The corresponding rectangular coordinates for point Q is (-3√3, 3)
How to convert polar coordinates to rectangular coordinates?To convert polar coordinates (r, θ) to rectangular coordinates (x, y). Use the following relations:
x = rcosθ
y = rsinθ
We have:
(r, θ) = (6, 5π/6)
x = 6 cos (5π/6)
x = 6 * -√3/2
x = -3√3
y = 6 sin (5π/6)
y = 6 * 1/2
y = 3
Therefore, the corresponding rectangular coordinates for point Q is (-3√3, 3)
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if the sin 0° = 0 then which statement is true
cos 90 = 1
cos 180 = 1
cos 90 = 0
cos 180 = 0
Step-by-step explanation:
If the sin 0° = 0, then which statement is true?
1) cos 90° = 0, because the cosine and sine are complements
2) cos 180° = 1, because the cosine and sine are supplements
3) cos 90° = 1, because the cosine and sine are complements
4) cos 180° = 0, because the cosine and sine are supplementscc
Simplyfiy the fraction 220/4 please.
Answer:
55
Step-by-step explanation:
You just need to divide 220 ÷ 4 = 55
Hope this helps :)
Pls brainliest...
A dog shelter is giving away 19 different dogs, but you have room for only 4 of them. How many different dog families could you create?
The 19 tykes given away by the Shelter, that have room for only 4 tykes per family.
The number of different canine families that could be created from the 19 tykes given away by the sanctum, we need to calculate the number of combinations. room for only 4 tykes , we need to choose 4 tykes from the aggregate of 19 tykes . The order of the tykes in the family doesn't count, as long as we choose different tykes for each family. The number of combinations can be calculated using the formula for combinations C( n, r) = n!/( r!( n- r)!) Where C( n, r) represents the number of combinations of choosing r particulars from a set of n particulars. In this case, we've n = 19( total number of tykes ) and r = 4( number of tykes per family). Plugging these values into the formula, we get C( 19, 4) = 19!/( 4!( 19- 4)!) Calculating the factorial values 19! = 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = ! = 4 × 3 × 2 × 1 = 24 15! = 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = Substituting these values into the formula C( 19, 4) = /( 24 ×) ≈ 91,390 The 19 tykes given away by the sanctum, considering that you have room for only 4 tykes per family.
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Subtract: (6f2-9f + 10)-(-2f²-f+3)
O8f²-8f +7
O 4f2 - 10f +7
O 4f2 - 10f + 13
O8f² -10f + 7
Step-by-step explanation:
therefore, the correct option is option number 1.
use equations to describe the rule and the nth term for the following patterns
1.10,14,18,22..
2.34,26,18,10,..
3.17;11;5;-1;-7;..
4.4;11;18;25;..
5.-35;-27;-19;-11;..
Al the nth term are,
1) a (n) = 6 + 4n
2) a (n) = 26 + 8n
3) a (n) = 23 - n
4) a (n) = 7n - 3
5) a (n) = 8n - 43
We have to given that;
All the sequence are,
1.10,14,18,22..
2.34,26,18,10,..
3.17;11;5;-1;-7;..
4.4;11;18;25;..
5.-35;-27;-19;-11;..
Now, WE can find the nth term as;
1) 10,14,18,22..
Here, a = 10
Common difference = 14 - 10 = 4
Hence, The nth term is,
a (n) = a + (n - 1) d
a (n) = 10 + (n - 1)4
a (n) = 10 + 4n - 4
a (n) = 6 + 4n
2) 34,26,18,10,..
Here, a = 34
Common difference = 26 - 34 = 8
Hence, The nth term is,
a (n) = a + (n - 1) d
a (n) = 34 + (n - 1)8
a (n) = 34 + 8n - 8
a (n) = 26 + 8n
3) 17;11;5;-1;-7;..
Here, a = 17
Common difference = 11 - 17 = - 6
Hence, The nth term is,
a (n) = a + (n - 1) d
a (n) = 17 + (n - 1) (- 6)
a (n) = 17 - 6n + 6
a (n) = 23 - n
4) 4;11;18;25;..
Here, a = 4
Common difference = 11 - 4 = 7
Hence, The nth term is,
a (n) = a + (n - 1) d
a (n) = 4 + (n - 1) (7)
a (n) = 4 + 7n - 7
a (n) = 7n - 3
5) -35;-27;-19;-11;..
Here, a = - 35
Common difference = - 27 + 35 = 8
Hence, The nth term is,
a (n) = a + (n - 1) d
a (n) = - 35 + (n - 1) (8)
a (n) = - 35 + 8n - 8
a (n) = 8n - 43
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sur le bord des routes se trouvent des bornes kilometriques formées d'un pavé et d'un demi-cylindre. calculer le volume de matiere qui la compose
write 2x+xto the power of 3 minus 1 in descending oreder
Answer:
x^3 + 2x - 1.
Step-by-step explanation:
To simplify the expression 2x + x^3 - 1, we can first rearrange the terms in decreasing order of the exponents:
x^3 + 2x - 1
So the simplified expression, rearranged in descending order, is x^3 + 2x - 1.
7)A point is chosen randomly inside rectangle ABCD with vertices A(4, 8), B(4, -3), C(-5, -3), and
D(-5, 8). whats the probability The point does not lie in circle P with center P(-2, 5) and radius 3.
Answer:
≈0.71441
Step-by-step explanation:
1. to calculate the area of the given circle;
2. to calculate the area of the rectangle ABCD;
3. to divide the area of the circle by the area of the rectangle ABCD
and to calculate the rest part.
All the details are in the attachment.
Solve the system of equations x-y=-1 and x+8y=35 by combining the equations
Answer:
(x, y) = (3, 4)
Step-by-step explanation:
You want to solve the system of equations by combining the equations:
x -y = -1 x +8y = 35 ObservationThe coefficients of x have the same value (1), so we can eliminate x by multiplying one of the equations by -1 and adding the result. Since we want the resulting coefficient of y to be positive, we choose to multiply the first equation by -1.
[tex]\begin{array}{c,l,l,l}-1&(x&-y&=-1)\\+1&(x&+8y&=35\,)\end{array}[/tex]
Combined equationsThen the sum is ...
[tex]\begin{array}{rcl}-x&+y&=1\\x&+8y&=35\\\cline{1-3}0x&+9y&=36\end{array}[/tex]
SolutionThe solution to this is ...
y = 36/9 = 4
x = y -1 = 4 -1 = 3 . . . . . . from the first equation
The solution is (x, y) = (3, 4).
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Which equation is not true?
A. 120 ounces = 7 pounds
B. 5 pounds = 80 ounces
C. 2.5 tons = 5,000 pounds
D. 60 ounces = 3.75 pounds
a student claimed that the function shown in the table is exponential. do you agree or disagree? explain
The correct statement that F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."
To determine whether the function shown in the table is exponential, we need to analyze the relationship between the x-values and y-values.
The table shows x-values that are increasing by a power of 2 (1, 2, 4, 8, 16, 32, 64) and y-values that are increasing by a constant rate of 1 (0, 1, 2, 3, 4, 5, 6).
The constant ratio between consecutive x-values indicates exponential growth or decay.
In this case, the function is growing exponentially because the y-values are increasing at a constant rate.
Based on this information, we can conclude that the function is exponential.
Therefore, we agree with statement F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."
The other statements are incorrect because they do not accurately describe the relationship between the x-values and y-values in an exponential function.
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A science class has a total of 32 students. the number of females is 14 less then the number of males. how many males and how many females are in the class?
Step-by-step explanation:
Let the boys be x
Girls = x - 14 (number of females is 14 less than the number of males)
x + x - 14 = 32
2x - 14 = 32
2x = 32 + 14 (add 14 to both sides or if 14 crosses over the bracket. The sign changes to plus or positive)
2x = 46
Divide both sides by 2
x = 23
Girls = x - 14 = 23 - 14
=9
Therefore, The boys are 23, while the girls are 9
Which equation represents a line which is parallel to the line
Y = -5x - 7
Y = -5x + 3 is the equation represents a line which is parallel to the line Y = -5x - 7 with y intercept 3
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We have to find the equation which represents a line which is parallel to the line Y = -5x - 7 with y intercept 3
We know that the parallel lines will have same slope
In the above equal -5 is the slope and y intercept -7
The equation of parallel line y =-5x+3
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Which equation represents a line which is parallel to the line
Y = -5x - 7 and of intercept 3
5.5.2 Question 6 of 15 A bag contains 6 blue marbles, 5 yellow marbles, 3 white marbles, and 1 red marble. What is the probability of not selecting a blue marble? O A. OB. B. O C. C. D. 236 25 23 Probability 33112 SUBMIT
The probability of not selecting a blue marble is 3/5
What is Probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. It is the rate of the number of favorable outcomes to the total number of outcomes of an event.
How to determine this
A bag contains 6 blue marbles, 5 yellow marbles, 3 white marbles and 1 red marble
i.e 6 + 5 + 3 + 1 = 15 marbles
To calculate the probability of not selecting a blue marble
When blue marbles = 6
= [tex]\frac{15-6}{15}[/tex]
= [tex]\frac{9}{15}[/tex]
= 3/5
= 0.65
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Find the volume of the figure below. Round to the nearest tenth.
The volume of the given triangular pyramid is 59.2 feet³.
Given figure is that of a triangular pyramid.
We have to find the volume of the pyramid.
Volume of a pyramid = 1/3 × base area × height
Here base is triangular.
Base area = 1/2 × 12 × 3.7
= 22.2 feet²
Height of the pyramid = 8 feet
Volume = 1/3 × 22.2 × 8
= 59.2 feet³
Hence the volume is 59.2 feet³.
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Calculate the Cash Cycle using the following information. (Assume 360 days in a year). Opening Balances Raw Material 4,00,000 WIP 80,000 Finished Goods 6,00,000 Debtors 2,50,000 Creditors 5,60,000 Closing Balances Raw Material 5,00,000 WIP 70,000 Finished Goods 7,25,000 Debtors 3,15,000 Creditors 6,25,000 Costs Incurred during the year Manufacturing Costs 10,45,000 Excise Duty 8,50,000 Selling and Distribution Expenses 4,20,000 Admin. Overheads 3,00,000 Total Sales 4,20,00,500 Total Purchases 3,23,00,000 30% of sales are on credit and 80% of purchases are on credit
Answer:
156.76 days (approx.)
Step-by-step explanation:
To calculate the Cash Cycle, we need to consider the time it takes for a company to convert its investment in inventory and receivables back into cash. The formula for Cash Cycle is as follows:
Cash Cycle = Inventory Conversion Period + Receivables Collection Period - Payables Deferral Period
Now, let's calculate each component of the Cash Cycle using the given information.
1. Inventory Conversion Period:
Inventory Conversion Period measures the average number of days it takes to convert raw materials into finished goods.
Average Inventory = (Opening Raw Material + Closing Raw Material) / 2
= (4,00,000 + 5,00,000) / 2
= 4,50,000
Manufacturing Costs per day = Manufacturing Costs / 360 days
= 10,45,000 / 360
= 2,902.77 (approx.)
Inventory Conversion Period = Average Inventory / Manufacturing Costs per day
= 4,50,000 / 2,902.77
≈ 155 days
2. Receivables Collection Period:
Receivables Collection Period measures the average number of days it takes to collect payments from customers.
Average Receivables = (Opening Debtors + Closing Debtors) / 2
= (2,50,000 + 3,15,000) / 2
= 2,82,500
Sales per day = Total Sales / 360 days
= 4,20,00,500 / 360
= 1,16,666.67 (approx.)
Receivables Collection Period = Average Receivables / Sales per day
= 2,82,500 / 1,16,666.67
≈ 2.42 days
3. Payables Deferral Period:
Payables Deferral Period measures the average number of days the company takes to pay its suppliers.
Average Payables = (Opening Creditors + Closing Creditors) / 2
= (5,60,000 + 6,25,000) / 2
= 5,92,500
Purchases per day = Total Purchases / 360 days
= 3,23,00,000 / 360
= 8,97,222.22 (approx.)
Payables Deferral Period = Average Payables / Purchases per day
= 5,92,500 / 8,97,222.22
≈ 0.66 days
Now, we can calculate the Cash Cycle using the formula mentioned earlier:
Cash Cycle = Inventory Conversion Period + Receivables Collection Period - Payables Deferral Period
= 155 days + 2.42 days - 0.66 days
≈ 156.76 days (approx.)
Therefore, the Cash Cycle is approximately 156.76 days based on the given information.
If Ryan is planning on retiring soon he needs to compute his Social Security benefit that he will receive monthly. Ryan has averaged $4,690 over his last
35-years of working. Using the formula, calculate his retirement benefit.
90% of the first $926
32% of the amount between $926 and $5,583
15% of the amount over $5,583
Ryan's Social Security retirement benefit, computed using the given formula, is $2,188.89 per month.
How to compute Ryan's Social Security retirement benefit?To calculate Ryan's Social Security retirement benefit, we'll break it down into three parts based on the given formula:
First, we shall estimate 90% of the first $926 of Ryan's average monthly earnings:
Benefit from level 1= 0.9 * $926
Next, we find out 32% of the amount between $926 and $5,583:
Benefit from level 2= 0.32 * ($5,583 - $926)
Lastly, we compute 15% of the amount over $5,583:
Benefit from level 3= 0.15 * (Ryan's average monthly earnings - $5,583)
Ryan's retirement benefit is the sum of the benefits from all three level:
Retirement benefit = Benefit from level 1 + Benefit from level 2 + Benefit from level 3
Benefit from level 1:
= 0.9 * $926 = $833.40
Benefit from level 2:
= 0.32 * ($5,583 - $926) = 0.32 * $4,657 = $1,489.44
Benefit from level 3:
= 0.15 * (Ryan's average monthly earnings - $5,583)
= 0.15 * ($4,690 - $5,583)
= 0.15 * (-$893)
= -$133.95 (Ryan's average monthly earnings are less than $5,583, this amount is negative)
We now calculate the retirement benefit:
Retirement benefit = Benefit from level 1 + Benefit from level 2 + Benefit from level 3
= $833.40 + $1,489.44 - $133.95
= $2,188.89
Therefore, Ryan's Social Security retirement benefit is $2,188.89 per month.
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What is the scale factor of the perimeters from figure A to figure B? Enter
a number answer only. Simplify any fractional answer. Round any
decimals to the nearest tenth.
12
A
10
18
B
15
The scale factor of the perimeters from figure A to figure B is 1.5. Scale factor is the ratio of any two corresponding lengths in two similar figures.
Here, the two figures are similar, that is why we can find the scale factor by dividing corresponding sides of one figure by the corresponding sides of another figure. We will find the scale factor for the perimeter of figures A and B below:Perimeter of figure A = 12 + 10 + 18 = 40 unitsPerimeter of figure B = 15 + 15 + 15 = 45 unitsTo find the scale factor of the perimeters, we divide the perimeter of figure B by the perimeter of figure
A:Scale factor of the perimeters = (Perimeter of figure B)/(Perimeter of figure A) = 45/40 = 1.125To simplify any fractional answer, we have to convert it to the lowest terms, which is 9/8. The decimal answer 1.125, when rounded to the nearest tenth is 1.1. Therefore, the scale factor of the perimeters from figure A to figure B is 1.5.
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Si una mosca real tiene una longitud de 9mm y su maqueta mide 18cm.cual a q escala se realizo la maqueta
The scale factor used is:
1 centimeter equals half millimiter.
How to find the scale factor?The scale factor tells us how many units in the sculpture represent a real unit.
We know that:
Real length = 9mm
Length in the sculpture = 18cm
Then we have the relation between the lengths:
18cm = 9mm
Dividing both sides by 18 we will get:
1cm = 9mm/18
1cm = 0.5mm
So the scale is 1 centimeter equals half millimiter.
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Please solve these questions
Answer:
The first one is g(x)=1/4x-7
Step-by-step explanation:
i need ans asap
4p + 2q = 2
8 = 5p + 7q
Find q, round answers to 1 decimal place.
Answer:
The answer is 3.1 to 1d.p
Step-by-step explanation:
1)4p+2q=2
2)5p+7q=8
3)7(4p+2q=2)
4)2(5p+7q=8)
3)28p+14q=14
4)10p+14q=16
18p=2
divide both sides by 18
18p/18=2/18
p=1/9
substitute into equation 1
4(1/9)+2q=2
4/9+2q=2
2q=2-4/9
2q=14/9
divide both sides by 2
2q/2=14/9/2
q=28/9
q=3.1 to 1d.p
What is the mean of this sample which consists of 10 Val randomly selected from the table
The mean of this sample data consisting of 10 randomly selected values from the table is 21.
What is the mean?The mean describes the average value in the data set.
The average is one of the measures of central tendency, including the median and the mode.
We can compute the mean or the average by dividing the total value in the data set by the number of items.
7+ 100 + 1 + 3 + 7 + 10 + 15 + 12 + 17 + 38
Total = 210
Mean = 21 (210 ÷ 10)
Thus, the mean is the quotient of the total value and the number of items in the data set or sample.
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Complete Question:What is the mean of this sample, which consists of 10 values randomly selected from the table?
7+ 100 + 1 + 3 + 7 + 10 + 15 + 12 + 17 + 38
[tex]\sqrt{x} -3\sqrt[4]{x} -4=0\\[/tex]
Answer:
Step-by-step explanation: [tex](\sqrt[4]{x})^{2} - 3\sqrt[4]{x} -4=0[/tex]
[tex]\sqrt[4]{x} = u[/tex] ⇒ u² - 3u -4 =0 ⇒ [tex]\left \{ {{u=4} \atop {u=-1}} \right.[/tex] choose u=4 ( [tex]\sqrt{x} > 0[/tex] )
⇒ x=256
You have a compound with a concentration of 3 g hydrocortisone powder in 150 g of petrolatum.
Determine the percentage strength of this compound.
The percentage strength of the compound is approximately 1.96%.
We have,
To determine the percentage strength of the compound, we need to calculate the ratio of the mass of the active ingredient (hydrocortisone powder) to the total mass of the compound and express it as a percentage.
Given:
Mass of hydrocortisone powder = 3 g
Mass of petrolatum = 150 g
Total mass of the compound
= Mass of hydrocortisone powder + Mass of petrolatum
= 3 g + 150 g = 153 g
To calculate the percentage strength, we divide the mass of the hydrocortisone powder by the total mass of the compound and multiply by 100:
Percentage strength = (Mass of hydrocortisone powder / Total mass of the compound) x 100
Percentage strength = (3 g / 153 g) x 100
Percentage strength ≈ 1.96%
Therefore,
The percentage strength of the compound is approximately 1.96%.
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Solution for this system of equations 2/3x + 3/5 y = 12 and 5/2y - 3x = 6
Answer:
To solve the system of equations:
2/3x + 3/5 y = 12 --- equation (1)
5/2y - 3x = 6 --- equation (2)
We can use the method of substitution or elimination. Here, we will use the elimination method to eliminate one variable and solve for the other.
Multiplying equation (1) by 5 and equation (2) by 3, we get:
10/3x + 9/5y = 60 --- equation (3) obtained from (1) by multiplying both sides by 5
15/2y - 9x = 18 --- equation (4) obtained from (2) by multiplying both sides by 3
Now, we can eliminate y by multiplying equation (3) by 10/9 and adding it to equation (4):
(10/3x + 9/5y) x 10/9 + (15/2y - 9x) = 0
Simplifying this equation, we get:
20x/9 - 27x/5 = -100/3
Multiplying both sides by 45, we get:
20x(5) - 27x(9) = -1500
Simplifying and solving for x, we get:
-65x = -1500
x = 23.08 (rounded to two decimal places)
Substituting x = 23.08 into equation (1), we can solve for y:
2/3(23.08) + 3/5 y = 12
15.39 + 0.6y = 12
0.6y = -3.39
y = -5.65 (rounded to two decimal places)
Therefore, the solution to the system of equations is x = 23.08 and y = -5.65.
So, the solution to the system of equations is (23.08, -5.65).
Hope this helps.
I hello I need help below
Answer:
Rate of slower train: 110 km/h
Rate of faster train: 122 km/h
Step-by-step explanation:
The explanation is attached below.
Which shows the correct way to
calculate the percent change if the
original value of your stock was $750
and the new value of your stock is
$1,000?
A. (1,000+ 750)/750 = 230%
B. (750-1,000)/1,000 = -25%
C. (1,000-750)/750 = 33%
The correct way to calculate the percent change between the original value of $750 and the new value of $1,000 is option C.
C. (1,000 - 750)/750 = 250/750 = 1/3 ≈ 0.3333 = 33.33%
Therefore, the correct answer is option C, which represents a percent change of approximately 33.33%.
Finding Missing Angles in a Polygon
Answer:
[tex]\huge\boxed{\sf x = 130\°}[/tex]
Step-by-step explanation:
Statement:In a quadrilateral (four sided polygon), the interior angles add up to 360 degrees.The angles with a small square on it represents 90 degrees.Solution:So,
90 + 90 + 50 + x = 360
230 + x = 360
Subtract 230 from both sidesx = 360 - 230
x = 130°[tex]\rule[225]{225}{2}[/tex]
I just need 1,2, and 3 to be solved.
The values of x and y are
1. x= 35 and y= 25
2. x = 4 and y = 1
3. x = 2 and y= 5
1. We know that opposite angle of parallelogram are equivalent
So, 2x = 70
x= 35
and, 3x +5 = x + 3y
105 + 5= 35 + 3y
110 - 35 = 3y
3y = 75
y = 25
2. Now, the diagonals bisect each other
3x = 12
x= 4
and, x + y = 5y
4 + y = 5y
4y = 4
y= 1
3. Now, opposite sides are congruent then
3x = 6
x= 2
and, x + 2= y-1
4 = y -1
y = 5
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1) The values of x and y are,
x = 35, y = 25
2) The values of x and y are,
x = 4, y = 1
3) The values of x and y are,
x = 2, y = 5
We know that;
Sum of opposite angles in a rectangle is 180 degree and diagonal are bisects each other.
And, Opposite sides of a parallelogram has equal length.
Hence, WE can formulate;
1) WE get;
2x = 70
x = 35
And, 3x + 5 = x + 3y
3 x 35 + 5 = 35 + 3y
105 + 5 = 35 + 3y
110 - 35 = 3y
3y = 75
y = 25
2) Since, diagonal are bisects each other.
Hence, we get;
3x = 12
x = 4
And, x + y = 5y
4 + y = 5y
4y = 4
y = 1
3) Opposite sides of a parallelogram has equal length.
Hence, WE get;
3x = 6
x = 2
And, x+ 2 = y - 1
2 + 2 = y - 1
y = 5
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3.3.2 √4x √4 calculate
Hello!
√4 = ±2
√4x = ±2x
