The amount of Suzy's instalment every month if it is agreed to repay equal amount monthly is $152
What is the amount of each instalment?Simple interest = principal × rate × time
= 4500 × 0.072 × 3
= $972
Total amount to repay = $4500 + $972
= $5472
Repayment time = 3 years
Suzy will repay every month
3 years= 12 months × 3
= 36 months
Since,
the repayment is equal every month
Amount of instalment every month= $5472 / 36
= $152
Therefore, Suzy will repay $152 each month instalmentally.
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Determine two unique values of 0 in the interval [0, 2pi)such that sin 0 = 1/2. ( picture included)
The two unique values of sin theta in radians are
π/67π/6When is Sin of angle = 1/2The sine function has a range of [-1, 1], so there are multiple angles that correspond to a sine of 1/2.
The most commonly used values are π/6 (30 degrees) and 7π/6 (150 degrees), which are in the first quadrant and second quadrant and have a positive sine value of 1/2.
It's worth noting that there are an infinite number of angles that correspond to a given sine value, since the sine function has period 2π. These angles are related to the angles by adding or subtracting multiples of 2π.
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an urn contains 3 red and 7 black balls. players a and b withdraw balls from the urn consecutively until a read ball is selected. find the probability that a selects the red ball
Players A and B withdraw balls from the urn consecutively until a read ball is selected, the probability that player A selects the red ball is approximately 0.408.
To find the probability that player A selects the red ball, we can use the law of total probability and consider all the possible ways the game could end. A selects the red ball on the first draw. The probability of this is simply the proportion of red balls in the urn, which is 3/10.
A selects a black ball on the first draw, followed by B selecting a black ball on their turn, and so on, until A finally selects the red ball. The probability of this is:
(7/10) * (6/9) * (5/8) * ... * (1/4) * (3/7)
Notice that the probability of selecting a black ball decreases by one after each turn, since the total number of balls in the urn decreases by one and the number of black balls decreases by one.
The probability of selecting the red ball on the last turn (after all the black balls have been selected) is 3/3 = 1. We multiply all these probabilities together to get the total probability of this sequence of events.
A selects a black ball on the first draw, followed by B selecting a black ball on their turn, and so on, until B finally selects the red ball. The probability of this is:
(7/10) * (6/9) * (5/8) * ... * (2/4) * (3/6)
Notice that the probability of selecting a black ball decreases by one after each turn, just like in the previous case. However, the probability of B selecting the red ball on their turn is now 3/6, since there are only six balls left in the urn at this point. We multiply all these probabilities together to get the total probability of this sequence of events.
Adding up these three probabilities, we get:
3/10 + (7/10) * (6/9) * (5/8) * ... * (1/4) * (3/7) + (7/10) * (6/9) * (5/8) * ... * (2/4) * (3/6) ≈ 0.408
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Kyle and Tina both think they figured out how to get Triangle ABC to transform to Triangle A'B'C', however they both did it in different ways. Kyle used a sequence of transformations, but Tina was able to do it in just one transformation. Assuming both students are correct, explain what each of them did in order to complete the problem.
Kyle: Rotation about the origin, then reflection across the x axis
Tina: Reflection over the line y = x
What is reflection in geometry?In geometry, reflection refers to a transformation that involves flipping a shape or object over a line, often called the "line of reflection".
This transformation preserves the size and shape of the original object, but changes its orientation by reversing the positions of all its points across the line of reflection.
Considering the image, rotation about the origin, then reflection across the x axis when compare with Reflection over the line y = x. will yield similar result.
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13.
14.
15.
Classify <1
Classify <2
Classify
Answer:
< 1 is acute (less than 90⁰)
<2 is acute
<BOA is obtuse (greater than 90⁰)
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Betty is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $51 for the meal, plus $2 per pound for the lobster she picks. At the second restaurant, Betty would pay $3 per pound for the lobster, in addition to $15 for the meal. Betty realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Betty pay for her dinner? What is the weight?
Dinner would cost $ __ at either restaurant if Betty's lobster weighed __ pounds.
Dinner would cost $123 at either restaurant if Betty's lobster weighed 36 pounds.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.In the context of this problem, the slope and the intercept are defined as follows:
Slope: cost of each pound of lobster.Intercept: cost of the meal.Hence the functions for each restaurant are given as follows:
y1(x) = 51 + 2x.y2(x) = 15 + 3x.The costs are the same when:
y1(x) = y2(x)
51 + 2x = 15 + 3x
x = 36.
The cost is of:
y = 15 + 3 x 36
y = $123.
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Evaluate the expression when x= -7 and y=2 .
X - 2y
Answer:-3
Step-by-step explanation: -7 -4
2. In rectangle HOME, HM and OE are diagonals that intersect at P.
Write at least 6 unique statements about HOME and justify your statements with definitions, postulates or theorems
1. It should be noted that HD = EM and HE = OM. In this case, the opposite sides are equal in the rectangle.
2. It should be noted that EHO = HOM = OME = MEH = 90°. In this case, all angles are equal to 90°.
What are postulate?Postulates are assertions that, in the absence of evidence, are taken to be true. Postulates have two functions: they define undefined terms and act as a foundation for the proof of subsequent propositions.
A line segment is determined by two points. A line segment may be extended along a line indefinitely. The other information is attached.
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Find 6x3/5. Use model at the right to find the product
The multiplication of the given fraction 6 × 3/5 is 15 or 3 3/5
How to multiply fraction?Fraction refers to numbers which comprises of a numerator and a denominator. A numerator is the upper or top value of a fraction while a denominator is the lower or bottom value of a fraction.
6 × 3/5
multiply the numerator and denominator separately
= (6 × 3) / (1 × 5)
= 18/5
= 3 3/5
Therefore, 3 3/5 is the solution to the multiplication of the fraction.
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Simplify the algebraic expression by combining like terms. Explain your answer or show your work.
2x + 5y + 6x - 5x+3y
Answer: 3x + 8y
Step-by-step explanation:
Combining like terms is simply adding all the terms which are similar.
2x+6x-5x= 3x
5y+3y= 8y
Hope it helps!
help me get this right i really have to pass
Answer:
yes
Step-by-step explanation:
A composite figure is shown. A five-sided figure with two parallel sides. The shorter one is 16 feet. The height of the figure is 22 feet. The portion from the vertex to the perpendicular height is 8 feet. The portion from a point to a vertical line created by two vertices is 4 feet. Which of the following represents the total area of the figure?
44 ft2
400 ft2
440 ft2
484 ft2
The solution is 440 ft² because the overall size of the image is 528 sq ft, which in itself is closest approaching 440 square feet.
What does parallel shape mean?Parallel forms are defined as having at least two even more parallel lines. If two lines never cross, they are considered to be parallel. There are different parallel shapes, however any parallel sides require an equitable distribution of sides in the shape.
Sum of the measurements of the two main sides divided by height equals the area of a trapezoid.
Let's refer to the longer parallel side's length as "L." The figure's height is 22 feet, while the shorter parallel side's length is 16 feet.
Area = (L + 16) / 2 * 22
We also knows that the distance between a point and the vertical line formed by two studs is 4 feet and the distance between a vertex and the opposing height is 8 feet. The Pythagorean theorem may be used to determine the length of the greater parallel side, L, since these two lengths create a right triangle.
L² = (8 + 4)² = 64
L = 8
We can now calculate the overall area using the formula for a trapezoid's area.
Area = (L + 16) / 2 * 22 = (8 + 16) / 2 * 22 = 24 * 22 = 528
The solution is 440 ft² because the overall size of the figures is 528 sq ft, that is closest towards 440 sq ft.
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which of the following statements is more accurate? question 42 options: observations are only as good as the hypotheses on which they are based. hypotheses are only as good as the observations on which they are based.
The more accurate statement is that hypotheses are only as good as the observations on which they are based.
A hypothesis is a tested assertion regarding the relationship between two or more variables or a suggested explanation for some observable occurrence in a scientific setting.
As a result, hypothesis are only as good as the observations upon which they are built.
For instance, if we stay up late, we will be fatigued the next day. Turning off your phone allows it to charge more quickly. All of them are hypotheses since they are based on observations and are only valid for as long as the observations stay true.
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Is the answer 126.26? Area of compound figures?
Answer:
Step-by-step explanation:
Jamie burned 480 calories in an exercise
class on Monday. She took a different class
the next day and burned 7/8 as many
calories as she did on Monday. How many
calories did she burn on Tuesday?
Answer: Jamie burned 420 calories on Tuesday
Step-by-step explanation:
Cross method is best for this question
Let x = calories burnt on tuesday
480 is 100%
x is 7/8 (or 87.5%)
∴
(480*87.5%) ÷ 100%
= 420 ÷ 100%
= 420
Therefore, Jamie burned 420 calories on Tuesday
12.5 × 1.989 pls help me
The length of a marathon is 138,435 ft. Each stride, or step, by a particular runner is 3 ft long. Does the number of strides the runner takes fit evenly into the length of the race? Explain.
Answer:
Yes
Step-by-step explanation:
length 138,435 ÷ 3 ft stride = 46,145 equally
Transcribed image text: (1 point) Give an example of a matrix A and a vector b such that the solution set of Ax = b is a line in Rº that does not contain the origin. A= b
Matrix A is: A = [1 2 3] and Matrix B is: B = [1]
[2 4 6] [2]
[1 1 1] [3]
An example of a 3x3 matrix A and a 3x1 matrix B such that the solution set of Ax = b is a line in R³ that does not contain the origin:
A = [1 2 3]
[2 4 6]
[1 1 1]
B = [1]
[2]
[3]
To check that the solution set of Ax = b is a line in R³, we can solve for x in terms of a parameter t:
Ax = b
[1 2 3] [x1] = [1]
[2 4 6] [x2] [2]
[1 1 1] [x3] [3]
Ax = b
x1 + 2x2 + 3x3 = 1
2x1 + 4x2 + 6x3 = 2
x1 + x2 + x3 = 3
Dividing the second equation by 2 and subtracting it from the first equation, we get:
-x1 - x2 = -1
Solving for x2 in terms of x1 and x3, we get:
x2 = -x1 + 1 - (3/2)x3
Solving for x3 in terms of a parameter t, we get:
x3 = t
Then, x1 can be expressed in terms of t as:
x1 = -t + 1
Therefore, the solution set of Ax = b is:
x = [-t + 1]
[-t + 1 - (3/2)t]
[t]
which is a line passing through the point (1, 1/2, 0) with a direction vector [-1, -3/2, 1].
A × [0; 0; 0] = [0; 0; 0]
Therefore, the origin is not on the line of solutions.
So, Matrix A is:
A = [1 2 3]
[2 4 6]
[1 1 1]
and Matrix B is:
B = [1]
[2]
[3]
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Some of the world's smallest horses
include: Thumbelina, who stands
17 inches tall; Black Beauty, who stands
18 inches tall; and Einstein, who stands
14 inches tall.
a. How much taller is Black Beauty
than Thumbelina?
Black Beauty stands one inch taller than Thumbelina, measuring 18 inches in height compared to Thumbelina's 17-inch stature.
Black Beauty is 1 inch taller than Thumbelina.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Thumbelina, who stands 17 inches tall
Black Beauty, who stands 18 inches tall.
Einstein, who stands 14 inches tall.
We have to find how tall is Black Beauty than Thumbelina.
To find out, we can subtract Thumbelina's height from Black Beauty's height:
Black Beauty's height - Thumbelina's height
= 18 inches - 17 inches = 1 inch
Therefore, Black Beauty is 1 inch taller than Thumbelina.
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Rewrite in simplest radical form
The simplest radical form is x⁵.
What is radical form?Radical form is the expression that involves radical signs such as square root, cube root, etc instead of using exponents to describe the same entity.
The given radical form is [tex]\frac{x^{\frac{5}{6} }}{x^{\frac{1}{6} }}[/tex].
The radical and root of a number are the same thing.
Simplifying a radical eliminates the square roots, cube roots, fourth roots, etc.
In the given expression, 1/6 is the 6th root, in both numerator and denominator cancel out 6th root x.
That is, [tex]\frac{x^{\frac{5}{6} }}{x^{\frac{1}{6} }}[/tex] =x⁵ ([tex]x^{\frac{1}{6} }[/tex] in the denominator is gets cancelled with [tex]x^{\frac{1}{6} }[/tex] in the numerator)
Therefore, the simplest radical form is x⁵.
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4 women and 5 men are eligible to be in a committee of three. find the probability that the committee has exactly two woman.
The probability that the committee has exactly two woman is 0.1758.
Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.The ratio of the favorable outcomes to the all possible outcomes.
Given that, 4 women and 5 men are eligible to serve on a committee.
A committee of 3 is randomly selected.
Choosing 2 women out of 3 women is
³[tex]C_{2}[/tex]
= 3
Choosing 1 men out of 5 men is
5C1
= 5
Total number of eligible person is = (4+5)=9
Choosing 3 member out of 9 member is
9C3
=84
The required probability is
=3*5/84
0.1785
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HELP PLEAES clarence made a scale drawing of a classroom. the scale in the drawing is 2 inches represenst 9 feet the actual length of the classroom is 36 feet what is the length of the classroom on the scale drawing
The length of the rectangular classroom will be 8 inches on the scale drawing.
What is a rectangle defined as?
Rectangles are four-sided polygons having internal angles of 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from the square in that its opposite sides are of equal length.
If one side of a rectangle is 20 cm long, the other side must be 20 cm long as well.
Two diagonals cross form a rectangle. Both diagonals are the same length.
P = 2 (Length + Width) defines the perimeter.
Rectangle Area=Length*Breadth
Now,
As total length of room =36 feet
and 9 feet = 2 inch on drawing scale
then length of classroom on drawing scale is = 36/9*2
=8 inch
Hence,
The length of the rectangular classroom will be 8 inches on the scale drawing.
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Find the perimeter and area of the rectangle below
Perimeter and area of the rectangle would be 2(10x² + 7xy²) and 70x²y².
What is Perimeter and area?
The perimeter of a shape is the distance around its outside. The space inside a shape is measured by area.
Given the length l = 10x² and width w = 7xy² of a rectangle, the perimeter P and area A can be calculated as follows:
1) Perimeter P:
P = 2(l + w)
= 2(10x² + 7xy²)
2)Area A:
A = l * w
= 10x² * 7xy²
= 70x²y²
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christian has a collection of 18 shark teeth. he identified them as 6 tiger shark teeth, 8 sand shark teeth, and the rest as bull shark teeth, what does the ration 6:8 represent in this situation
Answer:
Check below
Step-by-step explanation:
Number of tiger shark teeth = 6
Number of sand shark teeth = 8
Number of tiger shark teeth : Number of sand shark teeth
6 : 8
∴ 6 : 8 ratio representation
Answer:
6:8
Step-by-step explanation:
Consider the function f(x) = (x - 3)².
a. How could you restrict the domain of f(x) so that its inverse will be a function?
b. Graph f(x) with its restricted domain and then graph its inverse on the same set of axes.
c. Find the equation of the inverse of f(x) with its restricted domain.
The inverse of f(x) has no restriction on the domain.
The graph of the inverse function is given below.
The inverse equation is [tex]f^{-1}[/tex](x) = x² + 3.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = (x - 3)²
The inverse of f(x).
Step 1:
Make f(x) = y
y = (x - 3)²
Step 2:
Interchange x and y
x = (y - 3)²
Step 3:
Solve for y.
square root on both sides.
x² = y - 3
y = x² + 3
So,
[tex]f^{-1}[/tex](x) = x² + 3.
a)
[tex]f^{-1}[/tex](x) = x² + 3
we see that for any values of x, [tex]f^{-1}[/tex](x) is a function.
So,
There is no restriction on the domain.
b)
The graph is given below.
c)
The inverse equation is
[tex]f^{-1}[/tex](x) = x² + 3.
Thus,
The inverse of f(x) has no restriction on the domain.
The inverse equation is [tex]f^{-1}[/tex](x) = x² + 3.
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I need help with number 8
[tex](3x^2+5x+4)+(6x+1)~~ = ~~3x^2+11x+5 ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ (3x^5+15x^3+4)+(-3x^5+2x^2-8)\stackrel{ \textit{not on all cases} }{~~ = ~~15x^3+2x^2-4} ~~ \bigotimes[/tex]
Is Rainbow Six Siege Good
Answer:
yes beacuse he have nice grapics and u can play with your friends.
Step-by-step explanation:
Answer: Yes it is very good i recommend getting it, but it takes a ton of time to get use to it.
Step-by-step explanation:
if the sum of two consecutive even numbers is 42 find the number
Answer:
20 and 22
Step-by-step explanation:
if the sum of two consecutive even numbers is 42 find the number
42 - 2 = 40 remove the difference (2)
40 : 2 = 20 find the smallest number
20 + 2 = 22 find the largest number
------------------------------------
(20 + 22 = 42)
Bronze is a mixture of copper and tin. The copper and tin are mixed in the ratio 9:1 by weight.
a. How much copper is there in a bronze brooch weighing 360 g?
b. Another bronze brooch contains 670.5g of copper.
How much does it weigh altogether?
a. The amount of copper in a bronze of 360g is 324g
b. The mass of bronze with 670.5g of copper is 745g
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
The ratio of copper to Tin is 9:1. The total ratio is 10
a.therefore the amount of copper = 9/10 × 360
= 324g
b. The mass of copper = 670.5g
therefore the mass of the bronze =
= 9/10× y = 670.5
9y = 670.5 × 10
9y = 6705
y = 6705/9
y = 745g
therefore the total mass of the bronze is 745g
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Casey Na's average workweek during the first quarter of the year (13 weeks) was 43 hours. As part of his company's perfect attendance program, he earned a bonus of $975. Determine the extra overtime pay due Na for the first quarter
Casey Na is due an extra overtime pay of $1,170 for the first quarter as part of his company's perfect attendance program.
What is overtime pay?
Overtime pay is the additional compensation paid to an employee for any hours worked in excess of the standard working hours or beyond the standard workweek. The rate of overtime pay is usually higher than the regular rate of pay for an employee's normal working hours.
To determine the extra overtime pay due to Casey Na for the first quarter, we need to know his regular pay rate and the number of hours he worked each week.
Let's assume that Casey Na's regular pay rate is $20 per hour and that he worked 40 hours each week during the first quarter. This means that he worked 3 hours of overtime each week, for a total of 39 hours at his regular rate and 3 hours at his overtime rate.
To calculate his overtime pay for the first quarter, we can use the following formula:
Overtime pay = overtime hours x overtime rate
Since Casey Na worked 3 hours of overtime each week for 13 weeks, his total overtime hours for the first quarter were:
Total overtime hours = 3 hours/week x 13 weeks = 39 hours
His overtime rate is 1.5 times his regular rate, or $20 x 1.5 = $30 per hour.
Therefore, his overtime pay for the first quarter was:
Overtime pay = 39 hours x $30/hour = $1,170
Since he also earned a bonus of $975 for perfect attendance, his total extra pay for the first quarter was:
Extra pay = Overtime pay + Bonus = $1,170 + $975 = $2,145
Therefore, Casey Na is due an extra overtime pay of $1,170 for the first quarter as part of his company's perfect attendance program.
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© 31. Think About a Plan The Millenium Wheel, also known as the London Eye, contains 32 observation cars. Determine the angle of rotation that will bring Car 3 to the position of Car 18. • How do you find the angle of rotation that a car travels when it moves one position counterclockwise?
• How many positions does Car 3?
The angle of rotation that will bring Car 3 to the position of Car 18 is 11.25 degrees. The angle of rotation that a car travels when it moves one position counterclockwise is 168.75 degrees. Car 3 needs to move 15 positions counterclockwise to reach Car 18.
a. We have to determine the angle of rotation that will bring Car 3 to the position of Car 18 on the London Eye, so we will first calculate the number of positions that Car 3 needs to move counterclockwise to reach Car 18.
We know that there are 32 observation cars on the London Eye, so the distance between two adjacent cars will be 360/32 = 11.25 degrees.
b. To find the angle of rotation that a car travels when it moves one position counterclockwise, we will divide the full rotation of the London Eye by the number of observation cars (i.e. 32).
360/32 = 11.25 degrees
Next, to determine the angle of rotation that would bring Car 3 to the position of Car 18, we will multiply the number of positions that Car 3 needs to move counterclockwise and the angle of rotation for each position as follows -
15 x 11.25 = 168.75 degrees
Therefore, the angle of rotation that a car travels when it moves one position counterclockwise is 168.75 degrees.
c. To find the number of positions that Car 3 needs to move counterclockwise to reach Car 18, we will subtract the position number of Car 18 from that of Car 3 and then take the absolute value, as it is a cyclical rotation.
|18 - 3| = 15
Hence, Car 3 needs to move 15 positions counterclockwise to reach Car 18.
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