9514 1404 393
Answer:
simplify parenthesesdivide 39/13multiply 2(19)subtract 3-38Step-by-step explanation:
The order of operations tells you to evaluate parentheses first.
Step 1: simplify (12+1) and (4+15)
39÷13 -2×19
Then it tells you to do multiplication and division, left to right.
Step 2: divide 39÷13
3 -2×19
Step 3: multiply 2×19
3 -38
Finally, addition and subtraction are done, left to right.
Step 4: subtract 38 from 3
-35
Find the volume of the following cone.
Round your answer to the nearest integer
Check the picture below.
\(\textit{volume of a cone}\\ V = \cfrac{\pi r^2 h}{3}~~ \begin{cases} r = \stackrel{radius}{12}\\ h = \stackrel{height}{5} \end{cases} \\\\\\ V = \cfrac{\pi \cdot 144\cdot 5}{3}\implies V = 240\pi \implies V\approx 753.98\implies V = \stackrel{\textit{rounded up}}{754}\)
Find the unit rate (constant of proportionality) of the distance traveled.
Number of hours
0.25 1.5 2.5 3
Distance traveled (km) 3 18 30 36
Answer:
12.
Step-by-step explanation:
if to re-write the given condition, then
\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)
it is clear, the required constant is 12 (12 per hour).
Rewrite the equation by completing the square 3+x=x^2+3x
Answer:
the completed square is x=1, -3
O
Which of the following could be used to calculate the area of the sector in the circle sho
O
m(Sin)
O
WE OD
m(Sin)2
O n(30in)2
O
r-5 in 30
m(30in)
O
above? (5 points)
The Circle Sector Area correct answer is: O n(30in)2
To calculate the area of the sector in the circle, you would typically use the formula:
Area = (θ/360) * π *\(r^2\)
where θ is the angle of the sector in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
From the options you provided, the correct choice would be:
O n(30in)2
This option represents the square of the radius (30in) squared, which gives you the value of \(r^2.\)
Therefore, the Circle Sector Area correct answer is: O n(30in)2
For such more questions on Circle Sector Area
https://brainly.com/question/30607726
#SPJ8
Evaluate 5|7 - 9| - 2.
-12
0
1
8
\(\longrightarrow{\green{ D. \:8 }}\)
\(\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}\)
\(5 \: |7 - 9| - 2\)
\( = 5 \: | - 2| - 2\)
\( = 5 \times 2 - 2\)
\( = 1 0- 2\)
\( = 8\)
\(\bold{ \green{ \star{ \orange{Mystique35}}}}⋆\)
Suppose there is a simple index of two stocks, stock A and stock B. Stock A opens on Monday with 5000 shares at $2.75 per share. Stock B opens on Monday with 3000 shares at $4.30 per share. Stock A opens on Tuesday at $3.10 per share, and stock B opens on Tuesday at $4.85 per share. Both stocks have the same number of shares that they opened with on Monday. What is the rate of change of this simple index over 1 day?
The rate of change of the simple index over one day is approximately 12.78%.
To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.
On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:
Total value of Stock A on Monday = 5000 * $2.75 = $13,750
Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:
Total value of Stock B on Monday = 3000 * $4.30 = $12,900
The total value of the index on Monday is the sum of the values of Stock A and Stock B:
Total value of the index on Monday = $13,750 + $12,900 = $26,650
On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.
The total value of Stock A on Tuesday is:
Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500
The total value of Stock B on Tuesday is:
Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550
The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:
Total value of the index on Tuesday = $15,500 + $14,550 = $30,050
To calculate the percent change in the index, we use the formula:
Percent Change = ((New Value - Old Value) / Old Value) * 100
Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%
For more such question on index. visit :
https://brainly.com/question/15361818
#SPJ8
10. If 6 men can paint a fence in 2 days, how
many men, working at the same uniform rate,
can finish it in 1 day?
10-A 2
10-B 3
10-C 12
10-D 14
Answer:
C: 12
Step-by-step explanation:
If it takes 6 PEOPLE to paint the fence in 2 days, it would take twice as many people to make the time it takes 1 day because it is half the time. It would take 12 PEOPLE to paint the fence in 1 day.
Assumptions: Tax depreciation is straight-line over three years. Pre-tax salvage value is 25 in Year 3 and 50 if the asset is scrapped in Year 2. Tax on salvage value is 40% of the difference between salvage value and book value of the investment. The cost of capital is 20%.
Based on the given assumptions and calculations, the net present value (NPV) of the investment in the new piece of equipment is -$27,045.76, indicating that the investment is not favorable.
To calculate the after-tax cash flows for each year and evaluate the investment decision, let's use the following information:
Assumptions:
Tax depreciation is straight-line over five years.
Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4.
Tax on salvage value is 30% of the difference between salvage value and book value of the investment.
The cost of capital is 12%.
Given:
Initial investment cost = $50,000
Useful life of the equipment = 5 years
To calculate the depreciation expense each year, we divide the initial investment by the useful life:
Depreciation expense per year = Initial investment / Useful life
Depreciation expense per year = $50,000 / 5 = $10,000
Now, let's calculate the book value at the end of each year:
Year 1:
Book value = Initial investment - Depreciation expense per year
Book value \(= $50,000 - $10,000 = $40,000\)
Year 2:
Book value = Initial investment - (2 \(\times\) Depreciation expense per year)
Book value \(= $50,000 - (2 \times$10,000) = $30,000\)
Year 3:
Book value = Initial investment - (3 \(\times\) Depreciation expense per year)
Book value = $50,000 - (3 \(\times\) $10,000) = $20,000
Year 4:
Book value = Initial investment - (4 \(\times\) Depreciation expense per year)
Book value \(= $50,000 - (4 \times $10,000) = $10,000\)
Year 5:
Book value = Initial investment - (5 \(\times\) Depreciation expense per year)
Book value \(= $50,000 - (5 \times $10,000) = $0\)
Based on the assumptions, the salvage value is $10,000 in Year 5.
If the asset is scrapped in Year 4, the salvage value is $15,000.
To calculate the tax on salvage value, we need to find the difference between the salvage value and the book value and then multiply it by the tax rate:
Tax on salvage value = Tax rate \(\times\) (Salvage value - Book value)
For Year 5:
Tax on salvage value\(= 0.30 \times ($10,000 - $0) = $3,000\)
For Year 4 (if scrapped):
Tax on salvage value\(= 0.30 \times ($15,000 - $10,000) = $1,500\)
Now, let's calculate the after-tax cash flows for each year:
Year 1:
After-tax cash flow = Depreciation expense per year - Tax on salvage value
After-tax cash flow = $10,000 - $0 = $10,000
Year 2:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $0 - $0 = $0
Year 3:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $0 - $0 = $0
Year 4 (if scrapped):
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $15,000 - $1,500 = $13,500
Year 5:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $10,000 - $3,000 = $7,000
Now, let's calculate the net present value (NPV) using the cost of capital of 12%.
We will discount each year's after-tax cash flow to its present value using the formula:
\(PV = CF / (1 + r)^t\)
Where:
PV = Present value
CF = Cash flow
r = Discount rate (cost of capital)
t = Time period (year)
NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 + PV Year 5 - Initial investment
Let's calculate the NPV:
PV Year 1 \(= $10,000 / (1 + 0.12)^1 = $8,928.57\)
PV Year 2 \(= $0 / (1 + 0.12)^2 = $0\)
PV Year 3 \(= $0 / (1 + 0.12)^3 = $0\)
PV Year 4 \(= $13,500 / (1 + 0.12)^4 = $9,551.28\)
PV Year 5 \(= $7,000 / (1 + 0.12)^5 = $4,474.39\)
NPV = $8,928.57 + $0 + $0 + $9,551.28 + $4,474.39 - $50,000
NPV = $22,954.24 - $50,000
NPV = -$27,045.76
The NPV is negative, which means that based on the given assumptions and cost of capital, the investment in the new piece of equipment would result in a net loss.
Therefore, the investment may not be favorable.
Please note that the calculations above are based on the given assumptions, and additional factors or considerations specific to the business should also be taken into account when making investment decisions.
For similar questions on assumptions.
https://brainly.com/question/15424356
#SPJ8
The complete question may be like :
Assumptions: Tax depreciation is straight-line over five years. Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4. Tax on salvage value is 30% of the difference between salvage value and book value of the investment. The cost of capital is 12%.
You are evaluating an investment in a new piece of equipment for your business. The initial investment cost is $50,000. The equipment is expected to have a useful life of five years.
Using the given assumptions, calculate the after-tax cash flows for each year and evaluate the investment decision by calculating the net present value (NPV) using the cost of capital of 12%.
which of the following would be an acceptable first step in simplifying the expression tan^x/1+sec^x
The first step is replacing the given trigonometric functions by simpler ones and then taking the product of the denominators.
Which is the first step to simplifying the given expression?
Here we have the expression:
\(\frac{tan(x)}{1 + sec(x)}\)
Remember that:
\(tan(x) = \frac{sin(x)}{cos(x)}\\ \\sec(x) = \frac{1}{cos(x)}\)
Replacing that would be the "step zero", we can write:
\(\frac{tan(x)}{1 + sec(x)} = tan(x)*\frac{1}{1 + sec(x)} = \frac{sin(x)}{cos(x)} \frac{1}{1 + \frac{1}{cos(x)} }\)
The first step to simplify this, is taking the product between the denominators:
\(\frac{sin(x)}{cos(x)} \frac{1}{1 + \frac{1}{cos(x)} } = sin(x)*\frac{1}{cos(x) + \frac{cos(x)} {cos(x)} } = \frac{sin(x)}{cos(x) + 1}\)
If you want to learn more about trigonometric functions:
https://brainly.com/question/8120556
#SPJ1
Answer:
tanx(1-secx)/(1+secx)(1-secx)
Step-by-step explanation:
aP E
29.For n ≥ 3, a pattern can be made by overlapping n circles, each of circumference 1 unit, so that each circle passes through a central point and the resulting pattern has order-n rotational symmetry.
For instance, the diagram shows the pattern where n = 7.
If the total length of visible ares is 60 units, what is n?
The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.
To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).
In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.
Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:
2n = 60
Solving this equation, we find:
n = 60/2 = 30
Thus, the value of n is 30.
For more questions on number of visible arcs:
https://brainly.com/question/31336038
#SPJ8
Julia works for a company selling light bulbs. She sells fluorescent light bulbs for $5 a piece and incandescent light bulbs for $2. To meet her quota, she needs to sell over 100 light bulbs and make at least $350. If the solution region is the amount of light bulbs Julia needs to sell to meet her quota, which graph's shaded area represents the solution region? A.Y B.W C.Z D.
The solution to the amount of light bulbs Julia needs to sell to meet her quota is represented by the shaded area in graph X.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the incandescent light bulbs and y represent the fluorescent light bulbs. Therefore:
x + y > 100 (1)
Also:
2x + 5y ≥ 350 (2)
The solution to the amount of light bulbs Julia needs to sell to meet her quota is represented by the shaded area in graph X.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
A large soda-pop manufacturer wants to introduce a new design for the label on one of its signature soda-pop drinks. The manufacturer selects a random sample of 150 customers from people who purchase the drink at a large sporting event. Each selected customer is asked whether or not he or she prefers the new design. If the manufacturer were to take a second random sample of 150 customers at the sporting event, the two samples would give somewhat different results in the proportion who prefer the new design. This variation is a source of
Answer:
This variation is a source of
response error.
Step-by-step explanation:
A response error shows the lack of accuracy in the customer responses to the survey questions. A response error can be caused by a questionnaire that requires framing improvements, misinterpretation of questions by interviewers or respondents, and errors in respondents' statements. Some responses are influenced by the answers provided to previous questions, which introduces response bias.
evaluate the expression 2(8-4)^2-10/2
Answer: The answer is 27
Step-by-step explanation:
A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the gpa of male students are µ = 3. 5 and σ = 0. 5. Suppose a random sample of 100 male students is selected and the gpa for each student is calculated. What is the probability that the random sample of 100 male students has a mean gpa greater than 3. 42?
The probability that the random sample of 100 male students has a mean gpa greater than 3. 42 is 0.9452.
What is Standard deviation?A statistic known as the standard deviation is used to describe how volatile or dispersed a group of numerical values is. While a big standard deviation denotes that the values are scattered across a wider range, a low standard deviation indicates that the values tend to be close to the set mean.
From the given information, a scores random sample of 100 male students is selected and the GPA for each student is calculated which follows approximately normal with a mean of 3.5 and standard deviation of 0.5. That is,
µ = 3. 5 and σ = 0. 5
and the random sample of 100 male students has a mean GPA 3.42 is considered.
The z-score value is,
Z=( 3.42-3.5)/ (0.5/√100)
Z= -0.08/0.05
Z=-1.6
The value of z-score is obtained by taking the difference of x and µ. Then the resulting value is divided with the standard deviation by sample size.
The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is obtained below:
The required probability is,
P(X>3.42)=P(z>-1.6)
= 1- P(Z≤-1.6)
From the “standard normal table”, the area to the left of Z=-1.6 is 0.0548.
P(X>3.42)= 1- P(Z≤-1.6)
=1-0.0548
=0.9452
The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is 0.9452.
To learn more about standard deviation from the given link
https://brainly.com/question/475676
#SPJ1
Money is invested into an account earning 4.25% interest compounded annually. If the accumulated value after 18 years
will be $25,000, approximately how much money is presently in the account?
a $5,875
b. $11,820
c. $19,125
d. $23,960
Answer:
b. $11,820
Step-by-step explanation:
The 'rule of 72' tells you the doubling time of this account is about ...
(72 years)/(4.25) = 16.9 years
So, in 18 years, the amount will be slightly more than double the present value. That is, the present value is slightly less than half the future amount.
$25,000/2 = $12,500
The closest answer choice is ...
$11,820
__
The present value of that future amount is ...
PV = FV×(1 +r)^-t = $25,000×1.0425^-18 ≈ $11,818.73
The present value is about $11,820.
Answer:
B
Step-by-step explanation:
Hannah earns $10.25 an hour, H at her job at target. She spends $4 each day on gas getting 2 and from work. Write an algebraic expression to represent the total amount of money she will bring home each day
Answer:
x = 10.25h - $4
Step-by-step explanation:
x is the money she brings home each day
h is the amount of hours she works
subtract $4 for the gas every day
The algebraic expression representing the total amount Hannah will bring home is $(10.25H - 4), where H is the hours she spent at work.
What are algebraic expressions?An algebraic expression is a combination of terms consisting of variables and constants, separated by mathematical operations (addition, subtraction, multiplication, and division).
How do we solve the given question?In the question, we are informed that Hannah earns $10.25 an hour, H at her job at target. She spends $4 each day on gas getting 2 and from work.
We are asked to write an algebraic expression that represents the total amount Hannah will bring home each day.
We know that the total amount she will bring will be equal to her total earnings minus her total expenditure.
Assume the number of hours she works = H.
Hannah's earning in 1 hour = $10.25
∴ Her total earnings = $10.25*H
Her total expenditure given = $4 (spent on gas getting to and from work).
∴ The total amount she will bring home each day = $10.25*H - $4.
∴ The algebraic expression representing the total amount Hannah will bring home is $(10.25H - 4), where H is the hours she spent at work.
Learn more about the algebraic expression at
https://brainly.com/question/4344214
#SPJ2
PLEASE HELP
Which of the following values for X will make relation A shown below, a function?
A=(5,3),(4,9),(7,2),(x,6)
3
4 (I know 4 is wrong)
5
7
The value of x that makes the relation a function is 3.
Option A is the correct answer.
We have,
A = (5, 3), (4, 9), (7, 2), (x, 6)
Given the points (5, 3), (4, 9), (7, 2), and (x, 6), we need to ensure that x does not repeat in the relation.
If we substitute the given values of x (3, 4, 5, 7) into the relation, we find:
For x = 3: (3, 6)
For x = 4: (4, 6)
For x = 5: (5, 6)
For x = 7: (7, 6)
Now,
A function can not have the same output for the same input.
So,
(4, 6) and (4, 9) are not possible.
(5, 6) and (5, 3) are not possible.
(7, 6) and (7, 2) are not possible.
And,
(3, 6) is possible
Thus,
The value of x that makes a function is 3.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ1
If the odds against Deborah winning first prize in the chess tournament are 2 to 11, what is the probability of the event that she will win first prize? the probability of Deborah winning first prize is ______. (type an integer or a fraction).
The question says that the odds against Deborah winning first prize in the chess tournament are 2 to 11. These are the odds of her not winning.
Odds of an event is related to the probability of the same event occuring by the formula:
\(\begin{gathered} O=\frac{p}{1-p} \\ \\ \text{where,} \\ O=\text{Odds} \\ P=\text{probability} \\ \\ \end{gathered}\)Therefore, to calculate the probability of the event occurring, we simply make p the subject of the formula:
\(\begin{gathered} p=\frac{O}{O+1} \\ \\ \text{where,} \\ p=\text{probability} \\ O=\text{Odds} \end{gathered}\)Now that we have the formula for probability (p) in terms of odds (O), we can proceed to find the probability of Deborah NOT winning first prize. This is done below:
\(\begin{gathered} O=\frac{2}{11}\text{ (or 2 to 11)} \\ \\ p=\frac{O}{O+1} \\ \\ O+1=\frac{2}{11}+1=\frac{13}{11}_{} \\ \\ \therefore p=\frac{2}{11}\div\frac{13}{11} \\ p=\frac{2}{11}\times\frac{11}{13}\text{ (11 crosses out)} \\ \\ \therefore\text{Probability of Deborah NOT winning is:}\frac{2}{13} \end{gathered}\)The question asks us to find the probability that Deborah wins the first prize. This is the direct opposite event or the mutually exclusive event to her NOT winning.
The relationship between event (P) and its opposite, event (Q) is:
\(P=1-Q\)Therefore, to find the probability (Q) of Deborah winning first prize is:
\(\begin{gathered} \frac{2}{13}=1-Q \\ \\ \text{make Q the subject of the formula by adding Q to both sides and} \\ \text{subtracting 2/13 from both sides} \\ \\ \frac{2}{13}-\frac{2}{13}+Q=1-Q+Q-\frac{2}{13} \\ Q=1-\frac{2}{13} \\ \\ \therefore Q=\frac{11}{13} \end{gathered}\)Therefore the probability of Deborah winning the first prize is: 11/13
Evaluate the following expression.
(-3)0
Answer here
The expression (-3)0 has a value of 0 when evaluated because a number multiplied by 0 gives 0
Evaluating the expression (-3)0From the question, we have the following parameters that can be used in our computation:
(-3)0
The above statement is a product expression that multiplies the values of -3 and 0
Also, there is no need to check if there are like terms in the expression or not
This is because we are multiplying the factors
So, we have
(-3)0 = 0
This means that the value of the expression is 0 i.e a number multiplied by 0 gives 0
Read more about expression at
brainly.com/question/15775046
#SPJ1
Find measure of arc or angle indicated
NEED ANSWER ASAP!!
How much water should be added to 18 mL of 15% alcohol solution to reduce the concentration to 9%?
De 1.350 estudiante, sólo aprobaron el 62% del total de 850 hombres y de mujeres sólo aprobaron 400. ¿Qué porcentaje de estudiantes reprobó?
In total, 28.4% of the students failed the exam.
The total number of students is 1,350. Of this, 850 are male and 500 are female. Of the 850 males, 62% passed while of the 500 females, 400 passed. To find the percentage of students who failed, we must subtract the total number of students who passed from the total number of students.
The equation for this problem is as follows:
(1,350 - (850 x 0.62) - 400) / 1,350 x 100 = 28.4%
Therefore, 28.4% of the total students failed the exam.
Learn more about total number here:
https://brainly.com/question/14993202
#SPJ1
If rolling a pair of dice, what is the probability of rolling a sum of 12?
A) 1/6
B) 1/12
C) 1/24
D) 1/36
Answer:
D. 1/36
Step-by-step explanation:
yeah-ya.... right?
If you draw a card from a standard deck of 52 playing cards, what is the probability that it is a heart or a diamond?
Answer:
1/2
Step-by-step explanation:
In a deck of cards, there are 13 hearts and 13 diamonds
13+13 = 26 hearts or diamonds
P( hearts or diamonds) = numbers of hearts or diamonds / total
=26/52
= 1/2
Assets Liabilities and Net Worth Reserves $51 Checkable Deposits $140 Loans 109 Stock Shares 130 Securities 100 Property 10 Refer to the accompanying consolidated balance sheet for the commercial banking system. Assume the required reserve ratio is 30 percent. All figures are in billions. If the commercial banking system actually loans the maximum amount it is able to lend, excess reserves will be reduced to
If the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.
Given that the required reserve ratio is 30 percent and all figures are in billions, the following table shows the total reserves, excess reserves, and required reserves:
Required reserve ratio 30% Checkable deposits $140Billion Reserves required (30% of checkable deposits)$42Billion Reserves held $51Billion Excess reserves held $9Billion Loans outstanding $109Billion Total Securities $100Billion Total Property $10Billion Total Assets $260Billion Stock shares $130Billion Total liabilities $130Billion Net worth (total assets - total liabilities) $130Billion.
Therefore, the total reserves held is $51 billion, and the reserves required is 30% of $140 billion, which is $42 billion.
This implies that the excess reserves are $9 billion.The maximum amount the commercial banking system can lend out is $51 billion minus $42 billion, which is $9 billion.
This indicates that if the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.
For more such questions on commercial banking system, click on:
https://brainly.com/question/29638417
#SPJ8
Solve the linear equation for y in terms of x. -8x-y=12
Answer:
1.5
Step-by-step explanation:
Answer: y=-8x -12
Step-by-step explanation:
-8x - y =12 to solve for y add -8x to both sides
+8x +8x
-y = 12 +8x Now divide each side by -1
y = -8x -12
Suppose x=18,y=24, and z=30 in the figure, which is not drawn to scale. Determine the following values. Enter exact answers (as fractions), not decimal approximations. (e.g., enter 1/2 not 0.5)
cos(θ)=
sin(θ)=
tan(θ)=
cos(ϕ)=
sin(ϕ)=
tan(ϕ)=
Answer:
See explanation
Step-by-step explanation:
cos(θ)= 18/30 = 3/5
sin(θ)= 24/30 = 4/5
tan(θ)= 24/18 = 4/3
cos(ϕ)= 24/30 = 4/5
sin(ϕ)= 18/30 = 3/5
tan(ϕ)= 18/24 = 3/4
The value of the trigonometric ratios have been determined.
What are Trigonometric Ratios ?In a Right angled triangle , the trigonometric ratios are used to determine the value of angles and sides.
The side length of the triangle as given in the figure is 18 , 24 , 30
The value of the trigonometric ratios are
cos θ = Base / Hypotenuse
sin θ = Perpendicular / hypotenuse
tan θ = Perpendicular / Base
cos(θ)= 18/30 = 3/5
sin(θ)= 24/30 = 4/5
tan(θ)= 24/18 = 4/3
cos(ϕ)= 24/30 = 4/5
sin(ϕ)= 18/30 = 3/5
tan(ϕ)= 18/24 = 3/4
Therefore the value of the trigonometric ratios have been determined.
To know more about Trigonometric Ratios
https://brainly.com/question/13724581
#SPJ2
Do anyone know this youll get 20 points
Answer:
A. Acute
B. 80 degrees
Step-by-step explanation:
Given: XY and ZW intersect at point A.Which conjecture is ahvars true about the given statement?Just number 16
Given that the intersection of XY and ZW is at point A
For option A :
XA = AY
This will be true only if point A is the midpoint of the segment XY, since point A is any point on the line, this conjecture is not always true.
For option B :
Take note that the two angles formed by two intersecting lines will always sum up to 180 degrees
By the definition of the acute angle, which is an angle less than 90 degrees
If XAZ is acute, The other angle is must not be acute.
Because the sum of two acute angles will not have a sum of 180 degrees.
For example 89 degrees is an acute angle and the other angle must be 180 - 89 = 91 which is not an acute angle.
So this conjecture is not always true for it may have a value of 89 degrees which is an acute, but it can also have a value of 91 degrees which is not an acute angle.
For Option C :
XY is perpendicular to ZW
This will be true only if the slope of XY and ZW is the negative inverse of each other
Since lines XY and ZW are not restricted to any slope. Therefore, this conjecture is not always true.
For option D :
X, Y, Z, and W are noncollinear
If the lines only shares at exactly one point, then the lines are noncollinear
If the lines are noncollinear, therefore the points also are noncollinear
Since XY and ZW shares at exactly one point which is the Point A, therefore the points X, Y, Z and W are noncollinear
and This conjecture is always true
The correct answer is Choice D.
25 POINTS PLEASE HELP ILL GIVE BRAINLISt
Step-by-step explanation:
yes the area of the red square is 6^2 = 36.
the area of the bigger white square is 15^2 = 225.
36/225 = 0.16