Answer:
4.5Step-by-step explanation:
[tex]x \times 2 + 1 = 10[/tex]
[tex]2x + 1 = 10[/tex]
Move constant to R.H.S and change its sign
[tex]2x = 10 - 1[/tex]
Subtract the numbers
[tex]2x = 9[/tex]
Divide both sides of the equation by 2
[tex] \frac{2x}{2} = \frac{9}{2} [/tex]
Calculate
[tex]x = 4.5[/tex]
Hope this helps..
Best regards!!
In triangle $ABC$, $AB = BC = 25$ and $AC = 40$. What is $\sin \angle ACB$?
Answer:
Sine angle of <ACB = 38.68°
Step-by-step explanation:
Hello,
To solve this problem, we need a good representation of the sides and the angle.
See attached document for better illustration.
Assuming it's a right angled triangle,
AC = hypothenus
AB = opposite
BC = adjacent
AC = 40
BC = 25
AB = 25
From trigonometric ratios
Sinθ = opposite/ hypothenus
Sinθ = AB / AC
Sinθ = 25 / 40
Sinθ = 0.625
θ = sin⁻¹0.625
θ = 38.68°
Sine angle of <ACB = 38.68°
Which two features of igneous rocks are determined by their cooling rate?
color and shininess
shininess and hardness
hardness and crystal size
crystal size and rock texture
Answer:
crystal size and rock texture D
Step-by-step explanation:
:)
Hence, the option (D) is the correct answer i.e., crystal size and rock texture.
What is the texture?
The texture is defined as a tactile quality of an object's surface. It appeals to our sense of touch, which can evoke feelings of pleasure, discomfort, or familiarity.
The texture of an igneous rock is dependent on the rate of cooling of the melt slow cooling allows large crystals to form, fast coolng yields small crystals.
Hence, the option (D) is the correct answer i.e., crystal size and rock texture.
To know more about the texture
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Suppose 45% of the worlds population has type "O" blood type. A study was done to see if the percent differs for college students. 47% of the 1000 random selected college students have type O blood. conduct a hypothesis test to determine if the percent of college students with type o blood differs for college students?
Answer:
We accept H₀, with CI = 90 %, porcentage of O blood type in college students does not differ from the world population porcentage
Step-by-step explanation:
The test is a proportion two-tail test ( note: differs)
p₀ = 45 % or p₀ = 0,45
n = 1000
p = 47 % or p = 0,47
Test Hypothesis
Null hypothesis H₀ p = p₀
Alternative hypothesis Hₐ p ≠ p₀
CI we assume 90 % then α = 10 % α = 0,1 α/2 = 0,05
z score from z-table z(c) = 1,64
To calculate z(s) = ( p - p₀ ) / √ p₀q₀/ n
z(s) = ( 0,47 - 0,45 )/ √( 0,45)*(0,55)/1000
z(s) = 0,02/√( 0,2475)/1000
z(s) = 0,02/0,01573
z(s) = 1,2714
Now we compare z(s) and z(c)
z(s) < z(c) 1,2714 < 1,64
Then z(s) is in the acceptance region we accept H₀
Triangle RST was dilated with the origin as the center of dilation to create triangle R'S'T'. The triangle was dilated using a scale factor of 34. The coordinates of the vertices of triangle RST are given. You can use the scale factor to find the coordinates of the dilated image. Enter the coordinates of the vertices of triangle R'S'T' below. (Decimal values may be used.)
Answer:
Multiply every coordinate from the old one by 0.75
Step-by-step explanation:
I just did this question so I didn't need your photo. And I got it right. Hope this helps anyone else stuck on a similar question.
The rule is to multiply the old coordinates/sides by the scale factor, if its a fraction convert it to a decimal and then multiply like I did.
Answer:
x, y ----> 3/4x, 3/4y
Step-by-step explanation:
Determine the solution to the following set of linear equations by using the graph below
a) 2x + y = 5
2x - 2y = 2
Answer:
(2,1)
Step-by-step explanation:
Well first we single out y or x in one of the equations,
we’ll use 2x + y = 5 and single out y.
2x + y = 5
-2x to both sides
y = -2x + 5
So we can plug in -2x + 5 into y in 2x - 2y = 2.
2x - 2(-2x + 5) = 2
2x + 4x - 10 = 2
combine like terms,
6x - 10 = 2
Communicarice property
+10 to both sides
6x = 12
divide 6 to both sides
x = 2
If x is 2 we can plug 2 in for x in 2x + y = 5.
2(2) + y = 5
4 + y = 5
-4 to both sides
y = 1
(2,1)
Thus,
the solution is (2,1).
Hope this helps :)
1. Following is the Receipt and Payment A/c. of a club for the year ended 31-03-2014.
Receipt ₹ Payment ₹
To Balance b/d 75,000 By Salaries 22,000
To Subscription By office expenses 8,000
2012-13 35,000 By Sports equipment
2013-14 9,50,000 (Purchased on 1-10-2013) 6,00,000
2014-15 55,000 10,40,000 By Telephone charges 12,000
To Donation 90,000 By Electricity charges 18,000
To Entrance Fees 60,000 By Travelling Expenses 6,000
To Locker rent 20,000 By 10% Fixed Deposit
To Donation for Building 1,50,000 (made on 1-07-2013) 7,00,000
By balance c/d. 69,000
14,35,000 14,35,000
Additional information:
a) Outstanding subscription for 2013-14 ₹80,000. Outstanding salaries as on 1-04-2013 were ₹2,000 and as on 31-03-2014 were ₹4,000.
b) One third of Entrance fee to be treated as General income.
c) Locker rent rate is ₹2,000 per month.
d) Depreciation on sports equipment 10% p.a.
Prepare Income and Expenditure A/c. for the year ending 31-03-2014.
Answer:
Excess of income over expenditure is ₹1,185,500.
Step-by-step explanation:
Note: The data in this question are merged together. They are therefore sorted before answering this question. See the attached pdf file for the sorted question.
The question is now answered as follows:
Question: Prepare Income and Expenditure A/c. for the year ending 31-03-2014.
Answer and explanation:
Note: See the attached excel file for the Income and Expenditure A/c. for the year ending 31-03-2014.
Both receipts and payments account and income and expenditure account are prepared by not-for-profit organizations such as charity organizations, human right campaign, clubs, etc.
Receipts and payments account is an account gives a summary of all the cash transitions, cash received and paid, that the organization engaged in during a particular period. It is similar to the cash book prepared by profit making organizations. The receipts and payments account is prepared in or to determine the balance of cash in hand or at bank or bank overdraft at the end of the period.
Income and expenditure account is an account gives a summary of all incomes and expenses of an organization during a particular period. It is similar to the trading and profit and loss account prepared by profit making organizations. The income and expenditure account is prepared in order to determine whether there is a surplus or a deficit balance during the period.
In how many ways can you arrange 4 different colored balls? 4,8,4!,3!,5!
Answer:
We can arrange 4 different colored balls in 24 ways.
Step-by-step explanation:
We have to find the number of ways in which we can arrange 4 different colored balls.
Firstly, we have to decide that either we use Permutation or we use Combination.
A Permutation is used when the order of arranging the numbers matters while on the other hand, a combination is used when the order of arranging the numbers doesn't matter.
So, in our question; the ordering matters to us as a ball which is placed in the first place can't be put again put in other places.
Number of ways of arranging 4 different colored balls = [tex]^{4}P_4[/tex]
= [tex]\frac{4!}{(4-4)!}[/tex] {[tex]\because ^{n} P_r = \frac{n!}{(n-r)!}[/tex] }
= 4! = [tex]4 \times 3 \times 2\times 1[/tex]
= 24 ways
Hence, we can arrange 4 different colored balls in 24 ways.
Which is the best estimate of 90/7 divided by 1 3/4? 2 6 12 24
Answer:
6 is the best estimate.
Step-by-step explanation:
(90/7) / (1 & 3/4) == (90/7) / (7/4) == (90/7) * (4/7) == 360/49 > 7.
Choose 6 as your best approximation.
Please answer this in two minutes
Answer:
R = 21.8° to the nearest tenth
Step-by-step explanation:
To find Angle R we use tan
tan ∅ = opposite / adjacent
From the question
The opposite is 2
The adjacent is 5
So we have
tan R = 2/5
R = tan-¹ 2/5
R = 21.8° to the nearest tenthHope this helps you
La suma de dos números es 50 y la diferencia es 22. ¿Cuáles son los números?
Answer:
(3,2)
Step-by-step explanation:
Just took the test
A climbing structure needs to be built in the shape of a square-based pyramid. Look at the diagram below. What is the perimeter of the flat, orange shape? PLEASE HELP A GIRL OUT
Answer:
40 m
Step-by-step explanation:
The perimeter of the flat, orange shape is the sum of all the sides that forms a boundary around the shape.
The shape is made up of 4 triangles having 2 equal side lengths each, which surrounds the center square.
Each side length of the triangle, that forms a boundary round the shape = 5 m.
There are 8 of this equal side length.
Perimeter = 8(5m) = 40 m
Simplify: 34w-(-8w)
Answer: 42w
Step-by-step explanation:
Subtracting a negative is like adding.
what is 92.5% of 200
Answer:
185
Step-by-step explanation:
All you have to do is multiply 200 by 92.5/100 (because it is 92.5%). This gives you 185.
Hope this helps!
Answer:
185
We know 92.5% of 100 is 92.5%, so 92.5 of 200 is just 92.5×2.
In a competition, a school awarded medals in different categiories.40 medals in sport 25 medals in danceand 212 medals in music, if the total of 55 students got medals and only 6 students got medals in the three categories ,how many students get medals in exactly two of these categories?
Answer:
210
Step-by-step explanation:
Given:
Medals in sports = 40
Medals in dance = 25
Medals in music = 212
Total students that received medals = 55
Total students that received medals in all three categories = 6
Required:
How many students get medals in exactly two of these categories?
Take the following:
A = set of persons who got medals in sports.
B = set of persons who got medals in dance
C = set of persons who got medals in music.
Therefore,
n(A) = 40
n(B) = 25
n(C) = 212
n(A∪B∪C)= 55
n(A∩B∩C)= 6
To find how many students get medals in exactly two of these categories, we have:
n(A∩B) + n(B∩C) + n(A∩C) −3*n(A∩B∩C)
=n(A∩B) + n(B∩C) + n(A∩C) −3*6 ……............... (1)
n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)
Thus, n(A∩B)+n(B∩C)+n(A∩C)=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)
Using equation 1:
=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)−18
Substitute values in the equation:
= 40 + 25 + 212 + 6 − 55 − 18
= 283 - 73
= 210
Number of students that get medals in exactly two of these categories are 210
Suppose a geyser has a mean time between eruptions of 72 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 23 minutes. Complete parts (a) through (e) below.
(a) What is the probability that a randomly selected time interval between eruptions is longer than 82minutes? The probability that a randomly selected time interval is longer than 82 minutes is approximately nothing. (Round to four decimal places as needed.)
(b) What is the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes? The probability that the mean of a random sample of 13 time intervals is more than 82 minutes is approximately nothing. (Round to four decimal places as needed.)
(c) What is the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes? The probability that the mean of a random sample of 34 time intervals is more than 82 minutes is approximately nothing. (Round to four decimal places as needed.)
(d) What effect does increasing the sample size have on the probability? Provide an explanation for this result. Fill in the blanks below. If the population mean is less than 82 minutes, then the probability that the sample mean of the time between eruptions is greater than 82 minutes ▼ increases decreases because the variability in the sample mean ▼ decreases increases as the sample size ▼ decreases. increases.
(e) What might you conclude if a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes? Select all that apply.
A. The population mean may be less than 72.
B. The population mean must be more than 72, since the probability is so low.
C. The population mean cannot be 72, since the probability is so low.
D. The population mean is 72, and this is just a rare sampling.
E. The population mean may be greater than 72.
F. The population mean is 72, and this is an example of a typical sampling result.
G. The population mean must be less than 72, since the probability is so low.
Answer:
(a) The probability that a randomly selected time interval between eruptions is longer than 82 minutes is 0.3336.
(b) The probability that a random sample of 13-time intervals between eruptions has a mean longer than 82 minutes is 0.0582.
(c) The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is 0.0055.
(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.
(e) The population mean must be more than 72, since the probability is so low.
Step-by-step explanation:
We are given that a geyser has a mean time between eruptions of 72 minutes.
Also, the interval of time between the eruptions be normally distributed with a standard deviation of 23 minutes.
(a) Let X = the interval of time between the eruptions
So, X ~ N([tex]\mu=72, \sigma^{2} =23^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 72 minutes
[tex]\sigma[/tex] = standard deviation = 23 minutes
Now, the probability that a randomly selected time interval between eruptions is longer than 82 minutes is given by = P(X > 82 min)
P(X > 82 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{82-72}{23}[/tex] ) = P(Z > 0.43) = 1 - P(Z [tex]\leq[/tex] 0.43)
= 1 - 0.6664 = 0.3336
The above probability is calculated by looking at the value of x = 0.43 in the z table which has an area of 0.6664.
(b) Let [tex]\bar X[/tex] = sample mean time between the eruptions
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 72 minutes
[tex]\sigma[/tex] = standard deviation = 23 minutes
n = sample of time intervals = 13
Now, the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes is given by = P([tex]\bar X[/tex] > 82 min)
P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{13} } }[/tex] ) = P(Z > 1.57) = 1 - P(Z [tex]\leq[/tex] 1.57)
= 1 - 0.9418 = 0.0582
The above probability is calculated by looking at the value of x = 1.57 in the z table which has an area of 0.9418.
(c) Let [tex]\bar X[/tex] = sample mean time between the eruptions
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 72 minutes
[tex]\sigma[/tex] = standard deviation = 23 minutes
n = sample of time intervals = 34
Now, the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is given by = P([tex]\bar X[/tex] > 82 min)
P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{34} } }[/tex] ) = P(Z > 2.54) = 1 - P(Z [tex]\leq[/tex] 2.54)
= 1 - 0.9945 = 0.0055
The above probability is calculated by looking at the value of x = 2.54 in the z table which has an area of 0.9945.
(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.
(e) If a random sample of 34-time intervals between eruptions has a mean longer than 82 minutes, then we conclude that the population mean must be more than 72, since the probability is so low.
Answer:
The probability that a randomly selected time interval between eruptions is longer than 82minutes = [tex]0.3336[/tex]The probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes = [tex]0.0594[/tex]The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes = [tex]0.0057[/tex]Step-by-step explanation:
From the given data
mean, u = 72
Standard deviation [tex]\rho[/tex] = 23
A) Probability that a randomly selected time interval between eruptions is longer than 82minutes
[tex]P (x > 82) = P[\frac{x-u}{\rho} > \frac{82-72}{23}]\\\\P (x > 82) = P[z > 0.43]\\\\P (x > 82) = 0.3336[/tex]
B)
[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{13}}}]\\\\P (x > 82) = P[z > 1.5676]\\\\P (x > 82) = 0.0594[/tex]
C)
[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{34}}}]\\\\P (x > 82) = P[z > 2.5351]\\\\P (x > 82) = 0.0057\\\\[/tex]
D) If the mean is less than 82minutes, then the probability that the sample mean of the time between eruptions is greater than 83 minutes decrease because the variability in the sample mean decrease as the sample size increases
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What is the angle of rotation from figure A to figure A? Assume that the center of rotation is the origin.
A. 360° clockwise
B. 270° clockwise
C. 180° clockwise
D. 90° clockwise
Answer:
the answer is C. 180°clockwise
Find: ∠a ∠b ∠c Plaese help
Answer:
i believe a=105, b=29, and c=45
The volume of a cylinder is approximately 72 feet cubed. Which is the best approximation of the volume of a cone with the same base and height as the cylinder? 24 feet cubed 216 feet cubed 24 pi feet cubed 216 pi feet cubed
Hey there! I'm happy to help!
To find the volume of a cylinder, you multiply the base by the height and then divide by three. The volume of a cone is the same as the volume of a cylinder with the same dimensions divided by three.
So, since a cone's volume is 1/3 of that of a cylinder, we just divide 72 by 3!
72/3=24
Therefore, the volume of the cone is 24 feet cubed.
Have a wonderful day! :D
Answer: its 24.
Step-by-step explanation:
22. “n is less than 15 and greater than or equal to 3”
Complete the following steps to receive full credit for this question:
• The inequality translated in numerical form
• The solution graphed on a number line
• The solution in interval form
Answer:
3 ≤ n < 15
not nnot nyes nyes nyes nyes nyes nyes nyes nyes nyes nyes nyes nyes nnot n1-2. not n
3-4. yes n
5-6. yes n
7-8. yes n
9-10. yes n
11-12. yes n
13-14. yes n
15-16. not n
Step-by-step explanation:
Everything on this side is less than, < but everything on this side is greater.
Everything on this side could be equal or less, ≤ but everything on this side is
not.
I'm had a hard time with the number line, but imagine a line going through the periods and there being a dot where the yes ns end, and start.
Intervals has each point represent more than one number making the line shorter.
Which of the following shows the true solution to the logarithmic equation 3 log Subscript 2 Baseline (2 x) = 3 x = negative 1 x = 1 x = negative 1 and x = 1 x = 0, x = negative 1, and x = 1
Answer:
x = 1
Step-by-step explanation:
Using the rules of logarithms
log [tex]x^{n}[/tex] ⇔ n log x
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
3[tex]log_{2}[/tex] (2x) = 3
[tex]log_{2}[/tex] (2x)³ = 3
(2x)³ = 2³
8x³ = 8 ( divide both sides by 8 )
x³ = 1 ( take the cube root of both sides )
x = 1
Answer:
x=1 is the correct answer
Step-by-step explanation:
got it right on edge!!!!
The length of time a full length movie runs from opening to credits is normally distributed with a mean of 1.9 hours and standard deviation of 0.3 hours. Calculate the following: A random movie is between 1.8 and 2.0 hours. A movie is longer than 2.3 hours. The length of movie that is shorter than 94% of the movies
Answer:
0.260.911.43Step-by-step explanation:
given data
mean = 1.9 hours
standard deviation = 0.3 hours
solution
we get here first random movie between 1.8 and 2.0 hours
so here
P(1.8 < z < 2 )
z = (1.8 - 1.9) ÷ 0.3
z = -0.33
and
z = (2.0 - 1.9) ÷ 0.3
z = 0.33
z = 0.6293
so
P(-0.333 < z < 0.333 )
= 0.26
so random movie is between 1.8 and 2.0 hours long is 0.26
and
A movie is longer than 2.3 hours.
P(x > 2.3)
P( [tex]\frac{x-\mu }{\sigma}[/tex] > [tex]\frac{2.3-\mu }{\sigma}[/tex] )
P (z > [tex]\frac{2.3-1.9 }{0.3}[/tex] )
P (z > 1.333 )
= 0.091
so chance a movie is longer than 2.3 hours is 0.091
and
length of movie that is shorter than 94% of the movies is
P(x > a ) = 0.94
P(x < a ) = 0.06
so
P( [tex]\frac{x-\mu }{\sigma }[/tex] < [tex]\frac{a-\mu }{\sigma }[/tex] )
[tex]\frac{a-1.9 }{0.3 } = -1.55[/tex]
a = 1.43
so length of the movie that is shorter than 94% of the movies about 1.4 hours.
help please thank you
Answer:
(0,-3)
Step-by-step explanation:
Given f(x) = log x and g(x) = -x + 1,
which is the graph of
(fog)(x)?
Answer:
the third graph is correct
Step-by-step explanation:
edge
the second part is x<1
Answer:
the third graph and the send part it is x<1
Step-by-step explanation:
29 point plus brainiest
The function f(x) = −x2 − 7x + 30 shows the relationship between the vertical distance of a diver from a pool's surface f(x), in feet, and the horizontal distance x, in feet, of a diver from the diving board. What is a zero of f(x), and what does it represent?
x = 10; the diver hits the water 10 feet away horizontally from the board.
x = 3; the diver hits the water 3 feet away horizontally from the board. x = 10; the diver jumps in the pool at 10 feet per second.
x = 3; the diver jumps in the pool at 3 feet per second.
this is your answer..................
Select the correct answer. What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)? A. x2 + y2 − 4x + 2y + 1 = 0 B. x2 + y2 + 4x − 2y + 1 = 0 C. x2 + y2 + 4x − 2y + 9 = 0 D. x2 − y2 + 2x + y + 1 = 0
Answer:
x^2 +4x + y^2 -2y +1 =0
Step-by-step explanation:
First we need to find the radius
Since the y coordinate is the same, the radius is the difference in the x coordinate -2 - (-4) = -2+4 = 2
A circle can be written in the form
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x--2)^2 + (y-1)^2 = 2^2
(x+2)^2 + (y-1)^2 = 4
FOIL ing
x^2 +4x+4 + y^2 -2y +1 = 4
Combining like terms
x^2 +4x + y^2 -2y +5 -4 =0
x^2 +4x + y^2 -2y +1 =0
Answer and Step-by-step explanation:
Answer:
x^2 +4x + y^2 -2y +1 =0
Step-by-step explanation:
First we need to find the radius
Since the y coordinate is the same, the radius is the difference in the x coordinate -2 - (-4) = -2+4 = 2
A circle can be written in the form
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x--2)^2 + (y-1)^2 = 2^2
(x+2)^2 + (y-1)^2 = 4
FOIL ing
x^2 +4x+4 + y^2 -2y +1 = 4
Combining like terms
x^2 +4x + y^2 -2y +5 -4 =0
x^2 +4x + y^2 -2y +1 =0
What is the y-intercept of the function y=4-5x?
Answer:
4
Step-by-step explanation:
y=mx+b
b=y-intercept.
In this case...
mx=-5<-- this is the slope of the line.
b=4<-- y intercept.
Hope this helps, any further questions, please feel free to ask.
calculate the area and leave your answer in term of pie
Answer: [tex]2.25\sqrt{3}[/tex]
Not sure what you mean by terms of pi, unless you want us to find the area of the sector, not the triangle.
Step-by-step explanation:
Assuming you mean the area of the triangle...
First draw an altitude from the 120 degree angle to the opposite base. You will find that the altitude will also be a median. This forms 2 30-60-90 right triangles. Thus, the height of the altitude is 1.5 and the base of the triangle is 1.5*root3. Thus, the base of the triangle is [tex]3\sqrt{3}[/tex] and the height is 1.5. Thus, the area of the triangle is [tex]2.25\sqrt{3}[/tex]
Help asap please and please explain so I could try the rest on my own
Answer:
7
Step-by-step explanation:
It has a 45 45 90 ratio, so if the hypotenuse is 7 root 2, then the two sides have to be 7.
A spinner has six spaces that are all the same size. Three spaces are yellow, two are red, and one is blue. If the spinner is spun 150 times, it should land on yellow about ___ times, on red about ___ times, and on blue ___ times.
The spinner should land on yellow about 75 times, on red about 50 times, and on blue about 25 times.
How to solve the probabilityYellow: 3 spaces out of 6, so the probability is 3/6 = 1/2
Red: 2 spaces out of 6, so the probability is 2/6 = 1/3
Blue: 1 space out of 6, so the probability is 1/6
multiplying the probability of each color by 150:
Yellow: 1/2 * 150 = 75 times
Red: 1/3 * 150 = 50 times
Blue: 1/6 * 150 = 25 times
Terefore The spinner should land on yellow about 75 times, on red about 50 times, and on blue about 25 times.
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Question 5 of 10
Which of the following is the converse of the statement "If it is summer, then
it is warm outside"?
A. If it is warm outside, then it is summer.
B. If it is not warm outside, then it is summer.
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C. If it is warm outside, then it is not summer.
D. If it is not warm outside, then it is not summer.
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Answer:
If it is warm outside, then it is summer
Step-by-step explanation:
To find the converse, interchange the hypothesis and the conclusion
"If it is summer, then it is warm outside"
If it is warm outside, then it is summer
Answer:
A. If it is warm outside, then it is summer
Step-by-step explanation:
statement "If it is summer, then it is warm outside" : warm=summer
A. If it is warm outside, then it is summer. : warm = summer ✓
B. If it is not warm outside, then it is summer. : not warm = summer x
C. If it is warm outside, then it is not summer. : warm =not summer x
D. If it is not warm outside, then it is not summer. : not warm = not summer x