It will take 11 years for the investment to exceed £7000 if £5200 is invested over a year at a compound interest rate of 2.8%.
What is meant by compound interest?The addition of interest to the principal of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. It occurs when interest is reinvested, added to the lent capital instead of being paid out, or the borrower is required to pay it, resulting in the next period's interest being generated on the principal amount plus any accumulated interest.
In contrast to simple interest, which does not compound since past interest is not added to the current period's principal, compound interest allows for the accumulation of interest from prior periods.
We solve this problem by using compound interest.
Given,
£5200 is invested over a year at a compound interest rate of 2.8%.
£7000. 1.028 = 5 200 x 5200 × 1.028¹¹ = 7045.76 2.
So, number of years=11
Therefore, It will take 11 years for the investment to exceed £7000.
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Solve |x-5| + 7 = 15.
Answer:
C. x = 13 or x = -3
Step-by-step explanation:
|x - 5| + 7 = 15
|x - 5| = 8
x - 5 = 8 or x - 5 = -8
x = 13 or x = -3
Answer: C. x = 13 or x = -3
Find the equation of the line, given the following information:
Passes through (-9,3) and is perpendicular to y =1/2x+6.
Answer:
y = -2x - 15
Step-by-step explanation:
We are given 2 pieces of information: (1) a point our line passes through, and (2) a line it is perpendicular to. The only thing we need from (2) is the slope.
We know that perpendicular lines have opposite signs and are inverses (denominator and numerator switched). So our line must have a slope of
m = -2
Using our equation for a line: y = mx+b, our line so far is
(I) y = -2x + b
Let's use the point we have (-9,3) and substitute what we know into equation (I) to find b.
x = -9
y = 3
(I) (3) = -2(-9) + b
3 = 18+b
b= -15
Now we have m and b so we can write the equation of our line:
y = -2x - 15
2. What is the x-coordinate of the image of point (2,-5) after reflection in the
line y=x?
The X coordinate of the image is (-5,2)
What is meant by coordinate ?A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
The coordinates of one point in the coordinate system are included in an ordered pair. An ordered pair of the form of a point's name is (x, y). The x-coordinate is represented by the first integer, and the y-coordinate by the second. You must place a dot at the coordinates of the ordered pair in order to graph a point.
Given
The coordinates for x and y change when you consider the line y=x. The end product is (-5,2)
Because (-5,2) its reflection means x coordinate will y coordinate and y coordinate will x coordinate so the coordinate be (-5,2)
The complete question is : Find the coordinates of the image of point (2,-5) after a reflection in the line y=x
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Three sons inherited 2,179 ducats from their father. The father bequeathed the older brother 2 times more money than the younger one. At the same time, the middle brother should receive more than the younger one, but less than the older one. How many ways are there to fulfill the will of the father, if each son must receive a whole number of ducats?
Three sons inherited 2,179 ducats from their father. The number of ways the father can bequeath the resources is
108 waysHow to find the number of ways of fulfilling the fathers wishInformation from the problem helped in generating the following equations
The father bequeathed the older brother 2 times more money than the younger one
let the youngest receive an amount equivalent to y
then the eldest will receive 2y
let the middle receive x
Using the sharing formula described we have
y + 2y + x = 2179
3y + x = 2179
the middle brother should receive more than the younger one, but less than the older one
x > y
x < 2y
plotting the equations on a graphing calculator and getting the solutions we have
(544.75, 544.75) and (871.6, 435.8)
y ranges from 435.8 to 544.75 using whole numbers
436 to 544
The number of ways
= 544 - 436
= 108 ways
the number of ways of sharing according to fathers will is 108
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work out the surface area of this cylinder
Answer:207.24 and 483.56
Step-by-step explanation:
The formula for the surface area of a cylinder is:
A=2πrh+2πr2
Meaning that we only have to plug the values in.
2π(3)(8)+2π(3)²
=48π+18π
=66π
=66(3.14)
=207.24
Second Cylinder:
2π(7)(4)+2π(7)²
=56π+98π
=154π
=154(3.14)
=483.56
What are each step of the formula for a area of a trapezoid to find b2.
Answer:
Step-by-step explanation:
Explanation: To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.
Which of the following statements is true about similar triangles? *
A. The measurements of corresponding angles differ between the two triangles.
B. Their corresponding angles are congruent, and the corresponding sides are proportional.
C. If two triangles are similar, both their corresponding sides and angles are always congruent.
Two triangles are similar when their corresponding angles are congruent, and the corresponding sides are proportional. Hence, option C s the most appropriate answer to the given question.
When we are given triangles, we can prove that two triangles are similar to the given conditions by applying various tests of similarity.
Similar triangles are triangles that have the same shape, but they may have different sizes.
Hence, to prove them to be similar, we have to prove the corresponding angles are congruent and the corresponding sides are proportional. Hence, option C is the only right choice for the given question.
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PLEASE HURRY! Jacob is saving to buy an electronic tablet that costs $380 including tax and has saved $150. Jared plans to earn the rest of the money by mowing lawns and will charge $12 for each lawn he mows.
Write an inequality to find x, the minimum number of lawns Jacob will need to mow in order to buy the ticket.
Show how to solve the inequality and explain what the solution means.
Answer:
To find the minimum number of lawns Jacob will need to mow, we can set up the following inequality:
12x + 150 >= 380
To solve this inequality, we need to get x by itself on one side of the inequality. We can do this by subtracting 150 from both sides of the inequality:
12x >= 230
Then, we can divide both sides of the inequality by 12 to get the value of x:
x >= 19.17
Since x represents the number of lawns Jacob needs to mow, it must be an integer. Therefore, the minimum number of lawns Jacob will need to mow is 20.
This means that Jacob needs to mow at least 20 lawns in order to earn enough money to buy the electronic tablet. If he mows more than 20 lawns, he will have more than enough money to buy the tablet.
what are the hypothesis and the conclusion of the conditional? if anangle measures 130, then the angle is obtuse
The hypothesis of the conditional statement is "if an angle measures 130 degrees," and the conclusion is "the angle is obtuse."
A conditional statement is a statement in the form "if X, then Y," where X is the hypothesis and Y is the conclusion. In this case, the hypothesis is that the angle measures 130 degrees, and the conclusion is that the angle is obtuse.
An angle is obtuse if it measures more than 90 degrees but less than 180 degrees. Since 130 degrees is greater than 90 degrees but less than 180 degrees, the conclusion that the angle is obtuse follows logically from the hypothesis that the angle measures 130 degrees.
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Write an equation of the line that passes through the given points (-6,2) (1,0)
Answer:
Y= (-2/7)x + (2/7)
Step-by-step explanation:
0-2= -2
1-(-6)= 7
-2/7= -2/7. (slope)
y=mx+b
2=( -2/7)(-6)+b
2= 12/7 +b
2/7 =B
so Y= (-2/7) + (2/7)
I also plugged in the answer to make sure it matches up.
Use the graph to find the slope and write the equation of the line.
Answer:
The slope of the line is = 3/2
Answer:
Equation in Point Slope Form: y= 3/2x - 3
Step-by-step explanation:
Point slope form is y=mx+b
where m is the slope of the line (rise over run) which in this case is 3/2
b is the y intercept (where the line crosses the y axis) which in this case is at point (0,-3)
Melia get paid $40 for mowing her neighbor' lawn. She pend $16 on a bracelet and $7 on lunch. Which equation i written and olved correctly to how how much money (m) Melia ha left?
The equation written is m + 16 + 7 = 40 and the amount of money Melis has left is $17.
As mentioned, assuming the amount of money left be m. Sum of left money and spent money will be equal to earned amount of money. Representing this as equation -
m + 16 + 7 = 40
Performing addition on Left Hand Side of the equation
m + 23 = 40
Rewriting the equation
m = 40 - 23
Performing subtraction on Right Hand Side of the equation
m = 17
Thus, Melia is left with $17 from her earnings.
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Someone needs help with my homework, help me! Can you fill in the blinks of Angle chase?
Answer:
Solution in picture.
Step-by-step explanation:
A triangle has three angles which adds up to 180°.
First do the easy ones such as 90°. Then the Triangle. Then the vertical angles. Then the two angles of supplementary angles which adds up to 180°. Etc.
Q(2, -4), R(-6, -8), S(-10, 2), T(-2, 6)
The Least Common Multiplier of [tex]$q(2-4), r(-6-8), s(-102), t(-26)$[/tex] is [tex]$-9282 q r s t$[/tex].
What is Least Common Multiplier ?
The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.
Lowest Common Multiplier (LCM)
The LCM of a, b is the smallest multiplier that is divisible by both a and b
Factor [tex]$q(2-4): \quad-2 q$[/tex]
Factor [tex]$r(-6-8): \quad-2 \cdot 7 r$[/tex]
Factor [tex]$s(-102): \quad-17 \cdot 2 \cdot 3 s$[/tex]
Factor [tex]$t(-26): \quad-13 \cdot 2 t$[/tex]
Multiply each factor with the highest power:
[tex]$$-13 \cdot 17 \cdot 2 \cdot 3 \cdot 7 \cdot q \cdot r \cdot s \cdot t$$[/tex]
Simplify
[tex]$-9282 q r s t$[/tex]
Complete question: Find the Least Common Multiplier of Q(2, -4), R(-6, -8), S(-10, 2), T(-2, 6) is:
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Identify the measure of angle x please show work Bc I have too
Answer:
79°
Step-by-step explanation:
Angles on a line add to [tex]180^{\circ}[/tex].
[tex]28+x+73=180 \\ \\ 101+x=180 \\ \\ x=79[/tex]
Please help me on this someone.
Ariel is correct, the statement is false and the equation has no solutions.
Is Ariel correct or not?Ariel says that the given linear equation has no solutions, so we need to check that.
The linear equation is:
3y - 12 = 3*(y + 1)
If we expand the right side we will get:
3y - 12 = 3y + 3
Now we can subtract 3y in both sides, then we will get:
3y - 12 - 3y = 3y + 3 - 3y
-12 = 3
That is a false equation, thus there are no values of y such that the equation is true, then we don't have any solutions.
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June wah the window for two hour and 45 minute he finihed wahing window at 3:05 p. M. What time did he finih wahing window
June started washing the window at 12:20 PM.
June washed the window for 2 Hours and 45 minutes.
As he finished washing the window at 3:05 PM
For calculating at what time did he start washing the window we need to subtract the time taken in cleaning the window from the time at which he finished washing.
As, for finding the starting time, we need to subtract 2 Hr. and 45 minutes from 3:05 PM.
As, 3:05 PM can be also written as 5 minutes post 3 which will be equivalent to (60+5) = 65 minutes post 2. (As there are 60 minutes in 1 Hr).
Now, 45 minutes before 2:65 minutes will be 2:20
Again 2 Hr. before 2:20 PM will be 12:20 PM.
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The correct question may be
June washed the window for two hours and 45 minutes he finished washing the window at 3:05 P. M. What time did he start washing the window?
Which of the following is the solutionsto | x +11|< 17?
OA. x< 6 and x < -28
OB. x< 6 orx>-28
OC. x<6
OD. x< 6 and x > -28
Answer:
OB
Step-by-step explanation:
|x+11|<17
x+11<17
x<17-11
x<6
-(x+11)<17
-x-11<17
-x<17+11
-x<28\×(-)
x>-28
A motorboat is capable of traveling at a speed of 10 miles per hour in still water. On a particular day, it took 15 minutes longer to travel a distance of 6 miles upstream than it took to travel the same distance downstream. What was the rate of current in the stream on that day?
The rate of current in the stream on that day is; 2 miles per hour
What is the rate of speed?
When dealing with relative velocity, we can say that;
When the motorboat travels downstream, then it means the total velocity will be;
Total velocity = Velocity of the motorboat in still water + Velocity of the stream.
If the motorboat travels upstream, the total velocity will be;
Total velocity = Velocity of the motorboat in still water - Velocity of the stream.
Thus,
Upstream speed = (14 mi/h - S)
Downstream speed = (14 mi/h + S)
Where;
S is the rate of current in the stream.
We are told that going downstream, it takes 15 minutes more to travel 12 miles, then we can write the system of equations as;
(14 mi/h + S)*T = 12 mi
(14 mi/h - S)*(T - 15 min) = 12 mi
Making T the subject in the first equation gives;
T = (12 mi)/(14 mi/h + S)
Plugging in (12 mi)/(14 mi/h + S) for T in the second equation gives;
(14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi
Multiply both sides by (14 mi/h + S) to get;
(14 mi/h - S)*12 mi - (14 mi/h + S)*(14 mi/h - S)*(- 15 min) = 12 mi*(14 mi/h + S)
Since the speeds are in miles per hours, we can rewrite as:
- 15 min = -0.25 h
(14 mi/h - S)*12 mi - (14 mi/h + S)*(14 mi/h - S)*(- 0.25 h) = 12 mi*(14 mi/h + S)
168 mi²/h - 12mi*S + 49mi²/h + 0.25h*S² = 168mi²/h + 12mi*S
- 12mi*S + 49mi²/h - 0.25h*S² = 12mi*S
-24mi*S - 0.25h*S² + 49mi²/h = 0
Solving this quadratic equation with online quadratic equation solver gives us; S = 2 mph
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tell me about the relationship between first floor square footage (1stflrsf; column o) and sale price. what is the r-squared?
The Pearson correlation coefficient (r) is used to discover styles in matters while the coefficient of determination (R²) is used to discover the electricity of a model.
R-Squared is a statistical degree of healthy that suggests how a good deal version of a established variable is defined through the unbiased variable(s) in a regression version.Interpretation of R-squared/Adjusted R-squared.
R-squared measures the goodness of healthy of a regression version. Hence, a better R-squared suggests the version is a great healthy even as a decrease R-squared suggests the version isn't an awesome healthy.
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Please help it’s ASAP
27 is the test score of percentile score of 71 and the score of victor is 71.
What is Statistics?Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.
Given, the teacher recorded unit 4 test scores from class.
The scores are: 5,4,66,70,71,75,77,80,84,85,87,90,93,95 and 96.
A percentile is a value on a scale of one hundred that indicates the percent of a distribution that is equal to or below it.
The percentile rank of a score of 71 on the test is find by formula
[tex]R_{100} =\frac{100(N < )+\frac{1}{2} N}{N_{t} }[/tex]
=100×4+1/2(1)/15
=400+0.5/15
=400.5/15
=26.7=27th
Now we need to find the score of victor who has 60 th percentile.
[tex]R_{100} =\frac{100(N < )+\frac{1}{2} N}{N_{t} }[/tex]
60=Score/15
score=71
Hence, the percentile score of 71 on this test score is 27 and the score of victor is 71.
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PLEASE HELP!!!!!! IT IS URGENT!!!
how to do question no 9 b?
Answer:
4 records sold on Wednesday, 32 records sold on Thursday!
Step-by-step explanation:
To do 9b, you need to set up our own equation!
Let's use W to represent records sold on Wednesday and T to represent records sold on Thursday.
It said 36 total records were sold on Wednesday and Thursday. This can be represented with the following equation ...
W + T = 36
It also tell us that on Thursday (T), 8 times the number of records sold on Wednesday were sold on Thursday. In equation form, this looks like ...
T = 8 × W
Now, let's use all this info to solve!
Let's first solve the equation W + T = 36
But, we need values! We have one! We know what T equals!
Let's plug in T
T = 8 × W
W + ( 8 × W ) = 36
Solve
W + 8W = 36
9W = 36
W = 4
4 records were sold on Wednesday!
Let's plug in W in our T equation to see how many records were sold on Thursday.
T = 8 × W
T = 8 × 4
T = 32
32 records were sold on Thursday!
Wednesday can be represented with HALF A CIRCLE
and Thursday can we represented with FOUR CIRCLES
What is the missing number?
Answer:
42
Step-by-step explanation:
You want to know the missing denominator in the equation ...
2/35 = 1/30 +1/x
SolutionSubtract 1/30 from both sides and simplify.
2/35 -1/30 = 1/x
(2·30 -1·35)/(35·30) = 1/x
25/(35·30) = 1/x
1/(7·6) = 1/42 = 1/x
The missing denominator is 42.
a card is draw from a standard deck of 52 playing cards find the probability the card is a jack or a heart
Answer:
4/13
Step-by-step explanation:
The question asking to find P(jack or heart)
You have to use the formula below:
P(A or B) = P(A) + P(B) - P(A and B)
Event A here is jack and event B is heart, now let's find the three probabilities on the right side to be able to find the left side.
P(jack) =4/52 because there are 4 jacks in a standard deck of cards
P(heart) =13/52 because there are 13 heart cards
P(jack and heart) =1/52 because there is only one jack card with a heart symbol
Now, plug in the three answers in the above formula:
P(jack or heart) = 4/52 + 13/52 - 1/52
this equal to 16/52
Last step, reduce the result by dividing the top and the bottom numbers by 4
The final answer is 4/13
calculate the double integral. 3x sin(x + y) da, r = 0, π 6 × 0, π 3 r
The value of the double integral ∫∫3x sin(x + y) dA, R = [0, π/6] × [0, π/3] is 0.677
In this question we need to calculate the double integral. 3x sin(x + y) dA, R = [0, π/6] × [0, π/3]
i.e., to find ∫∫3x sin(x + y) dA, R = [0, π/6] × [0, π/3]
First we integrate the function 3x sin(x+y) as a function of y, treating the variable x as a constant.
G(x) = ∫_[0, π/6] (3x sin(x+y)) dy
G(x) = 0.402 xcos(x) + (3x sin(x) / 2)
Now we calculate the integral of the previous result as a function of x.
i.e., ∫_[0, π/3] G(x) dx
= ∫_[0, π/3] [0.402 xcos(x) + (3x sin(x) / 2)] dx
= 0.677
Therefore, the solution to the double integral. 3x sin(x + y) da, r = [0, π/6] × [0, π/3] is 0.677
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At a bakery 5 bagels and 5 breakfast sandwiches cost $30.00 and 8 bagels and 2 breakfast sandwiches cost $24.00.
Create a graph of the scenario, using x to represent the cost of a bagel and y to represent the cost of a breakfast sandwich.
Select two points on each line to graph the lines.
it equals = kwasia
30-24=6
Angles 1 and 7 are what type of angles?
A. Same side interior angles
B. Alternate exterior angles
C. Alternate interior angles
D. Corresponding angles
Help Quickly Please!!!
Answer:
B. Alternate exterior angles
Step-by-step explanation:
Alternate exterior angles are the pair of angles on the outer side of the two parallel lines but on the opposite side of the transversal. They have the same degree. So the answer is B
A student correctly draws a square with side lengths of 4 centimeters. Which statement about the resulting figure is true?
A. The figure has three 45°
angles and exactly one pair of parallel sides.
B. The figure has three 90° angles and exactly one pair of parallel sides.
C. The figure has four 60°
angles and exactly two pairs of parallel sides.
D. The figure has four 90°
angles and exactly two pairs of parallel sides.
D) The figure has four 90° angles and exactly two pairs of parallel sides.
What is parallel sides?In geometry, parallel lines are two lines that exist in the same plane, are equally spaced apart, and never cross one another. There is a range of possible shapes, both horizontal and vertical.
Zebra crossings, stacks of notebooks, and the nearby railroad tracks are just a few places where parallel lines can be observed. The distance between two parallel lines at their perpendicular intersections is constant.
Different shapes' sides go parallel to one another. The single arrow lines in the rectangle below are parallel to one another, and the double arrow lines are also parallel to one another.
The symbol for parallel lines is ||, which consists of two vertical lines placed between the names of the lines.
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32. Write a rule to represents the
function
(2, 10), (4, 20), (5, 25), (7, 35), (9, 45)
y equals x times 5 is the answer because 2 times 5 is 10 and so on and so forth hope this helps :D
The bird population on an island is declining at a rate of 2. 2% per year. The population was 3500 in the year 2009. Which answer is the best prediction of the population in the year 2014? responses 2730 2730 3062 3062 3132 3132 3423.
The best prediction of the bird population in the year 2014 is 3132.
Explain the term population decline?The population mean could be determined by dividing the number of values with in given data/population by the sum of any and all values in the data/population.A decrease in the number of people in a population is known as a population drop in humans (sometimes referred to as underpopulation, population reduction, or population collapse).The given data is-
2009 : 3,500 populationRate of decline ; 2.2% per year. 100% - 2.2% = 97.8%Difference of the years;
2014 - 2009 = 5 years
Decline = 3,500 * (0.978)^5
Decline = 3,500 * 0.89473
Decline = 3131.57
Thus, the population of the birds in 2014 will be 3,131.57 ≈ 3,132.
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