1. You borrow $500 from a bank with a 5% annual interest and
the maturity date is in 3 years
a. How much would you pay in interest at the end of the
loan if you pay simple interest
b. How much would you pay in interest at the end of the
loan if you pay in compound interest
Answer:
Step-by-step explanation:
Discussing interest starts with the principal, or amount your account starts with. This could be a starting investment, or the starting amount of a loan. Interest, in its most simple form, is calculated as a percent of the principal. For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5. The total amount you would repay would be $105, the original principal plus the interest.
Determine the angles θ where sin(θ)=12
A)30o and 120o
B)60o and 120o
C)30o and 150o
D)60o and 150o
PLEASE HELP ! Determine the type of triangle drawn below.
Answer:
Scalene,right angled triangle
Hope it helps
Solve the right triangle below. Round sides to the nearest thousandth and angles to the nearest degree.
Answer:
Option 4, BC = 12.689, m∠A = 58°, and m∠C = 32°
Hope this helps!
IF U GET CORRECT U GET BRAINLIEST
The last five houses built in town sold for the prices shown below. Find the mean price. Use pencil and paper. If a new house built in the town sold for $160,000, how would that affect the mean?
prices: $181,00; $187,00; $144,00; $176,00; $175,00
what is the mean price of the houses??
Answer:
172,600
Step-by-step explanation:
hii so basically the mean is the same as average so add all together and divide by how many prices in this case there originally were
so 181,000+187,000+144,000+176,000+175,000=863,000
then divide by 5
863,000/5=172,600
hope this helped !
I need help can someone tell me which choice is correct?
Answer: A, C, D
Step-by-step explanation:
A is correct because Audrey reads 40 pages a day, and David reads 20. When you divide 40 by 20, you get 2. This means that 2 times 20 would be 40, and anything multiplied by 2 is "twice".
40 ÷ 20 = 2
2 × 20 = 40
B is not correct because after 6 days, Audrey reads 240 pages, and David reads only 120. We can figure this out by multiplying the pages read by 6.
Audrey: 40 × 6 = 240
David: 20 × 6 = 120
C is correct because when you subtract 20 from 40, you get 20. Since Audrey reads 40 pages a day and David reads 20, you can use this equation: 40-20 to figure the answer out. Audrey reads 20 more pages every day.
[tex]40-20=20[/tex]
D is correct because after 2 days, Audrey will have read 80 pages, and David will have read 40 pages. When you subtract 40 from 80, you get 40 pages.
40 × 2 = 80
20 × 2 = 40
80 - 40 = 40
E is not correct because, after 3 days, Audrey will have read 120 pages, and David will have read 60 pages. One-third of 120 is 40, not 60. Three times 60 would be 180, not 120. So, This answer is incorrect.
Find the arc length of the partial circle.
Either enter an exact answer in terms of pi or use 3.14 for pi and enter your answer as a decimal.
HELP ME! Look at the stem-and-leaf plot. What is the mode of the numbers?
Given:
The stem-and-leaf plot or a date set.
To find:
The mode of data set.
Solution:
From the given stem-and-leaf plot, we get the numbers of the data set.
64, 67, 70, 70, 71, 75, 76, 78, 78, 80, 82, 82, 88, 91, 93, 94, 97, 98, 100, 100, 100
Mode of a date set is the most frequent value.
In the given data set the most frequent value is 100 with frequency 3.
Therefore, the mode of data set is 100. Hence, option A is correct.
Answer:it is A: 100
Step-by-step explanation:
i got it right
good luck with your test :)
Plato!! Please help!!!
Answer:
[tex]a =7[/tex] [tex]b = 2[/tex] [tex]c = -4[/tex]
Step-by-step explanation:
Given
[tex]\frac{3x}{x + 2} + \frac{4x}{x - 2} = \frac{ax^2 + bx}{x^2 + c}[/tex]
Required
Find a, b and c
[tex]\frac{3x}{x + 2} + \frac{4x}{x - 2} = \frac{ax^2 + bx}{x^2 + c}[/tex]
Take LCM
[tex]\frac{3x(x -2) + 4x(x+2)}{(x + 2)(x - 2)} = \frac{ax^2 + bx}{x^2 + c}[/tex]
Expand
[tex]\frac{3x^2 -6x + 4x^2+8x}{x^2 - 4} = \frac{ax^2 + bx}{x^2 + c}[/tex]
Collect like terms
[tex]\frac{3x^2 + 4x^2-6x+8x}{x^2 - 4} = \frac{ax^2 + bx}{x^2 + c}[/tex]
[tex]\frac{7x^2+2x}{x^2 - 4} = \frac{ax^2 + bx}{x^2 + c}[/tex]
By direct comparison:
[tex]ax^2= 7x^2 \to a = 7[/tex]
[tex]bx = 2x \to b = 2[/tex]
[tex]-4 = c \to c = -4[/tex]
What is the volume of the prism, In cubic inches?
Answer:
55 in²
Step-by-step explanation:
Base x Height
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Answer:
If in rectangular coordinates we have a point (x, y), then the angle defined between the x-axis and a ray that connects the point with the origin is defined by:
Tan(θ) = y/x
Cos(θ) = x/(√(x^2 + y^2))
Sin(θ) = y/(√(x^2 + y^2))
Ctg(θ) = x/y
Sec(θ) = √(x^2 + y^2)/x
Csc(θ) = √(x^2 + y^2)/y
Ok, now we have all the equations.
We know that:
Sec(C) = 30/24
Then:
√(x^2 + y^2) = 30
x = 24
Replacing x in the first equation we get:
√(24^2 + y^2) = 30
y = √(30^2 - 24^2) = 18
Then we have:
x = 24
y = 18
√(x^2 + y^2) = 30
So we can just replace these in the equations:
Tan(C) = y/x = 18/24
Cos(C) = x/(√(x^2 + y^2)) = 24/30
Sin(C) = y/(√(x^2 + y^2)) = 18/30
Ctg(θ) = x/y = 24/18
Sec(θ) = √(x^2 + y^2)/x = 30/24
Csc(θ) = √(x^2 + y^2)/y = 30/18
help me plzzzzzz!!!!!!!
Does this graph represent a function? Why or why not?
A. No, because it fails the vertical line test
B. No, because it is not a straight line
C. Yes, because it is a curved line
D. Yes, because it passes the vertical line test
Answer:
D. Yes, because it passes the vertical line test
Step-by-step explanation:
the first term of an arithmetic sequence is 10 and the sum of the first five terms is 250,find the sequence
Answer:
The sequence is:
10, 30, 50, 70, 90.....................
Step-by-step explanation:
We have,
First term (a) = 10
Common difference (d) = ?
Sum of first 5 terms ([tex]S_{5}[/tex]) = 250
or, [tex]\frac{n}{2} [{2a+(n-1)d}] = 250[/tex]
or, [tex]\frac{5}{2} [2*10 + 4d]=250[/tex]
or, [tex]\frac{5}{2} * 4[5+d]=250[/tex]
or, 10(5 + d) =250
or, 5 + d = 25
∴ d = 20
Now,
2nd term = a + d = 10 + 20 = 30
3rd term = a + 2d = 10 + 2*20 = 10 + 40 = 50
4th term = a + 3d = 10 + 3*20 = 10 + 60 = 70
5th term = a + 4d = 10 + 4*20 = 10 + 80 = 90
Help pls!
(The question are in the image)
A. -1/p
B. 0
C. 1
D. p
Why is it important for a company to create an income statement?
What is the remaining area
The area of the region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units.
(a, b) can't equal
The area of the given region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units. So, all the options satisfy the value of a and b except (7, -9).
How to find the area of a region?Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly.
Then summing all those pieces' area gives us the area of the main big region.
The area of the given region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units.
f(x) is a linear function, the area under the curve on the interval [0,4] is a trapezoid with a height of 4 and bases of lengths f(0) and f(4).
The area of a trapezoid is the height times the average of the bases.
a. f(x)=-2x+8 f(0)=8, f(4)=0;
area = 4(8/2) = 16
b. f(x)=x+2; f(0)=2, f(4)=6;
area = 4(8/2) = 16
c. f(x)=3x-2; f(0)=-2, f(4)=10;
area = 4(8/2) = 16
d. f(x)=5x-6; f(0)=-6, f(4)=14;
area = 4(8/2) = 16
e. f(x)=7x-9; f(0)=-9, f(4)=19;
area = 4(10/2) = 20
Thus, The area is NOT 16 for choice e.
Learn more about Area here:
https://brainly.com/question/13056790
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From first to last, when did the presidents serve?
Drag the presidents' names into the correct order according to when they served.
Answer:
The answer is Gerald R. Ford, Jimmy Carter, Ronald Reagan, and lastly George H.W Bush
Step-by-step explanation:
What is the volume of the composite figure below? (formula for volume of a prism is 1/3 Bh where B is the area of the base.)
Answer:
Last Option; 84 cu. mm
Step-by-step explanation:
We know that;
Volume = 1/3(Bh)
And that this is figure has a square base, therefore B that represents the area of the base will be: 6 * 6 = 36
And height = 7mm
Therefore we can say;
Volume = (1/3)*(6 x 6)*(7)
Volume = (1/3)*(36)*(7)
Volume = (12)*(7)
Volume = 84
Hope this helps!
Stream ecologists are interested in the number of distinct organisms found in streams and whether or not differences exist based on geography. Separate random samples are obtained from sites in Northeastern and Southeastern streams, and the number of distinct organisms is recorded. They are given as separate stemplots for Northeastern and Southeastern streams.
Northeastern Southeastern
0 0 5 5 7 8
1 5 1 1 2 3 5 9 9
2 0 3 9 2 2 7
3 1 4 7 8 8 3 3
4 4 8 8 4 1
5 5 7 5
Required:
What is the sample size obtained from Southeastern?
Answer:
14
Step-by-step explanation:
Given
See attachment for proper stem plots for both district
Required
The sample size for Southeastern
The stem plot for southeastern is:
[tex]Stem | Leaf[/tex]
[tex]0 | 5\ 5\ 7\ 8[/tex]
[tex]1 | 1\ 2\ 3\ 5\ 9\ 9[/tex]
[tex]2 |2\ 7[/tex]
[tex]3 | 3[/tex]
[tex]4 | 1[/tex]
[tex]5 |[/tex]
To get the sample size, we simply count the leaves
The leaves are:
[tex]Leaves = \{5, 5, 7, 8, 1, 2, 3, 5, 9 ,9,2,7,3,1\}[/tex]
The number of leaves is:
[tex]n(Leaves) = 14[/tex]
Hence, the sample size is 14
The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, what test score separates the top 5% of the students from the lower 95% of students?
Answer:
Hence, the answer is [tex]x>71.1515[/tex]
Step-by-step explanation:
We have,
[tex]n=100,\mu=70,\sigma=7[/tex]
The top percentage of the students is [tex]5\%[/tex]
The lower percentage of the students is [tex]95\%[/tex]
The lowest [tex]95\%[/tex] is the left area from the normal distribution table, the area [tex]0.95[/tex] lies in the z-table
[tex]z=1.645[/tex] from the z- table
[tex]P(z<1.645)=0.95\\P(z>1.645)=0.05\\z>1.645[/tex]
[tex]\frac{x-\mu}{\frac{\sigma}{\sqrt{\mu}} } >1.645\\x>1.645\times \frac{\sigma}{\sqrt{n}} +\mu[/tex]
[tex]>1.645\times \frac{7}{\sqrt{100}} +70[/tex]
[tex]\Rightarrow x>71.1515[/tex]
Which inequality can be used to represent this scenario?
Mikael needs to rent a scooter to get to work. The scooter charges $1.85 to activate it and $0.50 per mile Mikael has a gift card for
$10 and he can not spend more on the scooter
O 10 < 0.502 +1.85
O 10 < 1.85.1 +0.50
O 10 > 1.852 +0.50
O 10 > 0.503 +1.85
Answer:
[tex]10 > 1.85 + 0.5m[/tex]
Step-by-step explanation:
Price of the scooter:
Fixed price of $1.85 to activate plus $0.50 for each mile. This situation can be represented by a linear function, and it is given by:
[tex]P(m) = 1.85 + 0.5m[/tex]
Mikael has a gift card for $10 and he can not spend more on the scooter.
The spendings have to be less than 10. So
[tex]10 > P(m)[/tex]
[tex]10 > 1.85 + 0.5m[/tex]
A surveyor has a survey a triangular plot of land. One side of the plot lies along countryside road. This side is 400 ft long. The second side is the gore road, which intersects countryside road at an angle of 88 degrees. The third side of this plot of land is 550 ft long. Determine the distance of the gore road that makes up in the unknown side of plot to the nearest foot
9514 1404 393
Answer:
392 ft
Step-by-step explanation:
As in the attached figure, you seem to have sides b and c of the triangle, along with angle C. You want to find side 'a'. The law of sines can be used to find angle B, then angle A can be found from the sum of angles. Knowing angle A, we can find side 'a'.
sin(B)/b = sin(C)/c
sin(B) = (b/c)sin(C) = 400/550·sin(88°)
B = arcsin(8/11·sin(88°)) ≈ 46.621°
Then angle A = ...
A = 180° - B - C = 180° -46.621° -88° = 45.379°
Now, we can find side 'a' from ...
a/sin(A) = c/sin(C)
a = c·sin(A)/sin(C) ≈ 550·sin(45.379°)/sin(88°) ≈ 391.710 . . . feet
The unknown side of the triangle is about 392 feet.
Help me out it’s important thank youuuu
Answer:
120 000 centimeters
Step-by-step explanation:
Answer:
120,000 cm³
Step-by-step explanation:
Given :-
A block of hay with dimensions 100 cm × 40 cm × 30cm is given .And we need to find the volume of the hay . The hay is in the form of cuboid .We know that the volume of a cuboid is ,
[tex]:\implies[/tex] Volume = l × b × h
[tex]:\implies[/tex] Volume = 100cm*40cm*30cm
[tex]:\implies[/tex] Volume = 1,20,000 cm³
Hence the correct option is B .Please I need help badly please no links or I will report you
Answer:
17.5 is going to be your answer
The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration.
GPA Monthly Salary ($)
2.6 3,500
3.4 3,800
3.6 4,200
3.1 3,700
3.4 4,200
3.1 2,500
The estimated regression equation for these data is = 2090.5 + 581.1x and MSE = 21,284.
Required:
a. Develop a point estimate of the starting salary for a student with a GPA of 3.0
b. Develop a 95% confidence interval for the mean starting salary for all students with a 3.0 GPA (to 2 decimals).
c. Develop a 95% prediction interval for Ryan Dailey, a student with a GPA of 3.0 (to 2 decimals).
Answer:
1.) 3833.8
2.) (3428.81 ; 4238.79)
Step-by-step explanation:
1.)
Point estimate of the salary for student with GPA of 3.
Using the regression model given :
Y = 2090.5 + 581.1x
x = 3
Y = 2090.5 + 581.1(3)
= 3833.8
2.)
95% confidence interval :
Y ± Tcritical * √MSE
Y = point estimate at x =3 ; = 3833.8
MSE = 21,284
Tcritical at 95% ; df = n-2 = 6-2 = 4
Tcritical(0.025 ; 4) = 2.776
√MSE = √21284 = 145.89036
Lower boundary : 3833.8 - 2.776(145.89036) = 3428.81
Upper boundary : 3833.8 + 2.776(145.89036) = 4238.79
(3428.81 ; 4238.79)
How would I figure out a linear equation with two plot points with fractions? (1/3(6),3) and (1/2(19),-2) are my two plot points. I was able to graph them on Desmos, but I can't seem to figure out how I would go about figuring out the slope and y-intercept in this case... the fractions are what's throwing me off here. Please help!
Answer: [tex]m=\frac{-30}{79},\ y=5.40[/tex]
Step-by-step explanation:
Given
Points are [tex]\left(6\frac{1}{3},3\right),\ \left(19\frac{1}{2},-2\right)[/tex]
Convert mixed numeral to fraction
[tex]\left(6\frac{1}{3},3\right)\Rightarrow \left(\dfrac{19}{3},3\right)\\\\\left(19\frac{1}{2},-2\right)\Rightarrow \left(\dfrac{39}{2},-2\right)[/tex]
Slope of the line is
[tex]\Rightarrow m=\dfrac{3-(-2)}{\dfrac{19}{3}-\dfrac{39}{2}}\\\\\Rightarrow m=\dfrac{5}{\dfrac{38-117}{6}}\\\\\Rightarrow m=\dfrac{-30}{79}[/tex]
Equation of line
[tex]\Rightarrow \dfrac{y-3}{x-\dfrac{19}{3}}=\dfrac{-30}{79}\\\\\text{for y-intercept, put x=0}\\\\\Rightarrow \dfrac{y-3}{0-\dfrac{19}{3}}=\dfrac{-30}{79}\\\\\Rightarrow y-3=\dfrac{190}{79}\\\\\Rightarrow y=3+2.40\\\Rightarrow y=5.40[/tex]
Rodas is standing 100 feet from the Eiffel Tower and sees a bird land on the top of the tower (he has really good eyes!). If the angle of elevation from Rodas to the top of the Eiffel Tower is close to 84.6°, how tall is the tower? Round to two decimal places.
Answer:
1057.89 feet
Step-by-step explanation:
Trig time! Start with a diagram and listing out your trig functions, either mentally or on paper. SOH CAH TOA
The best trig function for this problem is likely tan:
tan84.6 = height / 100
100 * tan 84.6 = height
height = 1057.89 feet
Mandy and Jordan each bought some of the same notebook and the same three-ring
binder. Mandy paid $11.20 for 2 notebooks and 2 binders. Jordan paid $10.50 for 3
notebooks and 1 binder. What is the price of one of the notebooks?
Answer:
$11.20 + 2 = 1122 1050 +3 = 1053 hope this help .