Answers
Answer:
[tex]x = 24.75[/tex]
Step-by-step explanation:
Required
Find x
To find x, we have:
[tex]\angle PQR + \angle RPQ + \angle QRP = 180[/tex] -- angles in a triangle
Because [tex]\bar {PR}[/tex] is extended to S, then:
[tex]\angle QRS = \angle QRP[/tex]
So, we have:
[tex]2x + 6 + x - 7 + 5x -17 = 180[/tex]
Collect like terms
[tex]2x + x + 5x = 180 + 17 + 7-6[/tex]
[tex]8x = 198[/tex]
Divide by 8
[tex]x = 24.75[/tex]
Related Questions
Use the exact values of the ratios and find the value of tan 45° + sin 30°
Answers
Answer:
1.5
tan45=1
sin30=1/2
so 1+1/2=1.5 or 3/2
What is the tens digit in the sum 7! + 8! + 9! + … + 2006!
Answers
You can get the tens digit of any number n by computing the quotient
(n (mod 100)) / 10
and ignoring the remainder.
Taking the given sum (mod 100) gives
7! + 8! + … + 2006! ≡ 7! + 8! + 9! (mod 100)
since the last 1997 terms (i.e. 10! up to 2006!) in the sum are multiples of 100. That is,
• every term beyond 100! is obviously a multiple of 100
• every term beyond 25! contains a factor of both 4 and 25
• every term beyond 10! contains two factors each of both 2 and 5 (i.e. every factorial term contains 4, 5, and 10)
The remaining sum is easy to compute by hand:
7! + 8! + 9! = 7! (1 + 8 + 8 × 9) = 5040 × 81 = 408,240
so the tens digit is 4.
If someone can pls give the answer with steps that would be greatly appreciated :)
Answers
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]
The measures of [tex]x[/tex] and [tex]y[/tex].
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\: 210°\:and\:\:y\:=\: -30°}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
An exterior angle of a triangle is equal to sum of two opposite interior angles.
And so we have,
[tex] 40° = 70° + y[/tex]
[tex]➪ \: y= 40° - 70°[/tex]
[tex]➪ \: y = - 30°[/tex]
Also,
[tex]\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
[tex]y[/tex] + [tex]x[/tex] = [tex]180°[/tex]
[tex]➪ \: -30° + x= 180°[/tex]
[tex]➪ \:x = 180° + 30°[/tex]
[tex]➪ \:x = 210°[/tex]
[tex]\sf\purple{Therefore,\:the\:measures \:of\:the\:unknown\:angles\:are\:"x=210°"\:and\:"y=-30°.}[/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
Given that abcd ~Jklm. Find the value of x, y, and z
Answers
Answer:
x = 7.2
y = 10
z = 6
Step-by-step explanation:
Since ABCD ~ JKLM, therefore, the ratio of their corresponding sides would be equal. Thus:
JK/AB = KL/BC = LM/CD = JM/AD
Substitute
12/x = y/6 = 15/9 = 10/z
✔️Find x:
12/x = 15/9
12/x = 5/3
Cross multiply
x*5 = 3*12
5x = 36
x = 36/5
x = 7.2
✔️Find y:
y/6 = 15/9
y/6 = 5/3
Cross multiply
y*3 = 5*6
3y = 30
y = 30/3
y = 10
✔️Find z:
15/9 = 10/z
5/3 = 10/z
Cross multiply
5*z = 10*3
5z = 30
z = 30/5
z = 6
Defined the total variation distance to be a distance TV(P,Q) between two probability measures P and Q. However, we will also refer to the total variation distance between two random variables or between two pdfs or two pmfs, as in the following.
Compute TV(X,X+a) for any a∈(0,1), where X∼Ber(0.5).
TV(X,X+a) = ?
Answers
Answer:
1
Step-by-step explanation:
Computing Tv(X, X + a ) for any a∈(0,1)
Given that : X∼Ber(0.5)
∴ The probability mass function
P(X = 1 ) = 0.5
P(X = 0) = ( 1 - 0.5 )
and expectation E[X] = 0.5
hence ; TV ( X, X + a ) = 1
a cylindrical barrel (drum) contains 42 gallons of oil. the diameter of this barrel is 18 inches
determine the radius of a barrel (drum) in centimetre.
Answers
Answer: 1.345714286
Step-by-step explanation:
This is the full answer, if you want to round it up. Then your welcome to do so.
Having trouble with these questions, please help.
Answers
99.7 % random variable values are between
±
three standard deviation.
95 % random variable values are between
±
two standard deviation.
68 % random variable values are between
±
one standard deviation. There you go!
Answer:
(a)=50%(b)=2.1and(c)=16.1
Step-by-step explanation:
Hope this helps
Answer fast please and thanks!
Answers
Answer:
tan 30 = x / 15
General Formulas and Concepts:
Trigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tanθ = opposite over adjacentStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = 30°
Opposite Leg = x
Adjacent Leg = 15
Step 2: Solve for x
Substitute in variables [tangent]: tan 30 = x / 15Answer:
3rd one
Step-by-step explanation:
Recall that
Sin = opposite over hypotenuse
Cos = adjacent over hypotenuse
Tan = opposite over adjacent
For the angle with a measure of 30 degrees we are given it's adjacent side length and need to find it's opposite side length
When dealing with opposite and adjacent we use tangent
If tan = opposite over adjacent
Then tan30 = x / 15 and the correct answer choice is the third one
The police measured the skid marks made by a car that crashed into a tree. The formula used to approximate the distance in feet that it takes to stop a car after the brakes are applied for a car traveling at a rate of r miles per hour is d= 0.045 r^2 + 1.1 r . If the measurement gave a braking distance of 250 ft, was the driver exceeding the legal speed limit of 55 mi/h? Find the speed of the car before the brakes were applied.
Answers
Replace r in the equation with 55 mph and solve for d.
D = 0.045(55)^r + 1.1(55)
Simplify:
D = 0.045(3025) + 60.5
D = 136.125 + 60.5
D = 196.625
At the speed limit of 55 mph the skid mark would be 196.625 feet long.
Because the skid mark was greater than that it was going faster than 55 mph.
To find the speed the car was going replace d with 250 and solve for r:
250 = 0.045r^2 + 1.1r
Multiply both sides by 1000 to remove decimals:
250000 + 45r^2 + 1100r
Subtract 250000 from both sides
45r^2 + 1100 -250000 = 0
Use the quadratic formula to solve:
R = -1100 + sqrt(1100^2 14x45(-250000) /(2 x45)
R = 63.308 miles per hour
The speed of the car was 63.3 miles per hour
The lengths of nails produced in a factory are normally distributed with a mean of 5.16 centimeters and a standard deviation of 0.04 centimeters. Find the two lengths that separate the top 8% and the bottom 8%.
Answers
Answer:
The length that separates the top 8% is of 5.2162 centimeters, and the length that separates the bottom 8% is of 5.1038 centimeters.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 5.16 centimeters and a standard deviation of 0.04 centimeters.
This means that [tex]\mu = 5.16, \sigma = 0.04[/tex]
Length that separates the top 8%
The 100 - 8 = 92th percentile, which is X when Z has a p-value of 0.92, so X when Z = 1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.405 = \frac{X - 5.16}{0.04}[/tex]
[tex]X - 5.16 = 1.405*0.04[/tex]
[tex]X = 5.2162[/tex]
Length that separates the bottom 8%
This is the 8th percentile, which is X when Z has a p-value of 0.08, so X when Z = -1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.405 = \frac{X - 5.16}{0.04}[/tex]
[tex]X - 5.16 = -1.405*0.04[/tex]
[tex]X = 5.1038[/tex]
The length that separates the top 8% is of 5.2162 centimeters, and the length that separates the bottom 8% is of 5.1038 centimeters.
if the ratio of the volume of two cubes is 1 : 8 , then find the ratio of the total surface area of the two cubes
Answers
Answer:
V = L^3 where v is volume and L the length of one side
A = 6 * L^2 total area of cube with side L
A = 6 * V^2/3 area of cube expressed in V
A2 / A1 = (V2 / V1)^2/3 6 cancels
A2 / A1 = 8^2/3 = 4 ratio of areas
Jestina has A apples, she gave 5 to her sister, enter an expression to represent the number of apples jestina has now!! (show work please!)
Answers
Answer: A-5
Step-by-step explanation:
Jestina has A apples
she gave 5 away
so she has 5 fewer apples than she had before
so A-5 is the amount of apples she has now
Here is a table of values for y = f(x).
Х
-2 -1 0 1 2 3
4.
5
6
f(x) 5
6 7 8 9 10 11 12 13
Mark the statements that are true.
Answers
Step-by-step explanation:
the true answers are:
A. f(-1)=6
D. the domain for f(x) is the set
{-2,-1,0,1,2,3,4,5,6}
Use Pythagorean Theorem to find each missing length
please help with the steps
Answers
Answer:
25 is A and 26 is B
Step-by-step explanation:
25) a²+b²=c²
missing side can be=b
to find the missing side subtract 6.7² from 12.6²
b²=12.6²-6.7²
b²=158.76-44.89
the square root of b²= the square root of 113.87
b=10.67
the missing side is equal to 10.7(1d.p)
26) a²+b²=c²
c= hypotenuse
10.8²+11²=c²
116.64+121=c²
c²=237.64
the square root of c²= the square root of 237.64
c=15.42(2d.p)
the hypotenuse is=15.4
The places that I have "the square root of" you must replace it with the square root sign. I'm using my phone so I wasn't sure how to insert a square root sign.
simplification please
Answers
Answer:
5
Step-by-step explanation:
WHen we raise a power to a power, we multiply them, in this case 5 is the base so we can just ignore it for now and replace it with x.
(X^1/3)^3
Multiply 1/3 by 3 and we get 1
So:
X^1
Which does nothing, so we can simplify to just:\
X
Remember x is 5 so the answer is:
5
A geneticist conducts an experiment with peas, one sample of offspring consisted of 450 green peas and 157 yellow peas. Based on these results, estimate the probability of getting an offspring pea that is green.
Answers
Answer: 0.738
Step-by-step explanation:
11. Mendelian Genetics. When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value that was expected?
p0 = 428/(428 + 152) = 0.737931
If you round your answer of 0.737931 to three decimals you will
get 0.738.
Kin travels 180 miles by train at an average speed of 90 mph.
Ayaan flies the same distance at an average speed of 720 mph.
Find the difference between their travel times.
Give your answer in hours.
Answers
Answer:
1.75 hours
Step-by-step explanation:
time = distance / speed
Kin
t = 180 / 90 = 2 hours
Ayaan
t = 180 / 720 = 0.25 hours
Difference
2 - 0.25 = 1.75 hours
Answer:
1.75
Step-by-step explanation:
A rock group plans three concert tours over a period of 30 weeks. The tour in Britain will be twice as long as the tour in France and the tour in Germany will be 2 weeks shorter than the tour in France. How many weeks will they be in France?
Answers
Answer:
8 weeks
Step-by-step explanation:
Let x represent how many weeks they will be in France.
The tour in Britain can be represented by 2x, since it is twice as long as the one in France.
The tour in Germany can be represented by x - 2, since it is 2 weeks shorter.
Create an equation and solve for x:
(x) + (2x) + (x - 2) = 30
4x - 2 = 30
4x = 32
x = 8
So, they will be in France for 8 weeks
Bill notes that his apple tree is 45 the size of his pear tree. His apple tree is 4 meters tall. How tall is the pear tree?
Answers
Answer:
11.25 m
Step-by-step explanation:
45 divide by 4
because the Apple tree is 45 the size of pear tree
Answer: 5
Step-by-step explanation:
Which expression is equivalent to a^7
Answers
Answer:
here is your answer
Step-by-step explanation:
here is your answer
Estimate and classify the critical points for the graph of the function.
Answers
Answer:
Critical point is at (-1, 2) because it is the point where the slope is approximately zero.
Step-by-step explanation:
A critical point in a graph like this is simply the point where the slope is zero or undefined.
Looking at the graph given, the point at which the graph slope is zero is around the coordinate (-1, 2).
So we estimate that to be the critical point.
What the cubic inches…
Answers
Step-by-step explanation:
The radius r is 5 in (r = D/2). so the volume V of the beach ball is
[tex]V= \dfrac{4 \pi}{3}r^3 = \dfrac{4 \pi}{3}(5\:\text{in})^3[/tex]
[tex]\:\:\:\:\:= 523.6\:\text{in}^3[/tex]
Any help? Algebra I
Answers
9514 1404 393
Answer:
2p +3d = 18.25; 4p +2d = 27.50popcorn: $5.75; drink: $2.25Step-by-step explanation:
a) Let p and d represent the prices of a bag of popcorn and a drink, respectively.
Mohamed's purchase is ...
2p +3d = 18.25
Miguel's purchase is ...
4p +2d = 27.50
__
b) We can subtract half the second equation from the first to get an equation for the cost of a drink.
(2p +3d) -1/2(4p +2d) = (18.25) -1/2(27.50)
2d = 4.50 . . . . . . simplify
d = 2.25 . . . . . . divide by 2
4p +2(2.25) = 27.50 . . . . substitute for d in the second equation
4p = 23.00 . . . . . . . . . subtract 4.50
p = 5.75 . . . . . . . . . divide by 4
The cost of a bag of popcorn is $5.75; the cost of a drink is $2.25.
-5(-3x+1)= 45 solve for x
Answers
Answer:
x=[tex]\frac{10}{3}[/tex]
Step-by-step explanation:
Hi there!
We are given the equation -5(-3x+1)=45 and we need to solve for x
we do this by isolating x by itself on one side of the equation; the numbers (the value of x) is on the other side
First, do the distributive property and distribute -5 on -3x and 1 on the left side (multiply both -3x and 1 by -5)
15x-5=45
add 5 to both sides (-5+5=0)
15-5=45
+5 +5
_________
15x=50
divide both sides by 15 (15÷15=1)
15x=50
÷15 ÷15
________
x=[tex]\frac{50}{15}[/tex]
we can simplify this fraction by factoring five out of 50 and 15
x=[tex]\frac{10*5}{3*5}[/tex]
cancel 5 out of the numerator and denominator
x=[tex]\frac{10}{3}[/tex]
The answer can be left as an improper fraction
Hope this helps! :)
A cylindrical water tower has a volume of
10007 ft.
If the tower is 10 ft tall, what is the radius of the tower?
Answers
Answer:
r≈17.85
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.
Answer:
r=17.85
Step-by-step explanation:
i just got it and did the math
Taking 0.5 cm as 1 unit, plot the following points on the graph paper: A(1,3), B (-3,-1), C (1,- 4), D (- 2,3), E (0-8), F (1.0)
Answers
Answer:
It's letter c
Step-by-step explanation:
you have to × the 0.5 and 1
Simplify 3 · 2x. What is the coefficient?
• 2
• 3
• 6
Answers
Answer:
6x coefficient is 6. the number next to the letter
Step-by-step explanation:
Please help!! Will mark brainilest ☺️☺️
Answers
Can someone help with this
Answers
Answer: 28
Step-by-step explanation: ADB = 1/2 ACB
How many solutions are there to the equation below?
4(x – 5) = 3x + 7
Answers
Answer:
one solution
Step-by-step explanation:
4(x - 5) = 3x + 7
4x - 20 = 3x + 7
4x - 3x = 7 + 20
x = 27
Answer:
1 solution
Step-by-step explanation:
x = 27
distribution of 4 into x and -5
4x-20 = 3x +7
-3x+20=-3x+20
x = 27