Compound Interest
It occurs when the interest is reinvested rather than paying it out.
When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\mleft(1+{\frac{r}{n}}\mright)^{nt}}[/tex]Where:
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
Harry deposited an initial amount of P = $1500.
The savings account gives r = 6% = 0.06 interest
Since the interest is compounded monthly, n = 12 (there are 12 months in a year)
The time is t = 10 years.
Now we apply the formula:
[tex]\begin{gathered} {\displaystyle A=1500(1+{\frac{0.06}{12}})^{12\cdot10}} \\ \text{Calculating:} \\ {\displaystyle A=1500(1+0.005)^{120}} \end{gathered}[/tex]Using a calculator:
A = $2729.095
Rounding to two decimals,
A = $2729.10
Harry will have $2729.10 in his account after 10 years
Now for t = 20 years:
[tex]{\displaystyle A=1500(1+{\frac{0.06}{12}})^{12\cdot20}}[/tex]Calculating again:
A = $4965.31
Harry will have $4965.31 in his account after 20 years
Match the following.
The match of the given equations and choices of the properties of equality are;
If a = b and b = c then a = c ; Transitive Property
If a = b then a ÷ c = b ÷ c; Division property of =
a = a; Reflexive property
If x + a = b and x = c then c + a = b; Substitution Property
If a = b then a + c = b + c; Addition Property of =
If a = b then a•c = b•c; Multiplication Property of =
If a•b = a•c then a•c = a•b Symmetric Property
a•(b + c) = a•b + a•c; Distributive property
If a = b then a - c = b - c; Subtraction Property of =
What are the properties of equality?Properties of equality includes; addition, subtraction, transitive, reflexive, and symmetric properties of equality
Transitive PropertyThe transitive property of equality can be stated as follows; If two variables are each equal to a third variable, then the two variables are equal to each other.
Therefore; a = b and b = c then a = c represents the transitive property
Division property of equalityThe division property states that both sides of an equation remain equal, following a division of both sides by the same non zero number
Therefore;
If a = b then a ÷ c = b ÷ c; represents the division property of equality
Reflexive propertyThe reflexive property of equality states that a measure or number is always equal to itself
Therefore;
a = a represents the reflexive property
Substitution PropertySubstitution property indicates that if two variables are equal, then one can replace the other in an equation and the results will remain the same
Therefore;
If x + a = b and x = c then c + a = b; represents the substitution property
Addition and Subtraction Property of EqualityThe statement of the addition (and subtraction) property of equality is that both sides of an equation remain equal following the addition or subtraction of the same amount from both sides the same
Therefore;
If a = b then a + c = b + c; represents the addition property of equality
If a = b then a - c = b - c; represents the subtraction property of equality
Multiplication Property of EqualityThis states that both sides of an equation remain equal following the multiplication of both sides by the same value
Symmetric PropertyThe symmetric property states that two sides of an equation remain equal when their relative positions are interchanged
Distributive PropertyThis states that two sides of an equation remain equal following a distribution with multiplication over addition or subtraction.
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in the pic.............
Given -
a = 2.5 cm
b = 3.6 cm
∠A = 43°
To Find -
Remaining angles and sides =?
Step-by-Step Explanation -
We will start by drawing the diagram:
Now, we know
By, sine rule:
[tex]\begin{gathered} \frac{\sin A}{a}\text{ =}\frac{\sin B}{b}=\frac{\sin C}{c} \\ \\ =\text{ }\frac{\sin43}{2.5}\text{ = }\frac{\sin C}{3.6} \\ \\ =\text{ }\sin C\text{ = }\frac{3.6\times\sin44}{2.5} \\ \\ =\text{ }\sin C\text{ = 0.9820} \\ \\ C\text{ = }\sin^{-1}(0.9820) \\ \\ C\text{ = 79} \\ \end{gathered}[/tex]Now, we know N
A + B + C = 180 c°°
43 + B + 79° = 180°°
B = 180° - 799 - 43°°
B = 58°
Now, Side b =
[tex]\begin{gathered} \frac{\sin A}{a}\text{ = }\frac{\sin B}{b} \\ \\ \frac{\sin43}{2.5}\text{ = }\frac{\sin58°}{b} \\ \\ b\text{ = }\frac{2.5\times\sin58°}{\sin43°} \\ \\ b\text{ = 3.1} \end{gathered}[/tex]Final Answer -
∠B = 58B°
∠C = 797°
Side, b = 3.1 cm
Well GIVE U BRAINLIEST HELP ASAP
Question
Drag the numbers to order them from least to greatest.
Answer : -4/9 , -4/7 , -3/5 , -5/6
What is the solution to the system of equations? Use the substitution method to solve. 6=−4x+y− 5x−y=21 Enter your answer by filling in the boxes
The x and y solution of the system is x = -3 and y = -6
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
6 = −4x + y
− 5x − y = 21
Make -y the subject in the second equation, by adding 5x to both sides of the equation
5x − 5x − y = 21 + 5x
This gives
−y = 21 + 5x
Substitute −y = 21 + 5x in 6 = −4x + y
6 = −4x - 21 - 5x
Evaluate the like terms
5x + 4x = -6 - 21
This gives
9x = -27
So, we have
x = -3
Substitute x = -3 in −y = 21 + 5x
−y = 21 + 5 * -3
Evaluate
−y = 6
So, we have
y = -6
Hence, the solution for the system of linear equations 6 = −4x + y and − 5x − y = 21 is x = -3 and y = -6
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how do you find the equation of line passing through (0,0) and (4,4)
Answer:
y = mx
Step-by-step explanation:
It depends on what form of the line that you want. Usually the slope intercept form is wanted.
y = mx + b We need to have the m (slope) and the b (the y-intercept)
The slope is the change in y over the change in x.
Ordered pairs are in the form (x,y)
(0,0) and (4,4) Have x's of 4 and 0, and y's of 4 and 0. We subtract these to find the changes in y and x.
[tex]\frac{4-0}{4-0}[/tex] This is [tex]\frac{4}{4}[/tex] which is the same as 1. The slope (m) is 1.
Now we need to find the y -intercept. The y intercept is the point where x is 0 (0,b). They give us this point (0,0,) So the y -intercept is zero.
y = 1m + 0
or y =mx
HELP PLEASE WILL GIVE BRAINLIEST!!! I NEED HELP
Answer: y = -x + 3
Step-by-step explanation:
y = mx + b
We need to find the slope of the equation first.
Change in y: 7 - 0 = 7
Change in x: -4 - 3 = -7
Slope = Change in y / Change in x
slope = 7 / -7 = -1
Now, plug the slope into the equation to find b.
0 = -1(3) + b
b = 3
or 7 = -1(-4) + b
b = 3
3. Allison Separates 23 stickers into 4 4 equal piles. How many stickers does she have left over?
Volunteers are preparing identical backpacks for refugees. There are 32 maps and 24 dictionaries to use for the backpacks. What is the greatest number of backpacks they can prepare using all of the maps and dictionaries?
Considering the definition of greatest common divisor, the greatest number of backpacks volunteers can prepare using all of the maps and dictionaries is 8.
Definition of greatest common divisorConsidering that a divisor can be formally defined as that number that is contained in another exactly n times, the greatest common divisor is the largest number by which two or more numbers can be divided. That is, the greatest common factor is the highest number by which a set of numbers can be divided, resulting in a whole number.
To calculate the greatest common factor, the following steps must be followed:
Decompose each number into prime factors. [The prime factors of an integer are the exact divisors of that integer, that is, they have only two divisors: one and themselves]Then point out the common factors.In each of the common factors, choose the factor with the smallest exponent.Multiply the chosen factors.Greatest number of backpacks preparedIn this case, you must calculate the greatest common factor as follows:
Decomposition of 32: 2⁵Decomposition of 24: 2³×32 is the factor common to both numbers, with 3 being the smallest exponent found. Then the greatest common divisor is calculated as:
Greatest common divisor= 2³
Greatest common divisor= 8
This means that they can prepare 8 backpacks.
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I'm trying to find out if {(6,0), (-9,5), (1,-5), (0,0)} is a function or not
A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
In this case, it would be a function
5x-4=-3x+12
What is the answer
The answer is x = 2
I have attached a picture with the work
The difference of the ages of a father and his son is 25 years.Fifteen years ago.the father was six times of his son's age. Find their present ages.
Present age of father is 48 years and that of son is 23 years.
Let the age of father be x years
And the son's age be y years
According to the question,
x - y = 25 -----------1
15 Years ago, x= 6( y - 15 )
x= 6y - 90 -------------2
Substituting value of x from equation 2 in equation 1, we get
6y - 90 - y = 25
5y -90 = 25
5y = 25+90
5y= 115
y= 23
Therefore son's age is 23 years and from equation 1 we get x= 25+y = 25+23 = 48 years. So father's age is 48 years.
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The second angle of a triangle is 10 more than the first angle. The third angle is three times the first. Find the three angles.
First angle:
Second angle:
Third angle:
Answer:
First, let one angle be a variable (eg: x) so that you can form expressions and solve.
Let the first angle be x°.
Then we can form expressions for the second and third angles using the information given.
First angle = x°
Second angle = (x + 10)°
Third angle = (3x)°
Since sum of angles in a triangle is 180°, we can form an equation.
x + (x + 10) + 3x = 180
Simplify and solve for x.
5x + 10 = 180
5x = 170
x = 34
Substitute x into the expressions to find the angles.
First angle = 34°
Second angle = 34 + 10
= 44°
Third angle = 3(34)
= 102°
Determine the more basic function that has been shifted reflected stretched or compressed what does
The graph of a function f is the set of all points in the plane of the form (x, f(x)).
Step 1
iven
[tex]g(x)=-2\sqrt{x-1}+4[/tex]g(x) is a transformation of the function f(x)we have a root in the function, note that the variable x is inside the root, so we can conclude the basic function is
square tooroot
Step 2
rove
ow, lets's check the transformation of f(x)
[tex]f(x)=\sqrt{x}[/tex]a)1 was subtracted form the argument of the fucnction
[tex]\begin{gathered} f(x)=\sqrt{x} \\ f^{\prime}(x)=\sqrt{x-1} \end{gathered}[/tex]when you subtract a number b form the argument of the function you are shifting the function b units to the rigth
so
he function was shifteed 1 unit to rigth
) the resulting function was multiplied by 2-
[tex]\begin{gathered} f^{\prime}(x)=\sqrt{x-1}\text{ *-2} \\ f^{\prime}^{\prime}(x)=-2\sqrt{x-1} \end{gathered}[/tex]when you multplie by a negavitve constant you are reflecting the funciton acrros x-axis, and is is stretched vertically.
so
he funcition was reflected across x-axis an strtched vertically by a factor of 2
c) 4 was added to the function
[tex]\begin{gathered} f^{\prime\prime}(x)=-2\sqrt{x-1} \\ g(x)=-2\sqrt{x-1}+4 \end{gathered}[/tex]when you add a constant b to any function, the graph will be shifted b units up,so
he functinon was shifted 4 units up
hrerefore, we can conclude the answer is
[tex]f(x)=\sqrt{x}[/tex]I hope this helps you
In 2016 the Better Business Bureau settled 80% of complaints they received in the United States. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.80, the same as the overall proportion of complaints settled in 2016.In 2016 the Better Business Bureau settled 80% of complaints they received in the United States. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.80, the same as the overall proportion of complaints settled in 2016.
Using the binomial distribution, the mean and the standard deviation for the number of settled complaints among those received are given as follows:
Mean: 160 complaints.Standard deviation: 5.66 complaints.What are the mean and the standard deviation for the binomial distribution?The binomial distribution gives the probability of exactly x successes on n repeated trials, with p probability of a success on each trial. These parameters will be used to find the mean and the standard deviation, with formulas that are presented next.
The mean is given as follows:
[tex]E(X) = np[/tex]
The standard deviation is given as follows:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Considering that a sample of 200 complains are chosen, each with an 90% probability of being settled, the parameters are given as follows:
n = 200, p = 0.8.
Hence the mean is:
[tex]E(X) = np = 200 \times 0.8 = 160[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200 \times 0.8 \times 0.2} = 5.66[/tex]
What is the missing information?The problem states that 200 complaints were received, and asks for the mean and the standard deviation for the number of settled complaints among those received.
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What the area of the sphere if it's volume is 3x +1 cm³
Answer:
[tex]{ \tt{volume = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \tt{v = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \tt{area = \frac{dv}{dr} = 4\pi {r}^{2} }} \\ \\ { \tt{area = \frac{d(3x + 1)}{dx} }} \\ \\ { \tt{area = 3 \: {cm}^{2} }}[/tex]
the value of a share of stock on the stock market decreased by 15%. If it used to be worth $55.55, what is it worth now? Round to the nearest hundredth.
The worth of the share after a 15% fall will be $47.21.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that the value of a share of stock on the stock market decreased by 15%. If it used to be worth $55.55.
The value of the share after 15% fall will be calculated as:-
Decreased amount = 55.55 - ( 55.55 x ( 15 / 100)
Decreased amount = $47.21
Therefore, the worth of the share after a 15% fall will be $47.21.
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The value of the ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ does not rely on the values of the other variables in an expression or function, and its value determines the values of the other variables.
The value of the independent variable does not rely on the values of the other variables in an expression or function, and its value determines the values of the other variables.
What is an independent variable?An independent variable can be defined as the variable that is being manipulated, controlled, and which varies in an experimental or research study for the exploration of its effects.
It is termed “independent” because it's not affected or changed by other variables in an experiment or study.
It is known as a variable that is unaffected in a function and cannot be determined by the other variables in that function.
Other names for an independent variable includes;
Explanatory variableInput variableExposure variableControlled variablePredictor variableHence, the variable is independent.
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6
The exchange rate between pounds and US dollars is £1 = $1.27
a) Annie goes on holiday to the USA.
She buys £500 worth of dollars
She spends $550 and converts the rest back to £ at the same rate.
How much money does she receive?
Annie will receive 66.92 euros after converting the dollars into euros post her trip
The exchange rate between pounds and US dollars: 1 Euro = $1.27
Exchange rate: An exchange rate determines the price at which one currency will be exchanged for another and has an impact on international trade and money transfers.
Euro Annie spends to buy dollars = 500
Equivalent dollars received by Annie for 500 euros = 500*1.27
= $635
The money she spent in dollars = $550
Dollars remaining = 635-550 = $85
Euro she will receive after conversion = Dollars remaining/Conversion rate 85/1.27 = 66.92 Euros
So, After changing the dollars into euros after her vacation, Annie will receive 66.92 euros.
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A is shaped like a rectangle whose perimeter is 378ft . The length is 8 times as long as the width. Find the length and the width.
The length and width of the rectangle with a perimeter of 378ft are 168ft and 21ft respectively.
What is the length and the width of the rectangle?The formula used in calculating the perimeter of a rectangle is expressed as;
P = 2( l + w )
Where l is length and w is width.
Given the data in the question;
Let 'x' represent the width of the rectangle.
Width of the rectangle w = xLength of the rectangle l = 8xPerimeter P = 378ftPlug the given values into perimeter formula and solve for x .
P = 2( l + w )
378 = 2( 8x + x )
378 = 2( 9x )
378 = 18x
18x = 378
x = 378/18
x = 21
Now, we find the length and width of the rectangle.
Width of the rectangle w = x = 21ft
Length of the rectangle l = 8x = 8( 21 ) = 168ft
Therefore, the width of the rectangle is 21ft while its length is 168ft.
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Which property of multiplication is (ab)c = a(bc)
Answer: The Associative Property
Step-by-step explanation:
Example:
[tex]a * (b * c) = (a * b) *c[/tex]
[tex]2 *(4 * 5) = (2 * 4) * 5[/tex]
Please help I’ll mark you as brainliest if correct!!
Answer:The answer is 8
Step-by-step explanation:
21-13
You thought you had finished 35 pages, but you actually read 32 Pages. What was your percent error?
[tex]\frac{35-32}{32} \times 100=\frac{75}{8}=9.375\%[/tex]
Answer:
9.375%
Step-by-step explanation:
Percentage Error formula
[tex]\textsf{Percentage error}=\sf \left|\dfrac{estimated\:value\:-actual\:value}{actual\:value} \right| \times 100\%[/tex]
Given:
Estimated value = 35 pagesActual value = 32 pagesSubstitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Percentage error}&= \left|\dfrac{35-32}{32} \right| \times 100\%\\\\&=\left|\dfrac{3}{32} \right| \times 100\%\\\\&=0.09375 \times 100\%\\\\&=9.375\%\end{aligned}[/tex]
Therefore, the percentage error was 9.375%.
The sales tax is $52 on the purchase of a dining room set for $1040. Find the sales tax rate.
Answer:
Total price including tax: $ 1,092.00
Sales tax rate: 5%
Step-by-step explanation:
Brainlest, Please!
if we take 1040 to be the 100%, what is 52 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 1040 & 100\\ 52& x \end{array} \implies \cfrac{1040}{52}~~=~~\cfrac{100}{x} \\\\\\ 20=\cfrac{100}{x}\implies 20x=100\implies x=\cfrac{100}{20}\implies x=5[/tex]
A serving of rice is 5/6 of a cup. How many servings are there in a 3 1/3 cup bag of rice?
Answer:
there are 7 severeings of rice
Please answer I give Brainliest
Answer:
hmmm
Step-by-step explanation:
what does the j, k, m, and l stand for?
Factor 15cd − 45c ^2d.
3c ^2d(5 − 15)
5cd(3 − 15c ^2d)
3cd(5 − 15c)
5cd(3 − 45c ^2d)
3/2d
DIFFERENTIATE W.R.T. D
3
2
≈0.666666667
Use the table to answer the question. 2 6 10 12 10 30 50 60 Simplify each ratio in the table to prove that all the ratios are equivalent. (2 points) 210= , 630= , 1050= , 1260=
The expression given relating to the take all have an equivalent ratio of 1:5.
How to express the ratio?It should be noted that ratio is simply used to show the comparison between two or or more things.
In this case, in the table, the ratio given will be illustrated as:
2/10 = 1/5 = 1:5
6/30 = 1/5 = 1:5
10/50 = 1/5 = 1:5
12/60 = 1/5 = 1:5
In this case, it should be noted that for every number that was illustrated, we have an equivalent value of 1:5. Therefore, this explains that it's an equivalent ratio.
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Each question on a multiple choice exam has four choices. One of the choices is the correct answer, worth five points another choice is wrong but still carries partial credit of 1 point and other two choices are worth 0 points. If the student picks answers at random, what is the expected value of his or her score for a problem?
If a student picks randomly then the expected value of his or her score for a problem is 1.5.
Each question on a multiple-choice exam has four choices.
One of the choices is correct, worth four points.
Another choice is wrong but carries partial credit for one point.
The other two choices are wrong and worth a negative one point.
Each has a probability of getting selected is 0.25.
[tex]0.25*5+0.25*1+0.25*0+0.25*0[/tex]
[tex]1.25+0.25[/tex]
[tex]1.5[/tex]
What is the expected value?
The expected value denotes potential. The occurrence of a random event is the subject. Its fundamental notion is that something is probable to occur.
Actually, the anticipated value may be viewed as the mean of a random variable. This indicates that the anticipated value is the average of all the values acquired if a probability experiment were repeated again while keeping track of the outcomes. The anticipated value of a game of chance is what you should expect to occur over the long run of several trials.
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A data set has a correlation coefficient of 0.013. Which statement about the data is true? a. The data has little or no linear correlation. b. The data has a strong positive linear correlation. c. The data has a weak negative linear correlation. d. The data has a strong negative linear correlation.
Answer: Choice A
The data has little or no linear correlation
======================================================
Explanation:
r = correlation coefficient
The r values are within the interval [tex]-1 \le r \le 1[/tex]
In other words, r is between -1 and 1 inclusive of both endpoints.
r = -1 is the strongest negative correlationr = 1 is the strongest positive correlationr = 0 means there's no linear correlation at all. The data points are either randomly scattered about, or they perhaps fit on some kind of curve.For the case r = 0.013, it's very close to r = 0. This suggests there is very weak positive correlation or practically no linear correlation at all.
20PTS
Please help answer quickly
Answer:
second option