$85000 was paid at a short term note at 10% interest while $75000 was paid at a long term note at 7% interest.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the amount of fund at 10% and y represent the amount of fund at 7% interest, hence:
x + y = 160000 (1)
Also:
0.1x + 0.07y = 13750 (2)
From both equations:
x = 85000 and y = 75000
$85000 was paid at a short term note at 10% interest while $75000 was paid at a long term note at 7% interest.
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(c) Mohammed's height is 169 cm and Fatima's height is 156 cm.
The frame sizes of their bikes are in the same ratio as their heights.
The frame size of Mohammed's bike is 52 cm.
Calculate the frame size of Fatima's bike.
Answer:
156 : 48
Step-by-step explanation:
Solution:
Since
169 : 52 = 156 : X
Then we know
52/169 = X/156
Multiplying both sides by 156 cancels on the right
156 × (52/169) = (X/156) × 156
156 × (52/169) = X
Then solving for X
X = 156 × (52/169)
X = 48
Therefore
169 : 52 = 156 : 48
1. Find the volume of the pyramid.
5 in
11 in
9 in
74
The volume of the pyramid with the given length, width and height is 165in³.
What is the volume of the pyramid?The volume of a right rectangular pyramid is expressed as;
V = ( L × W × H ) / 3
Given that;
Length L = 11inWidth W = 9inHeight H = 5inWe substitute into the equation above.
V = ( L × W × H ) / 3
V = ( 11in × 9in × 5in ) / 3
V = 495in³ / 3
V = 165in³
The volume of the pyramid with the given length, width and height is 165in³.
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Which is the graph of y = 2 – square root of x?
On a coordinate plane, a curved line approaches the grid line at (3, 2.3), crosses the y-axis at (0, 1.5) and ends at (negative 2, 0).
On a coordinate plane, a curved line approaches the grid line at (negative 3, 2.3), crosses the y-axis at (0, 1.5) and ends at (2, 0).
On a coordinate plane, a curved line approaches the grid line at (3, 0.3), and ends at (0, 2).
Using translation concepts, the graph of [tex]y = 2 - \sqrt{x}[/tex] is described as follows:
On a coordinate plane, a curved line approaches the grid line at (3, 0.3), and ends at (0, 2).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Function [tex]y = 2 - \sqrt{x}[/tex], in blue in the graph, is the function [tex]y = \sqrt{x}[/tex], in red, reflected over the x-axis and shifted 2 units, as shown in the graph.
Hence the correct statement is:
On a coordinate plane, a curved line approaches the grid line at (3, 0.3), and ends at (0, 2).
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What is the relationship between the lines determined by the following two equations?
15x−3y=−12
y = 5x + 7
They are the same line.
neither parallel nor perpendicular
perpendicular
parallel
Answer:
D
Step-by-step explanation:
to determine the relationship between these two lines you have to find the slope.
=> if they have the same slope ,then they are parallel.
=> if they have negative inverse slope relative to each other ,then they are perpendicular.
=> if the slope for both equations is neither of the above cases ,then the two equations are neither parallel nor perpendicular.
so if we divide the first equation by 3 which is the commen factor for the whole equation and arrange it in the form y=mx +b it would give us y =5x +4. and since the two have the same slope which is 5 ,then we can conclude they are parallel lines.
suppose that prices of a certain model of new homes are normally distributed with a mean of $150000. Use the 68-95-99.7 rule to find the percentage of buyers who paid: between $150000 and $154800 if the standard deviation is $1600
Using the Empirical Rule, it is found that 49.85% of buyers paid between $150,000 and $154,800.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Considering the given mean and standard deviation, the interval between $150,000 and $154,800 corresponds to the interval between the mean and 3 standard deviations above the mean.
The normal distribution is symmetric(50% above the mean, 50% below), hence the percentage corresponding to this interval is:
P = 0.5 x 99.7% = 49.85%.
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A pet store has 11 puppies, including 4 poodles, 5 terriers, and 2 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random with replacement (they may both select the same one), find the probability that Rebecka selects a terrier and Aaron selects a retriever.
The probability that Rebecka selects a terrier and Aaron selects a retriever is 10/121
How to determine the probability?The distribution of the puppies is given as:
4 poodles, 5 terriers, and 2 retrievers
The probability of selecting a terrier is;
P(terrier) = 5/11
The probability of selecting a retriever is;
P(retriever) = 2/11
The required probability is
P = 5/11 * 2/11
Evaluate
P = 10/121
Hence, the probability that Rebecka selects a terrier and Aaron selects a retriever is 10/121
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Find the trigonometric form of the number 3 + √3i.
Any complex number [tex]z[/tex] can be written in trigonometric form as
[tex]z = |z| e^{i\arg(z)} = |z| \left(\cos(\arg(z)) + i \sin(\arg(z))\right)[/tex]
where [tex]|z|[/tex] is the modulus of [tex]z[/tex] and [tex]\arg(z)[/tex] is its argument, i.e. the angle [tex]z[/tex] makes with the positive real axis in the complex plane.
We have
[tex]|z| = \sqrt{3^2 + \left(\sqrt3\right)^2} = \sqrt{12} = 2\sqrt3[/tex]
and
[tex]\arg(z) = \tan^{-1}\left(\dfrac{\sqrt3}3\right) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) = \dfrac\pi6[/tex]
Then
[tex]3 + \sqrt3 \, i = \boxed{2\sqrt 3 \left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)}[/tex]
In 3 years, Dianna will be 4 times as old as she was 33 years ago. How old is Dianna now?
Choose the most logical value for the variable to represent.
Let x = .
Given that In 3 years, Dianna will be 4 times as old as she was 33 years ago, her present age is 45.
How old is Dianna now?
Given that, in 3 years, Dianna will be 4 times as old as she was 33 years ago.
Let x represent the age of Dianna presently.
Dianna's age in 3 years time will be: x + 3
Dianna's age 33 years ago is: x - 33
Since in 3 years, she will be 4 times as old as she was 33 years ago.
x + 3 = 4( x - 33 )
We solve for x
x + 3 = 4x - 132
3 + 132 = 4x - x
135 = 3x
x = 135/3
x = 45
Given that In 3 years, Dianna will be 4 times as old as she was 33 years ago, her present age is 45.
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3. Anneliese spent $58.00 on music items and paid $35.00 on a lay-away item. If she has
-142.00 left in her account, how much did she start with?
A $-49.00
B$93.00
C$135.00
D-$235.00
The amount Anneliese started with before her deductions is -$235.00.
Account balanceAmount spent on music items = $58.00Amount paid for lay-way item = $35.00Total amount spent = $58.00 + $35.00
= $93.00
Amount left in her account = $-142.00
Amount spent is a negative to her accountAmount Anneliese started with = -$93.00 - $-142.00
= -$235.00
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Which expression is equivalent to 1/2 (2 - 5x + 6)?
0 -5/4x+2
O -5 +6 1/2
O - 5/4x+1
O-5x+8
Answer two questions about Systems A and B:
−3x−2y=4
5x−8y=−1
5x−8y=−1
−3x−2y=4
1) How can we get System B from System A?
Choose 1 answer:
Swap the order of the equations
(Choice A, Checked, Correct)
CORRECT (SELECTED)
Yes
For the given systems we have:
1) Just swap the equations in system A.
2) Yes, the systems are equivalent.
How can we get System B from System A?Here we have the systems:
A:
-3x - 2y = 4
5x - 8y = -1
B:
5x - y = -1
-3x - 2y = 4
Notice that we have the same equations, just in a different order. So if we swap the first and second equations in system A, we get system B.
Are the systems equivalent?
Yes, because both systems are defined by the same equations.
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find the values of x for the following equations..[tex]x^{2} +4x-98=0[/tex]
Hello !
Look at the picture
What is the domain of the function y=2√x-6?
88AX<∞
O 0≤x<∞
3≤x<∞
6≤x<∞
Answer:
If the x-6 is all under the sqrt, the last answer is right:
6<= x <= infinity
If only x is under the sqrt and - 6 is NOT under the sqrt, then:
0 <= x <= infinity is the correct answer.
Step-by-step explanation:
You can look at the equation and or graph to determine the domain of a function. The domain is all the x's that may go into the equation or all the x's on the graph of the function. Inside of a squareroot symbol the number inside there must be positive. While considering the equation, only x's that keep that inside positive can be used.
For sqrt(x-6), x has to be 6 or bigger.
For sqrt(x) - 6, x has to be 0 or bigger.
mean mark of 3,2,0,1,9,12,3,5
Answer:
4.375
Step-by-step explanation:
First add all the numbers together. [tex]3+2+0+1+9+12+3+5=35[/tex] Second, divide the number you just got by how many numbers there are. [tex]35/8=4.375[/tex] Therefore, the mean is 4.375.
PLEASE HELP EMERGENCY 50 POINTS
Estimate the length of wire to the nearest inch. Suppose that it is coiled 11 times. Which numbers did you use to estimate the length of wire in the question above? Explain your process of estimation.
***the white bar spanning the yellow wire says 11 inches inside the little box, for some reason it got lost when moving the picture
Amanda, Rafael, and Michael served a total of 92 orders Monday at the school cafeteria. Rafael served 2 times as many orders as Michael. Amanda served 8 more than Michael.
How many orders did they each serve?
The number of orders Michael, Rafael and Amanda served are 16.8, 33.6, and 41.6 servings
respectively.
EquationMichael = xRafael = 2xAmanda = 2x + 8Total servings = 92 ordersx + 2x + (2x + 8) = 92
3x + 2x + 8 = 92
5x = 92 - 8
5x = 84
x = 84/5
x = 16.8 servings
Therefore,
Michael = x
= 16.8 servings
Rafael = 2x
= 2(16.8)
= 33.6 servings
Amanda = 2x + 8
= 33.6 + 8
= 41.6 servings
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A and B have coordinates –2 and 10 on a number line. If it is marked off into 6 congruent segments, which one of the following coordinates is NOT one of the marked points? a. 0 c. 3 b. 2 d. 8
Using proportions, it is found that the coordinate that is not marked is given by:
c. 3
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
There are 6 congruent segments between -2 and 10, hence the length of each segment is given by:
l = (10 - (-2))/6 = 2.
Then the points are: -2, 0, 2, 4, 6, 8, 10. 3 is not marked, hence option c is correct.
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Determine the measure of the interior angle at vertex C
A. 180
B. 54
C. 240
D. 144
The measure of the interior angle at vertex C is D. 144.
How to calculate the angle?Based on the information given, the angle will be calculated thus:
8x + 8x + 8x + 3x + 3x = (5 - 2) × 180
30x = 540
Divide both side by 30
30x/30 = 540/30
x = 18
Therefore, at vertex C, we have 8x. This will be:
= 8x
= 8 × 18
= 144
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One number is 2 less than a second number. Twice the second number is 5 less than 3 times the first. Find the two numbers.
Answer:
9 and 11
Step-by-step explanation:
First number = x -2
Second number = x
and 2x = 3(x-2) - 5
2x = 3x - 6 - 5
x = 11
first number = 11-2 = 9
HELP PLEASE QUICK!
What is the area of the irregular figure below
Simplify....
[tex] \frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{ {a}^{2} + 1 } - \frac{4a}{ {a}^{4} + 1 } \\ [/tex]
please help ty~
The simplified expression of [tex]\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex] is [tex]\frac{8a}{a^8 - 1}[/tex]
How to simplify the expression?The expression is given as:
[tex]\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]
Add the first two terms
[tex]\frac{a - 1 + a + 1}{(a + 1)(a - 1)} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]
Evaluate
[tex]\frac{2a}{a^2 - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]
Evaluate the first two terms
[tex]\frac{2a^3 + 2a - 2a^3 + 2a}{(a^2 - 1)(a^2 + 1)} - \frac{4a}{a^4 + 1}[/tex]
Evaluate
[tex]\frac{4a }{a^4 - 1} - \frac{4a}{a^4 + 1}[/tex]
Take the LCM
[tex]\frac{4a^5 + 4a - 4a^5 + 4a }{(a^4 - 1)(a^4 + 1)}[/tex]
Evaluate the like terms
[tex]\frac{8a}{a^8 - 1}[/tex]
Hence, the simplified expression is [tex]\frac{8a}{a^8 - 1}[/tex]
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The question is below please answer quickly
Answer:
50 metersStep-by-step explanation:
2cm = 5m, so we know that the length is 5m
4cm = 2cm * 2, so the width is 5m * 2, which is 10m.
Now, we multiply them together.
5*10 = 50
The backyard area is 50 meters
Answer:
50m^2
Step-by-step explanation:
A recent study of 28 city residents showed that the mean of the time they had lived at their present address was 9.3 years. The standard deviation of the population was 2 years. Find the 90% confidence interval of the true mean? Assume that the variable is
approximately normally distributed. Show all your steps
Answer:
We are 90% confident that the true mean lies between 8..6563 and 9.9437
Step-by-step explanation:
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. Confidence is another word for probability.
mean (x) = 9.3
standard deviation (s) = 2
sample size (n) = 28
T- Distribution:
degree of freedom = n - 1 = 28 - 1 = 27
90% Confidence Interval ==> α = 0.1
critical value, t = 1.703 ( t-table)
standard error, SE = s/√n = 2 /√28 = 0.3780
margin of error, E = t × SE= 1.703 × 0.3780 = 0.6437
Confidence Interval: x ± E = 9.3 ± 0.6437
lower limit: x - E = 9.3 - 0.6437 = 8.6563
upper limit: x + E = 9.3 + 0.6437 = 9.9437
Confidence Interval: 8.6563 < µ < 9.9437
Z - Distribution:
Formula: Confidence Interval = x ± z (s/√n)
Sample Mean = s/√n = 2/√28 = 2/5.29 = 0.3781
z = 1.645 (from z - table)
From formula, z (s/√n): 0.3781 x 1.645 = 0.620 (rounded)
x ± 0.62
lower limit: x - 0.62 = 9.3 - 0.62 = 8.68
upper limit: x + 0.62 = 9.3 + 0.62 = 9.92
Confidence Interval: 8.68 < µ < 9.92
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Write in expanded form. Use parentheses to indicate multiplication.
(-a)^3
The expanded form of the expression; (-a)^3 is; (-a)(-a)(-a).
What is the expanded for. if the expression?It follows from the task content that the expanded form of the expression given is to be written.
On this note, the expression (-a)³ can simply be rewritten in it's expanded form as; (-a)(-a)(-a).
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The answer to this problem?
The simplified expression of [tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex] is [tex]\frac{9}{x^9}[/tex]
How to simplify the expression?The expression is given as:
[tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex]
Divide 162 and 2 by 2
[tex]\sqrt{\frac{81x^9}{x^{27}}}[/tex]
Take the square root of 81
[tex]9\sqrt{\frac{x^9}{x^{27}}}[/tex]
Apply the quotient rule of indices
[tex]9\sqrt{\frac{1}{x^{27-9}}}[/tex]
Evaluate the difference
[tex]9\sqrt{\frac{1}{x^{18}}}[/tex]
Take the square root of x^18
[tex]\frac{9}{x^9}[/tex]
Hence, the simplified expression of [tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex] is [tex]\frac{9}{x^9}[/tex]
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I need help with this question please!
the price that they should charge on the 2 year extended warranty is in order to break even is $10.
what price should the company charge?the price at which the company would breakeven is:
= percentage of product that will fail x replacement cost
solving gives:
= 4% x 250
= $10
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The following stem-and-leaf plot represents the test scores for 26 students in a class on their most recent test. Use the data provided to find the quartiles.
Stem Leaves
6 0 1 2 2 4 7 8
7 0 1 2 5 8
8 3 6 6 7 9 9
9 0 1 2 2 2 4 5 8
Key:
6|0=60
Find the first quartile and third quartile
Considering the given data-set, the quartiles are given as follows:
The first quartile is of 67.5.The third quartile is of 91.5.What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.There is an even number of elements(26), hence the median is the mean of the 13th and 14th elements, the first half is the 12 elements from 1 to 12, and the second half is the 12 elements from 15 to 26.
The first quartile is the mean of the 6th and 7th elements, which are 67 and 68, hence:
Q1 = (67 + 68)/2 = 67.5.
The third quartile is the mean of the 6th and 7th elements of the second half, hence:
Q3 = (91 + 92)/2 = 91.5.
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Samantha is going to run in a 5K race. To prepare, she wants
to run an average of 40 minutes a day until the marathon
on Saturday. She ran 45 minutes on Monday, 30 minutes on
Tuesday, 55 minutes on Wednesday, and 25 minutes on
Thursday. How long should she run on Friday to reach her
goal?
The number of minutes Samantha needs to run on Friday to reach her goal is 45 minutes.
AverageMonday = 45 minutesTuesday = 30 minutesWednesday = 55 minutesThursday = 25 minutesFriday = x minutesAverage = (Monday + Tuesday + Wednesday + Thursday + Friday) / 5
40 = (45 + 30 + 55 + 25 + x) / 5
40 × 5 = 155 + x
200 = 155 + x
200 - 155 = x
45 = x
x = 45 minutes
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Which type of function best models the data in the table below
The function represented by the table is therefore y = -x -2 which is linear in nature
Linear functionsLinear function are functions that have a leading degree of 1. using the coordinate points on the graph
(0, -2) and (1, -3)
Note that the function will be linear since the dependent and independent variables both have the same common difference.
Determine the slope
slope = -3+2/1-0
slope = -1/1
slope = -1
For the intercept, it is -2 according to the coordinate (0, -2)
The function represented by the table is therefore y = -x -2 which is linear in nature
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9) James purchased a shirt at 20% off. The regular price was $14.95. What was the markdown? What was the final
price?
O a.) a. $2.89; b. $11.46
Ob.) a. $2.99; b. $11.96
Oc.) a. $2.99; b. $11.86