Annual interest rate will be 11.95% or 12% approx.
What is compound interest?
The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.
It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely calculated on the principal sum.
Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
P = principal
i = nominal annual interest rate in percentage terms
n = number of compounding periods
formula for compound interest is [tex]P [(1 + i)^n - 1][/tex]
According to the question
P=15000
i = ?
compound interest = 87,219.93
n=17 years
Therefore
[tex]87219.93=15000 [(1 + i)^1^7 - 1][/tex]
[tex]\frac{87219.93}{15000} = [(1 + i)^1^7 - 1][/tex]
[tex]6.814662 = (1+i)^1^7[/tex]
[tex](6.814662)^\frac{1}{17} = (1+i)[/tex]
i =1.1195-1
i =0.1195
i.e. 11.95%
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Solve the following system of linear equations by addition. Indicate whether the given system of linear equations has one solution, hasno solution, or has an infinite number of solutions. If the system has one solution, find the solution.7x + 7y = 281 4x + 4y = 16
Infinite number of solutions
Explanation:The given system of equations:
7x + 7y = 28........(1)
4x + 4y = 16.........(2)
Multiply equation (1) by 4
28x + 28y = 112..............(3)
Multiply equation (2) by -7
-28x - 28y = -112...............(4)
Add equations (3) and (4) together
0x + 0y = 0....................(5)
Since the right hand and left hand sides of equation (5) are equal, the equation has infinite number of solutions
6. An amusement park sells child and adult tickets at a ratio of 8:1. On Saturday, they sold 147 more child tickets than adult tickets. How many tickets did the amusement park sell on Saturday? 8. Stan's Steakhouse has a server to cook ratio of 5 to 2. The total numbor of servers and cooks is 42. How many servers doos Stan's Steakhouse employ?
The ratio between the child tickets to adult tickets is 8 : 1
The child tickets are more by 147
Let us use the ratio method to solve the question
Child : Adult : difference
8 : 1 : 7 (8 - 1)
x : y : 147
By using cross multiplication
[tex]\begin{gathered} x\times7=8\times147 \\ 7x=1176 \end{gathered}[/tex]Divide both sides by 7 to find x
[tex]\begin{gathered} \frac{7x}{7}=\frac{1176}{7} \\ x=168 \end{gathered}[/tex][tex]\begin{gathered} y\times7=1\times147 \\ 7y=147 \end{gathered}[/tex]Divide both sides by 7 to find y
[tex]\begin{gathered} \frac{7y}{7}=\frac{147}{7} \\ y=21 \end{gathered}[/tex]The total number of tickets = 168 + 21 = 189
The total number of tickets is 189
Knowledge check (probability) this is math not chemistry. I am looking at the tab
Answer:
5:13
Explanation:
Given that the probability of the box having a toy = 13/18
Therefore, the probability of the box not having a toy:
[tex]P(\text{ no toy\rparen}=1-\frac{13}{18}=\frac{5}{18}[/tex]The odds against an event is given as the ratio of the Number of unfavorable outcomes to number of favorable outcomes.
• Number of Unfavourable Outcomes = 5
,• Number of favourable Outcomes = 13
Thus, the odds against the box having a toy is 5:13.
- 16m’n-(-25m’n)+(-7m’n)Which of the following is equivalent to the expression above?
As a rule , - times - = + and - times + = -
[tex]\begin{gathered} -16m^2n-(-25m^2n)+(-7m^2n\text{ ) } \\ =-16m^2n+25m^2n-7m^2n\text{ ( based on the rule above )} \\ =+9m^2n-7m^2n\text{ ( -16 + 25 = + 9 )} \\ =+2m^2n \end{gathered}[/tex]Therefore the correct answer to the question is 2m squared n
points reflected over an axis graphically
The coordinate of the point N is (-6,2).
The point on reflection about x axis, the x -coordinate remain same and sign of y-coordinate changes.
Determine the coordinate of point N'.
[tex]N^{\prime}(-6,-1\cdot2)\rightarrow N^{\prime}(-6,-2)[/tex]Plot the point on the graph.
Gifty works out that the material for a dress cost R dollar per meter and 3 meters are required for the dress. Acessories cost $50.00. what is the total amount of money Gifty will need to spend on the dress in terms of R? If Gifty has $4000 to spend on her dress including accessories, what is the maximum value of R?
We are given that
Cost of dress per meter = $R
Total cost of dress = $ 3R
Cost of Acessories = $50
We want to find:
Part A
The total amount of money Gifty will need to spend on the dress in terms of R
To find the total amount, we just add up
Let T denotes the total amount of money
[tex]\begin{gathered} T=3R+50 \\ \end{gathered}[/tex]Thus, the total amount is $ (3R + 50)
Part B
If Gifty has $4000 to spend on her dress including accessories, what is the maximum value of R?
We only need to equate T to 4000 and solve for R
[tex]\begin{gathered} T=4000 \\ 3R+50=4000 \\ 3R=4000-50 \\ 3R=3950 \\ R=\frac{3950}{3} \\ R=1316.666667 \\ R=1316.67\text{ (to 2 decimal places)} \end{gathered}[/tex]Thus, the maximum value of R is $1316.67
Convert.4,130 cm = M
ANSWER
41.3 m
EXPLANATION
1 meter is 100 centimeters. To transform from centimeters to meters, we have to divide by 100:
[tex]\frac{4,130}{100}=41.3[/tex]4,130 centimeters is 41.3 meters.
Alice fills up the gas tank of her car before going for a long drive . The equation below models the amount of gas , g , in gallons , in Alice's car when she has driven m miles . What is the meaning of 32 in the equation ?
Solution
For this case we have the following equation given:
[tex]g=15-\frac{m}{32}[/tex]We want to know what represent the 32 value
So then the answer is:
Total of miles that can cover the car with 15 gallons of gas
How do you use the distance formula to figure out the area of the triangle. I don't really know how to solve this problem or use distance formula
The Area of a Right Triangle
The area of any triangle of base B and height H is:
[tex]A=\frac{B\cdot H}{2}[/tex]The base and the height must be perpendicular, i.e, the angle between them must be 90°.
The trick here is to prove the triangle is right at the point (15, 5).
If two lines are perpendicular, the product of their slopes is -1.
Calculate the slope of the line that joins the vertices at (5, 15) and (15, 5):
[tex]\begin{gathered} m_1=\frac{5-15}{15-5} \\ m_1=-\frac{10}{10} \\ m_1=-1 \end{gathered}[/tex]Calculate the slope of the line that joins the vertices at (20, 10) and (15, 5);
[tex]\begin{gathered} m_2=\frac{5-10}{15-20} \\ m_2=\frac{-5}{-5} \\ m_2=1 \end{gathered}[/tex]It can be verified that m1 * m2 = -1, thus the lines are perpendicular and we can use the formula given above to compute the area.
Find the length of both lines with the formula of the distance:
[tex]\begin{gathered} L_1=\sqrt[]{(5-15)^2+(15-5)^2} \\ \text{Calculating:} \\ L_1=\sqrt[]{200} \end{gathered}[/tex][tex]\begin{gathered} L_2=\sqrt[]{(5-10)^2+(15-20)^2} \\ L_2=\sqrt[]{50} \end{gathered}[/tex]Apply the formula of the area:
[tex]\begin{gathered} A=\frac{\sqrt[]{200}\cdot\sqrt[]{50}}{2} \\ A=\frac{\sqrt[]{10000}}{2} \\ A=\frac{100}{2}=50 \end{gathered}[/tex]The area is 50 square units
given f(x) = x² + 4x -5find f(x) inverse
The function is given as
[tex]f(x)=x^2+4x-5[/tex]To find the inverse of the function ,
[tex]y=x^2+4x-5[/tex]Replace x with y.
[tex]x=y^2+4y-5[/tex]Now solve for y,
Add 4 and subtract 4 in the RHS.
[tex]x=y^2+4y-5+4-4[/tex][tex]x=y^2+4y-9+4[/tex][tex]x=(y+2)^2-9[/tex][tex]x+9=(y+2)^2[/tex][tex](y+2)^2=x+9[/tex][tex]y+2=\pm\sqrt[]{x+9}[/tex][tex]y=\sqrt[]{x+9}-2[/tex][tex]y=-\sqrt[]{x+9}-2[/tex]Hence the inverse of the function is
[tex]y=\sqrt[]{x+9}-2,-\sqrt[]{x+9}-2[/tex]Example 10 in. 20 in. A carpenter builds the table shown. If the floor is level, how likely is it that a ball placed on the table will roll off? 20 in. 10 in.
According to the given image, the table has a flat surface, whcih means the ball would not roll off because there's no slope or inclination. Also, assuming that there's no other forces being applied, the ball should not roll off.
A box contains black chips and white chips. A person selects two chips without replacement. If the probability of selecting a black chip and a white chip is 15/56,and the probability of selecting a black chip on the first draw is 5/8,find the probability of selecting the white chip on the second draw,given that the first chip selected was a black chip
Answer:
Explanations:
Probability is the likelihood or chance that an event will occur. Mathematically:
[tex]\text{Probability}=\frac{Expected\text{ outcome}}{total\text{ outcome}}[/tex]According to the question, we are told that the probability of selecting a black chip on the first draw is 5/8, this shows that the total number of chips is 8 since it was a first draw (all chips are intact).
If the probability of selecting a black chip and a white chip is 24/56 without replacement, then;
[tex]\text{Probability (a black and a white)=Pr(a black c}hip\text{)}\times Pr(white)[/tex]Substitute the given probability into the formula to have:
[tex]undefined[/tex]How to round off 18,600 to the nearest 10,000
Answer:
The nearest 10,000 is;
[tex]20,000[/tex]Explanation:
We want to round off the given number to the nearest 10,000.
[tex]18,600[/tex]We will find the closest ten thousand to the given number;
[tex]18,600\rightarrow20,000[/tex]Therefore, the nearest 10,000 is;
[tex]20,000[/tex]
predict adjusted wages in 1998 does this prediction require interpolation or extrapolating
The required interpolation in adjusted 2020 is 0.50
Explanation:We find the interpolation using the formula:
[tex]y=y_1+\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Let us choose these points as follows:
[tex]\begin{gathered} x_1=7.69 \\ x_2=7.87 \\ y_1=3.80 \\ y_2=5.15 \end{gathered}[/tex]So,
[tex]\begin{gathered} y=3.80+\frac{5.15-3.80}{7.87-7.69}(x-7.69) \\ \\ =3.80+\frac{1.35}{0.18}(x-7.69) \\ \\ =3.80+7.5(x-7.69) \\ y=7.5x-53.875 \end{gathered}[/tex]In adjusted 2020, we have x = 7.25, using this, we have:
[tex]\begin{gathered} y=7.5(7.25)-53.875 \\ =54.375-53.875 \\ =0.50 \end{gathered}[/tex]what scale factor or multiplier of the dilation below
Given:
The triangle ABC is similar to the triangle A'B'C'
So, the corresponding sides are proportions
So, the factor of dilation will be:
[tex]\frac{A^{\prime}B^{\prime}}{AB}=\frac{8}{12}=\frac{2}{3}[/tex]so, the answer will be 2/3
Han spent a total of $221.76, before tax, on bags of chips for the basketball team, and each bag cost $3.52. What is the total number of bags of chips that Han bought?
Given:
a.) Han spent a total of $221.76, before tax, on bags of chips for the basketball team.
b.) Each bag cost $3.52.
Let's determine the number of bags of chips bought.
[tex]\text{ No. of bags of chips bought = }\frac{\text{ Total cost}}{\text{ Price of each bag}}[/tex][tex]\text{ = }\frac{\text{ 221.76}}{\text{ 3.52}}[/tex][tex]\text{ = 63}[/tex]Therefore, Han bought 63 bags of chips for the basketball team.
The answer is 63.
SaveSubmitD23567*9TO111213Which point represents the approximate location of V28?esApoint AB)point BpointD)point DHelp me almost done and tried
Thus, the point which represent square root of 28 should lie between 5 and 6 which is point B.
Thus, option (B) is correct.
24 2. Which two teams have equivalent ratios of wins to losses? Team Wins Losses Leopards 15 10 Pirates 12 8 Knights 14 7 Lions 18 10
The ratio wins to losses of each team are:
[tex]\begin{gathered} \text{Leopards:}\frac{15}{10}=\frac{3}{2} \\ \text{ Pirates:}\frac{12}{8}=\frac{3}{2} \\ \text{Knights:}\frac{14}{7}=2 \\ \text{Lions:}\frac{18}{10}=\frac{9}{5} \end{gathered}[/tex]Then, Leopards and Pirates have the same ratio
The probability that VSU and KSU both win a basketball game in the same week is 47%. Theprobability that VSU wins is 50%. What is the probability that KSU will win given that VSUhas already won?
EXPLANATION
Let the probability that KSU will win a game be Pr(A), and let the probability that VSU wins be Pr(B). Therefore;
[tex]\begin{gathered} Pr(A\cap B)=0.47 \\ Pr(B)=0.5 \end{gathered}[/tex]We can then use the conditional probability formula below.
[tex]Pr(A|B)=\frac{Pr(A\cap B)}{Pr(B)}[/tex]Therefore, the probability that KSU will win given that VSU has already won becomes
[tex]Pr(A|B)=\frac{0.47}{0.50}=0.94[/tex]Answer: 0.94
which box and whisker plot has the greatest interquartile range?
Calculate each interquartile: subtract the upper quartile to the lower quartile
1. 9-7 = 2
2. 105-97 = 8
3. 17-7.5= 9.5
4. 7 -4 = 3
The greatest interquartile is 9.5 (option 3)
A file that is 289 megabytes is being downloaded. If the download is 18.6% complete, how many megabytes have been downloaded? Round your answer to thenearest tenth.
Given:
289 megabytes
and 18.6% = 0.186
Therefore:
[tex]289\times0.186=53.754[/tex]Round to the nearest tenth: 53.8
Answer: 53.8 megabytes
Which mathematical property is demonstrated?5 • 7 • 4 = 5 • 4 • 7commutative property of additioncommutative property of multiplicationassociative property of additionassociative property of multiplication
What we can observe in equality is the commutative property of multiplication.
The answer would be Commutative Property of Multiplication
.
A culture of bacteria has an initial population of 220 bacteria and doubles every 8
hours. Using the formula Pt = Po · 2a, where P is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 11 hours, to the nearest whole number?
The population of bacteria in the culture after 11 hours is 581 using the exponential decay formula.
What is meant by population?The total number of people living in a particular area, such as a city or town, region, country, continent, or the entire world, is typically referred to as the population. Governments frequently conduct censuses to estimate the number of residents living within their jurisdiction. A census is a process for gathering, analyzing, compiling, and releasing statistics regarding a population.
A culture of bacteria has an initial population of 220 bacteria, which doubles every eight hours, according to the information provided.
By applying the formula,
P(t)=P₀.[tex]2^{t/d}[/tex]
P(t) is the population at the end of t hours.
P0 is the starting populace.
d is the doubling time, while t is the time in hours.
After 11 hours, we are asked to determine the bacteria population.
First, we will enter the following values in the doubling life formula as substitutes:
P(t)=220([tex]2^{t/8}[/tex])
Now we will substitute t=11 in our formula to find the population of bacteria after 11 hours as follows:
P(11)=220([tex]2^{17/8}[/tex])
P(11)=220([tex]2^{1.4}[/tex])
P(11)=220(2.639015822)
P(11)=580.5834807≈581
P(11)=581
Consequently, after 11 hours, there will be 581 bacteria.
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Find the quadratic function that y=f(x) that has the vertex (0,0) and whose graph passes through the point(-2,-8). Write the function in standard form
Given
The quadratic function that y=f(x) that has the vertex (0,0) and whose graph passes through the point(-2,-8)
Solution
Recall
[tex]y=a(x-h)^2+k[/tex][tex]\begin{gathered} Vertex\text{ =\lparen h,k\rparen} \\ \\ h=0 \\ k=0 \\ \\ y=a(x-0)^2+0 \\ y=ax^2 \end{gathered}[/tex]Given
Point (-2, -8)
[tex]\begin{gathered} x=-2 \\ y=-8 \\ -8=a(-2)^2 \\ -8=a4 \\ -8=4a \\ divide\text{ both sides by 4} \\ \frac{4a}{4}=-\frac{8}{4} \\ \\ a=-2 \end{gathered}[/tex]Now
[tex]\begin{gathered} y=a(x-h)^2+k \\ a=-2 \\ h=0 \\ k=0 \\ y=-2(x-0)^2+0 \\ y=-2(x)^2+0 \\ y=-2x^2 \end{gathered}[/tex]The standard form
[tex]y=ax^2+bx+c[/tex]Now
[tex]\begin{gathered} y=-2x^2+0x+0 \\ which\text{ is } \\ y=-2x^2 \end{gathered}[/tex]Checking with graph
The final answer
[tex]y=-2x^2[/tex]Use definitions of right-hand and left-hand limits to prove the limit statement.lim-1|x|X>0Since x approaches 0 from the left, x<0, (x = []).
First we need to understand what |x| means or what values it repressents
[tex]|x|=\begin{cases}x,x\ge0 \\ \\ -x,x<0\end{cases}[/tex]|x| indicates the absolute value of x, this is, x is always going to be positive, for example,
when x = 1 -> |x| = 1 , but also when x = -1 , then |x| = 1
Since, in this case, we need to find the limit when X approaches 0 from the left we are going to use |x| = -x , for x<0
this is...
[tex]\lim _{x\rightarrow0-}\frac{x}{|x|}=\lim _{x\rightarrow0-}\frac{x}{-x}=\lim _{x\rightarrow0-}(-1)=-1[/tex]At this point we have proved the limit statement.
So, in order to answer the question in the lower part... x approaches to 0 from the left, x<0, |x| = -x
In the graph you can see, whenever X<0 the value of the funcion will be negative and when it approaches 0 it becomes -1
On the other hand, when the function approaches to 0 from the right, the value of the function is +1. This is a discontinuity
[tex]\lim _{x\rightarrow0-}\frac{x}{|x|}=\lim _{x\rightarrow0-}\frac{x}{-x}[/tex]This way we eliminate the absolute value, because, remember, when x<0, |x| = -x
write an extended proportion to indicate the proportional corresponding sides of the triangles
The correct extended proportion is:
[tex]\frac{MN}{RS}=\frac{MP}{RT}=\frac{NP}{ST}[/tex]Since the other two options have some non-correspondant proportions.
Simple calculator test - determine the angle, θ, to the nearest whole degree from each of the following:A. cos(θ) = 0.2079B. tan(θ) = 0.2126C. sin(θ) = 0.5446
Step 1
Find the value of θ using the inverse sign of all the functions.
A)
[tex]\begin{gathered} cos(\theta)=0.2079 \\ \theta=\cos^{-1}(0.2079) \\ \theta\approx78^{\circ} \end{gathered}[/tex]B)
[tex]\begin{gathered} tan(\theta)=0.2126 \\ \theta=\tan^{-1}(0.2126) \\ \theta\approx12^{\circ} \end{gathered}[/tex]C)
[tex]\begin{gathered} sin(\theta)=0.5446 \\ \theta=\sin^{-1}(0.5446) \\ \theta\approx33^{\circ} \end{gathered}[/tex]i need help with this question parts 1 - 4
Given:
Given data points are (950,100) and (1000,40).
Required:
To find the linear model for this data.
Explanation:
The standard form of linear equation is
[tex]y=mx+b[/tex]Where
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{40-100}{1000-950} \\ \\ m=-\frac{60}{50} \\ \\ m=-\frac{6}{5} \end{gathered}[/tex]Now
[tex]y=-\frac{6}{5}x+b[/tex]Now we have to find b using the points (950,1000), we get
[tex]\begin{gathered} 1000=-\frac{6}{5}(950)+b \\ \\ 1000=-6\times190+b \\ \\ 1000=-1140+b \\ \\ b=1000+1140 \\ \\ b=2140 \end{gathered}[/tex][tex]y=-\frac{6}{5}x+2140[/tex]Final Answer:
[tex]y=-\frac{6}{5}x+2,140[/tex]Given f(x)=x^2+4x+5, what is f(2+h)-f(2)/h equal to?A. h^2 + 8hB. 2x + h + 4C. 8 + hD. h + 4
ANSWER:
C. 8 + h
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]f\mleft(x\mright)=x^2+4x+5[/tex]We evaluate each case and obtain the following:
[tex]\begin{gathered} f(h+2)=\left(2+h\right)^2+4\left(2+h\right)+5 \\ \\ f(2+h)=4+4h+h^2+8+4h+5 \\ \\ f(2+h)=h^2+4h+4h+4+8+5 \\ \\ f(2+h)=h^2+8h+17 \\ \\ \\ f(2)=\left(2\right)^2+4\left(2\right)+5 \\ \\ f(2)=4+8+5 \\ \\ f(2)=17 \end{gathered}[/tex]We substitute each function evaluated to determine the final result, just like this:
[tex]\begin{gathered} \frac{f(2+h)-f(2)}{h}=\frac{h^2+8h+17-17}{h} \\ \\ \frac{f(2+h)-f(2)}{h}=\frac{h^2+8h}{h} \\ \\ \frac{f(2+h)-f(2)}{h}=h+8=8+h \end{gathered}[/tex]Therefore, the correct answer is C. 8 + h
Would appreciate your help with this algebra question. Thank you!
The above function is to be used if the value of x is between 0 and 8. On the other hand, the function to be used when x ≥ 8 is -5x + 11.
Since the interval to be checked is from 2 to 7, we will be using the first function which is -2x + 4.
To determine the rate of change between those intervals, we have the formula below:
[tex]\text{rate of change = }\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]Let's solve f(x₂) first. Our x₂ = 7. Let's substitute the function above with x = 7.
[tex]\begin{gathered} f(x)=-2x+4 \\ f(7)=-2(7)+4 \\ f(7)=-14+4 \\ f(7)=-10 \end{gathered}[/tex]Let's solve f(x₁) first. Our x₁ = 2. Let's substitute the function above with x = 2.
[tex]\begin{gathered} f(x)=-2x+4 \\ f(2)=-2(2)+4 \\ f(2)=-4+4 \\ f(2)=0 \end{gathered}[/tex]So, we now have the value of f(x₂) = -10, and f(x₁) = 0. Let's use these values to the formula of the rate of change above.
[tex]\begin{gathered} \text{rate of change}=\frac{f(x_2)-f(x_1)^{}}{x_2-x_1} \\ \text{rate of change}=\frac{-10-0}{7-2} \\ \text{rate of change}=\frac{-10}{5} \\ \text{rate of change}=-2 \end{gathered}[/tex]Since the rate of change is a negative number, the function is decreasing over the interval [2, 7].