Using the concept of percentages the total earning of Cara can be found to be $4200.
What are percentages?Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.
How to solve percentages?Cara's earning = commission + basic salary
basic salary = $1800 (this is constant)
commission = 6% of $40000
= (6/100)*40000
= $2400
Cara's earning = 1800 + 2400
Hence, her earning is $4200
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find the exact length of the curve. y = ln 1 − x2 , 0 ≤ x ≤ 1 6
The exact length of the curve: y = ln 1 − x^2 , 0 ≤ x ≤ 1 6 will be[tex]$$\int \frac{d x}{a^2-x^2}=\frac{1}{2 a} \ln \left|\frac{a+x}{a-x}\right|+c$$[/tex]
[tex]$$\begin{aligned}y & =\ln \left(1-x^2\right), \quad 0 \leq x \leq \frac{1}{6} \\\frac{d y}{d x} & =\frac{1}{1-x^2} \cdot \frac{d}{d x}\left(1-x^2\right) \quad\left\{\frac{d}{d u} \ln u=\frac{1}{u}\right\} . \\& =\frac{-2 x}{1-x^2}\end{aligned}$$[/tex]
Now, the length of the curve is given by
[tex]$$\begin{aligned}L & =\int_a^b \sqrt{1+\left(\frac{d y}{d x}\right)^2} d x \\& =\int_0^{1 / 6} \sqrt{1+\left(\frac{-2 x}{\left.1-x^2\right)^2}\right.} d x \\& =\int_0^{1 / 6} \frac{\sqrt{\left(1-x^2\right)^2+4 x^2}}{\left(1-x^2\right)} d x \\& =\int_0^{1 / 6} \frac{\sqrt{1+x^4-2 x^2+4 x^2}}{\left(1-x^2\right)} d x\end{aligned}$$[/tex]
[tex]=\int_0^{1 / 6} \frac{\sqrt{1+x^4+2 x^2}}{1-x^2} d x\\\\=\int_0^{1 / 6} \frac{\sqrt{\left(1+x^2\right)^2}}{1-x^2} d x\\\\=\int_0^{1 / 6} \frac{1+x^2}{1-x^2} d x[/tex]
Now, since the degree of Numerator & degree of Denominator are the same,
So, we will perform a long division process
[tex]$$\begin{aligned}& \therefore \frac{1+x^2}{1-x^2}=-1+\frac{2}{1-x^2} \quad\left\{\begin{array}{l}1-x^2 \frac{-1}{\frac{x^2+1}{x^2+1}} \\\frac{2}{2}\end{array}\right. \\& \therefore L=\int_0^{1 / 6}\left(-1+\frac{2}{1-x^2}\right) d x \\&\end{aligned}$$[/tex]
[tex]$$\begin{aligned}& =\left[-x+2 \cdot \frac{1}{(271} \ln \left|\frac{1+x}{1-x}\right|\right]_0^{1 / 6} \\& =\left(-\frac{1}{6}+\ln \left|\frac{1+1 / 6}{1-1 / 6}\right|\right)-\left(0+\ln \left|\frac{1+0}{1-0}\right|\right) \\& =-\frac{1}{6}+\ln \left(\frac{7 / 6}{5 / 6} \cdot-(0+0)\right.\end{aligned}$$[/tex]
[tex]L=\frac{-1}{6}+\ln \left(\frac{7}{5}\right)\\[/tex]
L=0.1698 approximately 0.17 units
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The picture below shows the Apollo spacecraft that took astronauts to the Moon in 1969. The spacecraft weighed 6.1 million pounds, and its motors produced 7.5 million pounds of thrust.
When the spacecraft returned to Earth, it slowed until a parachute could be opened for a landing at sea. Which of the following best explains how the spacecraft slowed down for a safe landing?
a
The parachute created a downward force to resist the downward force of gravity.
b
The parachute created an upward force to resist the upward force of gravity.
c
The parachute created an upward force to resist the downward force of gravity.
d
The parachute created a downward force to resist the upward force of gravity.
Since the spacecraft returned to planet Earth and slowed until a parachute could be opened for a landing at sea, a statement which best explains how the spacecraft slowed down for a safe landing is that: C. the parachute created an upward force to resist the downward force of gravity.
What is the force of gravity?In Mathematics, the force of gravity is also referred to weight and it can be defined as the force that is acting on a physical object or body, especially due to the effect of gravity.
What is Newton's Third Law of Motion?Newton's Third Law of Motion states that for every action there is an equal but opposite reaction. This ultimately implies that, in every interaction, there is a pair of forces acting on the two interacting objects such as between a spacecraft and a parachute.
In this context, we can reasonably infer and logically deduce that the parachute would create an upward force in order to resist the downward force of gravity that is acting on it, in accordance with Newton's Third Law of Motion.
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Evaluating Expressions with Exponents
What is the value of the expression 3^3 + 1 x 2
Answer:
29
Step-by-step explanation:
First, you will calculate 3 cubed, which is 27, and then multiply 1 and 2. That will result in 27+2 which will be 29
Find all points of intersections of the graphs of the equation
p(x)=(2x+3)(x-5)
Answer:
The equation intersects the x or y axis a total ot three times:
(-1.5,0), (5,0), and (-15,0).
Step-by-step explanation:
I will assume that the "all points of intersection" refers to the intersection of the line with the x and y axes. One can find those points by either a mathematical or graphing approach.
1) MathematicalWe and to find all points that have a zero for either the x or y coordinate: (0,y) and (x,0)
(x,0): Solve p(x)=(2x+3)(x-5) for p(x) = 0:
0=(2x+3)(x-5)
(2x+3)=0 and (x-5)=0
(2x+3)=0
2x=-3
x= - 1.5 (-1.5,0)
and
(x-5)=0
X=5 (5,0)
The two points marking the intersection with the x axis are (-1.5,0) and (5,0).
--
(0,y): Solve p(x)=(2x+3)(x-5) for p(x) for x=0:
p(x) = (2x+3)(x-5)
p(x) = (2*0+3)(0-5)
p(x) = (3)*(-5)
p(x) = -15 (-15,0)
The equation crosses the y axis at one point: (-15,0).
2. Graphing
See the attached graph. The points of intersection can be located, as shown. They match the values obtained mathematically, but a free graphing utility (DESMOS) makes graphing a pleasant chore.
Is this right please help
The complete solution will be;
Jeremy cannot find the cost by adding the percent's.
The 25% off of $60 is $45,
The 25% off of $60 and then subtracting 10% from the cost is $39.
The two total cost are not equal.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Jeremy bought a $60 pair of sneakers on sale for 15%.
And, Then he used a coupon for additional 10% off.
Now,
Let the cost of the sneakers = x
So, We can formulate;
⇒ x - 15% of x - 10% of x = 60
Solve for x as;
⇒ x - 15x/100 - 10x/100 = 60
⇒ x - 25x/100 = 60
⇒ x - x/4 = 60
⇒ 3x = 60 × 4
⇒ x = 80
Thus, The cost of the sneakers = $80
Now,
The 25% off of $60 is,
⇒ 60 - 25% of 60
⇒ 60 - 25 × 60 / 100
⇒ 60 - 15
⇒ $45
And, The 25% off of $60 and then subtracting 10% from the cost.
⇒ 60 - 25% of 60 - 10% of 60
⇒ 60 - 15 - 6
⇒ 45 - 6
⇒ $39
By adding both percent we get;
⇒ $45 + $39
⇒ $84
Thus, The complete solution will be;
''Jeremy cannot find the cost by adding the percent's.
The 25% off of $60 is $45,
The 25% off of $60 and then subtracting 10% from the cost is $39.
The two total cost are not equal.''
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How many different 9-letter strings can be made by rearranging the characters in the word "WISCONSIN"? O 9^6 O 9!/8 O C(9,6)O 9!O 9!/6
In the given word "WISCONSIN" there are exactly 9 letters, but some are repeated, so we can rearrage the letters in the word in 9!/8 ways.
What is permutation?When the order of the arrangements counts, a permutation is a mathematical approach that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems. Permutations are commonly mistaken with combinations, a different mathematical concept. The sequence in which the components are selected does not, however, affect combinations. In other words, whereas ab and be are equivalent in combinations, they are deemed to be distinct arrangements in permutations.
What is the formula for calculating the permutation?The formula for calculating the permutation is:
p(n,k) = n! /(n-k)!
where , n - Total number of elements in a set
k - Number of selected elements
In the above question , the number of ways to rearrange 9 letters would be 9! but, since there are 2Ss , 2Ns and 2Is so the number of ways to rearrange 9-letter strings will be:
9!/(2!*2!*2!) = 9!/8
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The latitude of any location on Earth is the angle formed by the two rays drawn from the center of Earth to the
location and to the equator. The ray through the location is the initial ray. Use 3960 miles as the radius of the Earth.
Suppose City A is due north of City B. Find the distance between City A (north latitude 45°28′ N) and City B (latitude
39°52' N).
The distance between City A (north latitude 45°28′ N) and City B (latitude 39°52' N) is 286 miles.
What is latitude?
Latitude is the measurement of distance north or south of the Equator. It is measured with 180 imaginary lines that form circles around Earth east-west, parallel to the Equator. These lines are known as parallels.
The measure of the central angel is 45°28' - 39°52' = 5.8'
8' = 8 ° / 60
= 0.133333
θ = 4° + 0.133333
= 4.133333° × [tex]\frac{\pi }{180}[/tex]
= 4.133333° × 0.017453
≈ 0.072140 radian
now , θ ≈ 0.072140 radian and r = 3960 miles
S = θ r
= 3960 × 0.072140
≈ 285.6744
S = 286 miles
Therefore, the distance between City A (north latitude 45°28′ N) and City B (latitude 39°52' N) is 286 miles.
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A point i reflected in the x-axi followed by the y-axi. The reflected point i (-3, "-4). " What i the original point?
When the original point is mirrored in the x-axis, it becomes (-3,4).
What is coordinate?The horizontal and vertical distances from the two reference axes are used to define the location of a point on a coordinate plane. The x-value and y-value are often denoted as (x,y). To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to determine the y-coordinate.
Here,
The reflected point= (-3,-4)
A point reflected in the x-axis followed by the y-axis,
=(-3,4)
The original point is (-3,4) when point reflected in the x-axis followed by the y-axis.
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help me with this problem
Answer:
I x I > 6
Step-by-step explanation:
a chi-square test of independence is used to evaluate the relationship between two variables. if one variable is classified into 3 categories and the other variable is classified into 3 categories, what is the df for the chi-square statistic?
The df would equal in the chi-square statistic for this test is found as 4.
Define the term chi-square statistic?The discrepancy between the predicted and observed frequencies of the results of a group of events as well as variables is measured by the chi-square (X²) statistic. Chi-square is helpful in examining these variations in category variables, particularly ones that are nominal in character.The formula for the chi-square (X²) statistic is;
(X²) = ∑(O - E)²/E
For the given question-
The link between two variables is being assessed using the chi-square test for independence. Three categories are assigned to the given "A." The second "B" is divided into three categories.The answer to the query is;
We would determine whether two qualities, A and B, under examination are independent or not using the chi-square test.
Taking that as a given, the null hypothesis H0: The two factors are unrelated.
Now, the degrees of freedom in the independence test using chi-square is,
v = (r-1) (s-1) (s-1).
r = 3 and s = 3.
The degree of freedom are;
ν = (r-1) (s-1) = (3-1) (3-1) = 2×4
ν = 4
Consequently, let test statistic be,
(X²) = ∑(O - E)²/E
Consequently, df would equal in the chi-square statistic for this test is found as 4.
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Find the equation of a line parallel to the line 2x + y -7 =0 and passing through the intersection of the lines x + y -4 = 0 and 2x – y = 8 .
With explanation
Can someone please help me
Answer: y = 2x - 8.
Step-by-step explanation:
To find the equation of a line parallel to the given line, we need to find the slope of that line. The slope of the line 2x + y - 7 = 0, this can be found by taking the coefficient of the x term and the y term and dividing them. In this case, the slope is 2/1 = 2.
Now that we know the slope of the line we want to find, we can use the slope-intercept form of the line, y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). Since the line we are looking for is parallel to the given line, it will have the same slope, so we can use the same value for m.
The line x + y - 4 = 0 and 2x – y = 8 intersect at the point (4,0). We can use this point to find the value of b in the equation y = 2x + b. Substituting the values from the intersection point, we get 0 = 2(4) + b, which simplifies to b = -8.
Therefore, the equation of the line that is parallel to the given line and passes through the intersection of the two lines is y = 2x - 8.
What value of x is in the solution set of the inequality –2(3x 2) > –8x 6? –6 –5 5 6
The value of x in the solution set of the inequality: - 2(3x+2) > -8x + 6 is x>5.
- 2(3x+2) > -8x + 6
Let's solve the inequality by isolating the variable x.
or, - 6x -4 > -8x + 6
Add 4 on both sides
or, - 6x - 4 + 4 > -8x + 6 + 4
or, -6x > -8x + 10
Add 8x on both sides
or, -6x + 8x > -8x +8x +10
or, 2x > 10
Divide both sides by 2
or, 2x/2 > 10/2
0r, x > 5
Hence, the value of x in the solution set of - 2(3x+2) > -8x + 6 is x>5.
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The complete question is :
What value of x is in the solution set of the inequality -2(3x+2) > -8x + 6?
Answer:
5
Step-by-step explanation:
For what values of a and b does √a + √b = √a+b?
Answer:
Isolate the radical, then raise each side of the equation to the power of its index a=0
Step-by-step explanation:
a + b is not identity
find the area of the region enclosed by the curves y = x and 4x + y2 = 12.
On integrating we will find that the area enclosed by the curves given is 64 / 3.
First we will plot a graph ,
The graph for x = y will be a straight line passing through the origin and the graph for 4x + y2 = 12 will be a parabola.
Integration of 4x + y2 = 12
= ∫4/2x² + y² dx = C
= 2x² + y² x - C
On putting the value of x and y we get ,
the area as 64 / 3.
In integration we generally add various parts to form one single object. It is a mathematical concept and comes under the branch of calculus.
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Check all of the correct names for the object pictured below.
Answer:
B
F
Step-by-step explanation:
this is vector, and its to be moving from point to a point through line , and you have a direction of it's move , so it will be from T to S ( magnitude) and the arrow is the direction <--
Please help!!!
Find measure QR.
Answer:
QR = 20
Step-by-step explanation:
You want the measure of side QR of isosceles triangle PQR with congruent sides PQ and QR marked 5x and 3x+8, respectively.
Congruent sidesThe sides of the isosceles triangle are congruent, so we have ...
PQ = QR
5x = 3x +8
2x = 8 . . . . . . . subtract 3x
x = 4 . . . . . . . divide by 2
QR = 3x +8 = 3(4) +8 = 20 . . . . . . find the length of QR
The measure of QR is 20 units.
__
Additional comment
You will recognize that the segment QS is both the altitude and median of the triangle. That means the triangle is isosceles, so symmetrical about QS.
If you need a formal proof, you can observe that QS is congruent to itself, so the two right triangles are congruent by LL (or SAS).
if a stratified random sampling procedure is used, give one example of an effective variable on which to stratify in this survey. explain your reasoning.
The kids' judgments of the significance of excellent nutrition in the food given may vary based on the students' ages and, consequently, on school level, making this variable an useful one to stratify the survey on.
what is random sampling?Each sample has an equal chance of being picked when using the random sampling sampling approach. It is intended that a sample picked at random will be a fair reflection of the entire population. Two different approaches to sampling exist: Random selection is a key component of probability sampling, which enables you to draw robust statistical conclusions about the entire group. Non-probability sampling incorporates non-random selection based on practicality or other factors, making it simple to gather data.
The student's degree of education is one potential stratification factor. Depending on the kids' ages and, thus, on their academic ability, the students' judgments of the significance of nutritious meals may vary. In contrast to middle school and high school pupils, elementary school children may place different values on the food that is offered.
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If m21 = 80°, then m22 is:
60°
80°
100°
None of these choices are correct.
In a series of transformations, which transformation would make two figures similar as opposed to congruent?
Dilation and rotation are the a series of transformations, which transformation would make two figures similar as opposed to congruent.
Rotations, reflections and translations are known as rigid transformations; this means they do not change the size or shape of a figure, they simply move it. These rigid transformations preserve congruence.
Rotations is defined as the motion of an object around a center or an axis.
Dilation, however, are not rigid transformations, since they change the size of a shape. Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation.
This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape. A dilation should either stretch or shrink the original shape.
This would give us a similar, but not congruent, figure.
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In a series of transformations, which transformation would make two figures similar as opposed to congruent?
A) Rotation and translation
B) Dilation and rotation
C) Reflection and rotation
D) Translation and reflection
At wrestling competitions, the wrestling mat is placed on a square that has an area of 1,444 square feet.
What is the length of one side of the square?
*URGENT*
The sin(theta) = -2/5, and theta lies in quadrant IV. Find the exact values of the sine and cosine of 2theta.
Answer:
To find the exact values of the sine and cosine of 2 theta, we can use the trigonometric identities that relate these functions to the sine and cosine of theta.Since theta lies in quadrant IV, we know that the cosine of theta is negative. We can use the identity cos(theta) = sin(pi/2 - theta) to find the sine of theta:sin(theta) = sin(pi/2 - theta)
= -sin(theta)Solving this equation for sin(theta), we find that sin(theta) = -2/5.To find the cosine of 2 theta, we can use the identity cos(2 theta) = 1 - 2sin^2(theta):cos(2 theta) = 1 - 2sin^2(theta)
= 1 - 2(-2/5)^2
= 1 + 8/25
= 9/25To find the sine of 2 theta, we can use the identity sin(2 theta) = 2sin(theta)cos(theta):sin(2 theta) = 2sin(theta)cos(theta)
= 2(-2/5)(-cos(theta))
= 4/5cos(theta)Thus, the exact values of the sine and cosine of 2 theta are sin(2 theta) = 4/5cos(theta) and cos(2 theta) = 9/25.
Step-by-step explanation:
Challenge Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the wire they need. Andy needs 23 feet of the wire. Emily needs 15 yards of the wire. How much will each of them spend for wire?
Andy spent $8.28 on 23 feet wire and Emily spent $16.2 on 15 yards wire.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
From the table, we have (110, 3.30) and (145, 4.35).
Here, slope (m)=(y2-y1)/(x2-x1)
m=(4.35-3.30)/(145-110)
= 1.05/35
= 0.03
Substitute, m=0.03 and (x, y)=(110, 3.30) in y=mx+c we get
3.30=0.03(110)+c
3.30=3.3+c
c=0
Substitute, m=0.03 and c=0 in y=mx+c we get
y=0.03x
Andy needs 23 feet of the wire.
So, 23 feet =23×12
= 276 inches
Cost of 276 inches wire is y=0.03×276=$8.28
Emily needs 15 yards of the wire.
So, 15 yards =15×36
= 540 inches
Cost of 540 inches wire is y=0.03×540=$16.2
Therefore, Andy spent $8.28 on 23 feet wire and Emily spent $16.2 on 15 yards wire.
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a given exam has a normal distribution with a mean of 70 and a standard deviation of 10. a sample of size 25 is selected. what percentage of the time would you expect the mean of this sample size to fall below 66?
Answer:
we would expect the mean of the sample to fall below 66 about 5% of the time
Step-by-step explanation:
To answer this question, we can use the 68-95-99.7 rule, which states that in a normal distribution, approximately 68% of the values fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.
In this case, the mean of the sample is 70 and the standard deviation is 10, so the values that fall within one standard deviation of the mean are between 60 and 80. The values that fall below 66 are outside of this range, so we need to determine what percentage of the values fall within two standard deviations of the mean.
The values that fall within two standard deviations of the mean are between 50 and 90, so the percentage of values that fall below 66 is approximately (100 - 95) = 5%.
Therefore, we would expect the mean of the sample to fall below 66 about 5% of the time.
simplify the equation:
×[tex]\frac{(3xy^2)^3×(-4x^2y)}{(2x^2y^2)^2}[/tex]
by the way i dont know why the top has an A with a line on top it should be a multiplication sign; the second picture has what its supposed to like like clearly.
(3xy^2)^3×(-4x^2y)/(2x^2y^2)^2
= -108x^5y^7/4x^4y^4
= -108xy^3/4
Answer: -27xy^3
I NEED THIS SO BAD PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!
The sum of 30 and 40 by factoring out the greatest common factor
Answer:
To find the sum of 30 and 40 by factoring out the greatest common factor, first you need to find the greatest common factor (GCF) of both numbers. The GCF of 30 and 40 is 10. Then, you can divide both numbers by 10 to get 3 and 4 respectively. Finally, add the numbers together to get the sum of 7. Therefore, the sum of 30 and 40 by factoring out the greatest common factor is 7.
can anybody solve these for me? i have the answers written but i don’t know if they’re correct. it’s special right triangle. some are the 45-45-90 rule and some are the 30-60-90 rule. thanks!
The values of the x and y are:
I) x = 20 and y = 10√2.
J) x = 16.97 and y = 33.94.
K) x = 9.89 and y = 24.49.
L) x = 35.75 and y = 123.84.
What is the 45-45-90 rule and 30-60-90 rule?
One of these right triangles is known as a 45-45-90 triangle because its angles are 45 degrees, 45 degrees, and 90 degrees. This is a right triangle that is isosceles. The other triangle is known as a 30-60-90 triangle because its angles are 30 degrees, 60 degrees, and 90 degrees.
We have,
special right triangle, some are the 45-45-90 rule and some are the 30-60-90 rule.
in the 45-45-90 leg of the triangle is equal to a, then:
The second leg is also equal to a;
The hypotenuse is a√2;
The area is equal to a²/2; and
The perimeter equals a(2 + √2).
Assume that the shorter leg of a 30 60 90 triangle is equal to a. Then:
The second leg is equal to a√3;
The hypotenuse is 2a;
I) in the first triangle:
The second leg is also equal to y = 10√2;
The hypotenuse is y√2:
= y√2
= (10√2)√2
= 20
so, x = 20 and y = 10√2.
J) in the second is of 30-60-90 triangle:
x√3 = 12√6
x = 12√6 / √3
x = 16.97
y = 2x = 16.97 * 2
y = 33.94
so, x = 16.97 and y = 33.94.
K) the third diagram is of a 30-60-90 triangle:
2x = 14√2
x = 14√2 / 2
x = 9.89 = 10
z = x√3 = 10√3
y = z√2 = 10√3 * √2
y = 24.49
so, x = 9.89 and y = 24.49.
L) the fourth diagram is of a 30-60-90 triangle:
z = 16√10 * √2
= 71.5
2x = 71.5
x = 35.75
y = x√3
y = 123.84
so, x = 35.75 and y = 123.84.
Hence, the values of the x and y are:
I) x = 20 and y = 10√2.
J) x = 16.97 and y = 33.94.
K) x = 9.89 and y = 24.49.
L) x = 35.75 and y = 123.84.
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Indiana University Bloomington posts the grade distributions for its courses online. In a recent semester of a Business Statistics course, 45.7% of students received A's, 36.2% B's, 13.8% C's, 3.2% D's, and 1.1% F°s. Choose a Business Statistics student at random. The student's grade on a 4-point scale (with A = 4) is a random variable X with this probability distribution:
The student's grade on a 4-point scale (with A = 4) is a random variable X with a discrete probability distribution.
What are discrete and continuous probability distributions?The probabilities distributions are classified as discrete or continuous depending on the values assumed by their input variables, as follows:
Discrete distribution: Data can take only certain values.Continuous distribution: Data can take all values in a range.The students grades have these possible outcomes:
A = 4.B = 3.C = 2D = 1.F = 0.As there are only certain values, this is a discrete distribution.
Missing InformationThe problem asks to classify the distribution of the student's grade as discrete or continuous.
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£5200 is invested at 2.8% compound interest per annum.
How many years will it take for the investment to exceed £7000?
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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Raj combined white sand with black sand to make 1/4 pound mixture of sand. Raj then put an equal amount of this sand mixture into each of 5 vases. All of Raj's sand mixture went into the vases. How much sand was in each vase?
Answer:
1/20 pound of sand in each vase
Step-by-step explanation:
Raj made 1/4 and divided it into 5 vases.
1/4 ÷ 5
= 1/4 × 1/5
= 1/20
Each of the 5 vases had 1/20 lb. of sand.