Answer:
The total interest after 10 years is $10.
Step-by-step explanation:
Formula
[tex]Simple\ interest = \frac{Principle\times Rate\times Time}{100}[/tex]
As given
when the principal amount is $100, the annual simple interest rate is 1%, and the number of years is 10.
Principle = $100
Rate = 1%
Time = 10 years
Simple interest = T
Put in the formula
[tex]T = \frac{100\times 1\times 10}{100}[/tex]
[tex]T = \frac{1000}{100}[/tex]
T = $10
Therefore the total interest after 10 years is $10.
Final answer:
The equation for calculating the total interest T on a $100 principal at a 1% annual simple interest rate over 10 years is T = $100 x 0.01 x 10, which equals $10 of interest earned.
Explanation:
The equation representing the total interest, T, earned from a principal amount of $100 with an annual simple interest rate of 1% over 10 years can be calculated using the simple interest formula:
Interest (I) = Principal (P) × Rate (R) × Time (T)
Here, Principal (P) is $100, Rate (R) is 1% or 0.01 (when expressed as a decimal), and Time (T) is 10 years. So our equation will be:
T = $100 × 0.01 × 10
Now, we calculate the total interest:
T = $100 × 0.01 × 10 = $10
Thus, the total interest earned after 10 years will be $10.
Solve the system by substitution. Show your work. 4 pts 2) -2x - 3 y = -2 y = 2x + 6
Solve the system by elimination. Show your work. 4 pts
3) -x - 18 y = -3
7x - 9 y = 21
please help
I need this before midnight 12/19/2018
Answer:
2. x=-2 y= 2
3. x=3 y=0
Step-by-step explanation:
-2x - 3 y = -2
y = 2x + 6
The first step is to get x and y on the same side
Take the second equation and subtract 2x from each side
-2x+ y = 2x-2x + 6
-2x+y = 6
Multiply this by -1
-1(-2x+y) =-1*6
2x -y =-6
Add this to the first equation to eliminate x
-2x - 3 y = -2
2x -y =-6
--------------------
-4y = -8
Divide by -4
-4y/-4 = -8/-4
y =2
Now we need to find x
y = 2x + 6
Substituting in y=2
2 = 2x+6
Subtract 6 from each side
2-6 = 2x+6-6
-4 = 2x
Divide by 2
-4/2 = 2x/2
-2 =x
3) -x - 18 y = -3
7x - 9 y = 21
We will eliminate by by multiplying the second equation by -2
-2(7x - 9 y) = -2*21
-14x + 18y = -42
Now we will add this to the first equation
-x - 18 y = -3
-14x + 18y = -42
-------------------------
-15x = -45
Divide by -15
-15x/-15 = -45/-15
x =3
We still need to solve for y
-x -18y = -3
Substituting in x =3
-3 -18y = -3
Add 3 to each side
-3+3 -18y =-3+3
-18y =0
Divide by -18
y= 0
Sarah drove 40 miles per hour . In 3 hours sarah drove 120 miles . Which is a vaild proportion to represent the problem?
Answer:
Step-by-step explanation:
1/40=3/120
7) Days People 1 26 2 30 3 34 4 38 5 42 6 46 The chart shows how many people have signed up to go on a field trip each day. 62 students are allowed to go on the field trip. On which day would you expect that number to be reached? A) 8 B) 9 C) 10 D)
Answer:The answer is mostly C) 10
Step-by-step explanation:
It's C because when you go to day 9, you count after 58 by adding 4 more, which equals 62 and then, since day 10) is 68 people that means that the answer is C.
Answer: c 10
Step-by-step explanation:
Since each day 4 more people sign up, on day 7, 50 will have signed up; on day 8, 54 people; day 9, 58 people; and day 10, 62 people
1
8
of the boys at a high school tried out for the football team,
1
6
tried out for the baseball team, and
1
12
tried out for the football team and baseball team. What fraction of those who tried out for football also tried out for baseball?
Answer:
78
Step-by-step explanation:
112-18-16=78
Answer:
Correct answer is 2/3.
Step-by-step explanation:
How much will you save per lb, by buying the least expensive? Round to the nearest cent. 2.5 lbs for $8.75 or 3 pounds for $9.75.
Answer:
$0.25 per pound.
Step-by-step explanation:
Let us find unit rate for both quantities.
[tex]\text{Price per pound}=\frac{8.75\text{ dollars}}{2.5\text{ pound}}[/tex]
[tex]\text{Price per pound}=3.5\frac{\text{ dollars}}{\text{ pound}}[/tex]
Therefore, cost of per pound for first given rate is $3.5.
Now let us find unit rate for second quantity.
[tex]\text{Price per pound}=\frac{9.75\text{ dollars}}{3\text{ pound}}[/tex]
[tex]\text{Price per pound}=3.25\frac{\text{ dollars}}{\text{ pound}}[/tex]
We can see that price for second quantity is less than 1st. To find the savings per pound we will subtract 3.25 from 3.5.
[tex]\text{Savings per pound}=3.50-3.25[/tex]
[tex]\text{Savings per pound}=0.25[/tex]
Therefore, we will save $0.25 per pound by buying the least expensive.
Answer:
0.25
Step-by-step explanation:
If gasoline costs 2.14 per gallon and you drive 500 miles in a car that gets 30 mpg, what is the cost of gasoline
Answer:
35.7
Step-by-step explanation:
First, you would calculate how many gallons of gasoline the car gets. To do this, divide your total mileage of 500 miles by the mpg (30). Now you know how many gallons of gasoline will be used by the car. After calculating, you get 16.67. Multiply this by how much it costs per gallon of gasoline, and you get an answer of $35.7.
Anna wants to buy season passes to two theme parks. If one season pass costs $54.99 and Anna has $100 to spend on both passes, the second pass has to cost no more than what amount?
Answer:
54.01
If it’s an less than problem then
49.01<54.01<100
Step-by-step explanation:
100-54.99
= 54.01
98 points please help with math:
What is the equation of a line that is parallel to y=5/6x − 10 and passes through (12, 8) ?
Answer:
[tex] \displaystyle y _{ \text{parallel}} = \frac{5}{6} x- 2[/tex]
Step-by-step explanation:
we are given a equation of line
[tex] \displaystyle y = \frac{5}{6} x - 10[/tex]
we want to figure out the line Parallel to the given line and passes through (12,8)
to figure out the parallel line we need to figure out two things one is the Slope of the parallel line another is the y-intercept of the parallel line
figuring out the slope of the parallel line is easy because we know that parallel lines have the same slope therefore,
[tex] \displaystyle m _{ \text{parallel}} = \frac{5}{6} [/tex]
now we need to figure out the y-intercept and the equation to do so we can consider the following formula:
[tex] \displaystyle y - y_{1} = m(x - x_{1})[/tex]
we the point where the parallel line passes i.e [tex](x_1,y_1)=(12,8)[/tex] and we already got that the slope is ⅚ thus substitute:
[tex] \displaystyle y - 8= \frac{5}{6} (x- 12)[/tex]
we can figure out the equation by simplifying the above equation to slope-intercept form in order to do so
distribute:
[tex] \displaystyle y - 8= \frac{5}{6} x- \frac{5}{6} \times 12[/tex]
reduce fraction:
[tex] \displaystyle y - 8= \frac{5}{6} x- 5 \times 2[/tex]
simplify multiplication:
[tex] \displaystyle y - 8= \frac{5}{6} x- 10[/tex]
add 8 to both sides:
[tex] \displaystyle y = \frac{5}{6} x- 2[/tex]
and we are done!
As Jupiter revolves around the sun, it travels at a speed of approximately 8 miles per second. Convert this speed to miles per minute. At this speed, how many miles will Jupiter travel in 6 minutes? Do not round your answers.
speed: __ miles/minutes ?
distance traveled in 6 minutes: __ miles ?
Answer:
Thus; Jupiter travels at 480 miles/m and in 6 minutes, it will travel 2880 miles.
Step-by-step explanation:
First to convert it you need to multiply 8 miles per second by 60 seconds because there are 60 seconds in a minute:
8 miles x 60 s
1 second 1 min
The unit of seconds will cancel out so you will get 480 miles/ min
To get how far it travels in 6 min you need to multiply the speed by 6 minutes
480 miles x 6 min = 2880
1 min
The unit of minutes will cancel out to get 2880 miles
Which letter on the number line represents the solution to -2.5r = -20? A) Point P B) Point Q Eliminate C) Point R D) Point S
Answer:
Point R = 8
Step-by-step explanation:
-2.5 r = -20
The solution to this equation is represented by a number line
In the given equation we have only the variable 'r'
We will get the value of 'r' while solving the above equation
That 'r' value is the solution point R on number line
[tex]-2.5r = -20[/tex]
divide by -2.5 on both sides
[tex]r=\frac{-20}{-2.5}[/tex]
r= 8 is our solution
Select the equation which graphs to a vertical line at -3.
A) y=-3
B) x=-3
C) y=-3x
D) x=-3y
Answer: B) x = -3
Every point on this line has one thing in common: the x coordinate is -3. This is why x is fixed at -3, so we simply say the equation is x = -3
Some example points on this line are (-3,10) and (-3,2)
The y coordinate can be anything you want, so that is why it doesn't show up at all (because it doesn't affect how x will turn out).
HELPPP PLEASEEE!!! Find the perimeter of ΔTAP with vertices T(1, 4), A(4,4), and P(3,0) to the nearest tenth unit.
Answer: 11.6 units.
Step-by-step explanation:
1. Plot the points as you can see in the graph attached.
2. As you can see, the lenght TA is 3 units.
3. Apply the formula for calculate the distance between two points, to calculate the length TP and TA. The formula is:
[tex]d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
4. Therefore, you have:
[tex]TP=\sqrt{(1-3)^{2}+(4-0)^{2}}=4.47units[/tex]
[tex]AP=\sqrt{(4-3)^{2}+(4-0)^{2}}=4.12units[/tex]
5. The perimeter is the sum of the the lenght of each side, therefore:
[tex]Perimeter=3units+4.47units+4.12units\\Perimeter=11.59units[/tex]
6. To the nearest tenth unit:
[tex]Perimeter=11.6units[/tex]
Drew delivers packages in city.He makes 30$ for working an 8-hour day.He also makes $4.25 for each package he delivers. If X represents the number of packages he delivers, which equation describes his daily income?
Answer:
767
Step-by-step explanation:
What is the difference in height between an albatross flying at 100 m above the surface of the ocean and a shark swimming 30 m below surface? What is the distance between them if the shark is right below the albatross
Answer:
130 m
Step-by-step explanation:
Let surface of ocean be at 0 feet (sea level)
Albatross is 100 m ABOVE surface of ocean, andShark is 30 m BELOW the surface of oceanThe distance from albatross to surface is 100 and the distance from surface to shark is 30 m. The total distance between them is [tex]100+30=130[/tex]
Distance between shark and albatross is 130 m
Answer:
130 m
Step-by-step explanation:
Can someone please explain this question?
Answer:
The limit does not exist
Step-by-step explanation:
lim as we approach from below 7
x+5 when x=7
7+5
12
lim as we approach from above 7
5x-25 when x=7
5*7 -25
35-25
10
The limit does not exist since these numbers are not the same
Answer:
Limit [tex]7^{-}[/tex] (left hand side limit) is 12
Limit [tex]7^{+}[/tex] (right hand side limit) is 10
Limit at 7 DOES NOT EXIST
Step-by-step explanation:
Limit [tex]7^{-}[/tex] means the limit from left side of 7Limit [tex]7^{+}[/tex] means the limit from left side of 7Limit at 7 will exist and would be equal IF BOTH SIDE limits are EQUAL, or else LIMIT DOESN'T EXIST!Limit [tex]7^{-}[/tex]:
When we want to find limit of left side of 7, we take the first part of the function shown (since its defined for [tex]x\leq7[/tex]).
We check values very close to 7 but less than it:
checking 6.98: [tex]6.98+5=11.98[/tex]checking 6.99: [tex]6.99+5=11.99[/tex]So the limit is approaching 12.
Thus, left hand side limit is 12.
Limit [tex]7^{+}[/tex]:
When we want to find limit of right side of 7, we take the second part of the function shown (since its defined for [tex]x>7[/tex]).
We check values very close to 7 but greater than it:
checking 7.02: [tex]5(7.02)-25=10.1[/tex]checking 7.01: [tex]5(7.01)-25=10.05[/tex]So the limit is approaching 10.
Thus, right hand side limit is 10.
Limit at 7:
If both right hand side limit and left hand side limit equal, then the limit at that specific number exists and is equal to it.
Since we see that the left hand limit (12) and the right hand limit (10) ARE NOT EQUAL, so we conclude that the limit at 7 for the function given DOES NOT EXIST.
Amy paid ?$69.77 for a pair of running shoes during a 25 ?%-off sale. What was the regular? price?
Answer:
The regular price was $93.03
Step-by-step explanation:
In order to find the regular price, divide the amount spent by the percentage of which she paid for it. Since it was 25% off, she paid 75% of the overall price.
$69.77/75% = $93.03
A person who weighs 120 pounds on Earth weighs 20 pounds on the Moon. How much does a 93-pound person weigh on the Moon? A person who weighs 120 pounds on Earth weighs 20 pounds on the Moon. How much does a 93-pound person weigh on the Moon? Item 22 A person who weighs 120 pounds on Earth weighs 20 pounds on the Moon. How much does a 93-pound person weigh on the Moon?
The relationship between the weight of a person on Earth and the
person's weight on the Moon is a proportional relationship.
The weight of a 93 pounds person on the Moon is 15.5 pounds.Reasons:
The weight of the person on Earth = 120 pounds
Weight of the person on the Moon = 20 pounds
Required:
The weight of a person that weighs 93 pounds on Earth on the Moon
Solution:
Let x represent the factor (acceleration due to gravity) on Earth, let y
represent the factor on the Moon, and let m, represent the mass of the
person, we have;
x·m = 120
y·m = 20
Therefore;
[tex]\displaystyle \mathbf{\frac{x \cdot m}{y \cdot m}} = \mathrm{\frac{x}{y} } = \frac{120}{20} = 6[/tex]
For the person that weighs 93 pounds on Earth, we have;
[tex]\displaystyle \mathrm{\frac{x}{y} } = \mathbf{\frac{93}{Weight \ on \ the \ Moon}} = 6[/tex]
Which gives;
[tex]\displaystyle Weight \ of\ the \ person\ on \ the\ Moon = \frac{93}{6} = 15.5[/tex]
The weight of the person on the Moon = 15.5 pounds
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Solve the system of linear equations by substituting. Check your solution
I WILL MARK YOU BRAINLYEST
4# y=5x-7
-3x-2y=-12
5# -4x+y=6
-5x-y=21
6# -7x-2y=-13
x-2y=-13
A family purchased tickets for a concert. They paid a total of $90 for 7 adult tickets and 12 child tickets. The price of a child ticket was two-thirds the price of an adult ticket.How much was the price of an adult ticket
Answer: 7 + 2/3(12) = 15
90/15 = $6 for adult tickets
Write the quadratic equation in standard form for the following equations
(7,4);(-2,1);(1,9)
Answer:
[tex]y=-\frac{7}{18}x^2+\frac{41}{18}x+\frac{64}{9}[/tex]
Step-by-step explanation:
We need to write a quadratic equation so we can use standard quadratic equation:
[tex]y=ax^2+bx+c[/tex]
Plug the given points to get three equations.
for (7,4), we plug x=7 and y=4
[tex]4=a(7)^2+b(7)+c[/tex]
[tex]4=49a+7b+c[/tex] ...(i)
similarly using other two points, we get:
[tex]1=4a-2b+c[/tex] ...(ii)
[tex]9=a+b+c[/tex] ...(iii)
Now we solve those three equations by any method like substitution, or matrices or by any method and get:
[tex]a=-\frac{7}{18},\ b=\frac{41}{18},\ c=\frac{64}{9}[/tex]
Now plug these values into [tex]y=ax^2+bx+c[/tex], we get final equation as:
[tex]y=-\frac{7}{18}x^2+\frac{41}{18}x+\frac{64}{9}[/tex]
Simplify the expression 2+3i/4+3i
Please help
Answer:
17+6i
-----------
25
Step-by-step explanation:
2+3i
---------
4+3i
We want to multiply by the complex conjugate of the denominator
4+3i has a complex conjugate of 4-3i
2+3i 4-3i
--------- * --------------
4+3i 4-3i
Lets multiply the numerator
(2+3i) ( 4-3i)
2*4 +4*3i -3i*2 - 3i*3i =
8 +12i -6i - 9i^2
Remember i^2 = -1
8 +6i -9(-1)
17 +6i
Lets multiply the denominator
(4+3i) ( 4-3i)
4*4 +4*3i -3i*4 - 3i*3i =
16 +12i -12i - 9i^2
Remember i^2 = -1
16 -9(-1)
25
Putting numerator over denominator
17+6i
-----------
25
Shawn is coasting down a 500 cm long ramp on his inline skates. The wheels on his inline skates are 32 cm in circumference. How many rotations does each wheel make while Shawn is coasting down the ramp? Plz help
Answer:
16 rotations.
Step-by-step explanation:
We have been given that Shawn is coasting down a 500 cm long ramp on his inline skates. The wheels on his inline skates are 32 cm in circumference.
To find the number of rotations we will divide length of ramp by 32 as distance covered by wheels in one rotation will be equal to 32 cm.
[tex]\text{Number of rotations}=\frac{\text{Total distance}}{\text{Circumference of wheel}}[/tex]
[tex]\text{Number of rotations}=\frac{500}{32}[/tex]
[tex]\text{Number of rotations}=15.625\approx 16[/tex]
Therefore, each wheel must make 16 rotations while Shawn is coasting down the ramp.
Justing has 20 pencils, 25 erasers, and 40 paper clips. He organize them into groups with the same number of items and each group. All the items in. Group will be the same type. How many items can he put in each group?
Answer:
The answer is 17 items in 5 groups.
Step-by-step explanation:
If we have 20 pencils + 25 erasers + 40 paper clips; that´s a total of 85 items.
Then we just divide all the items into 5 groups so we can have the same amount of items in each group.
85 items ÷ 5 groups = 17 items each.
17 x 5 = 85.
Erica has 1 over 3 of a watermelon to share equally with 3 friends. How much will each person get
Answer:
1/9
Step-by-step explanation:
1/3 ÷ 3 is the set-up for the problem we are trying to solve.
Remember when we divide fractions we multiply by the reciprocal. So we have:
1/3 × 1/3 since the reciprocal of 3/1 is 1/3
Multiplying 1/3 x 1/3 we find the product is 1/9
Therefore, each person would receive 1/9 of the watermelon
It takes 28 minutes to play 8 songs on a radio.Every song is played for the same length of time.How does it take to play 1 song?Express your answer as a mixed number or a decimal
Answer:
you would divide 28 by 8 and get 3.5. so around 3:30 per song
Step-by-step explanation:
Answer:
Step-by-step explanation:28÷8=3.5 , each song is 3 and a half minutes long
What is an advantage that experimental probability has over theoretical probability?
a.
Experimental probability is more rigorously tested than theoretical probability.
b.
Experimental probability provides unique results, while theoretical probability only provides generic results which may not fit the situation.
c.
It is not always possible to calculate theoretical probability in complex situations, but experimental probability can be calculated any time experiments can be run.
d.
Experimental probability changes over time, while theoretical probability remains constant.
C. It is not always possible to calculate theoretical probability in complex situations, but experimental probability can be calculated any time experiments can be run.
The advantage of experimental probability over theoretical probability is that option C. It is not always possible to calculate theoretical probability in complex situations, but experimental probability can be calculated any time experiments can be run.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Experimental probability is the probability where the probability of something is found by real experiments.
This is not computed by assuming or calculation.
Theoretical probability is the probability where the probability of something is found theoretically.
The probability is found using formulas and calculation.
So, it is not always possible to calculate theoretical probability in complex situations.
But experimental probability can be found in any case using experiments.
Hence the correct option is C.
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Two polygons are similar. The perimeter of the larger polygon is 85 meters and the ratio of the corresponding side lengths is [tex]\frac{2}{5}[/tex]. Find the perimeter of the other polygon.
Suppose the polygons have 3 sides, [tex]s_1,s_2,s_3[/tex]. In the smaller polygon, the corresponding sides would have lengths [tex]\dfrac25s_1,\dfrac25s_2,\dfrac25s_3[/tex].
So if the perimeter of the larger polygon is
[tex]s_1+s_2+s_3=85[/tex]
then the perimeter of the smaller polygon would be
[tex]\dfrac25(s_1+s_2+s_3)=\dfrac25\cdot85[/tex]
so its perimeter would be 34 meters.
Final answer:
The perimeter of the smaller similar polygon is 34 meters, calculated by setting up and solving the proportion 2/5 = P/85.
Explanation:
When dealing with similar polygons, the ratio of their corresponding side lengths is the same as the ratio of their perimeters. Given that the ratio of the sides is 2 to 5, and the perimeter of the larger polygon is 85 meters, we can set up a proportion to find the perimeter of the smaller polygon.
Let the perimeter of the smaller polygon be P. The proportion will be 2/5 = P/85. To find P, we cross-multiply and get: 2 * 85 = 5 * P. Simplifying, we find that P equals 34 meters. Hence, the perimeter of the smaller polygon is 34 meters.
The parent function is f(x)=2^x−6+3 and the new function is g(x)=2^x − 3+2 .
How does the graph change from f(x) to g(x) ?
Select each correct answer.
The graph is shifted 3 units right.
The graph is shifted 1 unit up.
The graph is shifted 1 unit down.
The graph is shifted 3 units left.
Answer:
left 3 units
down 1 unit
Step-by-step explanation:
The required transformation is obtained by shifting of 3 units left and 1 unit down. The correct options are (c) and (d).
How to transform a graph of the function?The graph of a function can be transformed by either shifting it in the right, left, up or down.
When the transformation is rightwards, the function becomes as f(x - a).
The given functions are as below,
f(x) = [tex]2^{x - 6} + 3[/tex]
And, g(x) = [tex]2^{x - 3} + 2[/tex]
It can be rewritten as,
g(x) = [tex]2^{x - 3} + 2[/tex] = [tex]2^{x - 6 + 3} + 3 - 1[/tex]
It clearly shows as per the rule of transformation, f(x) is shifted 3 units left and 1 unit down to get g(x).
Hence, the parent function f(x) is shifted 3 units left and 1 unit down.
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(02.03)A bicyclist rides 14 miles in 112 minutes. If she continues at this speed, how long will it take her to travel 35 miles?
Answer:
280 minutes
Step-by-step explanation:
First, you must find the miles per minute:
112/14 = 8
Then you must multiply the miles per minute by the amount of miles:
35 * 8 = 280
Consider the functions. How do the graphs of these function compare to one another? (In picture)
Answer: True, False, True
Step-by-step explanation:
To determine steepness, compare the coefficients of each function:
f(x) = 4x² coefficient is: 4
g(x) = [tex]\dfrac{15}{4}x^2[/tex] coefficient is: 4.75
h(x) = [tex]\dfrac{4}{15}x^2[/tex] coefficient is: 0.27
f(x) ??? h(x)
4 > 0.27
f(x) is steeper than h(x)
h(x) ??? g(x)
0.27 < 4.75
h(x) is LESS steep than g(x)
g(x) ??? f(x)
4.75 > 4
g(x) is steeper than f(x)