Answers
Answer:
see below
Step-by-step explanation:
Because two sides are congruent, the triangle in the diagram is isosceles which means that angle c = angle e because of the Base Angles Theorem. We know that angle c = 63 degrees because we see that it's vertical to a 63 degree angle, and vertical angles. Since angle c = angle e, angle e = 63 degrees. Since angles e and b form a linear pair, they are supplementary, meaning that they add up to 180 degrees which means that angle b = 180 - 63 = 117 degrees. To find angle d, we notice that d and c are alternate interior angles, and since these angles are congruent in parallel lines, angle d = 63 degrees as well. To find angle a, we know that the sum of angles in a triangle is 180 degrees so angle a = 180 - 63 - 63 = 54 degrees.
See in the attachment.
Related Questions
Solve the formula for the perimeter of a rectangle, with width w and length I,
for the length.
P= 2W + 2/
Answers
Answer:
( P -2w) /2 = l
Step-by-step explanation:
P= 2W + 2l
Subtract 2W from each side
P= 2W -2W + 2l
P -2W = 2l
Divide by 2
( P -2w) /2 = l
Answer:
A. [tex]\frac{P - 2w}{2} = l[/tex]
Step-by-step explanation:
Well in,
P = 2w + 2l
to solve for l we need to single it out.
P = 2w + 2l
-2w
P - 2w = 2l
divide everything by 2
[tex]\frac{P - 2w}{2} = l[/tex]
Thus,
the answer is A.
Hope this helps :)
Find the sum of the following infinite geometric series
Answers
Answer:
[tex]\large \boxed{\ \ \dfrac{63}{5} \ \ }[/tex]
Step-by-step explanation:
Hello,
"Find the sum of the following infinite geometric series"
infinite
We will have to find the limit of something when n tends to [tex]+\infty[/tex]
geometric series
This is a good clue, meaning that each term of the series follows a geometric sequence. Let's check that.
The sum is something like
[tex]\displaystyle \sum_{k=0}^{+\infty} a_k[/tex]
First of all, we need to find an expression for [tex]a_k[/tex]
First term is
[tex]a_0=7[/tex]
Second term is
[tex]a_1=\dfrac{4}{9}\cdot a_0=7*\boxed{\dfrac{4}{9}}=\dfrac{7*4}{9}=\dfrac{28}{9}[/tex]
Then
[tex]a_2=\dfrac{4}{9}\cdot a_1=\dfrac{28}{9}*\boxed{\dfrac{4}{9}}=\dfrac{28*4}{9*9}=\dfrac{112}{81}[/tex]
and...
[tex]a_3=\dfrac{4}{9}\cdot a_2=\dfrac{112}{81}*\boxed{\dfrac{4}{9}}=\dfrac{112*4}{9*81}=\dfrac{448}{729}[/tex]
Ok we are good, we can express any term for k integer
[tex]a_k=a_0\cdot (\dfrac{4}{9})^k[/tex]
So, for n positive integer
[tex]\displaystyle \sum_{k=0}^{n} a_k=\displaystyle \sum_{k=0}^{n} 7\cdot (\dfrac{4}{9})^k=7\cdot \dfrac{1-(\dfrac{4}{9})^{n+1}}{1-\dfrac{4}{9}}=\dfrac{7*9*[1-(\dfrac{4}{9})^{n+1}]}{9-4}=\dfrac{63}{5}\cdot [1-(\dfrac{4}{9})^{n+1}}][/tex]
And the limit of that expression when n tends to [tex]+\infty[/tex] is
[tex]\large \boxed{\ \ \dfrac{63}{5} \ \ }[/tex]
as
[tex]\dfrac{4}{9}<1[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
factorize completely (2x+2y) (x-y)+(2x-2y)(x+y)
Answers
Explanation:
(2x + 2y)(x - y) + (2x - 2y)(x+y)
= 2(x+y)(x-y) + 2(x-y)(x+y)
= 2(x^2 - y^2) + 2(x^2 - y^2)
= (2 + 2)(x^2 - y^2) (combine like terms)
= 4(x^2 - y^2)
Find x and y, please solve with steps and leave answers in fraction form, THANK YOU
Answers
Answer:
Below
Step-by-step explanation:
Using the proprtionality relation:
● 8/10 =5/x
● (4*2)/(5*2) = 5/x
Simplify using 2
● 4/5 = 5/x
Multiply both sides by 5
● (4/5)*5 = (5/x)*5
● 4 = 25/x
Switch x and 4
● x= 25/4
■■■■■■■■■■■■■■■■■■■■■■■■■
Again use the proportionality relation but this time with y.
● 8/10 =7/y
8/10 = 4/5
● 4/5 = 7/y
Multiply both sides by 5
● (4/5)*5 =(7/y)*5
● 4 = 35/y
Switch 4 and y
● y = 35/4
According to medical data, the ages at which patients have their first knee replacement surgery
follows a normal distribution. The average age for a first knee replacement is 58 years of age, with a
standard deviation of 8.25 years. Therefore, doctors can expect the middle 68% of their knee
replacement surgery patients to be between what ages?
Answers
Answer:
The doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.
Step-by-step explanation:
68 % of the knee replacement surgery patients implies that the ages lies within x = x₀ ± σ where x₀ = mean age = 58 years and σ = standard deviation = 8.25 years
So, the ages lies between x₀ + σ and x₀ - σ
So, the ages lie between 58 - 8.25 = 49.75 years
and 58 + 8.25 = 66.25 years
So the doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.
The lowest temperature ever
recorded on earth was -89°C
in Antarctica. The average
temperature on Mars is about
-55°C. Which is warmer?
Write an inequality to support
your answer
Answers
Answer:
Mars
Step-by-step explanation:
America
Find the missing side of a triangle when one side is 3.16 and the other is 3
Answers
Answer:
0.992774 ≅ .993
Step-by-step explanation:
a²+b²=c²
a=x
b=3
c=3.16
x²+3²=3.16²
x²+9=9.9856
x²=.9856
x=0.992774
x≅0.993
The radius of a conical tent is 5.6 m and the slant height is 12 m. Then the length of canvas required
to make the tent, if the width of canvas is 4 m.
a) 106.6 m
b) 100 m
c) 52.8 m
d) 105.6m
who will answer it first I mark them as the brainlist
Answers
Answer:
c) 52.8 m
Step-by-step explanation:
The radius of a conical tent, r = 5.6 m
The slant height = 12 m.
The area of the canvas required to make the tent is equal to the lateral area of the cone.
[tex]\text{Lateral Area of a Cone}= \pi r l\\=\pi \times 5.6 \times 12\\=67.2\pi$ m^2[/tex]
Since the width of the canvas = 4 m
Let the length = l
Area of the canvas = 4l
[tex]4l=67.2\pi$ m^2\\l=67.2\pi \div 4\\l=52.8 m$ (correct to 1 decimal place)[/tex]
The length of the canvas required to make the tent is 52.8m.
Based on historical data, an insurance company estimates that a particular customer has a 2.6% likelihood of having an accident in the next year, with the average insurance payout being $1600.
If the company charges this customer an annual premium of $110, what is the company's expected value of this insurance policy?
Answers
Answer: $68.4
Step-by-step explanation:
Given: Annual Premium = $110
Average insurance payout = $1600
Likelihood of having an accident= 2.6% = 0.026 [we divide perecnt by 100 to convert it into decimal]
Then, Expected value = (Annual Premium) - (Likelihood of having an accident) x (Average insurance payout )
= $110 - (0.026) x ($1600)
= $(110-41.6)
= $68.4
Hence, the company's expected value of this insurance policy : $68.4
Forty percent of all undergraduates at a university are chemistry majors. In a random sample of six students, find the probability that exactly two are chemistry majors. 12. The probability that exactly two are chemistry majors is Type an integer or a decimal. Round to four decimal places as needed.)
Answers
Answer:
0.3110
Step-by-step explanation:
This is a binomial distribution with probability of success (being a chemistry major) p = 0.40.
The general formula for a binomial distribution is:
[tex]P(x=k)=\frac{n!}{(n-k)!k!}*p^k*(1-p)^{n-k}[/tex]
Where n is the sample size and k is the desired number of successes.
The probability of k=2 in a sample of n =6 is:
[tex]P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2} \\P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2}\\P(x=2)=3*5*0.4^2*0.6^4\\P(x=2)=0.3110[/tex]
The probability is 0.3110
Which is the solution to this question 4X equals 32
Answers
Answer:
8
Step-by-step explanation:
you would just divide 32 by 4
4x = 32
x = 32/4
x=8
Answer:
[tex]\large\boxed{\sf \ \ \ x=8 \ \ \ }[/tex]
Step-by-step explanation:
Hello
4x=32 we can divide both parts by 4 so
[tex]\dfrac{4x}{4}=\dfrac{32}{4}\\\\<=> x = 8[/tex]
Hope this helps
Find the linear correlation coefficient using only the four points in the lower left corner (for women). Will the four points in the upper right corner (for men) have the same linear correlation coefficient? The correlation coefficient for the points in the lower left corner is requals nothing.
Answers
Answer:
Yes, because the four points in the upper right corner from the same pattern as the four points in the lower left corner.
Step-by-step explanation:
The correlation coefficient for the points in the lower left corner equals zero.
The four points in the upper right corner have the same correlation coefficient because the four points in the upper right corner from the same pattern as the four points in the lower left corner.
Select the correct answer.
What are the x-intercepts of this function?
g(x) = -0.25x2 – 0.25x + 5
O
(-20,0) and (-4,0)
(4,0) and (20,0)
(5,0) and (-4,0)
(-5,0) and (4,0)
Answers
Answer:
[tex]\large \boxed{\sf \ \ (-5,0) \ and \ (4,0) \ \ }[/tex]
Step-by-step explanation:
Hello,
We need to find the zeroes of
[tex]-0.25x^2-0.25x+5=0\\\\\text{*** multiply by -4 ***} \\ \\x^2+x-20=0\\\\\text{*** the sum of the zeroes is -1 and the product -20=-5x4 ***}\\\\x^2+5x-4x-20=x(x+5)-4(x+5)=(x+5)(x-4)=0\\\\x=4 \ or \ x=-5[/tex]
and then g(4)=0 and g(-5)=0
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:(-5,0) (4,0)
I took the test hope it helps you (:
1. Find the Product of 8.02 and 6.1 and correct your answer to the highest whole number. 2. How many pieces of ribbon each 6cm long can be cut from a roll of ribbon 24m long?
Answers
2. 24/6=4cm
I hope it’s help u
A total of 32/3 strips can be derived from the ribbon.
What is quotients?In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.
Here, we have,
to determine the number of strips:
From the question, we have the following parameters
Length of a roll of ribbon = 4 meters
Also, from the question;
We have
Length of a piece of ribbon = 5/12 meter
The number of strips of ribbon is the quotient of the Length of a roll of ribbon and the Length of a piece of ribbon
This is represented as
Number of strips = Length of a roll of ribbon/Length of a piece of ribbon
So, we have
Number of strips = (4 )/(5/12)
Evaluate the quotient
Number of strips = 32/3
Hence, the number of strips is 32/3
Read more about quotients at
brainly.com/question/629998
#SPJ2
complete question:
How many strips of a ribbon can be cut from a roll of ribbon that is 4 4/9 meters long if each piece is 5/12 meters long
what are the coordinates of the vertex of the function f(x) = x2 -12x +5?
Answers
Answer:
[tex]\huge\boxed{(6;\ -31)}[/tex]
Step-by-step explanation:
METHOD 1:Let: [tex]f(x)=ax^2+bx+c[/tex].
The coordinates of the vertex:
[tex](h;\ k)\to h=\dfrac{-b}{2a};\ k=f(h)=\dfrac{-(b^2-4ac)}{4a}[/tex]
We have
[tex]f(x)=x^2-12x+5\to a=1;\ b=-12;\ c=5[/tex]
Substitute:
[tex]h=\dfrac{-(-12)}{2(1)}=\dfrac{12}{2}=6\\\\k=f(6)=6^2-12(6)+5=36-72+5=-31[/tex]
METHOD 2:The vertex form of an equation of a quadratic function:
[tex]f(x)=a(x-h)^2+k[/tex]
We have:
[tex]f(x)=x^2-12x+5\to a=1[/tex]
Complete to the square [tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]
[tex]x^2-12x+5=x^2-\underbrace{2(x)(6)}_{12x}+5=\underbrace{x^2-2(x)(6)+6^2}_{a^2-2ab+b^2}-6^2+5\\\\=\underbrace{(x-6)^2}_{(a-b)^2}-36+5=(x-6)^2-31\\\\h=6;\ k=-31\to(6;\ -31)[/tex]
Plz help this is an evil question
Answers
Answer:
18.9 units of fencing
Step-by-step explanation:
First find the perimeter
P = 2(l+w)
P = 2( 2.5+1.28)
P = 2( 3.78)
P =7.56m
We need 2.5 units of fencing for each meter
Multiply by 2.5
7.56*2.5
18.9 units of fencing
Answer:
Julio needs to purchase 18.9 units of fencing.
Step-by-step explanation:
I meter of the perimeter accounts for 2.5 units of fencing. Respectively 2 meters account for 2 times as much, and 3 meters account for 3 times as much of 2.5 units. Therefore, if we determine the perimeter of this rectangular garden, then we can determine the units of fencing by multiplying by 2.5.
As you can see this is a 2.5 by 1.28 garden. The perimeter would be two times the supposed length, added to two times the width.
2.5 x 2 + 1.28 x 2 = 5 + 2.56 = 7.56 - this is the perimeter. The units of fencing should thus be 7.56 x 2.5 = 18.9 units, or option d.
Chuck has 6$ and he spends 1/5 of his money on candy
Answers
Answer:
He spends $1.20 Which means he has $4.80 remaining.
Step-by-step explanation:
1/5 of 6 is 6/1 multiplied by 1/5 and that is 6/5 or 1 1/5
1/5 of a dollar is 20 cents. he has $1.20
6-1.20=4.80.
Answer:
[tex]4.80 => Answer[/tex]
Step-by-step explanation:
Use the information given.
1/5 of 6 is equal to 6/5
6/5 = 1.2
Now subtract.
[tex]6-1.2= 4.8[/tex]
So the answer is 4.80 or 4.8
Hope this helps! :)
By: ❤️BrainlyMagic❤️
Brainliest would be appreciated!
helppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
upper box is 0
middle box is 3 and
the downer box is 6
Step-by-step explanation:
Have a nice day
Y is directly proportional to x. Create an equation using k as the constant of proportionality.
Answers
Answer:
[tex]y = kx[/tex]
Step-by-step explanation:
y is directly proportional to x.
[tex]y \propto x[/tex]
[tex]y = kx[/tex]
Where k is as the constant of proportionality.
Answer:
y = kx
Step-by-step explanation:
Y is directly proportional to x which means that
=> y ∝ x
=> y = kx
Where k is the constant of proportionality.
What is the sum of a 54-term arithmetic sequence where the first term is 6 and the last term is 377? (1 point) 10,341 10,388 10,759 11,130
Answers
Answer:
10,341
Step-by-step explanation:
[tex]S_{n}=\frac{n}{2} (a_1}+a_{n})\\S_{54}=\frac{54}{2} (6+377)=27 \times 383=10,341[/tex]
The value of y varies inversely as the square of x, and y = 9, when x = 4.
Find the value of x when y = 1. Do not include "=" in your answer.
Answers
Answer:
The answer is
12Step-by-step explanation:
The above variation is written as
[tex]y = \frac{k}{ {x}^{2} } [/tex]
where k is the constant of variation
when y = 9
x = 4
We have
k = yx²
k = 9(4)²
k = 9 × 16
k = 144
So the formula for the variation is
[tex]y = \frac{144}{ {x}^{2} } [/tex]
when y = 1
[tex]1 = \frac{144}{ {x}^{2} } [/tex]
Cross multiply
x² = 144
Find the square root of both sides
x = √144
x = 12
Hope this helps you.
±2
Step-by-step explanation:
Find the surface area of a cylinder with radius 15.8 ft and height 4.4 ft. Use a
calculator. Round to the nearest tenth.
A. 1786.9 ft2
B. 1221.1 ft2
C. 3450.8 ft2
D. 2005.3 ft2
Answers
Hey there! I'm happy to help!
First, let's find the area of the two circles that make up the top and bottom of the cylinder. To find the area of a circle, you square the radius multiply it by pi (we will use 3.14)
15.8²=249.64
249.64×3.14=783.8696
Since there are two of these circles we multiply this by 2.
783.8696×2=1567.7392
Now, for the rectangle. To make a cylinder, you take a rectangle and wrap it around the top and bottom circles. One side of this rectangle is the height of the cylinder, and the other is the circumference of the circle (one side wraps all the way around the circle, which is the circumference).
The circumference is the diameter multiplied by 3.14 (pi). The diameter is twice the radius.
15.8×2=31.6
31.6×3.14=99.224
We multiply this by the height.
99.224×4.4=436.5856
Now, we add the areas of the circles and the rectangle.
1567.7392+436.5856=2004.3 (rounded to nearest tenth)
This is closest to D. 2005.3 ft². It is probably a bit off because I used 3.14 instead of actual pi.
Have a wonderful day! :D
A wire that is 76 feet long needs to be divided into lengths using the ratio 1 to 13. What is the longer length? Round your answer to two decimal places if necessary.
Answers
Answer:
70.59 feet
Step-by-step explanation:
There are a total of 14 parts when the wire is divided into a ratio of 1 to 13.
1. Divide 76 by 14
76 ÷ 14 = 5.43
2. Multiply the longer length of 13 parts
5.43 · 13 = 70.59
The longer length of the wire 70.59 feet
There are a total of 14 parts when the wire is divided into a ratio of 1 to 13.
1. Divide 76 by 14
76 ÷ 14 = 5.43
2. Multiply the longer length of 13 parts
5.43 · 13 = 70.59
What is a decimal in numbers?In algebra, a decimal number can be defined as a range whose entire number part and the fractional element are separated by means of a decimal point. The dot in a decimal range is referred to as a decimal point. The digits following the decimal factor show a price smaller than one.
Learn more about Algebra here https://brainly.com/question/723406
#SPJ2
Train passes the first 110 miles in 3 hours, and the next 240 miles at the rate of 60 mph. What was the average speed of the train for the entire trip?
Answers
Answer:
50 mph
Step-by-step explanation:
The total distance is 350 miles.
The total time is 3 hr + (240 mi / 60 mph) = 7 hr.
The average speed is 350 mi / 7 hr = 50 mph.
which equation can be used to solve for x in the following diagram? x° and (6x - 15)°
Answers
Answer:
= A
explanation :
the angle are right angle triangle which means it is always 90°11. A certain brand of margarine was analyzed to determine the level of polyunsaturated fatty acid (in percent). A sample of 6 packages had an average of 16.98 and sample standard deviation of 0.31. Assuming normality, a 99% confidence interval for the true mean of fatty acid level is:
Answers
Answer: (16.47, 17.49)
Step-by-step explanation:
Formula for confidence interval for the true mean if population stanmdard deviation is unknown:
[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = sample mean
n= sample size
s= sample standard deviation
[tex]t_{\alpha/2}[/tex] = Two tailed critical value.
We assume that the level of polyunsaturated fatty acid is normally distributed.
Given,
n= 6
degree of freedom = n-1 =5
[tex]\overline{x}[/tex] = 16.98
s= 0.31
significance level[tex](\alpha)[/tex] =1-0.99=0.01
Two tailed t- value for degree of freedom of 5 and significance level of 0.01 = [tex]t_{\alpha/2}=4.0317[/tex] [by student's t-table]
Now , the 99% confidence interval for the true mean of fatty acid level is:
[tex]16.98\pm 4.0317(\dfrac{0.31}{\sqrt{6}})\\\\=16.98\pm 4.0317(0.126557)\\\\=16.98\pm 0.51024\\\\=(16.98-0.51023,\ 16.98+0.51023)\\\\=(16.46977,\ 17.49023)\approx (16.47,\ 17.49)[/tex]
Hence, a 99% confidence interval for the true mean of fatty acid level is: (16.47, 17.49)
Solve polynomials 7/5 + 3/4 × 2 / 5-3 / 2
Answers
Answer:
Step-by-step explanation:
7/5 + 3/4 x 2/5 - 3/2
7/5 + 3/10 - 3/2
17/10 - 3/2
1/5
Step-by-step explanation:
Here, the given polynomial are,
=7/5+3/4×2/5-3/2
multiplying 3/4 and 2/5
= 7/5+6/20-3/2
taking LCM and adding them.
=(7×4+6×1-3×10)/20
by simplifying it we get, the answer is 1/5.
Hope it helps..
Ralph records the time it takes for each of his classmates to run around the track one time. As he analyzes the data on a graph, he notices that his classmates’ times are distributed symmetrically along the x-axis. Which component of data analysis is Ralph observing
Answers
Answer:
The overall shape of the data
Step-by-step explanation:
For us to know what shape a data is, it must fulfil 4 conditions
is it symmetrical?the amount of peaks available in the data set.is it uniform? Is it rightly or leftly skewed?From the question, Ralph observed that the classmates time are symmetrical along the x-axis.
Therefore he is observing the shape of the data since one of the conditions have been fulfilled.
Thank you!
Solve of the following equations for x: x – 6 = -2
Answers
Answer:
x = 4
Step-by-step explanation:
x - 6 = -2
Add 6 to each side
x-6+6 = -2+6
x = 4
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
[tex]x - 6 = -2[/tex]
Add 6 on both sides of the equation. The [tex]x[/tex] variable should be isolated on one side.
[tex]x - 6 +6= -2+6[/tex]
[tex]x=4[/tex]
The value of [tex]x[/tex] is 4.
What are the solutions to the system of equations graphed attached pic
Answers
Answer: C
Step-by-step explanation:
For system of equations, the solution is the point or points where the equations intersect. The point they meet signifies that they are the same at the x and y point.
Looking at the graph, we see 2 intersection points. They are (0,-8) and (4,8). Therefore, C is the correct answer.