Answer:
The person will pay $ 510 more as income tax per month .
Step-by-step explanation:
Given as :
The monthly income of person = $ 25000
The amount paid as income tax per year =$ 9000
So,The amount paid as income tax per month =$ [tex]\frac{9000}{12}[/tex] = $750
Or, x% is the income tax of the monthly income
I.e x % of 25000 = 750
∴ x % = [tex]\frac{750}{25000}[/tex]
Or, x = [tex]\frac{750}{25000}[/tex] × 100
I.e x = 3 %
Now, since the income tax is increase by 0.5 % per month
So, x' = 3 % + 0.5 % = 3.5 %
And The monthly income increase by $ 11000
I.e New monthly income = $ 25000 + $ 11000 = $ 36000
Now, The income tax which the person pay now is 3.5 % of $ 36000
i.e The income tax which the person pay now = 0.035×36000 = 1260 per month
so, The income tax which the person pay now as per year = 1260 × 12 = $ 15,120
∴ The increase income tax per month = $ 1260 - $ 750 = $ 510
Hence The person will pay $ 510 more as income tax per month . Answer
Final answer:
To calculate the additional income tax the person will pay per month, we add the tax increase due to the salary increase to the original increased tax after the 0.5% hike. The total increased monthly tax payment amounts to $930.
Explanation:
The question is asking how much more income tax a person will pay per month after their salary is increased and the government increased income tax by 0.5%. To find the additional income tax that a person will pay, we need to consider the initial monthly income, the new monthly income, the old annual tax amount, and the increased tax rate.
Originally, the person earned $25,000 per month and paid $9,000 in income tax yearly. With the 0.5% monthly increase in tax, we first need to calculate the monthly increase based on the initial salary. The monthly increase is 0.5% of $25,000, which is $125. Therefore, the new monthly tax without accounting for the salary increase is the old monthly tax plus the $125 increase.
The monthly tax paid before the income increase was $9,000 / 12 months = $750 per month. After the 0.5% monthly increase, the tax becomes $750 + $125 = $875 per month. But the person's monthly earnings were increased by $11,000, resulting in a new monthly income of $25,000 + $11,000 = $36,000.
To calculate how much more in income tax the person will pay on the additional $11,000 monthly earnings at the increased rate: 0.5% of $11,000 is $55. So the additional tax per month is $55. Therefore, the total increased monthly tax is $875 + $55 = $930.
A model is made of a car. The car is 3 meters long and the model is 3 centimeters long. What is the ratio of the length of the car to the length of the model? A. 3 : 3 B. 1 : 100 C. 1 : 3 D. 100 : 1
Answer:
D
Step-by-step explanation:
a meter is 100 centimeters so the ratio of the real car to the model is 300 centimeters to 3 centimeters, or 100:1 so D
.---------. _
'-O------O--'
One leg of a right triangle is 4 mm shorter than the longer leg in the hypotenuse is 4 mm longer than the longer leg find the links of the sides of the triangle
Answer:
Step-by-step explanation:
The right triangle has three sides which can be called legs. The legs are; shorter leg. Longer leg and hypotenuse
Let the longer leg be x
One leg of a right triangle is 4 mm shorter than the longer leg. This means
The shorter leg = x - 4
the hypotenuse is 4 mm longer than the longer leg. This means
The hypotenuse = x + 4
So the legs of the triangle are
Shorter leg or side = x-4
Longer leg or side = x
Hypotenuse = x + 4
The lengths of the sides of the triangle are 12 mm, 16 mm, and 20 mm.
Explanation:Let's use variables to represent the lengths of the sides:
Shorter leg: x mmLonger leg: x + 4 mmHypotenuse: x + 8 mmAccording to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse:
a² + b² = c²
Plugging in the values, we have:
x² + (x + 4)² = (x + 8)²
Expanding and simplifying, we get:
x² + x² + 8x + 16 = x² + 16x + 64
Combining like terms, we get:
x² - 8x - 48 = 0
Factoring the quadratic equation, we find:
(x - 12)(x + 4) = 0
Therefore, x = 12 or x = -4. We discard the negative value, so the lengths of the sides of the triangle are:
Shorter leg: 12 mmLonger leg: 16 mmHypotenuse: 20 mmAngelica has been depositing $280 each month into a savings account with an APR of 2.76% for the last 3 years. If she continues depositing this amount for an additional 12 years, what will the balance in her savings account be?
Answer:
$62,490.65
Step-by-step explanation:
If we assume her deposits are at the beginning of the month, and that the interest is compounded monthly, the future value is that of an "annuity due." The formula is ...
FV = P(1+r/n)((1+r/n)^(nt)-1)/(r/n)
where r is the APR (.0276), n is the number of yearly compoundings (12), P is the monthly payment ($280), and t is the number of years (15). Putting the numbers into the formula and doing the arithmetic, we get ...
FV = $280(1.0023)(1.0023^180 -1)/(.0023) ≈ $62,490.65
Angelica's account balance after 15 years will be $62,490.65.
_____
If her deposits are at the end of the month, the balance will be $62,347.25.
Consider the sequence:
5, 7, 11, 19, 35,....
Write an explicit definition that defines the sequence:
Group of answer choices
a_n=2n+3 a n = 2 n + 3
a_n=3n+2 a n = 3 n + 2
a_n=3n^2 a n = 3 n 2
a_n=2^n+3
Answer:
[tex]a_{n}=2^{n}+3[/tex]
Step-by-step explanation:
The given sequence is not arithmetic, it's a geometric sequence, that means the sequence is obtain using powers. The faster way to find the answer is to try options that fist with a geometric sequence. If we try the last one, we'll find that's the answer.
We need to try for n=1, n=2, n=3, n=4 and n=5:
a_{1}=2^{1}+3=5
a_{2}=2^{2}+3=4+3=7
a_{3}=2^{3}+3=8+3=11
a_{4}=2^{4}+3=16+3=19
a_{5}=2^{5}+3=32+3=35
Therefore, the right answer is the last choice, because as you can observe, it fits perfectly with the given sequence.
Simplify the function f(x) = 1/3 (81) 3x/4 Then determine the key aspects of the function.
Answer:
[tex]f(x)=3^{3x-1}[/tex].
The domain of the function is the set of all real number and the range is [tex](0,\infty)[/tex]
Step-by-step explanation:
Given:
The function is given as:
[tex]f(x)=\frac{1}{3}(81)^{\frac{3x}{4}}[/tex]
Using the rule of the exponents, [tex]a^{mn}=(a^m)^n[/tex],
[tex]f(x)=\frac{1}{3}((81)^{\frac{1}{4}})^{(3x)}\\f(x)=\frac{1}{3}(\sqrt[4]{81} )^{3x}\\f(x)=\frac{1}{3}(3)^{3x}\\f(x)=\frac{3^{3x}}{3^1}[/tex]
Using the rule of the exponents,[tex]\frac{a^m}{a^n}=a^{m-n}[/tex],
[tex]f(x)=3^{3x-1}[/tex]
Therefore, the simplified form of the given function is:
[tex]f(x)=3^{3x-1}[/tex]
Key aspects:
The given function is an exponential function with a constant base 3.
Domain is the set of all possible values of [tex]x[/tex] for which the function is defined.
The domain of an exponential function is a set of all real values.
The range of an exponential function is always greater than zero.
Therefore, the domain of this function is also all real values and the range is from 0 to infinity.
Domain: [tex]x \epsilon (-\infty,\infty)[/tex]
Range: [tex]y\epsilon (0,\infty)[/tex]
Answer: 1/3 27 all real numbers y>0
Step-by-step explanation:
11. Solve the problem. A company manufactures televisions in batches of 25 and there is a 1% rate of defects. Find the standard deviation for the number of defects per batch.
0.7
0.9
0.5
72.8
Answer: 0.5
Step-by-step explanation:
For binary distribution with parameters p (probability of getting success in each trial) and n (Total trials) , we have
[tex]\sigma=\sqrt{np(1-p)}[/tex]
We are given that ,
Total batches of televisions : n=25
The probability of defects : p= 0.01
Here success is getting defective batch .
Then, the standard deviation for the number of defects per batch will be :-
[tex]\sigma=\sqrt{(25)(0.01)(1-0.01)}\\\\=\sqrt{(25)(0.01)(0.99)}\\\\=\sqrt{0.2475}\\\\=0.497493718553\approx0.5[/tex] [Rounedde to the nearest tenth.]
Therefore, the standard deviation for the number of defects per batch =0.5
(x^2–x–4)multiplied by(x–5)
Answer:
x³ -6x² +x +20
Step-by-step explanation:
The distributive property is useful for making sure you have all of the partial products.
(x^2–x–4)(x–5) = x(x^2–x–4) -5(x^2–x–4)
= (x^3 -x^2 -4x) +(-5x^2 +5x +20)
= x^3 +(-1-5)x^2 +(-4+5)x +20
= x^3 -6x^2 +x +20
Evaluate (x + y)^0 for x = -3 and y = 5.
Answer:
The answer is 1.
Answer:
1
Step-by-step explanation:
any variable of power 0 equal to 1
Which percent is equivalent to 3/4 ?
A) 25%
B) 50%
C) 60%
D) 75%
Answer:
d is the correct answer
Answer:75
Step-by-step explanation:
You select a family with three children. If M represents a male child, and F represents a female child, the set of equally likely outcomes for the children's genders is { MMM, MMF, FFM, MFF, FFM, FMF, FFM, FFF }. Find the probability of selecting a family with nothing 6 male children.
Answer:
1/8
Step-by-step explanation:
This is actually pretty easy.
First, you have the sample of the children.
You know that the family with 3 children, can only have the following children:
MMM: all males
MMF: 2 males, 1 female
MFF: 1 male, 2 females
MFM: 2 males, 1 female (different order)
FMM: 1 female, 2 males
FFM: 2 females, 1 male
FMF: 2 females, 1 male
FFF: 3 females
If you count all of these possibilities, we have 8 possible cases of family with the childrens.
In only one of them, we have only females and no males, which is the last one, all 3 females.
Therefore, the probability to select a family with no male, is only 1/8.
In the set of all possible sets of genders for three children, which is {MMM, MMF, MFF, FMM, FFM, FMF, MFM, FFF}, the event of having no male children is 'FFF'. As there are 8 possible outcomes in total, the probability of selecting a family with no male children is 1/8, or 0.125.
Explanation:It seems like there is a typo in your question. It asks about the probability of selecting a family with 'nothing 6 male children', which doesn't quite make sense. However, if the question is to find the probability of selecting a family with no male children, we can certainly answer that. In your given set of outcomes, { MMM, MMF, FFM, MFF, FFM, FMF, FFM, FFF }, there seems to be a mistake as FFM is repeated three times. The correct set of equally likely outcomes for a family with three children should be { MMM, MMF, MFF, FMM, FFM, FMF, MFM, FFF }.
Each outcome is equally likely, hence, the probability of any particular outcome is 1 divided by the total number of outcomes. The total unique outcomes for the genders of three children is 2^3, or 8. The event of having no male child corresponds to the outcome 'FFF'. Since there is only one such outcome, the probability of a family with no male children is 1/8 or 0.125.
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5:3 =n:7 Solve for n.
(there fractions but i have to write them with : because i cant write fractions)
[tex] \frac{5}{3} = \frac{x}{7} [/tex]
you them cross multiply
5×7=35
3×X= 3x
35=3x
x(n)= 11.6
Answer:
n = 35/3 or 11 2/3.
Step-by-step explanation:
5/3 = n/7
Cross multiply:
3n = 5*7
3n = 35
n = 35/3
Please help me! Picture below
Answer:
A i think
Step-by-step explanation:
Tyler reads of a book on Monday, of it on Tuesday, of it on Wednesday, and of the remainder on Thursday. If he still has 14 pages left to read on Friday, how many pages are there in the book?
There are total of 32 pages in the complete book.
What are word problems?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Given is that Tyler reads 2/15 of a book on Monday, 1/3 of it on Tuesday, 2/9 of it on Wednesday, and 3/4 of the remainder on Thursday. He still has 14 pages.
Let the total number of pages in the book will be [x]. Then, we can write -
{2x/15} + {x/3} + {2x/9} + {3x/4} = x + 14
x{2/15 + 1/3 + 2/9 + 3/4} - 14 = x
259x/180 - 14 = x
1.44x - 14 = x
0.44x = 14
x = (14/0.44)
x = 32 (approx.)
Therefore, there are total of 32 pages in the complete book.
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In a research study conducted to determine if arrests were related to the socioeconomic class of the offender, the chi square critical score was 9.488 and the chi square test statistic was 12 2 We can conclude that:
A. The variables are dependent
B. The variables are independent
C. The probability of getting these results by random chance alone is 5
D. Being in a certain socioeconomic class causes arrests
The volume of a sphere is increasing at a constant rate of 141 cubic feet per minute. At the instant when the radius of the sphere is 11 feet, what is the rate of change of the radius? The volume of a sphere can be found with the equation V=4/3pi r^3 . Round your answer to three decimal places.
Answer:
0.093 ft/min
Step-by-step explanation:
V = 4/3 π r³
Take derivative with respect to time:
dV/dt = 4π r² dr/dt
Plug in values:
141 = 4π (11)² dr/dt
dr/dt = 141 / (484π)
dr/dt ≈ 0.093
The radius is increasing at 0.093 ft/min.
The increasing rate of the radius is equal to 0.093 ft/min.
What is the volume?Volume is defined as the space occupied by the object in a three-dimensional space. The sphere is the shape of a circular ball.
The volume is calculated by the formula below,
V = 4/3 π r³
Take the derivative with respect to time:
dV/dt = 4π r² dr/dt
Solve the equation for the rate of change of radius of the sphere,
141 = 4π (11)² dr/dt
dr/dt = 141 / (484π)
dr/dt ≈ 0.093
Therefore, the increasing rate of the radius is equal to 0.093 ft/min.
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Which statement best describes a polygon?
A. a closed plane figure with three or more sides that are straight
B. a closed plane figure with four or more sides
C. an open or closed plane figure
D. an open or closed plane figure with three or more sides Reset Next
The best statement that could be used describe a polygon is that it is a closed plane figure with three or more sides that are straight. Thus, the correct answer is A: a closed plane figure with three or more sides that are straight.
Hope this helps! :)
99 POINTS BRAINLIEST!!! No fake answers!
Find the mean for the binomial distribution. Round to the nearest tenth.
n=1632; p=0.57
A) 939.9
B) 937.5
C) 922.7
D) 930.2
ALSO QUESTION IN PICTURE PLEASE
Answer:
The mean of a binomial distribution is given by mean = n x p where n = the number of items and p equals the probability of success. Here we have:
mean = 1632 x 0.57 = 930.2
Step-by-step explanation:
The mean for a binomial substitution = n x p
Mean = 1632 x 0.57 = 930.24
The answer would be D.
Picture:
Multiply P(x) by X, then add those together:
0 x 0.42 = 0
1 x 0.12 = 0.12
2 x 0.34 = 0.68
3 x 0.05 = 0.15
4 x 0.07 = 0.28
Mean = 0 + 0.12 + 0.68 + 0.15 + 0.28 = 1.23
Fresh pond has a population of 854 and is increasing by 3 people per year. Strawberry has a population of 427 and is increasing by 10% per year. Write an equation that models the growth for each town.
Answer:
Fresh Pond: p(t) = 854 +3tStrawberry: p(t) = 427·1.10^tStep-by-step explanation:
(a) The general term of an arithmetic sequence is ...
an = a1 + d(n -1)
If we let the sequence of population numbers be modeled by this, and we use t for the number of years, we want n=1 for t=0, so n = t+1 and we have ...
p(t) = 854 +3(t+1-1)
p(t) = 854 +3t
__
(b) The general term of a geometric sequence is ...
an = a1·r^(n-1)
were r is the common ratio. Here, the multiplier from one year to the next is 1+10% = 1.10. Again, n=t+1, so the population equation is ...
p(t) = 427·1.10^(t+1-1)
p(t) = 427·1.10^t
The ___________ of a lens or mirror is a rotational symmetry axis of the surfaces.
Answer:
Optical axis
Step-by-step explanation:
Optical axis is the rotational symmetry axis of the surfaces.
A line with a certain degree of rotational symmetry is called as the optical axis in an optical system.
It is the straight line that passes through the geometric center of the lens and joins two curvature centers of its surfaces.
It is also called as the principal axis.
A man and a woman agree to meet at a certain location about 12:30 P.M. If the man arrives at a time uniformly distributed between 12:15 and 12:45, and if the woman independently arrives at a time uniformly distributed between 12:00 and 1 P.M., find the probability that the first to arrive waits no longer than 5 minutes. What is the probability that the man arrives first?
Final answer:
To find the probability that the first to arrive waits no longer than 5 minutes and the probability that the man arrives first, follow the provided detailed steps.
Explanation:
To find the probability that the first to arrive waits no longer than 5 minutes:
Man arrives first: 1/6
Woman arrives first: 1/4
Man and Woman arrive simultaneously within 5 minutes: 1/12
The probability that the man arrives first: 1/6
help me QUICK, plz! 15 points!
Answer:
t=8
Step-by-step explanation:
Subtract 12t from both sides
(12t-12t) + 16 = (13t-12t) + 24
16 = 1t (or just t) + 24
Then subtract 16 from both sides, and bring "t" over the equals sign making it a negative integer.
-t = 8
t = 8
Rover eats 3/4 of a can of cat food each day and Bono eats 1/2 of a can food each day.Cat food costs $5.00 for three cans.It is only sold in 3 can packs.How much does it cost for a 60 day supply of cat food?
Answer:
It would Cost $125 for a 60 day supply of cat food.
Step-by-step explanation:
Given:
Rover eats cat food each day = [tex]\frac{3}{4}[/tex] = 0.75 can
Bono eats cat food each day = [tex]\frac{1}{2}[/tex] = 0.5 can
Each day consumption for both cats = 0.75+0.5 = 1.25 can
Each day both cats consume = 1.25 cans
For 60 days both cats consume = Number of cans in 60 days.
By Using Unitary method we get;
Number of cans in 60 days = [tex]1.25\times60=75 \ cans[/tex]
Now Cans are sold in a pack of 3.
Hence we will divide number of cans in 60 days with 3 we get;
Number of can packs required for 60 days = [tex]\frac{75}{3}=25 \ can \ packs[/tex]
Now Cost for each Can packs(3 can) = $5.00
Hence Cost for 25 Can packs (75 cans) = Price for 25 can packs(75 can)
By Using Unitary method we get;
Price for 25 can packs (75 cans) = [tex]5\times 25 = \$125[/tex]
Hence Price for 25 can packs (75 cans) which are used for 60 supply of cat food is $125.
In the last math test andrew answered 80% of all the questions correctly.If he answered 32 questions correctly, what was the total number of questions in the math test?
Answer:
The total number of questions are 40
Step-by-step explanation:
let the total number of questions be "x".
percent of questions answered correctly are 80.
In fractions 80% is [tex]\frac{4}{5}[/tex]
The total number of correctly answered questions are 32.
the equation is,
[tex](\frac{4}{5})(x) = 32[/tex]
thus , x = [tex]\frac{(5)(32)}{4}[/tex]
x= 40
URGENT!!!
Find the equation x^2 + y^2 + Dx + Ey + F = 0
of the circle that passes through the points. To verify your result, use a graphing utility to plot the points and graph the circle.
(0, 0), (8, 8), (16, 0)
Answer:
D= -16
E= 0
F= 0
Step-by-step explanation:
The given equation is [tex]x^{2} + y^{2} + Dx + Ey + F = 0[/tex]
It is also given that the circle passes through (0,0) (16,0) and (8,8).
Inserting (0,0) in the equation, it gives
[tex]0 + 0 + 0 + 0 + F = 0[/tex]
This gives F = 0 .
Now inserting (16,0) , it gives
[tex]16^{2} + 0^{2} + D(16) + E(0) + 0 = 0[/tex]
[tex]D(16) = -256[/tex]
[tex]D = \frac{-256}{16}[/tex]
D = -16
Now inserting (8,8) , it gives
[tex]8^{2} + 8^{2} + (-16)(8) + (E)(8) + 0 = 0[/tex]
[tex]-16 + E = -16[/tex]
E = 0
Thus the equation of circle is
[tex]x^{2} + y^{2} + (-16)x = 0[/tex]
We can draw the following graph and thus verify that points (0,0) (8,8) and (16,0) lie on graph.
The equation of the circle passing through points (0, 0), (8, 8), and (16, 0) is x^2 + y^2 - 16x - 16y = 0. Solving the system of equations derived from substituting the given points into the circle equation confirms these coefficients for D and E.
Explanation:To find the equation of the circle that passes through the points (0, 0), (8, 8), and (16, 0), we can use the standard form of a circle's equation:
x
2
+
y
2
+ D
x
+ E
y
+ F = 0
Because the circle passes through the origin (0,0), we know that F = 0. With the remaining points (8, 8) and (16, 0), we can substitute these coordinates into the equation to form a system of equations.
Using point (8,8), the equation becomes:
64 + 64 + 8D + 8E + F = 0
Using point (16,0), the equation becomes:
256 + 16D + F = 0
Since F = 0, the system of equations is:
8D + 8E + 128 = 016D + 256 = 0Solving these equations, we get:
D = -16E = -16The equation of the circle is therefore:
x2 + y2 - 16x - 16y = 0To verify the result, plotting the points and the graph of the circle on a graphing utility should show that the points lie on the circumference of the circle.
Suppose that textbook weights are normally distributed. You measure 28 textbooks' weights, and find they have a mean weight of 76 ounces. Assume the population standard deviation is 12.3 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight. Round answers to 2 decimal places.
Answer:
Step-by-step explanation:
We want to find 95% confidence interval for the mean of the weight of of textbooks.
Number of samples. n = 28 textbooks weight
Mean, u =76 ounces
Standard deviation, s = 12.3 ounces
For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.
We will apply the formula
Confidence interval
= mean +/- z ×standard deviation/√n
It becomes
76 +/- 1.96 × 12.3/√28
= 76 +/- 1.96 × 2.3113
= 76 +/- 4.53
The lower end of the confidence interval is 76 - 4.53 =71.47
The upper end of the confidence interval is 76 + 4.53 = 80.53
Therefore, with 95% confidence interval, the mean textbook weight is between 71.47 ounces and 80.53 ounces
Late shows Some TV shows begin after their scheduled times when earlier programs run late. According to a network’s records, about 3% of its shows start late. To find the probability that three consecutive shows on this network start on time, can we multiply (0.97)(0.97)(0.97)? Why or why not?
Answer:
No because the probability of consecutive shows starting late are not independent events
Step-by-step explanation:
Is good begin with the definition of independent events
When we say Independent Events we are refering to events which occur with no dependency of other evnts. Basically when the occurrence of one event is not affected by another one.
When two events are independent P(A and B) = P(A)xP(B)
But for this case we can't multiply 0.97x0.97x0.97 in order to find the probability that 3 consecutive shows start on time, because the probability for shows starting late are not independent events, because if the second show is late, the probability that the next show would be late is higher. And for this reason we can use the independency concept here and the multiplication of probabilities in order to find the probability required.
Yes, you can multiply (0.97)(0.97)(0.97) because the events are independent.
Yes, you can multiply (0.97)(0.97)(0.97) to find the probability that three consecutive shows on this network start on time. This is because the events are independent; the outcome of one show starting on time does not affect the outcome of the others.
Therefore, the probability that three consecutive shows start on time is the product of the probabilities of each show starting on time: P(all three shows start on time) = 0.97 * 0.97 * 0.97 = 0.912673.
Which ordered pairs are on the line with equation 3x-y=2.
a) (0, -2) b) (-3, 4) c) (1, -5)
The ordered pair (0 , -2) lies on the line with equation 3 x - y = 2
Step-by-step explanation:
To prove that a point lies on a line
Substitute x and y in the equation by the coordinates of the pointIf the two sides of the equation equal each other, then the point lies on the lineIf the two sides of the equation not equal each other then the point does't lie on the lineThe equation of the line is 3 x - y = 2
a) Point (0 , -2)
∵ x = 0 and y = -2
- Substitute the values of x and y in the left hand side
∵ The left hand side is 3 x - y
∵ 3(0) - (-2) = 0 + 2 = 2
∴ The left hand side = 2
∵ The right hand side = 2
∴ The two sides of the equation are equal
∴ The ordered pair (0 , -2) lies on the line
b) Point (-3 , 4)
∵ x = -3 and y = 4
- Substitute the values of x and y in the left hand side
∵ The left hand side is 3 x - y
∵ 3(-3) - (4) = -9 - 4 = -13
∴ The left hand side = -13
∵ The right hand side = 2
∴ The two sides of the equation are not equal
∴ The ordered pair (-3 , 4) doesn't lie on the line
c) Point (1 , -5)
∵ x = 1 and y = -5
- Substitute the values of x and y in the left hand side
∵ The left hand side is 3 x - y
∵ 3(1) - (-5) = 3 + 5 = 8
∴ The left hand side = 8
∵ The right hand side = 2
∴ The two sides of the equation are not equal
∴ The ordered pair (1 , -5) doesn't lie on the line
The ordered pair (0 , -2) lies on the line with equation 3 x - y = 2
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If a weight hanging on a string of length 5 feet swings through 6° on either side of the vertical, how long is the arc through which the weight moves from one high point to the next high point?\
Answer:
1.047 ft
Step-by-step explanation:
The length of an arc is given by ...
s = rθ
where s is the arc length, r is the radius, and θ is the central angle in radians. Your arc subtends an angle of 12° = (12·π/180) = π/15 radians. The length of the arc is then ...
s = (5 ft)(π/15) = π/3 ft ≈ 1.047 ft
The weight swings through a total angle of 12°, corresponding to an arc length of approximately 1.047 feet on the circumference of the circle with radius 5 feet.
Explanation:To answer this question, we need to understand that the weight swings through an arc, and this arc is a part of the circumference of a circle. Given the length of string (5 feet) is the radius, and the weight swings through 6° on either side of the vertical, we can calculate the total arc length.
Firstly, you should know that the total angle a circle encompasses is 360°. So, the weight swings through a total angle of 6° x 2 = 12°.
Secondly, recall the formula for the circumference of a circle is 2πr, or in our case 2π x 5 feet. Now, to find the length of the arc corresponding to 12°, we will use the proportion of the swing angle to the total angle, i.e., (12/360) x (2π x 5 feet).
In this way, the length of the arc travelled is almost 1.047 feet.
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Daniela invested a total of $50,000, some in a certificate of deposit (CD) and the remainder in bonds. The amount invested in bonds was $5,000 more than twice the amount she put into the CD. How much did she invest in each account? Call the amount that Daniela invested in the CD d and the amount she invested in bonds b.
Answer:
The amount invested in bonds = 35,000
The amount invested in CD = 15,000.
Step-by-step explanation:
The total amount that Daniela invested is $50,000, this means if we call the amount invested in bonds [tex]b[/tex], and the amount invested in CD [tex]d[/tex], then we have:
[tex]b+d=50,000[/tex] this says the total amount Daniela invested is $50,000.
And since the amount invested in bonds [tex]b[/tex] is $5,000 more than twice the amount Daniela put into the CD, we have:
[tex]b=5,000+2d[/tex].
Thus, we have two equations and two unknowns [tex]b[/tex] and [tex]d[/tex]:
(1). [tex]b+d=50,000[/tex]
(2). [tex]b=5,000+2d[/tex],
and we solve this system by substituting [tex]b[/tex] from the second equation into the first:
[tex]b+d=50,000\\5,000+2d+d=50,000\\3d=45,000\\\\\boxed{d=15,000}[/tex]
or, the amount invested in CD is $15,000.
With the value of [tex]d[/tex] in hand, we now solve for [tex]b[/tex] from equation(2):
[tex]b=5,000+2d\\b=5000+2(15,000)\\\boxed{b=35,000}[/tex]
or, the amount invested in bonds is $35,000.
Brandon is an amateur marksman. When he takes aim at a particular target on the shooting range, there is a 0.1, point, probability that he will hit it. One day, Brandon decides to attempt to hit 10 such targets in a row.
Assuming that Brandon is equally likely to hit each of the 10 targets, what is the probability that he will hit at least one of them?
Answer:
.65
Step-by-step explanation:
Strategy:
In this situation it is much easier to calculate the probability of the event we are looking for (he hits at least one target) by calculating the probability of its complement (he misses every target), and subtracting from 1.
In other words, we can use this strategy:
P(at least one hit)=1-P(miss all 10)
Calculations:
P(at least one hit)
=1-P(miss all 10)
=1-(0.9)^10
≈1-0.349
≈0.65
Answer:
P(at least one hit)≈0.65
I hope this helps!!!
The probability that Brandon will hit at least one of them is 0.65 approx.
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
For the considered case, as each hit is independent of each other, and there is either hit or not hit, so this situation can be modeled by binomial distribution.
For this case, we get:
n = 10p = probability of success(we call it success if hit occurs) = 0.1X = count of successes in those 10 attemptsThen, we get: [tex]X \sim B(n=10,p=0.1)[/tex]
The probability that Brandon will hit at least one of them is written symbolically as:
[tex]P(X \geq 1)[/tex]
We can rewrite it as:
[tex]P(X \geq 1) = 1 - P(X < 1) = 1 - P(X = 0)[/tex]
Using the probability function of binomial distribution, we get:
[tex]P(X \geq 1) = 1 - \: ^{10}C_0(0.1)^0(1-0.1)^{10} = 1 -0.9^{10} \approx 0.65[/tex]
Thus, the probability that Brandon will hit at least one of them is 0.65 approx.
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