The amount invested at each rate is $30,000 at 4%, and $2000 at 6%.
Given that;
Larry Mitchell invested part of his $32,000 advance at 4% annual simple interest and the rest at 6% annual simple interest.
If his total yearly interest from both accounts was $1,340.
To find;
The amount invested at each rate.
Let x is the amount at 4%, therefore the amount at 6% is 32000 - x.
The total interest is:
0.04x + 0.06(32000 - x) = 1320
0.04x - 0.06x + 1920 = 1320
0.02x = 1920 - 1320
0.02x = 600
x = 600/0.02
x = 30,000
The amount at 6% is:
$32,000 - $30,000 = $2000
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Find the average rate of change of the function f(x) = 8x from x₁ = 0 to X₂ = 3.
Answer:
Step-by-step explanation:
average rate = f(3) - f(0) / 3 - 0 = 24 - 0 / 3 - 0 = 24 / 3 = 8
Please help! Need this but cannot find an answer for my hw
The equation of the line in y = mx + c form is y = (-25/4)(x) + 5.
Here, we are given a line as shown in the figure.
Let us take 2 points that the line passes through. We can see that the line passes through (0, 5) and (0.8, 0)
Now, we have two points, we can find the slope of the line.
Slope is taken to be m. Thus,
m = (y2-y1)/ (x2-x1)
here, (x1, y1) = (0, 5)
and (x2, y2) = (0.8, 0)
Therefore,
m = (0-5)/ (0.8 -0)
m = -5/0.8
we can simplify this as follows-
m = -50/8
m = -25/4
Thus, the slope of the line is -25/4.
Now, we already know that (0, 5) is a point on the line. Thus, the y intercept of the line is 5.
⇒ c = 5
Now, substituting the values in the equation we get-
y = (-25/4)(x) + 5
Thus, the equation of the line in y = mx + c form is y = (-25/4)(x) + 5.
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one hundred twenty one thousand, two hundred eleven using base ten numerals
A number system is defined as the representation of numbers by using digits or other symbols, one hundred twenty one thousand, two hundred eleven in base ten numerals is 10^5+2*10^4+10^3+2*10^2+10^1+1*10^0.
What is Number system?A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner
one hundred twenty one thousand, two hundred eleven is
121211
This can be written in base ten numerals.
121211
=100000+20000+1000+200+10+1
=10^5+2*10^4+10^3+2*10^2+10^1+1*10^0
Therefore one hundred twenty one thousand, two hundred eleven in base ten numerals is 10^5+2*10^4+10^3+2*10^2+10^1+1*10^0.
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25
x 120°
y = [? ]º???
Answer:
Step-by-step explanation:
Answer: the sum of one interior angle and one exterior angle is 180. x+120=180. x=180-120. x=60°. sum of angles in a triangle is 180.
From 2015 to 2016 the population of U.S. went up by 2.6 million, while that of India
went up by 15.8 million. Is this an absolute or a relative comparison? Explain your
answer and look up on the Web each Country’s population in 2015 and provide both
absolute and relative comparisons.
Saying that the populations of the U.S. and India went up by 2.6 million and 15.8 million respectively is an absolute comparison.
The relative comparison of the populations of the U.S. and India from 2015 to 2016 would be 0.81% and 1.21% respectively.
What is an absolute comparison?In terms of population growth, an absolute comparison is made when the increase in population is denoted through the use of whole numbers. No percentages or fractions are used.
By simply mentioning that the U.S. population rose by 2.6 million and that of India rose by 15.8 million is therefore absolute.
The relative comparison is found as:
= Change in population / Population in 2015
For the United States:
= 2.6 million / 320.7 million
= 0.81%
For India:
= 15.8 million / 1.31 billion
= 1.21%
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a rectangle of area 400 square yards is 8 times as long as its wide.find it's length and width and it's perimeter
Answer: 50 ft long and 6.25 ft wide
Step-by-step explanation:
How to solve 3, 7, 12 and 2 to equal 20
Answer:
Answer: 3 + 7 + 12 - 2 = 20
Step-by-step explanation:
construct a polynomial with the following properties: fifth degree, −1 is a zero of multiplicity 3, 2 is the only other zero.
So, the polynomial with the require properties is x⁵ + x⁴ - 3x³ - 5x² - 2x
What is a polynomial?A polynomial is an expression of the form aₙxⁿ + aₙ₋₁xⁿ⁻¹ + aₙ₋₂xⁿ⁻² + ... + a₂x² + a₁x + a₀ where aₙ are coefficients and n ≥ 2.
How to construct the given polynomail?Since we are given a polynomial with the following properties: fifth degree, −1 is a zero of multiplicity 3, 2 is the only other zero.
We have that it has zero at
x = -1 and x = 2⇒ x + 1 = 0 and x - 2 = 0
⇒ (x + 1) and (x - 2) are factors of the polynomial
We are told that the polynomial has a zero of -1 with multiplicity of 3. This implies that the factor (x + 1) is repeated 3 times. That is (x + 1)(x + 1)(x + 1)
So, multiplying all four factors we have a polynomial of fourth degree as p(x) = (x + 1)(x + 1)(x + 1)(x - 2)
= (x² + 2x + 1)(x + 1)(x - 2)
= (x³ + 3x² + 3x + 1)(x - 2)
= x⁴ + x³ - 3x² - 5x - 2
To obtain a polynomial of degree 5, we multiply through by x, so we have
g(x) =xp(x)
= x(x⁴ + x³ - 3x² - 5x - 2)
= x⁵ + x⁴ - 3x³ - 5x² - 2x
So, the required polynomial is x⁵ + x⁴ - 3x³ - 5x² - 2x
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1
Select the correct answer.
If function g has the factors (x-7) and (x + 6), what are the zeros of function g?
OA. -7 and 6
-6 and 7
6 and 7
-7 and -6
Reset
Next
Correct answer is B. The zeros of the function g will be ( -6 and 7.)
(x-7) and (x + 6) are factors in a function g.
To locate: The function g's zeros.
Because x-a=0 x = a, we know that if (x-a) is a function's factor, then x-a is the function's zero.
The fact that (x - 7) and (x + 6) are factors in the function g is a given.
x-7=0
x = 7
Likewise, x+6=0
x = -6
As a result, the function g's two zeros are -6 and 7.
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Which expression is equal to i^39?
=========================================================
Work Shown:
Method 1
List out the first few powers of 'i', where [tex]i = \sqrt{-1}[/tex]
i^0 = 1i^1 = ii^2 = -1i^3 = -ii^4 = 1The process repeats every four terms. Divide the exponent by 4 to look at the remainder.
39/4 = 9 remainder 3
Ignore the quotient 9. The remainder is all we care about
Since we get remainder 3, this means i^39 = i^3 = -i
----------------------
Method 2
i^39 = i^(36+3)
i^39 = i^36*i^3
i^39 = i^(9*4)*i^3
i^39 = (i^4)^9*i^3
i^39 = (1)^9*i^3
i^39 = 1*i^3
i^39 = i^3
i^39 = -i
This is a bit longer method, but it helps confirm that i^39 = i^3 = -i we found earlier in the previous section.
Trey is assembling furniture, and the table below shows the
length of parts A-D. Record the letter of the part that is the
longest.
PART
LENGTH (IN.)
A
277
B
1.3
C
1.15
D
21
20
The longest part is Part B, which is a little longer than Part A.
What is the length?The length is the measure of distance or total time from one point to another.
For example, when measuring dimensions, the length also shows the longest side of an object, especially the rectangle.
Together with the width, the length can be used to determine the area of an object or its perimeter.
Part A B C D
Length (IN.) 1²/₇ 1.3 1.15 ²¹/₂₀
Convert all lengths (A and D) into decimals:
Part A B C D
Length (IN.) 1.29 (1²/₇) 1.3 1.15 1.05 (²¹/₂₀)
Part B's length is the most extended length, followed by Part A, Part C, and lastly, Part D.
Thus, the most extended length of the four parts is Part B.
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Question Completion:Part A B C D
Length (IN.) 1²/₇ 1.3 1.15 ²¹/₂₀
I NEED HELP IM A 4th grader pls help
all of the values are either 3 beats per minute above the mean or 3 beats per minute below the mean. What is the mean absolute deviation (MAD) of this data set?
The mean absolute deviation (MAD) of this data set is 3
What is the mean absolute deviation (MAD) of this data set?The statement is given as
"all of the values are either 3 beats per minute above the mean or 3 beats per minute below the mean"
As a general rule, the mean absolute deviation of a dataset measures the average difference between each data element and the mean value of the dataset
From the statement, we have
Above/Below = 3 beats per minute
This means that
Mean absolute deviation = 3
Hence. the mean absolute deviation (MAD) of this data set is 3
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A truck enters a highway driving 60 mph. A car enters the highway at the same place 11 minutes later and drives 71 mph in the same direction. From the time the car enters the highway, how long will it take the car to pass the truck?
Answer:
The car passed the truck after 60 minutes.
Step-by-step explanation:
We should first find how far the truck was from the entrance to the highway when the car entered (after 11 minutes). We know that the distance travelled is the product of the time and speed, therefore, the location of the truck is given by [tex]d = 60 * 11 = 660[/tex].
Now we can build functions representing the distance from the entrance of both vehicles, in respect to the time travelled.
Truck's Function
[tex]x_0 = 660m \\ v = 60mph \\ \to x(t) = 660m + 60t[/tex]
Car's Function
[tex]x_0 = 0m \\ v = 71mph \\ \to x(t) = 71t[/tex]
Finally, we can equalize both functions to find out at what time the car passed the truck (when their graphs intercepted):
[tex]660 + 60t = 71t \\ \to 660 = 11t \\ \to t = 60m[/tex]
patricia serves the volleyball to amy with an upward velocity of 17 ft/s. the ball is 3.5 feet above the ground when she strikes it. how long does amy have to react, before the volleyball hits the ground
True Or False when multiplying by two digits you have to skip over a space in the second row (when multiplying by the tens digit)
Answer:
That's probably false.
Eight more than six times a number is the same as two less than 8 times the number. What is the number?
Considering the definition of an equation and the way to solve it, the number is -3/7.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it. This is, by changing the unknown to the solution, the equality must be true. To solve an equation, keep in mind:
Group the terms that contain the variable to be calculated in one member and the independent terms in the other.When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing "x" a number, and knowing that eight more than six times a number is the same as two less than 8 times the numbe, the equation in this case is:
8 + 6x= 2 - 8x
Solving:
6x + 8x= 2-8
14x= -6
x= (-6) ÷ 14
x= -3/7
Finally, the number is -3/7.
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the distance between (-1/2, -1) , (5/8, -1)
Solution : Distance between (-1/2, -1) , (5/8, -1) = .75
Distance Formula :
Distance between two points can be evaluated if we know the c
[tex]\sqrt{{(y2-y1)^{2} } +(x2-x1)^{2}][/tex] = XY
The difference between the x-axis coordinates gives the horizontal distance and the difference between the y-axis coordinates gives the vertical distance.
Distance between the points P and Q is calculated as follows:
S and T are the points on the x-axis which are endpoints of two parallel line segments PS and QT respectively.
⇒ PR = ST
Coordinates of S and T are (x1, 0) and (x2, 0) respectively.
OS = x1 and OT = x2
ST = OT – OS = x2 – x1 = PR
Similarly,
PS = RT
QR = QT – RT = QT – PS = y2 – y1
By Pythagoras theorem,
PQ2 = PR2 + QR2
PQ = √[(x2– x1)2+ (y2– y1)2]
Therefore,
Distance between two points (x1,y1) and (x2,y2) is given by:
[tex]\sqrt{{(y2-y1)^{2} } +(x2-x1)^{2}][/tex]
distance between (-1/2, -1) , (5/8, -1)
[tex]XY = \sqrt{{(-1-(-1))^{2} } +(5/8-(-1/2))^{2}]\\\\\\\\\\\\XY = \sqrt{9/16}\\\\\\XY = 3/4\\XY = .75\\[/tex]
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Two times the quantity of eight times a number plus two is equal to three the quantity of two times the same number minus seven
a. Write an equation to find the number
b. Solve the equation to find the number.
I NEED HELP ASAPP PLEASEEE
Answer: i got u
Step-by-step explanation:
2*8x+2=3*2x-7
16x+2=6x-7
-6x -6x
10x+2=-7
-2 -2
10x=-9
x=-9/10
A store is having a sale on walnuts and chocolate chips. For 4 pounds of walnuts and 8 pounds of chocolate chips, the total cost is 21$. For 2 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $9. Find the cost for each pound of walnuts and each pound of chocolate chips.
The cost for each pound of walnuts is $ 2.25 and each pound of chocolate chips is $ 1.5.
We are given that:
Cost of 4 pounds of walnuts and 8 pounds of chocolate chips = $ 21.
Cost of 2 pounds of walnuts and 3 pounds of chocolate chips = $ 9.
Let the cost of pounds of walnuts be x and the cost of pounds of chocolate chips be y.
So, we get the following equations:
4 x + 8 y = 21 …(1)
2 x + 3 y = 9
2 x = 9 - 3 y
x = 1 / 2 (9 - 3y) …(2)
Put the value of x in (1)
4 ( 1 / 2 (9 - 3y) ) + 8 y = 21
2(9 - 3y) + 8 y = 21
18 - 6 y + 8 y = 21
2 y + 18 = 21
2 y = 21 - 18
2 y = 3
y = 3 / 2
y = 1.5
x = 1 / 2 (9 - 3y)
x = 1 / 2 ( 9 - 4.5)
x = 1 / 2 ( 4.5)
x = 2.25
Therefore, we get that, the cost for each pound of walnuts is $ 2.25 and each pound of chocolate chips is $ 1.5.
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Which of the following is used to identify outliers in a set of data?
O 1.5(IQR)
1.5(range)
O2(mean)
O 2(median)
(A) 1.5 (IQR) is used to identify outliers in a set of data.
What is the Interquartile range (IQR)?The interquartile range is a measure of statistical dispersion, or the spread of the data, in descriptive statistics. The middle 50%, fourth spread, or H-spread are additional names for the IQR. It is described as the discrepancy between the data's 75th and 25th percentiles.The interquartile range is the best tool to use to find all of your outliers (IQR). Knowing the IQR makes it simple to identify outliers because it represents the middle portion of your data. Find the median (middle value) of the lower half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1.As it is given in the description itself, the interquartile range is the best tool to use to find all of your outliers (IQR).
Therefore, (A) 1.5 (IQR) is used to identify outliers in a set of data.
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The correct question is given below:
Which of the following is used to identify outliers in a set of data?
(A) 1.5(IQR)
(B) 1.5(range)
(C) 2(mean)
(D) 2(median)
Luis who works part -time as a nurse's aide in a nursing home , earns $11.90 per hour and works 28 hours per week. He is single and claims zero withholding allowances . He lives in a state with a flat rate income tax of 3.5%
Based on the amount that Luis earns per week, and the state flat rate income tax, Luis's state income tax for the week is $11.66
What is Luis's state tax?First, find out what Luis's earnings for the week were:
= Number of hours worked for the week x Earnings per hour
= 28 x 11.90
= $333.20
The state income tax is therefore:
= Amount earned weekly x State tax rate
= 333.20 x 3.5%
= $11.66
In conclusion, the state income tax of Luis for the week comes to an amount of $11.66.
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I need help I don’t understand
Answer: use your brain you can do it
Step-by-step explanation:
anything is possable with the power of imagination
Question
Write the inequality shown by the shaded region in the graph with the boundary line y = -3x - 4.
Provide your answer below:
-10 -5
10
-10
y
5
10
I
We get the inequality as:
y > -3x - 4y < -3x - 4y ≥ -3x - 4y ≤ -3x - 4There is no image to refer. So, here answering in general way.
Given,
The boundary line, y = -3x - 4
We can have 4 cases:
1) A dashed line and the shaded part is above the line.
y > -3x - 4
2) A dashed line and the shaded part is below the line
y < -3x - 4
Here we have dashed lines because the values of the line are not solutions for the inequality.
3) A solid line and the shaded part is above the line.
y ≥ -3x - 4
4) A solid line and the shaded part is below the line.
y ≤ -3x - 4
Here we have solid lines because the values in the line itself are solutions.
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Marcus ran 3.2 km and Cindy ran 1.95 km who ran farther. How much farther?
Answer:
Marcus Ran 1.25km farther than cindy
Step-by-step explanation:
After school, Marcus ran 3.2 km and Cindy ran 1.95 km. Who ran farther? How much farther? Marcus ran 1.25 km farther than Cindy.
Find the x- and y-intercepts of the graph of x - y = 17. State each answer as an
integer or an improper fraction in simplest form.
Answer:
y-intercept is -17
x-intercept is 17
Step-by-step explanation:
See attached
Adrian scored 40% of the goals by his soccer team. if his team scored a total of 60 goals during the season, how many did adrian score ? show your work
Answer:
24 goals
Step-by-step explanation:
40/100×60=Adrians goals(g)
g=2400/100
=24
Step-by-step explanation:
24 goals in total I think.
For the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number.
60,19
can i have help with this question
Answer: 4.1
Step-by-step explanation: You would do 8.2 m/2 because since 1cm =2m the opposite would be 2m = 1 cm so 8.2 = 4.1 because 2/2 = 1
Can someone help with this question?✨
Answer:
-3/4
Step-by-step explanation:
From a point on the graph, count down and count right until you get to a another point. For example, for this problem, you can use (0,-2) as a starting point. From here, if you go down 3 and go right 4, you get another point on the graph. So, the slope is -3/4.