Answer:
Rs. 80 is owed.
Step-by-step explanation:
Principle (P) = 2000
Time (T) = 2 years
Rate (R) = 2%
Interest (I) = ?
Here,
I = (P×T×R) / 100
= (2000×2×2) / 100
= (8000) / 100
= Rs. 80
Answer:
P= 2000
T= 2
R=2÷100
I = PTR
= 2000×2×2÷100
2÷100=0.02
2000×2×0.02= 80
So i is 80
Transform the polar equation to a Cartesian (rectangular) equation: r= 4sinθ
options include:
x^2+y^2 = 4y
x^2+y^2 = -4
x^2+y^2 = 4
x^2+y^2 = -4y
Answer:
x^2 +y^2 = 4y
Step-by-step explanation:
Using the usual translation relations, we have ...
r^2 = x^2+y^2
x = r·cos(θ)
y = r·sin(θ)
Substituting for sin(θ) the equation becomes ...
r = 4sin(θ)
r = 4(y/r)
r^2 = 4y
Then, substituting for r^2 we get ...
x^2 +y^2 = 4y . . . . . matches the first choice
Please answer this correctly without making mistakes
Answer:
2 13/15 miles
Step-by-step explanation:
Hey there!
Well first we need to find the distance between Lancaster and Hillsdale and Lancaster to Silvergrove.
9 + 7 13/15
= 16 13/15
LS is just 14 miles.
Now we can do,
16 13/15 - 14
= 2 13/15 miles
Hope this helps :)
Solve and graph the inequality. 45x + 5 < −3
Answer:
x < -8/45
Step-by-step explanation:
Step 1: Write out inequality
45x + 5 < -3
Step 2: Subtract both sides by 5
45x + 5 - 5 < -3 - 5
45x < -8
Step 3: Divide both sides by 45
45x/45 < -8/45
x < -8/45
Step 4: Graph
A maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use. In a random sample of 50 microwaves that are 5 years old, 12% needed repairs at a=.04 can you reject the makers claim that no more than 10% of its microwaves need repair during the first five years of use?
Answer:
We conclude that no more than 10% of its microwaves need repair during the first five years of use.
Step-by-step explanation:
We are given that a maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use.
In a random sample of 50 microwaves that are 5 years old, 12% needed repairs.
Let p = population proportion of microwaves who need repair during the first five years of use.
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 10% {means that no more than 10% of its microwaves need repair during the first five years of use}
Alternate Hypothesis, [tex]H_A[/tex] : p > 10% {means that more than 10% of its microwaves need repair during the first five years of use}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of microwaves who need repair during the first 5 years of use = 12%
n = sample of microwaves = 50
So, the test statistics = [tex]\frac{0.12-0.10}{\sqrt{\frac{0.10(1-0.10)}{50} } }[/tex]
= 0.471
The value of z-test statistics is 0.471.
Now, at a 0.04 level of significance, the z table gives a critical value of 1.751 for the right-tailed test.
Since the value of our test statistics is less than the critical value of z as 0.471 < 1.751, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.
Therefore, we conclude that no more than 10% of its microwaves need repair during the first five years of use.
You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each. If you sold twice as many silly string tickets as car wash tickets, and you have $1460 total. Write the matrix in the box below. Write the solution set for this system and include any necessary work.
Answer:
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Solution Set : { x = 123, y = 246, z = 11 }
Step-by-step explanation:
Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,
x + y + z = 380,
And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.
5x + 3y + 10z = 1460
The silly string tickets were sold for twice as much as the car wash tickets.
y = 2x
Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.
System of Equations :
[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,
[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three
And we can continue, canceling the leading co - efficient in each row until this matrix remains,
[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]
x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold
Write in words how we would say the following
3 square
Answer:
Three to the second power
Step-by-step explanation:
Hey there!
3 square
Can be written as the following,
Three to the second power
Hope this helps :)
the difference of 8 and 2, added to x"
Answer:
see below
Step-by-step explanation:
Difference is subtract
(8-2)
Then add this to x
(8-2) +x
6+x
5/3 x 6/7 real quick plz
Answer:
10/7 or 1 3/7. I hope this helps,
Step-by-step explanation:
Chelsea played her tuba from 4:25 pm until 5:07
Answer:
42 minutes
Step-by-step explanation:
if you are asking how long it takes Chelsea to play her tuba then you do: 67 - 25 = 42
Answer:
Step-by-step explanation:
jhngjnh
Logan wants to mix an 18% acid solution with a 48% acid solution to get 15L of a 38% acid solution. How many liters of the 18% solution and how many liters of the 48% solution should be mixed?
Answer:
5 gallons of 18% solution
10 gallons of 48% solution
Step-by-step explanation:
x = gallons of 18% solution
y = gallons of 48% solution
Total volume is:
x + y = 15
Total amount of fertilizer is:
0.18 x + 0.48 y = 0.38 (15)
Solve by substitution.
0.18 x + 0.48 (15 − x) = 0.38 (15)
0.18 x + 7.2 − 0.48 x = 5.7
0.3 x = 1.5
x = 5
y = 10
Traci Lynn currently walks to school from her apartment, which is 1.3 miles away from her first class. She typically walks at a speed of 3 miles per hour. She is considering buying a used bicycle from Deseret Industries to ride to campus. Traci Lynn assumes that if she were riding a bike, she could go about 5 miles per hour. How many minutes could Traci Lynn save getting to class each morning if she were to ride the bike?
5 minutes in bike and by walking 1 hours 3 minutes
Traci Lynn saves getting to class each morning if she were to ride 6.12 minute
What formula is used to find the time?The formula is used to find the value of time is;
Time = Distance/speed
Given that Traci Lynn currently walks to school from her apartment, which is 1.3 miles away from her first class.
If she goes to school from the apartment by walking, then it will take time is;
Time = 1.3/3
Time = 0.43 hours
If she goes to school from the apartment by bicycle, then it will take time is;
Time = 1.3/5
Times = 0.26 hours
Therefore,
The time in minutes could Traci Lynn save getting to class each morning if She ride the bike is;
0.43 - 0.26
= 0.17 hours
= 0.17 x 36 = 6.12 minute
Hence, Traci Lynn saves getting to class each morning if she were to ride 6.12 minute
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An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind. What is the speed of the plane in still air and what is the wind speed?
Answer:
Speed of plane in still air is 270 mph
Wind speed is 30 mph
Step-by-step explanation:
Check the picture.
The speed of the plane in still air is 270 mph and the speed of the wind will be 30 mph.
What is the distance formula?The distance traveled by an object is the product of the speed of an object and the time taken.
Distance = speed x time
An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind.
Let the speed of the plane be x
The speed of wind be y
Distance covered with the wind = (x + y)t
1200 = (x + y)4
(x + y) = 1200/4
(x + y)= 300 .....(a)
Distance covered against the wind = (x - y)t
1200 = (x - y)5
(x - y) = 1200/5
(x - y) = 240 .......(b)
By solving both the equation
(x + y)= 300
(x - y) = 240
Therefore the values will be x= 270mph and y = 30 mph
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What did this person do wrong? Honestly really stuck and do not remember geometry!
Answer:
See below.
Step-by-step explanation:
Using the right triangle altitude theorem, the correct proportions are:
[tex] \dfrac{AB}{AC} = \dfrac{AC}{AD} [/tex]
[tex] \dfrac{AB}{x} = \dfrac{x}{AD} [/tex]
[tex] \dfrac{25}{x} = \dfrac{x}{16} [/tex]
[tex] x^2 = 25 \times 16 [/tex]
[tex] x = 20 [/tex]
AC = 20 cm
[tex] \dfrac{AB}{CB} = \dfrac{CB}{DB} [/tex]
[tex] \dfrac{AB}{y} = \dfrac{y}{DB} [/tex]
[tex] \dfrac{25}{y} = \dfrac{y}{9} [/tex]
[tex]y^2 = 25 \times 9[/tex]
[tex]y = 15[/tex]
CB = 15 cm
Peter saved up $20,000 in an account earning a nominal 5% per year compounded continuously. How much was in the account at the end of two years? Round the answer to nearest dollar.
Answer: 22,103
Step-by-step explanation:
Compound interest is the interest calculated on the initial principal and the accumulated interest.
The amount in the account at the end of two years is $22,050.
What is compound interest?Compound interest is the interest calculated on the initial principal and the accumulated interest.
We have,
Principal = $20,000
Rate = r = 5%
It is compounded yearly.
Time = t = 2 years.
The formula for the amount having compound interest:
A = P [tex]( 1 + \frac{r}{n} )^{nt}[/tex]
A = 20,000 [tex](1 + \frac{5}{100\times1})^{2\times1}[/tex]
A = 20,000 ( 1 + 5/100 )²
A = 20,000 ( 105/100 )²
A = (20,000 x 105 x 105) / (100 x 100)
A = 2 x 105 x 105
A = $22,050
Thus the amount in the account at the end of two years is $22,050.
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Which values of x are point(s) of discontinuity for this function? Function x = –4 x = –2 x = 0 x = 2 x = 4
Answer:
x=0 and x=2
Step-by-step explanation:
We need to check at each point where the function changes definition
At x= -2
On the left side -4 on the right side = -( -2)^2 = -4 continuous
At x=0
The point is not defined since neither side has an equals sign
discontinuous
x =2
on the left side 2^2 =4 on the right side 2
It is discontinuous
Answer:
x = 0
x = 2
Step-by-step explanation:
Edge 2020
~theLocoCoco
Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 16 of 42 at one school and 18 of 34 at the other have ear infections. At the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools? Group of answer choices
Answer:
Step-by-step explanation:
The summary of the given data includes;
sample size for the first school [tex]n_1[/tex] = 42
sample size for the second school [tex]n_2[/tex] = 34
so 16 out of 42 i.e [tex]x_1[/tex] = 16 and 18 out of 34 i.e [tex]x_2[/tex] = 18 have ear infection.
the proportion of students with ear infection Is as follows:
[tex]\hat p_1 = \dfrac{16}{42}[/tex] = 0.38095
[tex]\hat p_2 = \dfrac{18}{34}[/tex] = 0.5294
Since this is a two tailed test , the null and the alternative hypothesis can be computed as :
[tex]H_0 :p_1 -p_2 = 0 \\ \\ H_1 : p_1 - p_2 \neq 0[/tex]
level of significance ∝ = 0.05,
Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.
The test statistics for the difference in proportion can be achieved by using a pooled sample proportion.
[tex]\bar p = \dfrac{x_1 +x_2}{n_1 +n_2}[/tex]
[tex]\bar p = \dfrac{16 +18}{42 +34}[/tex]
[tex]\bar p = \dfrac{34}{76}[/tex]
[tex]\bar p = 0.447368[/tex]
[tex]\bar p + \bar q = 1 \\ \\ \bar q = 1 -\bar p \\ \\\bar q = 1 - 0.447368 \\ \\\bar q = 0.552632[/tex]
The pooled standard error can be computed by using the formula:
[tex]S.E = \sqrt{ \dfrac{ \bar p \bar q}{ n_1} + \dfrac{\bar p \bar p}{n_2} }[/tex]
[tex]S.E = \sqrt{ \dfrac{ 0.447368 * 0.552632}{ 42} + \dfrac{ 0.447368 * 0.447368}{34} }[/tex]
[tex]S.E = \sqrt{ \dfrac{ 0.2472298726}{ 42} + \dfrac{ 0.2001381274}{34} }[/tex]
[tex]S.E = \sqrt{ 0.01177284105}[/tex]
[tex]S.E = 0.1085[/tex]
The test statistics is ;
[tex]z = \dfrac{\hat p_1 - \hat p_2}{S.E}[/tex]
[tex]z = \dfrac{0.38095- 0.5294}{0.1085}[/tex]
[tex]z = \dfrac{-0.14845}{0.1085}[/tex]
z = - 1.368
Decision Rule: Since the test statistics is greater than the rejection region - 1.96 , we fail to reject the null hypothesis.
Conclusion: There is insufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools
If the nth term is nn+1, then the (n+1)st term is:
Answer:
[tex]\large \boxed{\sf C. \ (n+1)^{n+1}+1}[/tex]
Step-by-step explanation:
[tex]n^n+1[/tex]
Plug in the value for n as n+1 in the nth term to find the (n+1)st term.
[tex](n+1)^{n+1}+1[/tex]
Answer:
[tex]\boxed{Option \ 3}[/tex]
Step-by-step explanation:
=> [tex]n^n+1[/tex]
Given that n = n+1
So,
=> [tex](n+1)^{n+1}+1[/tex]
If 2( a^2 +b^2 ) = ( a+b)^2 , then
a. a+b =0
b. a =b
c. 2a =b
d. ab =0
Answer:
the answer is a=b
Step-by-step explanation:
Find the common ratio for the following sequence. Type a numerical answer in the space provided. If necessary, use the
/ key to represent a fraction bar. Do not type spaces in your answer.
2,-2, 2, -2, ...
Answer:
-1
Step-by-step explanation:
the common ratio in this geometric series is -1
Molly’s house is located at point X. Molly wants Sophia and Cole to meet at her house because she thinks it is the same distance from Sophia’s house and Cole’s house. Which could prove that Molly’s house is the samedistance from Sophia’s and Cole’s houses?
Answer:
Cole's House
Step-by-step explanation:
Cole house is closer because molly and Sophia can go there together because there both girls
70 points! Please answer fast!
Answer:
slope = 2
Step-by-step explanation:
will make it so simple and short
slope = rise / run
slope = 6 / 3
slope = 2
Answer:
B
Step-by-step explanation:
The formula for slope is (y2-y1)/(x2-x1)
In this case it is (1+5)/(3-0)
6/3
2
10) How many possible outfit combinations come from six shirts, three
slacks, and five ties? *
A 15
B 18
C 30
D 90
Answer:
The answer is D)90
Hope I helped
The simplified form of the expression (5.23x + 3.76) − (3.67x − 6.39) is?
Answer:
1.56x+10.15
Step-by-step explanation:
Answer:
1.56x + 10.15
Step-by-step explanation:
(5.23x + 3.76) – (3.67x – 6.39)
(a + b) – (c – d) = a + b – c + d
Remove the parentheses and change the signs as needed:
5.23x + 3.76 – 3.67x + 6.39.
Group the like terms and simplify:
5.23x – 3.67x + 3.76 + 6.39
1.56x +10.15.
The simplified form of (5.23x + 3.76) – (3.67x – 6.39) is 1.56x + 10.15.
Subtract these polynomials.
(3x2 – 2x + 5) – (x2 + 3) =
Answer:
D. 2x^2 - 2x + 2
Step-by-step explanation:
(3x2 – 2x + 5) – (x2 + 3) add or subtract like terms
3x^2 - x^2 - 2x - 3 + 5 = 2x^2 - 2x + 2
Answer:
2x^2 - 2x + 2
Step-by-step explanation:
Ape-x
Given: 8(y + 2) = 48
Solve for “y.”
16
-6
20
4
The value of y will be equal to 4. The correct option is D.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given expression 8(y + 2) = 48 will be solved for y as below:-
8(y + 2) = 48
Divide both sides by 8 and solve.
[ 8 (y + 2) ] / 8 = 48 / 8
y + 2 = 6
Substract 2 from both the sides to get the value of y.
y + 2 - 2 = 6 -2
y = 4
Therefore, the value of y will be equal to 4. The correct option is D.
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Please help quick !
Answer:
vertical angles
Step-by-step explanation:
Angle 1 and 3 are vertical angles. The angles are made from the same lines and share a vertex. They are opposite it each other
find the h.c.f of 186,310,434
186|2
93|3
31|31
1
310|2
155|5
31|31
1
434|2
217|7
31|31
1
[tex]186=2\cdot3\cdot31\\310=2\cdot5\cdot31\\434=2\cdot7\cdot31\\\\\text{hcf}(186,310,434)=2\cdot31=62[/tex]
4(c+3) =4+c+c+c+c+17
16% of 242 = ?
Please help me solve this
Answer:
16% of 242 = 38.72
Step-by-step explanation:
16% = 16/100 = 0.16
242 * 0.16 = 38.72
Answer:
38.72
Step-by-step explanation:
242 * .16 = 38.72
Which of the following is the correct equation for the distance formula for the points (x1, y1) and (x2,y2)?
A. D=sqrt (x2-x1)^2+(y2-y1)^2
B. D=sqrt (x2-y2)^2+(y1-x1)^2
C. D=sqrt -(y2-y1)^2+(x2-x1)^2
D. D=sqrt (x1-x2)^2+(y2-y1)^2
Answer:
A. D=sqrt( (x2-x1)^2+(y2-y1)^2 )
Step-by-step explanation:
The distance between two points is the root of the sum of the squares of the differences in their corresponding coordinates. The equation of choice A is the usual formulation.
__
Comment on answer choices
Because the square of a number is the same as the square of its opposite, the formula in choice D is also correct.
