By working with fractions, we will see that the amount that Rollie borrowed from his sister is $31.50.
How much Rollie borrowed?Let's say that Rollie borrowed a quantity x.
The first month, Rollie returns one third of x + $3, so now he owes:
x - x/3 - 3 = (2/3)*x - 3
the second month returns another third of what he owes plus $3, so now he returns:
(1/3)*((2/3)*x - 3) + 3 = (2/9)*x + 2
So no he owes:
(2/3)*x - 3 - (2/9)*x - 2 = (4/9)*x - 5
Finally, on the third month he returns:
(1/3)*((4/9)*x - 5) + 3 = (4/27)*x - 5/3 + 3 = (4/27)*x + 4/3
Now he owes:
(4/9)*x - 5 - (4/27)*x - 4/3 = (8/27)*x - 19/3
And that is equal to $3, what he owes at the end of the third month, so we need to solve:
(8/27)*x - 19/3 = 3
(8/27)*x = 3 + 19/3 = 28/3
Solving for x, we get:
x = (27/8)*(28/3) = 31.5
So Rollie borrowed $31.5 from his sister.
If you want to learn more about fractions, you can read:
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Find the value of x.
91°
(7x)
Answer:
13
Step-by-step explanation:
This angle is called a reflective angle so the angles equal eachother. So put them equal to eachother and solve.
91=7x
x= 91÷7
x=13
circle theorem - find x - 2 lines are tangent to a circle
Answer:
B. 140
just do an elimination process to figure out 160 is more wider and 90 is just too small
so it was between 100 and 140
Danny’s supermarket has 1 litter water bottles normally priced at $1.50 reduced 25%
Marta’s supermarket has bottles of water still priced at $1.50 but offer 25% bigger bottle.
Which supermarket has the best buy?
Answer: Danny's supermarket
Step-by-step explanation:
Danny's price- 0.75x1.5= $1.12 for 1 liter water bottle
Marta's price- $1.50 for 1.25 liter water bottle
1.12x1.25=1.40, if Danny was selling a 25% bigger bottle(making the bottle size equal to Marta's) it would cost $1.40, the lower price
What is the answer to this?
Answer:
A ~ 34.63201
Step-by-step explanation:
I need help!
I need a answer quick!
Answer:
Step-by-step explanation:
1 1/4-2/3= 1 3/12-8/12= 15/12-8/12=7/12
7/12 simplified to 7/12
Answer:
kayla sold 7/12. Kayla sold less than Ethan
please answer I'll mark brainliest
Answer:
126.96
Step-by-step explanation:
Written as a simplified polynomial in standard form, what is the result when (x-2)^2(x−2) 2 is subtracted from 8x8x?
Answer: apply the distributive property to factor out the greatest cmoon factor of alll three terms
Step-by-step explanation: apply the distributive property to factor out the greatest cmoon factor of alll three terms
A line passes through the point (-8,6) and has a slope of -5/4
Write an equation in point-slope form for this line
Answer:
y = 5/4x + 6
Step-by-step explanation:
take the y coordinate in (-8,6) which is 6.
take the slope.
y = (put slope here)x + (put y coordinate here) !
thats it :) have a good day!
Mark said, "in the data set,4, 5, 5, 8, the mean and mode the same. " Is he correct? Explain why or why not in your explanation make sure to state the value of the the means and the mode
Answer:
No
Step-by-step explanation:
the mean is 16 (add 4+5+5+8, then divide answer by 4) and the mode is 5 (occurs most in data)
I NEED HELP PLEASE... HELPPPP MEEEE
Write a quadratic equation to represent each situation. Use your equation to answer each question. Be sure to define your variables and identify which is independent and which is dependent. Show all work. Round any decimals to the nearest hundredth.
1. A rocket is launched from a height of 10 meters with an upward velocity of 56 meters per second.
a. When will the rocket hit the ground?
b. What is the maximum height of the rocket?
c. After how many seconds does the rocket reach the maximum height?
2. A wooden deck of uniform width surrounds a rectangular pool as shown in the following image. The pool is 10 feet by 14 feet. What is the area of the wooden deck that surrounds the pool (not including the pool)?
a. If the deck is 3 feet wide, what is the area of the deck?
b. The area of the deck is 112 square feet. How wide is the deck?
3. A coffee shop sells 150 coffees a day at $3.50 apiece. They found for every $0.50 increase in price, they sell 10 fewer cups of coffee a day. The cups of coffee cost the shop $1.50 apiece.
a. How much should they charge to maximize their daily profits?
b. How many cups of coffee will they sell daily at that price?
c. What will their daily profits be?
Answer:
56. In the Vector Addition Lab, Anna starts at the classroom door and walks:
2.0 meters, West
12.0 meters, North,
31.0 meters, West,
8.0 meters, South
3.0 meters, East
Using either a scaled diagram or a calculator, determine the magnitude and direction of Anna's resulting displacement.
Answer: 30.3 meters, 172 degrees
To insure the most accurate solution, this problem is best solved using a calculator and trigonometric principles. The first step is to determine the sum of all the horizontal (east-west) displacements and the sum of all the vertical (north-south) displacements.
Horizontal: 2.0 meters, West + 31.0 meters, West + 3.0 meters, East = 30.0 meters, West
Vertical: 12.0 meters, North + 8.0 meters, South = 4.0 meters, North
The series of five displacements is equivalent to two displacements of 30 meters, West and 4 meters, North. The resultant of these two displacements can be found using the Pythagorean theorem (for the magnitude) and the tangent function (for the direction). A non-scaled sketch is useful for visualizing the situation.
Applying the Pythagorean theorem leads to the magnitude of the resultant (R).
R2 = (30.0 m)2 + (4.0 m)2 = 916 m2
R = Sqrt(916 m2)
R = 30.3 meters
The angle theta in the diagram above can be found using the tangent function.
tangent(theta) = opposite/adjacent = (4.0 m) / (30.0 m)
tangent(theta) = 0.1333
theta = invtan(0.1333)
theta = 7.59 degrees
This angle theta is the angle between west and the resultant. Directions of vectors are expressed as the counterclockwise angle of rotation relative to east. So the direction is 7.59 degrees short of 180 degrees. That is, the direction is ~172 degrees.
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57. In a grocery store, a shopper walks 36.7 feet down an aisle. She then turns left and walks 17.0 feet straight ahead. Finally, she turns right and walks 8.2 feet to a final destination. (a) Determine the magnitude of the overall displacement. (b) Determine the direction of the displacement vector relative to the original line of motion.
Answer: (a) 48.0 feet; (b) 21 degrees from the original line of motion
This problem is best approached using a diagram of the physical situation. The three displacements are shown in the diagram below on the left. Since the three displacements could be done in any order without effecting the resulting displacement, these three legs of the trip are conveniently rearranged in the diagram below on the right.
Now it is obvious from the diagram on the right that the three displacement vectors are equivalent to two perpendicular displacement vectors of 44.9 feet and 17 feet. These two vectors can be added together and the resultant can be drawn from the starting location to the final location. A sketch is shown below.
Since these displacement vectors are at right angles to each other, the magnitude of the resultant can be determined using the Pythagorean theorem. The work is shown below.
R2 = (44.9 ft)2 + (17.0 ft)2 = 2305 ft2
R = Sqrt(2305 ft2)
R = 48.0 feet
The angle theta in the diagram above can be found using the tangent function.
tangent(theta) = opposite/adjacent = (17.0 ft) / (44.9 ft)
tangent(theta) = 0.3786
theta = invtan(0.3786)
theta = 20.7 degrees
This is the angle which the resultant makes with the original line of motion (the 36.7 ft displacement vector).
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Vector Addition || Vector Components || Vector Resolution
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58. A hiker hikes 12.4 km, south. The hiker then makes a turn towards the southeast and finishes at the final destination. The overall displacement of the two-legged trip is 19.7 km at 309 degrees . Determine the magnitude and direction of the second leg of the trip.
Answer: 12.7 km, 347 degrees
Like the previous problem (and most other problems in physics), this problem is best approached using a diagram. The first displacement is due South and the resulting displacement (at 309 degrees) is somewhere in the fourth quadrant. (It is in the fourth quadrant because 309 degrees lies between 270 degrees or due South and 360 degrees or due East.) For communication sake, we will refer to the first displacement as A and the second displacement as B. Note that A + B = R. Since the magnitude and direction of the resultant is known, the x- and y-components can be determined using trigonometric functions. Since the angle of 309 degrees is expressed as a counterclockwise angle of rotation with due East, it can be used as the Theta in the equation.
Rx = R•cos(theta) = 19.7 km • cos(309 deg) = 12.398 km
Ry = R•sin(theta) = 19.7 km • sin(309 deg) = -15.310 km (the "-" means South)
Whatever the magnitude and direction of B is, it must add on to vector A in order to give a southward displacement of 15.310 km and a eastward displacement of 12.398 km. This could be expressed by mathematical equations as
A survey conducted in 2008 found that ______% of full-time college students surveyed were current drinkers of alcohol.
A survey conducted in 2008 found that 46% of full-time college students surveyed were current drinkers of alcohol.
What is survey?Survey can be defined as data or information collected from a population so as to draw or reach a conclusion.
Based on the survey that was carried out by the researcher in the year 2008 for full time college student the survey shows that 46% of the student consume alcohol.
Therefore 46% of full time college student are drinkers of alcohol.
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can someone simplify this?? ty!
-(x-8)²+4
Answer:
-x² + 16x - 60
Step-by-step explanation:
Given expression:
-(x - 8)² + 4Step 1. Insert brackets to isolate the "-" from the (x - 8)².
⇒ -(x - 8)² + 4
⇒ -[(x - 8)²] + 4
Step 2. Use the formula (a - b)² = a² - 2ab + b²
⇒ -[(x - 8)²] + 4
⇒ -[x² - 2(x)(8) + 8²] + 4
Step 3. Open the parenthesis
⇒ -[x² - 2(x)(8) + 8²] + 4
⇒ -x² + 2(x)(8) - 8² + 4
Step 4. Simplify as needed
⇒ -x² + 16(x) - 64 + 4
⇒ -x² + 16x - 60
Will give brainlest and 50 points. thanks!
Answer:
A 5(0.5)^x
B 3(2)^x
C 5(3)^x
D 8(1.25)^x
E 8(0.75)^x
F 10(0.5)^x
Step-by-step explanation:
A 5(0.5)^x
(-1,10) goes by 1/2
B 3(2)^x doubles
C 5(3)^x triples
D 8(1.25)^x * 1 1/4
E 8(0.75)^x by 3/4
F 10(0.5)^x x 1/2
For which interval is the average rate of change of f(x) negative?
The interval at which the average rate of change of f(x) is negative is from x = 0 to x = 2.5.
What is the average rate of change?The average rate of change is a type of function that describes the average rate at which a quanity decreases or increases with respect to another quanity.
Generally, for a function with a negative average rate of change, the graph must face down and have a negative slope.
Based on the graph shown in the image attached below, we can deduce that the interval for which the average rate of change of f(x) is negative is from x = 0 to x = 2.5.
Read more on functions here: https://brainly.com/question/4246058
quick?
Graph the circle with center (−1, 2) that passes through (−6, 2). Find the area in terms of π and to the nearest tenth. Use 3.14 for π.
Answer:
The area is 78.5.
Step-by-step explanation:
The formula for the area of a circle is π r^2
In this case, r = 5.
I've tried everything
Answer:
14,200 pounds.
1. Convert the mixed fraction into improper fraction:
To convert a mixed fraction into an improper fraction, we must multiply the whole number with the denominator and add the numerator to the product. The denominator of the improper fraction will remain the same as the denominator in the mixed fraction.
[tex]\implies 7 \dfrac{1}{10} = \dfrac{(7 \times 10) + 1}{10} = \dfrac{71}{10}[/tex]
2. Determine the number of pounds in 71/10 tons
It should be noted that:
Conversion: 1 ton = 2000 poundsNow, let's use the unitary method to determine the amount of pounds in 71/10 tons. Multiply both sides by 71/10 to do so.
[tex]\implies \text{1 ton = 2000 pounds}[/tex]
[tex]\implies \text{1 ton} \times \dfrac{71}{10} = 2000 \times \dfrac{71}{10}[/tex]
[tex]\implies \dfrac{71}{10}\text{ ton} = 200 \times 71[/tex]
Simplify as needed:
[tex]\implies \dfrac{71}{10}\text{ ton} = 14,200 \ \text{pounds}[/tex]
what is the mean of 45,40,47, 50,45,49, 40,46
Answer: 45.25
Step-by-step explanation: Add all the digits together and divide by 8
Mean is the average
Answer:
45.25
Step-by-step explanation:
The mean is the average. Add up all of the values (45+40+47+50+45+49+40+46). This is equal to 362. The amount of values in the set is 8. Divide 362 by 8 to get the mean of 45.25.
Mr Lok is putting a pool in his backyard. His backyard is 10 m long and 8 m wide, while the pool he wants has an area of 8m2. how much grass will be left in his backyard?
Answer:
hope this helps and make me brainliest
Step-by-step explanation:
. You have that:
- The homeowner want the length of the swimming pool to be 4 feet longer than its width.
- He wants to surround it with a concrete walkway 3 feet wide.
- He can only afford 300 square feet of concrete for the walkway.
2. Therefore, the tota area is:
At=L2xW2
L2 is the lenght of the walkway (L2=L1+3+3⇒L2=(W1+4+6)⇒L2=W1+10).
W2 is the width of the walkway (W1+3+3⇒W2=W1+6)
3. The area of the walkway is:
A2=At-A1
A2=300 ft²
4. Therefore, you have that the width of the swimming pool is:
A2=(W1+10)(W1+6)-(W1+4)(W1)
300=(W1²+6W1+10W1+60)-(W1²+4W1)
W1²+16W1+60-W1²-4W1-300=0
12W1-240=0
W1=240/12
W1=20 ft
5. And the length is:
L1=W1+4
L1=20+4
L1=24 ft
What is the y-intercept of the line 4y + 7 = 2x – 5
Answer:
the answer is -3
Step-by-step explanation:
Given that 1 centimeter is approximately 0.4 inches, how many inches
are in 58 centimeters?
Round your answer to the nearest tenth.
Answer:
Hello,
To find amount of inches in 58 centimeters, you need to use the information given.
0.4 inches = 1 centimeter
??? inches = 58 centimeter
58 x 0.4
= 23.20
Hence your answer is 23.2 inches are in 58 centimeters
Hope this helps ^^
Alexis put $2000 in a savings account. After 4 years, she had $2543 in the
account. What rate of interest did she earn? Use the formula A = Pert, where A
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2543\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]2543=2000e^{\frac{r}{100}\cdot 4}\implies \cfrac{2543}{2000}=e^{\frac{r}{25}}\implies \log_e\left( \cfrac{2543}{2000}\right)=\log_e\left( e^{\frac{r}{25}} \right) \\\\\\ \ln\left( \cfrac{2543}{2000}\right)=\cfrac{r}{25}\implies 25\ln\left( \cfrac{2543}{2000}\right)=r\implies 6\approx r[/tex]
A company claims that 9% of the items produced on a new machine are defective.
The factory will get rid of the machine if the data indicates that the proportion of defective items is more than 9%.
They take a random sample of 300 items and 50 are defective.
What null hypothesis is appropriate?
Considering the situation described, the appropriate null hypothesis is given by:
[tex]H_0: p = 0.09[/tex]
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is the expected one, that is, of 9%, hence:
[tex]H_0: p = 0.09[/tex]
At the alternative hypothesis, it is tested if there is enough evidence to conclude that the proportion is above 9%, hence:
[tex]H_1: p > 0.1[/tex].
More can be learned about an hypothesis test at https://brainly.com/question/26454209
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Sasha ordered a kite online. When it arrived the kite was missing the crossbar. What length crossbar does Sasha need to complete the kite?
4 in. 4 in.
crossbar
Answer:
[tex]\sqrt32} inches[/tex]
Step-by-step explanation:
The crossbar and two given lengths form a right triangle. We know this because we see a right angle marked on the diagram in between the two given sides.
-1/3-4/9 i don't know how to subtract fractions
Answer: -7/9
Step-by-step explanation: Get the LCM of the denominator 3 and 9
Place both fractions using same LCM
You will have - 3/9 -4/9 = -7/9
Because they both have negative signs, you will add 3 and 4
Determine the slope of the line that passes through the points (9,-3) and (-9,-6)?
Answer:
slope = 1/6
all steps in picture. :)
Slope:-
m=-6+3/-9-9m=-3/-18m=1/6What is the answer for this?
Answer:
I'm not so sure but I know that you have to multiply all the numbers... so that should be 689.04
Step-by-step explanation:
I hope that helped
please help me solve this
Answer:
solve by using pythagoras theorem then
square on both side
A man increased the amount of protein she eats every day from 48G to 54G by what percentage to Amanda increase the amount of protein she eats
Answer: 12.5%
Step-by-step explanation:
Increase is 54-48 = 6
6/48 × 100/ 1
600/48
i can't figure this out
Answer:
the answer would be -110(c⁴d²e³)
Hope this helps!
What is the perimeter of the triangle?
units
to calculate perimeter of triangle use a+b+c
hope it helps...!!!