Using a system of equations, Mike should invest $66,000 in investment A and $24,000 in investment B to earn $5,220 from both funds per year.
How are the amounts determined?We can solve a system of equations to determine the amounts that should be invested in each fund to earn the stated amount yearly.
A system of equations is also called simultaneous equations because they can be solved together.
The total investible funds = $90,000
The expected annual earnings = $5,220
The earnings from investment A = 5% or 0.05
The earnings from investment B = 8% or 0.08
Equations:A + B = 90,000 ... Equation 1
0.05A + 0.08B = 5,220 ... Equation 2
Multiply equation 1 by 0.05:
0.05A + 0.05B = 4,500 ... Equation 3
Subtract Equation 3 from Equation 2:
0.05A + 0.08B = 5,220
-0.05A + 0.05B = 4,500
=0.03B = 720
= 24,000 (720/0.03)
B = $24,000
From Equation 1, substitute B = 24,000 to get A:
A + B = 90,000
A + 24,000 = 90,000
= 66,000
A = $66,000
Thus, we can conclude that Mike with $90,000 should invest $66,000 in Investment A earning 5% per year, and $24,000 in Investment B earning 8% annually to earn a total of $5,220 from both funds.
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i need help especially for #4
The values of x in the first, second, third and fourth triangles are 4 units, 70°, 76° and 80° respectively
How to determine the values of x in the triangle?
To solve this problem, we need some angle geometry knowledge:
For the first triangle:
x = 4 (All sides in a rhombus are identical)
For the second triangle:
The missing side is also equal to x (base of isosceles triangles)
x + x + 40 = 180 (sum of angles in triangle)
2x+40 = 180
2x = 180-40
2x = 140
x = 70°
For the third triangle:
x = 76° (base of isosceles triangles are equal)
For the fourth triangle:
Check the image attached for labeling
m = 180-110 = 70° (angle on a straight line)
y = 70° (base of isosceles triangles are equal)
z = 180-70-70 = 40°
t = 90-40 = 50°
L = 50° (base of isosceles triangles are equal)
Thus, x = 180-50-50 = 80°
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If a sample is selected using random sampling methods, the primary reason that the sample mean might be different from the corresponding population mean is that the sample might be biased.
True
False
The given statement is false. If a sample is selected using random sampling methods, the primary reason that the sample mean might be different from the corresponding population mean is not that the sample might be biased.
Because random sampling ensures that results obtained from the sample should approximate what would have been obtained if the entire population had been measured. And the simplest random sample allows all the units in the population to have an equal chance of being selected. In this case, the sample might not be biased.
What is random sampling method?Random sampling is a part of the sampling technique where each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population.
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is the expression 16x⁸ equivalent to (16x⁴)²?
Answer:
Yes
Step-by-step explanation:
16x^4 x 16x^2= 16x^8
Determine the slope of the line represented by the equation: 1 x − 3 y = − 14
Answer:
The slope is 1/3
Step-by-step explanation:
The equation is equivalent to
x - 3y = -14
x = 3y - 14
x + 14 = 3y
(x + 14)/3 = y
11. Lourdes is making a square pattern. Each
side is 7 centimeters. Is the perimeter of
the pattern the same as the area of the
pattern?
The perimeter of the pattern the same as the area of the pattern is 20 cm.
Perimeter of a square is the total length (distance) of the boundary of a square
In a square all the sides are of equal lengths.
Hence, perimeter of a square = 4l
We know that all the sides of a square are equal.
Perimeter of a Square
Perimeter of the square ABCD
= AB + BC + CD + AD
= 2 cm + 2 cm + 2 cm + 2 cm
= (2 × 4) cm
= 8 cm
Perimeter of a square is 4 times of s side.
Perimeter of a square = 4 × length of a side..
1st method:
Perimeter of a square PQRS
= side + side + side + side
= 5 cm + 5 cm + 5 cm + 5 cm
= 20 cm:
2nd method
Perimeter of a square = 4 times side
= 4 × side
= 4 × 5 cm
= 20 cm
Therefore, Perimeter of a square = 4 × length of one side.
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help meeeeeeeeeee pleaseee
The number of acres owned for which the average intake is 2200 calories per day is 2 acres obtained by the algebraic expression that relates the acres of land and the calories per day.
What is an algebraic expression?An algebraic expression is formed by variables, constants, and arithmetic operations.An algebraic expression provides the relation between the input and output variables i.e., x and f(x) respectively.Calculation:It is given that, the number of calories consumed daily by a person owing x acres of land is given by the algebraic expression,
C(x) = 270 ln(x+1) + 1900
The average intake of calories consumed per day is given by C(x) = 2200
Here x is the number of acres of land. Then, the required number of acres of land is
C(x) = 270 ln(x+1) + 1900
⇒ 2200 = 270 ln(x+1) + 1900
⇒ 270 ln(x+1) = 2200 - 1900
⇒ 270 ln(x+1) = 300
⇒ ln(x+1) = 300/270 = 10/9
Applying base 'e' on both sides, we get
⇒ (x+1) = [tex]e^\frac{10}{9}[/tex]
⇒ x+1 = 3.0377
⇒ x = 3.0377 - 1 = 2.0377
When rounding the final answer to the nearest tenths, we get x = 2 acres.
When rounding the final answer to the nearest thousand, we get x = 2.038 acres.
Thus, for an average intake of 2200 calories per day, the number of acres of land owned is approximately 2 acres.
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two points with a slope of 0.
Answer:
(1,2) and (4,2)
(2,6) and (6,6)
Step-by-step explanation:
(when a line is horizontal the slope is 0)
[tex]slope = \frac{rise}{run} [/tex]
[tex]rise = y1 - y2[/tex]
[tex] = 2 - 2 \\ = 0[/tex]
[tex]run = x2 - x1 \\ = 4 - 1 \\ = 3[/tex]
[tex]slope = \frac{0}{3} \\ = 0[/tex]
second option
[tex]rise = 6 - 6 \\ = 0[/tex]
run=6-2
=4
slope= 0/4
=0
please Heart this....
40 PTS SHOW WORK!
Consider the data regarding car costs. The mean is $22,000 and the standard deviation is $2,000.
a) Not everyone pays the same price for the same model of car. Use the 68-95-99.7% Rule to find what percentage of buyers paid between $18,000 and $26,000.
b) The middle 99.7% of car costs are between what values?
c) What is the probability a car will cost less than $24,000?
d) What is the probability a car will cost more than $26,000?
a) The percentage of buyers that paid between $18,000 and $26,000 is; 95%
b) The middle 99.7% of car costs are between $16000 and $28000
c) The probability a car will cost less than $24,000 is; 68%
d) The probability a car will cost more than $26,000 is; 2.5%
How to use the empirical rule of statistics?The empirical rule of statistics states that 68% of data will be ± 1 standard deviations from the mean, 95% of data will be ± 2 standard deviations of the mean, and 99.7% of data will be ± 3 standard deviations from the mean.
a) We are given;
Mean; μ = $22000
Standard deviation; σ = $2000
$18,000 and $26,000 are both 2 standard deviations from the mean and so, the percentage of buyers is 95%.
b) Since the middle 99.7% of car costs, this is simply 3 standard deviations from the mean and as such it is between the values;
22000 - 3(2000) = $16000 and 22000 + 3(2000) = $28000
c) $24,000 is 1 standard deviation away from the mean and as such the probability will be 68% from empirical rule.
d) $26000 is 2 standard deviations from the mean and as such probability that a car will cost more than that is;
(100% - 95%)/2 = 5%/2 = 2.5%
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-3≤2x-1≤5
Step by step
Answer:
-1≤x≤3
Step-by-step explanation:
-3≤2x-1≤5
add 1 to all sides
-2≤2x≤6
divide all sides by 2
-1≤x≤3
What is the greatest common factor between 24, 56, and 72? 01 2 5 08
Answer: The common factor is 8
Step-by-step explanation:
Each is a variant of the number 8 and 2 but it called for the greater common factor so 8
Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes for $ 900 to double if it is invested at 6 % interest compounded monthly.
The money will double in value in approximately years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
The money will double in value in approximately 11.6 years.
How to determine the time when the money will double?From the question, we have the following parameters that can be used in our computation:
Principal amount, P = $900Rate of interest, R = 6%Number of years = tNumber of times compounded, n = 12 i.e. monthlyWhen the money doubles, the amount is
A = 900 * 2
A = 1800
The compound interest formula is given as
A = P(1 + r/n)^nt
Also from the question, we have
n = 12
This is so because the loan is compounded 12 times in a year as a result of being compounded monthly
Solving further, we replace the variables with their values in the above equation
1800 = 900 * (1 + (6%)/12)^(t*12)
Divide both sides by 900
2 = (1 + (6%)/12)^(t*12)
Also, we have
2 = (1.005)^(t*12)
Take the logarithm of both sides
12t = log(2)/log(1.005)
Evaluate the quotients
12t = 139
Divide both sides by 12
t = 11.6
Hence, the number of years is 11.6 years
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Can you help me fast please
math 1 , answer plssssssss
The figure below is a map showing 12 cities and 17 roads connecting certain pairs of cities. Paula wishes to travel along exactly 13 of those roads, starting at city A and ending at city L, without traveling along any portion of a road more than once. (Paula is allowed to visit a city more than once.)
A (0)
B (1)
C (2)
D (3)
E (4)
The number of routes that Paula can take using graph theory is; E: 4
How to find the number of possible routes?We will observe that out of the 12 cities, 6 of them possess 3 edges going in/out of them.
The 6 cities are such that there are 2 at the top, 2 at the bottom, and 1 on each side.
In graph theory terms, we can say that they are of degree 3.
Thus, at least 1 edge connecting to each of these cities cannot therefore be used. Furthermore, the same concept applies to the start and end points, due to the fact that we don't want to return to them.
There are 6 + 2 = 8 vertices that we can tell have 1 unused edge, and then we have 17 - 13 = 4 unused edges to work with due to the fact that we have 17 edges in total, and as such must use exactly 13 of them).
Finally, we notice that at each of the 2 cities marked with an O on a path in the image attached, that there are 2 possibilities such that it's either we continue straight and cross back over that same path later, or we will make a left turn, and then turn rightward when we approach the junction again.
This gives us a total of;
2 * 2 = 4 possible different routes
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Which point would not be a solution to the system of linear inequalities shown
below?
y > 2x - 2
O (-5,3)
O (-5, 10)
O (-10,8)
O(-10,-9)
Y >
6
5+8
The solution to the linear inequality y > 2x - 2 and y > 5x + 8 is -3.33 and -8.67
Graph of Linear InequalityThe graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.
Using a graphing calculator, the solution of y > 2x - 2 and y > 5x + 8 is
This will give us a value of x is -3.33 and y is -8.67
Kindly find attached graph below
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A number is such that it is as much greater than 112 as it is less than it Find the number.
Answer:: 111
Step-by-step explanation:
111 is greater than 112 I hope it helps!!!!
Simplify and state the restrictions on the domain:
The simplification of the given expression is (x - 1)²/ (x-2)(x+3) which restrictions on the domain of this expression are x ≠ 1, 2, -3.
The expression is given in the question as:
(x+3)(x-1)/(x-2) ÷ (x+3)/(x-1)
To simplify the expression (x+3)(x-1)/(x-2) ÷ (x+3)/(x-1), we can start by multiplying the numerator and denominator of the first fraction by the denominator of the second fraction:
(x+3)(x-1)/(x-2) ÷ (x+3)/(x-1)
= (x+3)(x-1) / (x-2) × (x-1) / (x+3)
Then, we can simplify the expression by combining like terms:
= (x - 1)² (x+3)/ (x-2)(x+3)
= (x - 1)²/ (x-2)(x+3)
The restrictions on the domain of this expression are that x cannot be equal to 2 or -3, because these values would make the denominator equal to zero, which is not allowed in a fraction.
Therefore, the domain of the expression is all real numbers except x = 1, x = 2, and x = -3. We can express this as:
Domain: x ∈ R, x ≠ 1, x ≠ 2, x ≠ -3
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help me please thank youuuu
Answer:
B. g(x) = -x² - 2
Step-by-step explanation:
f(x) = x²
g(x) = -x²
The graph now has a maximum of (0, 0) and is curving downwards. To make the graph go down by -2 subtract 2 from the equation
g(x) = -x² - 2
I hope this helps!
A fair coin is to be tossed 10 times. Let i/j, in lowest terms, be the probability that heads never occur on consecutive tosses. Find i+j.
The probability that there are 89/1024 ways in which heads never happen on consecutive tosses.
Explain the definition of probability?Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.For the stared question;
Think of the flips as either a string of [Head first Tail] or [Tail]. Let x stand for the quantity of [Head followed by Tail] and y for the quantity of [Tail]. If 2x + y = 10, then.Then, for every value of x, I completed casework:
The number of configurations of AAAAAAAAAA is bijective to x=0 and is 1.
The number of configurations of AAAAAAAAB is then bijective to x=1, which really is 9 and so forth.
These variables add up to 89, and there are 1024 different ways to flip them.
P(i + j) = 89/1024
Thus, there are 89/1024 ways in which heads never happen on consecutive tosses.
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Dave opens a savings account that has an annual simple interest rate of 0.1%. If he initially deposits $1500, find the amount in the savings account after 5 years. PLEASE HELP WILL GIVE 20 POINTS
The amount in his savings after 5 years will be $1507.5.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, P = 1500, r = 0.1, t = 5 years.
∴ SI = (1500×0.1×5)/100.
SI = $7.5.
Now, We know Amount = principle + SI.
∴ Amount = 1500 + 7.5 = $1507.5
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Z is the midpoint of XY. Complete the proof that ∠Y ≅ ∠X .
Statement Reason
Z is the midpoint of overline XY Given
WZ ⊥ XY Definition of perpendicular lines
angle WZX ≅ angle WZY Definition of isosceles triangle
line XA ≅ line YZ Definition of bisection
line WZ ≅ line WZ Reflexive Property of Congruence
Δ WXZ ≅ Δ WYZ Side - Angle - Side (SAS)
< Y ≅ < X Corresponding Parts of Congruent Triangles are Congruent
What is congruency in triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSSSide - Angle - Side = SASAngle - Side - Angle = ASA Angle - Angle - Side = AAS Hypotenuse and one leg = HLThe problem requires the prove by Side - Angle - Side = SAS to ensure that the the triangles are congruent
The SAS have it that the two triangles being compared should have their two sides and the included angle equal
Using Corresponding Parts of Congruent Triangles are Congruent CPCTC theorem ∠Y ≅ ∠X .
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Soro bought a $50.00 bus card at the beginning of the week. Each bus ride costs $2.50. He needs to have at least $20.00 on his card at the end of this month.To determine how many bus rides he can take between now and the end of this month, Soro wrote and solved the following inequality:
50 minus 2.5 x greater-than-or-equal-to 20. Negative 2.5 x greater-than-or-equal-to negative 30. x greater-than-or-equal-to 12.
What error, if any, did Soro make when writing or solving this inequality?
The inequality that best represents Soro's situation regarding the number of bus rides he can take between now and the end of this month is :
50 - 2.5y ≥ 20.
What is an inequality ?Inequality is defined as the unequal distribution of income and opportunity among various groups in society.In this case, y represents the number of bus rides that Soro will be able to take from the start of the week to the end of the week.The amount she will have to pay for y tickets is 2.5y. The amount she will have left over after the purchase will then be= 50 - 2.5y
This number must be at least 20. The inequality that best represents Soro's situation regarding the number of bus rides he can take between now and the end of this month is 50 - 2.5y ≥ 20.To learn more about inequalities refer to :
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What is a formula for the nth term of the given sequence 16,8,4
That is a geometric progression.
the common ratio is 1/2.(t2÷t1)
nth term= ar^n-1
16×1/2=8
tn=8^n-1
Describe and correct error
Fully simplify.
16x^5y^4(14x^2y^2)
16x
5
y
4
(14x
2
y
2
)
The fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² ) following from the laws of indices is; 8x³ y² / 7.
What is the fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² )?It follows from the task content that the fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² ) is to be determined.
Since the given expression is; 16x⁵y⁴ / ( 14x²y² ).
As evident in the task content; same base terms are present in the numerator and denominator; we therefore have that;
The expression can be simplified as follows using the laws of indices as follows;
[tex] \frac{16 {x}^{5} {y}^{4} }{14 {x}^{2} {y}^{2} } [/tex]
It follows from the quotient of exponents law of indices; we have that;
[tex] \frac{8}{7} {x}^{5 - 2} {y}^{4 - 2} [/tex]
= 8x³ y² / 7
Therefore, the fully simplified form of the given expression using the laws of indices is; 8x³ y² / 7.
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Use the formula A=P[1+r/n]nt to solve the compound interest problem.
Find how long it takes for $900 to double if it is invested at 6% interest comp
The money will double in value in approximately $\square$ years.
(Do not round until the final answer. Then round to the nearest tenth as need.
The money will double in value in approximately years.
(Do not round until the final answer. Then round to the nearest tenth as need
It will take around 0.24 months for the invested money to get doubled.
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
The formula to calculate the amount is as follows,
A = P[tex](1 + r)^{(nt)}[/tex]
Substitute all the corresponding values in the above expression to obtain,
A = P[tex](1 + 6/100)^{nt}[/tex]
1800 = 900[tex](1 + 6/100)^{nt}\\[/tex]
=> [tex](1 + 6/100)^{nt}[/tex] = 1800/900
=> [tex]1.06^{nt}[/tex] = 2
Since, there are 12 months in one year, n = 12.
[tex]1.06^{12t}[/tex] = 2
=> 12t = log(2) ÷ log(1.06)
=> 12t = 0.275
=> t = 0.02
Which is equivalent to 12 × 0.02 = 0.24 months.
Hence, it will take 0.24 months to double the invested money.
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11. FIND THE ERROR A student is finding a 6.5%
commission on $525.08 worth of sales. Find
the student's mistake and correct it. Let x
represent the amount of commission.
65
525.08 = 100
= 0.65
X
525.08
x = 341.30
The error student made was converting 6.5% to decimal
6.5% = 0.065
0.065 * 525.08 = $34.13
How to find the error the student madeinformation from the problem
A student is finding a 6.5% commission on $525.08 worth of sales
The question is a percentage problem, percentage deals with a fraction hundred and used as follows
6.5%
= 6.5 percent
= 6.5 / 100
= 0.065
The factor 0.065 of the commission on $525.08
= 0.065 * 525.08
= $34.13
The commission is $34.13
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what is the value of the logarithm? round answer to nearest ten thousand IN (175)
The logarithm value for the expression → ln(175) is equivalent to 5.17.
What is logarithm?Logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number. Mathematically -
[tex]$\log_{b}({b^x})=x[/tex]
Given is the following logarithmic expression, as follows -
ln(175)
We have the expression as -
ln(175)
Solving the expression further, we get -
ln(25 x 7)
ln(25) + ln(7) {Property : log(A x B) = log(A) + log(B)}
ln(5)² + ln(7)
2 x ln(5) + ln(7)
2 x 1.61 + 1.94
5.17
Therefore, the logarithm of the number 175 is equivalent to 5.17.
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helppppp right answers only with explanition.
Answer:
1
Step-by-step explanation:
anything to the power of 0 is 1
hopes this helps
Determine the work to empty a parabolic tank filled with water which can be seen as the rotation about the y-axis of the function Y=(x^2)/9 on the interval 0≤x≤8. Water weights 62.4 lb/ cubic feet.
It is necessary to compute in the volume of the rotated region while taking into account that each cross section piece is raised up by a height of h = 4 - y. Scale the results by 62.4 lb/ft3 as well.
The given parabolic region's volume of revolution about the y-axis is a parabolic cylinder. This solid is revolved, and it has circular disks as its cross section. The differential volume of one such disk situated at a differential height y above the x-axis must be determined. The weight of water in this volume can then be calculated by multiplying this volume by the density of water. The depth of this volume is then determined from the tank's top surface. Determine how much differential work is needed to lift this water layer to the top surface. Integrate this differential work now to calculate the overall effort needed to empty the tank.
Rotating the curve x=3y about the y-axis creates the region. Keep in mind that 62.5 = (125 / 2) As a result, using the disk method,
[tex]\int_{0}^{3} \left(\frac{125}{2} \pi (4-y) (3\sqrt{y})^2\right)\, dy \\ &=\int_{0}^{3} \left(\frac{1125}{2} \pi (4-y) y\right)\, dy &\text[/tex]
Integrate in relation to:
[tex]y\text{]} \\ &=\left(-\frac{1125}{2} \pi \left(\frac{y^3}{3}-2 y^2\right)\right)\bigg|_{0}^{3} \\ &=\frac{10125 \pi }{2} \\ &\approx 16045.7 \end{align*} \)[/tex]
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