Step-by-step explanation:
Sometimes it is hard to 'see' the factorization....so you can take the HCF out of the three terms to perhaps see it better:
Factor out a '4'
4* ( 2n^2 + 17n + 21 )
4 ( 2n +3 )(n +7 ) DONE.
you roll a aix sided die one time. what is the probability of not rolling a 1? write your answer as a percent rounded to the nearest whole number
The probability of not rolling a 1 when rolling a six-sided die is approximately 83%. This means that if you roll the die many times, you would expect to get a 1 about 1/6 of the time and not get a 1 about 5/6 of the time.
When you roll a six-sided die, there are six possible outcomes, each with equal probability. These outcomes are rolling a 1, 2, 3, 4, 5, or 6. If you want to find the probability of not rolling a 1, you can count the number of outcomes that are not 1 and divide by the total number of outcomes.
Since there are five outcomes that are not 1 (2, 3, 4, 5, and 6) and six total outcomes, the probability of not rolling a 1 is 5/6.
To write this as a percentage rounded to the nearest whole number, we can multiply by 100 and round to the nearest whole number:
5/6 × 100 ≈ 83%.
For such more questions on Probability:
https://brainly.com/question/3084656
#SPJ11
8) John wishes to make a line
plot of the heights in inches for a soccer team. The heights are
listed below. How many dots
would be above the greatest
height recorded?
Answer options
1
2
3
4
There are three dots in the greatest height recorded.
We have,
From the table,
We see that,
The greatest height is 75 inches.
The lowest height is 62 inches.
Now,
If we make a line plot with dots above the height as:
* *
* * * * *
* * * * *
62 66 68 72 75
Thus,
There are three dots in the greatest height recorded.
Learn more about line plots here:
https://brainly.com/question/29573088
#SPJ1
Can someone help me with 6-11. Directions: Find the volume of each figure. Round to the nearest hundredth when necessary.
The calculated volumes of the figures are 11264 cubic units, 14482.28 cubic units, 3744 cubic units, 475.2 cubic units, 18824.14 cubic units and 91.99 cubic units
How to find the volume of the figuresThe cylinder
The volume is calculated as
V = πr²h
Where
r = Radius
h = Height
So, we have
V = 22/7 * (32/2)² * 14
Evaluate
Volume = 11264
The cylinder
The volume is calculated as
V = πr²h
Where
r = Radius
h = Height
So, we have
(2r)² = 40² - 32²
(2r)² = 576
So, we have
r = 12
So, we have
V = 22/7 * (12)² * 32
Evaluate
Volume = 14482.28
The rectangular prism
The volume is calculated as
V = lwh
Where
l = Length
w = Width
h = Height
So, we have
V = 8 * 12 * 39
Evaluate
Volume = 3744
The triangular prism
The volume is calculated as
V = 1/2lwh
Where
l = Length
w = Width
h = Height
So, we have
V = 1/2 * 11 * 5.4 * 16
Evaluate
Volume = 475.2
The sphere
The volume is calculated as
V = 4/3πr³
Where
r = Radius
So, we have
V = 4/3 * 22/7 * (33/2)³
Evaluate
Volume = 18824.14
The sphere
The volume is calculated as
V = 4/3πr³
Where
r = Radius
So, we have
V = 4/3 * 22/7 * 2.8³
Evaluate
Volume = 91.99
Read more about volumes at
https://brainly.com/question/463363
#SPJ1
Write two numbers that multiply to the value on top and add to the value on bottom. 24 + - 25
The two numbers that multiply to the number 24 and add up to the number -25 as required to be determined are; -24 and -1.
What are the two numbers as described?It follows from the task content that the two numbers which multiply to give 24 and add up to give -25 are to be determined.
By observation, the two numbers in discuss are; -24 and -1. This follows from the fact that: -24 × -1 = 24 and also, -24 + -1 = -25.
Consequently the two numbers as required to be determined are; -24 and -1.
Read more on multiplication of negative numbers;
https://brainly.com/question/4784755
#SPJ1
The principal would like to assemble a committee of 7 students from the 15-member student council. How many different committees can be chosen?
Answer:
6,435
Step-by-step explanation:
The number of different committees that can be chosen can be calculated using the combination formula, also known as "n choose k," which calculates the number of ways to choose k items from a set of n items without regard to the order.
In this case, the principal wants to assemble a committee of 7 students from a student council of 15 members. Therefore, the number of different committees that can be chosen is given by the formula:
C(15, 7) = 15! / (7! * (15-7)!)
Calculating this expression gives:
C(15, 7) = 15! / (7! * 8!)
Simplifying further:
C(15, 7) = (15 * 14 * 13 * 12 * 11 * 10 * 9) / (7 * 6 * 5 * 4 * 3 * 2 * 1)
C(15, 7) = 6435
Therefore, there are 6,435 different committees that can be chosen from the 15-member student council.
4) Students in Ms. Udon
science class planted 13
conifers in different places
around the school yard. They
measured the heights (in inches)
of the conifers one month after
planting them. How many
conifers are greater than 6 1/4
inches tall but less than 8 1/2
inches tall?
Considering the dot plot, the tallest conifer is 3.25 inches taller than the shortest conifer.
This shows, with dots, the number of times that each of the measures appears in a data set.
For finding the dot plot, we have that:
The shortest conifer measures 6 and 1/4
= 6.25 inches.
The tallest conifer measures 9.5 inches.
The difference is:
9.5 - 6.25 = 3.25 inches.
Therefore the tallest conifer is 3.25 inches taller than the shortest conifer.
More can be learned about a dot plot at;
brainly.com/question/24912483
#SPJ1
PLEASE HELP MEEE RIGHT NOWWWW
Tell whether volume applies to the situation ( please tell a , b , c , d , and e)
A. Wrapping paper used to wrap a gift
B. Milk poured into a glass
C. Air needed to blow up a ball
D. Fabric for making a quilt
E. How much will fit in a suitcase
Last one
Describe another situation in which volume would apply.
THANKS
coordinate plane with segment AB located at A 0 comma 2 and B 2 comma 3 segment AB is dilated from the origin to create segment A prime B prime at A′ (0, 8) and B′ (8, 12). What scale factor was segment AB dilated by? one half 2 3 4
The required scale factor for the dilation of segment AB to create segment A'B' is 2.
If the length of the original segment AB is 5 units and the length of the dilated segment A'B' is 10 units, the scale factor can be calculated as follows:
Scale factor = Length of A'B' / Length of AB
Scale factor = 10 / 5
Scale factor = 2
Therefore, the correct scale factor for the dilation of segment AB to create segment A'B' is 2.
Learn more about dilation here:
https://brainly.com/question/29138420
#SPJ1
Sean says the value of a to the -3rd power is always less than 1 if a is positive.
Christine says the value of a to the -3rd power is always less than 1 when a is negative
Which one is correct, and for the one that is incorrect enter the number that proves in to be incorrect (if none say none).
Sean's statement is correct. Christine's statement is incorrect when a is negative.
The value of a to the -3rd power is always less than 1 if a is positive.
For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. Therefore, Sean's statement is correct.
The value of a to the -3rd power is always less than 1 if a is positive, but it is always greater than 1 if a is negative.
For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. But if a = -2, then a to the -3rd power is -1/8, which is greater than 1.
Therefore, Christine's statement is incorrect when a is negative.
Learn more about the numbers here:
https://brainly.com/question/28691894
#SPJ1
Which graph represents the PARENT function of y = x^2- 5?
Answer:
Graph A--------------------
The function y = x² - 5 is the translation of the parent function y = x² down by 5 units.
Since the parent function is y = x², it is a parabola that has its vertex at the origin and opens up as its coefficient is positive.
Looking at the answer choices, we see option A is the correct one.
Other options are incorrect:
Option B is reflection of parent function in the x-axis, Option C is translated down, Option D is translated to the right.The total number of atoms represented by Cd(CH₂CICO₂)2 is:
O a) 13
Ob) 16
O c) 17
Od) 15
Oe) 14
The total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.
What is addition?In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.
To find the total number of atoms represented by Cd(CH₂CICO₂)₂, we need to count the number of atoms of each element in the molecule and add them up.
Cd(CH₂CICO₂)₂ contains:
1 cadmium (Cd) atom
2 carbon (C) atoms
6 hydrogen (H) atoms
4 oxygen (O) atoms
2 chlorine (Cl) atoms
Adding these up, we get:
1 + 2 + 6 + 4 + 2 = 15
Therefore, the total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.
The answer is (D) 15.
To learn more about the addition;
brainly.com/question/29464370
#SPJ2
Consider the equation -3 x e^5w = -88
Solve the equation for (W) Express the solution as a logarithm in base-e.
___
Approximate the value of (W). Round your answer to the nearest thousandth.
___
The solution for w is given by the natural logarithm of 88 divided by 3x, all raised to the power of 1/5.
Exponential functions are always increasing or decreasing, depending on the sign of the base "a".
The graph of an exponential function has a characteristic shape that depends on the base "a". When "a" is greater than 1, the graph is an increasing curve that becomes steeper as x increases; when "a" is between 0 and 1, the graph is a decreasing curve that approaches the x-axis as x increases.
Starting with the equation:
[tex]-3xe^{(5w)} = -88[/tex]
We can first isolate the exponential term by dividing both sides by -3x:
[tex]e^{(5w)} = \dfrac{88 }{ (3x)}[/tex]
Then, taking the natural logarithm of both sides, we get:
[tex]5w = ln(\dfrac{88} { 3x})[/tex]
Finally, dividing both sides by 5, we obtain the solution for w:
[tex]w = (\dfrac{1}{5}) ln(\dfrac{88} { 3x})[/tex]
Therefore, the solution for w is given by the natural logarithm of 88 divided by 3x, all raised to the power of 1/5.
To know more about an exponential function follow
https://brainly.com/question/21336357
#SPJ1
THE ONE-EYED JACK MINE INVESTIGATION
The abandoned One-Eyed Jack Mine is about 31 miles off the main road adjacent to the Salmon River Wilderness area. There is only a rutted dirt track left where the access road used to run. It is so steep that when we hiked up it we had to pause every fifty feet or so to catch our breath. It seemed impossible but 3- 5 miles further we found remnants of the old wagons, the mineshaft, and the mill. The gold ore found in this mine was embedded in quartz and prospectors used the mill to grind up the quartz and rinse it with acid in huge shallow vats that were agitated so that the gold would sink to the bottom and the quartz could be washed away.
One arrangement of equipment we noticed included a circular vat about 18 feet in diameter which must have been connected by a huge belt to a smaller circular drive wheel 10 feet in diameter. The distance between the wheel and the vat was 8 feet. The equipment had been partially pre-fabricated then carried up the hill piece by piece to be re-assembled on the spot. Just the belt to connect the vat to the drive wheel would have been a major burden. We wondered how many times they had to carry new ones up to replace it. Calculate the length of belt needed to go around the drive wheel and the vat.
Answer:
The length of the belt needed to go around the drive wheel and the vat is approximately 79.6 feet. This is calculated by using the circumference formula C = 2πr where r is the radius of the wheel (5 feet) and the radius of the vat (9 feet). The total circumference is then 2 x 3.14 x (5 + 9) = 79.6 feet.
Answer:
79.6 feet.
Step-by-step exp
2 x 3.14 x (5 + 9) = 79.6 feet.
car cost #450,000 and is sold for #540,000. find the profit as a percentage of the cost price
The profit percentage is 20% when car cost 450000 and sold for 540000.
The formula i.e., Profit = Selling Price - Cost Price can be used to determine the profit when the price at which something is sold and the cost price of a product are known. The formula for calculating profit percentage is then applied, which is profit % = (profit/cost price) x 100 (A profit algorithm is used to determine how much profit was generated from the sale of a specific product.)
Cost Price= 4500000
Selling price= 540000
Profit = Selling price - cost price
Profit= 540000-450000
Profit = 90000
Profit as a percentage of cost price= [tex]\frac{90000}{45000}*100= 20%[/tex]
Therefore, the profit as a percentage of cost price is 20%.
To Know more about Profit Percentage Visit:
brainly.com/question/30938251
Option A above
Option B above
Option C above
Rewrite using rational exponents 2⁴√x⁷
Answer:
16x^(7/2)
Step-by-step explanation:
When rewriting radicals as fractions, the numerator is the power the term is to and the denominator is how many times the term is “rooted”:
2^4 sqrt(x^7) —> 16x^(7/2)
Given a polynomial, complete the following statements.
3x^4-9x^3-30x^2
In order to solve this polynomial, the equation MUST be set equal to ___
There are ___ (enter a number) roots for this polynomial.
The equation written in factored form is ____
The solution(s) for this polynomial is/are x= { _______}
The solutions are x = 0, 0, -2 and 5.
Given is a polynomial we need to solve it,
3x⁴-9x³-30x².
We know that a polynomial will have the number of solutions equal to its highest degree,
Here the highest degree of the polynomial is 4 so there will be 4 solutions.
3x⁴-9x³-30x²
[tex]= 3x^2\left(x^2-3x-10\right)[/tex]
[tex]= x^2-3x-10 =\quad \left(x+2\right)\left(x-5\right)[/tex]
[tex]= 3x^2\left(x+2\right)\left(x-5\right)[/tex]
Therefore, the solutions are x = 0, 0, -2 and 5.
Learn more about polynomial click;
https://brainly.com/question/11536910
#SPJ1
Gillians net worth is 90,500 based on the information in the table what is the amount of money gillans owens student loans
The amount of money Gillians owes for student loans is $12,250
How to determine this
When Gillians net worth = $90,500
House(Current value) = $87,900
Checking account = $950
Credit- card = -$2,650
Automobile(current value) = $10,300
Student loans = ?
Investment = $5,000
Personal loans = 1,200
Savings account = $2,450
To calculate the money Gillians Owen owes student loans
Let x represent the student loans
$90,500 = $87,900 + $950 - $2,650 + $10,300 + x + $5,000 - $1,200 + $2,450
$90,500 = $102,750 + x
Collect like terms
x = $90,500 - $102,750
x = 12,250
Therefore, the money Gillians owes student loans is $12,250
Read more about Loan
https://brainly.com/question/11897664
#SPJ1
The triangle below is isosceles. Find the length of side x to the nearest tenth.
The length of side x to the nearest tenth is equal to 2.4 units.
What is an isosceles triangle?In Mathematics and Geometry, an isosceles triangle simply refers to a type of triangle with two (2) sides that are equal in length (side lengths) and two (2) equal angles.
This ultimately implies that, an isosceles triangle comprises two (2) side lengths that are equal and two (2) angles with the same magnitude.
Therefore, we would apply Pythagorean theorem in order to find the length of side x as follows;
x² + x² = (√11)²
2x² = 11
x² = 11/2
x² = 5.5
x = 2.4 units.
Read more on isosceles triangle here: brainly.com/question/19238666
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
What is the range of the set of coordinates shown below?
(-10, 2), (-5, 3), (-7,4), (0, 0), (-10, 3), (3, 8)
Answer:
{0,2,3,4,8}
Step-by-step explanation:
What do you know about the graphs of polynomials with positive end behavior compared to the graphs of polynomials with negative end behavior?
If "positive" end behavior:
1. The graph hits the x-axis
2. The arrows point in opposite directions
3. The arrows point in the same direction
4. The right arrow is up
5. The graph hits the y-axis
6. The right arrow is down
If "negative" end behavior:
1. The graph hits the x-axis
2. The right arrow is down
3. The graph hits the y-axis
4. The right arrow is up
5. The arrows point in the same direction
6. The arrows point in opposite directions
The end behavior of a polynomial with positive leading coefficient is either "up-up" or "down-down" depending on the degree of the polynomial the end behavior of a polynomial with negative leading coefficient is either "up-down" or "down-up" depending on the degree of the polynomial.
Actually, the end behavior of a polynomial refers to the behavior of the function as the input variable (usually x) approaches positive or negative infinity.
The end behavior of a polynomial is determined by the degree and leading coefficient of the polynomial.
If the degree of the polynomial is even and the leading coefficient is positive, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial approaches the x-axis from above (the arrows point in opposite directions).
As x approaches positive infinity, the graph of the polynomial approaches the x-axis from below (the arrows point in opposite directions).
If the degree of the polynomial is even and the leading coefficient is negative, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial approaches the x-axis from below (the arrows point in opposite directions).
As x approaches positive infinity, the graph of the polynomial approaches the x-axis from above (the arrows point in opposite directions).
If the degree of the polynomial is odd and the leading coefficient is positive, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial goes down to negative infinity (the arrows point in the same direction).
As x approaches positive infinity, the graph of the polynomial goes up to positive infinity (the arrows point in the same direction).
If the degree of the polynomial is odd and the leading coefficient is negative, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial goes up to positive infinity (the arrows point in the same direction).
As x approaches positive infinity, the graph of the polynomial goes down to negative infinity (the arrows point in the same direction).
For similar questions on polynomial
https://brainly.com/question/4142886
#SPJ11
I need help with number three.
Answer:
1761 ft²
Step-by-step explanation:
The shape of the attic is a triangular prism.
It has 5 faces: The bases are 2 faces that are congruent triangles. The other 3 faces are rectangles, 2 of which are congruent.
surface area = area of the bases + area of 3 rectangles
surface area = 2 × area of triangle + 2 × area of rectangle + area of other rectangle
surface area = 2 × (1/2)bh + 2 × length × width + LENGTH × WIDTH
surface area = 2 × (1/2)(15 ft)(15 ft) + 2(15 ft)(30 ft) + (21.2 ft)(30 ft)
surface area = 225 ft² + 900 ft² + 636 ft²
surface area = 1761 ft²
Suppose that the common shares of Oceanic Luxury Vessels , Inc. , is trading for $ 38 a share and that 5 million shares are outstanding . The company also has 75,000 bonds outstanding , which are selling at 102 percent of par . If Oceanic Luxury Vessels , Inc. , was considering an active change to its capital structure so that the firm would have a D/E ratio of 1.6 , which type of security ( stocks or bonds ) would it need to sell to accomplish this , and how much would it have to sell ? A. Debt ; $ 349.9 million B. Stock : $ 445.2 million C. Debt ; $ 248.5 million D. Stock ; $ 289.4 million
Answer:
To have a D/E ratio of 1.6, Oceanic Luxury Vessels, Inc. would need to sell debt securities.
First, we need to calculate the market value of the company's equity.
Market value of equity = Number of shares outstanding × Market price per share
Market value of equity = 5,000,000 × $38
Market value of equity = $190,000,000
Next, we can calculate the current debt-to-equity (D/E) ratio of the company:
Current D/E ratio = Total debt / Total equity
Total debt = Number of bonds outstanding × Bond price per bond × Par value
Total debt = 75,000 × 1.02 × $1,000
Total debt = $76,500,000
Current D/E ratio = $76,500,000 / $190,000,000
Current D/E ratio = 0.403
To achieve a D/E ratio of 1.6, the company would need to increase its total debt by a factor of 1.6/0.403 = 3.97.
New total debt = 3.97 × $76,500,000
New total debt = $304,305,000
To calculate the amount of debt securities the company would need to sell, we can subtract the current total debt from the new total debt:
Amount of debt to be sold = $304,305,000 - $76,500,000
Amount of debt to be sold = $227,805,000
Therefore, the company would need to sell debt securities worth $227.8 million to achieve a D/E ratio of 1.6.
The correct answer is C. Debt; $248.5 million.
Carl has a ribbon that is 4/5 of a meter long. He wraps 2/5 of a meter of a meter of the ribbon around a package. He uses another 1/4 of a meter of the ribbon to tie a bow on a gift box. What is the length of the ribbon carl has left
A. 13/20 of a meter
B. 2/5 of a meter
C. 3/20 of a meter
D. 4/5 of a meter
Answer:
C. 3/20 of a meter
Step-by-step explanation:
Step 1: To find out how much ribbon Carl has left, we need to subtract the length of ribbon used from the total length of the ribbon.
Step 2: To add the lengths of the ribbon used, we need to find a common denominator for the fractions used. The least common multiple of 5 and 4 is 20, so we can convert both fractions to twentieths.
Step 3: 2/5 of a meter is equivalent to 8/20 of a meter, and 1/4 of a meter is equivalent to 5/20 of a meter.
Step 4: To add the lengths of ribbon used, we add the two fractions: 8/20 + 5/20 = 13/20.
Step 5: To find the length of ribbon Carl has left, we subtract the fraction of the ribbon used from the total length of the ribbon: 4/5 - 13/20 = 16/20 - 13/20 = 3/20.
Step 6: Therefore, Carl has 3/20 of a meter of ribbon left.
Which number is equivalent to 7/11
?
The equivalent fractions of 7/11 are 14/22, 21/33, 28/44 and 35/55
There are infinitely many numbers equivalent to 7/11
since 7/11 is a fraction that can be simplified in different ways.
We can multiply the numerator and denominator with the same number to get the equivalent fractions
7/11×2/2 = 14/22
7/11×3/3= 21/33
7/11×4/4 =28/44
7/11×5/5 =35/55
Hence, the equivalent fractions of 7/11 are 14/22, 21/33, 28/44 and 35/55
To learn more on Fractions click:
https://brainly.com/question/10354322
#SPJ1
desperately need help!!!
The classification , symmetry , maximum r-values and the zeroes of the function are solved
Given data ,
a)
Let the function be represented as A
Now , the value of A is
r² = 25 sin( 2θ )
The equation represents a cardioid
It is symmetric about the polar axis.
The maximum values of r occur at θ = (π/4) + kπ/2, and the maximum value of r is 5.
The equation has zeroes at θ = kπ/2, and the corresponding values of r are given by r = 0
b)
The equation represents a limaçon.
It is symmetric about the polar axis.
The maximum value of r is 7.
The equation has zeroes at θ = arccos(1/3) + 2kπ or θ = -arccos(1/3) + 2kπ, and the corresponding values of r can be found by substituting into the equation r = 4 - 3cos(θ).
c)
The equation represents an Archimedean spiral.
It does not possess any symmetry.
There is no maximum r value.
The equation has a zero at θ = 1/2.
Hence , the zeroes of the function are solved
To learn more about symmetry of functions click :
https://brainly.com/question/29292066
#SPJ1
Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is represented by the following function, where C(x) is measured in dollars/year. Find the following functions (in dollars) and interpret your results.
Find the average cost and marginal cost.
The marginal cost (MC) function tells us the additional cost of producing one more unit of the Senior Executive model.
To find the average cost, we need to know the fixed costs, which are not given in the problem. Therefore, we cannot calculate the average cost.
To find the marginal cost, we need to take the derivative of the total cost function with respect to x:
MC(x) = dC(x) / dx
MC(x) = [tex]0.3x^2[/tex] - 16x + 500
Interpreting the results, the marginal cost (MC) function tells us the additional cost of producing one more unit of the Senior Executive model. It is an increasing function, which means that the cost of producing an additional unit increases as the production level increases. When MC is greater than the price of the product, it is not profitable to produce additional units, and the optimal production level is reached when MC equals the price.
for such more question on marginal cost
https://brainly.com/question/8993267
#SPJ11
Question
Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is represented by the following function:
C(x) = 0.1x^3 - 8x^2 + 500x + 4000
where C(x) is measured in dollars/year.
$11,335
is invested, part at 9%
and the rest at 6%
. If the interest earned from the amount invested at 9%
exceeds the interest earned from the amount invested at 6%
by $865.35
, how much is invested at each rate? (Round to two decimal places if necessary.)
Answer:
9% : $10,3036% : $1032Step-by-step explanation:
You want the amounts invested at 9% and 6% if they total $11,335 and the interest from the 9% investment exceeds the interest from the 6% investment by $865.35.
SetupIf we let x represent the amount invested at 9%, the amount invested at 6% is (11335-x). The relation between the values of interest earned is ...
(x)·9% -(11335-x)·6% = 865.35
Solution0.15x -680.10 = 865.35 . . . . . simplify
0.15x = 1545.45 . . . . . . . . add 680.10
x = 10303 . . . . . . . . . . . divide by 0.15
11335 -x = 1032
$10,303 was invested at 9%; $1,032 at 6%.
__
Additional comment
It is convenient to use a single variable, and to let it represent the amount invested at the higher rate. If you use a system of 2 equations, you can effectively do this by substituting for the variable representing the amount invested at the lower rate. Using this approach keeps all of the numbers positive, tending to reduce errors.
Answer:
Amount invested at 9% = $6832.15; Amount invested at 6% = $4502.85
Step-by-step explanation:
We'll need a system of equations to find the amounts invested at both 9% and 6% and we'll need to convert the percentages to decimals (i.e., 0.09 and 0.06):
Let x represent interest earned from the 9% investmentLet y represent interest earned from the 6% investmentLet 0.09x represent the amount invested at 9%Let 0.06y represent the amount invested at 6%First equation in system:
We know that the interest earned from the 9% investment is $865.35 greater than the interest earned from the 6% investment.
Thus, one equation we can use is x = y + 865.35
Second equation in system:
We also know that the amount invested at 9% plus the amount invested at 6% equals $11335.00
Thus, our second equation is 0.09x + 0.06y = 11335
Step 1: We can use substitution to solve. We must plug in x from the first equation for x in the second equation to solve for y:
0.09(y + 865.35) + 0.06y = 11335
0.09y + 77.8815 + 0.06y = 11335
0.15y + 77.88 = 11335
0.15y = 11257.12
y = 75047.46667
y = 75047.47
Step 2: Now we can plug in 75047.47 for y into any of the two equations in our system to solve for y. Because the first equation is simpler, let's use this one:
x = 75047.47 + 865.35
x = 75912.82
Step 3: We can now find the amount invested by multiplying x by 0.09 and y by 0.06:
0.09x = 0.09(75912.82) = 6832.1538 = $6832.15
0.06y = 0.06(75047.47) = 4502.8482 = $4502.85
Optional Step 4: We can check that our numbers are correct by substituting 75912.82 for x and 75047.47 for y in the two equations in our system:
Checking solutions for first equation:
75912.82 = 75047.47 + 865.35
75912.82 = 75912.82
Checking solutions for second equation:
0.09(75912.82) + 0.06(75047.47) = 11335
6832.1538 + 4502.8482 = 11335
6832.15 + 4502.85 = 11335
11335 = 11335
Find the variance and standard deviation of each of the following scores.
x
1-3
4-6
7-9
10-12
13-15
16-18
19-21
f
1
9
25
35
17
10
3
The variance and standard deviation of the frequency distribution data are;
The variance, s² = 14
The standard deviation, s ≈ 3.742
What is a frequency distribution?A frequency distribution displays the number of data within a specified interval.
The steps to find the variance and the standard deviation of the grouped data are as follows;
The midpoints of the class intervals are found as follows;
Class interval [tex]{}[/tex] Midpoint
1 - 3 [tex]{}[/tex] 2
4 - 6 [tex]{}[/tex] 5
7 - 9 [tex]{}[/tex] 8
10 - 12 11
13 - 15 [tex]{}[/tex] 14
19 - 21 [tex]{}[/tex] 20
The mean is then found as follows;
(2×1 + 5×9 + 8×25 + 11×35 + 14×17 + 17×10 + 20×3)/(1+9+25+35+17+10+3)
The variance can then be found as follows;
s² = (2-11)²×1 + (5-11)²×9 + (8-11)²×25 + (11-11)²×35 + (14-11)²×17 + (17-11)²×10 + (20-11)²×3)/(1+9+25+35+17+10+3 - 1) = 14The standard deviation is therefore; s = √(14) ≈ 3.742Learn more on the standard deviation of a dataset here: https://brainly.com/question/11340286
#SPJ1
The ratio 5x +2 : y - 2 is equal to 6:5. Express y in terms of x .
Answer:
y = [tex]\frac{25x+22}{6}[/tex]
Step-by-step explanation:
express the ratios in fractional form
[tex]\frac{5x+2}{y-2}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )
6(y - 2) = 5(5x + 2) ← distribute parenthesis on both sides
6y - 12 = 25x + 10 ( add 12 to both sides )
6y = 25x + 22 ( divide both sides by 6 )
y = [tex]\frac{25x+22}{6}[/tex]