Two formulas:
Compound interest - A = P(1 + r/n)^nt
Simple interest = A = P(1 + rt)
A - final amount
P - initial principal balance
r - interest rate
n - number of times interest applied per time period
t - number of time periods elapsed
Suri --
A = 4,000(1+0.03/1)^5
A = $4,637.09
Carter --
A = 4,000(1+0.03*5)
A = $4,600
In 5 years, Suri makes $37.09 more than Carter
order 520, 475, 720, 580, 310, 170, 370, 220, 140 and 15 from least to greatest
Answer:
15,140,170,220,310,370,475,520,580,720
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
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A basketball player made 80 out of 100 attempted free throws. What percent of free throws was made?
I need a correct answer asap!
Percent of free throws = (number of free throws made / total attempts) x 100
Percent = (80/100) x 100 = 80%
The answer is 80%
Answer:
80%
Step-by-step explanation:
Which side lengths form a right angle?
Choose all answers that apply:
A) 3, square root 27, 6
B) 8, 15, 17
C) 5, 5, square root 50
Answer:
B and C
Step-by-step explanation:
Using the Pythagorean theorem a²+b²=c², those are the correct answers
use the protractor to find the measure of each angle:
a. CAB
b. FAB
c. EAB
d. HAF
Answer:
a. 20-degree
b. 110-degree
c.70-degree
d.50-degree
What is the perimeter of Quadrilateral ABCDwith vertices at A(−11, −6), B(−3, 0), C(1, 0), and D(1, −6)?
Answer:
32 units
Step-by-step explanation:
the perimeter =
(1 -(-3)) +(0-(-6)) + (1 -(-11) + (√(12-4)²+6²)
= (1+3) +(0+6) +(1+11) +(√(64+36))
= 4+6+12 + 10
=32 units
Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <2,-4>, v = <6,3> (5 points)
===========================================================
Explanation:
For any two vectors defined as follows
u = <a,b>
v = <c,d>
the dot product is computed by
u dot v = a*c + b*d
If the dot product of the vectors is 0, then the vectors are orthogonal. Meaning they are perpendicular to one another.
-------------------
Let's find the dot product of these two given vectors
u = < 2, -4 >
v = < 6, 3 >
u dot v = 2*6 + (-4)*3
u dot v = 12 - 12
u dot v = 0
Therefore, these two vectors form a right angle and are orthogonal
-------------------
Extra info:
If we can show that u = <a, b> and v = <ka, kb> for some real number k, then we have shown that vectors u and v are parallel.
What is the value of y?
Using the Pythagorean theorem,
[tex]6^{2}+y^{2}=(3+9)^{2}\\\\36+y^2=144\\\\y^2=108\\\\y=\boxed{6\sqrt{3}}[/tex]
A person's Body Mass Index (BMI) is a measure of the amount of fat in their body. The relationship between antioxidant food consumption per day in cups and the BMI of an individual is modeled by the following line of best fit: [tex]y=-1.2x+26[/tex] . Interpret the slope and intercept of the trend line within the context of the data.
DIRTY ANSWERS REPORTED
NO LINKS ALLOWED!
Answer:
The slope of -1.2 means that for each cup of antioxidant a person consumes per day, it's BMI decreases by 1.2.
The intercept of 26 means that a person that does not consume any cup of antioxidant food a day should have an BMI around 26.
Step-by-step explanation:
Line of best fit:
[tex]y = -1.2x + 26[/tex]
Slope:
The slope is the number that multiplies x, that is, -1.2. The slope of -1.2 means that for each cup of antioxidant food a person consumes per day, it's BMI decreases by 1.2.
Intercept:
Value of y when x = 0, that is, 26. The intercept of 26 means that a person that does not consume any cup of antioxidant food a day should have an BMI around 26.
Answer:
the slope is -1.2 and the intercept is 26.
Step-by-step explanation:
our line's equation is y= -1.2x + 26
In the equation y = mx + b, m is the slope and b is the y-intercept. So in this equation, look for where the numbers are placed and that it what you get.
please help i am actually so confused on this one
Answer:
C
Step-by-step explanation:
Using pythagoras theorem, you will find that AC= 12,
[tex]\sqrt{13^2-5^2}= 12[/tex]
Sin A = Opposite / Hypotenuse, in this case the opposite of A is CB which is 5ft, and then Hypotenuse of the right angled triangle is AB. which is 13ft.
So, Sin A = 5/13
Tan A= Opposite/ Adjacent,
Opposite is CB, which is 5ft, adjacent is AC, which is 12ft.
So, Tan A= 5/12
Cos A= Adjacent/Hypotenuse,
we know adjacent is 12ft and that hypotenuse is 13ft.
So Cos A= 12/13
However Sec A is the inverse of cos A.
So, Sec A= 13/12.
Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1.
Answer:
The equation of the parabola is y = x²/4
Step-by-step explanation:
The given focus of the parabola = (0, 1)
The directrix of the parabola is y = -1
A form of the equation of a parabola is presented as follows;
(x - h)² = 4·p·(y - k)
We note that the equation of the directrix is y = k - p
The focus = (h, k + p)
Therefore, by comparison, we have;
k + p = 1...(1)
k - p = -1...(2)
h = 0...(3)
Adding equation (1) to equation (2) gives;
On the left hand side of the addition, we have;
k + p + (k - p) = k + k + p - p = 2·k
On the right hand side of the addition, we have;
1 + -1 = 0
Equating both sides, gives;
2·k = 0
∴ k = 0/2 = 0
From equation (1)
k + p = 0 + 1 = 1
∴ p = 1
Plugging in the values of the variables, 'h', 'k', and 'p' into the equation of the parabola, (x - h)² = 4·p·(y - k), gives;
(x - 0)² = 4 × 1 × (y - 0)
∴ x² = 4·y
The general form of the equation of the parabola, y = a·x² + b·x + c, is therefore;
y = x²/4.
What is the sum of the factors?
Two factors of -48 have a difference of 19. The factor
with a greater absolute value is positive.
-19
-13
13
16
Answer:
13
Step-by-step explanation:
The two factors 16 and -3.
Which is a stretch of an exponential decay function?
f(x)=4/5(5/4)x
f(x)=4/5(4/5)x
f(x)=5/4(4/5)x
f(x)=5/4(5/4)x
the two solids below are similar and the ratio between the lengths of their edges is 4:7 what is the ratio of their surface areas? A 7:4 B 16:49 C 16:29 B 64:343
9514 1404 393
Answer:
B. 16:49
Step-by-step explanation:
The area ratio is the square of the edge length ratio:
area ratio = (4:7)² = 4²:7² = 16:49
_____
It might help you to recall that area is the product of two linear dimensions if each is multiplied by 4/7, the resulting product will be multiplied by (4/7)².
A = LW
A' = (4/7L)(4/7W) = (4/7)²(LW) = (16/49)·A
I need help please someone help me
Answer:
We know that the height equation is given by:
H(t) = -16*t^2 + 108*t + 28
in ft.
First, we want to find the maximum height of the ball.
The first thing we can see is that the leading coefficient of the quadratic equation is negative, this means that the arms of the graph will open downwards, so the vertex of the quadratic equation is the maximum.
We also know that the ball will reach its maximum height when its velocity is zero (this means that the object stops going upwards at this point).
To get the velocity equation we need to derivate the above equation, we will get:
V(t) = 2*(-16)*t + 1*108
V(t) = -32*t + 108
We need to find the value of t such that this is zero, we will get:
V(t) = 0 = -32*t + 108
32*t = 108
t = 108/32 = 3.375
So the ball reaches its maximum height after 3.375 seconds.
Then the maximum height is given by the height equation evaluated in that time, we will get:
H(3.375) = -16*(3.375)^2 + 108*3.375 + 28 = 210.25
Then the maximum height of the ball is 210.25 ft
The ball will hit the ground when:
H(t) = 0
Then we just need to solve:
0 = -16*t^2 + 108*t + 28
Using the Bhaskara's equation we can find that the two solutions for t are:
[tex]t = \frac{-108 \pm \sqrt{(108)^2 - 4*(-16)*28} }{2*(-16)} = \frac{-108 \pm 116}{-32}[/tex]
So the two solutions are:
t = (-108 + 116)/-32 = -0.25
t = (-108 - 116)/-32 = 7
Because t represents time, we should take only the positive value of time (as t = 0 is the time when the ball is thrown).
Then we can conclude that the ball hits the ground after 7 seconds.
When doing blood testing for a viral infection, the procedure can be made more efficient and less expensive by combining partial samples of different blood specimens. If samples from three people are combined and the mixture tests negative, we know that all three individual samples are negative. Find the probability of a positive result for three samples combined into one mixture, assuming the probability of an individual blood sample testing positive for the virus is 0.06.
Answer:
0.1694 = 16.94% probability of a positive result for three samples combined into one mixture.
Step-by-step explanation:
For each test, there are only two possible outcomes. Either it is positive, or it is negative. The probability of a test being positive or negative is independent of any other test, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability of an individual blood sample testing positive for the virus is 0.06.
This means that [tex]p = 0.06[/tex]
If samples from three people are combined and the mixture tests negative, we know that all three individual samples are negative. Find the probability of a positive result for three samples combined into one mixture.
It will be positive if at least one of the tests is positive, that is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.06)^{0}.(0.94)^{3} = 0.8306[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.8306 = 0.1694[/tex]
0.1694 = 16.94% probability of a positive result for three samples combined into one mixture.
The fencing William chooses costs $29.53 per foot, including installation. What will the fencing cost? Show your work.
Answer:
[tex]C = 29.53x[/tex]
Step-by-step explanation:
Given
[tex]Unit\ cost = \$29.53[/tex]
Required
The cost of fencing (C)
The cost is calculated as:
[tex]C = Unit\ Cost * Perimeter\ of fencing[/tex]
Let:
[tex]x \to Perimeter\ of fencing[/tex]
So, we have:
[tex]C = Unit\ Cost * x[/tex]
[tex]C = 29.53 * x[/tex]
[tex]C = 29.53x[/tex]
The question cannot be solved further since the dimension of the fence is not given
If you know the dimension, calculate the fence perimeter and substitute the value for x
PLEASE HELP ME WITH THESE TWO PROBLEMS ASAP !!!!!!! PLS
Answer:
1. 35 degrees
2. 44 degrees
Step-by-step explanation:
1). 35 degree
180-59=121
121+24+ m<1= 180
m<1= 35 degree
2) m<CED= 45 degree
As CED is a right angled triangle, one angle is of 90 degree while other 2 angles are of 45 degree which makes a sum of 180.
Can someone help pleaseee
Answer:
Ŷ = 76.4064+5.4254X
0.786
Strong positive relationship
Score = 98
Step-by-step explanation:
Using technology, the linear model obtained by fitting the data is :
Ŷ = 76.4064+5.4254X
Where, slope = 5.4254
y = test score ; x = study time
The Correlation Coefficient obtained is 0.786 ; which depicts that there exist a strong positive relationship between the two variables.
Using the model; test score, if x = 4
Ŷ = 76.4064+5.4254(4)
Y = 98.108
Test score = 98
Find the slope from the given equation. 9y = -3x + 5
Answer:
-3/9x
Step-by-step explanation:
You rearrange for 'y' so divide both sides by it's coefficient which is 9.
Answer:
The slope is -1/3
Is 12 rational? irrational? Whole? Integer?
Answer:
It is an Integer, but it can also be a rational number.
Step-by-step explanation:
My math teacher told meh
The distance that students drive to school is best modeled with a skewed right distribution that has a mean of 10 miles and a standard deviation of 2 miles. Suppose a sample of 100 students has been taken and the sample mean distance for the sample is calculated. Describe the shape of the sampling distribution of the sample mean
Answer:
The answer is "Approximately normal".
Step-by-step explanation:
sample size[tex]n=100[/tex]
Sample size [tex]n \geq 30[/tex]
It is because [tex]C \perp T[/tex] the sampling distribution of the sample means is approximately normal.
96 sq meters
144 sq meters
84 sq meters
102 sq meters
Pls show work I get different answers from people every time
Answer:
84 sq meters
Step-by-step explanation:
First, divide the shape in 2 or more parts so that you can find it step by step
Divide this shape in three parts:
One part (blue): 2 m and 3 m rectangle
Second part (orange): 5 m and 12 m rectangle
Third part (red): 6 m and 3 m rectangle
(you can also see this below: in the pic there are three parts so you figure out that which is the correct value for the sides)
Now, find area of each shape by multiplying its values:
1st shape: 3 x 2 = 6
2nd shape: 5 x 12 = 60
3rd shape: 6 x 3 = 18
As you have the area of all the different shapes,
add all of them:
6 + 60 + 18 = 84 sq meters
I hope this helps :)
Solve the equation for x
2(x - 7) = 10x + 18
Hi there!
»»————- ★ ————-««
I believe your answer is:
x = -4
»»————- ★ ————-««
Here’s why:
We will use inverse operations to solve for 'x'.⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x':}}\\\\2(x-7)=10x+18\\------------\\\rightarrow 2x-14 = 10x + 18\\\\\rightarrow 2x - 14 + 14 = 10x + 18 + 14\\\\\rightarrow 2x = 10x + 32\\\\\rightarrow 2x-10x=10x-10x+32\\\\\rightarrow-8x=32\\\\\rightarrow\frac{-8x=32}{-8}\\\\\rightarrow \boxed{x=-4}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
A pair of vertical angles has measures
(3x + 4) and ( 73 – 9)
What is the value of x?
Answer:
20
Step-by-step explanation:
Vertical angles are always equal to each other. So the answer is
3x + 4 = 73 - 9 Are you sure this is what the question is?
3x + 4 = 64 Subtract 4 from both sides
-4 -4
3x = 60 Divide by 3
3x/3 = 60/3
x = 20
simplify 22+[55-{72÷(7+5×2-11)+3}+2]
Answer:
The correct answer is 319.
Step-by-step explanation:
it is in the given picture.
( don't mind my writing!!)
Decrease
M720.00 by 25%
Answer:
540
Step-by-step explanation:
720 (100-25) to find the decimal to use (below 1.00 is decreasing)
720 (.75) = 540
The yearbook staff receive 75 submissions for yearbook articles. Paul will acceptſ of all submissions. Currently, Paul plans for the yearbook to have 156
pages.
How many more pages will Paul need to add to the yearbook to have 2 articles on every 13 pages? Show your work and explain your thinking.
Answer:
The correct answer is - 332 pages.
Step-by-step explanation:
Given:
number of articles submissions - 75
number of pages in the yearbook on current plan = 156
pages required for two articles = 13 pages.
The number of pages to add = ?
Solution:
1 article takes pages in the yearbook = 13/2
= 6.5
the number of pages required for 75 articles = 75*6.5
= 487.5
The number of pages to add in the yearbook = 487.5 - 156
= 331.5 or 332.
Thus, the correct answer is - 332 pages.
An auto repair shop charged a customer $170 to repair a car. The bill listed $50 for parts and the
remainder for labor. If the cost of labor is $30 per hour, how many hours of labor did it take to repair
the car?
The answer is attached. I hope this helps answer your question!
There are several vehicles in a parking lot. Some of them are motorcycles
(with 2 wheels), and some are cars (with 4 wheels). There are 10 vehicles in
the lot, and there are 32 wheels. How many vehicles of each type are in the
lot?
Answer:
There are four motorcycles and six cars.
Step-by-step explanation:
Let m represent the number of motorcycles and c represent the number of cars.
Since there are ten vehicles in total, the sum of the number of motorcycles and the number of cars must total ten. Hence:
[tex]m+c=10[/tex]
And since each motorcycle has two wheels and each car has four wheels and there are 32 wheels in total:
[tex]2m+4c=32[/tex]
Solve the system of equations. First, we can divide the second equation by two:
[tex]m+2c=16[/tex]
From the first equation, we can subtract c from both sides:
[tex]m=10-c[/tex]
Substitute:
[tex](10-c)+2c=16[/tex]
Simplify:
[tex]10+c=16[/tex]
Therefore:
[tex]c=6[/tex]
There are six cars.
Using the modified equation:
[tex]m=10-c[/tex]
Solve for m:
[tex]m=10-(6)=4[/tex]
So, there are four motorcycles and six cars.
A comet travels at an average speed of 233,000 km/h.
It takes 7 days for the comet to reach Earth.
Find the distance, in km, the comet travelled.
Answer:
39,144,000 km
Step-by-step explanation:
Hi there!
Distance traveled = time * speed
Given speed: 233000 km/h
Given time: 7 days
It's important to note that our speed is given in per hours and out time is given in days. So in order to find how far the comet has traveled we must convert days to hours.
There are 24 hours in 1 day.
So to convert days to hours simply multiply amount of days by 24
24 * 7 = 168
So the comet has traveled for 168 hours
Now we can find distance traveled
Once again distance traveled = time * speed
Given speed is 233000 km/h
Given time is 168 hours
Distance = 168 * 233000 = 39,144,000
So the comet has traveled for a total distance of 39,144,000 km