Answer:
The measure of the angle of each of the intercepted arc is 180°
Step-by-step explanation:
An intercepted arc is an encased (between chords) portion of the circumference of the circle. The chords that form the intercepted arc meet at a point
An inscribed angle is the angle is an angle formed between two chords that meet at a point called the end point
For the inscribed square, the symmetry has it that the diagonal is the same as the diameter of the circle as the diagonals bisect each other having equal distances on either side to the circumference of the circle.
Given that the angles in the vertices of the square are 90° and the point of intersection of the two chords forming the vertex are at the ends of the diameter of the circle, which passes through the center of the circle, the angle 90° at the vertex is half the angle at the center which is the angle of the intercepted arc
∴ The measure of the angle of each of the intercepted arc = 2× 90 = 180°.
A group of students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.01 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute?
Complete Question
The complete question is shown on the first uploaded image
Answer:
Yes the students are reasonably good at estimating one minute
a
Option A is correct
b
The test statistics is [tex]t = 0.354[/tex]
Step-by-step explanation:
From the question we are told that
The set of data is
68, 82 , 38 , 62 , 41, 25 , 57 , 64, 67, 47, 61, 71, 91, 87, 64
The population mean is [tex]\mu = 60[/tex]
The level of significance is given as[tex]\alpha = 0.01[/tex]
The critical value for this level of significance obtained from the normal distribution table is
[tex]Z_{\alpha } = 2.33[/tex]
The null hypothesis is
[tex]H_o : \mu = 60 \ seconds[/tex]
The alternative hypothesis is
[tex]Ha : \mu \ne 60 \ seconds[/tex]
Generally the sample mean is mathematically represented as
[tex]\= x = \frac{\sum x_i }{n }[/tex]
where n = 15
So
[tex]\= x = \frac{ 68+ 82 + 38 + 62 + 41+ 25 + 57 + 64+67+ 47+ 61+ 71+ 91+ 87+ 64}{15}[/tex]
[tex]\= x = 61.67[/tex]
The standard deviation is mathematically represented as
[tex]\sigma =\sqrt{ \frac{ \sum (x_i - \= x )^2}{n} }[/tex]
substituting values
[tex]\sigma =\sqrt{ \frac{ \sum (68-61.67)^2 + ( 82-61.67 )^2 + (38 -61.67)^2 + 62-61.67)^2 + (41-61.67)^2 +(25-61.67)^2 +( 57+61.67)^2 }{15} }[/tex] [tex]\sqrt{ \frac{ ( \cdot \cdot + ( 64-61.67)^2 + (67-61.67)^2 +(47-61.67)^2 + (61-61.67)^2+ (71-61.67)^2 + (91 -61.67)^2+( 87-61.67)^2 + (64-61.67)^2}{15} }[/tex]=> [tex]\sigma = 18.23[/tex]
The test statistics is evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{61.67 -60 }{ \frac{18.23 }{\sqrt{ 15} } }[/tex]
[tex]t = 0.354[/tex]
Now comparing the statistics and the critical value of the level of significance we see that the the test statistics is less than the critical value
Hence the we fail to reject the null hypothesis which mean that these times are from a population with a mean equal to 60 seconds
So we can state that yes the students are reasonably good at estimating one minute given that the sample mean is not far from the population mean
In the lab, Goran has two solutions that contain alcohol and is mixing them with each other. Solution A is 40% alcohol and Solution B is 10% alcohol. He uses 800 milliliters of Solution A. How many milliliters of Solution B does he use, if the resulting mixture is a 30% alcohol solution?
Answer:
400milliliters
Step-by-step explanation:
Let x=ml of 30% solution B used in resulting mixture.
800+x=ml of resulting 30% solution
40%(800)+10%x=30%(800+x)
Then we can simplify the expression
0.4(800)+0.10x= 0.30(800+x)
320+0.10x=240+0.30x
80=0.20x
x= 400milliliters
Therefore, 400milliliters of 10% solution B used in resulting mixture.
a cord of a circle is a line segment connecting any point on the circle to the center of a circle. true or false?
Answer:
true if I'm wrong I'm so sorry:/
How many single-scoop cones could be made from a choice of 2 types of cones, 3 flavors of ice cream, and optional toppings of peanuts and/or sprinkles?
Answer:
Number of different cones made = 18
Step-by-step explanation:
Given:
Types of cone = 2
Number of flavors = 3
Number of toppings = 2
Find:
Number of different cones made
Computation:
Number of different toppings = 1(peanuts) + 1(sprinkles) + 1(both) = 3
Number of different cones made = Types of cone × Number of flavors × Number of different toppings
Number of different cones made = 2 × 3 × 3
Number of different cones made = 18
Quadrilateral ABCD is a kite. A kite. Angle A is 90 degrees, angle B is unknown, angle C is 130 degrees, angle D is unknown. What is the measure of angle B? degrees
Answer:
70 degrees
Step-by-step explanation:
(360 - 90 - 130)/2=70
Write an equation of the line that passes through the point (–4, 6) with slope –4.
Answer:
y = - 4x - 10
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 4 , thus
y = - 4x + c ← is the partial equation
To find c substitute (- 4, 6) into the partial equation
6 = 16 + c ⇒ c = 6 - 16 = - 10
y = - 4x - 10 ← equation of line
Answer:
y = -4x+10
Step-by-step explanation:
Using the slope intercept form of a line
y = mx+b where m is the slope and b is the y intercept
y = -4x +b
Substituting the point in
6 = -4(-4) + b
6 = 16+b
Subtract 16 from each side
-10 =b
The equation is
y = -4x+10
Which inequality represents all possible solutions of -3(x+5)>12?
its A
Step-by-step explanation:
dividing or multiplying a negative number in this will completely change the sign to opp side
-3x + 15 < 12
-3x < -3
x > 1
Option d i.e x<-9 represents all possible solutions of -3(x+5)>12
What is Inequality?An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.
The given inequality is
-3(x+5)>12
-3x-15>12
-3x>12+15
-3x>27
Divide both sides by 3
-x>9
When we multiply negative sign on both sides the lesser than sign changes to greater.
x<-9.
Therefore option d represents all possible solutions of -3(x+5)>12.
To learn more on inequality click:
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How much water is wasted by the leaky faucet in 1 day? 15 drips per 30 seconds
Answer:
a. 43,200 drips
b. 4 gallons (approximately, actual value is 3.8)
c. 61 cups(approximately, actual value is 60.8, using 3.8 gallons and not 4 gallons)
Step-by-step explanation:
Here, we have a faucet wasting water at a rate of 15 drips per 30 seconds, now we want to calculate the number of drips wasted in a day
To find this, what we need to do is fund the number of seconds in a day first
There are 24 hours with 60 minutes, with each minute having 60 seconds
So the number of seconds in a day = 24 * 60 * 60 = 86,400 seconds
Now 15 drips is wasted in 30 seconds
x will be wasted in 86,400 seconds
x = (15 * 86400)/30 = 43,200 drips are wasted in a day
b. Mathematically , there are about 3,000 drips in a liter of water
So;
3,000 drips = 1 liter
43,200 drips = x liter
x = 43200/3000 = 14.4 liters of water
Mathematically,
1 liter = 0.264 gallons
So 14.4 liters = 14.4 * 0.264 = 3.8 gallon
which is equal to 4 gallons of water approximately
c. Mathematically;
1 gallon = 16 cups of water
So 3.8 gallons of water will measure 3.8 * 16 = 60.8 which is approximately 61 gallons of water
Solve this linear equation for x: 7 + 4 (5/4x - 1) = 18
Answer:
x=3
Step-by-step explanation:
7+4(5/4x-1)=18
7+5x-4=18
3+5x=18
5x=15
x=3
Answer:
x = 3
Step-by-step explanation:
18 = 7 + 4([tex]\frac{5}{4}[/tex]x - 1)
18 = 7 + 5x - 4
18 = 3 + 5x
15 = 5x
x = 3
Prove that. 1-sin2A=2sin^2(45-A)
Answer:
Proved
Step-by-step explanation:
2 sin square( 45°-A)
(therefore;
by trigonometry ratios
sin45°=1)
=2sin2(1-A)
=2sin(1-A)
=1+sin2A
hence proved
I HOPE THIS WILL HELP YOU
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Tysm
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two sides
of this triangle?
O 5cm and 8 cm
O 6 cm and 7 cm
O 7 cm and 2 cm
8 cm and 9 cm
Answer:
Choice D - 8cm and 9cm.
Step-by-step explanation:
The other sides are not greater than 13.
A: 5 + 8 = 13
B: 6 + 7 = 13
C: 7 + 2 = 9
However, D is greater than 13 and is the correct answer.
D: 8 + 8 = 16.
Option d: 8 cm and 9 cm.
There is a theorem in mathematics stating:
" The sum of length of two sides of any triangle is greater than the rest third side"
According to that theorem, first three given options cant form the sides of the given triangle whose one side is 13 cm.
The 4th option has 8 cm and 9 cm for which we have:
8 + 9 > 13
Thus this option follows the theorem.
Hence fourth option is correct.
For more information, refer this link:
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On August 8, 1981, American Savings offered an insured tax-free account paying 23.24% compounded monthly. If you had invested $90,000 at that time, how much would you have on August 8, 2014, assuming that you could have locked the interest rate at the time of deposit? Someone please help me!!
Answer:
$181,432,754
Step-by-step explanation:
We use the formula for compound interest here, to determine the amount
Mathematically, that would be;
A =I (1 + r/n)^nt
where A is the amount which we want to calculate
I is the initial amount which is $90,000
r is the rate = 23.24% = 23.24/100 = 0.2324
n is the number of times per year the interest is compounded = 12 (compounded monthly)
t is the number of years = 2014 - 1981 = 33
Substituting these values, we have;
A = 90,000(1 + 0.2324/12)^(33 * 12)
A = 90,000(1 + 0.0194)^396
A = 90,000(1.0194)^396
A = 181,432,754.27210504
Which is approximately $181,432,754 to the nearest whole dollars
The sum of two negative integers is always
Answer:
The sum of two negative integers is always negative.
Step-by-step explanation:
For example, add -1+-1 which =-2, which are the smallest neggative numbers possible.-100+-100=-200, and -4+-4=-8, so you see that the sum of two negative integers should always be negative.
When results from a scholastic assessment test are with their scores are also given. Suppose a test-taker scored at the 78th percentile for their verbal sent to test-takers, the percentiles associated 26) grade and at the 34th percentile for their quantitative grade. Interpret these results.
A) This student performed better than 22% of the other test-takers in the verbal part and better
B) This student performed better than 78% of the other test-takers in the verbal part and better
C) This student performed better than 22% of the other test-takers in the verbal part and better
D) This student performed better than 78% of the other test-takers in the verbal part and better than 66% in the quantitative part. than 34% in the quantitative part.
Answer:
B) This student performed better than 78% of the other test-takers in the verbal part and better than 34% in the quantitative part.
Step-by-step explanation:
In Statistics, Percentile refers to how specific variables can be divided according to the distribution of values in a population of 100 equal groups.
The data value of a given percentile can be determined as 100 times the cumulative relative frequency of that value.
From the given question.
Suppose a test-taker scored at the 78th percentile for their verbal sent to test-takers, the percentiles associated grade and at the 34th percentile for their quantitative grade.
This implies that ;
The student score shows the relation between a particular score of :
78% and the scores of the rest of a group for the verbal test takers &
34% and the scores of the rest of a group for the quantitative test takers.
Therefore; we can conclude that ;
This student performed better than 78% of the other test-takers in the verbal part and better than 34% in the quantitative part.
Find the equation of the line: With a slope of − 1 2 through (4, 5)
Answer:
y = -1/2x+7
Step-by-step explanation:
We have a slope of -1/2 and a point of (4,5)
Using the slope intercept form of a line
y = mx+b
y = -1/2 x +b
Substituting the point into the equation
5 = -1/2(4) +b
5 = -2+b
Add 2 to each side
5+2 = -2+2+b
7 = b
The equation of the line is
y = -1/2x+7
Helpp pleaseeeeeeeeeeee
Work Shown:
sin(angle) = opposite/hypotenuse
sin(40) = 24/x
x*sin(40) = 24
x = 24/sin(40)
x = 37.33737184465
x = 37.3
When you use your calculator, make sure it is in degree mode. One way to check is to compute something like sin(30) and you should get 0.5
Answer:
x = 37.3
Step-by-step explanation:
for the specified angle, the ratio of the length of the side that is opposite that angle to the length of the longest side (hypotenuse) of the triangle, it is sine.
[tex]\sin40^o=0.6428[/tex]
From triangle [tex]\sin40^o=\dfrac{24}x[/tex]
so:
[tex]0.6428=\dfrac{24}x\\\\0.6428\,x=24\\\\x=24\div0.6428=37.336652....\approx37.3[/tex]
Allen and Stephan went shopping for Mother's day. Stephan spent $30 for 4 roses and 2 CDs. Allen bought 2 roses and 3 CDs for $40. What was the cost of a rose and a CD?
Answer:
work is shown and pictured
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs $3.25Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most $30 before tax. The restaurant only sells pancakes in stacks of 4 pancakes for $5.50 Let S represent the number of stacks of pancakes that Benjamin buys.
Answer:
is the correct answer.
Step-by-step explanation:
As per the question statement:
Cost of Chocolate milk which is ordered already = $3.25.
Benjamin want his bill to be at most = $30
Each stack of pancakes contains 4 pancakes.
Each stack of pancake costs= $5.50
Given that S represents the number of stacks of pancakes bought.
We have, Cost of 1 pancake = $5.50
Now, let us calculate the cost of the number of stacks of pancakes bought.
[tex]\text{Cost of one stack of pancakes}\times \text{Number of stacks of pancakes bought}[/tex]
i.e.
[tex]5.50S[/tex]
So, total bill = Cost of chocolate milk shake + Money spent on stacks of pancakes = [tex]\$3.25+5.50S[/tex]
Now, this money should be lesser than or equal to $30 because maximum bill that Benjamin wants is $30.
So, the inequality can be written as:
[tex]\bold{3.25+5.50S \le 30}[/tex]
Please refer to https://brainly.com/question/17138529 as well.
3.25+5.50S < (with line under it) 30
To add on to what isyllus said...
3.25+5.50S < (with line under it) 30 is the equation
16 pancakes is the amount.
:) hope this helps!
Need help ASAP thankyou sorry if u can’t see the picture but u can zoom in :)
Answer:
a)Volume 390ft3. Surface area 450ft2
b)surface area
c)volume
Step-by-step explanation:
2*15*13=390
2*15*2=60+15*13*2=390
V
The
to prove A
triangle congruency theorem can be used
2 AONP.
M
N
o
Р
Answer:
The SAS(Side-Angle-Side) triangle congruency theorem can be used to prove Triangle MNL is congruent to ONP.
Step-by-step explanation:
We would use the side-angle-side theorem because the two triangles both have two equal sides and one angle. For instance, side MN has two lines and so does side ON has two lines. Same goes with sides NL and NP.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Answer:
See below
Step-by-step explanation:
The SAS triangle congruency theorem can be used to prove ΔMNL ≅ ΔONP.
The SAS (Side-Angle-Side) postulate will be used because two sides and one angle are congruent.
They are the following:
=> NM ≅ NO (Given)
=> NP ≅ NL (Given)
=> ∠LNM ≅ ∠PNO (Vertical Angles)
Mr Krishnan earned 2,400 rupees ,he spent 3/8 on food ,1/3 on taxes and 1/6 on other expenses. Find out how much all this in rupees and then find out how much he saved
Step-by-step explanation:
to find his total expenses, add all fraction spent
3/8 + 1/3 + 1/6
= 9+8+ 4/24
= 21/24. = 7/8
total fraction =1
subtract the fraction spent form the total fraction to know the fraction left for savings
1-7/8= 1/8
therefore if. 1 = 2,400
then 1/8=?
if less more divides
1/8 ÷ 1 ×2,400
1/8 × 1/1×2,400
1/8 × 2,400
=300.
therefore the man saved 300 rupees
Order from least to greatest
5% , 33%, 75%, 1/2 and how you lnow?
Answer:
5%, 33%, 1/2, 75%
Step-by-step explanation:
5% , 33%, 75%, 1/2
Change 1/2 to a percent.
1/2 = 0.5 = 0.5 * 100% = 50%
We are comparing
5%, 33%, 75%, 50%
From least to greatest:
5%, 33%, 50%, 75%
Now we convert 50% back to a fraction.
5%, 33%, 1/2, 75%
I really need help please
Answer:
1. 2.997
2. 29.93
Step-by-step explanation:
1. You gotta multiply the three sides given, to do this, they all have to be the same unit. Either convert them all to inches or feet then do the operation.
2. Same thing, gotta multiply all given values
Which of the following is a polynomial?
O A. x2 + 2
OB.
(x - 2)
(x+2+3)
O c. 1-1
x
O D. 7x7 - 2x-4 + 3
Answer: B
Step-by-step explanation:
When B is simplified, it becomes x^2-3x-10. This is a polynomial because it has more than two terms(3).
Hope it helps <3
The solution is: the following is a polynomial, A. 4x^2+9x+12 & C. 15x^4
Option A and C are correct.
What are Polynomials?Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.
Here, we have,
we know that,
A polynomial is defined as an algebraic expression that consists of variables and constants involving operations of addition, subtraction, multiplication and non-negative exponents.
A. 4x^2+9x+12 is a polynomial
B. 3-√2x is not a polynomial
C. 15x^4 is a polynomial
D. 6x^2+2/x is not a polynomial
So, Option A and C are correct.
Hence, The solution is: the following is a polynomial, A. 4x^2+9x+12 &
C. 15x^4 , Option A and C are correct.
Know more about Polynomials here:
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Find the surface area and volume of a rectangular prism with the following dimensions: Length = 4 cm, Width = 9 cm, Height = 2 cm
Answer:
the surface area is 124
the volume is 72
Step-by-step explanation:
Hi there! :)
Answer:
SA = 124 cm².
V = 72 cm³
Step-by-step explanation:
Volume of a rectangular prism: V = l × w × h
Given:
l = 4 cm
w = 9 cm
h = 2 cm
V = 4 × 9 × 2
V = 36 × 2
V = 72 cm³
Surface area: SA = 2(wl + hl + hw)
SA = 2((4 · 9) + (2 · 4) + (9 · 2))
SA = 2(36 + 8 + 18)
SA = 2(62)
SA = 124 cm².
Hope this helped you!
a pair of dice rolled many times and the result appears below. based upon these results,what is the experimental probability of rolling a multiple of 3
Answer:
There's no results that appear below
Solve 2(3x+6)=3(x-9) 2p-3=3p+2 2(3x-1)-7(5x+4)=9(2x-3)
Answer:
Step-by-step explanation:
1. 6x + 12 = 3x - 27
3x + 12 = -27
3x = -39
x = -13
2. 2p - 3 = 3p + 2
-p - 3 = 2
-p = 5
p = -5
3. 6x - 2 - 35x -28 = 18x - 27
-29x - 30 = 18x - 27
-47x - 30 = -27
-47x = 3
x = -3/47
What type of triangle has side lengths 9, 10and 130‾‾‾‾√
Answer:
Step-by-step explanation:
Triangle is an example of a polygon with three sides. The types of triangle we have are the equilateral, isosceles, scalene and right angled triangle.
An equilateral triangle is a triangle that has all its 3 sides and angles equal.
An isosceles triangle is a triangle that has two of its sides and angles equal.
A scalene triangle is a triangle that has none of its sides and angles to be equal.
According to the question, we are given a triangle of lengths 9, 10 and 130. It is seen that all the length of each sides of the triangle is different, this makes it a scalene triangle.
Find the perimeter of the shaded figure. Please help,thanks!
Answer:
I believe its 40
Step-by-step explanation:
Answer:
Hey there!
The perimeter can be expressed as 10+7+2+2+6+2+2+7, or 38.
Hope this helps :)
In a recent study, volunteers who had 8 hours of sleep were three times more likely to correctly on a math test than were sleep-deprived participants.
1) Identify the sample used in the study.
A) The sample is the math questions in the study.
B) The sample is the responses of the volunteers in the study.
C) The sample is the amount of sleep the volunteers got in the study.
D) The sample is the sleep-deprived participants in the study.
2) What is the sample's population?
A) The population is the collection of all the math questions from the math test.
B) The population is the collection of the responses of all individuals who completed the math test.
C) The population is the collection of all the individuals who completed the math test.
3) Which part of the study represents the descriptive branch of statistics?
1) Identify the sample used in the study: B) The sample is the responses of the volunteers in the study
2) What is the sample's population: B) The population is collected of the response of all individuals who completed the math test
3) Which part of the study represents the descriptive branch of statistics:
individuals who are not sleep deprived will be more likely to answer math questions correctly than individuals who are sleep deprived.
hope i helpd
-lvr