Isabella earns interest at an annual rate of 10% compounded annually on her savings account. She deposits $2,000 into her account. What is the total amount of money Isabella will have in her account after 2 years? (Use the formula to calculate compound interest: A = P(1 + r)')
As it indicates on the text, compound interest is represented by the following expression:
[tex]\begin{gathered} A=P(1+r)^t \\ \text{where,} \\ A=\text{ Amount} \\ P=\text{ Principal} \\ r=\text{ interest rate in decimal form} \\ t=\text{ time} \end{gathered}[/tex]Then, substituing the information given:
[tex]\begin{gathered} A=2,000(1+0.1)^2 \\ A=2,420 \end{gathered}[/tex]Isabella will have $2,420 after 2 years.
Please helpMe if your good with mathI appreciate it thank u!
Let x be the number of tshirt sold.
A/q,
[tex]\begin{gathered} 5x+40=125 \\ \Rightarrow5x=85 \\ \Rightarrow x=17 \end{gathered}[/tex]Thus the number of tshirt sold is 17.
A sample of 25 measurements at breaking strength of cotton thread gave a mean of 7.4 and a standard deviation of 1.2 gms. Find 95% confidence limits for the mean breaking strength of cotton thread.
Answer:
(6.9296, 7.8704)
Explanation:
Given:
• Sample Mean = 7.4
,• Sample Standard Deviation = 1.2
,• n = 25
First, determine the standard error.
[tex]S.E.=\frac{\sigma}{\sqrt{n}}=\frac{1.2}{\sqrt{25}}=\frac{1.2}{5}=0.24[/tex]At 95% confidence limits, Z=1.96.
Using the formula below:
[tex]\bar{x}-Z_{\frac{\alpha}{2}}(S.E)<\mu<\bar{x}+Z_{\frac{\alpha}{2}}(S.E)[/tex]The limits is calculated below:
[tex]\begin{gathered} 7.4-(1.96\times0.24)<\mu<7.4+(1.96\times0.24) \\ 7.4-0.4704<\mu<7.4+0.4704 \\ 6.9296<\mu<7.8704 \end{gathered}[/tex]At 95%, the confidence limits for the mean breaking strength of cotton thread is (6.9296, 7.8704).
A group of friends' dinner bill before tax is $122.75. The sales tax rate is 8%. They want to leave an 18% tip after tax. What is their total dinner bill,
including tax and tip, rounded to the nearest cent?
O $150.57
O $154.29
o $154.67
O $156.43
Their total dinner bill including sales tax rate is 8% and 18% tip will be $156.43 by using the concept of percentages and addition.
What is percent?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.
What is sales tax?A sales tax is a fee that is paid to the government when certain goods and services are sold. Typically, laws permit the seller to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing body.
Here,
$122.75 dollars to be paid without tax and tip,
=8% of $122.75
=$9.82.
=122.75+9.82
=$132.57
=18% of 132.57
=$23.86
=132.57+23.86
=$156.43
Using the addition and percentages concepts, they can calculate their total dinner bill, which is $156.43 after adding the 8% sales tax and 18% gratuity.
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i need help with this question
Answer:
8%.
Step-by-step explanation:
The perimeter = 2(20 + 30)
= 100 cm.
The new perimeter = 2(20 + 0.05*20 + 30 + 30*0.10)
= 2(21 + 33)
= 2*54
= 108 cm.
Percent increases = 8%.
Hoang has worked as a nurse at Springfield General Hospital for 6 years longer than her friend Bill. Two years ago, she had been at the hospital for twice as long. How long has each been at the hospital?
Ok let's take the information given and make an equations system with it.
I'm gonna use H for Hoang present working years and B for those of Bill. We know that right now Hoang has worked for 6 years longer than Bill, with this we can create the following equation:
[tex]H=B+6[/tex]We also have information from two years ago, at that time Hoang's working years doubled Bill's working years. One would feel tempted to write the equation H=2*B but you have to remember that this information is from the past and H and B stand for working years in the present. The correct way to approach this is change H and B by H-2 and B-2 so we consider that this information is from 2 years ago:
[tex]\begin{gathered} (H-2)=2\cdot(B-2) \\ H-2=2B-4 \\ H-2B=-2 \end{gathered}[/tex]So now we have constructed our equations system:
[tex]\begin{gathered} H=B+6 \\ H-2B=-2 \end{gathered}[/tex]Let's take the outcome of the first equation and use it in the second one:
[tex]\begin{gathered} H-2B=(B+6)-2B=-2 \\ B-2B+6=-2 \\ -B=-2-6=-8 \\ B=8 \end{gathered}[/tex]And going back to the first equation:
[tex]H=8+6=14[/tex]So Hoang has been working at the hospital for 14 years and Bill for 8 years.
what is the least common denominator for the two fractions 2 / 5 3 / 2
The multiples of the denominator of 2/5 is,
5,10,15,20,25....
The multiples of the denominator of 3/2 is,
2,4,6,8,10.....
Thus, the required least common denominator is 10.
Find the oth term of the geometric sequence 5,--25, 125,
Given the geometric progression below
[tex]5,-25,125,\ldots[/tex]The nth term of a geometric progression is given below
[tex]T_n=ar^{n-1},\begin{cases}a=\text{first term} \\ r=\text{common ratio}\end{cases}[/tex]From the geometric progression, we can deduce the following
[tex]\begin{gathered} T_1=a=5 \\ T_2=ar=-25 \\ T_3=ar^2=125 \end{gathered}[/tex]To find the value of r, we will take ratios of two consecutive terms
[tex]\begin{gathered} \frac{T_2}{T_1}=\frac{ar}{a}=\frac{-25}{5} \\ \Rightarrow r=-5 \end{gathered}[/tex]To find the 9th term of the geometric, we will have that;
[tex]\begin{gathered} T_9=ar^8=5\times(-5)^8=5\times390625 \\ =1953125 \end{gathered}[/tex]Hence, the 9th term of the geometric progression is 1953125
Simplify the numerical expression (3^2 * 5^-1)^2
Simplify the numerical expression
[tex](3^2\cdot5^{-1})^{2}[/tex][tex]\begin{gathered} (9\cdot\frac{1}{5})^{2}= \\ (\frac{9}{5})^{2}= \\ \frac{81}{25} \end{gathered}[/tex]Hi! I was absent today and did not understand this lesson please I will be really grateful if you help me ! I appreciate it this is classwork assignment does not count as a test
Answer:
Given:
[tex]\begin{gathered} \sin \alpha=\frac{40}{41}first\text{ quadrant} \\ \sin \beta=\frac{4}{5},\sec ondquadrant \end{gathered}[/tex]Step 1:
Figure out the value of cos alpha
We will use the Pythagoras theorem below
[tex]\begin{gathered} \text{hyp}^2=\text{opp}^2+\text{adj}^2 \\ \text{hyp}=41,\text{opp}=40,\text{adj}=x \\ 41^2=40^2+x^2 \\ 1681=1600+x^2 \\ x^2=1681-1600 \\ x^2=81 \\ x=\sqrt[]{81} \\ x=9 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \cos \alpha=\frac{\text{adjacent}}{\text{hypotenus}} \\ \cos \alpha=\frac{9}{41} \end{gathered}[/tex]Step 2:
Figure out the value of cos beta
To figure this out, we will use the Pythagoras theorem below
[tex]\begin{gathered} \text{hyp}^2=\text{opp}^2+\text{adj}^2 \\ \text{hyp}=5,\text{opp}=4,\text{adj}=y \\ 5^2=4^2+y^2 \\ 25=16+y^2 \\ y^2=25-16 \\ y^2=9 \\ y=\sqrt[]{9} \\ y=3 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \cos \beta=\frac{\text{adjacent}}{\text{hypotenus}} \\ \cos \beta=-\frac{3}{5}(\cos \text{ is negative on the second quadrant)} \end{gathered}[/tex]Step 3:
[tex]\cos (\alpha+\beta)=\cos \alpha\cos \beta-\sin \alpha\sin \beta[/tex]By substituting the values, we will have
[tex]\begin{gathered} \cos (\alpha+\beta)=\cos \alpha\cos \beta-\sin \alpha\sin \beta \\ \cos (\alpha+\beta)=\frac{9}{41}\times-\frac{3}{5}-\frac{40}{41}\times\frac{4}{5} \\ \cos (\alpha+\beta)=-\frac{27}{205}-\frac{160}{205} \\ \cos (\alpha+\beta)=-\frac{187}{205} \end{gathered}[/tex]Hence,
The final answer = -187/205
Solve the following quadratic equation by factoring. If needed, write your answer as a fraction reduced to lowest terms
The given equation is
[tex]y^2-5y-36=0[/tex]For solving it we will factorize the number 36 as 9 x 4 which on subtraction gives 5 and on multiplication gives 36.
Then, we have
[tex]\begin{gathered} y^2-(9-4)y-36=0 \\ y^2-9y+4y-36=0 \\ y(y-9)+4(y-9)=0 \\ (y-9)(y+4)=0 \\ y-9=0\text{ and y+4=0} \\ y=p\text{ and y=-4} \end{gathered}[/tex]Hence, the values of y are 9 and -4.
Place the numbers in the table to show them in order from least to greatest
Given the following question:
[tex]\begin{gathered} -\frac{3}{8},\frac{1}{8},-\frac{1}{4},-\frac{3}{5},\frac{1}{5} \\ \text{ Negatives go first} \\ -\frac{3}{8}>-\frac{3}{5}>-\frac{1}{4} \\ \frac{1}{5}>\frac{1}{8} \\ -\frac{3}{5}<\frac{-3}{8}<\frac{-1}{4}<\frac{1}{8}<\frac{1}{5} \end{gathered}[/tex]Can u help me with my math I’m confused and don’t know
We want to find the area of the rectangle.
The area of a rectangle is given by;
[tex]\text{Area}=\text{Length x Breadth}[/tex]The length is x + 7 and the breadth is given by x + 5.
Thus the area is;
[tex]\begin{gathered} A=(x+7)(x+5) \\ A=x^2+7x+5x+35 \\ A=x^2+12x+35 \end{gathered}[/tex]Therefore, the area is;
[tex]A=x^2+12x+35[/tex]A principal of $3100 is invested at 5.5% interest, compounded annually. How much will the investment be worth after 9 years? Round your answer to the nearest dollar.
Given:
[tex]\begin{gathered} \text{Principal(P)}=\text{ \$3100 } \\ r=5.5\text{ \%} \\ n=9 \end{gathered}[/tex][tex]Final\text{ amount=P(1+}\frac{r}{100})^n[/tex][tex]\begin{gathered} Final\text{ amount after 9 years=}3100(1+\frac{5.5}{100})^9 \\ =3100(1.6191) \\ =\text{ \$50}19.21 \end{gathered}[/tex]Therefore, the investment be worth after 9 years is $5019.21
The table shows the earnings and the number of hours worked for five employees. complete the table by finding the missing values.
The first employee
[tex]\begin{gathered} He\text{ earns a total of \$12.75} \\ \text{His working rate is \$}8.50\text{ per hour} \\ \text{Hours he workd can be calculated below} \\ \text{ \$8.50 = 1 hour} \\ \text{ \$12.75 =?} \\ \text{ number of hours=}\frac{12.75}{8.50} \\ \text{ number of hours = 1.5 hours} \end{gathered}[/tex]The second employee
[tex]\text{ earning per hour = }\frac{19.09}{2.3}=\text{ \$8.3 per hour}[/tex]The third employee
[tex]\begin{gathered} \text{ \$7.75=1 hour} \\ \text{ \$26.}35=\text{?} \\ \text{ number of hours=}\frac{26.35}{7.75}=3.4\text{ hours} \end{gathered}[/tex]The fourth employee
[tex]\text{earning per hour = }\frac{49.50}{4.5}=\text{ \$}11\text{ per hour}[/tex]The fifth employee
[tex]\text{earning per hour=}\frac{31.50}{1.5}=\text{ \$21 per hour}[/tex]In Mrs. Franco‘s class for every 64 is there a April right the ratio of boys to girls in simplest form
The ratio of boys to girls in Mrs. Franco's class is 3:2 .
The Ratio is defined as the comparison of two quantities that have the same units .
In the question ,
it is given that
In Mrs. Franco's class
For every 6 boys there are 4 girls in the class
we have to find the ratio of , boys to girls
the number of boys = 6
the number of girls = 4
So , the ratio can be written as
boys / girls = 6/4
writing the ratio in the simplest form , we get
boys/girls = 3/2
the ratio is 3:2 .
Therefore , The ratio of boys to girls in Mrs. Franco's class is 3:2 .
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Can the three segments below form a triangle? Explain how you will change the length of one or two of these segments to form each kind of triangle. If no changes needed enter the original length or state that no changes needed. scalene triangleAB=… BC=…. AC=… equilateral triangleAB = … BC = … AC = …isosceles triangleAB = … BC = … AC = …
ANSWERS
• They cannot form a triangle
,• Scalene triangle: ,AB = 7
,• Equilateral triangle: ,BC = 5, AC = 5
,• Isosceles triangle: ,AB = 8
EXPLANATION
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side,
[tex]\begin{gathered} 14+8>5\Rightarrow true \\ 14+5>8\Rightarrow true \\ 5+8>14\Rightarrow false \end{gathered}[/tex]Hence, these side lengths cannot form a triangle.
To form a scalene triangle one of the shortest sides must be larger, for example, AB should be 7, instead of 5. Other combinations are possible as well.
To form an equilateral triangle all sides must have the same length, for example, AB = BC = AC = 5
To form an isosceles triangle, two of the sides must have the same length, while the third side has a different length, for example, AB = 8
To form all three kinds of triangles, the first rule must be valid as well.
Which ordered pair represent points on the graph of this exponential function?f(x) = 2^x+1A(1, 3)B(-4, -7)C(-2, -3)D(4, 9)
Answer:
[tex]A(1,3)[/tex]Step-by-step explanation:
To determine which of the given ordered pairs belongs to the given function, substitute each x-value and see if the y-value is correct.
[tex]\begin{gathered} f(1)=2^1+1 \\ f(1)=3 \\ \\ f(-4)=2^{-4}+1 \\ f(-4)=\frac{17}{16} \end{gathered}[/tex][tex]\begin{gathered} f(-2)=2^{-2}+1 \\ f(-2)=\frac{5}{4} \\ \\ f(4)=2^4+1 \\ f(4)=17 \end{gathered}[/tex]Therefore, the only point that represents points on the given function is A(1,3)
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula,and solve the two equations for x and y.)midpoint (1,17), endpoint (-5,13)
The coordinates of a midpoint of a line delimited by two endpoints is:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2} \\ y_m=\frac{y_1+y_2}{2} \end{gathered}[/tex]Where (xm,ym) are the coordinates of the midpoint, (x1,y1) are the coordinates of the first endpoint and (x2,y2) are the coordinates of the second endpoint. We want to find (x2,y2), therefore:
[tex]\begin{gathered} 1=\frac{-5+x_2}{2} \\ 2=-5+x_2 \\ x_2=2+5=7 \end{gathered}[/tex][tex]\begin{gathered} 17=\frac{13+y_2}{2} \\ 34=13+y_2 \\ y_2=34-13 \\ y_2=21 \end{gathered}[/tex]The coordinates of the endpoint two are (7,21).
In the expression 27 = 9x3-4x2, explain why 27 = 9 is the first operation you would do.
You follow the rule
PEMDAS
When doing order of operation questions.
P - Parenthesis
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Note: You can interchange M and D. Also A and S.
Thus, in the expression shown, we can do the division first.
27 and 9
Can someone help me with this geometry question I don’t know if I’m right or wrong?
Given:-
A circle has a central angle 135 degrees.
The radius of the circle is 24.
To find the arc length.
So now we use the formula,
[tex]s=r\theta[/tex]Now we convert 135 degrees to radians. so we get,
[tex]135=\frac{135}{180}\times\pi[/tex]So now we substitute the value. so we get,
[tex]\begin{gathered} s=24\times\frac{135}{180}\times\pi \\ s=18\pi \end{gathered}[/tex]So the required value is,
[tex]18\pi[/tex]So the correct option is OPTION D.
4. You are making guacamole for a familygathering. Your first trip to the store, youpurchased 5 avocados and 3 pounds of tomatoesfor $13.30. The head count changed, and youwent back for an additional 3 avocados and 8pounds of tomatoes, spending another $22.55.What is the price per avocado and pound oftomatoes?
hello
to solve this question, we need to write an equation expressing the word problem and solve for the price of each item.
let x represent the cost of avocados
let y represent the cost of tomatoes
[tex]\begin{gathered} 5x+3y=13.30\ldots\text{.equation 1} \\ 3x+8y=22.55\ldots\text{.equation 2} \end{gathered}[/tex]from equation 1, let's make xthe subject of formula
[tex]\begin{gathered} 5x+3y=13.30 \\ 5x=13.30-3y \\ \text{divide both sides by 5 to solve for x} \\ x=\frac{13.30-3y}{5} \\ \text{this is equation 3} \end{gathered}[/tex]put equation 3 into equation 2
[tex]\begin{gathered} 3x+8y=22.55 \\ 3(\frac{13.30-3y}{5})+8y=22.55 \\ \frac{39.9-9y}{5}+8y=22.55 \\ \text{solve for y} \\ \frac{39.9-9y+40y}{5}=22.55 \\ \frac{39.9+31y}{5}=22.55 \\ 39.9+31y=22.55\times5 \\ 39.9+31y=112.75 \\ 31y=112.75-39.9 \\ 31y=72.85 \\ y=\frac{72.85}{31} \\ y=2.35 \end{gathered}[/tex]since y = 2.35, let's put that in either equation 1 or 2
from equation 2
3x + 8y = 22.55
put y = 2.35 and solve for x
[tex]\begin{gathered} 3x+8y=22.55 \\ y=2.35 \\ 3x+8(2.35)=22.55 \\ 3x+18.8=22.55 \\ 3x=22.55-18.8 \\ 3x=3.75 \\ x=\frac{3.75}{3} \\ x=1.25 \end{gathered}[/tex]from the calculations above, the price per avocado and pound of tomatoes are $1.25 and $2.35 respectively
In 2000, the population of a town was 46.020. By 2002 wpulation had increased to52,070. Assuming that the towns population is increasing linearly answer the followingquestions.a.What is the population of the town by 2006?
We know that the population increased linearly, so an adequate model for the population P in year t is:
[tex]P(t)=m\cdot t+b[/tex]We know that in 2000 the population is 46,020.
In 2002 the population is 52,070.
This are two points of the line that can be written as (2000, 46020) and (2002, 52070).
Then, we can calculate the slope m as:
[tex]m=\frac{P_2-P_1}{t_2-t_1}=\frac{52070-46020}{2002-2000}=\frac{6050}{2}=3025[/tex]With the slope value we can write the equation in slope-point form:
[tex]\begin{gathered} P-P_0=m(t-t_0) \\ P-46020=3025(t-2000) \\ P=3025(t-2000)+46020 \end{gathered}[/tex]With the linear equation defined like this (we don't need to calculate the y-intercept), we can calculate the population expected for 2006:
[tex]\begin{gathered} P(2006)=3025(2006-2000)+46020 \\ P(2006)=3025\cdot6+46020 \\ P(2006)=18150+46020 \\ P(20060)=64170 \end{gathered}[/tex]Answer: the population in 2006 is expected to be 64,170.
can you please solve this for me I'll make sure to give the best review
-9 is an integer
the location of -9 is with 41
6.3 is a repeating decimal
the location is with 5.86666...
-4/5 is a fraction
the location is with 11/12
Write the standard form of the equation of the circle described below
Given:
Center ( 8, -4)
Radius (r) = 3
Find-:
Standard equation of a circle
Explanation-:
The standard equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where,
[tex]\begin{gathered} (h,k)=\text{ Center} \\ \\ r=\text{ Radius} \end{gathered}[/tex]So equation of circle is:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \\ (h,k)=(8,-4) \\ \\ r=3 \end{gathered}[/tex][tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \\ (x-8)^2+(y-(-4))^2=3^2 \\ \\ (x-8)^2+(y+4)^2=9 \end{gathered}[/tex]Using trigonometry functions find the value missing in the diagram round to the nearest whole number
Given a right angle triangle
As shown:
Given ∠58
the opposite side to the angle = 22
The adjacent side to the angle = x
So,
[tex]\begin{gathered} \tan 58=\frac{\text{opposite}}{\text{adjacent}} \\ \\ \tan 58=\frac{22}{x} \end{gathered}[/tex]solve for x:
[tex]x=\frac{22}{\tan 58}\approx13.747[/tex]round to the nearest whole number
So, the answer will be x = 14
Order the following from least to greatest: 0.232, 1.2, 1.09, 0, 3, 0.9
Answer:
0, 0.232 , 0.9 , 1.09, 1.2 , 3
hi i need help here please help me i am in need of the helps
The area of the octagon shaped stop sign = areas of the 4 rectangles + 4 triangles + square = 478 in.².
How to Find the Area of a Triangle and the Area of a Rectangle?Area of rectangle = (length)(width).Area of triangle = 1/2(base)(height).Area of square = (side length)².If the octagon can be decomposed into 4 identical triangles, 4 identical rectangles, and a square, the following are the dimensions of each of the shapes given:
Height of the triangle = (24 - 10)/2 = 7 in.
Base of the triangle = 7 in.
Side length of the square = 10 in.
Length of rectangle = 10 in.
Width of rectangle = 7 in.
The area of the octagon shaped stop sign = 4(1/2 × base × height) + 4(length × width) + (side length)²
Substitute the values into the equation
The area of the octagon shaped stop sign = 4(1/2 × 7 × 7) + 4(10 × 7) + (10)²
The area of the octagon shaped stop sign = 478 in.².
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For each ordered pair, determine whether it is a solution to 7x - 4y = -5.(x,y)(-2,6) it is a solution yes or no(1,3) it is a solution yes or no(-3,4) it is a solution yes or no(4,2) it is a solution yes or no
If x=1, then:
[tex]\begin{gathered} 7(1)-4y=-5 \\ \Rightarrow-4y=-5-7=-12 \\ \Rightarrow y=\frac{-12}{-4}=3 \\ \\ y=3 \end{gathered}[/tex]therefore, a solution to the equation 7x-4y=-5 is (1,3)
the perimeter of the rectangle belowis 112 units. Find the value of y
Question:
Solution:
The perimeter of a rectangle is the sum of the lengths of its sides. According to this, we get the following equation:
[tex]P\text{ = 2(4y+2)+2(5y)}[/tex]since P = 112, we obtain:
[tex]112\text{ = 2(4y+2)+2(5y)}[/tex]Applying the distributive property, we obtain:
[tex]112\text{ = 8y+4+10y}[/tex]this is equivalent to:
[tex]18y\text{ = 112-4}[/tex]that is:
[tex]18\text{ y = 108}[/tex]solving for y, we get:
[tex]y\text{ = }\frac{108}{18}=6[/tex]that is:
[tex]y\text{ = 6}[/tex]so that, we can conclude that the correct answer is:
[tex]6[/tex]