -5.5 g(2) = 64(.25)= 16
when x= 3... when x= 3...
f(3) = 2.5(3) - 10.5 g(3) = 64(0.5)^3
f(3) = 7.5 - 10.5 = -3 g(3) = 64(0.125) =8
when x= 4... when x = 4...
f(4) = 2.5(4) - 10.5 g(4) = 64(0.5)^4
f(4) = 10 - 10.5 = -0.5 g(4) = 64(0.0625) = 4
when x= 5... when x= 5...
f(5) = 2.5(5) - 10.5 g(5) = 64(0.5)^5
f(5) = 12.5 - 10.5 = 2 g(5) = 64(0.03125) = 2
when x= 6... when x = 6...
f(6) = 2.5(6) - 10.5 g(6) = 64(0.5)^6
f(6) = 15 - 10.5 = 4.5 g(6) = 64(0.015625) = 1
Can someone help me with these three math problems pleaseeeeeeeeeee
Answers
2. 63
3. i have no clue
all triangles should add up to 180, so if you add the numbers up that you have you take ur answer and subtract 180 to get what the missing angle equals! sorry hope that helps a little lol
Answer:
75 should be the answer
60 = 5(1.07)^x
initial value:
a. 7%
b. 1.07%
c. 9.3%
d. 5
e. 60
growth or decay?
growth/decay rate?
a. 7%
b. 1.07%
c. 9.3%
d. 5
e. 60
Answers
Given:
The given equation is
[tex]60=5(1.07)^x[/tex]
To find:
The initial value and growth/decay factor.
Solution:
The general exponential growth/decay model is
[tex]y=a(1+r)^x[/tex] ...(i)
where, a is initial value, if r>0, then |r| is growth factor, if r<0, then |r| is decay factor and x is time.
We have,
[tex]60=5(1.07)^x[/tex]
It can be written as
[tex]60=5(1+0.07)^x[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=5\text{ and }r=0.07[/tex]
Here, initial value is 5 and growth factor is 0.07, i.e., 7%.
Therefore, the correct option for first question is d and correct option for second question is a.
Answer:
see image
Step-by-step explanation:
Plato/Edmentum
A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (0, 4) and (1, 1) The second line is labeled y - g(x) and is horizontal passing through (negative 2, 2), (0, 2), and (2, 2). The lines intersect at a point that is slightly to the right of (0.5, 2).
If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.
x = ______
Answers
Answer:
2/3
Step-by-step explanation:
cuz it is
Answer:
2/3
Step-by-step explanation:
what is the quotient of 8,187 divided by 24
Answers
Answer:
341.125
Step-by-step explanation:
Hope this helped, Have a Great Day!!
Let A = (1,2,3,4) and B= (0,1) use the set roster notation,to work each of the following sets and indicate the number of elements that are in each set?
a.A x B
b. bx A
c.A x A
d.B x B
Answers
Step-by-step explanation:
A={1,2,3,4}
B={0,1}
now,
a. A×B={1,2,3,4}×{0,1}
={(1,0)(1,1)(2,0)(2,1)(3,0)(3,1)(4,0)(4,1)}
b. B×A={(0,1)(0,2)(0,3)(0,4)(1,1)(1,2)(1,3)(1,4)}
c. A×A={(1,1)(1,2)(1,3)(1,4)(2,1)(2,2)(2,3)(2,4)(3,1)(3,2)(3,3)(3,4)(4,1)(4,2)(4,3)(4,4)}
d. B×B={(0,0)(0,1)(1,0)(1,1)}
hope it help u..
To make Diane's special punch it take 4 cups of juice for every 7 cups of Lime soda. How much juice will be needed if we have 21 cups of soda? Using J for juice and S for soda, how will the equation look?
Answers
Answer:
Step-by-step explanation:
4 cups of J for every 7 cups of soda 4:7
21 cups of soda will take 12 cups of J
If you take the 7 and multiply by 3 you get the 21.
So you will need to multiply the 4 by the 3 to get the 12. You need to keep everything in proportion.
4:7 same as 12:21
HELP ASAP PLEASE :)))
.
.
.
.
.
Answers
Answer:
The first one is not. The second one is. The third one is. The fourth one is not. The fifth one is not. The sixth one is.
Step-by-step explanation:
Answer: First one, no? I'm not sure its been a while
Step-by-step explanation:
Without actually going through the solution process. we can say that the equation
|5x-6| =6x cannot have a negative solution. Why is this true?
Answers
A positive number divided by a positive number is positive and the sum of two positive numbers is positive, thus the solution would have to be positive.
Do dis pls and don’t be toxic and take points
Answers
Simplify fully 56:16
Answers
Answer:
7/2
Step-by-step explanation:
LCM of 9 18 and 99 is :
Answers
Step-by-step explanation:
[tex]\begin{array}{c|ccc}\cline {2-4} 2 & 9 ,& 18 ,& 99 \\ \cline {2-4} 3 & 9 & ,9 & ,11 \\ \cline {2-4} 3 & 3 ,& 3, & 11 \\ & 1, & 1 , & 11 \end {array}[/tex]
LCM=2×3×3×11=198El 5% de los focos producidos por una fabrica son defectuosos. Al extraer una muestra de 6 focos. ¿Cual es la probabilidad de que menos de 3 focos sean defectuosos?
Answers
Answer:
3/10 no estoy segura pero creo que es esto
Of the 482 graduating seniors at Palmdale High School, approximately 5/8 are going to college, and approximately 1/2 of those going to college are going to an in-state school. Which of the following is the closest estimate for how many of the graduating seniors are going to an in-state school?
Answers
Answer:A
Step-by-step explanation:
trust
How can I figure out my screentime password.
100 points to whoever can tell me exactly how to do it and maybe even brainless if it works and it has to be an actual answer not just a random one!!!
Answers
Answer:
Screen record as your parent puts the password in or wipe off your screen and give the parent your phone to put the password in then look at the fingerprint circles and that where each number is, then try all the possible combinations
Step-by-step explanation:
12.
Name the coefficients in the expression 4x + 9- y.
9
O
4,9,0
0
4, -1
OR
Answers
Answer:
4, 9, and -1
Step-by-step explanation:
Please give me brainliest
Answer:
4x+9-y
The 4 is your coefficient. X and Y are your variables and 9 is your constant.
(Round to the nearest tenth of a percent.) In 2011, the IRS increased the deductible mileage cost to
55.5 cents from 51 cents.
Answers
Answer:
[tex]\%Change = 8.8\%[/tex]
Step-by-step explanation:
Given
[tex]Initial = 51\ cents[/tex]
[tex]Final = 55.5\ cents[/tex]
Required
Determine the percentage change
Percentage change is calculated as;
[tex]\%Change = \frac{Final - Initial}{Initial} * 100\%[/tex]
[tex]\%Change = \frac{55.5 - 51 }{51 } * 100\%[/tex]
[tex]\%Change = \frac{4.5}{51} * 100\%[/tex]
[tex]\%Change = \frac{4.5* 100\%}{51}[/tex]
[tex]\%Change = \frac{450\%}{51}[/tex]
[tex]\%Change = 8.8\%[/tex]
Hence, the percentage change is approximately 8.8%
Question 16
Mr. Twain asked the students in his class to draw the figure below using a scale factor of 3. Then, he asked students to tell him one of the new side lengths of the figure. Some student responses are below.
Student Response
Mark 5 in.
Samantha 6 in.
Divia 1.3 in.
Cheng 0.9 in.
Candice 11.7 in.
Select the student that answered Mr. Twain's question correctly.
A
Mark
B
Divia
C
Cheng
D
Candice
Answers
Answer:
C
Step-by-step explanation:
Your answer is C because got the question right when put C .
A triangle has sides that measure 5 units, 7 units, and 8 units. Is this a right triangle
Answers
Answer:
No
Step-by-step explanation:
Using the given lengths if we say this is a right triangle then 8 would be length of hypotenuse
From the Pythagorean theorem
8^2 = 5^2 + 7^2
64 = 25 + 49
64 = 74 is not a correct equation so the triangle is not a right triangle for the given lengths
Thanks for the help :)
Answers
A dog that weighs 14 pounds should eat 1 5/8 cups of a certain type of dog food per day. How much of the same type of dog food should be fed, per day, to a dog who weighs 26 pounds?
PLEASE HELP!!!!!!!!
Answers
(13/8)/14 = .116 or 13/112
.116 (26) = 3.016 or 169/56
9514 1404 393
Answer:
3 1/56 cups
Step-by-step explanation:
Apparently, you're to assume that the amount of food is supposed to be proportional to weight. If x is the amount of food for the 26-pound dog, then ...
cups/weight = (1 5/8)/14 = x/26
Multiplying by 26 we have ...
x = (26)(13/8)/14 = 338/112 . . . cups
x = 3 1/56 cups ≈ 3.02 cups
About 3.02 cups of the same type of food should be fed to a 26-pound dog.
A small deck of 5 cards consists of 3 red Jards and 2 green cards.
Draw 7 times with replacement.
Find the probability that a red card is drawn exactly 3 times.
Answers
Answer:
Approximately [tex]0.19[/tex].
Step-by-step explanation:
The cards were drawn with replacement. Therefore, the probability of drawing a red card will be [tex](3 / 5)[/tex] at every one of the seven draws. The probability of not drawing a red card would be [tex](1 - (3/5)) = (2/5)[/tex].
One way to get three red cards out of the seven draws would be [tex]\verb!red!\; \verb!red!\; \verb!red!\; \verb!green!\; \verb!green!\; \verb!green!\; \verb!green![/tex]. That corresponds to a probability of [tex](3/5)^3\, (2/5)^{7-3}[/tex].
However, there are many other ways to get three red cards during the seven draws. For example:
[tex]\verb!red!\; \verb!red!\; \verb!green!\; \verb!red!\; \verb!green!\; \verb!green!\; \verb!green![/tex], [tex]\verb!red!\; \verb!red!\; \verb!green!\; \verb!green!\; \verb!red!\; \verb!green!\; \verb!green![/tex].[tex]\cdots[/tex].[tex]\verb!green!\; \verb!green!\; \verb!green!\; \verb!green!\; \verb!red!\; \verb!red!\; \verb!red![/tex].There are [tex]\displaystyle {\genfrac{(}{)}{0}{0}{7}{3}} = 35[/tex] such ways in total to choose three draws out of seven draws.
These ways are mutually-exclusive. Each of these ways has a probability of [tex](3/5)^3\, (2/5)^{7-3}[/tex]. The probability for getting a red card on exactly three out of the seven draws would be:
[tex]\displaystyle {\genfrac{(}{)}{0}{0}{7}{3}} \, (3/5)^3\, (1 - (3/5))^{7-3} \approx 0.19[/tex].