The value of a is 80
Step-by-step explanation:
The distance of a point [tex](x_0,y_0)[/tex] from the y-axis can be written as
[tex]d_y = |x_0|[/tex]
because the x-coordinate of the y-axis is zero.
Similarly, the distance of a point [tex](x_0,y_0)[/tex] from the x-axis can be written as
[tex]d_x=|y_0|[/tex]
Since the y-coordinate of the x-axis is zero.
In this problem:
- The distance of the point A (−30, −45) from the y-axis can be written as
[tex]d_A = |-30|=30[/tex]
- The distance of point B (a,a) from the x-axis can be written as
[tex]d_B = |a| = a[/tex]
Since [tex]a>0[/tex].
We are told that 2/3 of the distance from the y-axis to point A (−30, −45) is equal to 1/4 of the distance from the x-axis to point B(a, a), which means
[tex]\frac{2}{3}d_A = \frac{1}{4}d_B[/tex]
Therefore,
[tex]\frac{2}{3}(30)=\frac{1}{4}a[/tex]
And solving for a,
[tex]20=\frac{1}{4}a\\a=80[/tex]
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Answer:
40
Step-by-step explanation:
Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of 4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment? Group of answer choices $104.54 $378.21 $450.71 $1225.56
Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of 4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?
$450.71
____________________________
*100% CORRECT ANSWERS
Question 1
A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 years and making monthly payments. What is the monthly payment?
$1082.84
Question 2
A family is purchasing a house and needs to finance a 195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 years and making monthly payments. What is the total amount the family will pay back to the bank (to the nearest dollar)?
$389,822
Question 3
Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of 4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?
$450.71
A pharmacist has a 6% solution of cough syrup and a 14% solution of the same cough syrup. How many ounces of each must be mixed to make 16 ounces of a 10% solution of cough syrup?
Answer:
8 ounces of each must be mixed to make 16 ounces of a 10%solution.
Step-by-step explanation:
The careful analysis and detailed calculation is as shown in the attached file.
Find the area of the shape (1,3) (5,3) (7,-1) (1,-1)
Step-by-step explanation:
The given four sides of quadrilateral = (1,3), (5,3), (7,-1) and (1,-1)
To find, the area of the shape (quadrilateral) = ?
We know that,
The area of quadrilateral = [tex]\dfrac{1}{2} [x_{1}( y_{2}-y_{3})+x_{2}( y_{3}-y_{4})+x_{3}( y_{4}-y_{1})+x_{4}( y_{1}-y_{2})][/tex]
= [tex]\dfrac{1}{2} [1( 3+1)+5( -1+1)+7( -1-3)+1}( 3-3)][/tex]
= [tex]\dfrac{1}{2} [1(4)+5( 0)+7( -4)+1}( 0)][/tex]
= [tex]\dfrac{1}{2} [4+0-28+0][/tex]
= [tex]\dfrac{1}{2} [32][/tex]
= 16 square units.
Thus, the area of the shape (quadrilateral) is 16 square units.
Multiples of 3 and 5 Problem 1 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000.
Answer: 233,168
Step-by-step explanation:
Formula: 1 + 2 + 3 + ... + n = n(n+1)/2
Sum of all the numbers below 1000 that is divisible by 3:
3 + 6 + 9 + ... + 999 = 3 (1 + 2 + 3 + ... + 333) = 3 x 333 x 334 / 2 = 166,833
Sum of all the numbers below 1000 that is divisible by 5:
5 + 10 + 15 + ... + 995 = 5 (1 + 2 + 3 + ... + 199) = 5 x 199 x 200 / 2 = 99,500
As we add up 166,833 and 99,500, the numbers that are divisible by 3*5 = 15 would be counted double. Therefore, subtract the result for numbers divisible by 15 just once:
Sum of all numbers below 1000 that is divisible by 15:
15 + 30 + 45 + ... + 990 = 15 (1 + 2 + 3 + ... + 66) = 15 x 66 x 67 / 2 = 33165
Therefore, [ 166,833 + 99,500 ] - 33,165 = 233,168
To find the sum of all the multiples of 3 or 5 below 1000, you need to find the sum of the multiples of 3 and 5 separately and then subtract the sum of the multiples of 15. The sum is 233,003.
Explanation:To find the sum of all the multiples of 3 or 5 below 1000, we can use the concept of arithmetic series. First, we need to find the sum of the multiples of 3 and the sum of the multiples of 5 below 1000. Then, we need to subtract the sum of the multiples of 15 (since numbers that are multiples of both 3 and 5 have been counted twice).
Using the formula for the sum of an arithmetic series, the sum of the multiples of 3 below 1000 is given by:
3 + 6 + 9 + ... + 999 = (1/2)(3 + 999)(333) = 166,833
Similarly, the sum of the multiples of 5 below 1000 is:
5 + 10 + 15 + ... + 995 = (1/2)(5 +995)(199) = 99,500
Finally, the sum of the multiples of 15 below 1000 is:
15 + 30 + 45 + ... + 990 = (1/2)(15 + 990)(66) = 33,330
Now, we can calculate the sum of all the multiples of 3 or 5 by adding the sum of the multiples of 3 to the sum of the multiples of 5 and then subtracting the sum of the multiples of 15:
166,833 + 99,500 - 33,330 = 233,003
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Below is the five-number summary for 136 hikers who recently completed the John Muir Trail (JMT). The variable is the amount of time to complete the 212-mile hike from Yosemite Valley across the high Sierras to the top of Mount Whitney. Five-number summary: Minimum: 9 days Q1: 18 days Median: 21 days Q3: 28 days Maximum: 56 days If we use the 1.5 * IQR rule to determine whether there are any outliers, what is the right boundary?
Answer:
43
Step-by-step explanation:
We have the following data:
Total number of hikers: 136
Minimum: 9 days
Q1 : 18 days
Median: 21 days
Q3: 28 days
Maximum: 56 days
Using the 1.5 Interquartile rule means:
Left boundary: Q1 - 1.5 × IQR
Right boundary: Q3 + 1.5 × IQR
We first calculate the IQR (Interquartile Range): Q3 - Q1
⇒ 28 - 18 = 10
Right boundary: 28 + 1.5 × 10
= 28 + 15
= 43
Hence the right boundary is 43.
Johns bank account increased in value from last year to this year by 8% to $250 if the the account increases by the same percentage over the next year what will be the value next year
A.$258
B.$260
C.$264
D.$268
E.$270
Answer:
$ 270
Step-by-step explanation:
Do 250 X 1.08 to get the answer
Using the percentage increase formula, John's bank account value of $250 will increase by 8% to $270 after one year.
To find the future value of John's bank account, we will use the percentage increase formula. If his account increased by 8% this year to $250, we can calculate next year's balance by multiplying $250 by 1.08 (which represents a 100% principal plus an 8% increase).
Step-by-step calculation:
Convert the percentage increase to a decimal: 8% becomes 0.08.Add 1 to the decimal equivalent of the percentage increase to find the growth factor: 1 + 0.08 = 1.08.Multiply the current year's value by the growth factor: $250 times 1.08.Calculate the result: $250 times 1.08 = $270.Therefore, the value of John's bank account if it increases by the same percentage over the next year will be $270.
Use the following recursive formula to answer the question.
a1=−3/2
an=an−1+1/2
What is a9?
Answer:
2 1/2
Step-by-step explanation:
Each term is 1/2 added to the previous term. The first term is -3/2, so the first 9 terms of the sequence are ...
-3/2, -1, -1/2, 0, 1/2, 1, 1 1/2, 2, 2 1/2
a9 is 2 1/2.
I'm pretty sure the answer to
a1=−32
an=an−1+12
is 5/2
A box of pencils costs $3.25 and a box of colored pencils costs $4.65. However, a box of pencils and a box of colored pencils are sold together at $6.50. If Alex wants to buy 6 boxes of pencils and 9 boxes of colored pencils, what is the least amount of money that Alex can pay?
Answer:
the least is 40
Step-by-step explanation:
if u multiply each money amount times the amount they bought you get the awnser
Can someone please help me?!?
Write an equation for the sine wave. What is the amplitude and period?
Now, you are going to determine the frequency of the tone you created.
Frequency=1/period
Part2
Finally, do some research on different frequencies. Pick 3 different sounds and determine their frequency. Compare and contrast those sounds to the frequency of your tone. What conclusions can you make about frequency?
Answer:
See the explanation.Step-by-step explanation:
Part 1:
An equation of sine wave can be written as y = 5 Sin(2x + 3).
The amplitude of the above equation is 5.
The period of the function is [tex]\frac{2\pi }{2} = \pi[/tex].
The frequency of the function is [tex]\frac{1}{\pi }[/tex].
Part 2:
[tex]y = 2 Sin(3x + 5) + 9.......(1)\\y = 5 Sin(4x + 8) + 12.....(2)\\y = 3 Sin(x + 6) + 2......(3)[/tex]
The above given equations numbered 1, 2 and 3 represents three different sound waves.
For (1), the frequency is [tex]\frac{1}{\frac{2\pi }{3} } = \frac{3}{2\pi }[/tex].
For (2), the frequency is [tex]\frac{4}{2\pi } = \frac{2}{\pi }[/tex].
For (3), the frequency is [tex]\frac{1}{2\pi }[/tex].
Frequency of sounds refers the speed of vibration.
The taken three siounds has different frequencies.
Guided Practice
Which of the following is a Pythagorean triple?
A. 15, 20, and 25
B. 15, 16, and 24
O
c. 15, 21, and 28
Answer:
A. 15, 20, and 25
Step-by-step explanation:
Note that 3-4-5 is a pythagorean triple via following:
[tex]\sqrt{ (3^2 + 4^2 )} = 5^2[/tex]
Dividing 15, 20, and 25 by 5 nets you the pythagorean triple 3-4-5.
If a line of one billion people standing shoulder to shoulder stretches 420,334 miles what is the average shoulder width in feet of the people in line
Answer:
2.21936352 feet
Step-by-step explanation:
420334*5280 (thats feet in a mile) divided by 1000000000
Yo sup??
Average shoulder width=total lenght / number of people
since we want it in inches therefore
Final answer=Average shoulder width*63360
=420334*63360/1,000,000,000
=26.62 inches
Hope this helps
A foot path of uniform width runs all around inside of a rectangle field 45m long and 36m wide.If the area of the path is 234 m , find the width of the path
Answer:
The width of path is 1.5 m
Step-by-step explanation:
We are given the following in the question:
Field:
Length = 45 m
Width = 35 m
Area of filed =
[tex]\text{Area} = \text{Length}\times \text{Width} = 45\times 36 = 1620[/tex]
The area of rectangular field the is 1620 square meter.
Area of path = 234 m
Let x be the width of path.
Area of field without path = 1620 - 234 = 1386 square meter.
Now, dimensions of field without path is:
Length = [tex]45 -x - x = 45 -2x[/tex]
Width = [tex]36 -x - x = 36 - 2x[/tex]
[tex]\text{Area} = \text{Length}\times \text{Width}[/tex]
Thus, we can write:
[tex](45-2x)(36-2x) = 1386[/tex]
[tex]1620 - 90x - 72x + 4x^2 = 1386\\4x^2 - 162x + 234 = 0\\2x^2 - 81x + 117 = 0\\(2x - 3)(x - 39) = 0\\x = 1.5, x = 39[/tex]
We cannot take the width as 39 m, thus, the width of path is 1.5 m.
A piece of wire 40 cm long is cut into two piece, each to be bent to make a square.The length of a side of one square is to be 4 longer than length of a side of the other. How should the wire be cut
Answer: the wire should be cut into 12 cm and 28 cm
Step-by-step explanation:
All sides of a square is equal.
The perimeter of a square is the distance around the square.
Let L represent the length each side of one of the squares. Then the perimeter of this square is 4L.
The length of a side of one square is to be 4 longer than length of a side of the other. This means that the length of each side of the other square is L + 4
The perimeter of the other square would be 4(L + 4) = 4L + 16
Since the piece of wire is 40 cm long, then
4L + 4L + 16 = 40
8L = 40 - 16 = 24
L = 24/8 = 3
The perimeter of the first square is
4L = 4 × 3 = 12
The perimeter of the second square is
4L + 16 = 4 × 3 + 16= 28
Final answer:
To make two squares with one side being 4 cm longer than the other, a 40 cm wire should be cut into pieces of 12 cm and 28 cm.
Explanation:
The question concerns cutting a 40 cm long piece of wire into two pieces to form two squares, where the length of a side of one square is 4 cm longer than the length of a side of the other square. Let's denote the length of the side of the smaller square as x cm. Thus, the side of the larger square will be x + 4 cm. Since the perimeter of a square is four times its side length, the total length of wire used for the smaller square will be 4x cm, and for the larger square will be 4(x + 4) cm.
Combining the total length of both squares, we have:
4x + 4(x + 4) = 40
This simplifies to:
8x + 16 = 40
Subtracting 16 from both sides, we get:
8x = 24
Dividing both sides by 8, we find:
x = 3
Therefore, the side of the smaller square is 3 cm, and the side of the larger square is 7 cm. To find out how long each piece of wire must be cut, we calculate the perimeters:
Smaller square wire length: 4(3) = 12 cm
Larger square wire length: 4(7) = 28 cm
So the wire should be cut into one 12 cm piece and one 28 cm piece.
A golden rectangle has side lengths in the ratio of about 1 to 1.62. To the nearest tenth, what is length of the shorter side of a golden rectangle with a longer side length of 40 inches?
Answer: The length of the shorter side of a golden rectangle is about 24.7 inches.
Step-by-step explanation:
Given : A golden rectangle has side lengths in the ratio of about 1 to 1.62.
Since 1.62 > 1 , so
[tex]\dfrac{\text{Length of shorter side}}{\text{Length of longer side}}=\dfrac{1}{1.62}[/tex]
If the length of the longer side is 40 inches , then we have
[tex]\dfrac{\text{Length of shorter side}}{\text{40 inches}}=\dfrac{1}{1.62}\\\\ \Rightarrow\ \text{Length of shorter side}=\dfrac{1}{1.62}\times \text{40 inches}\\\\ \Rightarrow\ \text{Length of shorter side}=24.6913580247\approx24.7\text{ inches}[/tex]
Hence, the length of the shorter side of a golden rectangle is about 24.7 inches.
To find the length of the shorter side of a golden rectangle with a longer side of 40 inches, divide 40 by the golden ratio (1.62), yielding approximately 24.7 inches as the length of the shorter side, rounded to the nearest tenth.
Explanation:To calculate the length of the shorter side of a golden rectangle with a longer side length of 40 inches, we use the ratio of the sides of a golden rectangle. Given that this ratio is about 1 to 1.62, we divide the length of the longer side by the golden ratio (approximately 1.62) to find the length of the shorter side.
Using this method:
Length of longer side = 40 inchesLength of shorter side = 40 inches / 1.62Let's do the calculation:
Length of shorter side ≈ 24.7 inches (rounded to the nearest tenth)
Maria went to the restaurant and waited 90 seconds to place her order. Use the trend line equation to predict how many employees were working. Round to the nearest whole number if necessary.
Answer:
3 employees
Step-by-step explanation:
The complete question is
The manager of a fast food restaurant collected data to study the relationship between the number of employees working registers and the amount of time customers waited in line to order. He made a scatter plot of the data and created a trend line with the equation y = -70x + 300, where y is the total amount of time waited in seconds and x is the number of employees working registers. Maria went to the restaurant and waited 90 seconds to place her order. Use the trendline equation to predict how many employees were working. Round to the nearest whole number if necessary.
Let
x ---> is the number of employees working registers
y ---> is the total amount of time waited in seconds
we have
[tex]y=-70x+300[/tex]
This is the equation of a line in slope intercept form
where
The slope is equal to
[tex]m=-70\ \frac{seconds}{employee}[/tex] ---> is negative because is a decreasing function
The y-intercept is equal to
[tex]b=300\ sec[/tex]
For y=90 seconds
substitute in the linear equation and solve for x
[tex]90=-70x+300[/tex]
[tex]70x=300-90\\70x=210\\x=3\ employees[/tex]
To predict the number of employees based on a 90-second wait time, substitute 90 into the given trend line equation and solve for y. For example, using y = -0.1x + 10, we get approximately 1 employee. Ensure you use the specific trend line equation provided for accurate results.
To predict how many employees were working based on Maria's wait time of 90 seconds, we need the trend line equation that describes the relationship between waiting time and the number of employees.
Assuming we have a trend line equation of the form y = mx + b,
where y represents the number of employees, x the waiting time in seconds, and m and b are constants,you can substitute 90 for x and solve for y.
For example, if the trend line equation is y = -0.1x + 10, substituting 90 for x:
y = -0.1(90) + 10
y = -9 + 10
y = 1
Therefore, according to this trend line, approximately 1 employee would be working. Always remember to check your specific trend line equation and solve accordingly.
Y=2x-7, 3x-2=9 solving systems
When using rational expectations, forecast errors will, on average, be ________ and ________ be predicted ahead of time. A) zero; cannot B) negative; can C) positive; can D) positive; cannot
Answer:
A) zero; cannot
Step-by-step explanation:
In line with the principle of rational expectations, expectation errors are unpredictable. The expectations of all available information will not differ from the optimal projections.The word optimal projection is inexorably intertwined with the best guess in rational expectations theory.
An array with m rows and n columns is not: A: An m-by-n array. B: An n-by-m array. C: A two-dimensional array. D: An n times m dimensional array.
Answer:
B, An n-by-m array.
Step-by-step explanation:
when working with 2D arrays, rows come first and then columns. so all options here are correct except option B
PLEASSEEEEEEEE HELP!!!
Answer:
Step-by-step explanation:
Triangle DEF is a right angle triangle.
From the given right angle triangle
DF represents the hypotenuse of the right angle triangle.
With m∠D as the reference angle,
DE represents the adjacent side of the right angle triangle.
EF represents the opposite side of the right angle triangle.
To determine EF, we would apply the Sine trigonometric ratio
Sin θ = opposite side/hypotenuse. Therefore,
Sin 26 = EF/4.5
0.44 = EF/4.5
EF = 4.5 × 0.44 = 1.98 yo 2 decimal places
State whether the data are best described as a population or a sample. A questionnaire to understand athletic participation on a college campus is emailed to 40 college students, and all of them respond.
Answer:
Sample
Step-by-step explanation:
The part or portion of a population is called as sample. The given data represents a sample because a questionnaire is given to the selected 40 college students for collecting response on athletic participation rather to all of the college students. Thus, the questionnaire is given to a part of population. So, the given data represents a sample.
Please help I've been stuck on this question for a while now. How do I solve (1/2)^4 (1/2)^-2? It has to do with Multiplying and Dividing Expressions with Exponents. Please show work so I may figure it out on my own.
The value of the expression is [tex]0.25[/tex]
Explanation:
The expression is [tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}$[/tex]
Since, the base of the expression is the same. Then, by "product rule", when multiplying two powers that have the same base, you can add the exponents.
Thus, we have,
[tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}=\left(\frac{1}{2}\right)^{4-2}$[/tex]
Adding the exponents, we have,
[tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}=\left(\frac{1}{2}\right)^{2}$[/tex]
Applying exponent rule, [tex]$\left(\frac{a}{b}\right)^{c}=\frac{a^{c}}{b^{c}}$[/tex], we have,
[tex]$\left(\frac{1}{2}\right)^{2}=\frac{1^{2}}{2^{2}}$[/tex]
Simplifying, we get,
[tex]\frac{1}{4}[/tex]
Dividing, we have,
[tex]0.25[/tex]
Thus, the value of the expression is [tex]0.25[/tex]
A pizza is cut into five pieces. Four of the pieces are the same size, and the fifth size is .5 the size of each of the others. What fraction of the pizza is the smallest piece
Answer:
1/10 of pizza
Step-by-step explanation:
Let x represent size of equal pieces.
We have been given that a pizza is cut into five pieces. Four of the pieces are the same size, and the fifth size is 0.5 the size of each of the others.
This means that size of small piece would be half the size of other pieces, that is [tex]\frac{x}{2}[/tex].
Since the pizza is divided in 5 pieces, so we will divide [tex]\frac{x}{2}[/tex] by 5 as:
[tex]\frac{\frac{x}{2}}{5}=\frac{x}{2\cdot5}=\frac{x}{10}=\frac{1}{10}x[/tex]
Therefore, the smallest piece is 1/10 of the pizza.
The person is a member for super for a female boss over in the and loss increased approximately linearly from 5% in 1974 to 9% in 1998. Predict when 9% of male workers will prefer a female boss.
Answer:
1998
y=6x+1944
Step-by-step explanation:
The percentage of Male workers who prefer a female boss over a male boss increased approximately linearly from 5% in 1974 to 9% in 1998. Predict when 9% of male workers will prefer a female boss
it is explicit from the question that 9% of male workers prefer female boss in 1998. but we can predict a model for this by getting the slope of the graph
y=the year
x=the percentage of men who prefer a female boss
s=y2-y1/(x2-x1)
s=1998-1974/(9-5)
s=24/4
s=6
therefore we have
y=mx+c
y=6x+c........1
when y=1998,x=9
1998=6(9)+c
c=1944
from equation 1
y=6x+1944
The formula for the perimeter of a rectangle with length and width is as follows. Suppose the length of the rectangle is 5 times the width. Rewrite in terms of only. It is not necessary to simplify?
Answer:
P = 2(5W + W)
Step-by-step explanation:
P = 2(L +W)
L = 5W
P = 2(5W + W)
P = 10W + 2W
P = 12W
An initial investment of $1000 is appreciated for 4 years in an account that earns 4% interest, compounded annually. Find the amount of money in the account at the end of the period.
Answer: $116.99
Step-by-step explanation:
By using compound interest formula which said:
A = P ( 1 + r/n )^(n×t)
P=Principal= 1000
r=rate=4/100
n=1
t= 4
Apply the above formula
A = P ( 1 + r/n )^(n×t)
A = 1000(1 + 0.04/1)^(1 × 4)
A= 100(1.04)^4
A= 100 × 1.17
A = 116.99
5 years ago, the age of a man was 7 times the age of his son. After five years, the age of the man will be 3 times the age of his son from now. How old are the man and the son now?
Answer:
10 years
40 years
Step-by-step explanation:
let present ag e of son=x
5 years ago age of son=x-5
5 years ago age of man=7(x-5)=7x-35
present age of man=7x-35+5=7x-30
after 5 years
age of son=x+5
age of man=7x-30+5=7x-25
also 7x-25=3(x+5)
7x-25=3x+15
7x-3x=15+25
4x=40
x=10
age of son=10 years
age of man=7*10-30=70-30=40 years
Final answer:
By creating equations from the given information and solving them, it was found that the man is currently 40 years old, and his son is 10 years old.
Explanation:
Let's solve the problem using algebra. Suppose the current age of the man is M years and the current age of his son is S years.
According to the problem, 5 years ago, the age of the man was 7 times the age of his son. Therefore, M - 5 = 7(S - 5).
After 5 years, the age of the man will be 3 times the age of his son from now. Therefore, M + 5 = 3(S + 5).
Solving these equations:
M - 5 = 7S - 35
M + 5 = 3S + 15
Simplifying both:
M = 7S - 30
M = 3S + 10
Equating both equations we get:
7S - 30 = 3S + 10
4S = 40
S = 10
Substituting the value of S in the first equation:
M = 7*10 - 30 = 40
Therefore, the man is currently 40 years old, and his son is 10 years old.
Amy has a collection of marbles in three sizes, small, medium, and large. She has five times as many small marbles as medium marbles. The number of large marbles is two more than three times the number of medium marbles. a. Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has. b.Write an algebraic expression to represent the number of large marbles she has. c.If Amy has a total of 560 marbles, how many of each size does she have? Show your work. (please i need help im really stuck)
Answer: she has 310 small marbles, 62 medium marbles and 188 large marbles.
Step-by-step explanation:
Let w represent the number of small marbles Amy has.
Let x represent the number of medium marbles Amy has.
Let y represent the number of large marbles Amy has.
a) She has five times as many small marbles as medium marbles. This means that
w = 5x
b) The number of large marbles is two more than three times the number of medium marbles. This means that
y = 3x + 2
c) If Amy has a total of 560 marbles, it means that
5x + x + 3x + 2 = 560
9x = 560 - 2
9x = 558
x = 558/9 = 62
w = 5x = 62 × 5
w = 310
y = 3x + 2 = 3 × 62 + 2
y = 188
Answer:
A. s = 5x
B. y = 3x + 2
C y=166
Step-by-step explanation:
Find S25 for 1/2 + 1 + 3/2 + 2 + ...
Step-by-step explanation:
The given sequence:
[tex]\dfrac{1}{2}+1+\dfrac{3}{2}+2+ ...[/tex]
Here, first term (a) = [tex]\dfrac{1}{2}[/tex], common difference(d) =[tex]1-\dfrac{1}{2}=\dfrac{1}{2}[/tex] and
the number of terms (n) = 25
The given sequence are in AP.
To find, the value of [tex]S_{25}[/tex] = ?
We know that,
The sum of nth terms of an AP
[tex]S_{n}=\dfrac{n}{2}[2a+(n-1)d][/tex]
The sum of 25th terms of an AP
[tex]S_{25}=\dfrac{25}{2}[2(\dfrac{1}{2})+(25-1)(\dfrac{1}{2})][/tex]
⇒ [tex]S_{25}=\dfrac{25}{2}[1+(24)(\dfrac{1}{2})][/tex]
⇒ [tex]S_{25}=\dfrac{25}{2}[1+12][/tex]
⇒ [tex]S_{25}=\dfrac{25}{2}[13][/tex]
⇒ [tex]S_{25}=\dfrac{325}{2}[/tex]
∴ [tex]S_{25}=\dfrac{325}{2}[/tex]
if you in invested $500 at 5% simple interest for 2 years, how much interest do you earn? show work and answer in complete sentances to earn full credit. if you invest $500 at 3% compound monthly for 2 years, how much interest do you earn? show work and answer in complete sentances to earn full credit which would you rather do?
Answer:
Step-by-step explanation:
1) The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T = 2 years
P = $500
R = 5%
Therefore
I = (500 × 5 × 2)/100
I = $50
2) Principal, P = $500
It was compounded monthly. This means that it was compounded 12 times in a year. So
n = 12
The rate at which the principal was compounded is 3%. So
r = 3/100 = 0.03
It was compounded for just 2 years. So
t = 2
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 500 (1+0.03/12)^12 × 2
A = 500 (1.0025)^24
A = $530.88
The interest is
530.88 - 500 = $30.88
A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a . 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a. Let f(x) = {((6)/(x)+(-5 x+18)/(x(x-3)), "if", x doesnt = 0 "and" x doesnt =3),( 3, "if", x=0) :} Show that f(x) has a removable discontinuity at x=0 and determine what value for f(0) would make f(x) continuous at x=0 . Must redefine f(0)= ?
The function f(x) has a removable discontinuity at x=0. To make f(x) continuous at x=0, we must redefine f(0) as -1/3.
To determine if f(x) has a removable discontinuity at x=0, we need to check if f(x) is either not defined or not continuous at x=0.
Looking at the definition of f(x), we see that f(0) is defined as 3. Therefore, f(x) is defined at x=0.
Next, let's examine the continuity of f(x) at x=0. We need to evaluate the limit of f(x) as x approaches 0.
Using the given definition of f(x), we have:
lim(x->0) (6/x) + (-5x + 18)/(x(x-3))
To evaluate this limit, we can simplify the expression by finding a common denominator. The common denominator is x(x-3):
lim(x->0) [6(x-3) + (-5x + 18)] / [x(x-3)]
Simplifying the numerator:
lim(x->0) (6x - 18 - 5x + 18) / [x(x-3)]
= lim(x->0) (x) / [x(x-3)]
Now, we can cancel out the x term:
lim(x->0) 1 / (x-3)
As x approaches 0, the denominator (x-3) approaches -3. Therefore, the limit is:
lim(x->0) 1 / (x-3) = 1 / (-3) = -1/3
Since the limit of f(x) as x approaches 0 exists and is equal to -1/3, we can redefine f(0) to be -1/3 to make f(x) continuous at x=0.
Thus, f(x) has a removable discontinuity at x=0, and we must redefine f(0)=-1/3 to make f(x) continuous at x=0.