Answers
Answer:
[tex] \boxed{\sf x \degree = 62 \degree} [/tex]
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
[tex] \sf \implies x \degree + 38 \degree = 100 \degree \\ \\ \sf \implies x \degree + (38 \degree - 38 \degree) = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 62 \degree[/tex]
In the given figure, the value of x is 62°.
What is angle ?An angle is the formed when two straight lines meet at one point, it is denoted by θ.
The given angles are,
x°, 38° and 100°.
To find the value of angle x, use exterior angle property.
According to exterior angle property,
The sum of two interior angles is equal to exterior angle.
Since, 100° is the exterior angle of x and 38.
x + 38 = 100
x = 100 - 38
x = 62.
The required value of angle x is 62°.
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Related Questions
An educator claims that the average salary of substitute teachers in school districts is less than $60 per day. A random sample of 8 school districts is selected, and the daily salaries are 60, 56, 60, 55, 70, 55, 60, and 55. Is there enough evidence to support the educator’s claim at 10% level of significance? (HELP: The sample mean is 58.88, and the sample standard deviation is 5.08)
Answers
Answer:
[tex]t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626[/tex]
The degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
The p value would be given by:
[tex]p_v =P(t_{(7)}<-0.626)=0.275[/tex]
Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60
Step-by-step explanation:
Information given
60, 56, 60, 55, 70, 55, 60, and 55.
We can calculate the mean and deviation with these formulas:
[tex]\bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
Replacing we got:
[tex]\bar X=58.875[/tex] represent the mean
[tex]s=5.083[/tex] represent the sample standard deviation for the sample
[tex]n=8[/tex] sample size
[tex]\mu_o =60[/tex] represent the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is less than 60, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 60[/tex]
Alternative hypothesis:[tex]\mu < 60[/tex]
The statistic would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626[/tex]
The degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
The p value would be given by:
[tex]p_v =P(t_{(7)}<-0.626)=0.275[/tex]
Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60
Prepare the journal entries on December 31, 2019, for the 40 extended contracts (the first year of the revised 3-year contract).
Answers
This is not the complete question, the complete question is:
P18-1 (LO2,3) (Allocate Transaction Price, Upfront Fees)
Tablet Tailors sells tablet PCs combined with Internet service, which permits the tablet to connect to the Internet anywhere and set up a Wi-Fi hot spot. It offers two bundles with the following terms.
1. Tablet Bundle A sells a tablet with 3 years of Internet service. The price for the tablet and a 3-year Internet connection service contract is $500. The standalone selling price of the tablet is $250 (the cost to Tablet Tailors is $175). Tablet Tailors sells the Internet access service independently for an upfront payment of $300. On January 2, 2017, Tablet Tailors signed 100 contracts, receiving a total of $50,000 in cash.
2. After 2 years of the 3-year contract, Tablet Tailors offers a modified contract and extension incentive. The extended contract services are similar to those provided in the first 2 years of the contract. Signing the extension and paying $90 (which equals the standalone selling of the revised Internet service package) extends access for 2 more years of Internet connection. Forty Tablet Bundle A customers sign up for this offer.
INSTRUCTION
a) Prepare the journal entries when the contract is signed on January 2, 2019, for the 40 extended contracts. Assume the modification does not result in a separate performance obligation.
b) Prepare the journal entries on December 31, 2019, for the 40 extended contracts (the first year of the revised 3-year contract).
Answer:
Step-by-step explanation:
(A)
Date Particulars Debit Credit
2-Jan-19 Cash 3600
Unearned Service Revenue 3600
40 * 90 = 3600
services in the extended period are the same as the services that were provided in the original contract period. As they are not distinct hence the modifications will be considered as part of the original contract.
(B)
Date Particulars Debit Credit
31-Dec-19 Unearned Service Revenue 2413
Service revenue 2413
internet = 300, price = 550, connection service = 500
(300/550) * 500 = 273
so
Original internet service contract = 40 * 273 = 10,920
Revenue recognized in 1st two years = 10,920 * 2/3 = 7280
Remaining service at original rates = 10920 - 7280 = 3640
Extended service = 3600
3640 + 3600 = $7240
7240 / 3 = $2413
Can you solve this????? Super hard!
Answers
Answer:
[tex]\textbf{J. }\dfrac{1}{x^2-x}[/tex]
Step-by-step explanation:
Factor the denominator and cancel the common factor.
[tex]\dfrac{x+1}{x^3-x}=\dfrac{x+1}{x(x^2-1)}=\dfrac{x+1}{x(x-1)(x+1)}=\dfrac{1}{x(x-1)}\\\\=\boxed{\dfrac{1}{x^2-x}}[/tex]
A simple random sample of size nequals15 is drawn from a population that is normally distributed. The sample mean is found to be x overbarequals18.3 and the sample standard deviation is found to be sequals6.3. Determine if the population mean is different from 24 at the alpha equals 0.01 level of significance. Complete parts (a) through (d) below.
(a) Determine the null and alternative hypotheses. Upper H 0: ▼ p sigma mu ▼ less than not equals equals greater than 24 Upper H 1: ▼ sigma mu p ▼ greater than not equals equals less than 24
(b) Calculate the P-value.P-valueequals nothing (Round to three decimal places as needed.)
(c) State the conclusion for the test.
A. Do not reject Upper H 0 because the P-value is less than the alphaequals0.01 level of significance.
B. Do not reject Upper H 0 because the P-value is greater than the alphaequals0.01 level of significance.
C. Reject Upper H 0 because the P-value is less than the alphaequals0.01 level of significance.
D. Reject Upper H 0 because the P-value is greater than the alphaequals0.01 level of significance.
(d) State the conclusion in context of the problem. There ▼ is not is sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.
Answers
Answer:
(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24
(b) The P-value is 0.004.
(c) Reject Upper H 0 because the P-value is less than the alpha = 0.01 level of significance.
(d) There is sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.
Step-by-step explanation:
We are given that a simple random sample of size n = 15 is drawn from a population that is normally distributed. The sample mean is found to be x overbar = 18.3 and the sample standard deviation is found to be s = 6.3.
Let [tex]\mu[/tex] = population mean
(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24 {means that the population mean is 24}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24 {means that the population mean is different from 24}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = 18.3
s = sample standard deviation = 6.3
n = sample size = 15
So, the test statistics = [tex]\frac{18.3-24}{\frac{6.3}{\sqrt{15} } }[/tex] ~ [tex]t_1_4[/tex]
= -3.504
The value of t-test statistics is -3.504.
(b) Now, the P-value of the test statistics is given by;
P-value = P( [tex]t_1_4[/tex] < -3.504) = 0.002 or 0.2%
For the two-tailed test, the P-value is calculated as = [tex]2 \times 0.002[/tex] = 0.004 or 0.4%.
(c) Since the p-value of the test statistics is less than the level of significance as 0.002 < 0.01, so we will reject our null hypothesis.
(d) This means that we have sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.
what is the domain of f(g(x)) if f(x)=
[tex] \sqrt{x} [/tex]
and g(x)=x-9
Answers
Step-by-step explanation:
f(g(x))=[tex]\sqrt{g(x)}[/tex]
--> g(x) >= 0 --> x-9>=0 --> x>=9
Quick and easy geometry thanks please help !!!!!
Answers
Answer:
Midpoint of segment AB= (-0.5, 0)
Step-by-step explanation:
The midpoint coordinates of the midpoint has the x coordinate on .5 and the y coordinate on 0.
Simon swapped of 2/5
his 40 marbles for 9 of
Saqib's. How many has
Simon got now?
Answers
Answer:
33
Step-by-step explanation:
2/5x40=16
40-16=24
24+9=33
33 marbles
2/5 is .4
Multiply .4 by 40 to get 16
Subtract 16 from 40 to get 24
Add 9 to 24 to get 33
Hope it helps <3
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The lengths of adult males' hands are normally distributed with mean 190 mm and standard deviation is 7.4 mm. Suppose that 45 individuals are randomly chosen. Round all answers to 4 where possible.
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For the group of 45, find the probability that the average hand length is less than 189.
Find the third quartile for the average adult male hand length for this sample size.
For part b), is the assumption that the distribution is normal necessary?
Answers
Answer:
a. The distribution of the sample means is normal with mean 190 mm and standard deviation 1.1031 mm.
b. The probability that the average hand length is less than 189 is P(M<189)=0.1823.
c. The third quartile for the average adult male hand length for this sample size is M_75=190.7440.
d. The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
Step-by-step explanation:
We have a normal distribution, with mean 190 and standard deviation 7.4.
We take samples of size n=45 from this population.
Then, the sample means will have a distribution with the following parameters:
[tex]\mu_s=\mu=190\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{7.4}{\sqrt{45}}=\dfrac{7.4}{6.7082}=1.1031[/tex]
The probability that the sample mean is less than 189 can be calculated as:
[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{189-190}{7.4/\sqrt{45}}=\dfrac{-1}{1.1031}=-0.9065\\\\\\P(M<189)=P(z<-0.9065)=0.1823[/tex]
The third quartile represents the value of the sample where 75% of the data is to the left of this value. It means that:
[tex]P(M<M^*)=0.75[/tex]
The third quartile corresponds to a z-value of z*=0.6745.
[tex]P(z<z^*)=0.75[/tex]
Then, we can calculate the sample mean for the third quartile as:
[tex]M=\mu_s+z^*\sigma_s=190+0.6745\cdot 1.1031=190+0.7440=190.7440[/tex]
The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
Scotland Beauty Products manufactures face cream, body lotion, and liquid soap in a joint manufacturing process. At the split-off point, the company has 300 pounds of face cream, 200 pounds of body lotion, and 300 pounds of liquid soap and has incurred $200,000 in joint costs. Using the physical units method, allocate the joint costs to: a. Face Cream $ b. Body Lotion $ c. Liquid Soap $
Answers
Answer:
a. 75,000
b. 50,000
c. 75,000
Step-by-step explanation:
The computation of allocating the joint cost using the physical units method is shown below:
[tex]Allocation\ rate = \frac{Joint\ costs}{Total\ number\ of\ products}[/tex]
[tex]= \frac{\$200,000}{300 + 200 + 300}[/tex]
[tex]Allocation\ rate = \frac{200,000}{800}[/tex]
= 250
For face cream
[tex]= Unit\ produced\times Allocation\ rate[/tex]
= [tex]300\times 250[/tex]
= 75,000
For body lotion
[tex]= Unit\ produced\times Allocation\ rate\\\\ = 200\times 250[/tex]
= 50,000
For Liquid soap
[tex]= Unit\ produced\times Allocation\ rate\\\\ = 300\times 250[/tex]
= 75,000
hence, we simply applied the above formula by multiplying the units produced with the allocation rate so that each one allocation cost could come
El numeral 32012(4) representado en el sistema decimal, porfavor
Answers
Answer: El número es 902 en el sistema decimal.
Step-by-step explanation:
Supongo que tenemos el número:
32012 en base 4, y lo queremos representar en base decimal.
Entonces, usando la regla general, podemos escribir este número como:
unidades*base^0 + decenas*base^1 + centenas*base^2......
Es decir, acá tenemos:
2*4^0 + 1*4^1 + 0*4^2 + 2*4^3 + 3*4^4 = 902
El número es 902 en el sistema decimal.
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answers
Step-by-step explanation:
Log T = 11.8 + 1.5.M (with T is the amount of energy released by the earthquake, Log refers to the logarithm to the base 10)
-->T = [tex]10^{11.8 +1.5*6.5}[/tex] ≈3.458 *[tex]10^{21}[/tex]
Answer: 2.00 x 10¹⁰⁹
Step-by-step explanation:
log T = 11.8 + 1.5M
Given: M = 6.5
log T = 11.8 + 1.5(6.5)
log T = 11.8 + 9.75
log T = 21.55
T = 10²¹⁻⁵⁵
T = 1.995 x 10¹⁰⁹
T = 2.00 x 10¹⁰⁹ rounded to the nearest hundredth
Need help please show how to complete
Answers
5).
A = (b x h)/2
6). A = b x h
7). A = b x h = 65 x 50 = 3250 ft^2
8). A = (b x h)/2 = (12 x 18)/2 = 108 inches^2
9). A = (b1 + b2)h/2 = (15 + 7)4/2 = 44m^2
Answer:
Step-by-step explanation:
P= 2*10+2*6=20+12= 32 mP= 4*7 = 28 cm P= 8+10+12 =30Given a triangle with: a =
150, A = 75°, and C = 30°
Using the law of sines gives: c = 0
Answers
Answer:
[tex] c = 77.6 [/tex]
Step-by-step explanation:
You may have entered the measure of a side as the measure of an angle.
[tex] \dfrac{\sin A}{a} = \dfrac{\sin C}{c} [/tex]
[tex] \dfrac{\sin 75^\circ}{150} = \dfrac{\sin 30^\circ}{c} [/tex]
[tex] c\sin 75^\circ = 150 \sin 30^\circ [/tex]
[tex] c = \dfrac{150 \sin 30^\circ}{\sin 75^\circ} [/tex]
[tex] c = 77.6 [/tex]
You are correct. Good job!
Select the correct car trips. Listed are the distances traveled by four cars and the time it took each car to cover that distance. Identify which cars traveled at the same speed.
Answers
Answer:
Speeds of car 1 and car 4 are same.
Step-by-step explanation:
Speed of an object = [tex]\frac{\text{Distance traveled}}{\text{Time}}[/tex]
For car 1,
Speed of car 1 = [tex]\frac{350}{5}[/tex]
= 70 miles per hour
For car 2,
Speed of car 2 = [tex]\frac{240}{4}[/tex]
= 60 miles per hour
For car 3,
Speed of car 3 = [tex]\frac{320}{5}[/tex]
= 64 miles per hour
For car 4,
Speed of car 4 = [tex]\frac{420}{6}[/tex]
= 70 miles per hour
Therefore, speeds of car 1 and car 4 are same.
Mauro has 140 feet of rope he will cut it into two peices so that the length of the longer peice is 3 times the length of the shorter peice
Answers
lg(3x-2) +lg(x+1) =2 –lg2
Answers
Answer:
x = 4 or x = -13/4 = -4.33
Step-by-step explanation:
log (3x - 2) + log (x + 1) = 2 - log 2
Note 2 is also equals to log 100
log (3x - 2) + log (x + 1) = log 100 - log 2
log (3x - 2)(x + 1) = log (100/2)
log 3x² + 3x - 2x - 2 = log 50
log 3x² + x - 2 = log 50
3x² + x - 2 = 50
3x² + x - 2 - 50 = 0
3x² + x - 52 = 0
find the number to multiply that will give you -52 × 3 = -156 and add to give you 1. The numbers are -12 and 13.
3x² - 12x + 13x - 52 = 0
3x(x - 4) + 13( x - 4) = 0
(3x + 13)(x - 4) = 0
x = 4 or x = -13/4 = -4.33
If you insert 4 in the logarithm equation you will see that the left side is equal to the right
log (3x - 2) + log (x + 1) = log 100 - log 2
log 10 + log 5 = log 50
log 50 = log 50
Write 48√3 - 15√12 + 2√75 in the form a√3 a = √3
Answers
Answer:
68√3
Step-by-step explanation:
48√3 - 15√12 + 2√75=
48√3 - 15√4*3 + 2√25*3 =
48√3 - 30√3 + 50√3= 68√3
what fraction is greater than 2/5 but less than 3/5
Answers
Hey there! I'm happy to help!
You haven't provided any answer choices but I can show you a trick to find any number between two numbers. This is will give you an instant answer to one being greater than one number and less than another.
What you do is you add the two numbers and divide by two!
2/5+3/5=1
1÷2=1/2
Therefore, 1/2 is a possible answer here.
I hope that this helps! Have a wonderful day!
each pair of figures is similar find the missing side
Answers
Answer:
17) 53.2
18) 17
Step-by-step explanation:
In similar triangles theorem, the ratio of the corresponding sides of two triangles are equal.
17) To determine x, ratio of the sides of 1st triangle/Ratio of the sides of 2nd triangle.
Ratio of base to the missing side:
7.6/x = 13.6/95.2
7.6/x = 13.6/95.2
7.6/x = 0.1428
7.6= 0.1429x
x = 53.2
18) ratio of shortest side/ longest side
3.4/7.9 = x/39.5
x = 3.4/7.9 × 39.5
x = 17
Which vector has an x-component with a length of 4?
Answers
Answer:
vector aStep-by-step explanation:
In order to locate the vector that has an x- component with a length of 4, we need to know the position of each vector on the Cartesian plane. Each of the vectors lies on the (x, y) coordinate.
For vector a, it lies on the coordinate A(1, 4), vector b lies on the coordinate B(1,1), vector c lies on the coordinate C(4,4) while vector d lies in the coordinate D(3, 4).
It can be seen that out of this four vectors, only vector C has an x- coordinate of 4. This shows that vector a is the only vector that has an x-component with a length of 4?
A circle is represented by the equation x2+y2=445. a) State the radius. b) Find y if point A(-9,y) is on this circle.
Answers
Answer:
R= sqrt 445
Y = 19
Step-by-step explanation:
Radius is the square root of 445
Find y
So, First step is to substitute what you have
-9^2 + y^2 = 445
81 + y^2 = 445
-81 -81
y^2 =364
Y is about 19
Let me know if I'm incorrect
Hope this helps :)
A traffic helicopter pilot 300 feet above the road spotted two antique cars. The angles of depression are 7.5° and 9º. How far apart are the cars? Round to the nearest tenth.
Answers
Answer:
384.6 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the trig relation involving sides adjacent and opposite the angle. Here, the road distance is adjacent to the angle of depression, and the altitude is opposite. So, you have ...
Tan = Opposite/Adjacent
tan(7.5°) = (300 ft)/(distance to car 1)
tan(9°) = (300 ft)/(distance to car 2)
Solving for the distances, we have ...
distance to car 1 = (300 ft)/tan(7.5°) ≈ 2278.73 ft
distance to car 2 = (300 ft)/tan(9°) ≈ 1894.13 ft
Then the separation between the cars is ...
distance apart = 2278.73 ft - 1894.13 ft
distance apart = 384.6 ft
i will give 50 points and brainliest
Answers
Answer:
240 m^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
The base is 16 and the height is 30
A =1/2 ( 16*30)
240 m^2
bh/2 is formula of triangle
b=16
h=30
16x30=480/2=240
given that f(x)= 2x+1 find f(2)
Answers
Answer:
f(2) = 5
Step-by-step explanation:
Simply plug in 2 for x:
f(2) = 2(2) + 1
f(2) = 4 + 1
f(2) = 5
A right triangle is shown. The length of the hypotenuse is 4 centimeters and the lengths of the other 2 sides are congruent. The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle? 2 cm 2 StartRoot 2 EndRoot cm 4 cm 4 StartRoot 2 EndRoot cm
Answers
Answer:
The leg measures 2 I believe
Step-by-step explanation:
Since the squares of the legs equal C ([tex]A^{2} +B^{2} = C^{2}[/tex]) the square root of 16 would be 4.
The Pythagorean theorem is a basic relationship between the three sides of a right triangle. The length of one leg of the triangle is 2√2 cm.
What is the Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]
Let the length of the perpendicular be x.
Given the length of the hypotenuse is 4 centimeters, while the length of the other two sides is the same, therefore, the length of the other two sides is x. Therefore, using the Pythagorus theorem we can write,
[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]
[tex]4^2 = x^2+x^2\\\\16=2x^2\\\\8=x^2\\\\x= 2\sqrt2[/tex]
Hence, the length of one leg of the triangle is 2√2 cm.
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on a map where each unit represents 100 miles , two airports are located at p(1,17) and q(12,10) what is the distance to the nearest whole mile between the two airports
Answers
Considering the distance between the two points in units, the real distance between the airports is of 1303 miles.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this problem, the airports are at points at p(1,17) and q(12,10), hence the distance in units is given by:
[tex]D = \sqrt{(10 - 17)^2 + (12 - 1)^2} = 13.03[/tex]
Since each unit represents 100 miles, the distance in miles is given by:
D = 13.03 x 100 = 1303 miles.
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Answer:
B. 1,304 miles.
Step-by-step explanation:
Using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.
How to Apply the Distance Formula?
The distance formula is: d = .
Given the following locations:
P(1,17) = (x1, y1)
Q(12,10) = (x2, y2)
Use the distance formula to find the PQ:
PQ = √[(12−1)² + (10−17)²]
PQ = √[(11)² + (−7)²]
PQ = √170
PQ ≈ 13.04 units
1 unit = 100 miles
PQ = 13.04 × 100
PQ = 1,304 mils
Thus, using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.
WILL GIVE BRAINLIEST What is the perimeter of the track, in meters? Use π = 3.14 and round to the nearest hundredth of a meter.
Answers
Answer:
Perimeter = 317 m
Step-by-step explanation:
Given track is a composite figure having two semicircles and one rectangle.
Perimeter of the given track = Circumference of two semicircles + 2(length of the rectangle)
Circumference of one semicircle = πr [where 'r' = radius of the semicircle]
= 25π
= 25 × 3.14
= 78.5 m
Length of the rectangle = 80 m
Perimeter of the track = 2(78.5) + 2(80)
= 157 + 160
= 317 m
Therefore, perimeter of the track = 317 m
the number 12,16, n, 23, 30 have a mean of 22.6 the value of n
Answers
Answer:
32
Step-by-step explanation:
Mean = Average = The data values added together/ the number of data values.
The mean of 5 numbers is 22.6=
[tex]\frac{12+16+n+23+30}{5} = 22.6[/tex]
Multiply both sides by 5. 22.6 becomes 113
12+16+23+30+n=113
n+81 = 113
n= 32
The value of n is 32.
What is the arithmetic mean?The arithmetic mean of m values [tex]x_1,x_2,..., x_m[/tex] is
[tex]\frac{x_1+x_2+...+x_m}{m}[/tex]
How to solve for n?The given
mean = [tex]\frac{12+16+n+23+30}{5}=22.6[/tex]
⇒12+16+n+23+30=22.6×5=113
⇒n=113-81=32
Hence, n=32
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Approximating square roots
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Without using a calculator, choose the statement that best describes the value of 215.
Choose 1 answer:
The value of 215 is between 13 and 13.5.
The value of 215 is between 13.5 and 14.
The value of 215 is between 14 and 1.5.
The value of v 215 is between 14.5 and 15.
Answers
Step-by-step explanation:
We know that
14^2=196, and
15^2=225
so we know that sqrt(215) is between 14 and 15.
How do we know if it is between 14.5 and 15?
we need to know the value of 14.5^2, which we can calculate in the head as follows:
The square of all numbers ending in 5 such as 15 can be calculated by breaking up the 5 and the preceding digit(s),
The preceding digit is 1. We multiply 1 by the next integer, 2 to get 2.
Attach 25 to 2 gives us 225 (as we saw above.
Example, 145*145 = 14*15 | 25 = 210 | 25 = 21025
so
14.5^2 = 210.25, which gives the more precise answer that
14.5^2 < 215 < 15^2, or
14.5 < sqrt(215) < 15 (fourth choice)
Since the third choice says sqrt(215) is between 14 and 1.5 (not 15), so the third choice is incorrect.
Note: if we eliminated the third choice, i.e. discard the likelihood of typo in the question, the only one left is the fourth choice.
The set G 5 {1, 4, 11, 14, 16, 19, 26, 29, 31, 34, 41, 44} is a group under multiplication modulo 45. Write G as an external and an internal direct product of cyclic groups of prime-power order.
Answers
Answer: G = (19) × (26) × (16)
Step-by-step explanation:
The isomorphism classes of Abelian groups of order 12 are Z₄ ⊕ Z₃ and Z₂ ⊕ Z₂ ⊕ Z₃
SO Let us calculate the orders of some of the elements of G
We have
4² = 16,
4³ = 64
= 19,
and
4^4 = 19.4
= 76
= 31.
furthermore,
4^5 = 31.4
= 124
= 34
and
4^6 = 34.4
= 136
= 1
Hence, 4 and 34 each have order 6, 16 and 31 each have order 3, and 19 has order 2.
Next, we calculate
11² = 121
= 31
and
11³ = 11.3
= 341
= 26
this is the calculation needed.
26² = 11^6
= 31³
= 1
since we already showed that 31 has order 3. This means that 26 has order 2
Since G has two distinct elements of order 2, it cannot be isomorphic to . We conclude
that G = Z₂ ⊕ Z₂ ⊕ Z₃
Finally, we will express as an internal direct product.
The previous calculations show that
(19) = { 1, 19 }
and (26) = { 1, 26 }
are cyclic subgroups of G of order 2 with trivial intersection. We have
(19) × (26) = { 1, 19, 26, 44 }
since
(16) = { 1, 19, 26, 44 }
has trivial intersection with (19) × (26), conclude that
G = (19) × (26) × (19)