Answer:
Step-by-step explanation:
8:2 doubled is 16:4
There is a number cube with faces numbered 1 to 6. There is also a coin with one side marked as heads and the other tails.
As a trial of an experiment, the number cube was rolled and the coin flipped. The number (1 to 6) from the roll and the side (H for heads and T for talls) of
the coin from the flip were recorded.
Here is a summary of the data from 1050 trials.
Outcome 1H 2H 3H 4H 5H 6H 1T 2T 3T 4T 5T 6T
Number of trials 79 99 89 88 89 96 92 86 97 79 77 79
Answer each part.
(a) Assuming the cube and the coin are fair, find the theoretical probability of this event: both
rolling a 1 ora 6 and flipping tails, in a single trial. Round your answer to the nearest
thousandth.
0
(b) Use the data to find the experimental probability of this event: both rolling a 1 or a 6 and
nipping talls, in a single trial. Round your answer to the nearest thousandth.
0
(c) Choose the statement that is true.
With a large number of trials, there might be a difference between the experimental
and theoretical probabilities, but the difference should be small.
With a large number of trials, there must be a large difference between the
experimental and theoretical probabilities.
With a large number of trials, there must be no difference between the experimental
and theoretical probabilities.
5
3ab−1=2ab−3 what is the value of ab
Answer:
ab = -2
Step-by-step explanation:
3ab - 1 = 2ab - 3
(minus 2ab on both sides of the equation)
ab - 1 = -3
(plus one of both sides of the equation)
ab = -2
Rectangle MPAT has vertices M(1, 2), P(1, 3), A(3, 3), and T(3, 2). Rectangle MPAT was translated 1 unit right and 2 units up to produce rectangle M'P'A'T Which coordinates describe the vertices of the image? O M'(1, 4), P'(1, 5), A'(3, 5), and T"(3, 4) O M'(2, 2), P'(2, 3), A'(4, 3), and T'(4, 2) O M'(2, 4), P' (2, 5), A'(4, 5), and T'(4,4) O M'(3, 3), P'(3, 4), A'(5, 4), and T'(5, 5)
The coordinate set that describes the image of rectangle MPAT after the translation of 1 unit right and 2 units up is:
M'(2, 4), P'(2, 5), A'(4, 5), and T'(4, 4).
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for the ordered pairs of the vertices of a figure are defined as follows:
Translation left a units: (x, y) -> (x - a, y).Translation right a units: (x, y) -> (x + a, y).Translation up a units: (x,y) -> (x, y + a).Translation down a units: (x,y) -> (x, y - a).The vertices of the original rectangle are given as follows:
M(1, 2), P(1, 3), A(3, 3), and T(3, 2).
The translation is given as follows:
1 unit right.2 units up.Hence the equation is:
(x, y) -> (x + 1, y + 2).
Then the coordinates of the vertices are given as follows:
M'(2, 4), P'(2, 5), A'(4, 5), and T'(4, 4).
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Match each division problem on the left to its quotient on the right.
When the denominator is zero, the divisor is undefined.
Define the term division?In mathematics, division is the process of dividing a quantity into equal pieces or groups. Division reverses the effects of multiplication because it is the inverse operation of multiplication. The amount being divided is referred to as the dividend in division, and the number by which it is being divided is referred to as the divisor. The quotient is the outcome of a division operation.
Explanation:
Left side Right side
0 ÷ 70 = 0 ⇒ Zero
862 / 0 ⇒ Undefined
97 ÷ 0 ⇒ Undefined
[tex]\frac{0}{764}[/tex] = 0 ⇒ Zero
When the denominator is zero, the divisor is undefined.
When the molecule is zero, the divisor is zeros.
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Explain two factors that could make the public resort to violent ways of protesting
There are a variety of factors that can lead to violent protests, but two significant factors are perceived injustice and lack of political representation.
Perceived injustice: When people feel that they have been wronged, marginalized, or oppressed by a system or institution, they may resort to violent protest as a way to express their anger and frustration. This is particularly true when people believe that peaceful means of protest have been ignored or have failed to bring about change. For example, if a community feels that they are being unfairly treated by the police, and previous attempts to seek redress through peaceful protests or other channels have failed, they may turn to violent protest as a last resort.
Lack of political representation: When people feel that their voices are not being heard, they may resort to violent protests as a way to force attention to their concerns. This can happen when marginalized groups feel excluded from the political process, or when they feel that their interests are being ignored by those in power. If people feel that their concerns are not being taken seriously, they may turn to violent protest as a way to make their voices heard.
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would appreciate if someone could help
Answer:
X AXIS WILL BE ON 4,2 AND Y AXIS WILL BE 4,2 ON BEHALF OF BOTH ANGLES HAVING QUADILATERAL AND THEN APPLY THEOREMS FOR THE EASY SOLUTIONS..
Help with pre calc question
Therefore , the solution of the given problem of angles comes out to be k can be any number, so θ = 0 + k180 or θ = 180 + k180
An angle meaning is what?A tilt is a form in Euclidean geometry made up of two lines, or conical faces, that divide at the structure's centre and apex. At their junctions, two rays may combine to form an angle. Angle is another outcome of two entities interacting. Dihedral shapes best describe them. A two-dimensional curve can be created by arranging two line beams in various configurations at their ends. The term "angle" was first used in the Latin term "angulus," which is translated as "horn" in English.
Here,
The solution can be factored to begin with:
=> tanθ(tanθ + 3) = 0
Either
=> tanθ = 0 or tanθ + 3 = 0
will result in the satisfaction of this equation.
When sin = 0, can be any integer multiple of 180 degrees, including zero.
We can find tan by solving for 3 when tan + 3 = 0.
=> tanθ = -3
There are no answers to this problem because there isn't any angle whose tangent is -3.
As a result, the following are the answers to the equation
tan²θ + 3tanθ = 0 :
k can be any number, so θ = 0 + k180 or θ = 180 + k180
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The area of a rectangle is 60 square inches. The length and the width can vary. Enter an equation to find the length (l) for any possible width (w).
Answer:
l=(60÷w)
Step-by-step explanation:
since area =l×w
thats 60=l×w
l=60÷w
jim makes $80,000 per year in gross income and must pay a required deduction of 30% in income tax ( federal,state,and local combined) he deducts no money for retirement savings.
Answer:
he pays 24,00 and he is left with 56000
Step-by-step explanation:
100% = 80000
30% = X
100%X= 2400000
2400000/100= 24,000
80,000-24,000= 56,000
6. These polygons are similar but not drawn to scale.
30
What is the value of x?
Ox=7.2
Ox 8.6
Ox=215
Ox-258
3
(1 point)
Answer:
look on the yt theres alot of helpful things on there and ive had to do this simliar things and stuff so thats why yt viedo of this should help you
Step-by-step explanation: try a yt viedo to help on this math i wish you luck
A parallel combination of a R1 = 5 ohms and R2 = 15 ohms, the IT
= 10 amps. What is the current drawn by R2? Express your answer in
milli amps?
The current drawn by R2 is 3.333A or 3333mA in parallel combination in ohms.
In a parallel combination, the voltage across both resistors is the same. However, the current is divided between the two resistors based on their individual resistances. Using Ohms law (V = IR), we can find the voltage across the resistors:
According to the specific resistances of the resistors in a parallel circuit, the current is distributed among them. More current will flow through the resistor with the lower resistance than the one with the greater resistance. This is due to the fact that the lower resistance provides less resistance to the current flow. In this instance, R1 will draw more current than R2 since it has a lower resistance than R2.
V = IR1 = (10A)(5Ω) = 50V
V = IR2 = (I)(15Ω)
We can find current I by solving this particular equation:
I = V/R2 = (50V)/(15Ω) = 3.33A
Convert this ampere value to milliamps, in which we have to multiply by 1000:
I = 3.33A * 1000 = 3333mA or 3.333A
Current drawn by R2 is 3.333A or 3333mA.
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Given that u is indirectly proportional to t^(3)-3, if u=24 when t=2, what is u when t=3 ?
If u is indirectly proportional to t³ - 3, the value of u when t = 3 is 5.
If u is indirectly proportional to t³ - 3, what is the value of u when t = 3?Proportional relationships are relationships between two variables where their ratios are equivalent.
Given that;
u is indirectly proportional to t³ - 3;
u ∝ 1/( t³ - 3)
u = k/( t³ - 3)
Where k is the proportionality constant.
First, we determine the proportionality constant.
To find k, we can use the initial condition that;
u = 24t = 224 = k / (2³- 3)
24 = k / (8 - 3)
24 = k / 5
k = 24 × 5
k = 120
Hence, the equation relating u and t is:
u = k/( t³ - 3)
Plug in k = 120
u = 120/( t³ - 3)
To find u when t = 3, we can substitute t = 3 into the equation:
u = 120/( t³ - 3)
u = 120/( 3³ - 3)
u = 120/( 27 - 3)
u = 120/24
u = 5
Therefore, the value of u is 5.
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A bag has 7 blue cubes, 4 red cubes, and 14 green cubes. If you draw a cube and replace it in the bag 100 times, which of the following amounts would you expect to pull? Select all that apply.
-
Video
A) Pull two times as many green cubes as blue cubes
B) Pull a blue cube 28 times
C) Pull 60 red cubes
D) Pull more blue cubes than green cubes
E) Pull a red cube 16 times
The correct options are A) Pull two times as many green cubes as blue cubes , B) Pull a blue cube 28 times, and E) Pull a red cube 16 times.
To determine which of the following amounts you would expect to pull, we need to calculate the probabilities of drawing each color cube and then apply that probability to 100 draws.
1. Calculate the total number of cubes in the bag:
Total cubes = 7 blue + 4 red + 14 green = 25 cubes
2. Calculate the probability of drawing each color:
P(blue) = 7/25
P(red) = 4/25
P(green) = 14/25
3. Apply the probabilities to 100 draws:
Blue: 100 × (7/25) = 28
Red: 100 × (4/25) = 16
Green: 100 × (14/25) = 56
Now we can evaluate the given statements:
A) Pull two times as many green cubes as blue cubes
56 green cubes is exactly 2 times 28 blue cubes, so A is correct.
B) Pull a blue cube 28 times
As calculated earlier, you would expect to pull a blue cube 28 times. B is correct.
C) Pull 60 red cubes
The expected number of red cubes is 16, not 60. C is incorrect.
D) Pull more blue cubes than green cubes
You would expect to pull 28 blue cubes and 56 green cubes, so D is incorrect.
E) Pull a red cube 16 times
As calculated earlier, you would expect to pull a red cube 16 times. E is correct.
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Mr. Smith's class has 7 boys and 10 girls. If two students are randomly selected, what is the probability they are both boys? After selecting the first student, he does not go back in the room before the second student is selected. Answer as a simplified fraction.
Answer:
21/136
Step-by-step explanation:
The probability of selecting a boy from the class on the first draw is 7 boys out of 17 students total, or 7/17.
After the first boy is selected, there will be 6 boys and 10 girls left in the class.
So the probability of selecting a boy on the second draw, given that a boy was already selected on the first draw, will be 6 boys out of 16 remaining students, or 6/16.
To find the probability that both students selected are boys, we can multiply the probabilities of selecting a boy on the first and second draws:
P(boy and then boy) = P(boy on first draw) x P(boy on second draw | boy on first draw)
P(boy and then boy) = (7/17) x (6/16)
P(boy and then boy) = 21/136
Therefore, the probability of selecting two boys from Mr. Smith's class is 21/136.
Answer:
[tex] \frac{21}{136} [/tex]
Step-by-step explanation:
[tex] \frac{7}{17} \times \frac{6}{16} = \frac{7}{17} \times \frac{3}{8} = \frac{21}{136} [/tex]
Calculate the speed of a car if it covers 660km in 4 hours
Answer:
[tex]\frac{660}{4} = 165[/tex] [tex]km/h[/tex]
help me pls this is another one that is due Saturday!!!!
Answer:
Your anser is u = 6
Step-by-step explanation:
[tex]\frac{6}{7} =\frac{8}{u+5}[/tex]
Cross multiply.
[tex]6*(u+5) =7*8\\\\6u+30=56\\\\6u=56-30\\\\6u=36\\\\u=6[/tex]
Suppose that car accidents along a stretch of road occurs independently and are described by the Poisson distribution at a rate of 0.1 per hour. Furthermore, the number of motorcycle accidents along the same stretch of road also occurs independently and are described by the Poisson distribution at a rate of 0.05 per hour. What is the probability that there will be at most one accident in the next 2 hours?
The probability of at most one accident in the next 2 hours is 82.15%.
Let X be the number of car accidents in the next 2 hours, and Y be the number of motorcycle accidents in the next 2 hours. Both X and Y follow Poisson distributions, with rates of λX = 0.12 = 0.2 and λY = 0.052 = 0.1, respectively.
To find the probability that there will be at most one accident (either car or motorcycle) in the next 2 hours, we need to find the probability of the events {X + Y = 0} and {X + Y = 1}:
P(X + Y ≤ 1) = P(X + Y = 0) + P(X + Y = 1)
To find these probabilities, we can use the joint Poisson distribution of X and Y:
P(X = i, Y = j) = e^-(λX+λY) * (λXᵃ /a!) * (λYᵇ / b!)
where a and b are non-negative integers.
For X + Y = 0, we have:
P(X + Y = 0) = P(X = 0, Y = 0) = e⁻⁽⁰ ²⁺⁰ ¹⁾ * (0.2⁰ / 0!) * (0.1⁰ / 0!) = e⁻⁰ ³ ≈ 0.7412
For X + Y = 1, we have:
P(X + Y = 1) = P(X = 0, Y = 1) + P(X = 1, Y = 0) = e⁻⁽⁰ ²⁺⁰ ¹⁾ * (0.2⁰/ 0!) * (0.1¹/ 1!) + e⁻⁽⁰ ²⁺⁰ ¹⁾ * (0.2¹/ 1!) * (0.1⁰ / 0!) = 20.20.1*e⁻ ⁰ ³ ≈ 0.0803
Therefore, the probability of there being at most one accident (either car or motorcycle) in the next 2 hours is:
P(X + Y ≤ 1) ≈ 0.7412 + 0.0803 ≈ 0.8215
So the probability of there being at most one accident in the next 2 hours is about 82.15%.
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0.67032
The given data is that car accidents and motorcycle accidents on a stretch of road occur independently and are described by the Poisson distribution at a rate of 0.1 and 0.05 per hour respectively. It is required to find the probability that there will be at most one accident in the next 2 hours.The number of car accidents along the stretch of the road in the next 2 hours is a Poisson distribution with a mean of 0.1 x 2 = 0.2. Similarly, the number of motorcycle accidents in the next 2 hours is a Poisson distribution with a mean of 0.05 x 2 = 0.1.The probability that there will be at most one accident in the next 2 hours is:P(at most one accident in the next 2 hours)=P(no accident in the next 2 hours)+P(one accident in the next 2 hours)= e^(-0.2) (0.2)^0 / 0! + e^(-0.2) (0.2)^1 / 1! + e^(-0.1) (0.1)^0 / 0! + e^(-0.1) (0.1)^1 / 1!= 0.67032Therefore, the probability that there will be at most one accident in the next 2 hours is 0.67032.
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We say that a point estimator is unbiased if (choose one):its sampling distribution is centered exactly at the parameter it estimates. The standard deviation of its sampling distribution decreases as the sample size increases. Its sampling distribution is normal. Its value is always equal to the parameter it estimates. Choices (A), (B), and (C) are all true. The next four questions refer to the following information:A study was conducted in order to estimate ?, the mean number of weekly hours that U. S. Adults use computers at home. Suppose a random sample of 81 U. S. Adults gives a mean weekly computer usage time of 8. 5 hours and that from prior studies, the population standard deviation is assumed to be ? = 3. 6 hours
The correct answer is (A): "its sampling distribution is centered exactly at the parameter it estimates."
An estimator is a statistic that is used to estimate an unknown parameter in a population. A point estimator is a single value that is used to estimate the population parameter. The goal of a point estimator is to provide an estimate that is as close to the true value of the parameter as possible.
One way to evaluate the quality of a point estimator is to look at its bias, which is the difference between the expected value of the estimator and the true value of the parameter it is estimating. An estimator is unbiased if its expected value is equal to the true value of the parameter it estimates. In other words, an unbiased estimator is centered exactly at the parameter it estimates.
In the context of the given problem, the sample mean of weekly computer usage time (8.5 hours) is a point estimator for the population mean weekly computer usage time. To evaluate whether this estimator is unbiased, we would need to look at its sampling distribution and check whether its expected value (i.e., the mean of the sampling distribution) is equal to the true population mean.
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Score on last try: 0 of 1 pts. See Details for more. Find \( \frac{d y}{d x} \), if \( y=u^{3}-2 u \) and \( u=2 x^{2}-1 \). \[ \frac{d y}{d x}= \] Question Help: B Video B eBook D Post to forum
The answer is [tex]\(\frac{dy}{dx} = 24x\left( 2x^{2}-1 \right)^{2}-8x\)[/tex]To find [tex]( \frac{d y}{d x} \)[/tex]), let's apply the Chain Rule.
It is the most popular technique for differentiating composite functions, and it involves applying the derivative to the outer function and then to the inner function, multiplied by the derivative of the inner function.
Expression [tex]\(y = u^3 - 2u\) and \(u = 2x^2 - 1\),[/tex] Let us apply the chain rule; [tex]\( \frac{d y}{d x}= \frac{dy}{du}\frac{du}{dx}\)[/tex] , So [tex]\( \frac{d y}{d x}= \left( 3u^{2}-2 \right)\left( 4x \right) \).[/tex]
Put the value of u in the above equation, we have\[tex]( \frac{d y}{d x}= \left( 3\left( 2x^{2}-1 \right)^{2}-2 \right)\left( 4x \right) \)[/tex] , Thus [tex]\(\frac{dy}{dx} = 24x\left( 2x^{2}-1 \right)^{2}-8x\)[/tex] is the answer.
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Which reason completes the proof for step 6?
A. Definition of midsegment
B. Definition of median
C. Definition of midpoint
D. Definition of slope
The correct answer is A. Definition of midsegment. In this step, the proof is demonstrating that the midsegment of a triangle is parallel to the median of the triangle.
What is a triangle?A triangle is a three-sided polygon. It is one of the basic shapes in geometry. It has three sides and three angles, with the sum of the angles of a triangle being always 180 degrees. Triangles come in various shapes and sizes, and are classified by their angles or sides. Examples of triangle shapes include equilateral, isosceles and scalene.
The midsegment is defined as the line segment that connects the midpoints of two sides of the triangle. The median is defined as the line segment that connects a vertex of the triangle with the midpoint of the opposite side. Therefore, in order to prove that the midsegment is parallel to the median, the definition of the midsegment must be used. The definition of the midsegment states that it is the line segment that connects the midpoints of two sides of the triangle, which is necessary in order to prove that it is parallel to the median. Therefore, A. Definition of midsegment is the correct answer for this step in the proof.
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17
Question 17/20
Ov <
> NEXT
Cami was building a shelf to put her trophies on.
The drawing of her shelf is shown below.
11 inches
33 inches
BOOKMARK
8 inches
11 inches
What is the volume of Cami's trophy shelf?
cubic inches
8 inches
10 inches
Cami's trophy rack has a volume of 2904 cubic inches.
What is volume?In mathematics, volume is the amount of space within a particular 3D object. For example, an aquarium is 3 feet long, 1 foot wide, and 2 feet high. To find volume, multiply length with width and height. This is 3x1x2, or 6. To calculate the volume of Cami's trophy rack, you need to multiply the length, width, and height of the rack. Looking at the drawing provided, you can see that the shelf is 8 inches high, 11 inches wide and 33 inches long.
So the volume of the trophy rack is:
V = 8x11x33
V = 2904 cubic inches
Therefore, the Cami Trophy Rack has a volume of 2904 cubic inches.
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Complete question is: Cami was building a shelf to put her trophies on. The drawing of her shelf is shown below.
11 inches
33 inches
8 inches
What is the volume of Cami's trophy shelf? (in cubic inches)
What is the area of this figure?
Answer:
223.67
Step-by-step explanation:
How high above the first floor is the second floor? Round to the nearest tenth.
The hight above the first floor to second floor is 15 ft , for this we have Trigonometry angles.
What is Trigonometry angles?Angles determined by the ratios of the trigonometric functions are known as trigonometric angles.
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.
Given h = 60 ft, we have to find p
Sin 15° = p/h
0.25 = p/60
p = 15 ft
So, the hight above the first floor to second floor is 15 ft.
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Pls help Algebra1 pls pls
Answer:
1,4,5
Step-by-step explanation:
Jist Multiply these
The curved surface area of a solid
cylinder is 660 cm2
.
The cylinder has height 10 cm.
a) What is the circumference of the
cylinder?
b) What is the radius of the cylinder?
c) What is the area of one circular
base?
d) What is the surface area of the
cylinder?
Answer:
a) The circumference of the cylinder can be found using the formula C = 2πr, where r is the radius of the circular base. Rearranging the formula, we get r = C/2π. To find the circumference, we can use the formula for the curved surface area: A = 2πrh, where h is the height of the cylinder. Substituting the given values, we get:
660 = 2πr(10)
r = 33/π
Now we can find the circumference:
C = 2πr = 2π(33/π) = 66
Therefore, the circumference of the cylinder is 66 cm.
b) The radius of the cylinder is given by r = 33/π, which we already found in part a).
c) The area of one circular base can be found using the formula A = πr^2. Substituting the value of r from part b), we get:
A = π(33/π)^2 = 1089/π
Therefore, the area of one circular base is 1089/π cm^2.
d) The surface area of the cylinder consists of the curved surface area and two circular bases. The area of one circular base was found in part c), so we just need to add the curved surface area to twice the area of one circular base:
Surface area = 2A + 2πrh
Substituting the given values, we get:
Surface area = 2(1089/π) + 2π(33/π)(10) = 2187/π + 660
Therefore, the surface area of the cylinder is 2187/π + 660 cm^2.
Step-by-step explanation:
Paige has some cards. Each card has a
colour on it.
If she chooses a card at random, then
P(blue) and P(white) = 1.
18'
=
Calculate P(neither blue nor white).
Give your answer as a fraction in its
simplest form.
The response will be P(neither blue nor white) = 0, in accordance with the information provided.
In math, what is a fraction?A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, in which the both the numerator and the denominator are divided. In a simple fraction, both are integers. The numerator or decrease of a complicated fraction contains a fraction. The numerator of an appropriate fraction is less than the denominator.
The total probability of all potential outcomes must equal 1. As P(blue) and P(white) are both 1, there cannot be any other card colors. P(neither blue nor white) is therefore equal to zero.
If there are additional cards of different colors and the information provided is insufficient or inaccurate, we can also apply the following formula:
P(neither blue nor white) = 1 - P(blue) - P(white)
Assuming that there are just three possible card colors (blue, white, and another color), the following equation can be constructed using the provided data:
P(blue) + P(white) + P(another color) = 1
P(white) and P(blue) are both 1, so we have:
1 + 1 + P(another color) = 1
When we simplify this equation, we obtain:
P(another color) = -1
The presented information does not support the notion that there are merely three possible card colors, hence this is not a legitimate probability. Hence, the only viable response is.
P(neither blue nor white) = 0
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The answer is 0/1, which can be simplified to 0.
what is probability?
Probability is a measure of the likelihood or chance of an event occurring.
If P(blue) and P(white) are both 1, it means that all the cards are either blue or white.
Let's assume there are a total of n cards. Then,
P(blue) + P(white) = 1
=> Number of blue cards + Number of white cards = n
Given that P(blue) = P(white) = 1, we can conclude that there are n/2 blue cards and n/2 white cards.
Therefore, the probability of choosing a card that is neither blue nor white is the probability of choosing a card of a different color. There are no other colors given, so we can assume that there are no cards of any other color.
Hence, the probability of choosing a card that is neither blue nor white is 0.
So, P(neither blue nor white) = 0.
Therefore, the answer is 0/1, which can be simplified to 0.
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5. A six-marble repeating pattern made up of
ebloured marbles is shown.
How many times does a red marble appear
in the first 20 marbles of this pattern?
Explain your answer.
Answer:
7 marbles
Step-by-step explanation:
For every 6 marbles, 2 marbles appear as red.
This pattern would repeat thrice as 6x3 = 18, and then the first 2 marbles (one blue and red) will be counted to make 20 marbles.
So total marbles will be 3x2 in the 18 marble set and 1 in the final 2 marbles.
so 3x2 + 1 = 6+1 = 7
We get 7 marbles as red if we continue in this pattern.
12.
Find x and y in trapezoid TRAP below.
Answer:
x = 115 , y = 40
Step-by-step explanation:
in a trapezoid
• each lower base angle is supplementary to the upper base angle on the same side.
∠ ART = 40° + 25° = 65°
then
∠ PAR = 180° - ∠ ART = 180° - 65° = 115° , so
∠ PAR = x = 115
the sum of the 3 angles in Δ PAR = 180° , that is
x + y + 25 = 180
115 + y + 25 = 180
140 + y = 180 ( subtract 140 from both sides )
y = 40
Suppose that the heights of adult women in the United States are normally distributed with a mean of 64. 5 inches and a standard deviation of 2. 2 inches. Jina is taller than of 90% the population of U. S. Women. How tall (in inches) is Jina? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place
Jina is taller than 90% of US women if her height is at least 67.3 inches. Jina's height is approximately 67.3 inches.
Jina's height can be found using the z-score formula: z = (x - μ) / σ, where x is Jina's height, μ is the mean height of US women, and σ is the standard deviation of the heights. We need to find the z-score such that the area under the normal curve to the right of it is 0.10 (since Jina is taller than 90% of the population).
Using a z-score table or a calculator, we find that the z-score corresponding to an area of 0.10 is approximately 1.28. Substituting into the z-score formula and solving for x, we get:
1.28 = (x - 64.5) / 2.2
x - 64.5 = 2.816
x = 67.316
Rounding to one decimal place, Jina's height is approximately 67.3 inches.
In other words, Jina is taller than 90% of US women if her height is at least 67.3 inches.
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Ten years ago the Jacksons bought a house, taking out a 30 year mortgage for $150,000 at 5.75%. This year (exactly 10 years later) they refinanced the house, taking out a new 30 year mortgage for the remaining balance at 4.375%.
What was the monthly payment on the original 5.75% mortgage?
What was the remaining balance after 10 years (the amount they then refinanced)?
How much interest did they pay during those first 10 years?
What is the monthly payment on the refinance 4.375% mortgage?
How much interest will they pay over the 30 year term of the refinance?
How much total interest will they pay over the full 40 years the Jacksons have a loan for the house?
The tοtal interest paid οver the full 40 years the Jacksοns have a lοan fοr the hοuse is apprοximately $137,986.85.
Tο sοlve this prοblem, we can use the fοrmula fοr a fixed-rate mοrtgage payment:
[tex]P = (Pv\times r) / (1 - (1 + r)^{(-n))[/tex]
Where:
Pv = present value οf the mοrtgage
r = mοnthly interest rate
n = tοtal number οf payments
a) Mοnthly payment οn the οriginal 5.75% mοrtgage:
Pv = $150,000
r = 5.75% / 12 = 0.004792
n = 30 years × 12 mοnths per year = 360
[tex]P = (150,000 \times 0.004792) / (1 - (1 + 0.004792)^{(-360))[/tex]
P ≈ $875.25
Therefοre, the mοnthly payment οn the οriginal 5.75% mοrtgage was apprοximately $875.25.
b) Remaining balance after 10 years:
Using an οnline amοrtizatiοn calculatοr οr fοrmula, we can find that the remaining balance after 10 years is apprοximately $111,138.77.
c) Interest paid during the first 10 years:
Using the same amοrtizatiοn calculatοr οr fοrmula, we can find that the tοtal interest paid during the first 10 years is apprοximately $54,316.57.
d) Mοnthly payment οn the refinance 4.375% mοrtgage:
Pv = $111,138.77
r = 4.375% / 12 = 0.003646
n = 30 years × 12 mοnths per year = 360
[tex]P = (111,138.77\times 0.003646) / (1 - (1 + 0.003646)^{(-360))[/tex]
P ≈ $554.62
Therefοre, the mοnthly payment οn the refinance 4.375% mοrtgage is apprοximately $554.62.
e) Tοtal interest paid οver the 30 year term οf the refinance:
Using the same amοrtizatiοn calculatοr οr fοrmula, we can find that the tοtal interest paid οver the 30 year term οf the refinance is apprοximately $82,670.28.
f) Tοtal interest paid οver the full 40 years:
Tο find the tοtal interest paid οver the full 40 years, we can add up the interest paid during the first 10 years and the interest paid οver the 30 year term οf the refinance:
Tοtal interest = $54,316.57 + $82,670.28
Tοtal interest = $137,986.85
Therefοre, the tοtal interest paid οver the full 40 years the Jacksοns have a lοan fοr the hοuse is apprοximately $137,986.85.
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