There is no value of x that would make the relation not a function.
What is function?The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h.
To determine whether the relation is a function or not, we need to check if there are any repeated x values with different y values. If there are, then the relation is not a function.
So, if we substitute each x value in the relation, we get:
When x = -3, the y value is -1.When x = x, we don't know the y value yet.When x = 5, the y value is 4.When x = 6, the y value is 13.Since we don't know the y value for x, there is no repeated x value with different y values. Therefore, the relation is a function for any value of x, including x.
So, there is no value of x that would make the relation not a function.
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Give an example of a unit rate that you have seen or used in your life recently.
The examples of unit rate are given below and this can be determined by using the definition of unit rate.
The unit rate is nothing but a ratio that represents the rate of something per unit.
Examples --
1) A car is driving at a speed of 50 kilometers per hour. The 50 km/hr represents the unit rate.
2) The cost of the potatoes is $2 per pound. The $2/pound represents the unit rate.
3) The density of a substance is 4 Kg per liter. The 4kg/lt represents the unit rate.
Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 190 miles per week to commute to work. With gas prices currently at $ 2.9 per gallon, he is considering buying a more fuel-efficient car, and wants to know if it would be a good financial decision. The old car Manny owns currently gets 18 miles per gallon for average fuel efficiency. It has been a great vehicle, but with its age, it needs repairs and maintenance that average $ 770 per year (as long as nothing serious goes wrong). The newer, more fuel-efficient car that he is looking at to purchase will cost a total of $ 6,500 over a three-year loan process. This car gets 32 miles per gallon and would only require an average of $ 10 per month for general maintenance. To help make a decision, Manny wants to calculate the total cost for each scenario over three years. He decides to use the quantitative reasoning process to do this.
The best decision to purchase a old car is cheaper compare to new car as per the total cost for each scenario over three years.
Compare the total costs of keeping his old car versus buying a new car, Manny needs to consider all the costs involved.
These include the cost of gas, the cost of maintenance and repairs, and the cost of purchasing the new car.
First, calculate the total cost of keeping his old car for three years.
Gas Cost,
Manny drives 190 miles per week,
which is approximately 9,880 miles per year 190 miles x 52 weeks.
With his old car's fuel efficiency of 18 miles per gallon,
He will use approximately 549 gallons of gas per year 9,880 miles ÷ 18 mpg.
At the current gas price of $ 2.9 per gallon, his annual gas cost will be $ 1,593 (549 gallons x $ 2.9 per gallon).
Over three years, his total gas cost will be $ 4,779.
Maintenance and Repairs Cost,
Manny's old car needs an average of $ 770 per year in maintenance and repairs.
Over three years, his total maintenance and repairs cost will be $ 2,310.
Total Cost of Keeping His Old Car,
Adding the gas cost and the maintenance and repairs cost,
Manny's total cost of keeping his old car for three years will be $ 7,089.
Now let's calculate the total cost of buying the new car.
Cost of Purchasing the New Car,
The new car costs $ 6,500, which he will pay over three years.
This works out to a monthly payment of approximately $ 181.94.
Gas Cost,
With the new car's fuel efficiency of 32 miles per gallon,
Manny will use approximately 309 gallons of gas per year (9,880 miles ÷ 32 mpg).
At the current gas price of $ 2.9 per gallon,
His annual gas cost will be $ 897.10 (309 gallons x $ 2.9 per gallon).
Over three years, his total gas cost will be $ 2,691.30.
Maintenance and Repairs Cost,
The new car will only require an average of $ 10 per month for general maintenance.
Over three years, his total maintenance and repairs cost will be $ 360.
Total Cost of Buying the New Car,
Adding the cost of purchasing the new car, the gas cost, and the maintenance and repair cost
= 6500 + 2691.30 + 360
=$9551.30
$9551.3 > $7089
Total cost of new car > Total cost of old car.
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15 points or 10 I don't know how brainly works to be honest.
Here's the question!
Answer:
(1/2)(3 - (-3))(4 - (-5)) = (1/2)(6)(9)
= 27 square units
7x+2y=6 in slope-intercept form
Answer:
[tex]y=\frac{-7}{2}x+3[/tex]
Step-by-step explanation:
This is currently in standard form, so get it into slope-intercept form instead:
Subtract '7x' from both sides:
[tex]2y=-7x+6[/tex]
Divide by 2 on both sides to isolate the 'y':
[tex]y=\frac{-7}{2}x+3[/tex].
How to solve this problem
a. The numbers are written as; -1 7 5 -10 0
b. In the form, Quotient + Reminder/x+ 2
-x⁴ - 7x³ - 5x² - 10 + 0/x + 2
What is synthetic division?Synthetic division can simply be described as a mathematical method that is used to perform the division operation on algebraic expressions such as polynomials when the divisor is in the form of linear factor.
The steps in performing the synthetic division are;
The polynomial should be in the standard form.Then, write the coefficients in the dividend's place and write the zero of the linear factor in the divisor's place.Bring the first coefficient down.Multiply it with the divisor and write it below the next coefficient.Add them and write the value under itFrom the information given, we have that;
-x⁴ + 5x³ + 19x² - 20 divided by x + 2
Then, we have;
-2) -1 5 19 0 -20
2 -14 -10 20
-1 7 5 -10 0
Then, we have;
-x⁴ - 7x³ - 5x² - 10
The remainder is 0
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An average silt loam soil with a depth of 4 ft has how many inches of available water capacity?
(Hint: Review the following USDA FAQ on Available Water Capacity and identify the AVERAGE value of the plant available water capacity for a silt loam soil. Note that this value is given as a fraction of the total volume. Thus, if the fraction is 0.18 and the rooting depth is 2.5 feet (30 inches), the Available Water Capacity would be 0.18*30 = 5.4 inches)
There are 48 inches of available water capacity.
Given that;
An average silt loam soil with a depth of 4 ft has.
Now, We know that;
1 feet = 12 inches
Hence, We get;
4 feet = 4 x 12 inches
= 48 inches
Thus, There are 48 inches of available water capacity.
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NO LINKS!!! URGENT HELP PLEASE!!!
1. Find the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2, 1)
(x, y) = ______________
2. Find a formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector "l" of segment AB.
A(-6, 3), B(8, -11)
Answer:
1. (-1, -3)
2. y = x - 5
Step-by-step explanation:
Question 1To find the values of a where the point (a, 3a) is a distance of 5 units from P(2, 1) use the distance formula.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where:\\ \phantom{ww}$\bullet$ $d$ is the distance between two points. \\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Given values:
d = 5(x₁, y₁) = (2, 1)(x₂, y₂) = (a, 3a)Substitute the given values into the distance formula and solve for a:
[tex]\begin{aligned}\sqrt{(a-2)^2+(3a-1)^2}&=5\\(a-2)^2+(3a-1)^2&=25\\a^2-4a+4+9a^2-6a+1&=25\\10a^2-10a-20&=0\\a^2-a-2&=0\\a^2-2a+a-2&=0\\a(a-2)+1(a-2)&=0\\(a+1)(a-2)&=0\\\\a+1&=0 \implies a=-1\\a-2&=0 \implies a=2\end{aligned}[/tex]
Substitute the found values of a into the point coordinate formula, (a, 3a):
[tex]a=-1 \implies (-1,-3)[/tex]
[tex]a=2 \implies (2, 6)[/tex]
As the point is in the third quadrant, this means that the x and y coordinates are negative.
Therefore, the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 units from P (2, 1) is:
[tex]\large\boxed{(-1, -3)}[/tex]
[tex]\hrulefill[/tex]
Question 2The perpendicular bisector of segment AB is the line that passes through the midpoint of AB and is perpendicular to AB.
To find the midpoint of AB, use the midpoint formula.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]
Let (x₁, y₁) = A = (-6, 3)
Let (x₂, y₂) = B = (8, -11)
Substitute the values into the midpoint formula:
[tex]\text{Midpoint of $AB$}=\left(\dfrac{8-6}{2},\dfrac{-11+3}{2}\right)=\left(1,-4\right)[/tex]
Therefore, the midpoint of AB is (1, -4).
To find the slope of AB, use the slope formula.
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-11-3}{8-(-6)}=\dfrac{-14}{14}=-1[/tex]
The slope of a line that is perpendicular to AB is the negative reciprocal of the slope of AB.
Therefore, the slope of the line perpendicular to AB is m = 1.
To determine the equation of the perpendicular bisector of AB that passes through the midpoint of AB and is perpendicular to AB, substitute the found slope, m = 1, and the midpoint (1, -4) into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-4)=1(x-1)[/tex]
[tex]\implies y+4=x-1[/tex]
[tex]\implies y=x-5[/tex]
Therefore, the formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector "l" of segment AB is:
[tex]\large\boxed{y=x-5}[/tex]
John has to type a 2,000-word business research report, and he types at a rate of 40 words per minute. The function R(m) = 2,000 40 m can be used to calculate the number of minutes required to finish after m minutes of typing. What is the domain for function R in this context?
The domain for the function is m ≥ 0
Given data ,
Let the function be represented as f ( x )
Now , the value of the function is
R ( m ) = ( 2000/40 ) - m
R(m) = 50 - m
The domain of a function is the set of all possible input values for which the function is defined. In this case, since we are dealing with time, the domain of the function should be non-negative values of m, as negative values of m do not make sense in the context of typing time.
Hence , the domain of function R is m ≥ 0
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Critical values for quick reference during this activity. Confidence level Critical value 0.90 z∗=1.645 0.95 z∗=1.960 0.99 z∗=2.576 Jump to level 1 In a poll of 1000 randomly selected voters in a local election, 403 voters were against school bond measures. What is the sample proportion p^? (Should be a decimal answer) What is the margin of error m for the 95% confidence level? (Should be a decimal answer)
What is the percentage equivalent to 11/50
5%
22%
39%
61%
Prove the following: In a group G , a subgroup of a subgroup of G is a subgroup of G?
The proof is the intersection of all subgroups in H is a subgroup of G containing S.
How do we explain?we start by showing that the intersection is a subgroup of G. Let A and B be two subgroups in H.
we define that A and B contain S which means that A ∩ B contains S as well, since every element in S is in both A and B. Moreover, A ∩ B is closed under the group operation and inverses, since A and B are subgroups. Therefore, A ∩ B is a subgroup of G.
we go ahead to show that the intersection contains S and it is known that S is a subset of each subgroup in H, it is also a subset of their intersection. Thus, the intersection of all subgroups in H contains S.
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1. To deliver mail in a particular neighborhood, the postal carrier needs to walk along each of the streets with houses (the dots). Create a graph with edges showing where the carrier must walk to deliver the mail.
The graph for the mail is attached below.
What is graph?
A function, which is a relation that matches every element in its domain with exactly one element in its range, can also be represented as a graph.
Linear function graph. Every linear function has the formula f(x)=ax+b, where an is not zero and a and b are real numbers. ...
Squaring Function Graph. A parabola, or U-shaped curve, is the common name for a squaring function graph. ...
A reciprocal function's graph.
Step Function's graph.
Piece-Wise Function Graph.
The dots on the given figure denoted the houses where the postal carrier needs to go.
The graph is attached below.
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The volume of the cone is 162 yd³. What
is the radius of the cone?
The radius of the cone is 9 yd.
We have,
Volume of Cone= 162π yd³
Height of Cone= 6 yd
Using the formula
Volume of Cone= 1/3πr²h
162π = 1/3πr² (6)
162 = 2r²
r² = 81
r= √81
r= 9 yd
Thus, the radius is 9 yd.
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Add 8.563 and 4.8292
After adding the 2 given values the resultant answer is 13.3922 respectively.
What is addiction?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division.
The entire amount or sum of the two whole numbers is obtained by adding them.
Mathematicians utilize addition as their main arithmetic operation to determine the sum of two or more numbers.
For instance, 7 plus 6 equals 13.
So, add the 2 given values as follows:
= 8.563 + 4.8292
= 13.3922
Therefore, after adding the 2 given values the resultant answer is 13.3922 respectively.
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Robert just purchased a house for $186,000 after down payment and fees, his loan is for 20 years at an APR of 4.8%. His monthly payment is $1,207.06. Using this information fill in the amortization chart for his first monthly payment.
Answer:
Step-by-step explanation:
AA'B'C' is the image of ABC under a dilation whose center is P and scale factor is 2/3 Which figure correctly shows AA'B'C' using the solid line?
A figure that correctly shows ΔA'B'C' using the solid line include the following: A. figure A.
What is dilation?In Mathematics and Geometry, a dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape. This ultimately implies that, the size of the geometric shape would be increased (enlarged) or decreased (reduced) based on the scale factor applied.
In this exercise, we would sketch the image of ABC after a dilation by a scale factor of 2/3 centered at P as shown in the image attached below.
Based on the image (see attachment), we can logically deduce that each vertex is 2/3 times as far from center P as the original vertex and each segment is 2/3 times as long as the original:
Scale factor = AP/A'P = BP/B'P = CP/C'P = 2/3
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Question 15(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane MC)
What is the vertical distance between (7, -12) to (7, 19)?
31 units
07 units
O-31 units
O-7 units
Answer:
1st option will be your answer
Step-by-step explanation:
An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.
The estimated total cost for a production volume of 800 units is $7,906.39.
To develop an estimated regression equation, we can use the least squares method to fit a linear equation of the form:
Total Cost = a + b * Production Volume
where a is the intercept and b is the slope of the line. We can use the given data to calculate the values of a and b as follows:
First, calculate the mean of production volume and total cost:
mean(Production Volume) = (400 + 450 + 550 + 600 + 640 + 700 + 750) / 7 = 586.43
mean(Total Cost) = (5000 + 6000 + 6400 + 6900 + 7400 + 8000) / 6 = 6783.33
Next, calculate the sum of squares of deviations:
SSx = Σ(Production Volume - mean(Production Volume))² = 166,950
SSy = Σ(Total Cost - mean(Total Cost))² = 11,223,333
Calculate the sum of cross-deviations:
SSxy = Σ((Production Volume - mean(Production Volume)) * (Total Cost - mean(Total Cost))) = 892,500
Calculate the slope:
b = SSxy / SSx = 892,500 / 166,950 = 5.34
Calculate the intercept:
a = mean(Total Cost) - b * mean(Production Volume) = 6783.33 - 5.34 * 586.43 = 3414.39
Therefore, the estimated regression equation is:
Total Cost = 3414.39 + 5.34 * Production Volume
For example, if the production volume is 800 units, the predicted total cost would be:
Total Cost = 3414.39 + 5.34 * 800 = 7906.39
Therefore, the estimated total cost for a production volume of 800 units is $7,906.39.
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A local event planner wants to cover a circular region with mud for an obstacle course. The region has a circumference of about 157 feet. The cost to cover 1 square foot with mud is $1.50. Approximate the cost to cover the region with mud. Round to the nearest ten dollars if necessary.
It will cost approximately $2940 to cover the circular region with mud.
What is cost?The term "cost" in mathematics usually refers to the sum of money or resources needed to acquire or manufacture something.
It can be quantified as a number, frequently in a particular currency.
The formula C = 2r, where r is the circle's radius, determines the circumference of a circle.
In this case, we know that the circumference is about 157 feet, so we can set up an equation:
157 = 2πr
Solving for r, we get:
r = 157 / (2π) ≈ 25
So the radius of the circular region is approximately 25 feet.
The equation A = r² determines a circle's surface area.
Using the radius we just found, we can calculate the area:
A = π(25)² ≈ 1963.5 square feet
The cost to cover 1 square foot with mud is $1.50, so the cost to cover the entire area with mud is:
1963.5 × $1.50 = $2945.25
Rounding to the nearest ten dollars, the cost is:
$2940
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In △ABC, we are told that a=17, ∡B=70∘, and ∡C=48∘. Solve for b and c.
The length of the other two sides in the triangle ABC using Law of Sines is b = 18.1 and c = 14.3.
Given a ΔABC.
Angles are given as, ∠B = 70° and ∠C = 48°.
∠A = 180° - (70° + 48°) = 62°
The sides are given as,
BC = 17
Using law of sines, if a, b and c are sides opposite to the angles A, B and C respectively, then,
a / sin A = b / sin B = c / sin C
Using the law of sines,
17 / Sin (62°) = b / Sin (70°) = c / Sin (48°)
Taking the first two,
17 / Sin (62°) = b / Sin (70°)
b = [17 × Sin (70°)] / Sin (62°)
b = 18.09 ≈ 18.1
Taking the other two,
17 / Sin (62°) = c / Sin (48°)
Solving,
c = 14.308 ≈ 14.3
Hence the lengths are b = 18.1 and c = 14.3.
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To solve for b and c, we can use the Law of Sines, which states that for any triangle △ABC,
a/sin(∡A) = b/sin(∡B) = c/sin(∡C)
Using this formula, we can write:
b/sin(∡B) = a/sin(∡A)
c/sin(∡C) = a/sin(∡A)
Substituting the given values, we get:
b/sin(70∘) = 17/sin(∡A)
c/sin(48∘) = 17/sin(∡A)
We can solve for sin(∡A) in both equations:
sin(∡A) = 17sin(70∘)/b
sin(∡A) = 17sin(48∘)/c
Setting the two expressions equal to each other, we get:
17sin(70∘)/b = 17sin(48∘)/c
Solving for c, we get:
c = (b*sin(48∘)*17)/(sin(70∘))
To solve for b, we can use the Law of Cosines, which states that for any triangle △ABC,
c^2 = a^2 + b^2 - 2ab*cos(∡C)
Substituting the given values and the value we found for c, we get:
((bsin(48∘)17)/(sin(70∘)))^2 = 17^2 + b^2 - 217b*cos(48∘)
Simplifying and solving for b, we get:
b ≈ 11.28
Substituting this value into the equation we found for c, we get:
c ≈ 14.08
Therefore, b ≈ 11.28 and c ≈ 14.08.
I hope this answer helps you!
BTW is this Khan Academy/Albert.io?
please help! Naira paddled 4.5 km with the current in the same amount of time as it took her to paddle 3 km against the current. Naira paddled at an average rate of 5 kmh relative to the water each way. Assume the speed of the current was constant.
What was the speed of the current?
This was an exceptionally dry year for portions of the southwestern United States. Monthly precipitation in Phoenix, Arizona, was recorded in the table and is modeled by y = –0.04088x2 + 0.4485x + 1.862.
In what month did Phoenix receive the lowest amount of precipitation?
Month (x) Precipitation
January 2.27 inches
February ?
March ?
April ?
May ?
June ?
July ?
August ?
September 2.59 inches
October ?
November ?
December ?
Sketch a graph or fill in the table to answer the question.
A) January
B) February
C) November
D) December
Answer:
D
Step-by-step explanation:
y = -0.04088x^2 + 0.4485x + 1.862
y is the amount of precipitation,
x is the month (1 for January, 2 for February, etc.)
The amount of precipitation from Jan to Dec are listed below
(generated with R language, a handy software)
2.26962 2.59548 2.83958 3.00192 3.08250 3.08132 2.99838 2.83368 2.58722 2.25900 1.84902 1.35728
The month with lowest precipitation is December
Answer:
D) December
Step-by-step explanation:
The given equation to model the monthly precipitation in Phoenix, Arizona is:
[tex]y = -0.04088x^2 + 0.4485x + 1.862[/tex]
where:
y is the monthly precipitation (in inches).x is the number of the month (January = 1).To determine the month in which Phoenix received the lowest amount of precipitation, fill in the table by inputting each value of x into the equation. Round the value of y to 2 decimal places.
[tex]\begin{array}{|l|c|c|}\cline{1-3}&x&y\\\cline{1-3}\sf January &1&2.27\\\cline{1-3}\sf February &2&2.60\\\cline{1-3}\sf March &3&2.84\\\cline{1-3}\sf April &4&3.00\\\cline{1-3}\sf May &5&3.08\\\cline{1-3}\sf June &6&3.08\\\cline{1-3}\sf July &7&3.00\\\cline{1-3}\sf August &8&2.83\\\cline{1-3}\sf September &9&2.59\\\cline{1-3}\sf October & 0&2.26\\\cline{1-3}\sf November &11&1.85\\\cline{1-3}\sf December &12&1.36\\\cline{1-3}\end{array}[/tex]
Reading from the table, the month in which Phoenix received the lowest amount of precipitation was December, when only 1.36 inches of precipitation was recorded.
A golfer hits an errant tee shot that lands in the rough. A marker in the center of the fairway is 150 yards from the center of the green. While standing on the marker and facing the green, the golfer turns 105 degrees toward his ball. He then paces off 50 yards to his ball. How far is the ball from the center of the green?
The ball is about ___ yards away from the center of the green.
The ball is about 170 yards away from the center of the green.
It is required to find the third side of the triangle.
From the figure,
Distance from the marker to the center of the green, a = 150,
Distance from the marker to the ball, b = 50 and
The angle between sides a and b, C = 105°
According to the Law of Cosines,
[tex]c^2 = a^2+b^2 - 2abcosC[/tex]
= [tex](150)^2 + (50)^2-2(150)(50)cos(105) \textdegree[/tex]
= 22500 + 2500 - 15000(-0.258)
= 25000 + 3882.28567
= 28882.28567
[tex]c^{2}[/tex] = 28882.28567
c = [tex]\sqrt{28882.28567}[/tex] = 169.94789 ≈ 170 yards
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In square ABCD, P is on BC such that BP = 4 and PC = 4, and Q is on CD such that BQ = 4 and QC = 4. Find sin angle PAQ.
Sin angle PAQ ≈ 0.6.
What is sin ratio?The sine ratio in trigonometry is the ratio of the hypotenuse's length to the length of the side that faces an angle in a right triangle. Theta is the angle opposed to the side whose length is the "opposite" side, hence sin(theta) = opposite/hypotenuse. The symbol for it is sin(theta) or just sin(theta). One of the six trigonometric ratios, the sine ratio is frequently employed to resolve issues concerning right triangles and angles.
What is a square?A square is a regular quadrilateral in which all four sides are of equal length and all four angles are right angles (90 degrees). It can be thought of as a special type of rectangle where the length and width are equal. The area of a square is calculated by multiplying the length of one side by itself, or by squaring the length of one side. The perimeter of a square is calculated by adding the length of all four sides together. Squares have many practical applications, including in construction, geometry, and design.
According to the question
The Pythagorean theorem can be used to determine the length of side AB first:
(BC - PC) = AB2 + BP22 AB 2 equals 4 + (8 - 4) 2 AB 2 equals 16 + 16 AB = 4
In a similar manner, we may determine side AD's length:
BQ² + (CD - QC) + AD² AD² = 4² + (8 - 4)² AD² = 16 + 16
AD = 4√2
The Pythagorean theorem can now be used to determine the diagonal AC's length:
AC2 equals AB2 + BC2 AC2 equals (42) + 82 AC2 equals 32 + 64 AC2 equals 4/6
The Pythagorean theorem can also be used to determine the length of the diagonal BD:
BD2 equals AD2 plus BC2 BD2 equals (42) + 82 BD2 equals 32 + 64
BD = 4√6
We know that APQC is a kite with diagonals AC and BD since a square's diagonals are perpendicular to one another and cut each other in half. As a result, we may calculate that PQ is half as long as diagonal AC:
PQ = AC/2 = (4√6)/2 = 2√6
We may determine the cosine of angle PAQ using the law of cosines:
cos(PAQ) equals (2 * AP * AQ)/(AP * AQ)
Since these numbers can be substituted in because AP = AQ = AB = 42:
cos(PAQ) is equal to (2(32) - (2(6))/2 * 32.
cos(PAQ) equals (64-24)/(64).
sin(PAQ) = 5/8
In order to determine the sine of angle PAQ, we can utilise the Pythagorean identity:
(1 - cos(PAQ)) = sin(PAQ)
(1 - (5/8)) = sin(PAQ)
sin(PAQ) is 0.6.
Sin angle PAQ thus equals 0.6.
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Thomas Van Tonder has been given R5 000 for his sixteenth birthday. Rather than spending it, he has decided to invest it so that he can put down a deposit of R10 000 on a car on his eighteenth birthday. What compound interest rate does he need to achieve this growth? Comment on your answer (10 Points).
Thomas needs to achieve a compound interest rate of approximately 41.4% per year in order to turn R5,000 into R10,000 in two years.
What are two types of interest ?Simple interest and compound interest are the two primary types of interest.
Simple interest does not account for any accumulated interest from prior periods and is computed just on the principal amount of a loan or investment. It can be computed using the following method and is often expressed as a percentage of the principal:
I = P * r * t
If P is the principal, r is the interest rate, and t is the time period, and I is the simple interest.
Compound interest, on the other hand, adds the principle amount to the accrued interest from earlier periods. This indicates that each period's interest is computed using a higher balance than the previous period's balance, resulting in a higher interest rate.
What is compound interest ?Compound interest is a way to calculate interest that accounts for both the original principal and the interest that has accrued over the course of prior periods. To put it another way, it is the interest that is generated on both the initial investment and the interest that has been accrued over time on that investment.
For instance, if you deposited $1,000 in a savings account with a 5% annual interest rate, you would have received $50 in interest after the first year (5% of $1,000). This $50 would be added to your principal debt using compound interest, resulting in interest being paid on both the initial $1,000 loan and the additional $50 in interest that was accrued the prior year.
Your investment may rise significantly as a result over time.
Compound interest is calculated using the following formula:
A = P(1 + r/n)nt
where A represents the overall sum, P represents the original principal, r represents the yearly interest rate, n represents the number of times the interest is compounded annually, and t represents the passage of time in years.
According to question,
Simple interest and compound interest are the two primary types of interest.
Simple interest does not account for any accumulated interest from prior periods and is computed just on the principal amount of a loan or investment. It can be computed using the following method and is often expressed as a percentage of the principal:
I = P * r * t
If P is the principal, r is the interest rate, and t is the time period, and I is the simple interest.
Compound interest, on the other hand, adds the principle amount to the accrued interest from earlier periods. This indicates that each period's interest is computed using a higher balance than the previous period's balance, resulting in a higher interest rate.
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Tamika has $800 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $482.62.
She buys 3 bicycle reflectors for $10.84 each and a pair of bike gloves for $24.49.
She plans to spend some or all of the money she has left to buy new biking outfits for $52.93 each.
Which inequality can be used to determine o, the maximum number of outfits Tamika can purchase while staying within her budget?
The inequality that can be used to determine x, the number of outfits Tamika can purchase is; 539.63+ 52.93x ≤ 800
The given parameters are:
Budget = $800
New bicycle = $482.62
3 bicycle reflectors = $10.84 each
Pair of a bike gloves = $24.49.
New biking outfits = $52.93each.
Let the number of new biking outfits be x So, we have;
New bicycle + 3 . price of bicycle reflectors + Pair of a bike gloves + New biking outfits <= Budget
This gives;
482.62 + 3( 10.84) + 24.49+ 52.93x ≤ 800
This gives;
539.63+ 52.93x ≤ 800
Solve the inequality;
52.93x ≤ 260.37
Divide by 52.93
x ≤ 4.91
Hence, the inequality is 539.63+ 52.93x ≤ 800
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What is the inverse of the given relation?
y=3x+12
[tex]y=\frac{1}{3}x-4[/tex].
Step-by-step explanation:1. Write the expression.[tex]y=3x+12[/tex]
2. Swap places between "y" and "x".[tex]x=3y+12[/tex]
• Now we start solving for "y".3. Subtract 12 from both sides of the equation.[tex]x-12=3y+12-12\\ \\x-12=3y[/tex]
4. Divide both sides of the equation by "3".[tex]\frac{x-12}{3} =\frac{3y}{3} \\ \\\frac{x-12}{3} =y[/tex]
5. Reorganize the expression.[tex]y=\frac{x-12}{3}[/tex]
6. Re-express the fraction and simplify.[tex]y=\frac{x}{3}-\frac{12}{3} \\\\y=\frac{1}{3}x-4[/tex]
Check the attached image to see both of the functions in the cartesian plane and how the domains and ranges are interchanged between each function.
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11) Write the formula for the
sequence.
11) 3, 23, 123, 623, 3123, ...
A) a = n²
4
C) an
O A
О в
О с
O D
=
n
* 1 point
B) a = 5" - 2
n
D) a =
n
2n + 1
n
The value of the formula for the sequence is,
⇒ a (n) = 5ⁿ - 2
We have to given that;
The sequence is,
⇒ 3, 23, 123, 623, 3123, ...
Now, We can formulate;
⇒ 3 = 5 - 2
⇒ 23 = 5² - 2
⇒ 123 = 5³ - 2
⇒ 623 = 5⁴ - 2
Thus, The value of the formula for the sequence is,
⇒ a (n) = 5ⁿ - 2
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A nutritionist is interested in testing whether tha mean sodium content of the 300-gram boxes of organic cornflakes differs from 130 milligram. From a sample of 36 boxes, the mean sodium content was 130.3 mg with a standard deviation of 0.75 mg.
Find the value of the test statistic,
. Round your answer to one decimal place.
Find the corresponding P-value,
. Round your answer to three decimal places.
a) The value of the test statistic is t = 0.4
b) The p value of the nutritionist is = 0.690
Given data ,
The sample mean (μ) : 130.3 mg
The sample standard deviation (s): 0.75 mg
The sample size (n): 36
For null hypothesis : Mean sodium content = 130 mg
Let the test statistic value be t , where
t = (x- μ) / (s / √(n))
where μ is the sample mean, μ is the hypothesized population mean (in this case, 130 mg), s is the sample standard deviation, and n is the sample size.
Plugging in the given values, we get:
t = (130.3 - 130) / (0.75 / √(36))
t ≈ 0.4
b)
Since the sample size is large (n = 36), we can assume that the sampling distribution of the sample mean is approximately normally distributed
Therefore, the P value is associated with the calculated t-value
The P-value for a t-value of 0.4 (or -0.4) is 0.690
Hence , the corresponding P value is 0.690
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The equation of line Q, shown below, can be
written in the form y = mx + c.
What are the values of m and c?
Give each of your answers as an integer or
as a fraction in its simplest form.
Y
61
5-
4
3
-2-
1
-5 -4 -3 -2 -10
-1
-2
-3-
-44
Line Q
1 2 3 4 5
X
Answer: c=3 m=5
Step-by-step explanation:
c is where it hits the y-axis
c=-3
m=slope, count rise/run = 5/1 = 5 pick points that hit the grid squarely
The equation of the line, represented in the graph is y = 5x +15.
And the value of m is 5 and the value of c is 15.
Use the concept of the equation of line defined as:
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.
And the equation the line passing through (x₁ , y₁) and (x₂, y₂):
y - y₁ = m(x - x₁)
Where the slope of the line,
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
In the figure, it is shown that,
The line is passing through the points:
(0, -3) and (1, 2)
Then the slope of this line is,
[tex]m = \dfrac{2 +3 }{1-0}\\\\m = 5[/tex]
Now the equation of line be,
y - 0 = 5(x + 3)
y = 5x + 15 which is of the form y = mx + c
Now after comparing we get,
m = 5 and c = 15
Hence,
The equation of the line is y = 5x + 15:
m = 5 and c = 15
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