The price of an item with a 15% discount would be 85% of the original price, so if the original price was x, the discounted price would be: [tex]\frac{85x}{100}[/tex]
Can you solve this????? Super hard!
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]
My friend needs help again :)
Which of the following numbers can be expressed as a decimal that terminates? 3 over 2, 2 over 3, 3 over 4, 5 over 7 3 over 2 and 2 over 3 3 over 4 and 5 over 7 3 over 2 and 3 over 4 2 over 3 and 5 over 7
Answer:
Hey there!
3/2= 1.5, which is good.
2/3=0.666666666666... no
3/4=0.75, which is good.
5/7= 0.71428... no
Answer:
3/23/53/4these sequences are limited
you can try it in a calculator
Prepare the journal entries on December 31, 2019, for the 40 extended contracts (the first year of the revised 3-year contract).
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
El numeral 32012(4) representado en el sistema decimal, porfavor
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.
A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 559 randomly selected Americans surveyed, 370 were in favor of the initiative. Round answers to 4 decimal places where possible.
a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between and .b. If many groups of 506 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about percent will not contain the true population proportion.
Answer:
a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between 0.6290 and 0.6948.
b. If the sample size is changed, the confidence interval changes as the standard error depends on sample size.
About 90% percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about 10% percent will not contain the true population proportion.
Step-by-step explanation:
We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.6619.
[tex]p=X/n=370/559=0.6619[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.6619*0.3381}{559}}\\\\\\ \sigma_p=\sqrt{0.0004}=0.02[/tex]
The critical z-value for a 90% confidence interval is z=1.6449.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.6449 \cdot 0.02=0.0329[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.6619-0.0329=0.6290\\\\UL=p+z \cdot \sigma_p = 0.6619+0.0329=0.6948[/tex]
The 90% confidence interval for the population proportion is (0.6290, 0.6948).
i will give 50 points and brainliest
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
what fraction is greater than 2/5 but less than 3/5
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!
Square ABCD is shown below with line EF and passing through the center:
Answer: B) contain the points E and F
Step-by-step explanation:
Dilation of 2 means to multiply both the x- and y-coordinates by 2
see image below
The only option that is true that E'F' contains points E and F
Answer:
contains the points E and F
Step-by-step explanation:
The center of dilation is an invariant point. It doesn't move, regardless of the dilation factor.
Likewise, any line through the center of dilation will not move. It is not rotated or translated by dilation--it simply is stretched (or compressed) along its length. It is still an infinite line, and it still goes through all of the points it went through before dilation.
The line through the center of dilation that contains points E and F, after dilation, ...
contains the points E and F.
A survey asks, "If the husband in a family wants children, but the wife decides that she does not want any children, is it all right for the wife to refuse to have children?" Of 705 subjects, 581 said yes. a. Find a 99% confidence interval for the population proportion who would say yes. (Use ascending order. Round to four decimal places as needed.) Can you conclude that the population proportion exceeds 75%? Why? in 2 A. No, we cannot conclude that the population proportion exceeds 75%, because 75% is below the lowest believable value of the confidence interval B. Yes, we can conclude that the population proportion exceeds 75% because 75% is above the lowest believable value of the confidence interval C. No, we cannot conclude that the population proportion exceeds 75% because 75% is above the lowest believable value of the confidence interval D. Yes, we can conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval. b. Without doing any calculations, explain whether the interval in (a) would be wider or narrower than a 95% confidence interval for the population proportion who would say yes. The 99% confidence interval would be wider than a 95% confidence interval. The 99% confidence interval would be narrower than a 95% confidence interval.
Answer:
a. The 99% confidence interval for the population proportion is (0.7872, 0.8610).
D. Yes, we can conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval.
b. The 99% confidence interval would be wider than a 95% confidence interval.
As the confidence level increases, the width interval increases, as we are requiring more confidence with the same information (there is no new sample). This means that, to be more confident, the only way is to include more values in the interval.
Step-by-step explanation:
We have to calculate a 99% confidence interval for the proportion.
The sample proportion is p=0.8241.
[tex]p=X/n=581/705=0.8241[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.8241*0.1759}{705}}\\\\\\ \sigma_p=\sqrt{0.000206}=0.0143[/tex]
The critical z-value for a 99% confidence interval is z=2.5758.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=2.5758 \cdot 0.0143=0.0369[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.8241-0.0369=0.7872\\\\UL=p+z \cdot \sigma_p = 0.8241+0.0369=0.8610[/tex]
The 99% confidence interval for the population proportion is (0.7872, 0.8610).
We can conclude that there is, at least, 99% chances that the true proportion is higher than 0.7872. So there is at least 99% chances that the population proportion is higher than 0.75.
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.
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
Approximating square roots
Go to le
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.
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.
QUESTION 6
Find Future Value Using Compound Interest Formula:
You deposit $300 in an account earning 7% interest compounded semi-annually. How much will you have in the account in 20 years?
A. $720
B. $596.94
C. $1,187.78
D. $1,140
QUESTION 7
Find Future Value Using Compound Interest Formula:
You deposit $3,000 in an account earning 3% interest compounded monthly. How much will you have in the account in 15 years?
A. $3,091.25
B. $4,702.30
C. $4,507.25
D. $3,033.62
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 $
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
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.
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 :)
darius is camping in the woods. he notices on a map that his campsite is 50 yards from the ranger station. he walks 18 yards towards the ranger station the tree forms the altitude of a right triangle that connects the top of the tree darius's campsite, and the ranger station. sketch a diagram of the situation and determine the angle of depression formed by darius sightline to the ranger station.
Answer:
The angle of depression formed by Darius's sight line to the ranger station is 53.13°.
Step-by-step explanation:
Denote Darius's camp site as C, the ranger station as R and the tree as T.
Consider the triangle CTR.
TX is the altitude of the right angled triangle TXR.
The altitude of a right angled triangle forms two triangle that similar to each other.
So, ΔTXC [tex]\sim[/tex] ΔTXR.
Compute the measure of TX as follows:
[tex]\frac{CX}{TX}=\frac{TX}{RX}\\\\TX^{2}=CX\times RX\\\\TX=\sqrt{CX\times RX}[/tex]
[tex]=\sqrt{18\times 32}\\\\=24\ \text{yd}[/tex]
The angle d represents the angle of depression formed by Darius's sight line to the ranger station.
Compute the value of d as follows:
[tex]tan\ d^{o}=\frac{RX}{TX}\\\\d^{o}=tan^{-1} [\frac{RX}{TX}][/tex]
[tex]=tan^{-1} [\frac{32}{24}]\\\\=53.13[/tex]
Thus, the angle of depression formed by Darius's sight line to the ranger station is 53.13°.
What are (a) the x component and (b) the y component of a vector in the xy plane if its direction is 250° counterclockwise from the positive direction of the x axis and its magnitude is 7.3 m?
Answer:
(-2.497, -6.860)
Step-by-step explanation:
For any magnitude r and direction θ, the translation to rectangular coordinates is ...
(r, θ) ⇒ (x, y)
(r, θ) ⇒ (r·cos(θ), r·sin(θ))
Your coordinates translate to ...
(7.3, 250°) ⇒ (7.3·cos(250°), 7.3·sin(250°)) ≈ (-2.497, -6.860)
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!
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
Simon swapped of 2/5
his 40 marbles for 9 of
Saqib's. How many has
Simon got now?
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
(If it does, please mark brainliest, only need 1 more to get rank up :) )
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
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.
Learn more about Pythagoras Theorem:
https://brainly.com/question/14461977
#SPJ2
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
Sofia vai colar um pedaço de barbante no contorno de uma moldura quadrada de lado 20 cm. Qual deverá ser o comprimento desse barbante?
Answer:
A corda deve ter um comprimento mínimo de 80 cm.
The string should have a minimum length of 80 cm.
Step-by-step explanation:
Espera-se que a corda seja colada em todo o contorno da moldura quadrada.
Isso significa que a cadeia precisa cobrir pelo menos todo o perímetro da moldura quadrada pelo menos uma vez.
Perímetro de um quadrado = 4L
L = comprimento lateral do quadrado.
O comprimento lateral da moldura quadrada = 20 cm
Comprimento mínimo da corda necessária = Perímetro da moldura quadrada = 4 × 20 = 80 cm.
Espero que isto ajude!!!!
English Translation
Sofia is going to glue a piece of string to the outline of a square frame 20 cm from the side. How long should this string be?
Solution
The string is expected to be glued all around the outlne of square frame.
This means the string needs to at least cover the whole perimeter of the square frame a minimum of one time.
Perimeter of a square = 4L
L = side length of the square.
The side length of the square frame = 20 cm
Minimum length of the string required = Perimeter of the square frame = 4 × 20 = 80 cm.
Hope this Helps!!!!
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?
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.
each pair of figures is similar find the missing side
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
Not sure what it would be
Answer:
negative
Step-by-step explanation:
The slope of the line is negative because it goes from the upper corner down to the lower corner.
I remember it as negative because a rock would roll down it, if I would have to push it, it is positive.
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.
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)
Two spheres have scale factor of 1:3. The smaller sphere has a surface area of 16 square feet. Find the surface area of the larger sphere
Answer:
48
Step-by-step explanation:
16*3=48
Given a triangle with: a =
150, A = 75°, and C = 30°
Using the law of sines gives: c = 0
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!
Please help ill mark you the brainlist The scale on a map indicates that 1 cm represents 50 km. If two cities are 400 km apart, then how far apart would the cities be on this map?
Answer:
8 cm
Step-by-step explanation:
divide 400 by 50 which is 8.
lg(3x-2) +lg(x+1) =2 –lg2
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
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.
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.