well, from the end of year 5 to the end of year 6 is only 1 year later, so
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$3315.30\\ P=\textit{original amount deposited}\dotfill & \$3203.19\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 3315.30=3203.19[1+(\frac{r}{100})(1)] \implies \cfrac{3315.30}{3203.19}=1+\cfrac{r}{100} \\\\\\ \cfrac{3315.30}{3203.19}-1=\cfrac{r}{100}\implies 100\left( \cfrac{3315.30}{3203.19}-1 \right)=r\implies \stackrel{\%}{3.5}\approx r[/tex]
A grocer mixes two kinds of n ur s. One kind costs $5.00/kg and the other $5.80/kg. How many kilograms of each type are needed to make 40kg of a blend worth $5.50/kg?
15 kilograms of the first type should be mixed with 25 kilograms of the other kind
How to determine the kilograms of each type needed to make 40kg?If the blend costs $5.50/kg, then:
on each kg at $5.00/kg, gain = $0.50 ($5.50 - $5.00)
on each kg at $5.80/kg, loss = $0.30 ($5.50 - $5.80)
Hence 3kg of the first kind must be mixed with 5kg of the second so that the gain on the first (3 x $0.50) is exactly the same as the loss on the second (5 x $0.30)
The required proportion is 3:5
In order to find how many kilograms of each type are needed to make 40kg, we will use the proportion obtained:
We have 3:5, total share = 3+5 = 8
First kind share = 3/8 x 40 kg = 15 kg
Second kind share = 5/8 x 40 kg = 25kg
Therefore, 15 kilograms of the first type is needed and 25 kilograms of the other kind is needed
Learn more about mixtures on:
https://brainly.com/question/2914376
#SPJ1
sorry i put the wrong pic in here my question i do need help so im putting in more point
Answer:
A. (10x^2) / (5x + 4y)
B. (8xy) / (4y + 5x)
Step-by-step explanation:
A. Factor the numerator and denominator, then cancel out like terms
(10x^2(2a + 3b)) / (2a(5x + 4y) + 3b(5x + 4y))
(10x^2(2a + 3b)) / ((2a + 3b)(5x + 4y))
(10x^2) / (5x + 4y)
B. Factor the numerator and denominator, then cancel out like terms.
(8xy(3p - 4q)) / (3p(5x + 4y) - 4q(4y + 5x))
(8xy(3p - 4q)) / ((3p - 4q)(4y + 5x))
(8xy) / (4y + 5x)
The amount of money that Ryan earns is directly proportional to the number hours that he works. How much does Ryan earn per hour?
The earnings of Rayan per hour is $5 per hour
The first point = (1, 5)
The second point = (2, 10)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the function
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line m = (10-5) / (2-1)
Subtract the terms
= 5 / 1
= $5 per hour
Hence, the earnings of Rayan per hour is $5 per hour
Learn more about slope of the line here
brainly.com/question/16180119
#SPJ1
Which pair of lines are perpendicular?
A. y = -8 and y = 2
B. x = 4 and y = -1
C. x-y = 7 and y = x + 3
D. y = -4x + 1 and 8x + 2y = -10
Applying the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.
There are 4 different pairs of lines given to us.
We have to find out the pair of lines that are perpendicular to each other.
We know that the general equation of a line in slope-intercept form is represented as -
y = mx + c --- (1)
where
(x, y) = coordinates of the lines
m = slope of the line
c = y-intercept
It is also known to us that for two lines to be perpendicular the product of their slope must be equal to -1.
A. y = -8 and y = 2
Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.
So, these two pair of lines are not perpendicular.
B. x = 4 and y = -1
Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.
So, these two pair of lines are not perpendicular.
C. x - y = 7 and y = x + 3
Now, x - y = 7
=> -y = 7 - x
=> y = x - 7
Comparing this to the equation (1), we have slope of the line, m = 1.
Also, y = x + 3
Comparing this to the equation (1), we have slope of the line, m = 1.
We see that the product of the slope of these pair of lines is not equal to -1.
So, these two pair of lines are not perpendicular.
D. y = -4x + 1 and 8x + 2y = -10
Now, y = -4x +1
Comparing this to the equation (1), we have slope of the line, m = -4.
Also, 8x + 2y = -10
=> 2y = -8x - 10
=> y = -4x - 10
Comparing this to the equation (1), we have slope of the line, m = -4.
We see that the product of the slope of these pair of lines is not equal to -1.
So, these two pair of lines are not perpendicular.
Thus, according to the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.
To learn more about slope-intercept form visit https://brainly.com/question/9682526
#SPJ1
77 is 0.7% of what number? Use pencil and paper. Would you expect the answer to be a lot less than 77, slightly less
77, slightly greater than 77, or a lot greater than 77? Explain.
77 is 0.7% of 11000
this number is a lot greater than 77.
Let 77 is 0.7% of m
0.7 percent of m = 77
(0.7/100) * m = 77
m = 77 * (100/0.7)
m = 11000
Therefore, 77 is 0.7% of 11000
this number is a lot greater than 77.
Learn more about percentage here:
https://brainly.com/question/16797504
#SPJ1
What is the length of BD?
Answer:
D stays for 1 and as B is -6
the length of BD should be 7
good luck <3!
What is the value of 0.3 + 0.4? Write your answer as a fraction in lowest terms
Answer: 7/10
Step-by-step explanation:
This is the lowest term because you add the numbers.
Brainliest if correct 5 points
Answer:
NOT CONGRUENT
Step-by-step explanation:
There are several types of congruence:
ASA - Angle Side Angle
AAS - Angle Angle Side
HL - Hypotenuse Leg
This image shows two triangles which have 2 congruent sides and one congruent angle.
Is it ASA?
There is only one congruent angle, so this cannot be congruent by ASA
Is it AAS?
By the same reasoning, it cannot be congruent by AAS.
Is it HL?
Although there are 2 congruent sides, neither one is the hypotenuse. Is is not congruent by HL.
There is no such thing as SSA congruence, because it is actually possible to have 2 non-congruent triangles who have 2 congruent sides and 1 congruent angle. Therefore, these are NOT CONGRUENT
The median monthly rent in 2005 was $694 and $810 in 2010. What was the percent increase in the median monthly rent prices from 2005 to 2010? Round to the nearest tenth of a percent.
The percent increase in the median monthly rent prices is 14.3%
How to calculate the percentage?From the information, the median monthly rent in 2005 was $694 and $810 in 2010.
The increase in the amount will be:
= $810 - $694.
= $116
The percent increase in the median monthly rent prices from 2005 to 2010 will be:
= Increase in amount / Old rent × 100
= 116/810 × 100
= 14.3%
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
Help find intercept and the slope of the line?
slope= -3/2, y-intercept=8
y=mx+b m is the slope while b is the y-inteecept
if I have 10 pancakes and I give 5 to jimmy how many pancakes do I have
Answer: 5 is the ancer
Step-by-step explanation:!
write an equation in point slope form of the line through point J(4,1) with slope -4
Answer:
y - 1 = - 4(x - 4)Step-by-step explanation:
Point- slope form:
y - y₁ = m(x - x₁), where m- the slope, (x₁, y₁) - the point on the lineGiven:
m = - 4,Point J(4, 1)Substitute into equation to get the line:
y - 1 = - 4(x - 4)The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume days in a year.
P = 7000$, r = 7.5%,15 t = months
The simple interest owned for the use of the money is $2625.
What is Simple Interest?
Simple interest is a quick and simple way to figure out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of many forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest. A loan is a sum of money that someone borrows from a bank or other financial institution to cover expenses. Home loans, auto loans, student loans, and personal loans are a few instances of loans.
In the given question we have:
Principal amount = 7000$,
Rate of interest r = 7.5%,
Time t = 15 months;
So, applying the formula to calculate simple Interest:
S.I = [tex]\frac{PRT}{100}[/tex]
S.I = [tex]\frac{7000 \times 7.5 \times 15}{ 12 \times 100}[/tex]
S. I = $2625;
Hence, The Simple Interest owed for the use of the money. is $ 2625.
To learn more about: Simple Interest, visit:
https://brainly.com/question/25793394
#SPJ1
Please I need help I don’t understand
For give expression Ben's work is correct.
In this question, Ben and Jerry both simplified the expression √24x⁵y³
where x > 0, y > 0
We need to determine which student is correct.
First we simplify given expression.
√24x⁵y³
= √(2)(2)(2)(3)(x)(x)(x)(x)(x)(y)(y)(y)
= √(2²)(2)(3)(x²)(x²)(x)(y²)(y)
= √(2²) * √(2) * √(3) * √(x²) * √(x²) * √(x) * √(y²) * √(y) ...(seperate the radical symbol)
= 2 * √(2) * √(3) * x * x * √(x) * y * √(y) ...........exponent rule
= 2x²y√(2)(3)(x)(y) ........(combine terms with same powers)
= 2x²y √6xy
So, Ben's work is correct.
We observe that by rule of exponents, the fourth step in Jerry's work is incorrect.
Therefore, Ben's work is correct.
Learn more about the expression here:
https://brainly.com/question/1859113
#SPJ1
Freida would like to invest 200 into a saving account that earns 3% interest. how much interest will Frieda have earned at the end of the year
Answer: 6 dollars
Step-by-step explanation:
Freida would have earned at the end of the year an interest of $6 for the $200 investment at 3% interest for 1 year.
The principle amount is $200
The saving account earns a interest of 3%
We need to calculate that Frieda have earned at the end of the year.
Interest = PRT/100
where p is principle
r is rate of interest
and t is the time period
= 200 x 3 x 1 / 100
= 6
Therefore, Freida would have earned an interest of $6 for the $200 investment at 3% interest for 1 year.
To learn more about interest refer here
https://brainly.com/question/25793394
#SPJ1
There are 7 highway routes from City A to City B, 8 highway routes from City B to City C, and 10 highway routes from City
C to City D. How many different highway routes are there if you want to travel to City A, B, C, and D in that order?
highway routes from City A to City D.
There are how many highway routes from city a to city d
The number of highway routes from A to D is 560
Number of highway routes from A to B = 7 highways
Number of highways routes from B to C = 8 highways
Number of highways routes from C to D = 10 highways
Number of routes from A to D = Number of highway routes from A to B × Number of highways routes from B to C × Number of highways routes from C to D
Here we have to use multiplication
Substitute the values in the equation
Number of routes from A to D = 7 × 8 × 10
= 560 highways
Hence, the number of highway routes from A to D is 560
Learn more about multiplication here
brainly.com/question/14667283
#SPJ1
The data lists the salaries at a company:
#1 - $25,000
#2- $10,000
#3- $15,000
#4- $10,000
#5- $15,000
#6- $10,000
#7- $15,000
#8- $10,000
#9- $10,000
#10- $80,000
a) Identify any outliers in the data.
b) Which measure would you use to describe the central tendency of the
dataset? (mean, median,mode)
a) Examining the data, the outlier in the data are
#1 - $25,000#10 - $80,000b) The measure I would use to describe the central tendency of the data is median
What is outlier as used in data analysis?Outlier as used in data analysis refers to a data that is abnormally away from other data. Outliers show high variability
In the given problem, $80 000 is the data that is farther away than any other data and hence the only outlier
The mean is usually a better measure of central tendency how ever the presence of outliers affects the result projected by mean.
The better choice to use here is the median
Learn more about outliers in statistics here
https://brainly.com/question/24123584
#SPJ1
Multiply the following using repeated addition: 4(-3)
For the function f(x) = x + 7, construct and simplify the difference quotient
f(x+h)-f(x) Over h
H
The value of f(x+h)-f(x) = h.
Given function:
f(x) = x + 7
difference quotient = f(x+h) - f(x)
= (x+h) - 7 - (x - 7)
= x + h - 7 - x + 7
= x - x + 7 - 7 + h
= 0 + 0 + h
= h
Therefore the value of f(x+h)-f(x) = h.
Learn more about the function here:
https://brainly.com/question/5975436
#SPJ1
Coffee Roasters has five main markets for the distribution of their premium coffee at the location coordinates given in the table below. The monthly demand at each distribution center (in 000's of lbs.) is also provided. Coffee Roasters is interested in locating a distribution center to serve these markets.
Table 2
Markets
Coordinates Demand
(‘000s lbs.)
A (20, 15) 75
B (10, 12) 50
C (15, 10) 60
D (15, 20) 80
E (12, 12) 50
Use the information in Table 2 above. What are the x and y coordinates for the center of gravity?
The center of gravity of the distribution center is located at (14.84, 12.84)
What is the center of gravity?The center of gravity is a point at which the total weight of a body can be thought to be located for calculation purposes.
The coordinates of the five distribution centers using the x and y coordinates are;
A(20, 15) 75, B(10, 12) 50, C(15, 10) 60, D(15, 20) 80, E(12, 12) 50
The center of gravity is found using the formula;
[tex]x = \dfrac{m_1\cdot g\cdot x_1+ m_2\cdot g\cdot x_2 + m_3\cdot g\cdot x_3}{m_1\cdot g+ m_2\cdot g + m_3\cdot g}[/tex]
[tex]y = \dfrac{m_1\cdot g\cdot y_1+ m_2\cdot g\cdot y_2 + m_3\cdot g\cdot y_3}{m_1\cdot g+ m_2\cdot g + m_3\cdot g}[/tex]
Coordinates of the center of gravity of the distribution center is therefore;
[tex]x = \dfrac{75\times 20+ 50\times 10+ 60\times 15+80\times 15+50\times 12}{75+50+60+80+50} \approx 14.92[/tex]
[tex]y = \dfrac{75\times 15+ 50\times 12+ 60\times 10+80\times 20+50\times 12}{75+50+60+80+50} \approx 12.84[/tex]
The coordinates of the center of gravity of the distribution center is; (14.92, 12.840
Learn more about the center of gravity here:
https://brainly.com/question/14420084
#SPJ1
In a model, the distance from the sun to Earth is 7 inches and the distance from the sun to Neptune is 19 inches. If the actual distance from the sun to Earth is 91.549 million miles and the actual distance from the sun to Neptune is 2,780.5 million miles, are the model’s distances proportional to the actual dimensions of the solar system?(1 point)
Responses
Yes, because the ratios of model length to actual distance are equal for the two planets.
Yes, because the ratios of model length to actual distance are equal for the two planets.
No, because the ratios of model length to actual distance are different for the two planets.
No, because the ratios of model length to actual distance are different for the two planets.
No, because the model is in inches and the actual distances are in millions of miles.
No, because the model is in inches and the actual distances are in millions of miles.
No, because the ratios cannot be reduced.
The model’s distances isn't proportional to the actual dimensions of the solar system as B. No, because the ratios of model length to actual distance are different for the two planets.
What is ratio?Ratio demonstrates how many times one number can fit into another number. It is used to show the comparison between two or more things
In this case, in model, the distance from the sun to Earth is 7 inches and the distance from the sun to Neptune is 19 inches. This can be illustrated as:
= 7/19
= 0.368
If the actual distance from the sun to Earth is 91.549 million miles and the actual distance from the sun to Neptune is 2,780.5 million miles, the ratio is:
= 91.549 / 2780.5
= 0.0329
Therefore, since they're different numbers, the information doesn't illustrate a proportional ratio.
Learn more about ratio on:
brainly.com/question/2328454
#SPJ1
Solve for x. Round to the nearest tenth, if necessary.
Answer:
46.9
Step-by-step explanation:
sin54=x/58
58sin54=46.922
20. Find the area of each of the following shaded regions in
parts (a)-(d). Assume all arcs are circular with centers marked. Leave all answers in terms of Pi
The area of each of the following shaded regions in parts (a)-(d) is 2
How Find the area of each of the following shaded regions?There is a space in the shaded area. Because we are given two circles inside one larger circle, the size of the darkened zone is equal to the area of the circle less the area of the circle.
They are equal to the circle to an area of circle minus an area of circle three. You can calculate the radius of the larger circle as this is likewise 1 cm. The radius refers to the location of the larger circle's center. Keep in mind that all measurements are in cm square. C2's surface area is the same as that of three.There will only be one square. The area is located in the area that is darkened. The region is equal to the size of C1 minus the areas of C2 and C3. As a result, C will be the first. C 2 and C three are the same, and the area is four pi.The answer is 2, and square meters are not the appropriate unit.
The area of each of the following shaded regions in parts (a)-(d) is 2
To learn more about area refer to:
https://brainly.com/question/25292087
#SPJ1
Truck Transport
A truck driver is beginning her haul across the country. The warehouse is 15 miles
from the highway. Once she gets on the highway she maintains a constant rate for
several hours. Complete the table of values for the sequence below that relates hours on
the highway and distance from the warehouse in miles.
Refer to the attachment for the required table:
What is the unit rate?
A unit rate is a cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
From the table,
For 0 hours, distance = 15 miles
For 1 hour, distance = 80 miles
Difference between distances= 80-15=65 miles
Since it is given that, it is at a constant rate, for every hour there is an increase of 65 miles in distance.
The completed table is shown in the attachment.
To learn more about the unit rate from the given link
https://brainly.com/question/4895463
#SPJ1
what's the skskksks of slskksksk
The height of the blade of a wind turbine as it turns through an angle of is given by the function h()=8.5sin(+180⁰) + 40, with height measured in meters.
Find the maximum and minimum positions of the blade.
Explain what the value of 40 in the equation represents.
What is the amplitude? Explain what it represents.
Sketch the function over two cycles.
Considering the sine function in this problem, we have that:
The minimum position in the table is of: 31.5The maximum position in the table is of: 48.5.The value of 40 is the vertical shift of the function.The amplitude is of 8.5.The graph of two cycles is given by the image at the end of the answer.How is the sine function defined?
The general sine function has the definition presented as follows:
f(x) = asin(b(x+c))+d.
The coefficients are given as follows:
a is the amplitude of the sine function.b: The period of the sine function is of 2π/b.c is the phase shift of the sine function.d is the vertical shift of the sine function.For this problem, the function is:
h(θ ) = 8.5 sin (θ + 180°) + 40
The amplitude is of:
a = 8.5.
The function should oscillate between:
-8.5 and 8.5.
However, with the vertical shift of 40, the minimum and maximum values are given as follows:
Minimum value: -8.5 + 40 = 31.5.Maximum value: 8.5 + 40 = 48.5.The measure of each cycle of the cosine function is of:
2π = 360º.
The function has a phase shift to the right of 180º, hence the graph is given by the image at the end of the answer, for two cycles, that is, between 0 and 4π.
More can be learned about sine functions at https://brainly.com/question/29403369
#SPJ1
megan left her house and walked 5 blocks north and 4 blocks east to a friends house. From there,she walked 5 blocks north and 6 blocks west to school for volleyball pratice. Describe where the school is in the relation to Megan's house in words and using notations
Answer: School is 10 blocks north and 2 blocks west of Megan's house. A straight line from Megan's house to school is 10.2 blocks long, Northwest
Step-by-step explanation:
5 blocks north, then 4 east, then 5 north is a total of 10 blocks north. The last turn is 6 blocks west. So she walks 4 blocks west to get her back to due north of her house then an additional 2 more blocks west.
Use the pythagorean theorem to calculate the straight line if Megan were able to take a straight path there:
Question 8
Angel Garcia deposited his $750 federal income tax refund check into his savings account.
The account pays 5% and he made no other deposits or withdrawals. How much is in the
account after 3 months?
O $937.50
$787.50
O $759.38
1 pt
O $752.12
The amount his account will have after 3 months be $ 759.38.
Given, Angel Garcia deposited his $750 federal income tax refund check into his savings account. The account pays 5% and he made no other deposits or withdrawals.
we have to find the amount in the account after 3 months,
So, the amount he made is,
Amount = 750(1 + 5/100)^0.25
Amount = 759.38
So, the amount his account will have after 3 months be $ 759.38.
Learn more about Compound Interest here https://brainly.com/question/24274034
#SPJ1
Write the equvalent fractions using 35 as a common denominater
The equvalent fractions of 5/7 using 35 as a common denominator is 25/35.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, it should be noted that the fraction given is 5/7.
The equivalent fraction will be:
= 5/7 × 5/5
= 25/35
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
Complete question
Write the equvalent fraction of 2/5 using 35 as a common denominater
What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation?
x^2+32+116=12x
Answer:
Below
Step-by-step explanation:
x^2 + 32 + 116 = 12x 1st intermediate step: put everything on one side
x^2 -12x + 148 = 0 2nd intermediate step : re-arrange with constant on R
x^2 -12x = -148 3 rd intermediate step : take 1/2 of the 'x' coefficient
square it and add to both sides
x^2 -12x + 36 = -148 + 36 4th intermediate step : simplify
(x-6)^2 = -112